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CHAPTER 3

STATIC VAR COMPENSATOR FOR VOLTAGE

SECURITY ENHANCEMENT

3.1 INTRODUCTION

In the previous chapter, generation rescheduling was considered for

voltage stability enhancement. This chapter explores the application of static

VAr compensator (SVC) for voltage security enhancement. SVC provides fast

acting dynamic reactive compensation for voltage support during contingency

events which would otherwise decrease the voltage for a significant length of

time. Identification of suitable location is very much essential to get the

benefit of the SVC. In this work, the L-index of the load buses, explained in

the previous chapter is used to identify the weak buses and hence the location

of SVC. To identify the optimal setting of the control variables, the problem

is formulated as a multi-objective optimization problem, with minimization of

the voltage stability margin and the minimization of investment cost of the

VAr sources as the objectives. MOGA is applied to solve this complex multi-

objective optimization problem.

3.2 STRUCTURE AND MODELING OF STATIC VAR

COMPENSATOR (SVC)

SVC is a shunt connected static var generator or consumer whose

output is adjusted to exchange capacitive or inductive so as to maintain or

control specific parameters of electrical power system, typically, a bus

voltage. The main function is to regulate the voltage at a given bus by

controlling its equivalent reactance. SVC is built of reactors and capacitors,

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Controlcircuit

Inputsignals

TCR

FC

Line voltage

BSVC

controlled by thyristor controlled reactors (TCR) which are parallel with

capacitor bank. Basically it consist of a fixed capacitor (FC) and a TCR. As

shown in Figure 3.1 it is connected in shunt with the transmission line through

a transformer. The model considers SVC as shunt variable susceptance, BSVC

which is adapted automatically to achieve the voltage control. The TCR

consists of a fixed reactor of inductor L and a bi-directional thyristor valve.

The thyristor valves are fired symmetrically in an angle of a control range of

90o to 180o, with respect to the SVC voltage. This type of SVC can be

considered as a controllable reactive admittance which, when connected to the

ac system, faithfully follows (within a given frequency band and within the

specified capacitive and inductive ratings) an arbitrary input (reactive

admittance or current) reference signal. Figure 3.2 shows the V-I

characteristics of the SVC. The V-I characteristic represents the steady state

relationship. A typical V-I characteristic determines the range of inductive

and capacitive current supplied by the SVC. The V-I characteristic of the

SVC indicates that regulation with a given slope around the nominal voltage

can be achieved in the normal operating range defined by the maximum

capacitive and inductive currents of the SVC.

Figure 3.1 SVC employing FC - TCR

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LL max

InductiveLC max

Capacitive0

II

Vmax

I

VT

Figure 3.2 V-I Characteristics of the SVC

In the active control range, current/susceptance and reactive power

is varied to regulate voltage according to a slope (droop) characteristic. The

slope value depends on the desired sharing of reactive power production

between various sources, and other needs of the system. The slope is typically

1-5 percent. At the capacitive limit, the SVC becomes a shunt capacitor. At

the inductive limit, the SVC becomes a shunt reactor (the current or reactive

power may also be limited).

The TCR at a fundamental frequency can be considered to act like a

variable inductance XTCR is given as:

2sin)(2TCRX (3.1)

where XTCR is the reactance caused by the fundamental frequency without

thyristor control and is the firing angle. Hence, the total equivalent

impedance of the controller can be written as

LC

LCSVC

XX

XXX

]2sin)(2[

(3.2)

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By controlling the firing angle of of the thyristors (the angle with

respect to zero crossing of the phase voltage), the device is able to control the

bus voltage magnitude current. The amount of reactive power consumed by

the inductor L for =90o, the inductor is fully on, whereas for =180o the

inductor is off. The basic control strategy is typically to keep the transmission

bus voltage within certain narrow limits defined by a controller droop and the

firing angle limits (90o< < 180o). Figure 3.3 represents the equivalent

steady state model of the SVC.

