Modal Analysis of Power Systems with Doubly Fed Induction ...611637/FULLTEXT01.pdf · Figure 2.1...

i

Modal Analysis of Power Systems with Doubly Fed Induction Generators

Master Thesis

by

Jialin Li

XR-EE-ES 2010002

Royal Institute of Technology School of Electrical Engineering

Division of Electric Power Systems

Stockholm Sweden 2010

ii

iii

Abstract To ensure the reliable operation of the power system stability analysis considering the interaction between wind power and power system must be understood In this thesis the impact of wind power on the stability of Nordic32A power system is of interest Many wind farms nowadays employ doubly fed induction generator (DFIG) variable speed wind turbines In this thesis a third order DFIG model and its control circuits are employed The particle swarm optimization algorithm is developed to tune the power system stabilizer which can greatly increase the computational efficiency and improve the damping of the power system Modal analysis is conducted to investigate the behavior of a wind power plant in a conventional power system The interaction between generators is investigated when we add wind power plants in different locations In some cases some unstable oscillation modes may be observed due to the inter-area and local oscillations among different synchronous generator groups in the system

iv

v

Acknowledgements My heartfelt acknowledgement would go to my beloved parents for their continuous support and encouragement all through my life All that I am or ever hope to be I attribute all my success in life to them

vi

vii

Contents Abstract iii Acknowledgement v Content vii1 Introduction 1 11 Background 1 12 Test systems 3 121 Two area system 3 122 Nordic32A system 4 13 Outline 6 2 Literature review 7 21 Overviews 7 22 Doubly fed induction generator 8 23 Synchronous generator 10 24 Control scheme 11 25 Power system stabilizer 133 Tuning algorithm 15 31 Iterative Residue Algorithm 15 311 Introduction 15 312 Problem statement 17 32 Particle swarm optimization 19 321 Introduction 19 322 Problem statement 21 323 Implementation and comparison 234 Case studies 315 Conclusions and future work 37 51 Conclusions 37 52 Future work 38 Appendix A Data of two area system 39 Appendix B Data of Nordic32A system 41Bibliography 49

viii

- 1 -

Chapter 1 Introduction 11 Background With the global awareness of the finiteness of the non-renewable resources (mainly fossil fuels) of the earth as well as the adverse effects they cast to our environments people are making great effort to look for alternative sources that can provide electricity continuously while minimize the environmental impact on the earth which are known as renewable energies Among various renewable energies wind power which converts the kinetic energy of moving air into electricity is the most competitive one due to its advantages in relatively mature technology Wind power has experienced a rapid global growth since the 1990rsquos with a worldwide installed capacity of 1208 GW at the end of 2008 Over 27 GW of wind power came online in 2008 alone representing a 36 growth rate in the annual market These figures show that there are huge and growing global demands for emissionsndashfree wind power which can be installed quickly virtually everywhere in the world The US passed Germany to become the number one market in wind power while Chinarsquos total capacity doubled for the fourth year in a row The total installed capacity top 10 countries and new installed capacity top 10 countries in 2008 are shown in Figure 11 Global cumulative installed capacity and global annual installed capacity are shown in Figure 12 and Figure 13 respectively [1] At present many wind farms employ doubly fed induction generator (DFIG) variables speed wind turbines DFIG is a wound rotor machine with slip rings to allow control of the rotor winding current [2] Compared with other wind turbine types ie fixed speed wind turbine limited variable speed wind turbine DFIG offers several obvious advantages control of DFIG is flexible windmill efficiency is improved mechanical stress is reduced torque oscillations are not transmitted into the grid as well as the active power and the reactive power or voltage can be controlled independently [3]

- 2 -

Until September 2009 about 3654 MW wind power has been connected into the Swedish power system while 4371 MW are under construction [4] With the increasing penetration of wind power into the Nordic power systems more comprehensive studies are required to identify the interaction between wind farms and the power system which initialize the investigation of wind power on the stability of Nordic32A power system in this thesis

Figure 11 Top 10 Countries of total installed capacity and new installed capacity in 2008 [1]

- 3 -

Figure 12 Global cumulative installed capacity 1996-2008 [1]

Figure 13 Global annual installed capacity 1996-2008 [1]

12 Test systems 121 Two area system A two area power system as illustrated in Figure 14 [5] is used as an example to investigate how a wind farm comprised of DFIGs equipped with a Power system stabilizer (PSS) manifests itself in the dynamic behavior of a power system

- 4 -

Figure 14 Two area system [5]

The system consists of two similar areas connected by a weak tie Each area consists of two coupled generators having a rating of 900MVA and 20kV each The generator is connected to the system by a step-up transformer each on 900 MVA and 20230 kV base The transmission system operates at 230 kV At buses 7 and 9 the loads and reactive power are supplied by the shunt capacitors More detailed data of the two areas are given in Appendix A 122 Nordic32A system Since the rapid development of wind energy in Nordic countries study about the phenomena when new DFIGs are installed in this area is of interest In this thesis the Nordic32A system as illustrated in Figure 15 is employed The Nordic32A system is fictitious but has dynamic properties which are similar to the Swedish and Nordic power system The system is intended for simulation of transient stability and long term dynamics The system is long with transfers from a hydro dominated part to a load area with a large amount of thermal power Network data and models are standardized The number of nodes and generators is quite limited 32 and 22 respectively Each generator represents a power plant or aggregate of plants The conventional power plants are represented by the synchronous generator model while the wind power plants are represented the third order DFIG model The data used for simulation in this thesis is presented in Appendix B [6] The network consists of four major parts

bull ldquoNorthrdquo with basically hydro generation and some load

- 5 -

Figure 15 Nordic32A system

- 6 -

bull ldquoCentralrdquo with much load and rather much thermal power generation

bull ldquoSouthwestrdquo with a few thermal units and some load

bull ldquoExternalrdquo connected to the ldquoNorthrdquo has a mixture of generation and load 13 Outline This thesis consists of five chapters In Chapter 1 brief introduction of current development and trend of wind power in the world are given In Chapter 2 literatures on which this thesis is based are reviewed Models used in this thesis are presented and explained These models include a DFIG model developed initially in [7] which represents a wind power plant a classical synchronous generator model which represents a conventional power plant a control scheme model which is equipped on DFIG and a PSS model In Chapter 3 two PSS tuning algorithm are presented to increase power system stability One is the iterative algorithm based on the participation factor and residue The other is particle swarm optimization algorithm which can ease the heavy calculation burden of conventional iterative algorithm and improve the calculation efficiency and PSS performance dramatically In Chapter 4 the modal analysis when wind power is installed in the Nordic32A power system is investigated Situations when no DFIG installed one DFIG installed at various locations are explored In Chapter 5 the conclusions based on the exploration of this thesis are given suggestions about future works are provided

- 7 -

Chapter 2 Literature review 21 Overviews Wind power has arisen global interest recently and quite a lot of work has been done on relative issues From the view of system dynamics wind power has been found can improve the angular behavior under small disturbances when located in the vicinity of a conventional power system thus having a positive contribution on the system damping [7] The impact of wind power on the damping and the frequency of power system oscillations depend on the wind turbine concept as well as the wind power penetration [8]

Among various different generator concepts for wind power applications in use today many wind turbines installed either offshore or onshore operate at variable speed and use DFIGs [9] Various DFIG models are presented recently [10 11 12] Depending on whether the stator transients are neglected DFIG model can be further divided into the third order model and the fifth order model While the latter represents the generator behavior in more detail the third order model is adequate for classical phasor domain electro-mechanical dynamic studies [13] The design and implementation of control scheme for DFIG are of great importance Quite a lot of different control techniques have been developed [7 14 15 16] Appropriate tuning also plays great role to the effect of controller on the overall dynamic performance of the power system The residue method is usually suitable for different control devices to damp inter-area oscillations [17] The performance of controller also depends on the selection of implement location and input signal [18] To overcome the drawbacks of many conventional techniques which are iterative and require heavy computation burden due to system reduction procedure optimization algorithms ie particle swarm optimization algorithm [19] are employed to optimize the tuning of controller parameters [20]

