Abstract: This paper addresses an optimal Reactive Power Planning (RPP) of power system. The Static Var Compensator (SVC) is introduced into power system in order to reactive power support and voltage control. The locations and the outputs of SVCs are determined using our proposed optimal reactive power planning model. The proposed method optimizes several objective functions at the same time within one general objective. The optimized objectives are minimization of total investment in reactive power support, average voltage deviation and minimization of total system loss. These objective functions are one of the most important objectives for every transmission and distribution systems. Simulated Annealing technique (SA) is used to solve the optimization problem. The validity of the proposed method is tested on a typical power system

Ali Javadian

Mehdi Ghasemi Naraghi

Mehdi Nikzad

Mohammad Bigdeli Tabar

Shamsabad Farahani

Shoorangiz Shams

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Australian Journal of Basic and Applied Sciences, 5(7): 570-575, 2011
ISSN 1991-8178
Corresponding Author: Mehdi Nikzad, Department of Electrical Engineering, Islamic Azad University, Islamshahr branch,
Tehran, Iran. P. O. Box 3135-369.
Ph:+982188043167; +989122261946; Fax: +982188043167
E-mail: mehdi.nikzad@yahoo.com
570
Reactive Power Planning for Loss Minimization Using Simulated Annealing
1Mehdi Nikzad, 2Shoorangiz Shams Shamsabad Farahani, 3Mohammad Bigdeli Tabar, 4Mehdi
Ghasemi Naraghi, 5Ali Javadian
1,2,3,4,5Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University,
Tehran, Iran.
Abstract: This paper addresses an optimal Reactive Power Planning (RPP) of power system. The
Static Var Compensator (SVC) is introduced into power system in order to reactive power support and
voltage control. The locations and the outputs of SVCs are determined using our proposed optimal
reactive power planning model. The proposed method optimizes several objective functions at the same
time within one general objective. The optimized objectives are minimization of total investment in
reactive power support, average voltage deviation and minimization of total system loss. These
objective functions are one of the most important objectives for every transmission and distribution
systems. Simulated Annealing technique (SA) is used to solve the optimization problem. The validity
of the proposed method is tested on a typical power system.
Key words: Reactive Power Planning; Static Var Compensator; Multi Objective Optimization;
Simulated Annealing (SA).
INTRODUCTION
The losses are naturally occurring in electrical system components such as transmission lines, power
transformers, measurement systems, etc. due to their internal electrical resistance. It is not possible to achieve
zero losses in a power system, but it is possible to keep them at minimum. The losses are becoming higher
when the system is heavily loaded and transmission lines are transmitting high amount of power. The
transmitted power for this case consists of active and reactive power. Necessity of reactive power supply
together with active power is one of the disadvantages of the power generation, transmission and distribution
with alternating current (AC). Reactive power can be leading or lagging. It is either generated or consumed
in almost every component of the power system. In AC system, Reactance can be either inductive or
capacitive, which contribute to reactive power in the circuit. In general, most of the loads are inductive and
they should be supplied with lagging reactive power. We need to release the power flow in transmission lines
for partially solving of problem of supply the reactive power locally where it is highly consumed in a system.
In this way the loading of lines would decrease. It would decrease the losses also and with this action the
problem of voltage drops could be solved also. By means of reactive power compensation transmission system
losses can be reduced as shown in many papers in the literature (Conejo, 2001; Abdel-Moamen, 2003;
Mamandur, 1981; Iyer, 1984). It has also been widely known that the maximum power transfer of the
transmission system can be increased by shunt reactive power compensation, typically by capacitors banks
placed at the end of the transmission lines or a the load terminals (Wollenberg, 2002). Therefore, planning of
reactive power supports would give benefits to the users of the transmission systems, in terms of loss
reduction, among other technical benefits, such as improving steady-state and dynamic stability, improve system
voltage profiles, etc. which are documented in (Timothy, 1982). The reactive power planning problem involves
optimal allocation and sizing of reactive power sources at load centers to improve the system voltage profile
and reduce losses. However, cost considerations generally limit the extent to which this can be applied.
This paper presents an optimal reactive power planning of power system using the Static Var Compensator
(SVC). The proposed planning optimizes several objective functions at the same time within one general
objective. The optimized objectives are minimization of average voltage deviation, minimization of total system
loss and total system cost. 
Aust. J. Basic & Appl. Sci., 5(7): 570-575, 2011
571
Simulated Annealing (SA) is used to solve the optimization problem. Simulation results emphasis on the
validity of the proposed method. Rest of the paper is structured as follows: In section 2, problem is formulated
and required equations are introduced. In section 3, a brief description about SA technique is given. In section
4 a modified Graver system is considered as test system. In section 5, results and discussions are presented.
And finally, the paper is concluded in section 6.
2. Problem Formulation:
As referred before, in this paper three different parameters are considered as objective function. These
parameters are: total investment cost, average voltage deviation and total system loss. Also the power system
constrains such as generation reactive limits, voltage limits and etc, should be incorporated in planning.
Therefore, the objective functions are as follows:
  (1) 1 0i 1i i iJ c c q u
Bi N
 
