50

CHAPTER 3

STABILIZATION OF A SINGLE MACHINE INFINITE BUS

SYSTEM WITH FACTS DEVICES

3.1 INTRODUCTION

The availability of flexible A.C. trqnsmission system (FACTs)

devises such as Static Var compensators (SVCs), Static Compensator

(STATCOM), Thyristor Contzolled Series Compensators (TCSCs), Static

Synchronous Series Compensators (SSSC) and Unified Power Flow

Controllers (UPFC) has led their use to control real and reactive power flows

in transmission lines and bus voltage. In addition to steady state qower flow

and voltage control these devices can also be used effectively for improving

the small signal stability of a power system.

The objective of this chapter is to investigate the impact of the

FACTS devices namely Static Var Compensator (SVC), Thyristor Controlled

Series Capacitor (TCSC), Static Compensator (STATCOM), Static

Synchronous Series Compensator (SSSC) and Unified Power Flow Controller

(UPFC) on the small signal stability of a single machine infinite bus system.

A single machine infinite bus system is first chosen to analyze the damping

capabilities in a detailed manner.

51

3.2 BASIC APPROACH FOR SMALL SIGNAL STABILITY

ENHANCEMENT

The basic approach used for enhancing the small signal stability of

the single machine infinite bus (SMIB) system with FACTS based damping

controller is as follows.

1. Get the linearized model of the SMIB system without the

FACTS device and its damping controller around the nominal

operating state and compute the damping ratio of the electro

mechanical mode. If the damping ratio of electromechanical

mode is less than 0.1, it is considered as a critical mode.

2. If the FACTS device is shunt connected (SVC, STATCOM)

then the device is located between the HT bus and ground,

connected to the synchronous machine. If the device is series

connected (TCSC, SSSC, UPFC) then the device is located in

one of the high reactance lines between the generator and the

infinite bus.

3. Compute the stabilizing gain and time constant of the FACTS

based damping controller to maximize the damping ratio of

the critical mode using the parameter constrained optimization

algorithm which is presented in section 3.4.

4. Compute the elements of the linearized model with the

optimized gain and time constant obtained from step 3 and

compute the damping ratio of the electromechanical mode.

5. Check whether the damping ratio of the electromechanical

mode is small signal stable.

52

6. The robustness of the FACTS based damping controllers are

confirmed by computing the damping ratio of the

electromechanical mode in heavily loaded operating

condition (total system load increased by 20%) and lightly

loaded operating condition (total system load reduced by

20%).The real power absorbed by the loads is increased by

20% for this study. The increase in real power absorbed by

the loads is compensated by the slack bus. If the damping

ratio of the electromechanical mode is stable for this operating

condition then go to step 7.

7. Terminate the algorithm for small signal stability

enhancement.

The following section present the modeling details of the single

machine infinite bus system.

3.3 MATHEMATICAL MODEL OF SINGLE MACHINE

INFINITE BUS SYSTEM FOR SMALL SIGNAL ANALYSIS

The single line diagram of a SMIB system is shown in Figure 3.1.

Re and Xe denote the total equivalent resistance and reactance of the

synchronous machine and transmission network.

Figure 3.1 Single Line diagram of SMIB system

53

The network equation for the SMIB system can be written with the

following three steps.

(i) Express the synchronous machine voltage equations in qd

coordinates.

(ii) Get the expression for terminal voltage equation in terms of

the infinite bus voltage and drop in the external impedance.

(iii) Compare the expressions obtained in step (i) and (ii) which

yields the expression for current components in qd

coordinates.

The direct axis leads the quadrature axis in the direction of

transformation (Ramanujam 2009).

The voltage equations of the synchronous machine after ignoring

stator resistance are:

' 'V = X I + Eq qd d (3.1)

V = -X Iq qd

The direct axis of the synchronous machine leads the quadrature

axis in the direction of rotation.

