tabu search approach to alarm processing in power systems

Tabu search approach to alarm processing in power systems

F.S.Wen C.S.Chang

Indexing terms: Alarm processing, Genetic algorithm, Tabu search , Set covering theory

Abstract: A tabu search (TS) based approach is proposed for alarming processing in power systems. First, several existing evaluation criteria describing the alarm processing problem are briefly discussed, and a new criterion is proposed. Secondly, a novel method is developed to solve this problem using a TS based method. Finally, two examples are used to demonstrate the feasibility and efficiency of the developed method. The paper also presents a comparison between the developed TS based and the more established genetic algorithm (GA) based approaches to the alarm processing problem. Many simulation results show that the TS-based approach is more efficient than the GA based approach. Key features of this proposed method are that it has solid mathematical foundation and can find multiple global optimal solutions directly and efficiently in a single run. This is very suitable for complex alarm processing problems especially for situations with missing or false alarms, because different combinations of events can produce the same set of alarms under these circumstances. The test results suggest that the developed TS based method is promising.

List of symbols

e = event a = alarm E, As ne n, D M C = matrix reflecting the characteristic relation

M+ = subset of M which identifies the observed

= system set of events = system set of alarms = number of possible events = number of possible alarms = finite nonempty set of disorders (events) = finite nonempty set of manifestations (alarms)

between events and alarms

manifestations (alarms)

0 IEE, 1997 IEE Proceedings online no. 19960716 Paper first received 5th February 1996 and in final revised form 15th May 1996 The authors are with the Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore

hypothesis expressed in a vector form of ne elements actual state vector of all possible alarms which identifies the reported alarms simulated state vector of all possible alarms if E applies trial solution vector to an optimisation problem current solution vector single move exchange move best solution vector for the alarm processing problem maximum permitted iteration number for the tabu search tabu tenure neighbourhood sampling number in each iteration of the tabu search

1 Introduction

The alarm processing problem is to interpret a large number of alarms in a control centre under stress con- dition. The objective for developing an alarm processor is to help operators to understand what has happened in abnormal situations by providing a summary of synthesised information instead of a flood of raw alarm data. In other words, it is to find which event(s) can cause the reported alarms. The problem is not directly concerned with the locations of the fault(s) or malfunc- tioned devices [l, 21. The early alarm processing method [I] established the logical tables to define, in Boolean form, the relationship between the event occurrence and the related alarm patterns at first. It then uses these logical tables and the reported alarms to determine the appropriate events. The principal dis- advantage of this method is its lack of flexibility: each state is defined in terms of specific instances of devices and database points. In recent years, the alarm processing problem has been an active research area, and several new methods have been developed [3-111, such as the filtering, prioritising and grouping based [3], the expert system based [4-81, the pattern recognition technique based [9], and the artificial neural network based [IO, 111 methods. Of these methods, the expert system based method is the most established. The filtering, prioritising and grouping method [3] can reduce the number of alarms significantly, but it can not easily be used to obtain synthesised alarms of high information content. The feasibility of expert system applications to

31 IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. I , January 1997

the alarm processing was identified by Wollenberg [4]. Following his pioneer contribution, much research work on this respect has been done [5-8]. By utilising the heuristic knowledge and logic inference to process raw alarms, this kind of methods can obtain both the summary and synthesised alarms, and can conclude the event occurrence. Up to now, many expert systems have been developed using the conventional knowledge representation and inference procedure such as the rule based [4-61 and model based [7, 81 approaches. To achieve precise inference especially in the complex cases, the expert system based on production rules must involve a great number of rules describing the complicated system behaviour. Maintenance of the large knowledge base is very difficult. On the other hand, the model based system is easy to maintain, but the inference process is time consuming. Several authors have suggested that the alarm processing problem can be treated as a classification problem, and can be solved by pattern recognition techniques [9] or artificial neural networks [lo, 111. The main advantage of these two kinds of methods is that they are easily implemented by various electric utilities with minimal customisation effort. Although some test results based on small systems show that these two kinds of methods can come to correct conclusions with high probability, the correctness cannot be guaranteed theoretically. Moreover, these two kinds of methods can find one optimal solution at most, but multiple optimal solutions may exist for the alarm processing problem especially for the situations with missing or false alarms. This is because different combinations of events can cause the same set of alarms under these circumstances.

