Optimum Coordination of Overcurrent Relays

Using CMA-ES Algorithm

Manohar Singh, and B.K. panigrahi

Electrical Engineering Department

Indian institute of Technology, Delhi-110016

Delhi, India

Manoharsingh33@gmail.com,

Rohan Mukherjee

Electrical Engineering Department

Jadavpur University-700 032

kolkata

rohanmukherjee@gmail.com

Abstract— Coordination of directional overcurrent relays in a

meshed power system is a challenging task for the protection

engineers. In the earlier days it was done manually. Linear and

non-linear programming optimizing techniques were very

frequently used for Coordination of overcurrent relays.

Presently, artificial intelligence (AI) techniques are applied for

optimal co-ordination of directional overcurrent relays (DOCR).

This paper discusses application of Covariance Matrix

Adaptation Evolution Strategy (CMA-ES) for optimal

coordination of DOCR relays in a looped power system.

Combination of primary and backup relay is chosen by using Far

vector of LINKNET structure, to avoid mis-coordination of

relays. Coordination of DOCR is tested for IEEE 30 bus

distribution systems using CMA-ES. The objective function

(OF) is formulated to minimize the operating time between

backup and primary relays (coordination time interval). Results

are compared with the optimized values of Time dial setting

(TDS) and Plug setting (PS) values obtained from modified

differential evolution algorithm. The proposed algorithm (CMA-

ES) gives optimal coordination margin between 0.3 to 0.8 second

and no miscoordination between primary and backup pairs.

Index Terms-- Distribution system; directional overcurrent

relay; optimal relay coordination; CMA-ES;

1. INTRODUCTION

Relay Coordination in a meshed power network in highly

tedious and time consuming affair [1]. Earlier coordination of

OCRs was performed manually, which was very time

consuming. The use of computer in the relay coordination has

relived protection engineering from laborious calculation.

Basically there are two approach are used for coordination of

OCRs, conventionally philosophy and parameter optimization

techniques. In conventional technique fault analysis are

conducted first and then meshed network are broken in radial

form, relay at far end is set first and there after corresponding

backup relay is set, process is repeated until all relays are

taken into account. This process is iterative in nature. Final

time dial and plug setting values depends upon selection of

initial relays known as break points. Break points are selected

using graph theory approach [2].

In late eighties, conventional optimization technique was

used for relay coordination problem [3]. Linear programming

technique gained good popularity but, only helpful in

optimizing the time dial setting, as operating time of

overcurrent relay are linear function of time dial setting[4]-[5].

In order to optimize the both time dial setting (TDS) and plug

setting (PS) non-linear optimization were used. Among the

non-linear optimization sequential quadratic programming [6],

random search technique and gradient search technique [7] are

reported in literature. Conventional optimization techniques

have a drawback, some time they may trap to local minima

and fails to give global optimal solution. Moreover, as the size

of system increases the convergence is also weak.

Optimization algorithms based on artificial intelligence are

free from these drawbacks as seen in case of conventional

optimization techniques [8]. They are capable for handling

large size system with highly non-linear in both objective

function and in constraints sets. Genetic algorithm [9]-[10],

2012 IEEE International Conference on Power Electronics, Drives and Energy Systems December16-19, 2012, Bengaluru, India

978-1-4673-4508-8/12/$31.00 ©2012 IEEE

particle swam optimization [11]; hybrid non-linear

programming and genetic algorithm [12] are successfully

applied for optimization of relay coordination problem.

Application of Differential evolution algorithm for overcurrent

relay coordination is also reported in literature. [13].

In this paper, time multiplier setting and plug setting of

DOCR are optimized using Covariance Matrix Adaptation

Evolution Strategy (CMA-ES). LINKNET structure (using

only Far vector) is used for identify the backup pairs for each

primary relay, which eliminates the need of graph theory

approach. Application of CMA-ES algorithm for relay

coordination gives more promising result as compare to other

artificial intelligence (AI) algorithm. The proposed method is

tested for IEEE 30 bus system. It is seen that total summation

of primary relay operation time of DOCRs is optimized and

the number of mis-coordination pairs are also eliminated.

II. OPTIMAL OVERCURRENT RELAY PROBLEM

FORMULATION

In the relay coordination program, two types of tap settings,

namely current settings (PS) and time dial settings (TDS) must

be calculated [3]. The current setting for each relay is

determined by two parameters, namely the minimum fault

current and the maximum load current. For TDS and PS

calculation, objective function is optimized using optimization

technique. The objective function is sum of total operating

time of all the overcurrent relays installed at critical faults F1

and F2.