Let the infinite bus voltage be jE = E eB B . Let the infinite bus

voltage in qd coordinates be given by

-jˆ ˆE = E + jE = E eBq BBqd Bd-j( )= E eB (3.2)

54

The d and q components of EB are given by

E = E cos( )Bq BE = -E sin( )BBd

(3.3)

Expressing Vqd in terms of the infinite bus voltage EBqd in terms of

the network reactance,

ˆ ˆ ˆV = E + (R + jX )Ie eqd Bqd qd (3.4)

Separating into d and q components we get,

V = E + R I - X Iq e q eBq d (3.5)

V = E + R I + X Ie e qd Bd d

After comparing equations (3.5) and (3.1), linearizing we get

' 'I-(X + X ) R E + E sin(e e qdd B 0=I E cos(R (X + X ) qe q e B 0

(3.6)

The expressions for incremental changes in currents are

-(X + X ) R cos( ) - (X + X )sin( ) 'I q e e q e E0 01 qd = 'I D ER R sin( ) + (X + X )cos( )q e e e B0 0d

(3.7)

where 2 'D = R +(X + X )(X + X )e e q ed

55

Substituting (3.7) in the differential equations of the synchronous

machine with exciter in (2.2), (2.4) and torque equation (2.3) yields the

system state space matrix with five state variables namely ' '[E ,E , ,E ]q FDd .

The differential equations describing the dynamic behavior of the

synchronous machine with the excitation system are given by the equations as

described in chapter two. Equation (2.2) describes the dynamic behavior of

the synchronous machine without exciter. Equation (2.4) models the

dynamics of the exciter circuit. Equations (2.5) and (2.6) govern the dynamics

of the power system stabilizer, which uses speed deviations as the feedback

signal. The complete set of state variables describing the dynamics of the

synchronous machine with the inclusion of the PSS is as follows.

T ' 'x = [E ,E , ,E ,X ,X ]q mFDd mod (3.8)

For the purpose of developing the small signal stability program all

the FACTS devices (TCSC, SSSC, UPFC) are represented as current

injections in two nodes of the network. However, if the device is a shunt

connected device (SVC, STATCOM) then the injections are confined only to

one node.

The following section gives the mathematical modeling of SMIB

system with FACTS devices.

3.3.1 Mathematical Model of SVC

The dynamic equations of the SVC for small signal analysis are

given by (2.18-2.20). The complete set of state variables describing the

dynamics of the single machine infinite bus system with the inclusion of the

SVC in the network is as follows.

56

T ' 'x = [E ,E , ,E ,B , X , X ]wq FD Ld le (3.9)

where ' 'E ,E ,qd are the differential equations associated with the

synchronous machine EFD is the exciter variable and BL is the shunt

susceptance modulated by the SVC regulator.

3.3.2 Mathematical Model of STATCOM

The SVC becomes a fixed capacitive admittance at its full output as

it is composed of reactors and capacitors. With STATCOM the maximum var

generation or absorption changes linearly with the ac system voltage

(Hingorani and Gyugyi, 2000). The dynamic equations of STATCOM with

the damping controller are given by equations (2.25) to (2.31) described in

chapter 2. The complete set of state variables used for linear analysis is given

by T ' 'x = [E ,E , ,E ,X ,X ,X ,m ,V , ,V ]wq FD 2d le sh dcx1 dc (3.10)

where X2 is the output of the ac voltage measuring circuit in STATCOM.

msh is the modulation index of the shunt converter of STATCOM.

Vdcx1 is the output of the dc voltage measuring circuit in

STATCOM. is the phase angle modulated by the voltage source

converter.

3.3.3 Mathematical Model of TCSC

The differential equations describing the dynamic behavior of

TCSC are given by equations (2.34-2.36). The set of state variables which

describe the small signal dynamics of the system with TCSC in the network is

given by T ' 'x = [E ,E , ,E ,X ,X ,X ]q FD W TCSCd le (3.11)

where XTCSC is the series reactance controlled by the TCSC regulator.