Although much work has been done on the alarm processing problem, the essential problem is still not well solved, that is, how to describe this problem in a reasonable and strict mathematical manner. In [7], a formal description to this problem is presented, and two criteria reflecting the objective of the problem are developed. It is pointed out in [I21 that these two criteria are not versatile for any power systems. A new criterion is proposed in [12], but as for the two criteria developed in [7], it is also intuitive and subjective. A probabilistic criterion is introduced in [ 131 to describe the alarm processing problem, which is deemed more reasonable than the criteria developed in [7, 121. Regretfully, this probabilistic criterion employs some probability information of the occurrence of events, which is not easy to obtain.

Recently, a new method is proposed to solve the alarm processing problem using a genetic algorithm (GA) in [12, 131. The fundamental principle of this method is to formulate the alarm processing problem as an optimisation problem and to solve it using a global optimisation method such as GA. Although the work presented in [12, 131 is preliminary, the simulation results have shown that this method is promising.

In this paper, a new method to the alarm processing problem in power systems is developed based upon the tabu search (TS) technique [ 14-22]. The work presented in [l2, 131 is further developed, and a new criterion to describe the alarm processing problem is presented. The main contributions of this paper include the following two aspects. First, a new criterion to describe the alarm processing problem based upon the well developed parsimonious set covering theory [23, 241 is proposed. This criterion is more reasonable than those

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developed in [7, 121, and does not employ any probability information as in [13]. Secondly, the alarm processing problem is formulated as a unconstrained 0- 1 integer programming problem, and a TS-based method is developed for solving this problem. TS is a heuristic search strategy for efficiently solving combinatorial optimisation problems, and has achieved impres- sive practical successes in extensive application areas [1422]. Two sample studies are served for testing the developed TS-based alarm processing method. It is shown by many simulation results that this method is efficient and can find multiple global optimal solutions directly and efficiently in a single run. This is very suitable for complex alarm processing problems especially for the situations with missing or false alarms, because different combinations of events can produce the same set of alarms under these circumstances. Moreover, the comparison between the developed TS-based and the existing GA based [12, 131 alarm processing methods has also been carried out, and it is shown by many simulation results that the developed TS-based method is more efficient than the GA based method.

2 processing problem

Before proceeding to describe the alarm processing problem, it is necessary to define the alarm and the event. The description of an alarm is a matter of inter- pretation and differs from utility to utility. The most commonly used descriptions for an alarm are [7]: (a) an analogue value measured by a transducer exceeds a limit, (b) a digital value changes state, and (e) an application program generates message. An event 1s usually referred to a disturbance which can cause a group of alarms to be emitted. These alarms make up an alarm set (the system set of alarms), and all possible events make up an event set (the system set of events). The relationship between an event and its corresponding alarm pattern can be described as [7]

Mathematical description of the alarm

e, + A, 2. = 1 , 2 , . . . ,ne (1)

e, E E, (2)

A, = (~~k1.k E A, A k E N A } ( 3 )

with

where e, is an event i. A, is the associated characteristic set of alarms. The symbol - denotes the relationship between e, and A,. ne is the number of possible events. E, is the system set of events. A, is the system set of alarms. NA = { 1,2, ..., nu}, and nu is the number of possible alarms.

Eqn. 1 says that an event can produce a set of characteristic alarms. Now, the alarm processing problem can be described as follows: provided a set of reported alarms denoted by A, and A C A,, the goal is to determine which event(s) can explain A. When the reported alarm set A is one of the predefined characteristic alarm set A, introduced in eqn. 1, the answer to this question can very easily be given, that is, e,. In practice, however, the set A may match none of the characteristic alarm set A, exactly. Thus, some criteria should be specified to reflect how well an event or a combination of events can explain a set of reported alarms, or in other words, how to define the word ‘explain’.

Although the problems of alarm processing and fault

IEE Proc -Gener Tvansm Distrib , Vol 144, No 1, January 1997

diagnosis have different meanings in the power system community, from the viewpoint of an artificial intelligence (AI) community, the alarm processing problem is a typical multiple fault diagnosis (MFD) problem [23-251. The ‘event’ and ‘alarm’ in the alarm processing problem as stated above correspond to the ‘disorder’ and ‘manifestation’ in the MFD problem, respectively. There is much in the theory and methods from the MFD area that we can make use of for solving the alarm processing problem. Thus, we can examine first which criteria have been used in the MFD problem, and then develop a suitable criterion to the alarm processing problem according to the features of the problem.