Figure 3.3 Equivalent Steady State Model of the SVC

SVC model is developed with respect to a sinusoidal voltage, and

can be written as

KSVCSVC VjBI (3.3)

Where the variable susceptance BSVC represents the fundamental

frequency equivalent susceptance of all shunt modules making up the SVC as

shown in Figure 3.3 .

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Static var compensators are used by utilities in both transmission

and distribution systems. The main function of SVC is to control the voltage

at weak nodes in the system. Installation of SVC in load buses used for load

compensation help in containing the voltage fluctuations, improve load power

factor and also voltage profile. Installation of SVC in transmission networks

helps to provide dynamic reactive power injection support to maintain the bus

voltage close to the nominal value under varying load conditions and also

improve voltage stability. SVC also provides fast response to control the bus

voltage under disturbed conditions.

3.3 PLACEMENT OF SVC

To improve the voltage stability level of the system, SVC has to be

placed at the proper locations. To determine the best location, L-index is

calculated as explained in the previous chapter. The bus with maximum L-

index value is the most vulnerable bus in the given system and there the

compensator devices have to be placed. Weak buses are identified based on

the L-index values of the load buses. The buses with high values of Lmax are

the weak buses of the system from the voltage stability point of view. The L-

indices are calculated for the system by running the power flow analysis.

Computing L-index value for load buses (including the generator buses

treated as PQ bus), it is found that the L-index values are higher at each bus

by repeating the power flow with only one generator bus and other generator

buses as PQ buses. Hence it is concluded that the number of buses makes a

significant change in the L-indices results. If we take SVC bus as generator

bus and compute the L-indices, we get L-index values reduced significantly

compared to the SVC bus treated as load bus. With same compensation as

obtained for maintaining the same voltage as in previous output, obtain the L-

indices. These L-indices are higher at each bus compared to previous case

when SVC bus was assumed as PV bus. This gives indication that while

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computing L-indices, it is reasonable to treat SVC bus as load bus than

generator bus.

3.4 PROBLEM FORMULATION

With the increasing size of power system, there is a thrust on

finding the solution to maximize the utilization of existing system and to

provide adequate voltage support. VAr devices if placed optimally can be

effective in providing voltage support, controlling power flow and in turn

resulting into lower losses. The problem of voltage security enhancement is

formulated as a multi-objective optimization problem. The objectives

considered here are minimization of VAr cost and maximization of voltage

stability margin. This is achieved by proper adjustment of real power

generation, generator voltage magnitude, SVC reactive power generation of

capacitor bank and transformer tap setting. Power flow equations are the

equality constraints of the problems, while the inequality constraints include

the limits on real and reactive power generation, bus voltage magnitudes,

transformer tap positions and line flows. The expression representing the

objective functions and the constraints are given below:

3.4.1 Objective functions

The voltage security problem is to optimize the steady state

performance of a power system in terms of one or more objective functions

while satisfying several equality and inequality constraints. The objective

functions considered in this work are given below:

3.4.1.1 Minimization of SVC devices cost

Investment costs of SVC devices are broken into two components:

fixed and variable cost. The fixed cost is comprised of the physical

installation and additional equipment costs (such as switchgear and breakers).

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The variable component is the procurement cost which depends on the

amount of nominal reactive power installed at a system bus. Mathematically,

this is stated as,

hrQCCFMinimizeCN

i

cicifiC /$)||(

1

(3.4)

where

Cfi is the fixed installation cost of the reactive power sources at the

ith bus($)

Cci is the cost of the SVC compensation devices at the ith bus

($/MVAr)

Qci is the reactive compensation at the ith bus (MVAr)

Nc is the number of possible buses for the installation of the

compensation devices.

3.4.1.2 Voltage stability margin

Minimize L max (3.5)

This is presented in the previous chapter in section 2.2. Using

equation (2.3) L-index values are calculated for all the load buses. The

maximum of the L- indices give the proximity of the system to voltage

collapse.

