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Pergamon 0952-1976(95)00025-9

Engng Applic. Artif. lntell. Vol. 8, No. 4, pp. 449-460, 1995 Elsevier Science Ltd. Printed in Great Britain

Contributed Paper

An Expert-system-assisted Reliability Analysis of Electric Power Networks

ISTVAN MATIJEVICS Po|ytechnical Engineering College, Subotica, Serbia

LAIOS JOZSA J. J. Strossmayer University, Osijek, Croatia

(Received January 1993; in revised form December 1994)

This paper presents an implementation of expert systems in the reliability analysis of electric power networks. The reliability model uses the method of Markovian minimal cut sets, which allows the consideration of several stochastic dependencies concerning the state space, such as common-mode failures, limited repair capacities and outage postponabilities, and the simultaneous performance of maintenance and repair by the same team. On the other hand, approaching the reliability problem from the view-point of expert systems opens a wide range of possibilities for very complex treatment of reliability problems. This means not only the calculation of reliability indices, but fault-tree construction, performance of sensitivity analysis and finding the appropriate modifying actions.

Keywords: Expert systems, knowledge-bases, databases, inference engines, user interfaces, work- ing memory, data-driven strategy, pattern matching, reliability, electric power networks, Markovian minimal cut sets, fault-trees, stochastic dependencies.

I. INTRODUCTION

As is well-known, the reliability evaluation of electric power networks above a certain number of network components becomes rather cumbersome when using conventional methods like Markov processes, logical parallel and series structures, animal tie sets and mini- mal cut sets, especially when considering some stochas- tic dependencies between their outage events. 1 Furthermore, all these methods yield in many cases only numerical results, which are hard to interpret. In contrast, the application of expert systems in the relia- bility analysis of electric power networks offers more, generally using artificial intelligence, knowledge bases and databases, especially the combination of the Markovian state-space method and the minimal cut set method (Markovian minimal cut set) along with the fault tree method. That is, in dialogue with the user and on the basis of numerical values for reliability indices, the expert system provides advice and alternatives at the planning phase, as well as a means of improving reliability at the exploitation phase. 2'3 For reasons of

Correspondence should be sent to: Professor L. J6zsa, J. J. Strossmayer University, Department of Power Engineering, Istarska 3, 54000 Osijek, Croatia.

449

brevity, the implementation of expert systems within the reliability analysis will be presented here for solving only a part of the entire reliability problem in electric power networks, i.e. for fault-tree construction in order to obtain the minimal cuts.

2. EXPERT SYSTEMS

The quintessence of expert systems (ES) is briefly expressed by their name; they are computer-based application systems which provide an adequate expert service in bounded special fields, and solve complex tasks independently, or in close co-operation with the user. The feature of such systems is that they take into account the uncertainty of both the rules and the data. Their modular structure consists of the following: knowledge base, inference engine or reasoning mecha- nism and user interface (Fig. 1):

--The knowledge base contains the expert's knowl- edge in the form of facts and rules. Rules are conditional statements that give the action that occurs if a specific condition is satisfied, and they are generally based on the problem-solving exper- tise developed by human experts.

--The inference engine is a computer program which simulates the user's deductive thinking. It applies a

450 ISTV,~N MATIJEVICS and LAIOS JOZSA: ANALYSIS OF ELECTRIC POWER NETWORKS

Expert system

Knowledge base I

Inference engine ~ User interface 12

Fig. 1. The structure of an expert system.

User

==J Iput I Output

reasoning strategy, and generates solutions based on the rules in the knowledge base and the data collected by the ES.

- -The user interface links the ES with the user and makes possible the data input about the special subject under discussion.

Table 1 shows the main differences between conven- tional programming and an ES. Whereas in conven- tional programs the data get mixed in with the control structures, the constituents of an expert system make separate units, thus improving their flexibility. The problem-solving methods of expert systems are pre- dominantly heuristic, in contrast with conventional pro- grams, which are more suited to numerical solutions. The ES of course makes use of numerical methods, that is conventional programming, too.

3. RELIABILITY EVALUATION OF ELECTRICAL POWER NETWORKS USING THE METHOD OF MARKOVIAN MINIMAL CUT SETS, TAKING

INTO ACCOUNT SOME STOCHASTIC DEPENDENCIES

Taking account of various stochastic dependencies related to component outages in electric power networks results in a more accurate evaluation of the reliability parameters for the system. A brief discussion of some stochastic dependencies is presented in Appendix A. It is convenient to build them into the state space of the Markovian minimal cut sets, which can be derived from the physical structure of the network. As is well-known, only the influence of the first-, second- and third-order minimal cuts on the system reliability indices is of interest. The stochastic dependencies considered and built into the state space of minimal cuts, obtained by the fault-tree method and

Table 1. Comparison of conventional programming and ES

Conventional Expert system program

Problem --Knowledge based Numerical solution --Numerical Method --Heuristic search Algorithmic

--Algorithmic The knowledge --Precise Precise used --Fuzzy Programming Modular Structured strategy (flexible) (rigid)

described mathematically by the method of most prob- able transitions, are as follows: common-mode failures, limited repair capacities, outage postponabilities and simultaneous performance of maintenance and repair by only one repair team (Appendix A).