Fig.1. Near end far end fault

Normal Coordination Constraints (only overcurrent relay

coordination) [12]

1) Limits on Problem Variables:

I) Bounds on time dial setting (TDS) of each relay

maxmin

iii TDSTDSTDS ≤≤ (1)

min

iTDS and max

iTDS are minimum and maximum value

of TDS of relay iR .

min

iTDS and max

iTDS are taken as 0.025

and 1.2 sec.

II) Relay characteristic, Bounds on pickup current pI setting

of each relay

maxmin

pickupppickup III ≤≤ (2)

For standard IDMT relay, γ is 0.02 and α is 0.14

2) Limits on Primary Operation Time:

All of the primary operating time corresponding to each

possible fault location should be less than a maximum allowed

time delay and more than some minimum predefined time

considering transient conditions.

3) Coordination criteria (Selectivity Constraint):

Fault is sensed by both primary as well as secondary relay

simultaneously. To avoid mal-operation, the backup relay

should take over the tripping action only after primary relay

fails to operate. If iR is the primary relay for fault at k, and

jR is backup relay for the same fault, then the coordination

constraint can be stated as;

ttt kjki ∆=− ,, (3)

where, jit , is the operating time of the primary relay

jR , for

fault at k; kit , is the operating time for the backup relay iR ,

for the same fault at k, t∆ is the coordination time interval

(CTI) generally taken as 0.2 sec [14].

III. CMA_ES WITH DIRECTIONAL TARGET TO

BEST SCHEME

The Covariance Matrix Adaptation Evolution

Strategy (CMA-ES) is an improved strong

minimization strategy. By virtue of this algorithm

the full covariance matrix of the normal mutation

search distribution is adapted. The main feature of

the Covariant Matrix Adaptation (CMA) with

Evolution Strategy (ES) is the ability of being

invariant to landscape transformations and scaling

modulation [15]. The CMA-ES is also invariant to

applications of rotation, reflection and translation,

besides maintaining order and monotonicity. It

offers no discrepancy in behavior towards varied

nature of functions and is easily generalizable [9-

10].

Complexity of algorithm is largely reduced with

update schemes of CMA-ES and thus it offers an

extremely prospective mode of minimization in

single-objective function landscapes.

In CMA-ES λ individuals for the next are

updated by virtue of the equation:

2( 1) ( ) ( ) ( )~ ( , )g g g g

k Wx N x Cσ+

(4)

Where ( , )N Cµ implies a normally distributed

random vector with mean µ and covariance matrix

C.The update equation for these λ individuals can

be best approximated as:

)1,0(~),,( )()()()()()()(2

NDBxCxNgggg

w

ggg

w σσ + (5)

The recombination point ( )g

Wx is the weighted mean

of the selected individuals and is mathematically

defined as

( ) ( )

:1

g g

W i iix w x

µ

λ==∑ , where 0iw > for all 1....i µ=

and 1 iiw

µ

=∑ =1, and :i λ denotes the i -th best

individual.

The Algorithm depends of two types of adaptation

for the mutation parameters:

Adaptation of covariance matrix ( )gC .

Adaptation of global step size ( )gσ .

Directional Target to Best Scheme[16]:

Each member of the population is updated

according to the equation:

)()()1( _.( g

i

g

i

g

i XIndividualBestAXX −+=+ ) (6)

Where, Ar

is mathematically defined as:

If randuuuuur

be a normally distributed random vector,

i.e. (1, _ _ )rand randn No of Variables=uuuuur

then || ||

randA

rand=

uuuuurr

uuuuur and this is nothing but the unit

vector in the direction of the random normal vector

randuuuuur

.The ifitness is thereby updated.

This scheme efficiently guides the particles towards

globally best position in the fitness landscape. The

unit random vector in the direction of best

individual of the population ensures better

exploitation of thee landscape and converging on

global optima.

IV. IMPLEMENTATION OF PROPOSED

ALGORITHM

A. CASE STUDY

A Case study shown in Fig. 2 consists of 15 lines, 14 buses,

3 transformers, and 2 generators. LINKNET structure is used

to store the network configuration. It is very helpful for data

generation, updating and retrieval of data during the relay

coordination problem formulation. Another important

application of LINKNET structure is determination of primary

and backup pairs in a complex looped network. There are 30

digital overcurrent relays with IDMT characteristics and

tripping direction away from the buses is installed in

system. Faults are generated on each bus ends. If fault occurs

near a bus and relay on the same bus clears it, then this type of

fault is known as near end fault. If relay on the other end of

line clears the same fault, then it is known as far end fault.

