20 I 0 International Conference on Advances in Energy Engineering

Optimal Overcurrent Relay Coordination using Genetic Algorithms

Dusit Uthitsunthom and Thanatchai Kulworawanichpong

Power System Research Unit, Suranaree University o/Technology, THAILAND dusit.sut@gmail.com , thanatchai@gmail.com

Abstract

This paper presents an intelligent approach for

overcurrent relaying coordination design. Due to a

powerful search scheme of the selected intelligent

method, genetic algorithms (GA), digital relays are

well coordinated to satisfY a large number of constraints, which are complicated over the ability of

the conventional relay setting. The proposed scheme

was demonstrated through a 6-bus power system, in

which fourteen digital overcurrent relays were situated

to be coordinated smartly. Also, the results obtained

from GA were compared with those obtained by

applying an efficient non-linear quasi-Newton method.

It strongly confirms the effectiveness of the proposed

method

1. Introduction

Short-circuit conditions can occur unexpectedly in any part of a power system at any time due to various physical problems. Such situations cause a large amount of fault current flowing through some power system apparatus. The occurrence of the fault is harmful and must be isolated promptly by a set of protective devices. Over several decades, protective relaying has become the brain of power system protection [1]. Its basic function is to monitor abnormal operations as a "fault sensor" and the relay will open a contractor to separate a faulty part from the other parts of the network if there exists a fault event. To date, power transmission and distribution systems are bulky and complicated. These lead to the need for a large number of protective relays cooperating with one another to assure the secure and reliable operation of a whole. There-fore, each protective device is designed to perform its action dependent upon a so-called "zone of protection" [2]. From this principle, no protective relay is operated by any fault outside the zone if the system is well designed. As widely known that old

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fashion analog relays are inaccurate and difficult to establish the coordination among protective relays, the relay setting is typically conducted based on the experience of an expert or only a simple heuristic algorithm. However, with the advancement of digital technologies, a modem digital protective relay is more efficient and flexible to enable the fine adjustment of the time-dial setting (TDS) different to that of the old fashion electromagnetic one.

This paper proposes an intelligent relay coordination method based on one of the most widely used intelligent search algorithms, called the genetic algorithms (GA) [3,4], for digital relaying, in which the time-dial setting is appropriately adjusted in order to minimize operating time while coordinated relays are also reliable. In this paper, the coordination of digital relaying systems is explained in Section 2 in such a way that the GA method is employed to achieve the system objective. A case study of a 6-bus power system protection, where setting of fourteen digital over-current relays was challenged, was discussed in Section 3. The last section provides the conclusions and future work.

2. Relay coordination problem

Overcurrent relays are devices which have ability to interrupt electricity supply service due to some severe fault. In a modem electrical power system, network interconnection is very complicated. This affects the difficulty of key parameter setting of protective relaying devices. When a total number of overcurrent relays to be coordinated is increased according to a complex transmission network, relay coordination setting is more difficult and cannot be performed by a simple hand calculation. The following is to propose a scheme of digital overcurrent relay coordination based on genetic algorithms.

The relay coordination task described in this paper is in form of constrained optimization problems.

ICAEE 2010

Before solving such a problem, its objective function and constraints must be defined, accordingly.

2.1 Overcurrent relay characteristics

An overcurrent relay is a typical protective relay that allows a protected load operating within a preset value of the load current. The overcurrent relay is placed at the secondary side of the current transformer. The operating time of the overcurrent relay can vary due to relay type, time-dial setting (TDS) and magnitude of fault currents. For the inverse time overcurrent relay which corresponds to the ANSI device number of 51, the operating time of the overcurrent relay can be expressed as shown in (1) according to the IEC standard 255-4 [5].

Where

j3xTDS t=--'----PSMa -1

PSM = Iaet CTS

a and j3 are arbitrary constant PSM is plug setting multiplier CTS is the current tap setting of the relay Iaet is the actual current seen by the relay

(1)

(2)

a and j3 are constant. In this paper, a type of very

inverse time overcurrent relay is used. Therefore, a

and j3 can be specified according to the IEC standard as follows.