2.1 Parsimonious set covering theory for the multiple fault diagnosis problem The multiple fault diagnosis problem can be defined as a 4-tuple: <D, M, C, M+> where D = {d,, ..., dn] is a finite nonempty set of disorders (events), M = {m,, ..., mk} is a finite nonempty set of manifestations (alarms), and C is a relation expressed in a matrix form to reflect the relation between events and manifestations. For the alarm processing problem, C reflects the characteristic alarms corresponding to each event. M+ is a subset of M which identifies the observed manifestations (reported alarms). Note that manifestations not identified in M+ are assumed to be absent.

One of the leading theories for the MFD problem is based upon the notion of parsimoniously covering a set of observed manifestations (reported alarms), M+. The premise of the parsimonious covering theory is that a diagnosis hypothesis must be a cover of M+ in order to account for the presence of all manifestations in M+ [23, 241. However, not all covers of M+ are equally plausible as the hypotheses for a given problem. The principle of parsimony, or Occam’s Razor, is adopted as a criterion of plausibility: a ‘simple’ cover is prefera- ble to a ‘complex’ one. Therefore, a plausible hypothesis, or an explanation of M+, is defined as a parsimonious cover of M+, that is, a set of disorders (events) that covers M+ and satisfies some notion of being parsimonious or ‘simple’. Thus, an essential problem in this theory is: what is the nature of ‘parsimony’ or ‘simplicity’? or, in other words, what makes one cover of M+ more plausible than the other? Math- ematically, this problem is equivalent to how to define a suitable criterion to describe ‘parsimony’. Up to now. several different criteria have been proposed [24], such as: (i) single disorder restriction. A cover D, of M+ is an explanation if it contains only a single disorder; (ii) relevancy. A cover D, of M+ is an explanation if it only contains the disorders that causally associate with at least one of the manifestations in M+; (iii) irredun- duncy. A cover DI of M+ is an explanation if it has no proper subsets which also cover M+, or in other words, removing any disorder from DI results in a noncover of M+; (iv) minimality. A cover D, of M+ is an explanation if it has the minimal cardinality among all covers of M+, that is, it contains the smallest possible number of disorders needed to cover M+.

2.2 Evaluation criteria for the alarm processing problem Obviously, the single disorder (event) restriction criterion is not suitable for the alarm processing problem, because multiple events may occur

IEE Psoc-Gener. Trunsm. Dzstsib.. Vol. 144, No. 1, Junuury I997

simultaneously. On the other hand, the relevancy criterion is not a good one for our problem, because it is too loose and may result in many solutions. This criterion is used in [7], and has been claimed to be an irrational one in [12]. The irredundancy criterion is generally quite an attractive one. Unfortunately, there are two difficulties with directly generating the set of all irredundant covers [24]. First, this set may itself be quite large in some applications, and may contain many explanations (solutions) of very little probability. Secondly, and more serious, it may still miss identifying the most reasonable solutions in some cases. The minimality criterion is intuitively a reasonable criterion, because the occurring probability of complex events is generally smaller than that of the simple events. This criterion is also used in [7]. But in fact, the minimal covers are not always the most reasonable ones. For example, the simultaneously occurring probability of two common events may be greater than that of a rare event, thus this criterion will result in incorrect results for this case. The probabilistic criterion introduced in [13] is mathematically sound, but it requires some probability information which is not easy to obtain from actual power systems.

An also noteworthy criterion is presented in [12], which is beyond the category of the parsimonious covering theory. This criterion suggests that a reasonable solution to the alarm processing problem should be an event or a combination of events which causes some alarms of the minimum amount of inconsistency with the reported alarms. Different from the criteria stated above, this criterion allows one or more manifestations (alarms) unexplained. In other words, it is deemed possible that the presence of one or more manifestations (alarms) may not be the result of any disorder (event), that is, some manifestations (alarms) may be incorrect.

It is our opinion that the minimality criterion and the criterion developed in [I21 reflect the requirements of the alarm processing problem in two different aspects. Thus, if we can combine these two criteria in a reasonable way, a better criterion than these two can be obtained. This will be dealt with in the following Section.

