Optimal Filter Placement and Sizing Using Ant Colony Optimization in Electrical Distribution System

8/17/2019 Optimal Filter Placement and Sizing Using Ant Colony Optimization in Electrical Distribution System

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Optimal Filter Placement and Sizing using Ant

Colony Optimization in Electrical Distribution

System

Fawaz Masoud Alhaddad

Student Member, IEEE

Department of Electrical and Computer Engineering,

Dalhousie University Halifax, Nova Scotia, Canada

E-mail: [email protected]

Mohamed El-Hawary

Fellow, IEEE

Department of Electrical and Computer Engineering,

Dalhousie University Halifax, Nova Scotia, Canada

E-mail: [email protected]

Abstract — This paper presents an application of the AntColony algorithm for optimizing filter placement and sizing on a

radial distribution system to reduce power losses and keep theeffective harmonic voltage values and the total harmonicdistortion (THD) within prescribed limits. First, a harmonic loadflow (HLF) algorithm is performed to demonstrate the effect ofharmonic sources on total power loss. Then the Ant Colonyalgorithm is used in conjunction with HLF to place a selection offilter sizes available at each possible location so that both powerloss and THD are minimized. As a result the optimal adjustmentof location and size of the filter are determined. Results ofcomputational experiments on standard test systems arepresented to demonstrate improvement and effectiveness of usingthe filters at the optimal location. The methodology used can beeasily extended to different distribution network configurations.

Keywords—Radial Distribution Systems (RDS), Harmonic Load

Flow (HLF), Ant Colony System (ACS)

I. I NTRODUCTION

As a result of the increasing penetration of energy fromrenewable sources into the power grid, power quality hascurrently become a recurring problem. The cause of such

problems can be attributed to two main sources, the injectedharmonics from renewable energy sources and abnormaloperating conditions. Some of the generated power is lost dueto harmonic injections of different elements at each stage of adistribution system. Harmonics result from the presence ofharmonic producing equipment that causes overheating andmalfunctioning of those devices; these are undesirable as theycause power losses and also affect the voltage profile. Thevoltage drop also occurs at distribution feeder due to variations

in load demand and many times it falls under the workableoperating limits. The unequal loading phases can also makedistribution systems less effective.

It would be less expensive and time saving if the harmonicsand the effects of abnormal operating conditions could bereduced. In order to work efficiently, the distribution systemneeds to be upgraded. Low pass filters can solve this problem ifoptimized by using an effective technique [1, 2].

Harmonic filters like low pass harmonic filters (LPHF) arecommonly used elements in distribution systems to improve

power quality by enhancing voltage profiles. The placementand sizing of these filters play a critical role not only inimproving the power quality but reducing the total generation

cost. Recently some Heuristic techniques have proven reliablein solving such optimization problems. Ant ColonyOptimization is one such technique. Hence, this study focuseson reducing the total power loss and suppressing the effect oftotal harmonic distortion caused by harmonics present in thesystem by optimally placing and sizing the low pass harmonicfilter by combining the Harmonic Load Flow analysis with AntColony algorithm.

After introduction, the discussion on radial distribution loadflow and harmonic load flow (HLF) algorithms is presented insection II. Ant Colony System (ACS) is explained briefly insection III. Section IV contains the implementation of ACSalgorithm for optimization of LPHF followed by results anddiscussion in Section V. Finally the last section comprises of

conclusion.

II. HARMONIC POWER FLOW FOR R ADIAL DISTRIBUTION

SYSTEMS

A. Backward/Forward Sweep Algorithm for RDS

Backward-forward sweep power flow algorithm for RadialDistribution Systems (RDS) developed by Teng [3] is used inthis study. In this radial distribution power flow algorithm(RDPF), two matrices namely [BIBC] and [BCBV] are formedto get the power flow solution. [BIBC] is the relationshipmatrix between bus current injections and branch currents.Whereas, [BCBV] represent the relationship between branchcurrents and bus voltages. In order to explain the backward-

forward sweep method a radial distribution system isconsidered having ‘n’ buses. The single line diagram is

presented in Fig. 1 below:

Fig. 1. Single line diagram of n-bus RDS

2014 Electrical Power and Energy Conference

978-1-4799-6038-5/14 $31.00 © 2014 IEEE

DOI 10.1109/EPEC.2014.41

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2014 Electrical Power and Energy Conference

978-1-4799-6038-5/14 $31.00 © 2014 IEEE

DOI 10.1109/EPEC.2014.41

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When a filter is placed at bus ‘i', the bus current injection

is given by:

(1)

Where is the reactive power injection of filter is placed

at bus ‘i’. Now, the Kirchhoff’s current law (KCL) is applied by backward current sweep starting from the last bus ‘n’ to the

source bus 1 to obtain the branch currents.