- 8 -

To conduct more comprehensive studies about wind power and its impact a precondition is accurate models for various wind generators as well as their associated control and protection schemes 22 Doubly fed induction generator Among various different generators concepts for wind power applications in use today many wind turbines installed either offshore or onshore operate at variable speed and use DFIGs both for the reason of network compatibility and mechanical loads reduction [9] A doubly fed induction machine is basically a standard wound-rotor induction machine with a frequency-converter connected to the slip-rings of the rotor which is shown in Figure 21 In this thesis the DFIG model derived in [7] will be employed Its electrical dynamics and mechanical dynamics will be represented briefly below

Figure 21 Doubly fed induction generator system [7]

The relations between the voltages v resistances R currents i and flux linkages ψ of a three-phase induction machine can be found from the fundamental Kirchhoffrsquos and Faradayrsquos law using standard dq -coordinate system and per unit system

01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt

ψ ψω ωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤minus= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)

where the subscriptions s and r denote stator and rotor values the subscriptions d and q demote d and q axes of the dq -coordinate system respectively the symbol sω is the

- 9 -

synchronous speed and the symbol rω is the electrical rotor speed the symbol 0ω is the speed of the reference frame with respect to the stator circuit thus the symbol 0 rω ωminus is the speed of the reference frame with respect to the rotor circuit The flux-current relations are

ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)

r lr mX X X= + (26) The subscripts l and m denote leakage reactance and magnetising reactance The mechanical equation is described as

⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)

where the symbol mP is the mechanical input power the symbol eP is the electrical output power the symbol H is the inertia constant of the turbine shaft and generator in seconds the symbol nS is the rated power of the machine the symbol bS is the base power Equations (21) (22) (23) (24) and (27) comprise the fifth order DFIG model We can express quantities using complex substitutions here

dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)

It is convenient to represent the stator side of DFIG as an internal electromotive force Eprime behind a transient impedance XjRs prime+

( ) sss iXjREv prime+minusprime= (29) by introducing

- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ

ω and sR for its little impact on the system dynamics [7] Equation

(22) can be rewritten as

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime

minusprimeminusminus=prime

sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)

is the transient open-circuit time constant To simplify the expression we make the substitutions

mr r

r

Xv vX

prime = (214)

Expand Equation (212) we get

( )0 00

1d s ss qr s r q d ds

dE X X XT v T E E vdt T X X

ω ω ωprime primeminus⎛ ⎞prime prime prime= minus + minus minus +⎜ ⎟prime prime⎝ ⎠

(215)

( )0 00

1q s ss dr s r d q qs


ω ω ωprime primeminus⎛ ⎞prime prime prime= minus minus minus +⎜ ⎟prime prime⎝ ⎠

(216)

Rewrite Equation (27) as

⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)

where the symbol sP is the power produced on the stator side of the DFIG Equations (215) (216) and (217) comprise the third order DFIG model [10]

- 11 -

23 Synchronous generator In order to investigate the effect of wind power on a general power system which consists of synchronous generators the classical model is employed in this thesis to avoid the complexity associated with higher order of the synchronous generator models The dynamic of the classic model are given by the equations below [21] δ ω=amp (218)

( )2

qsm

d

E VP

H xωω δ θ

prime⎛ ⎞= minus minus⎜ ⎟prime⎝ ⎠

amp (219)

where the symbol ω is the electrical speed the symbol sω is the synchronous speed the symbol H is the inertia constant of the turbine shaft and generator in seconds the symbol mP is the mechanical input power the symbol qE prime is the q -axis transient emf the sectsymbol dxprime is the d -axis transient reactance the symbol δ is the angular position from the q -axis with respect to the real-axis which rotates at synchronous speed the symbol θ is the angular position of the terminal voltage V with respect to the real-axis The terminal voltage is represented in polar coordinates

jsv Ve θ= (220)

In this thesis we use the inbuilt classical model of synchronous machines from Simpow [22] 24 Control scheme A control scheme will be used in Chapter 3 to design the PSS tuning algorithm therefore some words about the control scheme is needed here The control scheme designed in [7] will continue to be used in this thesis which is illustrated in Figure 22 Like all conventional design of DFIG control systems this controller is also based on rotor current vector control with dq decoupling [23] A four quadrant ac-ac converter to the rotor windings of a DFIG is implemented as illustrated in Figure 21 The rotor voltage drv prime and qrv prime of the generator are to be regulated independently by taking input signals from the power system

- 12 -

Figure 22 Control Scheme [7]

In this controller 1=pdK 1=pqK 10=iqK the references for gP and V are used to

generate xrv prime and yrv prime which will be fed to DFIG Here a new xy reference frame are used by rotating the dq reference frame through an angle θ as illustrated in Figure 23 The dq reference is used in Section 22 for its advantage in making the real and imaginary components of network phasors equal to the d and q components in the dq reference Represent the stator voltage in polar coordinates as in Equation (220) and compare it with Equation (28) we can observe

cosdsv V θ= (221) sinqsv V θ= (222)

Transfer the the dq reference frame into the xy reference frame using the transformation

( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ

⎡ ⎤ ⎡ ⎤prime primeminus minus minus⎡ ⎤⎢ ⎥ ⎢ ⎥= ⎢ ⎥minus minus⎢ ⎥prime ⎢ ⎥prime⎣ ⎦ ⎣ ⎦⎣ ⎦

(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -

Figure 23 xy frame respect to dq frame [7]

The inputs to the system illustrated in Figure 22 are

( )Rg g gP P PΔ = minus minus (226)

RV V VΔ = minus (227) where the symbol gP is the generated active power of the generator in question the symbol V is the terminal voltage of the generator in question and the superscript R denotes reference values Two PSS output signals PSS xV minus and PSS yV minus are set to zero when the DFIG is without a PSS In order to modify the mode of oscillation the chosen input and output signals should provide adequate observability and controllability [24] We can calculate drv prime and qrv prime by using the transformation

( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ

⎡ ⎤ ⎡ ⎤prime primeminus⎡ ⎤⎢ ⎥ ⎢ ⎥= ⎢ ⎥⎢ ⎥ ⎢ ⎥prime prime⎣ ⎦⎣ ⎦ ⎣ ⎦

(228)

More detailed information about the derivative procedure of this control scheme can be found in reference [7] 25 Power system stabilizer In Chapter 3 PSS will be used as well

- 14 -

The general form of the PSS employed in the thesis is illustrated in Figure 24 The input signal is initially processed through block to provide the gain followed by a washout term to eliminate any control contribution under steady conditions Then it passed through two compensators that provides the necessary phase shift In Figure 24 the symbol s is Laplace operator To make this question clearer we have to review the principle of Laplace transformer briefly Laplace transform is a widely used integral transform In engineering domain it is used for analysis of linear time-invariant systems The Laplace transformer is often interpreted as a transformation from the time-domain in which inputs and outputs are function of time to the frequency-domain where the same inputs and outputs are functions of complex angular frequency The Laplace transform of a function ( )f t defined for all real numbers 0t ge is the

function ( )F s defined by

( ) ( ) ( )0

stF s L f t e f t dtinfin minus= = int (229)

where the parameter s is a complex number which refers to as complex frequency s iσ ω= + (230) with real numbers σ and ω

