Distance Measure Based Rules for Voltage Regulation with Loss Reduction

doi:10.4236/jemaa.2009.12013

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J. Electromagnetic Analysis & Applications, 2009, 2: 85-91

doi:10.4236/jemaa.2009.12013 Published Online June 2009 (www.SciRP.org/journal/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: [email protected].kumamoto-u.ac.jp, hiya[email protected]

Received March 19th, 2009; revised May 25th, 2009; accepted May 28th, 2009.

ABSTRACT

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

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)

where

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.

nref

CEItap tap







(2)

where

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

device

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

randomly.

Figure 2. Voltage profile of the network obtained for initial

conditions

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



 (3)

and

***Ra vdb qlccl



 (4)

where

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

45.

Figure 5. Mean value of voltage deviation factor for the 45

simulations

Figure 6. Mean value of the number of operations for the 45

simulations

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

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

method.

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

Distance Measure Based Rules for Voltage Regulation with Loss Reduction

Appendix C

Appendix B

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