Table 1. Characteristic of overcurrent relay [5]

Type a @ Normal Inverse 0.02 0.14

Very Inverse 1.00 13.5 Extremely Inverse 2.00 80 Long-time Inverse 1.00 120

2.2 Primary and backup relaying constraints

A primary or main protective device is a relay that is in the nearest position to the fault and must respond to the fault as fast as possible. To achieve a reliable protection system backup, relays are devices which will be initiated within a certain amount of time after the main relay fails to break the fault. An amount of delay time, called time grading margin, must be added to the main relay operating time. This can be explained by Fig. 1. Relay m and b are the main and the backup

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relays, respectively. FJ and F2 are two fault cases seen by both relays. The operating time of the backup relay must be at least the operating time of the main relay plus the time grading margin for every fault case.

�'k"prel'Y �i",�:Y 3

1� m 1 Near-end-fault Far-end-fault

Figure 1. Simple feeder for overcurrent protection

To generalize the backup relaying constraint, (3) is defined [6] as follows.

Where tb(Fi) is the operating time of the backup relay

due to Fault Fi tm(Fi) is the operating time of the main relay

due to Fault Fi TGM is the time grading margin, 0.3 - 0.5 s FC denotes a set of fault cases

2.3 Objective function

To coordinate the protective relaying devices, the operating time of the main relay is minimized. As mentioned in the previous sub-section, the operating time of the backup relay is set as inequality constraints. The objective function [6] used in this paper is given as follows.

Where

f=w1I t ,2 +W2 2: [Mmb -w3 (Mmb -IMmbOf (4) i=l jEFC

WI. W], W3 is the weighting factors n is a total number of relays

3. Genetic algorithms

There exist many different approaches to adjust the motor parameters. The GA is well-known [3,4,7], there exist a hundred of works employing the GA technique to identify system parameters in various forms. The GA is a stochastic search technique that leads a set of population in solution space evolved using the principles of genetic evolution and natural selection, called genetic operators e.g. crossover, mutation, etc. With successive updating new generation, a set of updated solutions gradually converges to the real solution. Because the GA is very

popular and widely used in most research areas where an intelligent search technique is applied, it can be summarized briefly step-by-step as follows.

I. Initialization: Randomly initialize populations or chromosomes and set them as a search space and then evaluate their corresponding fitness value via the objective function.

2. Evolution: Apply the genetic operators to create an offspring population as the sequence below,

a. Selection: Form a set of mating pool with the same number of the population size by using a random procedure, e.g. the roulette-wheel or tournament schemes, with the assumption that each chromosome has a different chance (probability to survive. The higher the fitness value, the higher the chance or probability.

b. Crossover: This operation is applied to a subset of the mating pool by taking a pair of chromosomes called the parents. The parents will yield a pair of offspring chromosomes. This operation involves exchanging sub-string of the parent chromosomes. It is performed by choosing a random position in the string and then swapping either the left or right sub­strings of this position (one-point crossover) with its chromosome mate.

c. Mutation: For the chromosome to be mutated, the values of a few positions in the string are randomly modified. To prevent complete loss of the genetic information carried through the selection and crossover processes, mutation (if use at all) is limited to typically 2.5% of the population.

3. Fitness Test: Evaluate the fitness value for the generated offspring population.

4. Convergence Check: Check for violation of all termination criteria. If not satisfied, repeat the evolution process.

4. Simulation results

In this paper, a 6-bus test power system [6] as given in Fig. 2 was chosen as a test system. This test case consisted of fourteen overcurrent relays to be coordinated. Information of load current, CT ratio at all relay locations is presented in Table 2. Fault currents used for coordination are also shown in Table 3.

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• '-"'-____ -"-"'!.!U0 "'

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Figure 2. 6-bus test power system

m -- -- --- ------- -- ----------- -----I I I I • Best fitness I : I I

� --+-- �---�--� -- �--�---� -- +-- �---I I J J I I I I I I I

I I J J I I I I I I I 60 - - T - - J - - -1- - - r - - -, - - -1- - - r - - ,. - - -1 - - -I

55 .. - 1 ___ I ___ 1 ___ L __ J ___ 1 ___ L __ 1 ___ 1 ___ I I j J I I I I I I I I I J I I I I I I I

50 �� - - � - - -:- - - � - - � - - -:- - - � - - � - - � - - - : I I

" 45 - - T.- - ..., - - -1- - - r - - ..., - - - 1- - - r - - -r ----, ---I :\......:. I I I I I : I I