57

3.3.4 Mathematical Model of SSSC

The differential equations, which govern the dynamics of SSSC in

the network, are given by equations (2.39-2.45). The complete set of state

variables used for linear analysis with SSSC in the network is given by

T ' 'x = [E ,E , ,E ,X ,X ,X ,m ,V , ,V ]wq seFD 1d le dcx dc (3.12)

3.3.5 Mathematical Model of UPFC

The mathematical model of UPFC used for dynamic analysis

combines the dynamic equations of SSSC (2.39–2.45) for the series converter

and equations (2.25- 2.29) for the shunt converter. The damping controller

loop is connected in DC voltage controller of series converter as is done with

SSSC. The complete set of state variables describing the dynamics of the

single machine infinite bus system with UPFC given by

T ' 'x =[E ,E , ,E ,X ,X ,X ,m ,V , ,X ,m ,V , ,V ]q seFD W 1 2d le dcx sh dcx1 dc (3.13)

The optimal tuning procedure for the PSS and FACTS stabilizers is

explained in the following sections.

3.4 OPTIMAL TUNING OF CONTROLLER PARAMETERS

The gains and time constants of the power system stabilizer/FACTS

stabilizer are tuned using a non-linear optimization algorithm, which

maximizes the damping ratio of the electromechanical modes power system.

The problem formulation for the optimization problem is given below.

From the linearized model of the power system without damping

controllers (PSS and FACTS stabilizers) the critical electromechanical modes

58

are identified which cause dynamic instability in the system. . For this study

the electromechanical modes, which have a damping ratio of 0.1, are taken as

dominant modes.

To determine the gain and time constant of the damping controller

(Kstab,T1) the optimization problem is formulated as given below.

Statement of the problem:

Maximize : stab 1 stab 1f(K ,T ) = (K ,T ) (3.14)

subject to constraints : stab stab stabKmin K Kmax (3.15)

1 1 1Tmin T Tmax (3.16)

where is the damping ratio of the critical electromechanical mode.

3.4.1 Optimal Tuning of Power System Stabilizer

This section relates the damping ratio of the electromechanical

mode in terms of the control variables of the power system stabilizer namely

Kstab, T1.The action of the PSS is effective through the transfer function block

GEP(s) between the electric torque and the reference voltage input with

variations in the machine speed assumed zero. The expression for the transfer

function GEP(s) can be derived from the Phillips- Heffron Model shown in

Figure 3.2.

T K K Ke PSS 2 3 AGEP(s) = = 'V (1+ sK T )(1+ sTA) + K K Ks 3 3 6 Ado (3.17)

K1 – K6 are the Phillips-Heffron constants. Vs is the stabilizer output.

59

The PSS transfer function can be expressed from Figure 3.1 as follows

Vs = K G (s)G (s)wcstab(s) (3.18)

where Kstab – stabilizer gain; Gw(s) – Washout transfer function = sTw1+sTw

Gc(s) – Phase compensator transfer function =1+sT11+sT2

K 4 K 5

K 6

K 2

K 31 + s K 3 T ' d o

K A1 + s T A

1s1

M s + D

K 1

P S S

Figure 3.2 Phillips-Heffron Model of single machine infinite bus

system with PSS

Equation (3.18) can be written as

V / T ) T / (s) = K G (s)G (s)ws e e cPSS PSS stab (3.19)

Tm

Vs

Te P S S

60

The damping torque introduced by the PSS is given by,

T = De EPSS (3.20)

Te PSS = DE(s) (3.21)

from equation (3.19)

[1/GEP(s)]*[DE] = Kstab Gc(s) Gw(s) (3.22)

Assuming, Gw(s) =1 because Tw>>1, the damping induced by PSS is given by

D = K G (s)GEP(s)cE stab (3.23)

Substituting for DE from the characteristic equation of the system electro

mechanical loop

2(Ms + (D + D )s + K ) = 0E 1 (3.24)