2.3 New criterion for alarm processing problem In our opinion, a reasonable solution or set of solutions to the alarm processing problem should reflect the following three requirements: (i) It is a cover of M+. This is because the occurrence probability of false alarms is small. (ii) The characteristic alarms corresponding to the event or events in a solution or solutions should be consistent with the reported alarms as much as possible. This reflects the requirement of the criterion developed in [12]. (iii) The solution or solutions with a minimum number of events are preferred to the more complex explanations. This reflects the requirement of the minimality criterion.

A criterion reflecting these three requirements is a modified minimality criterion. and can be described mathematically as follows: To minimise f ( E ) = w,lVAI + walAAl + w31El (4)

where E is a hypothesis expressed in a vector form of ne elements. Each element in vector E represents the state

33

of an event included in E,, and takes the value of 0 (if the appropriate event is assumed not to have occurred) or 1 (if the appropriate event is assumed to have occurred). jEl denotes the number of nonzero elements in E.

The other symbols are defined as follows: VA is a vector of na elements, and is determined by

two other vectors A, and Am(E). A, is the actual state vector of all possible alarms (or

the system set of alarms). Each element in A, takes the value of 0 (if the appropriate alarm has not been reported) or 1 (if the appropriate alarm has been reported). A, represents the reported alarms.

A,(@ is the simulated state vector of all possible alarms if E applies. Each element in Am(E) takes the value of 0 (if the appropriate alarm does not belong to the characteristic set of alarms associated with the event E ) or 1 (if the appropriate alarm belongs to the characteristic set of alarms associated with the event

VA is determined using the following method: if the jth element in A, is 0, then set thejth element in VA to be 0; if the jth elements in A, and Am(E) are both 1, then set thejth element in VA to be zero, otherwise to be 1. IVAI denotes the number of nonzero elements in VA.

AA is a vector of n, elements, and AA = A, - Am(@. IVAI denotes the number of nonzero elements in AA.

IVAI is a criterion to reflect if a solution of eqn. 4 is a cover of A,. If yes, lVAl = 0, otherwise IVAI reflects the proximity of a solution to a cover. The smaller is IVAI, the more proximate to a cover the solution is. lAAl reflects the inconsistency between the reported alarms and the characteristic alarms corresponding to E. The smaller lAAl is, the more consistent the expected states and the reported alarms are. They are fully consistent when lAAl = 0. lEl represents the number of occurred events in E. The three terms at the right hand side of eqn. 4, respectively, reflects the three requirements for a solution or solutions to the alarm processing problem as stated above.

w1 to w3 in eqn. 4 are positive weighting coefficients to reflect the relative importance of the three requirements as stated at the beginning of this subsection. It is our opinion that the priorities of these three requirements should decline progressively, so w1 through w3 should be specified to decrease successively. w1 should be big enough, and be specified as the biggest among these three coefficients to ensure that the solution or solutions of eqn. 4 is a cover or covers of A,. in this work, wl, w2, and w3 are specified to be 100, 10 and 1, respectively, and these values should be applicable for the alarm processing problem in any power systems. The minimisation off(E) leads to a modified minimality criterion. if w2 is set to be 0, then the minimisation off(E) leads to the minimality criterion. if w1 and w3 are set to be zero, then the minimisation off(@ leads to the criterion developed in [12]. Thus, the minimality criterion and the criterion developed in [12] are two special cases of this new criterion.

The remaining problem is how to find the occurred event(s) by utilising eqn. 4 and the reported alarms A,, or in other words, how to find E which minimises f (E) . Obviously, this is a 0-1 integer programming problem. In the following Section, we will introduce a tabu search (TS) method to solve this problem. The motivation for adopting the TS for solving this

E) .

34

problem lies in its ability for finding multiple global optimal solution(s) efficiently.