Fig.2. IEEE 30 bus distribution system [17]

B. OPTIMISED RELAY SETTING

Time dial setting (TDS) and plug setting (PS) value are

optimized using CMA-ES with selected control parameters.

Optimal settings are tabulated in Table. I. The minimized

value of objective function is 18.59 using differential

evolution (DE) but CMA-ES gives more minimized value

15.8929.

Table.I. Optimal TDS and PS setting of overcurrent relays for IEEE 30 bus system

Relay DE CMA

Relay DE CMA

TDS PS TDS PS TDS PS TDS PS

1 0.15 0.25 0.1 1.5 16 0.9 1.35 0.9 0.85

2 0.05 0.25 0 0.25 17 0.05 0.25 0.05 0.25

3 0.05 0.25 0.05 0.25 18 1.05 1.45 1.05 0.75

4 0.05 0.25 0.05 0.25 19 1.1 0.7 0.9 0.85

5 0.05 1.3 0.05 1.3 20 0.05 0.3 0.05 0.25

6 0.1 0.25 0.1 0.25 21 1.1 0.5 0.65 1.15

7 0.05 0.9 0.05 0.85 22 0.15 1.15 0.1 1.1

8 0.05 0.6 0.1 0.3 23 0.1 0.45 0.1 0.45

9 0.05 0.25 0.05 0.25 24 0.05 1.5 0.05 1.5

10 0.05 0.25 0.05 0.25 25 0.05 0.25 0.05 0.25

11 0.05 1.5 0.05 1.5 26 0.3 0.25 0.25 0.3

12 0.05 1.45 0.05 1.2 27 0.05 0.25 0.05 0.25

13 0.05 0.9 0.15 0.35 28 0.45 0.25 0.15 1

14 0.05 0.25 0.05 0.25 29 0.2 1 0.25 0.35

15 0.4 0.3 0.15 1.2 30 0.1 0.25 0.1 0.25

Coordination time intervals (CTI) are tabulated in Table. II.

Positive value for each margin means there is sufficient time

margin for the backup relay operate and coordination of

overcurrent relays to overcurrent relays are well maintained.

Result is compared with optimized value obtained from

differential evolutionary. q is backup relay for each primary

relay p. Maximum value of CTI is 0.8 and minimum value is

0.2 using CMA-ES optimization. While for same value of

objective function the upper limit of CTI are violated when

differential evolution algorithm is used.

Table.II Coordination time interval for IEEE 30 bus system

p q CTI

p q CTI

CMS-ES DE CMS-ES DE

1 7 0.21207 0.24852 16 19 0.23157 0.20143

2 1 0.86713 0.91471 17 30 0.20716 0.20716

3 7 0.95704 1.18960 18 16 0.23767 0.22753

4 1 0.75871 0.95482 19 21 0.21624 0.30107

5 1 0.55315 0.74926 20 18 2.41672 3.19732

6 1 0.60860 0.80472 21 18 0.20654 0.26113

7 8 0.21464 0.22584 22 29 0.23019 0.21177

8 7 0.75635 1.07038 23 26 0.20744 0.26825

9 5 0.20394 0.20394 24 26 0.69703 0.77918

10 6 0.23239 0.23239 25 23 0.20964 0.20964

11 13 0.25396 0.28180 26 29 0.35743 0.71393

12 5 0.23032 0.20902 27 29 0.57185 0.98916

13 12 0.27358 1.49137 28 22 0.20475 0.21777

14 5 0.28473 0.28473 29 15 0.21755 0.22672

15 28 0.22757 0.29969 30 28 0.43501 0.79060

CONCLUSION

Overcurrent relay coordination in an interconnected

distribution system with heavily meshed distribution system

becomes complex problem. Multiple backup relays are

identified with the help of LINKNET structure. Coordination

problem becomes more complex, when relay setting are

optimized for near and end far end faults simultaneously for

bidirectional power feed networks. Proposed CMA-ES

algorithm is applied for IEEE 30 bus distribution system and

result are compared with other AI optimization algorithms.

The performance of proposed algorithm is better as compare

to DE algorithm proposed earlier.

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