(2)

(3)

Now in the forward voltage sweep and apply Kirchhoff’s

voltage law (KVL) to obtain the bus voltages and second

relationship matrix as follows:

(4)

(5)

Hence, by substituting (3) in (5), in terms of bus

current injections is expressed as follows:

(6)

(7)

Where [DLF] = the relationship matrix between voltage

drops and bus current injections. Moreover, the following

equations are solved iteratively to get the power flow solution:

(8)

(9)

(10)

Where initial bus voltage vector. The iterative

process stops when the absolute of difference between

previous bus current injection and most recent bus current

injection is less than or equal to a prescribed tolerance :

(11)

The total real power loss can be calculated by the

following equation:

(12)

(13)

Where is the magnitude of the ith branch current, R is

the ith branch resistance and br is the number of branches inRDS.

B. Harmonic Power Flow Algorithm

The harmonic power flow algorithm (HPF) was introduced by Teng in [4]. Backward-forward sweep technique is also

employed here but the effect of harmonics is also considered.In this study, harmonic sources of order 3rd, 5th, 7th, 11th,13th and 15th are used. Each source generates these harmonicsand multiple sources are placed at different nodes in the RDS.

The backward sweep in HPF algorithm is used to obtain therelationship matrix [A] which represents the relationship

between branch currents and bus current injections for the hthharmonic order, on the other hand the forward sweep generatesthe relationship matrix [HA] which gives the relationship

between harmonic bus voltages and harmonic bus currentinjections. To explain, the harmonic power flow algorithm, anunbalanced n-bus RDS, is considered and the single linediagram is demonstrated as follows:

Fig. 2. Single line diagram of n-bus unbalanced RDS

In the above figure, bus 1 is assumed to be the

generator and is considered a slack bus. The hth harmonic buscurrent vector is:

(14)

Where is the hth harmonic currents contributed

by loads and is the harmonic current absorbed by filter.

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In order to find the current flowing in branches, backward

current sweep is employed with KCL:

(15)

(16)

Where is the relationship matrix between bus

current injection and branch current flows at hth harmonic.

Furthermore the forward voltage sweep and KVL is applied to

calculate harmonic bus voltages and is expressed in vector

form as follows:

(17)

Where is the harmonic bus voltages vector and

is the relationship matrix between the harmonic bus

voltages and currents. The harmonic bus voltage of the filter is

determined by:

(18)

Where is the row vectors of the matrix

associated with the bus at which filter is placed. The

harmonic voltage of filter placed at bus i in terms of itsharmonic impedance is given as follows:

(19)

Where the harmonic current of filter placed at

bus i and is the harmonic impedance of filter placed at

bus . The RDS assumed consists of (n -1) loads and a single

phase filter placed at bus i. Hence (18) becomes:

(20)

Where denote the harmonic current

vector of loads and is the harmonic current absorbed by

the filter which can be found by following equation:

(21)

(22)

Where represent the elements of

which are related to the harmonic currents of loads, while

is related to the harmonic current of the filter placed at

bus i. Once the harmonic current absorbed by the filter isobtained, the harmonic branch currents and bus voltages can

also be known by using backward sweep as in (16) and

forward sweep as in (17) respectively. The harmonic busvoltages are calculated iteratively until a predefined tolerance

is reached.

(23)

Where is the harmonic voltage of bus i for

iteration k +1. is the harmonic voltage of bus i for

iteration k . The total real power loss for hth harmonic isdefined by:

(24)

(25)

Where is the smallest harmonic order, is the

highest harmonic order, is the magnitude of the ith

branch current for the hth harmonic order and is the ith

branch resistance for the hth harmonic order. The root mean

square values of the bus voltages ( ) can be known from

the harmonic bus voltages calculated for all harmonic

frequencies by utilizing the process described above:

(26)

Where is the magnitude of bus voltage at fundamental

frequency. Finally, the total harmonic distortion at bus i can be

calculated from the following equation:

(27)

III.