Where, c0 and c1 are fixed and variable costs of locally reactive sources. q is amount of locally reactive
source in bus i and ui is a binary vector that indicates whether or not to install reactive power sources at bus
k.
  (2)2 lossJ P
  (3)
n
2
3 ref i
i 1
J (V V )

 
Where, J1 shows the investment cost due to locally reactive sources. J2 shows the system losses and J3
presents the voltage deviation. These objective functions should be converted to a unique unit. The coefficients
ω convert the proposed functions to a unique unit. Eventually, reactive power planning formulation can be
represented as follows:
Min ω1J1+ ω2J2 + ω3J3   (4)
Subject to
  (5)i Gi DiP (V, ,n)-P P 0  
  (6)i Gi Di iQ (V, ,n)-Q Q -q 0  
      #      #   (7)minGiP GiP
max
GiP
      #       #        (8)minGiQ GiQ
max
GiQ
  (9)
min max
i i iV V V 
Sfrom# Smax (10)
Sto# Smax(11)
(12)
min max
i i iq q q 
Equations (5) and (6) introduce the conventional equations of AC power flow and (7) and (8) show the
limits for real and reactive power for generators. Equation (9) presents the limits for voltage magnitude.
Capacity limits of the line flows are presented by (10) and (11). Equation (12) presents the limit for locally
reactive sources. 
Aust. J. Basic & Appl. Sci., 5(7): 570-575, 2011
572
The elements of vectors                and      in       (5), (6) are calculated as follows (Rider, 2007):iP (V, ,n) iQ (V, ,n)
(13)   
B
i i j ij ij ij ij
j N
P (V, ,n) V V G n cosθ B n sinθ

    
(14)   
B
i i j ij ij ij ij
j N
Q (V, ,n) V V G n sinθ B n cosθ

    
The elements of bus admittance matrix (G and B) are calculated as follows (Rider, 2007):
(15)
   
   
1
ij ij
ii ij
j Ω
G n g
G
G n g

  
  

(16)
   
   
1
ij ij
sh sh
ii i ij ij
j Ω
B n b
B
B n b b b

  
       