It should be pointed out that the minimisation of f ( E ) can also be solved by using a conventional integer programming method, such as the branch and bound method or the Lagrangian relaxation method. Up to now, some special classes of 0-1 integer programming problems have been efficiently solved by operations research and mathematical programming solution techniques [25]. However, the alarm processing problem does not apparently fall into any of these special cases. In addition, the alarm processing problem can have multiple optimal solutions and must be fast enough for online applications, thus the conventional integer programming methods, such as the branch and bound method, are unlikely to be very suitable. In recent years, there has been an enormous amount of interest in the applications of genetic algorithms (GA) [25-281, simulated annealing (SA) [29, 301 and tabu search (TS) [14-22] for solving some difficult or poorly characterised optimisation problems with multimodal or combinatorial nature. These methods are generally called ‘modern heuristic’ techniques. Many successful applications of these methods in solving large scale practical problems have been reported recently. SA is powerful in obtaining the optimal solutions but its computation burden is heavy, so it is suitable for some planning problems which are not time critical. The alarm processing problem is a time critical problem, thus SA is not a good candidate for solving this problem. GA has been demonstrated to solve the set covering problem efficiently [25], and its computation speed is faster than that of SA. Moreover, some optimisation pro- grams based on GA are able to solve very large scale and complex problems. Thus, GA may be a suitable candidate for solving the alarm processing problem, and has been employed in [12, 131. TS has emerged as a new, highly efficient, search paradigm for quickly finding high quality solutions to combinatorial optimisation problems. It is characterised by gathering knowledge during the search, and subsequently profit- ing from this knowledge. TS has been successfully applied to solve many large scale and complicated combinatorial optimisation problems in many areas includ- ing power systems [14-221, but its application to the alarm processing has not yet been explored. One of the main issues of this paper is to investigate its efficiency in solving the alarm processing problem and compare it with GA, with an objective to seek for a more efficient method. Based upon many simulation research results, it is found that the computation efficiency of TS is better than that of GA. in addition, as same as GA, TS can find the multiple optimal solutions directly in a single run, so TS is selected for this application.

3 processing problem

With its roots going back to the late 1960s and early 1970s, the tabu search was proposed in its present form a few years ago by Glover [14-171. It has now become an established optimisation approach that is rapidly spreading to many new fields. For example, the successful applications of TS have been reported recently in solving some power system problems, such as the hydrothermal scheduling [ 191, multilevel reactive source planning [20], capacitor placement in radial distribution systems [21] and thermal unit maintenance

Tabu search and its application to the alarm

IEE Proc.-Gener. Transm. Distrib., Vol. 144, No. 1, January 1997

scheduling [22]. Together with the SA and GA, TS has been singled out by the Committee on the Next Decade of Operations Research [ 141 as ‘extremely promising’ for the future treatment of practical applications.

TS is a restricted neighbourhood search technique. The fundamental idea of TS is the use of flexible mem- ory of search history which thus guides the search process to surmount local optimal solutions. To describe the workings of TS, we consider a combinatorial optimisation problem in the following form:

where Xis a vector of dimension n, and its elements are integers. C(X) is the objective function (cost or penalty function), and can be linear or nonlinear. The first step of TS is to produce an initial (current) solution XCurrent either randomly or using an existing (heuristic) method to the given problem. The second step is to define a set of moves that may be applied to the current solution to produce a set of trial solutions. As an example, the move can take the form of X r L a l = XCUrrenf 2 AX. Here, Axis a vector with the same dimension as X. In fact, a move produces a neighbourhood search. Among all the trial solutions thus produced, TS seeks the one that improves most of the objective function. In certain situations, if there are no improving moves, a fact which means some local optimum exists, TS chooses the one that least degrades the objective function. The most basic components of the tabu search are the ‘moves’, ‘tabu list’ and ‘aspiration level (criterion)’, which are briefly introduced below.

3. I Moves The search process of TS is implemented by the ‘moves’. A trial solution can be created by a move. Many kinds of moves are currently available [14-221, and the following two kinds of moves [20] are adopted in this work for solving the 0-1 integer programming problem of eqn. 4.

To minimise C ( X ) ( 5 )

(i) Single move (denoted as m,)

+ U , Z = 1 , 2 , . . . , n (6 ) where U , is a vector with the same dimension as X, and its ith element is 1 (if the ith element of Xcurrent is 0) or -1 (if the ith element of Xcurrent is 1) and all the other elements are zero.

