55
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 multiobjective 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,
56
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.
Line voltage
BSVC
Control
circuit
FC
TCR
Input
signals
Figure 3.1 SVC employing FC - TCR
57
VT
Vmax
I
I
I
LC max
Capacitive
0
LL max
Inductive
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:
X TCR
where
2(
) sin 2
(3.1)
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
X SVC
XC X L
XC
[ 2(
) sin 2 ] X L
(3.2)
58
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
I SVC
jBSVC VK
(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 .
59
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 Lindex 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 Lindices 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 Lindices. 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
60
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).
61
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,
NC
(C fi
Minimize F C
C ci | Q ci | ) $ / hr
(3.4)
i 1
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
62
2.3.3. In addition the SVC reactive power generation constraint is represented
as follows:
SVC reactive power generation limit
min
Q svc
Q svc
max
Q svc
;i
Nc
(3.6)
Aggregating the objectives and constraints, the problem can be
mathematically formulated as a non- linear constrained multi-objective
problem as follows:
Minimize F T
[ F C , Lmax ]
(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.
63
Figure 3.4 Convergence curves of the VSCOPF
Table 3.1 Result of VSCOPF Algorithm (IEEE 30-bus system)
Control variables
P1
P2
P5
P8
P11
P13
V1
V2
V5
V8
V11
V13
T11
T12
T15
T36
QC10
QC12
QC15
Variable setting
68.9229 MW
77.1429 MW
41.6667 MW
35.0000 MW
29.0476 MW
36.8889 MW
1.0500 P.U
1.0310 P.U
1.0262 P.U
1.0167 P.U
1.1
P.U
1.0238 P.U
0.9
0.9571
1.1
0.9857
4.2857
MVAr
5.0
MVAr
1.4286
MVAr
64
Table 3.1 (Continued)
QC17
QC20
QC21
QC23
QC24
QC29
Cost
Lmax
2.8571
5.0
5.0
5.0
5.0
2.8571
822.2797
0.1034
MVAr
MVAr
MVAr
MVAr
MVAr
MVAr
$/hr
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
65
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
66
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
67
Figure 3.5 Pareto Optimal Front
Table 3.4 Control variables for IEEE 30- bus system Extreme Solutions
Control variables
Minimum installation
cost solution
P1 (MW)
29.9654
P2 (MW)
95.7833
P5 (MW)
48.9274
P8 (MW)
33.9137
P11 (MW)
24.2062
P13 (MW)
54.5317
V1 (P.U)
1.0479
V2 (P.U)
1.0749
V5 (P.U)
1.0852
V8 (P.U)
1.0665
V11 (P.U)
1.0931
V13 (P.U)
1.0959
T11
1.0750
T12
0.9750
T15
1.0750
T36
1.0250
SVC1(MVAr)
0.9750
SVC2(MVAr)
2.3796
SVC3(MVAr)
0.8512
SVC4(MVAr)
1.4825
SVC5(MVAr)
2.8413
Installation Cost($/hr)
515
Lmax
0.115
Maximum voltage stability
margin solution
53.5209
88.1262
49.4162
34.9039
24.3695
41.8188
1.0704
1.0295
1.0188
0.9898
1.0776
1.0705
1.0968
0.9
0.9750
1.1
2.4912
0.8512
1.4829
2.8413
2.3731
550
0.0729
68
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.