Normalization of (3.24) yields

2 2(s + 2 s + ) = 0 (3.25)

Assuming system damping D=0, Comparing (3.24) with (3.25),

D = 2 ME (3.26)

For a critical oscillatory mode frequency corresponding to hs = j from

equation (3.17),(3.23) and (3.16)

61

2K (1+ T ) K K K1 2 3 Ahstab=2 2 ' 2 (2 M ) (1+ T ) (1+ K T )(1+ T ) + K K K )2 3 A 3 6 Ah i h h do h

(3.27)

where s=j h. The parameters Tw and T2 are fixed in the optimization program.

3.4.2 Optimal Tuning of FACTS Stabilizers

This section presents the mathematical background for tuning the

parameters of the FACTS stabilizers in a SMIB system.

The linearized state space model of the single machine infinite bus

system is given by

.x = A x + B u , y = C x (3.28)

where Ty = [ T y]e and u =[ U ]s

The output equation y = C x is written to relate the stabilizing

signal used for the damping controller input and the machine states. eT is the

change in generator electrical torque due to the FACTS stabilizer, y is the

stabilizing signal used for the FACTS stabilizer. sU is the output of damping

controller in the FACTS device.

The impact of FACTS stabilizers on the electromechanical

oscillation loop of the critical synchronous generator is obtained by using the

concept of induced torque coefficient. A perturbation in the input signal to

FACTS stabilizer induces on shaft of the critical generator, a component of

electrical torque Te . Ts is the change in electrical torque due the

synchronizing loop of the generator (Figure 3.3).

62

The induced torque is related to the speed perturbation of generator,

( ) by a complex induced torque coefficient hD , defined by

hT ( ) = D )e h h (3.29)

whereT ( )eh hD =

)h (3.30)

y (s)T (s) T (s) U (s)h e e s 1D (s) = =(s) U (s) y (s) (s)s 1

(3.31)

T (s)eG(s) =U (s)s

andU (s)sH(s) =y (s)1

(3.32)

where G(s) is the transfer function between reference input of FACTS

device and the electrical torque output of generator ( Te) in the forward path

(Figure 3.3)

1G(s) = C [sI - A] Bq* (3.33)

From Figure 3.3 Ts is the change in electric torque of the

generator following the inherent rotor angle change in the machine

(synchronizing torque loop)

H(s) is the transfer function of the FACTS based stabilizer between

the stabilizing signal and the FACTS device input. Cq* is the state output

vector corresponding to the real power generation of machine i.

63

If only the hth complex mode of rotor oscillation h is excited then

the relationship between the speed perturbation on any machine and any

system output is given by

Cy (s) q* *hl =(s) h

(3.34)

*h is the right eigenvector corresponding to the critical electromechanical

mode. h is the element corresponding to the speed state of machine

from *h .

hD = G(s) H(s) (C / )q* *h h (3.35)

Comparing equation (3.35) with the coefficient of the damping

term in the second order system equation 2 h(Ms + (D + D )s + K ) = 01 and

neglecting system damping

hD = 2 Mh (3.36)

Assuming, Gw(s) =1, because Tw>>1 the damping ratio of the

electro mechanical mode can be written in terms of the FACTS stabilizer gain

as given below.

2K (1+ T ) G(s) (C )( )s = j q*h 1 *hstab h=2 (1+ T ) (2 M)( )hh 2 h

(3.37)

64

Figure 3.3 Impact of FACTS stabilizer on the SMIB system

The damping ratio of the critical electromechanical mode is related

to the stabilizer gain as given in equation (3.37). The optimization algorithm

is employed iteratively until the objective function (3.15) is maximized. The

optimization starts with pre selected initial values of the controllers. The

parameters so determined are the optimal parameters of the damping

controllers used with PSS and FACTS controllers.

