2009_IJEEE_88

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Transmission line shunt and seriescompensation with voltage sensitive loads

Ulas Eminoglu3, M. Hakan Hocaoglu1and Tankut Yalcinoz3

1Department of Electronics Engineering, Gebze Institute of Technology, Kocaeli, Turkey2Department of Electrical and Electronics Engineering, Nigde University, Nigde, Turkey3Department of Electrical and Electronics Engineering, Meliksah University, Talas, Kayseri,

Turkey

E-mail: [email protected]

Abstract This paper presents an analysis of the effects of shunt and series line compensation

levels on the transmission line voltage profile, transferred power and transmission losses for different

static load models. For this purpose, a simple model is developed to calculate the series and/or shunt

compensated transmission line load voltage. Consequently, different shunt and series compensation

levels are used with several voltage sensitive load models for two different line models. It is observed

that the compensation level is significantly affected by the voltage sensitivities of loads. Moreover,

the voltage level of the transmission is an important issue for the selection of the shunt and series

capacitor sizes when load voltage dependency is used.

Keywords selection of capacitor sizes; shunt and series compensations; transmission systems;

voltage sensitive loads

In electrical power systems, shunt capacitive compensation is widely employed

to reduce the active and reactive power losses and to ensure satisfactory voltag

levels during excessive reactive loading conditions. Shunt capacitive compensation

devices are normally distributed throughout transmission or distribution system

so as to minimise losses and voltage drops. There are two types of shunt compensa

tion: active and passive. For passive compensation, shunt capacitors have beenextensively used since the 1930s. They are either permanently connected to the

system, or switched, and they contribute to voltage control by modifying character

istics of the network.1 Improvements in the field of power electronics have had

major impact on the development of shunt active compensators, which are Static

Var Compensator (SVC) and Static Compensator (Statcom) devices. One of th

most important applications of such devices is to keep system voltage profiles a

desirable levels by compensating for the system reactive power. By employing thes

devices for reactive power compensation, both the stress on the heavily loaded lineand losses are easily reduced as a consequence of line loadability, which i

2

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Shunt and series line compensation 35

In electrical power systems, load modelling is a difficult problem due to the fac

that the electrical loads of a system comprise residential, commercial, industrial and

municipal loads. It should also be noted that variation of the loads over time and

number of uncertainties, spanning from economic parameters to the weather condi-

tions, significantly increase the complexity of the load modelling process. On theother hand, aggregate load models, which represent the load as an algebraic equation

have extensively been used for various power system studies to understand and

analyse system behaviour under various conditions. Traditionally, most of the con

ventional load flow methods, for transmission and distribution systems, use the

constant-power load model. The constant-power load model is highly questionable

especially for a distribution system where most of the buses are uncontrolled. For

transmission systems, where loads are generally served through transformers

equipped with OLTCs (on-load tap changers), it is reasonable to use a constan

power model for the analyses. However, economic and environmental force con-

strains the system operators to exploit existing power structure to the limits. This

can cause voltage stability problems and increases the risk of voltage collapse.5I

is widely recognized that, for weak power systems, the dynamic behavior of OLTC

contributes to the voltage collapse. Accordingly, OLTC blocking becomes a usua

practice among the operators of weak systems.6Therefore, like distribution systems

the constant power load model becomes questionable for particularly weak transmis

sion systems. Accordingly a number of studies, found in the literature, deal with the

effects of static load models on various power systems phenomena.715

In Ref. 7, the authors analysed the effect of static loads modelled as an exponentia

form on the optimal load flow solution. The load flow solutions are compared with

the standard optimal load flow solutions. The authors showed that the differences in

fuel cost, total power loss and voltage values are significant. Moreover, they con

cluded that the required iteration numbers are higher when the system is heavily

loaded. For distribution systems with constant-power, constant-current and constanimpedance loads, a new load flow algorithm has been proposed and the effects of

these load models on the convergence pattern of the load flow method have been

studied by Haque in Ref. 8. Results of the load flow show that the constant powe

load model gives the lowest voltage profile while the constant impedance load mode

provides the highest voltage profile. It is seen from the results that the convergence

of the load flow solutions gets difficult when load exponents increase. The effect

of voltage-dependent load on the convergence ability of the load flow method for

different characteristics of the distribution system are also analysed in Ref. 9. In thisstudy, the convergence ability of the proposed power flow algorithm has been com

10

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356 U. Eminoglu, M. H. Hocaoglu and T. Yalcino

equations is established for radial systems by considering power balance and injected

power in terms of system parameters; consequently these equations are solved fo

three types of loads: constant power, constant current and constant impedance load

