J. Electromagnetic Analysis & Applications, 2009, 2: 85-91
doi:10.4236/jemaa.2009.12013 Published Online June 2009 (www.SciRP.org/journal/jemaa)
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage
Regulation with Loss Reduction
Y. Rosales Hernandez, T. Hiyama
Department of Computer Science and Electrical Engineering, Kumamoto University, Kumamoto, Japan.
Email: yoelcuba@st.eecs.kumamoto-u.ac.jp, hiyama@cs.kumamoto-u.ac.jp
Received March 19th, 2009; revised May 25th, 2009; accepted May 28th, 2009.
This paper presents a rule-based technique to control the voltage in a power transmission network. Transformers with a
tap changer installed in the system are selected by the proposed technique as control devices. For each bus under volt-
age violation, the most effective control device is selected by using the minimum electric distance criteria. In order to
demonstrate the efficiency of the method, several simulations were performed using an IEEE 30-bus network as a model
system. The distance measure technique is compared with classic voltage regulation approach and a genetic algorithm
based. The results obtained show the robustness of the proposed method.
Keywords: Knowledge Based Systems, Losses, Voltage Control
1. Introduction
Current approaches to the operation of a modern distribu-
tion network demand high operational performance of the
system and consequently require highly effective control
strategies. Although voltage deviation control is one of
the problems that has been extensively investigated, it
still remains as an important topic to deal with. Voltage
control algorithms may be classified into two categories:
rule-based and network model-based. Rule-based algo-
rithms use rules that control switched capacitors and
transformer tap changers based on real-time measure-
ments and past experience. Network model-based sys-
tems use network topology, impedance, real-time meas-
urements and statistical information to establish the cur-
rent state of the system. It then applies optimization tech-
niques to get the best possible solution. Within the net-
work models-based systems there are many different ap-
proaches. A simulated annealing technique for global
optimal solution is presented in [1]. The authors propose
a knowledge-based expert system which detects buses
with maximum voltage deviations and operates the near-
est available transformer control unit to correct the prob-
lem. Then, a simulated annealing algorithm is utilized to
solve the problem of capacitors manipulation. The paper
shows a very good result in terms of power loss reduc-
tions but does not guarantee an economical use of trans-
formers operations. Restriction in the number of switch-
ing operation is the focus in [2]. Here, dynamic pro-
gramming and fuzzy logic algorithms are combined to
control voltages and reduce power losses. The problem is
decomposed into two sub-problems: first, the control of
the load tap changers (LTC) and capacitor banks at sub-
station level and second, the control of the capacitor
banks installed at the feeder level. Dynamic program-
ming is used in sub-problem 1 and fuzzy logic is adopted
for the second sub-problem. Simulation results show the
excellent performance of the proposed approach. The use
of genetic algorithms is another approach to the control
of voltage and reactive power in the system. The ap-
proach in [3] combines the benefits of a linearized system
model and genetic algorithms (GA). Whenever a voltage
correction is demanded, an initial calculation of the sen-
sitivity matrix is done in order to identify an initial popu-
lation for the GA. Then the GA finds a proper set of con-
trol actions to execute. The method offers good solutions
to the voltage/reactive power problem and also reduces
the number of control actions. Authors in [4] use a
method based on an artificial neural network to find the
suitable capacitor switching regime for every load state.
The main objective is to reduce power losses and the only
constraint considered is bus voltage. The advantage of
this method is the short calculation time. However, in real
applications, it might be difficult to use because the sys-
tem requires training sessions every time any small
change is made to the network topology.
