Optimal Allocation of the Active Filters Based on the Tabu Algorithm in Distribution Network

Wang Yan-song1, Shen Hua1, Liu Xue-min1 College of Information and Control Engineering

China University of Petroleum Dongying, China

Liu Jun2, Gou Song-bo2 Shengli Oilfield Power Management Company

Dongying, China

Abstract—It is an effective measure to reduce voltage distortion and guarantee power quality by allocating active filters in distribute network. The location and parameter of active filters are coded firstly, then the active filter’s capacity is calculated through solution variable based on calculation of the harmonic power flow.This ensures the filter’s safty operation constraint. The current optimal variables are founded in adjacent area with the evaluation function that the investment of active filters is smallest. The current optimal solution is judged by the constraints of voltage distortion standards to obtain wheather it satisfies the commands. The current optimal solution is updated through Tabu movement. Example shows that the location and parameter of active filters allocated by the Tabu algorithm can restrict harmonic voltage distortion in each node of distribution network effectively.

Keywords-active filter; Tabu algorithm; harmonic voltage distortion; harmonic power flow

I. INTRODUCTION With the development of power electronics, the numbers of

frequency conversion speeder, electric arc furnace and various power electronic energy-saving equipments are increasing continuously. These loads have the characteristics of nonlinear, surge and imbalance, which have caused severe harmonic pollution in distribution network. Harmonics not only affects the power quality of power network, but also endangers the safety and economic operation of power network and electric equipment, disturbs measurement devices, protection devices and adjacent communication systems. Therefore, the study of the harmonic elimination by the application of harmonic filters gets wide attention at home and abroad.

Reference [1] allocate passive filters with genetic algorithm. The location and capacity of filters are determined by the node of most serious voltage distortion on the worst situation. The whole network harmonics will be eliminated gradually and the harmonic contents will be limited under the standard eventually. But it does not take account of the various operating constraints of passive filter. Reference [2] optimizes the parameters of passive filters with genetic algorithms, and the genetic operation has been improved. Reference [3] optimizes the node locations and parameters of passive filters using genetic algorithm, but it does not consider the constraints of each harmonics. Reference [4] allocate passive filters using hierarchical genetic algorithm with the objective to minimize

the total capacity of capacitors for fixed passive filters. References [6]-[8] allocate passive filters with heuristic method and change filter parameters through rule step by step. Reference [9] reduces the harmonic voltage using an active filter. It uses dichotomy to solve the problem according that the property of the solution of each node in the distribution network is determined by Lagrange multipliers. Reference [10] reduces the harmonic voltage using an active filter and converts multi-node multi-harmonic problems to single-node multi-harmonic problems and multi-node single-harmonic problems. References [11]-[12] allocate filters using non-linear programming. The solving method and constraint condition are simplified. Reference [13] allocate the filter in the harmonic sources. It uses particle swarm optimization to optimize the magnitude of each order harmonic current poured in distribution network with the condition of total voltage harmonic distortion rate and the objective function of the cost of active filters. Reference [14] optimizes the allocations of capacitors with particle swarm optimization considering the condition of voltage harmonic distortion rate.

II. THE MATHEMATICAL MODEL OF THE OPTIMAL ALLOCATION OF FILTER DEVICES IN DISTRIBUTION SYSTEM The paper optimizes the allocations and parameters of

active filters and minimizes the investment under the premise that the containing rate of each order harmonic voltages and total voltage harmonic distortion rates of each node satisfy the harmonic standards and filters operate safely and reliably.

A. The objective function The paper uses the objective function that the network

investment of all filters is least.

1

( )N

i i Nii

f Sν=∑ (1)

Where, N is the total node number of the network, 1iν = means that filter branch is installed at node i, 0iν = means that filter branch is not installed at node i, NiS is the capacity of active filter at node i, ( )i Nif S is the function of cost and capacity of active filters.

2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.351

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2010 International Conference on Electrical and Control Engineering

978-0-7695-4031-3/10 $26.00 © 2010 IEEE

DOI 10.1109/iCECE.2010.351

1418

We can use the following linear form to calculate ( )i Nif S :

0 1( )i Ni i ij Nif S b b S= + (2)

The capacities of active filters are determined by rms value of the compensated total current:

2 2 21

2 2

( )( )H H

i i hi Ahi Ahih h

S U U I I= =

= +∑ ∑

(3)

where, AhiI is the compensated hth harmonic current at node i, it is depended on the coefficient of hth harmonic current absorbed by active filter. The harmonic current absorbed by active filter is depended on control law used to the compensated current in practical operation. The common control law is: active filter absorb the node harmonic currents only in a certain percentage, hia represents the coefficient of hth harmonic current absorbed by active filter.