Figure 24 Power system stabilizer

- 15 -

Chapter 3 Tuning algorithm Power system stabilizer (PSS) is one of the most cost effective solutions capable of providing supplementary damping However the effects of the different PSS parameters on the overall dynamic performance of the power system depend greatly on the appropriate tuning The conventional techniques are iterative and require heavy computational burden due to system reduction procedure [25] To overcome those drawbacks an evolutionary computation technique named particle swarm optimization (PSO) has been applied in this thesis Both the conventional iterative algorithm and the PSO algorithm are presented below 31 Iterative residue algorithm 311 Introduction The iterative residue algorithm used in this thesis is a conventional method to tune the PSS parameters It is based on the participation factor and the residue of power system modal analysis Here let us briefly review the basics of using residue for control design Firstly let us consider the transfer function of the closed-loop system illustrated in Figure 31

Figure 31 Transfer function

An open-loop transfer function can be described as

x A x B uΔ = Δ + Δamp (31)

- 16 -

y C x D uΔ = Δ + Δ (32) where the symbol A is the state matrix the symbol xΔ is the state vector the symbol

uΔ is a signal input vector the symbol yΔ is a signal output vector the symbol C is a row vector the symbol B is a column vector we assume y is not a direct function of u (ie 0D = ) The required transfer function is

( ) ( )( ) ( ) 1y s

G s C sI A B Du s

minusΔ= = minus +Δ

(33)

where the symbol I is the unit matrix The symbol ( )KH s is the transfer function of the controller the symbol K is a constant gain The transfer function can be expressed as

( ) ( )1

ni

i i

RG ss λ=

=minussum (34)

where the symbol iλ is the system eigenvalue

i i ijλ σ ω= plusmn (35) The real component iσ gives the damping of iλ the imaginary component iω gives the oscillation frequency The symbol n is the number of system state variables The symbol iR is the residue associated with i th mode

r li i iR CV V B= (36)

where r

iV and lrV represent the right and left eigenvectors associated with the i th

eigenvalue respectively The relation between the residue of an eigenvalue iλ and a controller transfer function

( )KH s is

- 17 -

( )i i iR KHλ λΔ = (37) Now we can use a conventional PSS shown in Figure 23 to shift the residue to the negative axis as illustrated in Figure 32

Figure 32 Direction of eigenvalue shift

The parameters in Figure 32 can be calculated as

180i iH Rφ = ang = degminusang (38) ( )( )

1

2

1 sin1 sin

MTT M

φα

φ+

= =minus

for 0 90φdeg lt lt deg (39)

where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)

M is the number of compensation stages The angle compensated by each block should not exceed 60deg

( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R

⎧ deg le le deg⎪⎪= deg le lt deg⎨⎪

deg le lt deg⎪⎩

(313)

312 Problem statement A conventional lead-lag PSS is considered in this study which can be described as

1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i

sT sT sTSignal K SignalsT sT sT

+ +=

+ + + (314)

- 18 -

where the symbol wT is the washout time constant the symbol _in iSignal is the PSS input

signal at the thi generator the symbol _out iSignal is the PSS output signal at the thi generator The time constant wT is usually pre-specified The stabilizer gain iK and time constants

1iT 2iT 3iT and 4iT remain to be determined Firstly using the method described in Section 311 to identify the number compensation stages m as well as the values of 1iT 2iT 3iT and 4iT Increase K iteratively subject to

min maxi i iK K Kle le (315)

Stopping criteria

( ) ( )min min 1i iς ς minuslt (316)

( ) ( )min min 1 01i if f minusminus gt (317) The calculation procedure of iterative residue algorithm is detailed in Figure 33

- 19 -

Figure 33 Iterative residue algorithm

32 Particle swarm optimization 321 Introduction Generally PSO is characterized as a simple concept easy to implement and computationally efficient It has a flexible and well-balanced mechanism to enhance the global and local exploration abilities

- 20 -

PSO was firstly introduced in 1995 by Kennedy and Eberhart [19] Here it is referred as classic PSO The classic PSO is initialized from a set of solutions or alternatives called ldquoparticlesrdquo at a given iteration Each particle moves according to a rule defined by three factors from one iteration to the next In this rule the PSO needs to keep record of the best point ib founded by the particle in its past life and the current global best point gb found by the swarm of particles in their past lives

new newi i iX X V= + (318)

( ) ( ) ( )0 1 1 2 2 1new

i i i i i i i gV Dec t w V Rnd w b X Rnd w b X= + minus + minus (319) In Equation (318) the symbol iX is a candidate solution of the objective function the symbol iV is the velocity of moving particle i which is defined by Equation (319) In Equation (319) the first term of the summation represents inertia or habit the second represents memory and the third represents cooperation exchange The parameters ikw are weights fixed in the beginning of the process the symbol

xRnd are random numbers sampled from a uniform distribution in [01] the symbol

( )Dec t is a function decreasing with the process of iterations reducing progressively the importance of the inertia term the symbol ib is the local best candidate solution of last iteration while the symbol gb is the global best candidate solution of last iteration [20] The movements of particles are illustrated in Figure 34

Figure 34 PSO particle movement [29]

- 21 -

322 Problem statement Consider the same lead-lag PSS described in Equation (313)

1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)

The time constant wT is usually pre-specified The stabilizer gain iK and time constants

1iT 2iT 3iT and 4iT remain to be optimized To increase the system damping to electromechanical modes we define an eigenvalue-based objective function J which is the damping ratio of one electromechanical mode eigenvalue usually the minimum one or the sum of the damping ratios of a group of electromechanical mode eigenvalues of interest In the optimization process we aim to maximize J in order to increase the damping of electromechanical modes The problem constraints are the bounds of the parameter to be optimized Therefore the design problem can be formulated as Maxmize J (321) Subject to

min maxi i iK K Kle le (322) min max

i i iT T Tle le (323) Typical ranges of the optimized parameters are [0001-50] for iK [26] [002-2] for leadlag time constant iT and [110] for wash-out time constant wT [27] To simplify the calculation and reduce the number of parameters to be optimized in this thesis we set

wT to be a constant Stopping criteria

maxiI Igt (324) where maxI is the maximum iteration number assigned in advance The calculation procedure of PSO algorithm is detailed in Figure 35 an example of the convergence of the objective function is illustrated in Figure 36

- 22 -

Figure 35 PSO algorithm

- 23 -

Figure 36 Convergence of PSO objective function

323 Implementation The proposed PSOndashbased tuning algorithm was implemented using Matlab To demonstrate the effectiveness of this algorithm two examples of two area systems shown in Figure 14 are considered Generator G1 is a wind farm whose power and voltage are identical to conventional plants described in [5] The detailed data of the system are represented in Appendix A Example 1 Optimize system damping of one oscillation mode Here I optimize the oscillation mode with the least damping ratio given in the eigenvalue analysis thus improve the damping of the whole system Three input signals are selected which are identical to those employed in [7] The input signals are θamp The speed of the voltage angle of Bus 1

78P The power on one transmission line between Bus 7 and Bus 8

dω The difference in rotor speeds of generators participate most in the inter-area oscillation mode in this case 2 3dω ω ω= minus

- 24 -

PSS parameters [26] are

10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)

2 4T T= (329) 0 50Kle le (330) The objective function is Maximize minJ ς= (331) where minς is the least damping ratio of the eigenvalues of the electromechanical mode Maximum Iteration 200 Simulation results got by PSO algorithm are presented in Table 31 Simulation results got by iterative residue algorithm under the same situation are presented in Table 32 In Table 31 the starred value is not within the range of the PSS gain however since the value is not greater too much than the top boundary of K and the damping ratio reaches its global best these set of parameters are include in this table If only from the perspective of damping ratio it can be observed that in all cases using PSO algorithm can reach a better result Another merit of PSO is that it requires much shorter calculation procedure than the iterative residue algorithm does which is quite helpful especially when dealing with large and complex systems like the Nordic32A system It should be mentioned that since the parameters are chosen randomly through PSO algorithm the value of iK 1iT 2iT 3iT and 4iT will not be the same each time PSO is ran while the optimum of the damping ratio are more or less the same This problem will not occur in