The approach presented in this paper is rule-based and
is a new decision-making tool for centralized control of
voltage. When the system lacks automatic function con-
trol the task has to be performed manually by the super-
Distance Measure Based Rules for Voltage Regulation with Loss Reduction
visor in the dispatch center. Due to the complexity of a
modern power system and the severe consequences to the
economy of power failures, reliable algorithms have to be
part of the daily support tools in the dispatch center. This
research was motivated by the necessity to design a sim-
ple and effective support algorithm for the voltage con-
trol process. The algorithm is based on the identification
of a bus having the worst voltage violations and the
nearest bus where a voltage control device is installed. A
control device setting is changed in order to improve the
voltage situation of the bus in violation. A 30 bus net-
work was used as a case study. Some classic control ele-
ments such as transformers with tap changers, shunt ca-
pacitor banks, synchronous condensers, and generators
were modeled. Although the control strategy reported
here is focused on tap changer, is possible to use all in-
stalled devices as controllable elements. The important
features of the case study system, the proposed method,
and the search algorithm are explained in Sections 2-4.
Simulation results of the 30-bus system under different
load conditions are discussed in Sections 5 and 6.
2. Case Study System
The modeled system is an IEEE 30-bus scheme. The sys-
tem bus data is given in Table 1, and with Figure 1 show-
ing the single line diagram. Shunt capacitor banks are
located at bus 10 and 24. The capacitor bank found at
node 10 contains up to 10 units with a reactive power
capacity of 1.9 Mvar for each unit. In the case of bus 24,
banks have been installed containing up to 3 units of
0.8 Mvar each
Table 1. Bus data
Figure 1. 30-bus IEEE scheme
one. The tap changer settings ranges are modeled at set-
tings from 0.9 to 1.1 with a step of 0.01 per unit. Four
synchronous condensers are also considered at buses 5, 8,
11 and 13.
3. Proposed Method
Usually, the system is exposed to overload and un-
der-load conditions in 24 hour intervals. When the system
is in the overload condition, transferred power trough
lines and transformers might causes excessive voltage
drops and consequently appear bus voltages below the
minimum limit. In the case of an under-load condition,
shunt capacitance of the lines inject an excessive reactive
power into the network and the voltage in some buses
might be above the maximum limit. A safe voltage op-
eration range is considered to be from 0.95 to 1.05 per
unit. A rule-based approach is proposed to bring the sys-
tem to a normal point of operation, with rules being pre-
sented in Table 2. The ranking list order is based on the
electrical distance criteria between every voltage control
device and the target bus. Once the nearest voltage con-
trol device is selected, the device settings have to be
modified using a minimum number of steps in order to
avoid unnecessary control actions.
Table 2. Voltage control procedure
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage Regulation with Loss Reduction 87
4. Distance Measure Algorithm
The shortest route from the bus under worst voltage con-
dition to a corresponding control device location is cal-
culated using Dijkstra’s algorithm [5]. The basic opera-
tion of this algorithm uses edge relaxation. In this case,
the edges are the electrical distance Lij of the transmis-
sion line between buses i and j. The electrical distance is
defined in (1).
ijij ij
LRX (1)
R: is the resistance of brach i-j
X: is the reactance of brach i-j
Once the minimum paths are found, a ranking of dis-
tance measures is established in order to develop a deci-
sion strategy to solve the problem of voltage violation.
5. Simulation Results
For the controllable devices to have a long operating life
it is vital to avoid unnecessary control actions. Therefore,
only strictly necessary actions are allowed. A control
effort index, CEI, is defined to count the number of con-
trol actions used in every simulation. The CEI definition
is presented below.
CEItap tap
i: is the i-th controllable device
s: actual tap position of the i-th controllable device
ref : is the reference tap position of the i-th controllable
In the initial state of the system, the voltage violations
are under the minimum voltage limit. It was for this rea-
son that the shunt capacitors were not adjusted in these
simulations. Also, it is important to note that the mini-
mum tap modification is 0.01 in per unit so that if the
CEI value is 0.36, it means that 36 operations of the tap
were made.
The simulation results are shown in three parts. The
first part is a comparison between a local control strategy,
an evolutionary search based on a genetic algorithm and
the distance based method. The second part illustrates the
performance of the proposed method under a load varia-
tion during a period of 24 hours. In the last section, there
is also a power losses analysis.