Where, gij and bij show conductance and susceptance of the transmission line or transformer ij.      shows
sh
ijb
shunt susceptance of the transmission line or transformer ij (if ij is a transformer          ) and      showsshijb 0
sh
ib
shunt susceptance at bus i. Ω1 indicates Set of all load buses. 
Elements (ij) of vectors Sfrom and Sto of (10) and (11) are given by the following relationship:
(17)   2 2from from fromij ij ijS P Q 
(18)   2 2to to toij ij ijS P Q 
Where:
(19) 2 cos sinfromij i ij i j ij ij ij ijP V g VV g b   
(20)   2 sin cosfrom shij i ij ij i j ij ij ij ijQ V b b VV g b     
(21) 2 cos sintoij j ij i j ij ij ij ijP V g VV g b   
(22)   2 sin costo shij j ij ij i j ij ij ij ijQ V b b VV g b     
The proposed formulation in used to find the best place of SVCs. In this paper Simulated Annealing (SA)
is used to solve the optimization problem. In the next section a brief introduction about SA is presented.
3. Simulated Annealing:
In the early 1980s the method of simulated annealing (SA) was introduced in 1983 based on ideas
formulated in the early 1950s. This method simulates the annealing process in which a substance is heated
above its melting temperature and then gradually cooled to produce the crystalline lattice, which minimizes
its energy probability distribution. 
Aust. J. Basic & Appl. Sci., 5(7): 570-575, 2011
573
This crystalline lattice, composed of millions of atoms perfectly aligned, is a beautiful example of nature
finding an optimal structure. However, quickly cooling or quenching the liquid retards the crystal formation,
and the substance becomes an amorphous mass with a higher than optimum energy state. The key to crystal
formation is carefully controlling the rate of change of temperature.
The algorithmic analog to this process begins with a random guess of the cost function variable values.
Heating means randomly modifying the variable values. Higher heat implies greater random fluctuations. The
cost function returns the output, f, associated with a set of variables. If the output decreases, then the new
variable set replaces the old variable set. If the output increases, then the output is accepted provided that:
(23)
Where, r is a uniform random number and T is a variable analogous to temperature. Otherwise, the new
variable set is rejected. Thus, even if a variable set leads to a worse cost, it can be accepted with a certain
probability. The new variable set is found by taking a random step from the old variable Set as (24).
Pnew = dPold (24)
The variable d is either uniformly or normally distributed about pold. This control variable sets the step size
so that, at the beginning of the process, the algorithm is forced to make large changes in variable values. At
times the changes move the algorithm away from the optimum, which forces the algorithm to explore new
regions of variable space. After a certain number of iterations, the new variable sets no longer lead to lower
costs. At this point the value of T and d decrease by a certain percent and the algorithm repeats. The algorithm
stops when T•0.The decrease in T is known as the cooling schedule. Many different cooling schedules are
possible. If the initial temperature is T0 and the ending temperature is TN, then the temperature at step n is
given by (25).
Tn=f(T0, TN, N, n) (25)
Where, f decreases with time. Some potential cooling schedules are as follows:
a. Linearly decreasing: Tn=T0-n(T0-Tn)/N
b. Geometrically decreasing: Tn=0.99 Tn-1
c. Hayjek optimal: Tn=c/log(1+n), where c is the smallest variation required to get out of any local minimum.
Many other variations are possible. The temperature is usually lowered slowly so that the algorithm has
a chance to find the correct valley before trying to get to the lowest point in the valley. This algorithm has
been applied successfully to a wide variety of problems (Randy, 2004).
4. Illustrative System:
Figure 1 shows a typical electric power system. Modified Graver system is considered as illustrative
system. The system data are presented in appendix (Rider, 2007). The fixed and variable costs of locally