3.4.2 Problem constraints

The minimization problem is subject to the equality constraints of

the equations (2.6, 2.7) and the inequality constraints of the equations (2.8,

2.9) and (2.10, 2.11) of the previous chapter in section 2.3.2 and in section

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2.3.3. In addition the SVC reactive power generation constraint is represented

as follows:

SVC reactive power generation limit

csvcsvcsvc NiQQQ ;maxmin

(3.6)

Aggregating the objectives and constraints, the problem can be

mathematically formulated as a non- linear constrained multi-objective

problem as follows:

],[ maxLFFMinimize CT (3.7)

subject to the above constraints.

Multi-objective Genetic Algorithm explained in the previous

chapter is applied to solve the multi-objective security enhancement problem.

3.5 SIMULATION RESULTS

To demonstrate the effectiveness of the proposed approach IEEE

30-bus system is considered.

Case (i): Voltage security constrained OPF (VSCOPF) using GA

Contingency analysis was conducted on the system by simulating

single line outages to identify the critical contingencies. From the contingency

analysis, it is found that the line outage 1-2 is the most severe one from the

voltage security point of view and the system reached a maximum Lmax

value of 0.2910 during this contingency state. The Lmax value of contingency

1-2 is included in the objective function of the OPF problem along with the

base case fuel cost and the GA- based algorithm was applied to solve this

voltage security constraint optimal power flow problem. Figure 3.4 shows the

convergence diagram. The optimal control variable setting obtained in this

case is tabulated in Table 3.1 along with the Lmax value.

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Figure 3.4 Convergence curves of the VSCOPF

Table 3.1 Result of VSCOPF Algorithm (IEEE 30-bus system)

Control variables Variable setting

P1 68.9229 MW

P2 77.1429 MW

P5 41.6667 MW

P8 35.0000 MW

P11 29.0476 MW

P13 36.8889 MW

V1 1.0500 P.U

V2 1.0310 P.U

V5 1.0262 P.U

V8 1.0167 P.U

V11 1.1 P.U

V13 1.0238 P.U

T11 0.9

T12 0.9571

T15 1.1

T36 0.9857

QC10 4.2857 MVAr

QC12 5.0 MVAr

QC15 1.4286 MVAr

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Table 3.1 (Continued)

QC17 2.8571 MVAr

QC20 5.0 MVAr

QC21 5.0 MVAr

QC23 5.0 MVAr

QC24 5.0 MVAr

QC29 2.8571 MVAr

Cost 822.2797 $/hr

Lmax 0.1034

To assess the voltage security of the system, contingency analysis

was conducted using the variable setting obtained in the base case and voltage

stability constraint OPF. The maximum Lmax values corresponding to the four

critical contingencies are given in Table 3.2. From the result it is observed

that the Lmax index value has reduced appreciably for all contingencies in the

voltage stability constraint OPF. This shows that the proposed algorithm has

helped to improve the voltage security of the system.

Table 3.2 Lmax

under contingency state

No Contingency Lmax

(base case) Lmax

(VSCOPF)

1 1-2 0.2910 0.1311

2 9-10 0.2176 0.1672

3 4-12 0.2152 0.1712

4 4-6 0.1932 0.1506

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Case (ii) Multi-objective optimal power flow for voltage security