In distribution network, the relation between harmonic current vector AhI absorbed by M active filters and hI poured by harmonic sources in distribute network is:

1 1

1

2i i

hM

0 00 0

0 0

Ah hh

hAh h

hi

hMAhM

I IaaI Ia

aI I

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥= ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎦

(4)

The network node-harmonic-voltage equation after installing active filters is:

( ) 1( ) ( )hh h hU Y E A I−= −

(5)

where, E is unit matrix.

B. The constraint of harmonic standard The containing rate of each order harmonic voltage and

total voltage harmonic distortion rate should satisfy the power quality standards:

1( / ) 100%hi hi i HRUHRU U U C= × ≤ (6)

21

2( / ) 100%

H

i hi i THDUh

THDU U U C=

= × ≤∑

(7)

where hiHRU , iTHDU are the containing rate of the hth harmonic voltage and total voltage harmonic distortion rate at node i respectively. hiU , 1iU are rms values of the hth harmonic voltage component and the fundamental voltage component

respectively. HRUC , THDUC are the limit values of the containing rate of the hth harmonic voltage component and total voltage harmonic distortion rate respectively.

C. The security operation constraint To ensure the safety operation of active filter, the

constraints of the active filters’ capacity is:

i S NiS K S≤

(8)

where, NiS is the rated capacity of active filter, SK is the allowable over-capacity factor of active filter.

III. THE TABU ALGORITHM TO OPTIMIZE FILTER’S

LOCATION AND PARAMETER

A. Code the solution variables into coding string The locations and parameters of active filter in i node are

formed solution-code, i.e 32, , , , ,i i i hi Hii

x a a a aν⎡ ⎤= ⋅⋅ ⋅ ⋅ ⋅⋅⎣ ⎦ . where, 1iν = means that filter branch is installed at node i,

0iν = means that filter branch is not installed at node i, hia represents the coefficient of the hth harmonic current absorbed by active filter. Its value is within 0 to 1. So the coded string is formed by connecting all solution-code of active filters in order:

[ ]1 2, , , , ,i MX x x x x= ⋅⋅⋅ ⋅ ⋅ ⋅ (9)

B. The evaluation function The active filter’s capacity NiS can be calculated by each

harmonic injection current and the coding string. Then the evaluation function can be calculated as following:

1

( ) ( )N

i i Nii

Fitness X F f Sν=

= −∑

(10)

where, F is an appropriate positive real number to make sure the evaluation function’s value of any solution is greater than zero.

C. The Tabu algorithm to optimize filter’s location and parameter

The Tabu algorithm uses a flexible memory technology from which the search knowledge is obtained and the search

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direction is guided in next step. New solution can be obtained by moving. When the algorithm reach a local optimal solution, Tabu makes the search direction point at the direction that the degradation of objective function is smallest The steps using tabu algorithm to optimize filter’s location and parameter are:

step1 Read the original data: node load: line parameter,

harmonic injection current, the size of Tabu table, the adjacent samples number maxN , maximum iterations maxK .

step2 Generate an initial solution initialX as current solution current initialX X= . Set the current solution as the local optimal

solution opt currentX X= ,then calculate the corresponding evaluation function value.

step3 Generate a set of test solutions: A group of ( maxN ) viable test solutions

max1 2, ,...... NX X X can be obtained by acting single move and exchange move on currentX , then calculate the corresponding evaluation function value.

step4 Search adjacent area: A best test solution *X can be obtained by optimizing the above test solutions using evaluation function. If it isn’t included in the Tabu table or is included in Tabu table but satisfy the release criteria, then update current currentX solution with the best test solution *X . If it is included in Tabu table and doesn’t satisfy the release criteria, then find second best test solution, repeat this process.

