OPTIMIZING TOPOLOGY OF THE POWER DISTRIBUTION

NETWORK USING GENETIC ALGORITHM

Martin Paar

1

, Lukas Oliva

2

and Jana Jilkova

3

1

Center for Research and Utilization of Renewable Energy Sources, Brno University of Technology

Technicka 3058/10, Brno, Czech Republic

2

Department of Radio Electronic, Brno University of Technology, Purkyňova 118, Brno, Czech Republic

3

Department of Radar Technology, University of Defence, Kounicova 65, Brno, Czech Republic

Keywords: Distribution network reliability, Genetic algorithm, Power losses, Reconfiguration, Multi-criterion

optimization.

Abstract: The article deals with application of genetic algorithm to the minimization of the operational cost of

distribution network. The optimization is achieved by the change of the network topology or reconfiguration

in terms of power network terminology. The optimization algorithm changes the setup of the switchgears to

get such a configuration which leads to the minimum costs for power loss and minimum financial

penalization for not delivering the electric power and therefore violating standards of the power supply

continuity. The Finnish continuity standard at systems level and Portuguese continuity standard at single-

customer level were selected for evaluation of the impact of power supply discontinuity and their impact is

compared and discussed. The Genetic algorithm is designed as multi-attribute optimization with mono-

objective evaluation using binary coding. Also since the optimization involves reconfiguration of the

topology a simple solution to cope with invalid solution is described and discussed.

1 INTRODUCTION

During past decade, new challenges caused by the

liberation process in electrical energy market of the

European Union were introduced. While the

liberation does not carry only new opportunities for

the business but also new requirements given by

state regulator, a way to minimize the risks of the

penalization for the violation of the regulations was

necessary to be found. The method of estimating

these risks is well known and widely used and is

based on the probabilistic model of the outages in

the power network. Because the distribution

companies are naturally monopolistic, the market in

this area needs to be regulated by state. The task of

the state regulator is to keep the requirements of

customers, distribution company stockholders and

power systems itself balanced. To cover the needs of

customers and power systems the power quality

standards were defined. One part of power quality

standards is based on the monitoring of electrical

energy supply continuity followed by costs

evaluation of continuity violation. It enables the

evaluation of network reliability and provides some

clues about network's condition. It is also one of the

tools to secure the investment to network by its

owners. The electrical energy supply continuity is

directly related to reliability of distribution network.

The reliability improvement requires usually high

investment to the networks’ parts e.g. changing

overhead lines by cables and so on. Therefore the

distribution companies seek for cheaper solutions.

The one of almost cost-free solution is a

reconfiguration – changing the topology.

2 CURRENT DEVELOPEMENT

Using the reconfiguration of the power network to

optimize the power network parameters started in

middle 80’s (Sarfi, 1996) but the main development

took place in 90’s of 20th century. The optimizations

were mainly concern to decrease of power losses

(Sarfi, 1996) or to balance power distribution

(Baran, 1989) and heuristic method: Greedy search

(Baran, 1989) or artificial intelligence: Genetic

algorithms (Vitorino, 2009) or Swarm intelligence

(Hosseini, 2008) were used. The power network

239

Paar M., Oliva L. and Jilkova J..

OPTIMIZING TOPOLOGY OF THE POWER DISTRIBUTION NETWORK USING GENETIC ALGORITHM.

DOI: 10.5220/0003675602390244

In Proceedings of the International Conference on Evolutionary Computation Theory and Applications (ECTA-2011), pages 239-244

ISBN: 978-989-8425-83-6

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

reliability in connection with reconfiguration has

been studied since 2003 (Brown, 2003). The main

development in this field started in the beginning of

the 21st century when liberalization of electric

energy market was introduced in European Union

(Hosseini, 2008), (Vitorino, 2009).

3 APPLICABLE NETWORKS

The electrical power networks are divided to

transmission networks and distribution networks.

The transmission networks create the central part of

the system and are used for the transfer of the energy

from the power plants or international connection

points to the main points of consumption like big

cities or important industry centres. These networks

work on the voltage level up to 200 kV and usually

operate as meshed networks. Between the

transmission networks and end users, there are the

distribution networks operating on variety of voltage

levels from 110 kV (High voltage - HV) over 35 kV

(middle voltage - MV) for industry to 400 V for low

voltage (LV) customers. Each voltage level has its

own properties and operated topology and it can be

diverse in different countries and areas depended on

historical and technical conditions. The article is

based on the situation in the Czech Republic.