In this study, the effects of shunt capacitor levels on load voltage magnitude are

analysed for voltage levels lower than 1 p.u. It is demonstrated that the effect oshunt capacitor sizes on the voltage magnitude increases with decrease of voltage

sensitivity of the static load. El-Metwally13has developed a method for assessing

the loadability limit of high voltage compensated transmission lines taking into

account the effect of load characteristics. The effect of voltage and/or frequency

dependent load on the maximum power transfer limit and critical voltage of the

series and shunt compensated lines are investigated. Results show that the critica

voltage and maximum power transfer limit of the less voltage-sensitive loads are

greater than the more sensitive load. Ramalingam and Indulkar14have presented th

effects of load characteristics on the load voltage and current magnitudes, load phas

angle, active and reactive power losses of transmission lines for different static load

types. Results show that when load voltage sensitivity increases, the transferred

power and the transmission line power loss decrease. The same authors15have also

analysed the effects of tap-changing transformer control on the power voltage char

acteristics of compensated EHV transmission lines for different static load types. I

should be noted that authors have only studied under 1 p.u. line voltage level. The

effect of high voltage level is not studied in all references cited above.

This paper presents the effects of shunt and series compensation levels on the

transmission system voltage profile, transferred power, and line losses for differen

static load models. For this purpose a simple model is developed to calculate serie

and/or shunt compensated transmission line load voltage. The developed theory

takes into account voltage dependency of static loads, transmission line parameters

and series and/or shunt compensator reactance. Two different line models (nomina

circuit model and distributed line model) are used for analysing the effects of different static load models on transmission system performance. Effect of voltag

sensitivity of loads on the selection of shunt capacitor sizes for different voltage

levels is also analysed giving particular emphasis to the voltage level higher than

1 p.u.

Static load models

In electric power system analysis, loads may be modelled as a function of voltag

and/or frequency and this type of modelling is considered static. Common static load

models for active and reactive powers are expressed in a polynomial or an exponen

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Where Poand Qoare the active and reactive load powers, respectively, at the nomina

voltage of Voand Vis the actual voltage magnitude in p.u. The parameters np and

nqstand for the voltage sensitivities of the static load.

The polynomial load model is a static load model that represents the power-

voltage relationship as a polynomial equation of voltage magnitude. It is usuallyreferred to as the ZIP model and consists of a combination of three different expo

nential load models, namely constant impedance (Z), constant current (I) and con

stant power (P). The active and reactive power characteristics of the ZIP load model

are given by:

P P a aV

Va

V

Vo o

o o

= + +

1 22

(3

Q Q b bV

Vb

V

Vo o

o o

= + +

1 2

2

(4

Where

aoand boare the parameters for constant power load component;

a1and b1are the parameters for constant current load component;

a2and b2are the parameters for constant impedance load component.

The values of these coefficients are determined for different load types in transmis-

sion and distribution systems. Usually data, determined from experience, could be

used for the estimation. Common values for the exponents of static load model for

different load components are widely analysed in the literature. These static loads

may have high voltage dependency such as battery charge or televisions.16 The

aggregate load model may attain high values of exponents in the system nodes where

the proportion of such devices is significant. These exponents may be valid for onlya limited voltage range, which are 10% of the 1 p.u. voltage level. At very highand low voltage magnitude levels the models are inadequate for some load types

such as motors and lighting.1617

Transmission line compensation

Transmitted real and reactive power of the transmission line, which is shown in

Figs 1(a) and (b), can be derived in terms of the ABCD parameters of line using the

following notation:

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Fig. 1 The circuit models of a transmission line. (a) Nominal TT-circuit model;

(b) distributed parameters model.

B and A, and s and r for the voltage of bus s and bus r. The value of A and B

changes according to the line model. Equations (5) and (6) can be rewritten as:

cos cos B s rs r

r

s

B A

P B

V V

A V

V +( )= + ( ) (7

sin sin B s rs r

r

s

B AQ BV V

A VV +

( )= + ( ) (8

by using the trigonometric identity

cos sin2 2 1 B s r B s r +( ) + +( )= (9

and substituting eqns (1)(2) and (7)(8) into eqn (9), the polynomial equation o

the load voltage for the exponential load model is obtained as follows:

A V A V B P V Q V V V

P

r r o r np B A o rnq B A s r

o

2 4 2 2 2

2

2+ ( ) + ( )( ) +

cos sin

VV Q V Brnp

o rnq2 2 2 2 0+( ) =

(10

Equation (10) has a straightforward solution and depends on the voltage dependency

terms of exponential static load model and line parameters. It is noted that from th

solutions for Vrthat only the highest positive real root of this equation is used in the

analyses. When polynomial load model is used, the voltage equation can be obtained

by using eqns (3) and (4) instead of eqns (1) and (2), and then the function of the

load voltage can be written as:

A V A V B P V V2 4 2 22 ( ) ( )(

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used for power factor correction and to improve the system voltage profile by eco

nomical means. The principal advantages of shunt capacitors could be listed as their

low cost, flexibility on installation and practical operations. To show the effect o

shunt compensation on the system voltage profile, a simple two-bus system given

in Fig. 1 is used and a shunt capacitor is added.. The effect of shunt compensationcan be introduced using Thevenins theorem by keeping the load phase angle at a

constant value. For this case, the Thevenin equivalent voltage (Vth) and impedance

(Zth) seen from the end of the line (point of r) can be written for each line model

given in Fig. 1, by neglecting the active losses of the shunt capacitor.

When the nominal circuit model of a transmission line, given in Fig. 1(a), is

used the VthandZthseen from the end of the line (point of r) can be written as:

V ZZ r jX

VthS

S

S= + +( ) (12

ZZ r jX

Z r jXth

S

S

= +( )+ +

(13

Z jX X

X XS

C Sh

C Sh

= +

(14

XY

Sh

Sh

=2

(15

When the distributed model of a transmission line, given in Fig. 1(b), is used, the

cascaded system parameters and Vthseen from the end of the line (point of r) with

the shunt compensation (jXc) can be written as:

V

I

A jB X B jAX

C jD X D jCX

V

I

s

s

C C

C C

r

r

=

+

+

(16a

when there is no current on the receiving end, the solution of the receiving end

voltage of eqn (16a) gives the Thevenin equivalent voltage as:

VA jB X

VthC

S= +1

(16b

and, similarlyZthseen from the end of the line (point of r) can be written by using

the ratio of open circuit voltage and short circuit current as:

jBX

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Xcis the shunt capacitor reactance;

AandBare parameters of the transmission line.

The Thevenin equivalent voltage (Vth) and equivalent impedance (Zth) increase with

the shunt compensation levels by causing an increase on the load voltage magnitudeThe effect of shunt capacitor on the load voltage can be analysed by substituting VtandZthinto eqns (10) and (11) instead of VsandB. When the Thevenin equivalen

circuit is used, load voltage varies with shunt capacitor reactance, line parameter

and load nominal power. In this case, theAparameters of each transmission line ar

chosen asA=1 in eqns (10) and (11).

Series compensation

Series capacitive compensation in a.c. transmission systems can yield several benefits such as increases in power transfer capability and enhancement in transient sta

bility. For the series compensation, series capacitors are connected in series with th

line conductors to compensate the inductive reactance of the line. This reduces th

transfer reactance between buses to which the line is connected, increases maximum

power that can be transmitted, and reduces effective reactive power loss. Although

series capacitors are not usually installed for voltage control, they do contribute to

improving the voltage profile of the line.

When the nominal circuit model of a transmission line, which is given in Fig1(a), is used, the effect of series compensation on the transmission line voltage

profile, transferred power and line losses can be analysed by using eqn (18) in the

calculation of the parameters ofAandBgiven in eqn (10) for exponential load mode

and in eqn (11) for polynomial load model.

z r j x xS= + ( ) (18

Wherexis the line series reactance,xSis the series capacitor reactance, and ris th

line series resistance. In addition, the effect of series compensation on the transmission line voltage profile can be analysed by using the ABCD parameters of the serie

capacitor reactance when a distributed parameters line model is used. In this case

the equivalent ABCD parameters of the compensated line can be calculated by using

matrix multiplication of cascaded line and series capacitor parameters.

Analysis of shunt and series compensations

A two-bus power system is used and analysed for different static load models with

different shunt and series capacitor sizes. The two-bus system parameters are selectedas Vs =1.1 p.u., Po =7.0 p.u. and Qo = 1.0 p.u. with the base of 100 MVA and

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eqn (10). Variations of the load voltage magnitude with different compensation

levels are given in Fig. 2 for two line models and in Fig. 3 for the nominal mode

of a transmission line.

From Figs 2 and 3, it is seen that shunt compensation has approximately the same

effect on the load magnitude for high values of exponents of static load models. Onthe other hand, the effect of shunt compensation on the voltage profile for low value

of the exponents is more significant than the high values of the exponents. From

these figures it is seen that load voltage magnitude varies with the load model, with

the increase in shunt capacitor size being highest for the system when load voltage

dependency decreases. It should be noted that for a load voltage magnitude at 1 p

u., the load exponents have no effect on the shunt compensation level, as can be

seen from eqn (10). Moreover, the nominal circuit model has a lower voltage leve

than the distributed parameters line model for each load model and the slopes change

with the load model with different shunt capacitor size being the same for each line

model.