- x

Xtrzal - current -x

(ii) Exchange move (denoted by mil) +uZ-u3 i , 3 = 1 , 2 , . . . , n a n d a # j

where U, is a vector with the same dimension as X , and its ith element is 1 (if the ith element of Furrent is 0) or -1 (if the ith element of Xcurrent is 1) and all the other elements are zero. U] is a vector with the same dimension as X, and itsjth element is 1 (if thejth element of Furrent is 1) or -1 (if thejth element of Xcurrent is 0) and all the other elements are zero. Obviously, an exchange move can be implemented by two single moves.

Xtrza l - current

(7)

3.2 Tabu list To prevent from returning to the local optimum just visited, the reverse move that is detrimental to achiev- ing the optimum solution must be forbidden [21]. This is done by storing this move in a tabu list. The elements of the tabu list are called tabu moves. The reverse moves are restricted from regions the search already explored. Due to the enforcement of tabu moves, the search process can escape from the local

IEE Proc-Gener. Transm. Distrib., Vol. 144, No. 1, January 1997

optimal solutions. The dimension of the tabu list is called the tabu list

size. Obviously, how to specify the tabu list size in the searching process plays an important role in the search of good solutions. In general, the tabu list size should grow with the size of the given problem, but how to specify the optimal tabu list size is still an open problem. Up to now, the tabu list size is determined experi- mentally. In addition, how to manage the tabu list such as how long (how many iterations) a move can be retained in the tabu list is also an important problem. Many methods to implement and manage the tabu list have been developed [14-221, and the methods used in this work are described below.

In this work the tabu list is updated iteration by iteration [20]. At the end of each iteration, the new move is added to the tabu list, and an old move may be removed if it has been in the tabu list for T,,, iterations. T,, is called the tabu tenure which plays an important role in finding good solutions. The detailed implementation is as follows. (i) if a single move m, is selected in the kth iteration, then the following moves will be added to the tabu list:

-mz, m.7z j = 1 , 2 , . . . , n, j f i (ii) if an exchange move mo is selected in the kth iteration, then the following moves will be added to the tabu list:

-m,,ml,

m.7 > m.71

1 = 1 , 2 ,..., n,l f i 1 = 1 , 2 ) . . . , n , l f j

3.3 Aspiration level (criterion) An important component of TS is the incorporation of an aspiration level (criterion) for any tabu move in the tabu list. The role of the aspiration level is to provide an added flexibility to choose good moves by allowing a tabu move to be overridden if its aspiration level is attained. This is because the tabu list may forbid certain worthy moves possibly leading to a better solution than the best one found so far. An aspiration level is used to allow tabu moves to be released if they are judged to be worthy or interesting [21]. In other words, the aspiration level is to allow an ‘excellent’ tabu move to be selected if this level is attained. Many implementation strategies for the aspiration level are available [14], and in this work the aspiration level is defined as [14, 211: if a tabu move from the current solution Furrent can reach a solution which is better than the best solution found so far, then the aspiration level for this tabu move is attained and can be overridden.

3.4 Framework for solving the alarm processing problem using tabu search The general algorithm of TS-based alarm processing can be described as follows: (i) Randomly generate an initial (current) solution E*, and set the iteration counter k = 0. Set the best solution vector Ebest = E*. (ii) If k is equal to a prespecified maximum permitted iteration number k,, then output Ebest as the final results and stop. Otherwise, set k = k + 1, and go to step (iii). (iii) Select a trial solution Etrial from the neighbourhood of l? by applying the two kinds of moves as defined in Section 3.1 and compute the corresponding f(Etrial).

35

Repeat this process until the specified neighbourhood sampling number, Smax, has been reached. (iv) If Ebesf is not better than the best trial solution which has the smallest objective function value, then assign this best trial solution to Ebest. Otherwise, go to step (v). (v) E* is updated to the best trial solution which has the smallest objective function value as evaluated in step (iii) and the corresponding move is not in the tabu list or its aspiration level is attained. Then, put the move in the tabu list, and go to step (ii). If the best trial solution corresponds to a tabu move and its aspiration level is not attained, then check the next best trial solution, and repeat this step.