Table 31 PSS parameters based on particle swarm optimization algorithm

Signal Channel K T1 T2 T3 T4 Damping Ratio

No input NA 0 10000 10000 10000 10000 00203 θamp PSS xV minus -561999 00727 01221 00727 01221 01349

78P PSS xV minus 24157 00217 02215 00217 02215 01349

dω PSS xV minus -168431 19981 06751 19981 06751 01349 θamp PSS yV minus 05589 19870 04904 19870 04904 00344

78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -

Table 32 PSS parameters based on iterative residue algorithm



78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345

dω PSS yV minus 69392 04520 01274 04520 01274 01360 iterative residue algorithm It also can be observed that the effectiveness of PSO depends on its initial conditions greatly How to set the initial conditions still needs further study We can also examine how the system behaves under disturbances two cases are taken into consideration

bull Small disturbance The disturbance is a three phase to ground fault at Bus 8 The fault is cleared after 100 ms

bull Large disturbance The disturbance is a three phase to ground fault at Bus 8 The fault is cleared after 100 ms by tripping the line between Bus 8 and Bus 9

The power along the line connecting Bus 7 and Bus 8 subject to those disturbances using different tuning algorithms is illustrated in Figure 37 all signals are feedback into PSS xV minus From Figure 37 and Tables 31 and 32 it can be observed that for small disturbance the PSSs using PSO tuning algorithm have better damping ratios than those using the iterative residue algorithm no matter which input signals are chosen although in some cases the PSOrsquos advantages are not so obvious for example in Figure 37(a) Considering all these optimal solutions are reached in very short time PSO can be regarded as a good way to tune PSS However for the large disturbance PSO algorithm has no obvious advantages than iterative residue algorithm sometimes like in Figure 37 (f) the performance of PSO algorithm even worse than iterative residue algorithm

- 26 -

(a) Small disturbance input θamp

(b) Large disturbance input θamp

- 27 -

(c) Small disturbance input 78P

(d) Large disturbance input 78P

- 28 -

(e) Small disturbance input dω

(f) Large disturbance input dω

Figure 37 Dynamic response of 78P subject to different input signals and tuning algorithm

- 29 -

Example 2 Optimize system damping of multiple oscillation modes Although the least damping ratio is critical to a power system it is not the only mode we should take care of in certain situations Sometimes we may like to see if the damping of other modes with different frequencies can be improved as well Therefore I further investigated the possibility to realize this function using PSO In this example I optimized all oscillation modes between a frequency window to improve the damping of the whole system The frequency window is set as 05 Hz ndash 2 Hz in this study The effectiveness of PSO depends on the sum of damping ratios of all these oscillation modes Thus every oscillation mode should be assigned a weight factor which represents the importance of different oscillation modes in the whole system The input signals are chosen the same as those in Example 1 PSS parameters are

10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)

2 4T T= (336) 0 100Kle le (337) The object function is

Maximize 1

n

i ii

J w ς=

= sdotsum (338)

where n is the number of all the target oscillation modes iς is the damping ratio of the target oscillation modes iw is the weight associated to the given damping ratio as shown in Table 33

Table 33 Weight table Damping Ratio iς Weight iw

Floor value Cap value 08 000 005 07 005 010 06 010 015 05 015 020 04 020 040 03 040 060 02 050 080 01 080 100

- 30 -

Maximum Iteration 200 Simulation results are presented in Table 34 Due to the different condition and evaluation criteria it is difficult to compare the results got in Example 2 and in Example 1 The asterisks in Table 34 represent an optimum can not be achieved due to the improper initialization of PSO algorithm Example 1 can be regarded as a special case of Example 2 However we can still find that though the optimum objective function are nearly the same the least damping ratios vary with different input signals Although the least damping ratio is not the only consideration factor it does make great sense to the PSS performance How to set the evaluation criteria and weigh different oscillation modes is crucial to Example 2 and still need further exploration

Table 34 Simulation results PSS-x PSS-y

Signal Objective Function

Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -

Chapter 4 Case studies In this chapter a number of case studies are conducted on Nordic32A power system We aim to investigate the effect of a wind farm on the Nordic32A system on the base that a number of generators which are close together and behave similarly can be represented by a single generator [28] Therefore an aggregate of DFIGs such as wind farms can be represented by a single DFIG while an aggregate of synchronous generators such as general power systems which is typically made up of synchronous generators can be represented by a single synchronous generator Five cases are presented In Case 1 all generators are synchronous generators represented by classical model inbuilt in Simpow[22] In Case 2 one DFIG is installed while the system remains stable The results are compared with Case 1 to investigate the impact of DFIG In Case 3 one DFIG is installed in the North while the system is unstable In Case 4 one DFIG is installed in the Centre while the system is unstable In Case 5 one DFIG is installed in the South while the system is unstable The results of cases 3 4 and 5 are then compared Case 1 Nordic32A system without DFIG In this case modal analysis of the Nordic32A system is conducted when DFIG is not installed in the system We linearise the system on its stable operating point 44 non-zero eigenvalues are given Since all generators are represented by classical synchronous generator models which have no inherent damping eigenvalues only have imaginary

- 32 -

parts Here the inter-area oscillation mode with the lowest frequency between 05-2 Hz is of great interest in this case 000000 1s plusmn0580645 Hz We examine the participation factors of eigenvalue 000000 1s 0580645 Hz to get some idea of which state variable has the most significant influence We plot the participation factors associated with the generator speed which is identical with the participation factors associated with the generator angle in this case in a column chart as illustrated in Figure 41 Since in this thesis we are not interested in the sensitivity information contained in participation factors very much it is more convenient to normalize the participation vectors so that the largest element is unity The negative bars simply represent the angle of these participation factors are opposite with those positive ones Since in this case the participation factors do not give very clear information about the angle relations we use the information of corresponding right eigenvectors as a substitute which should give the identical information theoretically Different regions of the system are marked in different colors the Northern part combine the ldquoExternalrdquo and ldquoNorthrdquo region in Figure 15 From Figure 41 it can be observed that the participation factors associated with Generator BUS472G1 located in the North are the highest followed by the Generator BUS463G1 and BUS463G2 in the Southwest All generators in the Central and Southwestern part as well as several generators in the North but close to the Central part oscillate against Generator BUS472G1 A small group of generators located in the North oscillate in the same direction with Generator BUS472G1 with very small participation factors Thus this case can be regarded as a small group of generators in the North oscillate against all the other generators especially those in the Southwest

-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1

Synchronous Generators

Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)

North Central Southwest

Figure 41 Participation analysis of eigenvalue 000000 1s 0580645 Hz ς= 0

Case 2 Nordic32A system with one DFIG in the North

- 33 -

In this case modal analysis of the Nordic32A system is conducted when one DFIG is installed on Bus 1022 No turbine governor and automatic voltage regulator (AVR) are equipped We linearise the system on its stable operating point There are 45 non-zero eigenvalues All eigenvalues lie on the left side of the complex plane Compared with Case 1 the damping of all oscillation modes have been improved to different extent although most damping ratios are still quite small without turbine governor and AVR Now let us further examine some modes of interest Among the total 45 eigenvalues there are 3 eigenvalues without imaginary part which represent the speed q -axis transient emf and d -axis transient emf of the DFIG separately through participation analysis Furthermore we also notice an oscillation mode -105738 1s plusmn482048 Hz has the largest damping ratio and frequency which is caused by DFIG Although the damping ratios of all oscillation modes have been improved to different extent DFIG has obvious better effect to increase the damping ratio of certain mode than others The participation analysis result of eigenvalue -0380637E-01 1s 0581809 Hz the one with the lowest frequency except the 3 eigenvalues without imaginary parts is illustrated in Figure 42 The participation factors associated with Generator BUS472G1 are still the dominant participation factors All generators located in the Central and the Southwestern parts as well as a small group of generators located in the Northern part but close to the Central part oscillate against Generator BUS472G1 Some generators have relatively high participation factors especially in the Southwest All generators oscillation in the same direction with Generator BUS472G1 are located in the North Similar with Case 1 this case is a small group of generators in the North oscillate against all the other generators especially those in the Southwest