A NT COLONY SYSTEM (ACS)The Ant Colony System (ACS) was inspired by the

foraging behavior of ants. Biologists have determined that antsalways find the shortest distance between food and their nests

because they leave pheromone trails, which allows them tocommunicate with each other and transfer information about

paths to food. The search for food generally begins by a groupof ants choosing random paths. During the initial searches,they leave constant density trails as to their movements in time.

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Subsequently , the density of the trails on the shorter pathsincreases and assists them in finding the shortest route to food.The ant colony algorithm, which parallels this ant behavior,

begins a search among a population by measuring thecompetence of individual members of the population based ona cost function until the individuals all converge to an optimum[5].

IV. IMPLEMENTATION OF ACS ALGORITHM FOR LPHF

OPTIMIZATION

In order to implement ant colony algorithm the first step isto create a matrix of all the available filter sizes and all the

possible bus locations. Each available filter size is consideredas a stage i (i = 1, 2… n) and bus location as states j (j = 1, 2…m). Here, n and m are the filter sizes and possible buslocations. Then a suitable number of ants are selected. The totalnumbers of ants selected in this case are half the total numberof possible bus locations. Each ant starts its tour by selecting arandomly chosen state of first stage. Each ant selects its firststage randomly and tours around all the available states. TheACS algorithm is implemented as follows:

First all states of stages receive a certain and equal amountof pheromone. Then, M ants start their tour depending on the

pheromone level, heuristic information and a probabilityfunction. After touring around all states, the pheromone of allstates is locally updated. Furthermore, the value of theobjective function is calculated for all ants. This objectivefunction is the total real power loss. The state which results inminimizing the objective function the most is selected as bestsolution and recorded. After that, a global update of

pheromone levels of all the states passed by respective ant andthe best ant is made. This process is repeated until themaximum iterations are reached. ACS is implemented asfollows:

A.

Step 1: InitializationGenerate a matrix for the total number of available filter

sizes as stages and the number of possible bus locations asstates and select a suitable value for control parameters (α, ß),coefficient of pheromone evaporation (ρ), the number of ants,states and stages. Also generate initial pheromone and

heuristic information for all states. is set to be the

reciprocal of filters to be placed so if a bigger filter size isselected by an ant the heuristic information is less attractive.This is done because larger size filters are more expensive.

(28)

Where is the filter size selected.

B. Step 2: Selection of a state (bus)

Ants use heuristic information which is the objectivefunction and pheromone trails to select optimal allocation filter.An ant with randomly selected filter j will select a node i on the

basis of the following rule:

(29)

Where is the total real power injection by the load on bus i, is the set of available states(buses) for randomlyselected stage (filter).i is selected according to the probabilitydistribution as follows:

(30)

C. Step 3: Local Updating

Update the pheromone of all states passed by ants in Step 2using the following equation:

(31)

Where is the evaporation coefficient so thatrepresent the pheromone evaporation and is the

contributions of ant k that used filter j and selected bus i toconstruct its solution. is basically the amount of trail laid

on edge (ij) by ant k which is calculated by:

(32)

Where is the objective function of ant k (total real power loss). The objective function is total real power loss so iffilter j placed in bus i results in small power loss it will mean

that the pheromone level of that particular ant will be bigger.

D. Step 4: Calculation of Objective Function

Calculate the objective function for all ants. The objectivefunction is the total real power loss. Here the Radial PowerFlow (RPF) and Harmonic Power Flow (HPF) algorithms areused to calculate total real power loss. The RPF calculates real

power loss due to fundamental frequency and HPF calculatesthe real power loss due to harmonics. So the total power loss isgiven as follows:

(33)

E. Step 5: Calculation of Objective Function

Update the pheromone of all states passed by ant whichgave the best objective function using following equation:

(34)

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Where is the contribution of ant which used

filter j and selected bus i to and resulted in best objectivefunction. It is calculated as:

(35)

(36)

Where is the best objective function achieved and

is the maximum number of ants.

F. Step 6: Convergence Criterion Checking

If total number of iterations reaches a maximum, the program is terminated and the results are presented, otherwise,increase iteration by 1 and go to step 2 and the whole process isrepeated.

V.

R ESULTS AND DISCUSSION

The ACS algorithm explained was applied on 13-bus radialdistribution test system. The single line diagram of the testsystem is as follows:

Fig. 3. 13-bus radial distribution system

The line and bus data of test system can be found inAppendix A. Bus 1 is the generation bus. All the remaining

buses are load buses and distribute generated power to theloads connected to each bus. Total demand is distributedamong 12 load buses respectively. The total real power in thesystem is 1115 KW. The harmonic sources are placed at

buses5, 7, 9, 10, 12 and 13. Harmonic sources inject harmoniccurrents of order 3, 5, 7, 9, 11, 13 and 15.

