16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
284
Voltage Regulator Placement In Radial
Distribution Network Using Plant Growth
Simulation Algorithm
P.V.V.RamaRao
S.Sivanagaraju
Abstract— This paper presents Voltage Regulator Placement in
radial distribution network using Plant Growth Simulation Algorithm
for reduction of power losses and voltage profile enhancement. It is
one of the core responsibilities of a utility to maintain suitable
consumer’s terminal voltage. The proposed method obtains optimal
voltage control and maximum net savings. The algorithm makes the
initial selection, installation and tap setting of the voltage regulators to
provide a smooth voltage profile along the network. The effectiveness
of the proposed method is illustrated with 33 node and 69 node radial
distribution networks.
Keywords-Voltage Regulator (VR); Plant Growth Simulation
Algorithm (PGSA); Radial Distribution Network (RDN); Tap Setting.
I. INTRODUCTION
A
Voltage regulator (VR) is used to hold the voltage of a
circuit at a predetermined value, within a band which the
control equipment is capable of maintaining and within
accepted tolerance values for distribution purposes. Many
papers were published showing the placement of capacitor
banks to reduce the power loss and improving the voltage
profile in distribution networks [1-2]. Research papers [3-5]
deals with the determination of the optimal solutions for the
voltage regulators and capacitors, in order to minimize the
peak power and energy losses and provide a smooth voltage
profile along a distribution network. The proposed algorithm,
for optimal reactive power and voltage control, suitable for
large distribution networks, starts with implementing a
partitioning and Kron's reduction technique in order to reduce
the size of the problem [6]. The paper [7] addresses what
factors to be considered when deciding whether regulators,
capacitors, or load balancing or a combination is most
appropriate to provide the needed voltage support. A computer
algorithm for the voltage control of large radial distribution
networks is presented in [8]. The multi-objective problem of
minimizing power losses and voltage deviation locating
voltage regulators is solved as a single objective function using
Genetic Algorithm in [9].
P.V.V.Rama Rao is with EEE Department, Arjun College of Technology &
Sciences, Hyderabad. (email: pvvmadhuram@gmail.com)
S.Sivanagaraju is with EEE Department, JNTUK College of Engineering,
Kakinada. (email: sirigiri70@yahoo.co.in)
P.V.Prasad is with EEE Department, Chaitanya Bharathi Institute of
Technology, Hyderabad. (email: pvp_reddy@yahoo.co.uk)
P.V.Prasad
The problem of the placement and size of both voltage
regulators and capacitors in unbalanced electrical distribution
systems has been modeled as a nonlinear optimization problem
with mixed variables and solved with a simple Genetic
Algorithm [10].
The proposed method deals with initial selection of voltage
regulator buses by using Power Loss Indices (PLI) and Plant
Growth Simulation Algorithm (PGSA) is used for optimal
location and number along with tap setting of the voltage
regulators, which provides a smooth voltage profile along the
network. The main objective of this paper is to minimize the
number of voltage regulators which in turn reduces the overall
cost. The proposed algorithm is tested on 33 node and 69 node
radial distribution networks.
II. PROBLEM FORMULATION
The VR problem consists of two sub problems, that of
optimal placement (candidate node identification) and optimal
choice of tap setting. The first sub problem determines the
location and number of VR to be placed and the second sub
problem decides the tap positions of VR. The objective
function is formulated as maximizing the net saving function,
Objective Function
Max. F=Ke×Plr×8760×LLf-KVR×N (α + β)
Where Ke = Energy loss cost
Plr = Power loss reduction
LLf = Loss factor
KVR = Capital cost
N = Number of VRs
α = Regulator setting for resistance compensation
β = Regulator setting for reactance compensation
(1)
Constraints
The voltage should be with in the limits
Vi,min ≤ Vi ≤ Vi,max
Where Vi voltage at node i
Vi,min Minimum voltage limit
Vi,max Maximum voltage limit
The power loss index (PLI) is useful in determining the
number of candidate nodes for voltage regulator placement.
The PLI is calculated as
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
PLI [ i ] =
(Loss .reduction [i ] − Min .reduction )
(Max .reduction − Min .reduction )
(2)
The load flow method given in ref.[11] is used to calculate the
line losses and voltage profile.
