Fuzzy decision-making model to determine the parameters for intelligent design of power system protection

L.F. Liu Z.D. Gao Q.X.Yang B.Z. Liu

Indexing terms: Protection design, Parameters decision, Expert system, Fuzzy theory

Abstract: There are many parameters involved in every aspect of power system protection design. Many of them need to be determined unequivocally. However, in practical engineering, both the factors affecting them, and the design knowledge to determine them, may contain uncertainties, which result in fuzziness of the parameters and defects in the design quality. The paper proposes a fuzzy decision-making method for an expert system to deal with the uncertainty of the parameters decision both in knowledge representation and in the inference model. An application of the decision-making system is presented, demonstrating that the method is reasonable and effective. The model proposed has been incorporated into the design of an expert system, greatly extending the capability and scope of intelligent design.

1 Introduction

On the basis of expert system (ES) technology, intelli- gent computer-aided design (ICAD) is much more widely used in the machine and architecture industry [I] than in the power system industry since the latter has much more complicated design knowledge. It is exciting that recently the application of ES has begun to increase in power systems, for power system plan- ning [2, 31, designing electrical auxiliary systems of power plants [4], designing and testing substation ground grids [5 ] and so on. With respect to power sys- tem protection, only protective relay setting and co- ordinating for transmission lines has attracted research- ers’ attentions [6, 71; but now the authors have devel- oped a practical expert system for power transformer protection design 181, which can determine the protec-

0 IEE, 1998 IEE Proceedings online no. 19981732 Paper first received 26th November 1996 and in revised form 9th September 1997 L.F. Liu, Z.D. Gao and Q.X. Yang are with the Electrical Power Department, North China University of Electric Power, PO Box 18, 071003, Baoding Hebei, People’s Republic of China B.Z. Liu is with the North China Electric Power Design Institute, Beijing, 100043, People’s Republic of China

tion system, choose the protective modes, deploy cur- rent transformers (CTs), potential transformers (PTs) and relays, calculate CT turn-ratios, 5;et and select relays from relay manufacturer’s catalogues, and pro- vide a database to present designs graphically. How- ever, with the expert system operation we have found that some design tasks need considerable user interven- tion since the expert system had no fuzzy decision mak- ing mechanism.

In fact, uncertainties exist everywhere in the whole of the design process, and the more fuzzy knowledge we can handle, the better the design results we can achieve. Therefore, a key to the application of intelligent design for power system protection lies in how to represent and deal with fuzzy knowledge. Fuzzy set theory [9, IO] provides a suitable way of solving the problems. This paper proposes a fuzzy decision-making method for an expert system, to deal with the uncertainties of the determination process of the parameters both in knowl- edge representation and the inference: model. The expert system incorporated with the model is not only able to achieve the function proposed iin [SI, but also can deal with the fuzzy decision for the parameters, which greatly extends the design scope. The expert sys- tem developed is applied to design work. of the North China Electric Power Design Institute (NCEPDI) to check its operation.

2 Fuzzy knowledge to determine the parameters in protection system design

In protection design, some parameters need to be deter- mined in unequivocal values, such as safety factor, sen- sitivity factor and motor starting factor, etc. Nevertheless, there is no specific formula other than those gained by experience to determine them, which may result in only vague solutions of the parameters. For example, when designing the overload protection for a distribution transformer, we should set the oper- ating current Iset in order to choose suitable relays. I,,, is usually determined from the relation

Iset == K , Km I , where, Z, is the rated current through thLe transformer, Ks is a safety factor ranging from 1.2 to 1.3, and K, (ranging from 1.5 to 8 ) is the motor starting factor of the adjoining load, which indicates the effect of motor starting current. Obviously, to set I,,, we must deter- mine the factors K, and Km first, which generally relies

(1)

169 IEE ProcGener . Trunsm. Distrib., Vol. 145, No. 2, March 1998

on experience. According to experience, we summarise the mine the parameter K, in Table 1.