5.1 A Comparison of Voltage Local Control, Ge-
netic Algorithm Based Correction, and the Pro-
posed Voltage Control Algorithm
Voltage local control is a classic method based on the
local monitoring and operation of each control device. It
means that at every node where a control device is in-
stalled, a local and independent control strategy is fol-
lowed, and control actions are executed exclusively
where voltage problems appear. Figure 2 illustrates an
initial voltage profile of the network under a hypothetical
load scenario which is assumed to be the maximum load
scenario. The voltage profile shows several nodes violat-
ing the minimum voltage limit. Buses which are under
violation and where a control device is installed are
marked with a circle. In this initial condition only trans-
former operations are available because all capacitor
banks are already connected.
Table 3 lists the positions of transformer taps in the
initial state, during two partial solutions and for the final
solution. The final solution is reached when the four
buses highlighted in Figure 2 are out of the violation zone.
The final solution, shown in Figure 3, does not solve the
problem of voltage at nodes other than those where the
control devices are installed.
The second reference point for this comparison is a
genetic algorithm (GA). GAs are considered more flexi-
ble and robust than most of deterministic search methods
because it requires only information concerning the qual-
ity of the solution produced by each parameter set. This is
unlike many traditional methods that require derivative
information or worse yet, completed knowledge of the
problem structure and parameters [6]. For this GA, deci-
sion variables are expressed as integers. Each gene
represents the tap position of a transformer. Integer vari-
ables are used in order to avoid unnecessary coding and
recoding. By using this non-binary coding, which is a
closer representation of real system parameters, it is ex-
pected that there should be an increment in the velocity
of convergence [7]. The representation of one individual
is shown in Figure 4. The initial population is generated
Figure 2. Voltage profile of the network obtained for initial
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage Regulation with Loss Reduction
Table 3. Operation of the controllable devices using the con-
trol method of local voltage
Figure 3. Voltage profile of the network obtained after exe-
cution of voltage local control
Figure 4. Integer representation of one individual
Then, chromosomes are evaluated through a fitness
function (see Equations 3 and 4) where the objective
function is the minimum number of adjustments to the
tap changers. The voltage deviation at each bus, the reac-
tive limit violation at each generator and maximum line
current limit are considered as constraints. The evaluation
is based on Newton-Raphson power flow calculations,
provided by the MatPower package [8]. The genetic op-
erators are tournament selection, one-point crossover, and
uniform mutation. The stopping criterion is the number of
generation being 60 with the probability of mutation be-
ing 15%.
min ref
tap tapR
***Ra vdb qlccl
 (4)
s: actual tap position
i: ith-tap transformer
ref : reference of tap position
vd: violation of voltage deviation
ql: violation of generated reactive power
cl: violation of current in lines
a: weight for violation of limits of voltages
b: weight for violation of limits of generated Var
c: weight for violation of limits of current flowing
through lines
In order to get a clear solution with the GA, a total of
45 independent simulations were executed with a com-
mon initial condition, (the conditions being as shown in
Figure 2). Figure 5 shows the mean value of voltage de-
viation factor at each generation. The mean value of
number of control actions are shown in Figure 6, where
most of the simulations reach a common solution with
fewer than 43 operations. The mean value of fitness for
each generation are illustrated in Figure 7. In these three
Figures each curve represent one of the 45 simulations.