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -

Figure 42 Participation analysis of eigenvalue -0380637E-01 1s 0581809 Hz ς= 10412E-02

Case 3 Nordic32A system with one DFIG in the North In this case one DFIG is installed on Bus 4021 which is close to the location in Case 2 Some different phenomena are observed Among 45 eigenvalues 4 eigenvalues have positive real part indicating the system is unstable These eigenvalues are 0166623E-04 1s 103217 Hz 0166623E-04 1s -103217 Hz 0138778E-14 1s 130496 Hz and 0138778E-14 1s -130496 Hz Now we further examine the eigenvalue 0166623E-04 1s 103217 Hz which has relatively lower frequency to investigate which state variables influence this eigenvalue most The participation analysis result is illustrated in Figure 43 We observe that Generator BUS451G1 oscillates against Generator BUS447G1 and Generator BUS447G2 all of which locate in the Central part The significance of other generators is relatively ignorable Most of generators located in the North except Generator BUS232G1 and BUS431G1 oscillate against Generator BUS451G1 Thus this case can be regarded as a local oscillation within the Central part

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)

North Central Southw est

Figure 43 Participation analysis of eigenvalue 0166623E-04 1s 103217 Hz ς= -25692E-06 Case 4 Nordic32A system with one DFIG in the Centre In this case one DFIG is installed on Bus 4041 which is located in the middle of Central part Three pairs of unstable oscillation modes are observed We examine the eigenvalue 0268868E-01 1s 0575597 Hz which has the lowest frequency among the three The participation analysis result is illustrated in Figure 44 The situation is also similar with Case 1 The participation factors associated with Generator BUS472G1 are the dominant

- 35 -

participation factors All generators located in the Central and the Southwestern parts as well as a small group of generators located in the North but close to the Central part oscillate against Generator BUS472G1 Generators in the Southwest have relatively high participation factors All generators with positive participation angles are located in the North Thus in this case a small group of generators in the North oscillate against all the other generators

-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


Figure 44 Participation analysis of eigenvalue 0268868E-01 1s 0575597 Hz ς= -74341 E-03 Case 5 Nordic32A system with one DFIG in the South In this case one DFIG is installed on Bus 4051 which locates in the south of Central part Two pairs of oscillation modes are observed The eigenvalue 0499708E-01 1s 0572276 Hz is of interest in this case The participation analysis result is illustrated in Figure 45 Similar phenomena are observed Generator BUS472G1 is still the dominant generator in this case and oscillates against generators in the Centre and Southwest

- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


Figure 45 Participation analysis of eigenvalue 0499708E-01 1s 0572276 Hz ς= -13896 E-02

- 37 -

Chapter 5 Conclusions and future work 51 Conclusions This thesis focuses on the impact of wind power on the Nordic power system due to the rapid development of wind power in this region We employ the Nordic32A system as the model of the power network Conventional power plants are represented by the classic model of synchronous generator which aims to eliminate the complexity introduced by higher order models Wind power plants are represented by a DFIG model Two PSS tuning algorithm are presented to increase power system stability The iterative algorithm is based on the participation factor and residue which can be applied in various cases with reliable results but requires heavy computation burden The particle swarm optimization algorithm can ease this problem and improve the calculation efficiency dramatically with better damping However its results depend on the selection of its parameters calculation domain and the characters of the system greatly Using proper algorithm in different situation can achieve good tuning results Wind power is capable of improving the damping of the system Its performance depends on the oscillation mode in question and the location where wind power is installed In addition in some cases some unstable oscillation modes may be observed when wind power is installed These unstable modes are caused by the inter-area oscillations between synchronous generators in different part of the system or local oscillations between synchronous generators in the same part of the system A general finding is that Generator BUS472G1 is usually the dominant generator that has the biggest influence on inter-area oscillation modes no matter if wind power is installed or not Inter-area oscillation occurs between a small group of generators in the North and all the other generators in the North Centre and the Southwest Most generators with relatively larger influences on the inter-area oscillation modes are observed to have large active power and reactive power production

- 38 -

52 Future work This thesis can be regarded as a further exploration of [7] However due to the limitation of the capability of author as well as the time of the project many phenomena still remain for further study The PSO algorithm developed in this thesis aims to ease the heavy computation burden of conventional iterative algorithm and reach an optimal solution however although theoretically PSO can always reach an optimum its performance still depends on some constraints very much The setting of initialization parameters will influence the performance since an optimum can not exist alone but depends on constraints How to initialize PSO parameters still needs further study In addition when dealing with multiple targets like the damping ratios of multiple oscillation modes in this thesis how to design a reasonable weight criterion is also of interest The performance of PSS differs with different input signals How to choose these signals and compare their results automatically to achieve the optimum is something can be addressed further Due to the complexity of the Nordic32A power system in this thesis all conventional power plants are represented by the classic synchronous generators It will be very interesting to represent these power plants by more complicated models according to their way to produce electric power in reality This will bring this project closer to reality It is a challenge to get the system stable when introducing new generators Further attempts to investigate the dynamic impact of the Nordic32A system when multiple DFIGs are employed can be made in the future

- 39 -

Appendix A Two area system data Synchronous generator

900bS MVA= 20bU kV= 18dX = 17qX = 02lX = 03dX prime = 055qX prime = 025dX primeprime = 025qX primeprime = 00025aR = 0 80dT sprime = 0 04qT sprime =

0 003dT sprimeprime = 0 005qT sprimeprime = 0015SatA = 96SatB = 1 09Tψ = 65H = (for G1 and G2) 6175H = (for G3 and G4) 0DK =

Transformer

900bS MVA= 20 230bU kV= 0 015Z j= + 10TR = Lines

230bU kV= 00001 r pu km= 0001 Lx pu km= 000175 cb pu km=

Generating units G1 700P MW= 185Q MVar= 103 202tE = ang deg G2 700P MW= 235Q MVar= 101 105tE = ang deg G3 719P MW= 176Q MVar= 103 68tE = angminus deg G4 700P MW= 202Q MVar= 101 170tE = angminus deg Shunt capacitors Bus 7 700LP MW= 100LQ MVar= 200CQ MVar= Bus 9 1767LP MW= 100LQ MVar= 350CQ MVar= Doubly fed induction generator

- 40 -

The DFIG has the same power and voltage ratings as the conventional machine it replaces

001rR = 31sX = 31rX = 3mX = 05H = 01sprime = minus

Regulator

300AK = 001AT = Controller

1pdK = 0idK = 1pqK = 01iqK =

- 41 -

Appendix B The Nordic32A system data Bus data

NAME BSKV (KV) BUS TYPE VOLT

(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)