A. Location and Number of VRs
Following algorithm explains the methodology to identify
the candidate nodes, which are more suitable for voltage
regulator placement.
Step 1. Read radial distribution network data.
Step 2. Perform the load flows and calculate the base case
load flow results.
Step 3. By setting the voltage at each node to maximum
voltage limit of 1.05 p.u and perform the load flows to
calculate the active power losses in each case.
Step 4. Calculate the power loss reduction and Power Loss
Index (PLI) using eqn. (2).
Step 5. Select the candidate node whose PLI > tolerance.
Step 6. Stop.
The PLI tolerance is taken in the range [0-1], which maximizes
the objective function.
B. Selection of tap position of VRs
By finding optimal number and location of VR, the tap
positions of VR are determined as follows.
In general, VR position at bus ‘i’ can be calculated as
(3)
Vj1 = Vj ± tap × V rated
where, Vj1= Maximum desired voltage
Vi = Minimum desired voltage
Tap position (tap) can be calculated by comparing voltage
obtained before VR installation with the lower and upper limits
of voltage
‘+’ for boosting of voltage
‘-’ for bucking of voltage
The node voltages are computed by load flow analysis for
every change in tap setting of VR’s, till all node voltages are
within the specified limits. Then obtain the net savings, with
above tap settings for VR’s.
III. IMPLEMENTATION OF PGSA TO VOLTAGE REGULATOR
PLACEMENT
The plant growth simulation algorithm [12], which
characterizes the growth mechanism of plant phototropism, is a
bionic random algorithm. By simulating the growth process of
plant phototropism, a probability model is established. In the
model, a function g(Y) is introduced for describing the
environment of the node Y on a plant. The smaller the value of
g(Y), the better the environment of the node Y for growing a
new branch. The main outline of the model is as follows: A
plant grows a trunk M from its root B0. Assuming there are k
nodes BM1, BM2, BM3 ……… BMk that have better environment
than the root B0 on the trunk M, which means the function g(Y)
of the nodes BM1, BM2, BM3 ……… BMk and B0 satisfy g(BMi) <
g(B0) (i=1, 2, 3….k), then the morphactin concentrations CM1,
CM2, CM3 ……… CMk of the nodes BM1, BM2, BM3 ……… BMk can be
calculated using
C
∆
=
Mi
1
=
285
g ( B 0 ) − g ( B Mi )
( i = 1 , 2 , 3 .... k )
∆1
∑
k
i=1
(g (B0) − g (B
Mi
(4)
))
Fig.1. Morphactin concentration state space
The significance of (4) is that the morphactin
concentration of a node is not dependent on its environmental
information but also depends on the environmental information
of the other nodes in the plant, which really describes the
relationship between the morphactin concentration and the
environment.
It can be used to derivate
∑
k
i =1
C Mi = 1 , which means
that the morphactin concentrations CM1, CM2, CM3 ……… CMk of
the nodes BM1, BM2, BM3 ……… BMk form a state space shown in
Fig.1. Selecting a random number β in the interval [0, 1], β is
like a ball thrown to the interval [0, 1] and will drop into one
of CM1, CM2, CM3 ……… CMk in Fig. 1, then the corresponding
node that is called the preferential growth node will take
priority of growing a new branch in the next step. In other
words, BMT will take priority of growing a new branch if the
T
selected β satisfies 0 ≤ β ≤ ∑
C Mi ( T = 1 ) or
i =1
∑
T −1
i =1
CMi < β ≤∑i=1 CMi (T=2, 3 ... k). For example, if
T
random number β drops between an interval [1 2], which
means
∑
1
i =1
CMi < β ≤∑i=1 CMi , then the node will grow a
2
new branch m. For j=n to m (with step length one) where n and
m are minimum and maximum tap- setting of regulator
respectively.
Algorithm
Step 1. Input the system data such as line and load details the
distribution system, constraint limits etc.
Step 2. Form the search domain by identifying the no. of
candidate nodes as decision variables for the voltage
regulator which corresponds to the length of the trunk
and the branch of a plant;
Step 3. Identify the candidate nodes for voltage regulator
placement using Power Loss Indices.