First the total power loss is calculated and then ACSalgorithm is applied in order to find the best size and location

of the filter. The result of ACS is shown in Fig. 4. The filtersize selected is 600 Kvar and the best location found to place itis bus 7. The maximum number of iterations selected is 100.ACS for 13-bus test system converged in 35 iterations.

The result of harmonic load flow analysis before and after placing filter is presented in Table I. Fig. 5 demonstrates thereduction in THD and Fig. 6 shows reduction in power losswith respect to fundamental and harmonic frequencies as aresult of optimal filter placement.

Fig. 4. 13-bus radial distribution system

TABLE I. HARMONIC LOAD FLOW A NALYSIS BEFORE AND AFTERFILTER PLACEMENT

Vrms (pu)

Bus Before Placement After Placement

1 0 0

2 0.979 0.981

3 0.975 0.977

4 0.973 0.975

5 0.966 0.970

6 0.961 0.967

7 0.958 0.966

8 0.965 0.969

9 0.972 0.974

10 0.969 0.971

11 0.961 0.965

12 0.960 0.964

13 0.960 0.964

Ploss (KW)

Fundamental 49.36 35.06

Harmonics 12.63 8.85

Total 61.997 43.91

Fig. 5. THD Before and After filter placement

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Fig. 6. Ploss Before and After filter placement

It can be seen that after placing the filter, the THD issuppressed as demonstrated in Fig. 5. This has resulted in animproved voltage profile as presented in table I. Also the powerloss at fundamental frequency which was 49.365 KW is

improved by 28.98% to 35.060 KW. Other noticeable lossesare 6.931, 2.495 and 1.273 KW each at 3rd, 5th and 7th orderharmonics which are reduced to 4.857, 1.743 and 0.892 KWeach. 30% improvement is seen for harmonic losses. Finally,the total power loss has been reduced from 61.997 KW to43.91 KW giving an overall improvement of 29.17% and asaving of almost 18 KW.

VI.

CONCLUSION

This paper presents an application of the Ant Colony

System based algorithm for optimizing filter placement and

sizing on a radial distribution system in order to reduce power

losses and keep the root mean squared voltages and total

harmonic distortion (THD) to lie within prescribed limits. A

radial distribution power flow (RDPF) and harmonic powerflow (HPF) algorithms are employed which use backward-

forward sweep techniques to produce power flow solution.

RDPF and HPF are performed to demonstrate the effect of

harmonic sources on total power loss. Then the Ant colony

algorithm is used in conjunction with both power flow

algorithms to select a filter size from a number of available

sizes and place it at the best possible location so that both

power loss and THD are minimized. A 13-bus radial

distribution test system is used to validate the results.

It takes 35 iterations for ACS algorithm to find the

best possible solution. By placing the harmonic filters the

effect of harmonics is suppressed. It resulted in a decrease in

total real power loss and improving voltage profile. Filters area cheaper solution and low voltage systems like the three test

systems can prove to be more economically efficient solution

than by using shunt capacitor as done in [6, 7, 8, 9 and 10].

Furthermore ACS has proven to be fast in convergence. Best

filter size chosen by ACS for the test systems is 600 Kvar and

the best locations found to place this filter is 7. The real power

loss is reduced by 29.17% of the power loss before placing the

filter. Also, THD on every bus is suppressed and voltage

profile improved.

APPENDIX A

TABLE II. 13-BUS RDS LINE AND BUS DATA

Lineno.

FromBus

ToBus R(Ω) X(Ω)

P(kW)

Q(kVAR)

1 1 2 0.117 0.048 100 30

2 2 3 0.107 0.044 20 730

3 3 4 0.165 0.046 150 225

4 2 5 0.150 0.042 50 10

5 5 6 0.150 0.042 120 540

6 6 7 0.314 0.054 40 700

7 5 8 0.210 0.036 75 90

8 2 9 0.314 0.054 50 150

9 9 10 0.210 0.036 125 825

10 5 11 0.131 0.023 210 800

11 11 12 0.105 0.018 80 300

12 11 13 0.157 0.027 95 30

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Optimal Filter Placement and Sizing Using Ant Colony Optimization in Electrical Distribution System