The flowchart describes the working of the optimization algorithm

is shown in Figure 3.4. The optimization problem is solved using sequential

quadratic programming. The algorithm attempts to find a constrained

minimum of a scalar function of several variables starting at an initial

estimate. This is generally referred to as constrained nonlinear optimization.

Te1

Tm

UsYl

Te

o/s

Ts

Dh

Cq* *h/ ih

65

P A R A M E T E RS E T

K s t a b , T 1

I N I T I A L G U E S S O F

P A R A M E T E R S ( K S T A B & T 1 )

P A R A M E T E RC O N S T R A I N E D

N O N L I N E A RO P T I M I Z A T I O N

S Q P

V A L I D A T EP A R A M E T E R

C O N S T R A I N T S

F I N A L P A R A M E T E RS E T K S T A B , T 1

E I G E N V A L U E A N A L Y S I SF O R N O M I N A L

O P E R A T I N G C O N D I T I O N

E N D

E V A L U A T EO B J E C T I V EF U N C T I O N :

D A M P I N G R A T I O

B E G I N

Figure 3.4 Flow chart for tuning the parameters of Damping Controllers

The optimized gain and time constants of the PSS and FACTS

based damping controllers are given in Table 3.1.The lower bound values for

gains are fixed as 40 and the higher limit is fixed as 90.

Table 3.1Optimized Damping Controller Parameters

S.No. Damping Controller used Kstab T1(seconds)1 PSS 49.89 0.154

2 SVC 48.61 0.145

3 STATCOM 47.42 0.132

4 TCSC 47.95 0.153

5 SSSC 47.28 0.139

6 UPFC 46.31 0.129

3.5 NUMERICAL EXAMPLE

The test system taken up for small signal stability enhancement

with FACTS /PSS controllers is shown in Figure 3.5 (Kundur 1994).

66

j0.15

Transformer

j0.54* 555 MVA

EB

INFINITEBUS

j0.93

LT HT

CCT2

CCT1

E tP,Q

Figure 3.5 Single Machine Infinite Bus System

The plant output in per unit on 2220 MVA, 24 KV base is P=0.9

p.u. and Q=0.3 p.u. Et=1.0 p.u. The real power flow in line CCT1 is 1555

MW and CCT2 is 836 MW.

Table 3.2 presents the results of the eigenvalue analysis of the

SMIB system without PSS in the excitation system and FACTS devices in the

network.

Table 3.2 Eigenvalue analysis of the SMIB system

S.No.

EigenvalueDamping ratio

)Frequency

(Hz)Nature of mode

1 0.4146 ± 6.8083i -0.060783 1.0841 Hz Swing mode, ( , )Local Mode ofoscillation

2 -2.2522 ± 6.1843i 0.3422 0.9848 Exciter mode (Efd, Eq’)

3 -1.0000 - Exciter Mode (Efd)

4 -20.0000 - (Ed’, Eq’)

5 -0.2000 - (Ed’)

Table 3.2 reveals that the damping ratio of the swing mode

associated with the rotor angle is negative with a damping ratio of -

67

0.060783.Hence when the system is subjected to small disturbances it will

lead to oscillatory instability in the system. The other complex modes are the

exciter mode with a frequency of 0.98 Hz. The exciter modes are stable with a

damping ratio of 0.3422.

3.5.1 Eigenvalue Analysis with PSS/shunt FACTS Device

It was illustrated in section 3.5 that the test system chosen is small

signal unstable with a damping ratio of -0.06, which will lead to, sustained

oscillations in rotor angles and speeds of the synchronous generators. To

arrest the low frequency oscillations normally power system stabilizers are

provided which give an additional input to the excitation system connected.

With PSS connected to the excitation system, the damping ratio increases to

0.1405.

The shunt FACTS devices are located at the HT bus as shown in

Figure 3.6.

HTLTINFINITE

BUS

EB

SHUNT FACTSDEVICE

CCT1

CCT2

X=0.5 p.u

X=0.93 p.u

j0.15 p.u.