Step 4. Give the initial solution Xo (Xo is a vector with the
length of no. of nodes required for VR placement)
which corresponds to the root of a plant, and calculate
the initial value objective function (net saving);
Step 5. Let the initial value of the basic point Xb, which
corresponds to the initial preferential growth node of a
plant, and the initial value of optimization X best equal
to Xo, and let F best that is used to save the objective
function value of the best solution X best be equal to f
(Xo), namely, X b = Xbest = Xo and F best = f(Xo);
Step 6. Initialize iteration count, count=1;
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
Step 7. Search for new feasible solutions: Starting from basic
point X b = [x1b, x2b..xi b…xn b], where X b corresponds
to the initial tap setting corresponding to each
regulator.(n is no. of candidate buses for regulator
placement).
Step 8. Let X p be a new solution obtained by replacing i th
decision variable by j th tap-setting.
Step 9. For the found solution X p ; check the constraints, if it
satisfies then go to next step, otherwise abandon the
possible solution X p .
Step 10. Calculate the objective function f (X p ), and compare
f (X p) > f (X b), if it does not satisfy abandon the
possible solution X p and increment ‘j’ then go to step
9.
Step 11. Save the best possible solution from obtained feasible
solutions.
Step 12. If count >Nmax go to step 17; otherwise go to next
step.
Step 13. Calculate the probabilities C1, C2, … Ck of feasible
solutions X 1, X 2, X 3, … X k by using eqn. (4), which
corresponds
to
determining
the
morphactin
concentration of the nodes of a plant.
Step 14. Calculate the accumulating probabilities ∑C1,
∑C2,….∑Ck of the solutions X 1, X 2, … X k. Select a
random number β from the interval [0 1], β must
belong to one of the intervals [0 ∑C1], [∑C1, ∑C2],
….,[∑Ck-1, ∑Ck], the accumulating probability of
which is equal to the upper limit of the corresponding
interval, and it will be the new basic point X b for the
next iteration, which corresponds to the new
preferential growth node of a plant for next step.
Step 15. Increment count by count+1 and return to step 7.
Step 16. Print the results and stop.
286
and at nodes 5 and 6 the voltage regulator is in boost position
by 7.5% and 1.25% respectively. From Table I, it can be
observed that without voltage regulators the power loss is
202.707 KW and voltage regulation is 8.7 %. With voltage
regulators the power loss is 152.17 KW and voltage regulation
is 2.85%. The loss reduction is 50.54KW. The net saving is Rs.
24, 42, 460.81/- The voltage profile with and without voltage
regulator is shown in Fig.2. The variation of objective function
with number of iterations is shown in Fig.3.
TABLE I. SUMMARY OF TEST RESULTS OF 33 NODE RDN
Description
Without
VR
With VR
Node
2
3
4
5
6
Optimal locations and Size
(KVAr)
Tap-Set
0
0
0
12
2
152.17
Real power loss(KW)
202.71
Reactive power loss (KVAr)
135.23
101.88
------0.9130
8.7
2442460.81
2377865.44
2438725.26
24.93
0.971532
2.85
-------
94
-------
32.056219
Best
Net Saving(Rs.)
Worst
Average
Percentage loss reduction
Min. Voltage (p.u)
Voltage Regulation (%)
No. of times best solution
occurred
Execution time (Sec)
IV. RESULTS & ANALYSIS
The effectiveness of the proposed method is tested on two
systems consisting of 33 node and 69 node radial distribution
networks.
Test System 1: Consider 33 node radial distribution network
whose line and load data are given in [13]. For the positioning
of voltage regulators, the upper and lower limits of voltage are
taken as ±5% of base value. The voltage regulators are of 11
KV, 200 MVA with 32 steps of 0.625% each. The summary of
test results is given in Table I. The maximum benefit is
obtained with the PLI tolerance value of 0.6. From the Load
flow results, it is observed that most of the node voltages
violate the lower limit of 0.95 p.u. (except 1 to 5). Ideally
voltage regulators are to be installed at all nodes except 1 to 5.
However, in practice, it is not economical to have more number
of voltage regulators at all nodes to get the voltages within
specified limits. Hence by applying proposed PGSA algorithm,
the required optimal number of voltage regulators that will
maintain the voltage profile within limits is determined.