enhancement

Contingency analysis

Next, the proposed MOGA approach was applied for solving the

voltage security enhancement to IEEE 30-bus test system. L-index method is

adopted here to identify the weak buses. The buses having high values of Lmax

are the weak buses, which require reactive power support. For each

contingency, L-index values are computed. According to the values, the most

severe contingencies were the outages of lines (1-2), (4-12), (9-10), (6-7) and

(28-27). L-indices are evaluated for the above severe contingencies and the

first five buses with high values of L-index are identified for reactive power

compensation. They are tabulated in Table 3.3. Finally, the common buses

among the identified weak buses are selected for placing the SVC. From the

weak bus identified, the candidate locations for placement of SVC are buses

30, 29,25,12,19. The main purpose of identifying the weak buses is to

maintain control of voltages at these buses in particular to prevent voltage

collapse. Here identifying weak buses can also give correct information to

determine which buses are most severe and need to have new reactive power

sources installed. The algorithm was run with minimization of SVC

investment cost and Lmax value as the objectives. The initial population was

randomly generated between the variable’s lower and upper limits. Fitness

proportionate selection was applied to select the members of the new

population. Blend crossover and non uniform mutation were applied on the

selected individuals. The performance of MOGA for various crossover and

mutation probabilities in the range 0.6-0.9 and 0.001-0.01 respectively was

therefore evaluated. It was applied by considering several sets of parameters

in order to prove its capability to provide acceptable trade-offs close to the

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Pareto optimal front The optimal settings of the MOGA were obtained by the

following parameters are given below:

Generations : 50

Population size : 50

Crossover rate : 0.85

Mutation rate : 0.01

Figure 3.5 represents the Pareto-optimal front curve. It is worth

mentioning that the proposed approach produces nearly 21 Pareto optimal

solutions in a single run that have satisfactory diversity characteristics and span

over the entire Pareto optimal front. From the Pareto front, two optimal solutions

which are the extreme points to represent the minimum SVC investment cost and

maximum voltage stability margin are noted. The optimal values of the control

variable are given in Table: 3.4. This shows the effectiveness of the proposed

approach in solving the optimal power flow problem.

Table 3.3 Identification of weak buses

Line outage Weak buses

1-2 3,30,29,12,25,27

4-12 12,14,19,29,30

9-10 25,30,27,26,24

6-7 12,19,30,9,29

28-27 30,29,25,24,21

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Figure 3.5 Pareto Optimal Front

Table 3.4 Control variables for IEEE 30- bus system Extreme Solutions

Control variables Minimum installation

cost solution

Maximum voltage stability

margin solution

P1 (MW) 29.9654 53.5209P2 (MW) 95.7833 88.1262P5 (MW) 48.9274 49.4162P8 (MW) 33.9137 34.9039P11 (MW) 24.2062 24.3695P13 (MW) 54.5317 41.8188V1 (P.U) 1.0479 1.0704V2 (P.U) 1.0749 1.0295V5 (P.U) 1.0852 1.0188V8 (P.U) 1.0665 0.9898V11 (P.U) 1.0931 1.0776V13 (P.U) 1.0959 1.0705T11 1.0750 1.0968T12 0.9750 0.9T15 1.0750 0.9750T36 1.0250 1.1SVC1(MVAr) 0.9750 2.4912SVC2(MVAr) 2.3796 0.8512SVC3(MVAr) 0.8512 1.4829SVC4(MVAr) 1.4825 2.8413SVC5(MVAr) 2.8413 2.3731

Installation Cost($/hr) 515 550Lmax 0.115 0.0729

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Thus the problem is formulated as a bi-objective optimization

considering the minimization of SVC cost and the maximization of voltage

stability margin as the conflicting objectives. MOGA has been applied to

solve this multi-objective optimization problem. The results of MOGA are

presented in the above Table 3.4.From this table it is observed that the cost

obtained with maximization of voltage margin as objective is 550$/hr,

whereas the cost of the pareto solutions with SVC cost as one of the

objectives (multi-objective case) is less than this value. It is also observed

that the non-dominated solutions are diverse and well distributed over the

Pareto-front.

3.6 CONCLUSIONS

This chapter has presented a MOGA algorithm approach to obtain

the optimum values of the optimal power flow including the voltage security

enhancement. It is considered as an optimization criterion, the minimization

of SVC investment cost and the maximum voltage security enhancement. It is

evaluated by L-index value. The effectiveness of the proposed method is

demonstrated on IEEE 30-bus system with promising results. The

performance of the proposed algorithm is performed well when it was used to

characterize Pareto optimal front of the multi-objective power flow problem.