Table 1: Decision-making experience for the parameter

ign handbook and n method to deter-

Km

Feature of the adjoining load of K, range

Range General rules to set K, in each

Pure power load with a single 4-8 motor

Pure power load with multimotors

Synthetic load 1.5-2.5

2-3

1 I The longer the loss-voltage time, the bigger K, 2. The longer the load distance from the source the smaller K, 3 The larger the power load ratio, the bigger K, when the load is synthetic

Table 1 shows that the range of K, is dependent on the adjoining load, and by use of the general rules in the table we can obtain a solution. However, the rules are vague, and the environment factors, such as ‘loss- voltage time’ ‘load distance’ and ‘power load ratio (the ratio of the power load part to the whole load)’ affect- ing the parameters may be fuzzy too, which will cer- tainly result in vague solutions. For instance, during practical design the value of the factor ‘load distance from the source’ is often given in a fuzzy linguistic term such as ‘longer’ but it should be crisp. Then by the rules in Table 1 only the vague value ‘smaller’ will be obtained for K,. It is necessary for designers to select an unequivocal value for the parameters by means of qualitative and quantitative analysis. With respect to an expert system, the analysis is called ‘fuzzy decision- making’. Parameter decision problems are numerous in electrical engineering design and we describe them as follows.

3 Fuzzy representation of the parameters

Let the range of the parameter y’ be P’ = [Pa, pb] (i.e. the set of decision alternatives or decision space), its discrete form be P‘ = (p’,,, ..., p’,) and all of the fac- tors affecting the decision making compose the uni- verse discourse D = (dl, d2, ..., d,). Then the problem is to synthetically evaluate D and determine p’ over P’, i.e. to map the factor set D into P’. In order to build consistent fuzzy decision-making model, we normalise the decision space from P = Qfn, P ’ ~ , ..., p’,) to P = bo, P I , ...> pn) E [O, 11:

(2) For example, let n = 10; P will be (0, 0.1, 0.2, 0.3, ...,

During electrical design, the set of the fuzzy linguistic terms, M ( t ) = (‘small’, ‘smaller’, ‘medium’, ‘bigger’, ‘big’) = ( t l , t2, t3, t4, ts) , is more often used to describe the parameters than the universe set P, where t , is a fuzzy subset in P. Thus the proposition ‘Km is t’z, can be characterised by a possibility distribution. Let p be a variable taking values in P and F be a fuzzy set in P. F has a fuzzy restrictive function Vb), associated with p , which forms a possibility distribution function denoted as n,(p). n, is defined to be numerically equal to the membership function ,LA) of F, that is zp = ,up Then

0.9, 1.0).

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the proposition 9 is smaller’ associates with y the pos- sibility distribution: 7rp = 0.8/0.1+1.0/0.2+0.8/0.3+0.5/0.4+0.1/0.5 in which a term such as 0.810.3 signifies that the possi- bility that p is 0.3, given that p is smaller, is 0.8. Gener- ally, there is a point p = c in P malting n (e) greatest (i,e. zp(c) = 1). The point c is called the core’ of the fuzzy set F, about whlch a possibility distribution np(p) can be constructed by choosing fuzzy restriction func- tion V(x):

P

V(Z) = max{0,1 - Imlb) ( 3 ) where, we choose a = 3, b = 2, with respect to the five fuzzy subsets in M(t), five ‘cores’ are defmed by ck E

(0, 0.2, 0.5, 0.8, 1 .O). Possibility distribution functions of these are described as

‘ i ~ ~ ( c k ) = max(0, I - 9(p - Q ) ~ } p E P, k = 1 , 2 , 3 , 4 , 5 (4)

Fig. 1 shows the curves of zp(ck). By virtue of normali- sation of the parameter range, during fuzzy reasoning the inference engine will add automatically zp(ck) corre- sponding to the term tl,. For instance, with respect to ‘smaller’ described as the fuzzy subset t2, the distribu- tion function zp(c2) = max {(I, 1 - 9@ - 0.2)2) will be added automatically.

tl t,=np(c,) 5 t4 t5

0 4 -Tsx5z.r 0 2 0 0.2 0.4 0.6 0 8 1 0

D

Fig. 1 Curves of the possibility dis~nb~tion functions

4 rules

Representation of the parameter decision

In the decision-making process of the protection parameter we found that some knowledge could be expressed in three kinds of rules as described in the fol- lowing subsections.