From candidate node identification algorithm, the optimal
nodes for voltage regulator placement are 2,3,4,5 and 6. From
PGSA method the tap positions are {0, 0, 0, 12, 2}, at nodes 2,
3, 4, 5, and 6 respectively. At node 2, 3, 4 the tap position is 0
means that the voltage regulator at bus 2, 3, 4 can be omitted
Fig.2 Voltage Profile for 33-node RDN before and after VR placement
Fig.3 Objective function for 33-node radial distribution network
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
287
Test System 2: Consider 69 node radial distribution network
whose line and load data is given in [14]. The voltage profile
before and after placing voltage regulators is shown in Fig.4.
The maximum benefit is obtained with the PLI tolerance value
of 0.8. From candidate node identification method the suitable
nodes for voltage regulator placement are 56, 57, 58, 59 and 60.
From PGSA method the tap positions are {0, +7, 0, 0, +12}, at
nodes 56, 58 and 59 the tap position is 0 means that the voltage
regulator at these nodes can be omitted. From Table II, it is
observed that the power loss without voltage regulators is
225.44 KW and voltage regulation is 9.17%. With voltage
regulators at nodes 57 and 60, the power loss is 155.75 KW and
voltage regulation is 4.12%. The loss reduction is 69.69KW.
The net saving is Rs. 34, 99, 626.16/-. The variation of
objective function with number of iterations is shown in Fig.5.
Fig.5 Objective function for 69-node RDN
TABLE II. SUMMARY OF TEST RESULTS OF 69 NODE RDN
V. CONCLUSION
Description
Without
VR
With VR
Node
56
57
58
59
60
Real power loss (KW)
225.44
Tap-Set
0
7
0
0
12
155.75
Reactive power loss (KVAr)
107.12
76.17
-----
3499626.16
3062917.49
3490891.99
Percentage loss reduction
-------
30.91
Min.Voltage (p.u)
Voltage Regulation (%)
No. of times best solution
occurred
Execution time (Sec)
0.908308
9.17
0.958787
4.12
-------
98
-------
30.763057
Optimal locations and Size
(KVAr)
Net Saving
(Rs.)
Best
Worst
Average
In radial distribution networks it is necessary to maintain
voltage levels within limits at various nodes. This paper aims
at discussing the maintenance of voltage levels by using
voltage regulators in order to improve the voltage profile and
to maximize the net savings. The proposed method deals with
initial selection of VR by using power loss indices (PLI) and
then PGSA has been used for optimal location and number
along with tap setting of the voltage regulators to maintain
voltage profile within the desired limits and reduce the losses.
The proposed algorithm has been tested with two systems
consisting of 33 node and 69 node radial distribution systems.
The results show the quality of the solution.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Fig.4 Voltage Profile for 69-node RDN before and after VR placement
[9]
H. D. Chiang, I. C. Wang, and G. Darling, “Optimal Capacitor
Placement, Replacement and Control in Large-Scale Unbalanced
Distribution Systems: System Solution Algorithms A Numerical
Studies,” IEEE Trans. on PWRS, Vol. 10, No. 1, pp. 363–369, February
1995.
H. D. Chiang, I. C. Wang, and G. Darling, “Optimal Capacitor
Placement, Replacement and Control in large-Scale Unbalanced
Distribution Systems: System Modeling and A New Formulation,” IEEE
Trans. on PWRS, Vol. 10, Vo. pp. 356–362, February 1995
J. J. Grainger and S. Civanlar, “Volt/Var Control on Distribution System
with Lateral Branches Using Shunt Capacitors and Voltage Regulators,
Part 1: The Overall Problem,” IEEE Trans. On PAS, Vol. 104, No. 11,
pp.3278–3283, November 1985.
J. J. Grainger and S. Civanlar, “Volt/Var Control on Distribution System
with Lateral Branches Using Shunt Capacitors and Voltage Regulators,
Part 11: The Solution Method,” IEEE Trans. on PAS, Vol. 104, No.
11,pp. 3284–3290, November 1985.
S. Civanlar and J. J. Grainger, “Volt/Var Control on Distribution System
with Lateral Branches Using Shunt Capacitors and Voltage Regulators,
Part III: The Numerical Results,” IEEE Trans .on PAS, Vol. 104, No. 11,
pp. 3291–3297, November 1985.