reactive sources are as c0 = 100$ and c1 = 0.3$/kvar, respectively. 
Fig. 1: Schematic of modified Graver system.
Aust. J. Basic & Appl. Sci., 5(7): 570-575, 2011
574
It should be noted that SA algorithm is run several times and then optimal parameters is selected
respectively. Also 110% and 90% of the nominal value are used for the maximum and minimum voltage
magnitude limits.
RESULTS AND DISCUSSIONS
In this section the result of the SVC placement based on the SA is presented. The SVC places are
accuracy calculated using SA and the results are listed in Table 1. The locally reactive sources are places near
to load buses and it is due to compensation of reactive demands. In this way, the current in transmission lines
are reduced and the total loss is reduced. Also, because of locally supply of reactive demands, the congestion
of lines is reduced. The flows in transmission lines are listed in Table 2. It is clearly seen that the maximum
admissible flows are not violated. The power flow results are also presented in Table 3. The voltages are in
allowable limits.
Table 1: Optimal SVC places.
Bus Locally Reactive Source (MVAR)
4 34.5636
5 6.5
Table 2: Flows in transmission lines.
From bus To bus S_ij (p.u.) S_ji (p.u.) S_ij max (p.u.)
Bus1 Bus4 0.28346 0.27333 1.0
Bus1 Bus2 0.18 0.17341 1.2
Bus5 Bus1 0.38822 0.40553 1.2
Bus2 Bus4 0.24616 0.24638 1.2
Bus3 Bus2 1.0649 0.99677 1.2
Bus3 Bus6 0.17673 0.18168 1.2
Bus5 Bus3 1.03 1.1074 1.2
Bus5 Bus3 1.03 1.1074 1.2
Bus2 Bus6 0.76119 0.836 1.2
Bus2 Bus6 0.76119 0.836 1.2
Bus4 Bus6 1.0836 1.189 1.2
Table 3: Power flow results.
Bus  (PG-PL) [MW] (QG-QL)[MVAR] V [p.u.]
Bus1 80 32 0.99237
Bus2 -240 -48 0.95604
Bus3 315.17 93 1.0214
Bus4 -160 2.5636 0.95693
Bus5 -240 -41.5 0.95
Bus6 260.6903 120.0024 1.05
Conclusion:
The SA approach has been developed for solving the Reactive Power Planning (RPP) problem in large-
scale power systems. The application studies on the modified Graver system show that SA gives suitable results
and always leads to the global optimum points of the multi-objective RPP problem. By the SA approach, more
savings on the energy and installment costs are achieved and the violations of the voltage and reactive power
limits are eliminated.
ACKNOWLEDGEMENT
The authors gratefully acknowledge the financial and other support of this research, provided by Islamic
Azad University, Islamshahr Branch, Tehran, Iran.
Appendix:
Table 4 shows the Modified Graver system data.
Table 4: Modified Graver system data.
Bus Data
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Bus Type PD [MW] QD [MVar]  P
max
G [MW] P
min
G [MW]  Q
max
G [MW] Q
min
G [MW]
1 VΘ 80 16 150 0 48 -10
2 PQ 240 48 - - - -
3 PV 40 8 360 0 101 -10
4 PQ 160 32 - - - -
5 PQ 240 48 - - - -
6 PV 0 0 600 0 183 -10
Aust. J. Basic & Appl. Sci., 5(7): 570-575, 2011
575
Table 4: Continue.
Branch Data
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Bus From Bus To rij[p.u.] xij[p.u.]  bshij [p.u.] S
mzx
ij [MVA] cij [US$]  n
o
ij n
max
ij
1 2 0.040 0.400 0.00 120 40 1 5
1 3 0.038 0.380 0.00 120 38 0 5
1 4 0.060 0.600 0.00 100 60 1 5
1 5 0.020 0.200 0.00 120 20 1 5
1 6 0.068 0.680 0.00 90 68 0 5
2 3 0.020 0.200 0.00 120 20 1 5
2 4 0.040 0.400 0.00 120 40 1 5
2 5 0.031 0.310 0.00 120 31 0 5
2 6 0.030 0.300 0.00 120 30 0 5
3 4 0.059 0.590 0.00 120 59 0 5
3 5 0.020 0.200 0.00 120 20 1 5
3 6 0.048 0.480 0.00 120 48 0 5
4 5 0.063 0.630 0.00 95 63 0 5
4 6 0.030 0.300 0.00 120 30 0 5
5 6 0.061 0.610 0.00 98 61 0 5
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Performance. IEEE Transactions on Power Apparatus and Systems, 103(6). 
Mamandur, K.R.C., R.D. Chenoweth, 1981. Optimal Control of Reactive Power Flow for Improvement
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using AC model. IET Generation Transmission and Distribution, 1(5): 731-742.
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Reactive Power Planning for Loss Minimization Using Simulated Annealing

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Reactive Power Planning for Loss Minimization Using Simulated Annealing

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