BUS1011 130 1011 LD 14593 01517 2000 800 00 00 BUS1012 130 1012 PU 14690 37195 3000 1000 00 00 BUS1013 130 1013 PU 14885 70064 1000 400 00 00 BUS1014 130 1014 PU 15080 95890 00 00 00 00 BUS1021 130 1021 PU 14300 79361 00 00 00 00 BUS1022 130 1022 PU 13822 -116853 2800 950 00 500 BUS1041 130 1041 LD 12487 -758093 6000 2000 00 2000 BUS1042 130 1042 PU 13000 -592167 3000 800 00 00 BUS1043 130 1043 PU 12865 -701621 2300 1000 00 1500 BUS1044 130 1044 LD 12785 -611078 8000 3000 00 2000 BUS1045 130 1045 LD 12880 -654335 7000 2500 00 2000 BUS2031 220 2031 LD 23171 -290089 1000 300 00 00 BUS2032 220 2032 PU 24200 -169701 2000 500 00 00 BUS4011 400 4011 PU 40400 -09167 00 00 00 00 BUS4012 400 4012 PU 40400 10198 00 00 00 -1000 BUS4021 400 4021 PU 40331 -286087 00 00 00 00 BUS4022 400 4022 LD 39755 -137735 00 00 00 00 BUS4031 400 4031 PU 40400 -319591 00 00 00 00 BUS4032 400 4032 LD 40546 -371876 00 00 00 00 BUS4041 400 4041 PU 40000 -472747 00 00 00 2000 BUS4042 400 4042 PU 40000 -505568 00 00 00 00 BUS4043 400 4043 LD 39610 -570607 00 00 00 2000 BUS4044 400 4044 LD 39528 -577022 00 00 00 00 BUS4045 400 4045 LD 39864 -626598 00 00 00 00 BUS4046 400 4046 LD 39629 -577255 00 00 00 1000 BUS4047 400 4047 PU 40800 -527934 00 00 00 00 BUS4051 400 4051 PU 40800 -650772 00 00 00 1000 BUS4061 400 4061 LD 39283 -510225 00 00 00 00 BUS4062 400 4062 PU 40018 -469241 00 00 00 00 BUS4063 400 4063 PU 40000 -428546 00 00 00 00 BUS4071 400 4071 PU 40400 00003 3000 1000 00 -4000 BUS4072 400 4072 SW 40400 0 20000 5000 00 00 BUS41 130 41 LD 12811 -504158 5400 1283 00 00 BUS42 130 42 LD 12765 -535924 4000 1257 00 00 BUS43 130 43 LD 12622 -608178 9000 2388 00 00

- 42 -

NAME BSKV

(KV) BUS TYPE VOLT (KV)

ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)

BUS46 130 46 LD 12585 -61911 7000 1937 00 00 BUS47 130 47 LD 13015 -550383 1000 452 00 00 BUS51 130 51 LD 13010 -682221 8000 2532 00 00 BUS61 130 61 LD 12540 -549569 5000 1123 00 00 BUS62 130 62 LD 12770 -504243 3000 800 00 00 BUS63 130 63 LD 12633 -463353 5900 2562 00 00

Comments TPYE LD Load bus PU PU-bus PQ PQ-bus SW Slack bus VOLT Data based on the results of load flow ANGLE Data based on the results of load flow

- 43 -

Generating plants data

NAME GEN BSKV (KV) BUS TPYE VOLT

(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)

BUS1012 1 130 1012 PU 14690 6000 849 4000 -800 BUS1013 1 130 1013 PU 14885 3000 440 3000 -500 BUS1014 1 130 1014 PU 15080 5500 821 3500 -1000 BUS1021 1 130 1021 PU 14300 4000 447 3000 -600 BUS1022 1 130 1022 PU 13910 2000 1250 1250 -250 BUS1042 1 130 1042 PU 13000 3600 790 2000 -400 BUS1043 1 130 1043 PU 13000 1800 1000 1000 -200 BUS2032 1 220 2032 PU 24200 7500 1458 4250 -800 BUS4011 1 400 4011 PU 40400 6685 943 5000 -1000 BUS4012 1 400 4012 PU 40400 6000 25 4000 -1600 BUS4021 1 400 4021 PU 40000 2500 300 1500 -300 BUS4031 1 400 4031 PU 40400 3100 1134 1750 -400 BUS4041 1 400 4041 PU 40000 00 90 3000 -2000 BUS4042 1 400 4042 PU 40000 6300 2650 3500 00 BUS4047 1 400 4047 PU 40800 10800 3042 6000 00 BUS4047 2 400 4047 PU 40800 10800 3042 6000 00 BUS4051 1 400 4051 PU 40800 6000 2174 3500 00 BUS4062 1 400 4062 PU 40000 5300 00 3000 00 BUS4063 1 400 4063 PU 40000 10600 1768 6000 00 BUS4063 2 400 4063 PU 40000 10600 1768 6000 00 BUS4071 1 400 4071 PU 40400 3000 543 2500 -500 BUS4072 1 400 4072 SW 40400 20000 1940 10000 -3000

Comments VOLT Data scheduled

- 44 -

Generator units data

NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D

BUS1012 1 800 300 220 220 030 01 03 BUS1013 1 600 300 220 220 030 01 03 BUS1014 1 700 300 220 220 030 01 03 BUS1021 1 600 300 220 220 030 01 03 BUS1022 1 250 300 220 220 030 01 03 BUS1042 1 400 600 110 110 025 01 03 BUS1043 1 200 600 110 110 025 01 03 BUS2032 1 850 300 220 220 030 01 03 BUS4011 1 1000 300 220 220 030 01 03 BUS4012 1 800 300 220 220 030 01 03 BUS4021 1 300 300 220 220 030 01 03 BUS4031 1 350 300 220 220 030 01 03 BUS4041 1 300 200 155 155 030 01 03 BUS4042 1 700 600 110 110 025 01 03 BUS4047 1 600 600 110 110 025 01 03 BUS4047 2 600 600 110 110 025 01 03 BUS4051 1 700 600 110 110 025 01 03 BUS4062 1 600 600 110 110 025 01 03 BUS4063 1 600 600 110 110 025 01 03 BUS4063 2 600 600 110 110 025 01 03 BUS4071 1 500 300 220 220 030 01 03 BUS4072 1 4500 300 220 220 030 01 03

Comments H Inertia constant

XD Direct-axis synchronous reactance chosen based on the data in [6] and the synchronous generator classical model

XQ Quadrature-axis synchronous reactance chosen based on the data in [6] and the synchronous generator classical model

XDP Direct-axis transient reactance chosen based on the data in [6] SE1D Saturation factor at the quadrature-axis air-gap flux V1Q which equals to 1 SE2D Saturation factor at the quadrature-axis air-gap flux V2Q which equals to 12

- 45 -

Transmission lines data

FROM-BUS TO-BUS NAME BSKV BUS NAME BSKV BUS

LINE R (pu)

X (pu)

B (pu)