40 __ + ___ ;-- : __ J __ I ___ I ___ i ___ I __ _ 35 �� __

� __

_L __

_L

__ �

__ �

__ L_ __ L_

�

__

� 0p a 100 200 300 400 500 600 700 800 900 1000 LJ Generation

Figure 3. GA solution convergence

Table 2. Load current and CT ratio at relay locations

Line portion

Relay No. Load Current CT

From To Ratio bus bus

1 2 1 24.942 100/5 2 1 3 112.584 300/5

3 3 4 52.232 150/5 4 4 5 45.069 150/5 5 5 6 87.626 250/5

6 6 2 24.942 100/5 7 1 6 47.352 150/5

Table 3. Load current and CT ratio at relay locations

Main Backup Primary fault Secondary

Relay Relay current fault current

8 9 4961.7704 4 1 0.8226

8 7 4961.7704 1520.8911

2 7 5362.2983 1528.0660

2 5362.2983 804.8782

3 2 3334.5 1 91 3334.5 1 91

4 3 2234.3308 2234.3308

5 4 1352.8751 1352.8751

6 5 4965.0442 4 1 1.3675

6 14 4965.0442 1522.9084

14 I 4232.7243 794.0920

14 9 4232.7243 407.2292

I 6 2682.4959 2682.4959

9 10 1443.6699 1443.6699

10 11 2334.65 1 5 2334.6515

II 12 3480.75 1 1 3480.7511

12 14 5365.0609 1529.3638

12 13 5365.0609 805.5618

13 8 2490.7454 2490.7454

7 5 4232.6340 407.2472

To find a set of optimal relay coordination, genetic algorithms or GA was employed as the proposed method. However, the quasi-Newton based on BFGS formula was also apllied for comparison. Refer to (4), weighting factors used in the objective function were assigned below. The set of optimal parameter setting of all the relays was presented in Table 4. Fig. 3 also showed the solution convergence of the GA method.

WI = 1, W2 = 2 and W3 = 100

Table 4. Optimal overcurrent relay setting

Relay Pickup Optimal TDS

No. current Quasi-Newton GA

1.55 1.0010 2.3962

2 2.34 0.9990 0.8861

3 2.17 0.9973 0.7343

4 1.87 1.0008 1.16 1 1

5 2.19 1.0051 1 .5 1 96

6 1.55 0.9969 0.6242

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7 1.97 0.5036 0.5000

8 1 .55 0.9968 0.6259

9 2.34 1.0070 1.6106

10 2.17 1.00 1 5 1 .4973

11 1.87 0.9997 0.9367

1 2 2.19 0.9984 0.8 1 72

1 3 1.55 1.00 1 0 2.2558

1 4 1.97 0.9976 0.7214

Objective value 49.8838 38.9896

5. Conclusion

This paper described the use of the GA search method to coordinate the overcurrent relaying system. In this paper, a 6-bus test power system with fourteen relays are tested. The results show that the solution by the GA method gave the lowest objective value when compared with the Quasi-Newton method.

6. References

[1] J.L. Blackburn, Protective Relaying, Marcel Dekker, 1987.

[2] S.H. Horowitz and A.G. Phadke, Power System Relaying, Research Study Press, 1995.

[3] T. Charuwat and T. Kulworawanichpong, "Genetic based distribution service restoration with minimum average energy not supplied", The 8'h Int. Can! Adaptive and Natural Computing Algorithms, 11-14 April 2007, pp. 230-239.

[4] K. Somsai, A. Oonsivilai, A. Srikaew, and T. Kulworawanichpong, "Optimal PI controller design and simulation of a static var compensator using MATLAB's SIMULINK", The 7'h WSEAS Int. Can! on POWER SYSTEMS, Beijing, China, pp. 30 - 35.

[5] IEC Standard 255-4.

[6] F. Razavi, H.A. Abyaneh, M. Al-Dabbagh, R. Mohammadi, H. Torkaman, "A new comprehensive genetic algorithm method for optimal overcurrent relays coordination", Electric Power System Research, Vol. 78, 2008, pp. 713-720.

[7] C.W. So, K.K. Li, K.T. Lai, K.Y. Fung, "Application of Genetic Algorithm to Overcurrent Relay Grading Coordination", The 4th Int. Can! On Advances in Power System Control, Operation and Management (APSCMP-97), Hong Kong, November 1997, pp. 283-287.