The transmission networks generally operate as a

meshed network where reliability calculation is

actually very complicated and where the

reconfiguration operations are executed with

different focus – primarily to the stability of the

system. The networks on HV (110 kV) level in the

Czech Republic do not contain sufficient number of

reconfiguration points for proper optimization, on

other hand the available data from the power

networks on LV (0.4 kV) level do not currently

provide enough information for practical evaluation.

Power networks, fulfilling both requirements for

optimization (enough data and possibility of

effective reconfiguration), operate on MV (35kV

and 22 kV) level. MV networks in Czech Republic

are designed as meshed networks and they are

operated as radial networks to enable simple

dispatching control.

4 POWER NETWORK

OPTIMIZATION

The optimization is based on four components–

network topology reconfiguration, evaluation of the

continuity standard, power losses calculation and

quite basic version of genetic algorithm. The

network reconfiguration is necessarily built-in the

GA implementation.

4.1 Reconfiguration and Coding

Reconfiguration is a process of changing the

topology of the power network using circuit breakers

or section switches without disconnection of any

end-point customer. The set of switches state

(on/off) defines one solution (or a single individuum

in terms of GA). Therefore the algorithm uses

naturally binary coding system. Apart from 1

(switched on) and 0 (switched off) the third status

(-1) is used for the situations when the status of the

switch is unknown during the optimization. The -1

marker has to be used to distinguish a state when the

change of the switch position may break any of set

condition. This marker arises during the GA

operators processing and practically means that the

individual should be corrected so that it represents a

viable solution (given only by a set of 0 or 1).

Figure 1: Model of the network.

The switch position in the chromosome (locus) is

mapped to a single switch position in the network.

The mapping is constant during the whole

simulation. During the optimization, each valid

individuum represents a valid set of switches state

fulfilling the conditions of 1) all the customers being

connected and 2) providing no loops (radiality

condition). The way to achieve the reconfiguration

from one set of switches to another is not taken into

account during optimization and is considered to be

practically possible.

Figure 2: Representation of the model network.

07

02

01

03 04 05 06

1713 14 15 16

08 09

10 11 12

18

switch

close

switch

open

switch

line

Substation or

transformation

station

01 02 03 04 05 06

07

08

09

13

10

14 15 16 17 18

11 12

ECTA 2011 - International Conference on Evolutionary Computation Theory and Applications

240

Figure 3: Representation of Figure 2.

During the whole optimization process two

representations of coded solution - one for genetic

algorithm usage and another for the criteria function

evaluation process is used. The representation used

for GA is describes a non-oriented graph where

vertices stand for the elements of network i.e.

substations, transformation stations, overhead lines,

cables etc, and switches represented by the graph

edges. Example of the network topology is shown on

Figure 1, its representation for GA purposes is on

Figure 2, encoded equivalent of Figure 2 is shown

on Figure 3 on the row "switch set". The GA

representation is used to split the network to radial

subnetworks by the modified Depth-first search

(DFS) algorithm described in (Paar, 2008). Logical

division of the network to subnetworks is essential

for the evaluation process and also it is one of the

conditions of the practical network operation.

4.2 Evaluation of the Solution

The evaluation is composed of the 1) cost of power

losses calculation and 2) a penalization calculation

for given continuity standard (Finnish continuity

standard at system level or Portuguese continuity

standard at single-customer level is used). Before

evaluation an individuum is transcoded into the

second representation using the Breadth-first-search

algorithm (BFS). Contrary to DFS, BFS transforms

the subnetwork to a structure without switches

where vertices are represent substations or

transformation stations and edges represent overhead

line and cables. This structure allows to the steady

state calculation and also determines the placement

of so called protection zones in all the radial

subnetworks. Protection zone are the areas affected

by interruption of power supply on particular cable

leading to the consequent continuity standard

violation and penalization.

4.2.1 Power Losses Costs Calculation

The first evaluated criterion is focused on power

losses cost. Power losses are calculated by using

steady state calculation with power consumptions

specified by electric currents and are independent

from the voltage applied to their terminal point.

These simplifications cause calculation to suffer

from lower accuracy comparing to the power-flow

calculation methods, such as the Newton-Raphson or

Gauss-Seidel method. The main benefit is faster

calculation and with satisfactory resolution of results

(convergence of aforementioned iteration methods

cannot be guaranteed). Costs of power losses (in

€/year) are given by:

n

p

= c

l

P

l

T

l

(1)

where c

l

is a specific unit on a middle voltage level,

P

l

is power losses of whole network and T

l

is

utilization time of power losses.