At last, judge whether or not the new current solution satisfying the constraints,. If not, repeat the above analysis.

step5 Update Tabu table: record the implemented move into Tabu table. If the Tabu table is full, remove the first recorded moved firstly.

step6 Update optimal solution optX : If *( ) ( )optFitness X Fitness X< , then update optX with *X , or

optX remains unchanged. step7 Determine the termination condition: If the value of

objective function doesn’t not improve in several successive iterations or reaches the maximum allowable iterations（ maxK）, then stop optimizing, and output results. Or the time of iteration plus one and go to step 3 to continue iterating

IV. EXAMPLE ANALYSIS The paper analyzes 10kV distribution system with 20 nodes

given in Fig.1. There are 8 transformers and the total capacity is 760 kVA. The total length of the line is 4.2kM. The total active power and reactive power of the load are 72.15kW and 107.37 kVar respectively.

01

234

5

6

7 8

9

10

11

12

13

14

15

16

1718

19

Figure 1. Distribution system topology

There are four harmonic sourses locating at node 3、10、12、17 respectively. Each harmonic injection current of them is in tableⅠ.

TABLE I. HARMONIC INJECTION CURRENTS OF DISTRIBUTION SYSTEM

node Magnitude(A) Phase(degree)

5 7 11 5 7 11

3 6.5 4 1 80 -75 -24 10 5.5 3.6 3 60.5 -83 -14 12 5.5 0 2 150 0 -20 17 3 3 1 140 -80 -50

After optimizing the example by Tabu algorithm, the locations and optimal parameters of filters are given in TableⅡ.

TABLE II. THE RESULTS AFTER THE OPTIMAL ALLOCATION OF ACTIVE FILTERS

node iν 5,ia 7,ia 9,ia capacity (kVA)

3 1.0000 0.5031 0.9379 0.9140 1.776

10 1.0000 0.4815 0.9366 0.5611 1.952 12 0 0 0 0 0 17 0 0 0 0 0

The harmonic voltages of each node in whole network befor and after allocating filters are given in tableⅢ.

TABLE III. THE HRU(%) AND THDU(%) OF EVERY NODE BEFORE AND AFTER FILTING

node 5 times HRU % 7 times HRU % 11 times HRU % THDU %

before after before after before after before after

0 3.8245 2.6628 3.1451 1.6863 2.7285 1.3605 5.6536 3.4330

1 3.8270 2.6645 3.1471 1.6874 2.7303 1.3614 5.6572 3.4352

2 3.8266 2.6640 3.1467 1.6871 2.7295 1.3609 5.6564 3.4344

3 4.4569 2.9397 3.6851 1.8998 2.9467 1.3858 6.4905 3.7645

4 3.8216 2.6605 3.1424 1.6848 2.7253 1.3588 5.6486 3.4297

5 3.8209 2.6601 3.1419 1.6845 2.7248 1.3586 5.6476 3.4292

6 3.3106 2.3048 2.7012 1.4482 2.3077 1.1506 4.8561 2.9552

7 3.8194 2.6590 3.1405 1.6837 2.7234 1.3579 5.6451 3.4277

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8 3.5177 2.4489 2.8727 1.5402 2.4585 1.2258 5.1643 3.1420

9 3.8299 2.6674 3.1496 1.6891 2.7339 1.3636 5.6623 3.4390

10 4.2986 2.8391 3.6466 1.8442 3.3468 1.4483 6.5557 3.6823

11 3.8303 2.6683 3.1497 1.6895 2.7342 1.3644 5.6628 3.4403

12 4.2057 3.1392 3.1850 1.7084 3.1817 1.7881 6.1608 3.9964

13 3.8301 2.6682 3.1496 1.6897 2.7340 1.3643 5.6626 3.4403

14 3.8297 2.6680 3.1493 1.6895 2.7336 1.3641 5.6619 3.4399

15 3.6017 2.5092 2.9372 1.5757 2.5092 1.2522 5.2817 3.2166

16 3.8302 2.6685 3.1500 1.6901 2.7340 1.3645 5.6628 3.4408

17 3.9307 2.7946 3.3496 1.8893 2.8377 1.4697 5.8926 3.6796

18 3.8298 2.6682 3.1496 1.6899 2.7335 1.3642 5.6621 3.4404 19 3.6687 2.5559 2.9751 1.5963 2.5145 1.2550 5.3510 3.2643

V. CONCLUSION (1) The Tabu algorithm can allocate the locations and

parameters of active filters reasonably which will reduce the voltage distortion caused by multi-harmonic sources in distribution network.

(2) Each node harmonic voltage can be calculated by the node harmonic voltage equation of the distribution network after allocating active filters.

(3) The capacities of active filters are contained in the evaluation function so that the security operation constraint of active filter cab be satified. The evaluation function value is smallest under the premise that the active filters operate safely and reliably.

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