P,QE t

4* 555 M VA

Figure 3.6 Single Machine Infinite Bus System with SVC/STATCOM

From Table 3.3 it can be observed that the damping ratio of the

swing mode with PSS is 0.1405 and with SVC is 0.1774.

68

Table 3.3 Eigenvalue analysis of the SMIB system with PSS / shuntFACTS device

Without DampingController

With PSS With SVC With STATCOM

0.4146 ± 6.8083i

=-0.060783f=1.0841 Hz

-1.0604 ± 7.4717i

=0.1405

-1.3571 ± 7.5297i

= 0.1774

-1.8471 ± 7.2934i

= 0.2455

The damping ratio of the SMIB system is 0.1774 with SVC and

0.2455 with STATCOM in the HT bus. This is because that STATCOM is a

voltage source converter based FACTS device, which has a faster transient

response than a SVC, which is a passive thyristor switched device.

3.5.2 Eigenvalue Analysis with Series Connected FACTS Devices

The TCSC is connected in line CCT2 near the HT bus to

compensate for 50% of the line reactance in the steady state. The power

injections of SSSC and UPFC are adjusted such that the initial steady state

power flow between the HT and infinite bus is maintained. (Figure 3.7) from

Table 3.4 it can be observed that the damping ratio of the oscillatory mode

has increased significantly with UPFC in the network in line CCT2.

j0.15

Transformer

4* 555 MVA

p.u.HT

X1=0.5p.u.LTINFINITE

BUS

X2=0.93 p.u.

CCT2

CCT1

SERIES FACTS DEVICE(TCSC,SSSC,UPFC)

Figure 3.7 Single Machine Infinite Bus System with Series Connected

FACTS device

69

This is due to the fact, that UPFC also has the capability to exercise

voltage control through its shunt branch, which also acts as a source of real

power for the series converter, whereas with a SSSC the real power exchange

is only due to the adjustment of the voltage phase angle of the series

converter.

Table 3.4 Eigenvalue analysis of the SMIB system with TCSC, SSSC and

UPFC

Without DampingController

With TCSC With SSSC With UPFC

0.4146 ± 6.8083i = -0.060783

f= 1.0841 Hz

-2.0706 ± 7.3141i

= 0.2724

-2.4405 ± 7.3377i

= 0.3156

-3.8821 ± 7.2930i

= 0.4699

Table 3.5 presents the results of eigenvalue analysis of the SMIB

system when the system load is increased by 20 % and decreased by 20%.

Operating condition 1 corresponds to the nominal operating state.

Operating condition 2 corresponds to a case when the system load is

increased by 20% and operating condition 3corresponds to a case when the

initial system load is reduced by 20%. It can be observed that without

damping controller the damping ratio of the SMIB system is negative when

the generator exports 2391 MW to the lines CCT1 and CCT2. The damping

ratio is negative at both operating conditions 1 and 2. The damping ratio of

system is 0.01 (1%) under lightly loaded operating condition. With power

system stabilizer the system damping improves to 0.13 (13%) for the heavily

loaded operating condition 1 and 0.14 (14%) with lightly loaded operating

condition 2.

70

With SVC, the damping ratio improves to 0.17 for the heavily

loaded operating condition and 0.18 for the lightly loaded operating condition.

However, with STATCOM the damping ratio increases to 0.2455 and 0.2130

for the two different operating conditions. This is due to the superior dynamic

response of STATCOM compared to that of passive SVC.

With TCSC, the system damping improves to 0.2724 under lightly

loaded and 0.2420 for heavily loaded operating condition. With SSSC, the

damping ratio improves to 0.3125 under heavily loaded condition and 0.3166

for the lightly loaded condition. With UPFC, the damping ratio increases

significantly to 0.4574 for the heavily loaded operating condition 2. If

damping ratio of the swing mode becomes weak after load change then design

the controller parameters for the weakest mode in this operating condition.