4.2.2 Valuation of Penalization Standards

The second criterion is made of the total number and

the total duration of power supply interruptions

evaluated by specified continuity standard. Number

and duration of the outage is provided by the

reliability model using Monte Carlo method. The

reliability model is based on direct generation of

random failures given by probability distribution

based on statistic numbers of annual supply

interruptions. The set of interruptions numbers is

generated with one year time step for selected

individual network components together with

corresponding interruptions duration. This technique

is described more in detail in (Dětřich, 2006). One of

the main advantages of this approach is that it

provides the results even for limited range of input

data of examined network.

Every generated outage is bounded to specific

networks elements. Each element fall within a

specified protection zone whose size and topology is

given with by the network topology and is defined as

a protected part of the network by single protection

element located directly in feeders or in important

switch stations. The outage in any single element

affects the whole protection zone where element is

located and all protection zones fed by the affected

protection zone. Number of affected zones and

network elements gives the number of disconnected

switch

name

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18

element

before

switch

S1 L01 T1 L02 T2 L03 T1 T2 T3 L04 L05 L06 T4 L07 T5 L06 T6 L09

switch set

1 1 1111100011111111

element

after

switch

L01 T1 L02 T2 L03 T3 L04 L05 L06 T4 T5 T6 L07 T5 L06 T6 L09 S2

OPTIMIZING TOPOLOGY OF THE POWER DISTRIBUTION NETWORK USING GENETIC ALGORITHM

241

customers and the total duration of interruptions, the

amount of non-delivered power to customers (in

kWh) and enables calculation of the financial

penalization for a given standard.

4.2.3 Finnish Continuity Standard at System

Level

The Finnish continuity standard is used by Finnish

Energy Market Authority and belongs to so called

system level continuity standards which regulate the

power quality without opportunity of direct payment

to customers. The penalization payment is a part of

complex metrics to set the network charges and also

to evaluate the efficiency of whole network. The

standard is described in (FEMA, 2007) (Paar, 2010).

4.2.4 Portuguese Continuity Standard at

Single-customer Level

Portuguese standard expresses the maximal number

of interruptions per year and maximum interruption

duration annually. The limits specified in the

standard are distinguished according to the voltage

levels (HV, MV and LV) and population density. As

Finland’s standard was focused on system level, the

computation is aimed to the Portuguese single-

customer standard and excluded Portuguese standard

at system level (Paar, 2010), (CEER, 2005).

4.3 Genetic Algorithm

The optimization of power network configuration

leads to combinatorial problem with huge solution

space where classical computation methods fail or

don’t bring useful results. Using the global

optimization method can enable solution of such

problems. The selected optimization method is quite

basic implementation of the Genetic algorithm. The

application uses GA with tournament selection,

single point crossover, random mutation and elitism.

Following chapters describe the main modifications

done to solve the described problem.

4.3.1 Initialization

The initial population of GA is created by a specific

function. The usage of binary coding of solution by

switch setup is does not by itself guarantee proper

network topology (like as feeding all parts of the

network or radial structure of subnetworks). For

small network, the quantity of non-allowed solution

may not be problematic but it grows with the

network size. Therefore the modified Depth-first

search algorithm (MDFS) that includes some

random features is used to guarantee viability of the

initial population.

4.3.2 Fitness Function

The fitness function is designed as a weighted sum

of two input parameters and a penalization function

given by following formula:

fitness = α n

p

+ β n

C

+ γ

(2)

where α and β are balance coefficients, n

p

is power

losses costs of whole network and n

C

is penalization

costs given by selected continuity standard. Function

γ is used to discriminate inappropriate solutions (out

of set limits) and is determined by this formula:

1max

1

2max

1

cond

cond

n

i

i

n

i

i

duu

dII

(3)

where d

1

and d

2

are weighting coefficients, Δu is a

voltage drop vector in the network, Δu

max

is maximal

permitted voltage drop, I

i

represents vector of

currents flowing in the network and I

max

is maximal

current-carrying capacity, Г is specific penalization.

4.3.3 Crossover

The classical single point crossover operator does

not make sure that the new individual will represent

a valid solution so it had to be modified. After the

crossover, the comparison is made between

offspring with one of parents. The result of

comparison is parent solution with -1 numbers at all

genes where offspring chromosome differs. The

offspring is then corrected through a correction

algorithm to repair all the damaged genes. This way

ensures viability of the new generation while saving

the computational time too since is not necessary to

investigate all parts of the network but only the

“damaged” one.