M. M. A Salama, N. Manojlovic, V. H. Quintana, and A. Y. Chikhani,
“Real-Time Optimal Reactive Power Control for Distribution Networks,”
International Journal of Electrical Power & Energy Systems, Vol. 18,
No. 3, pp. 185–193, 1996.
Sen, P. K. and Larson, S. L., “Fundamental Concepts of Regulating
Distribution System Voltages,” IEEE Rural Electric Power Conference,
Department of Electrical Engineering, Colorado University, Denver, CO,
1994.
G. J. Salis and A.S. Safigianni, “Optimal Voltage Regulator placement in
a radial power distribution network”, IEEE Transactions on Power
Systems, Vol. 15, No. 2, pp. 879-886, May 2000
E. López, M. López, J. Mendoza, D. Morales, J.C. Vannier : “Optimal
location of voltage regulators in radial distribution networks using
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
[10]
[11]
[12]
[13]
[14]
genetic algorithms”, 15th Power Systems Computation Conference,
August 22-26, 2005, Liege (Belgium).
G. Carpinelli, C. Noce, D. Proto, P. Varilone, "Voltage Regulators and
Capacitor Placement in Three-phase Distribution Systems with Nonlinear and Unbalanced Loads", International Journal of Emerging
Electric Power Systems, Vol. 7, No. 4, 2006.
D.Das, H.S.Nagi, D.P.Kothari “Novel method for solving Radial
distribution system” IEE proc. Generation, Transmission, Distribution.
Vol.141, No.4, pp.291-298, July-1994.
Chun Wang, H. Z. Chengand L. Z Yao, “Optimization of network
reconfiguration in large distribution systems using plant growth
simulation algorithm,” DRPT 2008 Conference, Nanjing, China, pp.771774, 6-9, April 2008.International Journal of Electrical Power and
Energy Systems Engineering 1;2 © www.waset.org Spring 2008
M. E. Baran and F. F. Wu, “Optimal Capacitor Placement on Radial
Distribution System,” IEEE Trans. on Power Delivery, vol. 4, no. 1, pp.
725–734, January 1989.
M. E. Baran and F. F. Wu, “Optimal Sizing of Capacitors Placed on a
Radial Distribution System,” IEEE Trans. on Power Delivery, vol. 4, no.
1, pp. 735–743, January 1989.
Rama Rao P.V.V obtained his B.Tech degree in Electrical & Electronics
Engineering from J.N.T.University Hyderabad in 1998. He obtained his
M.Tech degree in Electrical Power Engineering from J.N.T.University
Hyderabad. He is presently working as Professor & Head in the department of
Electrical and Electronics Engineering in Arjun College of Technology &
Science, Hyderabad, Andhra Pradesh, India. His areas of interest are Power
Systems, Electrical Distribution Systems, Simulation of Electrical Systems.
S. Sivanaga Raju received his Masters degree in 2000 from IIT, Kharagpur
and did his Ph.D from J.N.T. University in 2004. He is currently working as
Associate Professor in the department of Electrical & Electronics Engineering,
J.N.T.U.K. College of Engineering (Autonomous) Kakinada, Andhra Pradesh,
India. He had received two national awards (Pandit Madan Mohan Malaviya
memorial prize award and Best paper prize award) from the Institute of
Engineers (India) for the year 2003-04. He is referee for IEE Proceedings Generation Transmission and Distribution and International journal of
Emerging Electrical Power System. He has 50 publications in National and
International journals and conferences to his credit. His areas of interest are in
Distribution Automation, Genetic Algorithm application to distribution
systems and power system.
P. V. Prasad was born in India. He received B.Tech. in Electrical and
Electronics Engineering from Sri Venkateswara University in 1997, M.Tech
in Electrical Engineering from J.N.T.University College of Engineering,
Anantapur in 2000 and Ph.D from JNTUH, Hyderabad in 2008. Presently, He
is working as Associate Professor in Chaitanya Bharathi Institute of
Technology (CBIT), Hyderabad. He is referee for JEEER. He has 25
publications in National and International journals and conferences to his
credit. His research interests include distribution system automation, planning,
Power system operation and control etc
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
288