BUS1011 130 1011 BUS1013 130 1013 1 001000 0070 0014 BUS1011 130 1011 BUS1013 130 1013 2 001000 0070 0014 BUS1012 130 1012 BUS1014 130 1014 1 001402 0090 0018 BUS1012 130 1012 BUS1014 130 1014 2 001402 0090 0018 BUS1013 130 1013 BUS1014 130 1014 1 000698 0050 0010 BUS1013 130 1013 BUS1014 130 1014 2 000698 0050 0010 BUS1021 130 1021 BUS1022 130 1022 1 003000 0200 0030 BUS1021 130 1021 BUS1022 130 1022 2 003000 0200 0030 BUS1041 130 1041 BUS1043 130 1043 1 001000 0060 0012 BUS1041 130 1041 BUS1043 130 1043 2 001000 0060 0012 BUS1041 130 1041 BUS1045 130 1045 1 001497 0120 0025 BUS1041 130 1041 BUS1045 130 1045 2 001497 0120 0025 BUS1042 130 1042 BUS1044 130 1044 1 003799 0280 0060 BUS1042 130 1042 BUS1044 130 1044 2 003799 0280 0060 BUS1042 130 1042 BUS1045 130 1045 1 005000 0300 0060 BUS1043 130 1043 BUS1044 130 1044 1 001000 0080 0016 BUS1043 130 1043 BUS1044 130 1044 2 001000 0080 0016 BUS2031 220 2031 BUS2032 220 2032 1 001200 0090 0015 BUS2031 220 2031 BUS2032 220 2032 2 001200 0090 0015 BUS4011 400 4011 BUS4012 400 4012 1 000100 0008 0200 BUS4011 400 4011 BUS4021 400 4021 1 000600 0060 1800 BUS4011 400 4011 BUS4022 400 4022 1 000400 0040 1200 BUS4011 400 4011 BUS4071 400 4071 1 000500 0045 1400 BUS4012 400 4012 BUS4022 400 4022 1 000400 0035 1050 BUS4012 400 4012 BUS4071 400 4071 1 000500 0050 1500 BUS4021 400 4021 BUS4032 400 4032 1 004000 0040 1200 BUS4021 400 4021 BUS4042 400 4042 1 001000 0060 3000 BUS4022 400 4022 BUS4031 400 4031 1 000400 0040 1200 BUS4022 400 4022 BUS4031 400 4031 2 000400 0040 1200 BUS4031 400 4031 BUS4032 400 4032 1 000100 0010 0300 BUS4031 400 4031 BUS4041 400 4041 1 000600 0040 2400 BUS4031 400 4031 BUS4041 400 4041 2 000600 0040 2400 BUS4032 400 4032 BUS4042 400 4042 1 001000 0040 2000 BUS4032 400 4032 BUS4044 400 4044 1 000600 0050 2400 BUS4041 400 4041 BUS4044 400 4044 1 000300 0030 0900 BUS4041 400 4041 BUS4061 400 4061 1 000600 0045 1300 BUS4042 400 4042 BUS4043 400 4043 1 000200 0015 0500 BUS4042 400 4042 BUS4044 400 4044 1 000200 0020 0600 BUS4043 400 4043 BUS4044 400 4044 1 000100 0010 0300 BUS4043 400 4043 BUS4046 400 4046 1 000100 0010 0300 BUS4043 400 4043 BUS4047 400 4047 1 000200 0020 0600 BUS4044 400 4044 BUS4045 400 4045 1 000200 0020 0600 BUS4044 400 4044 BUS4045 400 4045 2 000200 0020 0600 BUS4045 400 4045 BUS4051 400 4051 1 000400 0040 1200 BUS4045 400 4045 BUS4051 400 4051 2 000400 0040 1200 BUS4045 400 4045 BUS4062 400 4062 1 001100 0080 2400 BUS4046 400 4046 BUS4047 400 4047 1 000100 0015 0500 BUS4061 400 4061 BUS4062 400 4062 1 000200 0020 0600 BUS4062 400 4062 BUS4063 400 4063 1 000300 0030 0900 BUS4062 400 4062 BUS4063 400 4063 2 000300 0030 0900

- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000

Comments The data of resistance inductance and shunt capacitance are given in per unit which is related to system base

100bS MVA= 400bU kV= 220kV and 130kV respectively

2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data

FROM BUS TO BUS NAME BSKV NAME BSKV

TRANS R (pu)

X (pu)

SIZE (MW) RATIO STEP

BUS1011 130 BUS4011 400 1 00000 01000 1250 112 00625 BUS1012 130 BUS4012 400 1 00000 01000 1250 112 00625 BUS1022 130 BUS4022 400 1 00000 01002 835 107 00625 BUS1044 130 BUS4044 400 1 00000 01000 1000 100 00100 BUS1044 130 BUS4044 400 2 00000 01000 1000 100 00100 BUS1045 130 BUS4045 400 1 00000 01000 1000 100 00100 BUS1045 130 BUS4045 400 2 00000 01000 1000 100 00100 BUS2031 220 BUS4031 400 1 00000 01002 835 105 00625 BUS4041 400 BUS41 130 1 00000 01000 1000 100 00100 BUS4042 400 BUS42 130 1 00000 00975 750 100 00100 BUS4043 400 BUS43 130 1 00000 01050 1500 100 00100 BUS4046 400 BUS46 130 1 00000 01000 1000 100 00100 BUS4047 400 BUS47 130 1 00000 01000 250 100 00100 BUS4051 400 BUS51 130 1 00000 01050 1500 100 00100 BUS4061 400 BUS61 130 1 00000 00975 750 100 00100 BUS4062 400 BUS62 130 1 00000 01000 500 100 00100 BUS4063 400 BUS63 220 1 00000 01000 1000 100 00100

- 48 -

- 49 -

Bibliography [1] Global Wind Energy Council Global Wind 2008 Report wwwgwecnet 2009 [2] James F Manwell Jon G McGowan Anthony L Rogers Wind Energy Explained

Theory Design and Application John Wiley amp Sons Ltd 2002 [3] Pablo Ledesma Julio Usaola Doubly Fed Induction Generator Model for

Transient Stability Analysis IEEE Transactions on Energy Conversion vol20 no2 pp388-397 June 2005

[4] Svensk Vindenergi 2009 09 01 Vindkraftprojekt under byggnad och i drift gt 10 MW wwwsvenskvindenergiorg 2009

[5] Prabha Kundur Power System Stability and Control McGraw-Hill Inc 1994 [6] CIGRE CIGRE Task Force 38-02-08 Long term dynamics phase II 1995 [7] Katherine Elkinton Modelling and Control of Doubly Fed Induction Generators in

Power Systems Royal Institute of Technology (KTH) Sweden Stockholm April 2009

[8] JGSlootweg WLKling The impact of large scale wind power generation on power system oscillations Electric Power System Research vol67 issue 1 pp9-20 October 2003

[9] SMuller M Deicke RWDe Doncker Doubly fed indcution generator systems for wind turbines IEEE Ind Applicat Mag pp 26-33 MayJune 2002

[10] Andreacutes Feijoacuteo Joseacute Cidraacutes Camilo Carrillo A third order model for the doubly-fed induction machine Electric Power System Research vol56 issue 2 pp121-127 November 2000

[11] JG Slootweg H Polinder WLKling Dynamic modeling of a wind turbine with doubly fed induction generator IEEE Power Eng Soc Summer Meeting Vancouver BC Canada July 15-19 2001

[12] JanakaB Ekanayake Lee Holdsworth Xueguang Wu Nicholas Jenkins Dynamic modeling of doubly fed induction generator wind turbines IEEE Transactions on Power Systems vol 18 issue 2 pp 803-809 May 2003

[13] JB Ekanayake LHoldsworth N Jenkins Comparison of 5th order and 3rd order machine models for DFIG wind turbines Electric Power System Research vol67 issue 3 pp207-215 December 2003

[14] Lie Xu Phillip Cartwright Direct Active and Reactive power Control of DFIG for Wind Energy Generation IEEE Transactions on Energy Conversion vol21 no3 pp750-758 September 2006

[15] F Michael Hughes Olimpo Anaya-Lara Nicholas Jeenkins Goran Strbac Control of DFIG-Based Wind Generation for Power Network Support IEEE Transactions

- 50 -

on Power Systems vol20 no4 pp1958-1966 November 2005 [16] Feng Wu Xiaoping Zhang Keith Godfrey Ping Ju Modeling and Control of Wind

Turbine with Doubly Fed Induction Generator IEEE Power System Conference and Exposition 2006 pp 1404-1409 October 2006

[17] Ning Yang Qinghua Liu James D McCally TCSC Controller Design for Damping Interarea Oscillations IEEE Transactions on Power Systems Vol13 No4 November 1998

[18] Annissa Heniche Innocent Kamwa Assessment of Two Methods to Select Wide-Area Signals for Power System Damping Control IEEE Transactions on Power Systems Vol23 No2 May 2008

[19] James Kennedy Russell Eberhart Particle Swarm Optimization IEEE International Conference on Neural Networks Pert Australia IEEE Service Center Piscataway NJ 1995