4. I Rules for determining the set of the decision alternatives P‘ Generally, the rules to determine the decision alterna- tives can be obtained from design handbooks. By means of them we caii narrow the search space of the parameter. The rules are defined as:

rule range: If D’ = ( d i , d i , . . , d $ ) Then (select P’ = b a , p b ]

as a value-range) ( 5 ) where D’ is the set of factors affecting the decision alternatives P’. For example, the knowledge listed in Table 1, ‘If the feature of the load is synthetic load, then the search range of IC, is P’ = [1.S, 2.5]’, should be expressed by rule eqn. S.

4.2 Rules for mapping the factors set D into P Let D = (dl, d2, ..., d,) be the set of factors affecting the solution. A mapping rule ri is used to determine the

IEE Proc -Gener Transm Distrib , Vol 145, No 2 March 1998

fuzzy solution of the parameter p corresponding only to a single factor dz, i.e. to map the factor d, into the decision alternatives P to form the solution distribution np. We propose the rule with a variable:

If (d, = t J ) Then select ( p = tq , ) ) and ( T ~ ( C ~ ( ~ ) ) )

rule map:

(6) where t, is a variable taking its value from the linguistic terms set M(t) defined above, and k(j) is function o f j according to the form of rule r,:

when r, has the form ‘the more, the bigger’ when r, has the form (7) k ( J ) = 6 - J (I ‘the more, the smaller’

wherej = 1, 2, 3 , 4, 5. In this way, the number of deci- sion rules can be reduced significantly. For instance, let the factor ‘load distance from the source’ be d2, thus the rule ‘The longer d,, the smaller K,’ can be con- verted into

rule map 2: If (dz = t,) Then select ( p = t6--3) and ( ‘ i ~ ~ ( c g - ~ ) )

( 8 )

4.3 Rules forming the weight matrix W The rules to form the weight matrix W are represented as:

rule W: If D = ( d l , & , . . , d m ) and D ’ = (d i ,db , . . . , d:)

Then (W = (w1, w2,. . . , w,)) (9) where

m

and z = 1

Weight w,, determined according to expert experience, signifies the relative importance of factor d, in the deci- sion making.

5 for the parameters

Having converted some knowledge for decision making into the rules mentioned above, it is necessary to build subroutines for normalisation of the range, fuzzy syn- thetic evaluation of the multifactors, and determination of the crisp solution, etc. We propose a decision-mak- ing process to solve the problem as follows. Step 1. Classification of the factors to affect the deci- sion. Initially, the user of the expert system inputs the states of the factors set D’ = (d , , dZ, ..., d,) affecting the decision alternatives, and D = ( d l , d2, ..., d,) stand- ing for those to decide the solution of the parameter. Step 2. Determination of the set of decision alternatives P’ by the rules (eqn. 9, then build the discrete and nor- malised set P according to eqn. 2. Step 3. Mapping a single factor into P. Generally, each factor d, is combined with a mapping rule (eqn. 6), and from each rule r, by which we can get a fuzzy subset t k and its distribution function zp(clc) denoted by vector R,

Step 4. Building the relation mapping matrix R. Com- bine all of the distribution vectors R, into the matrix R that represents the mapping from the factors set D into

Fuzzy decision-making procedure and model

- ~ (?io> ril, VIZ, ‘ 7 .in> on P.

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the solution space P:

. . * J . . . . . . . . . . . . TmO rm1 rm2 ‘ ’ . rmn

(10) Step 5. Determination of the fuzzy sollution B of the parameter. As a result of the factor <jets D, D’ and weight rule eqn. 9, weight matrix W can be formed. According to the fuzzy mapping principle [lo], the fuzzy solution B, called the synthetic fiuzzy evaluation matrix, can be described as follows:

B = W @ R = = [ b o bl . . . b,] b, = w1q3 + 1 0 2 ~ 2 , + . . . + w,rm3

Step 6. Determination of the crisp solution pmax of the parameter in P. We can map the fuzzy ,subset B, which is only a fuzzy solution of the parameter, onto the crisp one. In order to make the solution pmax both unequivo- cal and reasonable, we make full use of all information obtained (i.e. we do not exclude the influence of factors with a smaller contribution to the possibility distribu- tion B), and we define the following evaluation func- tion which equals the crisp normalised solution:

3 = 0 , 1 , 2 , ” ’ , 71. (11)

n n n

J=O J=O J=O

Step 7. Determination of the actual solution in P’. By eqn. 2 we can convert the normalised solution pcnax in P into the actual solulion plmax.