3.5 Method to find multiple optimal solutions by tabu search The tabu search technique as stated above is powerful in finding the global or near global optimal solution of an optimisation problem. But it is shown from the simulation results that the TS can usually find only one global or near global optimal solution. For the alarm processing problem, multiple solutions may exist especially for complex cases. To find all reasonable solutions, the TS must be modified. The modification is as follows. At the first iteration, we put the initial solution in a specially designed array. In each of the follow-up iteration, we check if the best trial solution(s) in the current iteration is better than the solution(s) stored in the array. If yes, we use the best trial solution(s) in the current iteration to replace the record of the array. If the best trial solution(s) in the current iteration is as good as the solution(s) stored in the array and they are not the same solutions, then we put the best solution(s) in the current iteration into the array, thus the array is expanded. Otherwise, we do not change the record of the array. Please note that the array only contains those solutions which are found to be the best up to the current iteration, and only a copy can be stored in the array for each of the best solutions. Thus, at the end of the TS operation, the array will contain all the different best solutions found during the operation. If the parameters of TS (i.e. k,,,\, S,,, and T,,,,,) are properly specified, the multiple global optimal solutions can be found by this way. This has been verified by the following numerical examples. A similar method has also been used in a genetic algorithm based fault section estimation method [27] for finding the multiple global optimal solutions.

Table 1: System set of alarms for the first test example

Code Alarm message description

a,

a2

a3

a,

as a6 Any trip commands

a7

a,

a,

a,,

a,,

36

Any circuit breaker position changes

Any pair of circuit breaker position changes closing or opening Circuit breaker position changes to on

Circuit breaker position changes to off

Circuit breaker position leaving the off position

Trip commands of busbar protection devices Trip commands of transformer protection devices

Any indications of starting relays (neutral or phase)

Indications of starting relays (phase only) Any indication about blocking of automatic reclosing

4 Test results

We have used two sample studies to test the developed TS-based alarm processing method. The first sample example, from [7, 91, contains 11 alarms and 10 events. The system sets of alarms and events, and the characteristic set of alarms corresponding to each event are shown in Tables 1-3, respectively.

Table 2: System set of events for the first test example

Code Event description

e1 Fault on busbar

e2 Tripping of transformers

e3 Tripping after closing

e4 Tripping of lines

e5 Unsuccessful fast reclosing

e6 Successful fast reclosing e? External incident

e8 Blocked reclosing

e, Switching operation

e,, Maintenance activities

Table 3: Events and their corresponding characteristic sets of alarms for the first test example

Event Characteristic set of alarms

e,

e2

e3

e4

e5

e6

4 e8

e,

e1 n

a,, a,, a,, a7 a,, a4, as, a,

a,, aqr agr a,, a,,

a,, a,, a,, a,,

a,, a3, a4, a,, a,,

a,, a3, a,

a, a1 1

a,, a2

a1

Table 4: Some test results for the first test example

No. Reported alarms Estimated events

7

8

9

10

a,, a,, as, a7, a,

a,, a2, a,, a6. a,

a,, a,, a,, a,,

a,, as, a,, a,, a,,, a,, a,, a2, a3, a,

a,, a3, a4, agr a,, alo

a,, a3, a,, a,, a,,

e,, e7

e,, e9

e7, e,, e,

e5,

e6r

there are two solutions: (i) ea, e,; (ii) e3, e6 there are two solutions: (i) e,, e,; (ii) e*, e5

e,, e,

e,, e3 there arc two solutions: (i) e,, e,, e3, e5, e8, e,; (ii) e,, e2, e,, e6, e,, e,

More than 30 test cases have been completed for this example. It is shown that the developed TS-based method is feasible and can find multiple global optimal solutions for complicated cases with missing or false alarms. Only 10 test cases are illustrated in Table 4 for saving space. The optimal solutions for all test cases of

IEE Proc.-Gener. Transm. Distrib , Vol. 144, No. 1, January I997

this sample example can be obtained by setting the parameters in TS as follows:

&,,, = 20, s,,, = 10, T,,, = 5

Table 5: Events and their corresponding characteristic sets of alarms for the second test example

Characteristic set of alarms

Characteristic set of Event alarms

Event

e3

e4

e5

4

e8

e9

e10

e1 1

e1 2

el 3

e14

el 5

e16

e17

el e19

e20

e2 1

e22

e23

e24

e25

e,,

e29

e30

e3 1

e33 e34

e35

e36

e 3 7

e38

e39

1

en2 e43

e44

e45

e46

e47

e4s

e49

Table 6: Some test results for the second test example

No. Reported alarms Estimated events

5

6

10

e13

e29r

e22r e32, e36

there are two solutions: (i) eZ1, eZ9, e44; Wezl, e,,, en4

e32, e4X

there are two solutions: (i) el, eZ5, e31; (Wel, e31, e,, e1xr e21

elor e21r

6, eIsr e,,, eal

The second sample study contains 70 alarms and 50 events The characteristic sets of alarms corresponding to different events are shown in Table 5. More than 100 test cases have been carried out. It is shown that the developed TS-based method is efficient and can find the multiple global optimal solutions for complicated cases with missing or false alarms. Due to space