Table 3.5 Electromechanical Modes of the SMIB system under three

different operating conditions

OperatingCondition 1

(Nominal OperatingCondition)

OperatingCondition 2

(Heavily Loaded)

OperatingCondition 3

(Lightly Loaded)

WithoutDamping Controller

0.4146 ± 6.8083i = -0.060783

0.89486 ± 6.6517i= -0.13333

-0.1319 ± 7.0218i=0.0188

With PSS -1.0604 ± 7.4717i =0.1405

-0.9289 ± 7.0864i= 0.1300

-1.1063 ± 7.4302i=0.1473

With SVC -1.3571 ± 7.5297i = 0.1774

-1.2457 ± 7.2146i=0.1702

-1.4071 ± 7.5336i= 0.1836

With STATCOM -1.8471 ± 7.2934i=0.2455

-1.6520 ± 7.5788i = 0.2130

-1.9894 ± 7.6260i= 0.2524

With TCSC -2.0706 ± 7.3141i=0.2724

-1.9166 ± 7.6830i =0.2420

-2.2057 ± 7.6511i= 0.2770

With SSSC -2.4405 ± 7.3377i=0.3156

-2.5243 ± 7.6722i =0.3125

-2.5637 ± 7.6813i= 0.3166

With UPFC -3.8821 ± 7.2930i=0.4699

-3.9332 ± 7.6467i =0.4574

-3.9613 ± 7.6570i= 0.4595

71

3.6 DYNAMIC SIMULATION OF THE SMIB SYSTEM FOR A

SOLID THREE-PHASE FAULT

To check the robustness of the FACTS based stabilizers following a

major disturbance a three-phase fault is simulated in line CCT 2 near the HT

bus at 1 sec, which is subsequently cleared by tripping the line in 1.1 seconds.

It can be observed that the rotor angle oscillations settle down with PSS in the

excitation system after 4 seconds (Figure 3.8).

Figure 3.8 Rotor angle Response of the SMIB system – Effect of Power

System Stabilizer

The oscillations decay to the initial prefault value after 6 seconds

with PSS. With STATCOM the oscillations are damped out in 3 seconds. The

settling time with SVC is 3 seconds and with STATCOM the settling time is 2

seconds (Figure 3.9)

72

Figure 3.9 Rotor angle responses of the SMIB system – Effect of shunt

FACTS device

From Figure3.10 it can be concluded that after the three-phase fault

the peak overshoot is higher with TCSC in the network and the settling time is

5 seconds. With SSSC/UPFC, the settling time is 2 seconds and 1 second

respectively.

73

Figure 3.10 Rotor angle response of the SMIB system - Effect of series

FACTS device

3.7 CONCLUSION

In this chapter, eigenvalue analysis is performed on a single

machine infinite bus system without and with PSS / FACTS based damping

controllers for different operating conditions.

A single machine infinite bus (SMIB) system was chosen for

carrying out detailed investigations on different FACTS based stabilizers. A

generalized small signal stability model based on current injections of FACTS

devices is developed for the SMIB system. This section has developed the

optimization model required to tune the parameters of the damping controller

74

of FACTS devices to enhance the damping ratio of the critical

electromechanical mode. The robustness of the designed damping controllers

are confirmed by conducting eigenvalue analysis with increased system

loading by 20%.From the results it is observed that among shunt connected

devices, STATCOM is effective in enhancing the small signal stability

compared to SVC. Among series devices SSSC is effective in enhancing the

damping ratio of the critical mode. It is observed that the system is stable with

UPFC in the network with a damping ratio of 0.4.

For any specific operating condition (not discussed) if the damping

ratio of the swing modes are not stable then the tuning process can be carried

out for the most critical mode in that operating condition for example a line

outage.

Transient stability simulations are carried out to confirm the

robustness of stabilizer design following a large disturbance. It is observed

that STATCOM, SSSC and UPFC are effective in damping out

electromechanical oscillations following the three-phase fault.