[20] Angelo Mendonca JA Pecas Lopes Simultaneous Tuning of Power System Stabilizers Installed in DFIG-Based Wind Generation IEEE Lausanne Power Tech July 2007

[21] Mehrdad Ghandhari Dynamic analysis of Power System Part II Compendium IR-EE-ES 2006016 Electric Power System Royal Institute of Technology Stockholm Sweden 2007

[22] STRI AB Simpow User Manual 110 June 2008 [23] Stefan Oumlstlund Electrical Machines and Drives Royal Institute of Technology

Stockholm Sweden 2008 [24] Graham Rogers Power System Oscillations Kluwer Academic Publishers Boston

USA 2000 [25] William Stallings Reduced Instruction Set Computer Architecture Procedings of

the IEEE vol 76 no 1 pp 38-55 1988 [26] MAAbido Optimal Design of Power System Stabilizers Using Particle Swarm

Optimization IEEE Transactions on Energy Conversion vol 17 Issue 3 September 2002

[27] httpwwwmeppicomProductsGenerator20Excitation20Products 20DocumentsPower20System20Stabilizerpdf

[28] VAkhmatov H Knudsen An aggregate model of a grid-connected large-scale offshore wind farm for power stability investigates-importance if windmill mechanical system International Journal of Electrical Power and Energy Systems vol 24 no9 pp709-717 2002

[29] Angelo Mendonca Nuno Fonseca JPecas Lopes Valdimiro Miranda Robust Tuning of Power Systems Stabilizers Using Evolutionary PSO httpwwwengenheirospt~nunomikelpapersartigo180pdf

ii

iii


iv

v


vi

vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















iii


iv

v


vi

vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















iv

v


vi

vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















v


vi

vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















vi

vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















vii


viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















viii

- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 1 -


- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 2 -



- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 3 -




- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 4 -




- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 5 -


- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 6 -




- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 7 -



- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 8 -




01ds ds ds qss

qs qs qs dss s

v i dRv i dt

ψ ψωψ ψω ω

minus⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤= minus + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (21)

01dr dr dr qrrr

qr qr qr drs s

v i dRv i dt



⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ (22)


- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 9 -


ds s ds m dr

qs s qs m qr

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(23)

dr r dr m ds

qr r qr m qs

X i X iX i X i

ψψ

+⎡ ⎤ ⎡ ⎤= minus⎢ ⎥ ⎢ ⎥+⎣ ⎦ ⎣ ⎦

(24)

where

s ls mX X X= + (25)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= e

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (27)


dd q

q

jξ

ξ ξ ξξ⎡ ⎤

rarr + =⎢ ⎥⎣ ⎦

(28)



- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 10 -

m

rr

XE jX

ψprime = (210)

2m

sr

XX XX

prime = minus (211)

Neglecting 1 s

s

ddtψ



( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛primeprimeminus

+primeprime


sss

rsrr

ms v

XXX

EXX

EjTvXX

jTTdt

Ed ωωω 000

1 (212)

where

rs

r

RXT

ω=0 (213)


mr r

r

Xv vX

prime = (214)


( )0 00




(215)

( )0 00




(216)


⎟⎟⎠

⎞⎜⎜⎝

⎛minus= s

r

sm

n

bsr PPSS

Hdtd

ωωωω

2 (217)


- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 11 -


( )2

qsm

d

E VP

H xωω δ θ


amp (219)


jsv Ve θ= (220)


- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 12 -






( ) ( )( ) ( )

cos sinsin cos

xr dr

yr dr

v v

v v

θ θθ θ


(223)

In this frame

xsv V= (224) 0ysv = (225)

- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 13 -





( ) ( )( ) ( )

cos sinsin cos

dr xr

qr yr

v v

v v

θ θθ θ


(228)


- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 14 -



( ) ( ) ( )0




- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 15 -





- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 16 -



( ) ( )( ) ( ) 1y s

G s C sI A B Du s


(33)


( ) ( )1

ni

i i

RG ss λ=

=minussum (34)




where r



( )KH s is

- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 17 -





1

2

1 sin1 sin

MTT M

φα

φ+

= =minus


where

1

i

Tω α

= (310)

1T Tα= (311) 2T T= (312)


( )( )( )

1 120 1802 60 1201 0 60

i

i

i

RM R

R


deg le lt deg⎪⎩

(313)


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (314)

- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 18 -





Stopping criteria



- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 19 -



- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 20 -



( ) ( ) ( )0 1 1 2 2 1new





- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 21 -


1 3_ _

2 4

1 11 1 1

w i iout i i in i

w i i


+ +=

+ + + (320)







- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 22 -


- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 23 -





- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 24 -


10wT s= (325)

1002 2s T sle le (326)

1 3T T= (327)

2002 2s T sle le (328)





78P PSS xV minus 24157 00217 02215 00217 02215 01349


78P PSS yV minus -230810 00881 04141 00881 04141 01460

dω PSS yV minus 186440 08280 03888 08280 03888 01783

- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 25 -




78P PSS xV minus 60055 00706 08156 00706 08156 00668


78P PSS yV minus -21897 01633 03527 10000 10000 01345





- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 26 -



- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 27 -



- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 28 -




- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 29 -


10wT s= (332)

10001 1000s T sle le (333)

1 3T T= (334)

20001 1000s T sle le (335)


Maximize 1

n

i ii

J w ς=

= sdotsum (338)




- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 30 -




Least Damping Ratio

Objective Function

Least Damping Ratio

No input 01914 00203 01914 00203 θamp 16901 00753 ---- ----

78P 17000 00987 ---- ----

dω 17000 01353 17000 00512

- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 31 -


- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 32 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)




- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 33 -


-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)


- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 34 -



-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 35 -


-1

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS442G1

BUS447G1

BUS447G2

BUS451G1

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 36 -

-08

-06

-04

-02

0

02

04

06

08

1

12

BUS112G1

BUS113G1

BUS114G1

BUS121G1

BUS122G1

BUS142G1

BUS143G1

BUS232G1

BUS411G1

BUS412G1

BUS421G1

BUS431G1

BUS441G1

BUS442G1

BUS447G1

BUS447G2

BUS462G1

BUS463G1

BUS463G2

BUS471G1

BUS472G1


Part

icip

atio

n Fa

ctor

s (N

orm

alis

ed)



- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 37 -


- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 38 -


- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 39 -




Transformer




- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 40 -



Regulator



- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 41 -



(KV) ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)


- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 42 -

NAME BSKV


ANGLE (DGREE)

PLOAD (MW)

QLOAD (MVAR)

SHUNT (MWMVAR)



- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 43 -



(KV) PGEN (MW)

QGEN (MVAR)

QMAX (MVAR)

QMIN (MVAR)



- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 44 -


NAME GEN MBASE (KV)

H ( MWsMVA)

XD (pu)

XQ (pu)

XDP (pu) SE1D SE2D






- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 45 -



LINE R (pu)

X (pu)

B (pu)


- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 46 -


LINE R (pu)

X (pu)

B (pu)

BUS4071 400 4071 BUS4072 400 4072 1 000300 0030 3000 BUS4071 400 4071 BUS4072 400 4072 2 000300 0030 3000



2b

pu nomb

SR RU

= sdot

2b

pu nomb

SX XU

= sdot

2b

pu nomb

SB BU

= sdot

- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 47 -

Transformers data


TRANS R (pu)

X (pu)



- 48 -

- 49 -















- 50 -
















- 48 -

- 49 -















- 50 -
















- 49 -















- 50 -
















- 50 -
















Modal Analysis of Power Systems with Doubly Fed Induction ...611637/FULLTEXT01.pdf · Figure 2.1...

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Transcript of Modal Analysis of Power Systems with Doubly Fed Induction ...611637/FULLTEXT01.pdf · Figure 2.1...