The superposition of the curves demonstrates the similar-
ity of the solutions for each simulation. The best solution
at each simulation are shown in Figure 8. With 41 control
operations being the minimum value that can be reached
by the GA. The best solution for each simulation has no
constraint violations. For example, Figure 9 shows the
best solution for the voltage profile simulation number
Figure 5. Mean value of voltage deviation factor for the 45
Figure 6. Mean value of the number of operations for the 45
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage Regulation with Loss Reduction 89
Figure 7. Mean value of fitness for the 45 simulations
Figure 8. Number of control action for the best solution at
each simulation
Figure 9. Voltage profile for the best solution at simulation
number 45
Table 4. Operation of the controllable devices using the
distance measure method
In the case of the proposed rule-based method, the ini-
tial state is the same as that showed in Figure 2. The
worst voltage is located at node 30 and transformer T7 is
the best control device to solve the problem. The tap po-
sition in transformer 7 was moved from 0.96 to 1.00 and
the voltage problem in node 30 was solved. Then bus 19
appeared as the worst bus and the most effective control
device was transformer 2. The process was repeated sev-
eral times until a final solution was reached. Table 4
shows the initial conditions of tap positions, two partial
solutions and the final solution. Values in boldface font
Figure 10. Voltage profile of the network obtained in sub-
solution 1
Figure 11. Voltage profile of the network obtained in sub-
solution 2
Figure 12. Voltage profile of the network obtained in the
final solution
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage Regulation with Loss Reduction
represent a new modification of the tap position. In Fig-
ure 10, 11 and 12 the voltage profile for the two partial
solutions and the final result are presented respectively.
Final voltage profile shows the capacity of the rule-based
method to find a suitable solution, and the total CEI=0.42,
means that the number of control actions is 42, which is
very close to the optimal solution of the GA-based
5.2 Performance of the New Method Applied for
a Load Variation over a 24 Hour Interval
It is well known that power demand in a real system is
changing continually during the day, and consequently
state variables are varying as well. Thus, it is necessary to
study the effectiveness of the proposed method for this
typical behavior. Load variation was modeled as coinci-
dent in time. Appendix A shows the percentage of the
rate load at every bus and the voltage at 6 buses after
application of the distance measure method. Other than
the buses shown in Appendix A, the rest are kept within
the non-violating voltage zone. The variations in the
transformer taps are illustrated in Appendix B. In the case
of capacitor bank adjustment, none were executed be-
cause all the banks were connected in the initial state and
the voltage violations that appeared were of the un-
der-voltage type.
6. Analysis of Power Loss Reduction
In addition to voltage correction, power losses were also
monitored and analyzed. This new control method yields
a very flat voltage scenario which is very important in
order to reduce power loss. Appendix C illustrates how
the power losses are reduced gradually in each partial
solution obtained by the proposed method. The final so-
lution gives a 0.67 % power loss reduction.
7. Conclusions
In this paper a Rule-based method was presented for
regulating voltage deviations and to reduce power losses
of a transmission system. The control method is based on
simple rules. Which allow to operate only the most effec-
tive devices to solve voltage violations. Thus, control
actions were executed under the principle of imposing the
fewest number of operations of control devices. Several
simulations were done to compare a local voltage control
strategy and GA-based method with the new method. The
results proved that:
1) The new method achieves the goal where the local
voltage control strategy fails. The most important issue,
which is voltage correction, is not successfully accom-
plished with the approach based on local control.
2) The rule-based method was compared with several
simulations of a GA-based method and the results are
very similar. The number of control actions from
GA-approach is 41 while for the rule-based method is 42.
There are no constraint violations in the solutions pro-
vided by both methods.
3) The rule-based method significantly reduces power
losses of the system under maximum load condition and
under a load variation period of 24 hours. Voltages at all
buses were maintained out of the voltage violation zone.
4) Although the proposed method is based on very
simple rules, where significant approximations are used
to determine a ranking list of effective controllable de-
vices, this approach can be used as a useful, simple and
fast tool for dispatcher engineers in a situation requiring
correction of voltages.
Appendix A
Copyright © 2009 SciRes JEMAA
Distance Measure Based Rules for Voltage Regulation with Loss Reduction
Copyright © 2009 SciRes JEMAA
Appendix C
Appendix B
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Electrical Power and Energy Systems, Vol. 24, pp.
271-276, May 2002.
[3] Y. Malachi and S. Singer, “A genetic algorithm for the
corrective control of voltage and reactive power,” IEEE
Transactions on Power Systems, Vol. 21, pp. 295-300,
February 2006.
[4] B. Das and P. K. Verma, “Artificial neural network-based
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[8] MATPOWER, http://www.pserc.cornell.edu/matpower/.