( assign the value of the factor sets D’, D )--

Y determine the specific search range P 7 Y convert P into discrete and normalised P 7

( combine Ri into the fuzzy relation matrix R )

display W and adj:sting W, manually 7- ( determine the fuzzy distribution solution B

r------ evaluate the crisp normalised solution P,, 7

satisfied ? P (‘ output solution Pma )

Fig. 2 Fuzzy decision-muking proceduture for purumt?ters

The seven stages mentioned above make up the whole fuzzy decision making procedure shown in Fig. 2. The user is requested to do no more than input

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the states of the factor sets D’ and D. The system will reason the solution out automatically. Of course the user can interfere in the procedure when an acceptable solution is not obtained, caused by unreasonable weight w, or incorrect factors d; and d’i. The knowledge utilised in the process can be incorporated into design- ing an expert system as a fuzzy decision-making model comprising a fuzzy database, a decision rule base and some decision programs, as shown in Fig. 3. The capa- bility of the system is demonstrated in the application example next Section.

‘ decision- making procedure base, subroutine for making the range discrete and normalised subroutine for formng fuzzy relation matrix R fuzzy synthetic evaluation function subroutine for forming crisp and actual solution

inference engine precise knowledge base,

database

==I

rule base procedure base

fuzzy decision-making knowledgo base: fuzzy parameter database parameter decision making rule base

determination of the parameter- -Km

Fig. 3 Expert system with f i z zy decisiort-mdking model

6 Application example

The expent system with the fuzzy decision-making model developed in the preceding Sections is imple- mented on a 486iDX2-50 personal computer using ESTEDW (Expert System Tool for Electrical Design within Windows) developed ourselves. It has been applied to the parameter determination of a protection system design for power transformer and generator. Now we take Table 1 as an example again to determine the motor starting parameter K, when the expert sys- tem designs a protection system for a distribution transformer.

load feature: I synthetic 1-1 loss-voltage time:

load distance:

power load ratio’

Fig. 4 Dialogue frame for value assignment of the factors

The execution of the expert system is an interactive process. When the design work gets access to selection of an overcurrent relay for overload protection, in order to calculate the settings of the relay, the system

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displays a dialogue frame for the user to input some necessary information, as shown in Fig. 4.

The dialogue frame explains to the user what the sys- tem is doing, afld provides drop-down list boxes to enable choice of a suitable value for each factor.

Having answered the questions displayed in Fig. 4, all the factors affecting KM are classified into two sets. One set is

where dl stands for the factor ‘load feature’, and its lin- guistic value is

Another set is

D’ = ( d i ) (13)

d i = ‘synthetic’ (14)

D = (dl, d2, d3) (15) where dl stands for ‘loss-voltage time’, d2 for ‘load dis- tance’ and d3 for ‘power load ratio’ and they have been assigned the following vague values:

dl = ‘longer’ dz = ‘longer’ dy = ‘large’ (16) Then the data drive the inference engine to match the

rules in the decision rule base. As a result the following rule is activated:

Rule range 5: If (dl = ‘synthetic’) Then (pa = 1.5) and (Pb = 2.5) and Call DAN ba, pb)

By the rule the decision alternatives P of Km is deter- mined:

P’ = b,,pb] = [1.5,2.5] (17) then calls the subroutine DAN( ) to obtain the discrete and normalised form P:

P = (0,0.1,0.2,0.3, ,0.9,1.0) (18) and the relation between variable p’ E P’ and p E P:

P = ( P ’ - P a ) / ( p a - P b ) = P ’ - 1 5 (19) The next step is to map each factor affecting the

solution of K, into P and form the corresponding dis- tribution vector R, by the following rules:

Rule map 12: If (d, = tJ) Then (p = tJ) and Call DVR(p, RI)

Rule map 13: If (d2 = tl) Then (p = t6J and Call DVRb, R2)

Rule map 14: If (d3 = 5) Then (p = 5) and Call DVR 01, R3)

where 5 is a variable corresponding to the input data d,, and subroutine DVR( ) is called to produce the vec- tor R, representing the distribution function np(ck0).