Required reactive powers to keep the load voltage at predetermined levels are

presented in Fig. 4 for two line models and Fig. 5 for a nominal circuit line model

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As depicted in figures, load models have a significant effect over the required com

pensation power. If load exponents decrease, the required reactive power increase

when the voltage level is lower than 1 p.u. On the other hand, if load exponentdecrease, the required reactive powers decrease when the voltage level is higher than

1 p.u. From Fig. 4 it is seen that to keep the load voltage at 0.96 p.u. for the nomina

and distributed parameters line models, 33.41 and 31.57 MVAr capacitors would

be needed in the case of a constant power load, whereas 2.67 and 2.61 MVAr capaci

tors are required if the load is modelled as a constant impedance load respectively

and for each line model the magnitude of required reactive powers decrease when

load exponents increase. On the other hand, to keep the load voltage at 1.04 p.u

127.28 and 125.59 MVAr capacitors are required if the load is modelled as a constanpower load, whereas 162.38 and 160.5 MVAr capacitors are required if the load i

Fig. 3 Variation of the load voltage magnitude (p.u.).

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Results show that transferred active power and reactive power increase withincrease of compensation level for each load type due to increase in load voltage

magnitude. It is clearly seen that for the load which has low voltage sensitivities

the transferred active and reactive power attain higher values than the load with

high voltage sensitivities, for each compensation level when the voltage magni-

tude is lower than 1 p.u., which concurs with the previous findings. On the othe

hand, transferred powers have higher values for more sensitive loads whenvoltage magnitude is higher than 1 p.u.

Fig. 4 Variation of required reactive power for different load voltage levels (MVAr).

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Analysis of series compensation

The effect of series line compensations on voltage profile, transferred power, and

power losses of transmission systems for exponential static load models is analysed

for the same system for two transmission line models by locating the series capacito

in the middle of the line. Transmission line series reactance is compensated a

10%60% ratios to show the effects of load characteristics on the load voltage profil

with different series compensation levels. Results are given in Fig. 7 for two line

models and in Fig. 8 for only the nominal line model.As illustrated in Figs 7 and 8, the effect of series compensation on voltage profil

Fig. 5 Variation of required reactive power (MVAr).

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Fig. 6 Variation of transmission line losses (p.u.).

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compensation levels. It is seen that the nominal circuit model overestimates th

voltage when line reactance is compensated less than 50% for given parameters setOn the other hand, the model underestimates the voltage magnitude when line reac

tance is compensated more than 50%. Overestimation attains a maximum 1.8% o

1 p.u. and gradually decreases when the compensation level increases. Moreover

the line model affects only the voltage magnitude of the load and the slopes chang

with the load model, with different series capacitor size being the same for each lin

model.

For different series compensation levels, variations of transferred active and reac

tive powers, and transmission losses with different voltage sensitivities of loadmodels are analysed and transmission losses are given in Fig. 9 in the case of using

Fig. 8 Variation of the load voltage magnitude (p.u.).

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significant effect on the transmission line performance and a selection of series

compensation levels.

Conclusions

This paper presents an analysis of the effects of shunt and series compensation level

on the transmission system voltage profile, transferred power, and line losses for

different static load models. The voltage expressions, which are derived for differen

load models, depend on load nominal active and reactive power, voltage sensitivities

of load and line parameters. Then, different shunt and series compensation levelswere used for shunt and series compensation with several voltage sensitive load

Fig. 9 Variation of transmission line losses (p.u.).

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levels decrease with increasing voltage sensitivity of the loads below a voltage

magnitude of 1 p.u. On the other hand, required shunt compensation levels increas

with voltage sensitivity of loads above the voltage magnitude of 1 p.u. for th

1 p.u. voltage magnitude, voltage sensitivities of loads are not important and al

loads require the same amount of shunt capacitor size. The voltage dependency oloads is the primary factor in the determination of series and shunt capacitor sizes

Therefore the nature of the served load in terms of dependence on the voltage should

be known and taken into account. The nominal circuit model has a lower voltage

level than the distributed parameters line model for each load model in the case o

shunt compensation. It is seen that the nominal circuit model overestimates th

voltage magnitude when line reactance is compensated at low levels (less than

1 p.u.). On the other hand the model underestimates the voltage magnitude when

line reactance is compensated at high level. These differences of voltage magnitude

decrease with increasing line series compensation levels and the line voltage reache

a higher value than the voltage magnitude of the nominal line model when lin

series reactance is compensated at a high ratio. Slopes change with the load model

with different shunt and series capacitor sizes being nearly the same for each lin

model.

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