IEE Proc.-Gener. Transm. Dutrrh., Vol. 144, No. I , January I997

limitation, only 10 test cases are illustrated in Table 6. The optimal solutions for all test cases of this sample study can be obtained by setting the parameters in TS as follows:

K,,, = 100, S,,, = 50, T,,, = 50 In addition, the computing time for each test case of the second sample example is about 3s on a 486 microcomputer, so the proposed TS-based method is of potential for practical applications.

To demonstrate the advantage of the developed TS- based method, it is necessary to compare it with the existing GA based method [ 12, 131. As stated in Section 2.3, both TS and C A are powerful in obtaining the multiple optimal solutions for combinatorial optimisation problems, so they are both the suitable candidates for solving the alarm processing problem. Thus, the computation efficiency and solution quality will be two vital factors in comparing these two methods. The adopted GA is as same as the one presented in [26, 271 except that the single-point crossover operator is replaced by a more powerful uniform crossover operator [25, 281. Due to space limitation, the details of the GA are not presented here, please refer to [25-281. Because of the heuristic nature of TS and GA, it is very difficult to compare them from their computational mechanism. Thus, we have to resort to numerical examples to make the comparison. Even so, it is still not easy to make a fair comparison between them. This is because some parameters in TS (that is Kmax, S,,,, and T,,,) and GA (that is the population size ‘pops’, the maximum permitted iteration number ‘MG’, the crossover probability ‘Pc’, and the mutation probability ‘P,’ [26, 271) are determined by experience, and the optimal tuning of these parameters is still an open problem both for TS and CA. To make a fair comparison, 50 test cases for the second test example have been utilised. 20 sets of different values for the parameters in TS and in GA are specified, respectively. For any set of the specified parameter values, we carry out all the 50 test cases using these two methods, and record the corresponding evaluation numbers of the objective function f ( E > in eqn. 4 for each method, respectively. If the TS-based or GA-based method can find all optimal solutions for all the 50 test cases under a set of specified parameter values, then this set of parameter values are called ‘a feasible set of parameter values’ for the corresponding method. In other words, under their respective feasible sets of parameter values, the solutions obtained by TS and GA are the same and are both the optimal ones. Among all feasible sets of parameter values for each method, the set, whose corresponding evaluation number of f ( E ) is the smallest, is called the ‘best parameter set’ (among the 20 sets of specified parameter values) of this method. We compare the performance of the TS-based and GA-based methods under their respective best parameter sets. In this way, we can obtain the best tuning set of parameter values for each method among the 20 sets of prespecified parameter values, and can compare their relative computation efficiency under the same solution quality for both methods. The best parameter set for the TS-based method is: K,,, = 100; S,,, = 50; T,,, = 50, while the best parameter set for the GA-based method is: pops = 500; MG = 50; P, = 0.9; P,, = 0.001. In addition, the stop criterion for the GA-based method is that the maximum permitted iteration number has been reached. The calculation time con-

31

sumed for each test case is about 15s by the GA-based method, and about 3s by the TS-based method on the same 486 microcomputer. Thus, the computation speed of the TS-based method is about five times faster than that of the GA-based method.

In this paper a new alarm processing approach has been developed using the tabu search technique. First, an essential and important issue on how to describe the alarm processing problem is discussed, and a new and reasonable criterion presented. Then, a new method was proposed for solving the alarm processing problem using the tabu search technique.

The test results on two sample examples have shown that the developed TS-based method is feasible, efficient, and of potential for practical applications. In our experiences, the parameters in TS, such as the maximum permitted iteration number K,,,, the neighbourhood sampling number S,,, and the tabu tenure Tman, can easily be tuned in the solution process. Future work will be to test the developed TS-based approach for actual power systems.

6

1

2

3

4

5

6

7

8

9

References

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tabu search approach to alarm processing in power systems

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