By Rule map 12, tJ = ‘longer’, selecting mapping valuep = tJ = ‘bigger’, we obtain RI:

RI = (0,0,0,0,0,0.19,0.64,0.91,1.0,0.91,0.64)

R, and R3 can also be obtained by Rule map 13, Rule map 14. Combine all Ri into the relation mapping

(20)

mafrix R:

R = c RZ R1

L R3

lo 1 0 0 0 0 0.19 0.64 0.91 1.0 0.91 0.64

0.64 0.91 1.0 0.91 0.64 0.19 0 0 0 0 0

0 0 0 0 0 0 0 0.19 0.64 0.91 1.0

(21) = L

IEE Puoc.-Gener. Tuansm. Distrib.. Vol. 145, No. 2, March 1998

On the other hand, the following rule for weight matrix W is matched:

Rule W 7: If (dl = ’synthetic’) and (d2 = ‘longer’) Then W = (0.2 0.4 0.4) and W is assigned by the rule. Then the system displays the results of W as shown in Fig. 5.

=3 determination of the parameter- -Km

you can adjust the weight w, to change the relative importance of factor di affeaing the decision making process,

default modified

w, for ‘loss-voltage time’: 0.2

w2for ‘load distance’: 0.4 I 0.4 I w3 for ‘power load ratio’: 0.4 I 0.4 I

[OK] [,,,,,I] (help]

Fig. 5 Dialogue frame for value adjustment of the weights

The default values of W are obtained by activating the weight rules, and the user can modify them accord- ing to own experience. If the default values are accepted, press the key OK directly and the weight matrix W is available. Then determine the synthetic fuzzy solution matrix B by eqn. 11:

B = (0.256 0.364 0.4 0.364 0.256 0.114 0.204 0.438 0.564 0.582 0.492)

(22)

(23)

Using evaluation function eqn. 12, we get the crisp solution:

p,,, = 2.28114.034 = 0.565 Finally, according to the relation eqn. 19 the actual parameter solution is determined:

Km = pmax - p,,, + 1.5 = 2.065 (24) Various cases are summarised in Table 2. The

weights come from the experience of the experts at NCEPDI. The results show that the values of design parameters can be determined exactly and are approxi- matly the same as the values (in brackets) evaluated qualitatively by the design experts.

Although the application example is for the design of overload protection for a distribution transformer, the method can easily be applied to more complex protec- tion systems. The authors have demonstrated the flexi- bility and effectiveness of the method by designing the differential protection system for a generator-trans- former set. The safety factor and nonperiodic factor of

1 -

the protection were determined successfully. In order to realise the mechanics, the fuzzy decision-making proce- dure base in Fig. 3 has been incorporated into the design expert system, and the corresponding fuzzy parameter data base arid decision-making rule base have been built up. Applications show i.hat the greater the number of factors affecting the parameter, the more obvious the advantages of the method.

However, the effectiveness of the method greatly depends on reasopable factor weights and decision- making rules. The knowledge engineer must consult with skilled designers to determine them.

7 Conclusions

Table 2: Executed results of the proposed system

With respect to the characteristics of power system protection design, the authors describe the recently developed technique of fuzzy decision-making in deter- mination of parameters. The proposed technique can easily handle the uncertainty factors and knowledge to determine some fuzzy parameters in the process of intelligent design based on an expert system. A fuzzy decision-making model with qualitative and quantita- tive analysis is incorporated into the expert system in order to make the design more reasonable and efficient, and to greatly enlarge the design scope the expert sys- tem can deal with. This ensures that the design method is not only suitable for 1 he elements arid transmission line protection but also can be spread to the whole electrical engineering design. Nevertheless, the mechan- ics proposed cannot handle all fuzzy design knowledge yet, and must be considered a first step. Other fuzzy knowledge, such as fuzzy rules and facts of design will be tackled in the near future.

8 References

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6

7

Synthetic load P = [1.5, 2.51 A motor load P = [4,81 Factor

9 wj K,,, tj wj Km tj wj Km

Loss-voltage time longer 0.2 longer 0.3 longer 0.4

2’303 shorter 0.6 (2.3)

Load distance longer 7.147 (7.0) 2’065 shorter 0.4

0.4 (2.0) . . - - Power load ratio large 0.4 large 0.3

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