5 SIMULATION AND RESULTS

The results of the optimization show how the

selected continuity standards affect the output

parameters SAIFI (System Average Interruption

Frequency Index that express average number of

interruptions that affected customer per year; A

similar parameter - SAIDI is focused on the average

interruption duration) and power losses on the model

of real middle voltage (22 kV) cable network.

The network covers area between two

substations (110/22 kV) which together feed over 44

ECTA 2011 - International Conference on Evolutionary Computation Theory and Applications

242

800 customers by 288 power transformation stations.

The power network contains more than 300 cables

and 628 section switches or circuit breakers.

The GA setup was following:

600 generations

16 individuals in one population (1 elite)

crossover probability 0,95

mutation probability 0,1

5.1 Results

The stochastic nature of genetic algorithm requires

more optimization runs to be done. To show

valuable results, each of the result graphs (Figure 4-

6) contains, selected simulation run with duration

close to the arithmetic average of all tested solutions

(fitness function) and the maximum and minimum

(both dotted line) of the fitness function for all the

individuals for solution on current situation

(original solution without any optimization, dot-and-

dashed).

Figure 4: Duration of fitness function for Finnish and

Portuguese continuity standards.

The overall penalization between the Portuguese

and Finnish continuity standards is not directly

comparable because of the differences in both

approaches (system versus customer oriented). Each

continuity standard serves for the different purposes;

the Finnish standard is part of the complex

metrology hence given total values of penalization

do not affect the distribution companies directly. In

simulations the Portuguese standard does not reach

as high values as the Finnish but it must be noted

that the direct impact to distribution company money

is present since the penalization may make important

portion of the network operational costs (Figure 4

shows the differences between fitness functions that

shows the approximate difference in the operation

costs of the network between the original and the

optimized topology. The optimized version shows

the decreased amount of money spent for

penalizations approximately by a factor of 5.

To illustrate the difference in the reliability,

SAIFI and power losses are showed on Figure 6. As

it can be seen, the SAIFI parameter for the case of

Finnish standard was decreased by 10%.

Figure 5: Evolution of power losses during generations for

Finnish and Portuguese continuity standards.

Even more interesting is the impact to the power

losses (see Table 1). The total power losses were

decreased by 20% for optimization to the Finnish

standard or even by 30% for the Portuguese on.

Figure 5 depicts higher decrease of the power losses

for simulations with the Portuguese standards. As

can be seen on Figure 6, parameter SAIDI during

optimization is improved but second part of

optimization returns back close to original value.

The Finnish standard is less affected by power losses

costs in criterion function though the decreasing of

power losses in this optimization is shown as well,

the improvement of SAIFI and SAIDI parameters

indispensible compare to Portuguese continuity

standard.

Figure 6: SAIFI duration during generations.

0 100 200 300 400 500 600

0

0.5

1

1.5

2

2.5

3

x 10

5

Generation

Fitness function [Euro/year]

Fit. FI

Fit. PT

Orig. Fit. FI

Orig. Fit. PT

0 200 400 600

200

220

240

260

280

300

320

340

Generation

p [kW/year]

p FI

p PT

Orig.

p

0 200 400 600

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

Generation

SAIFI [year

-1

]

SAIFI FI

SAIFI PT

Orig. SAIFI

OPTIMIZING TOPOLOGY OF THE POWER DISTRIBUTION NETWORK USING GENETIC ALGORITHM

243

Table 1: Results for Finnish and Portuguese continuous standards.

standard

penalisation SAIFI SAIDI P

final orig. final orig. final orig. final

10

3

Euro year

-1

year

-1

% min/year min/year % kW kW %

FI 220 0,48 0,43 9,9 32,6 29,3 10,4 338 267 21

PT 43,5 0,48 0,48 0,2 32,6 32,5 0,4 338 235 30

6 CONCLUSIONS

The article describes application of the genetic

algorithms to the problem of the distribution

network reconfiguration with the multi-criterion

function with the aim to minimize the interruption of

energy supply penalisation and at the same time also

to minimize the power losses costs. Details of the

algorithm caused by the combinatorial nature of the

problem were described. The application was tested

on model of a real MV cable network for two

continuity standards.

The results show that power losses are

inconsiderable part of multi-criterion function

mainly when Portuguese continuity standard is used.

The results imply that significant savings could be

reached for very negligible expenses in the

distribution networks.

The future work will be focused to the

optimization with truly multi-objective nature.

ACKNOWLEDGEMENTS

This paper was written with the support from

MSM0021630516 project of the Ministry of

Education, Youth and Sports of The Czech

Republic.

Author gratefully acknowledge financial support

from European Regional Development Fund under

project No. CZ.1.05/2.1.00/01.0014.

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