In connection with the development of the state space for minimal cuts (Appendix B) and the evalu- ation of the reliability of the electric power network, the following general assumptions were made:

1. The supply and load points in the network will be assumed to be 100% reliable.

2. The network protection system will also be assumed to be 100% reliable.

3. Both spontaneous and postponable outages will be taken into account. This means that the com- ponents will immediately be selectively switched off by short circuits or heavy transformer fail- ures, while the switch-off will follow at an appro- priate moment after line-to-ground faults in networks with low-impedance neutral earthing for fault current limitation, or slight transformer failures. Automatic circuit reclosing for the elimination of temporary line-to-ground faults are not considered as outages.

4. False breaker operations (openings) are excluded.

5. Lines and transformers represent the system components. All components are assumed to have unlimited transmission capacity, i.e. follow- ing an outage of one of them, another one is able to take over the entire loading without overload- ing.

6. The repair (or replacement) of components which are not operational starts immediately. Only one team is available for repair, as well as for maintenance. This means that the component which is not operational (or is being maintained) first will also be by an outage of a second compo- nent repaired (or maintained) first.

7. The components are maintained at stated inter- vals, assuming that switch-offs for maintenance cannot be scheduled during process-determined out-of-operation periods of the network (if such exist).

8. Simultaneous maintenance of several compo- nents is excluded.

9. The switching-off for maintenance of a compo-

ISTV/~N MATIJEVICS and LAIOS JOZSA: ANALYSIS OF ELECTRIC POWER NETWORKS 451

nent can be postponed if other components are non-operational.

10. Maintenance cannot be interrupted, i.e. if during the maintenance of one component an outage of a second one occurs, the maintenance of the first one must be finished before starting with the repair of the second component.

11. The following common-mode failures will be considered: An additional outage of one component as a

consequence of an outage of another compo- nent, e.g. multiple line-to-ground faults in networks with earth-leakage compensation or a double-line outage due to flashover caused by a lightning stroke into the shield wire.

An additional outage of one component as a consequence of the maintenance of another component, e.g. maintenance switch-offs can cause further outages, due to mis-switchings or overloading.

When using the first-order minimal cut the common- mode failure is non-existent; moreover, the third-order minimal cut's state space is fairly complicated. The inclusion of the above-mentioned stochastic dependen- cies is therefore best illustrated by the second-order one. Figure A12 in Appendix A shows the state-space diagram for a two-component system, with limited repair capacities already included, i.e. both mainten- ance and repair are performed by only one team. This model corresponds to a second-order minimal cut, and will further be used as a basis for developing a cut- model which is modified by both the remaining stochas- tic dependencies.

Now, building the common-mode failures and the outage postponabilities from Appendix A into this base model, one can finally get the overall second-order cut model, modified by all the stochastic dependencies, as shown in Fig. 2. All the explanations concerning states and transitions given in Appendix A are valid here as well. In addition, if the proportion of simultaneous outages of component k when component i is non- operational, related to component i's total number of outages is denoted by PGA.ki, the common-mode outage rate becomes PGA,ki " 2Ai" Likewise, if the proportion of simultaneous outages of component k when component i was being maintained related to component t's total number of maintenances is denoted by P~w.ki, the common-mode outage rate becomes P,,.ki "~,,~. AS shown in Appendix A, in cases where both the spon- taneous and the postponable outages are considered, the overall outage rate of component i equals the sum of both outage rates: ADi which represents the postpon- able outages, and 2si which represents the spontaneous outages.

The third-order minimal cuts, including stochastic dependencies, could be developed in a similar manner. In order to determine the minimal cuts from the distri- bution network's scheme, the fault-tree method was

applied. Finally, the reliability indices of the system can be calculated by the minimal cut set method, consider- ing only the most probable state-transitions within the minimal cut's state space. In this way, only the direct, decoupled paths without any loops between the starting and ending states will be passed through (shown here by thick lines in all the state-space diagrams), and are then easy to treat mathematically.

It is apparent from Fig. 2 that the outage postponabilities do not have a direct influence on the reliability calculations, since all transitions to or from such postponed outage states are not parts of the most probable paths. However, there is an indirect influence through the outage rate As = 2 - 2D-

4. EXPERT-SYSTEM-ASSISTED FAULT-TREE ANALYSIS

This section presents an ES-based approach for fault- tree construction in electrical network reliability analy- sis, using the network graph and yielding the minimal cuts for the further evaluation of the reliability indices.

The fault-tree (bT) method is widely used in the qualitative and quantitative reliability analysis of elec- trical networks. 4 The b-q" analysis is, basically, a syste- matic discussion of the system failure events, as well as of the subsystem and component failure events causing them. Figure 3 shows the structure of the principle of the ES-assistance in the fault-tree and reliability analy- sis.

The fault-tree analysis (FTA) is based on graph theory. The tree is a graph, branches of which are connected without forming any loops. It is sometimes impossible to satisfy this condition by an VI" construc- tion for electrical networks, so the loops which are formed must then be solved in an appropriate manner.

An FT is a logical tree where the branches represent the failure events at the system, subsystem or compo- nent levels, and the nodes represent logical operations which relate the failure events to their inputs and outputs. An FT originates from a single event at the root of the tree, called the top event. All the events causing the top event appear on the next level, and the tree is continued in this manner through all the subse- quent levels. The top event always represents the system failure, which must be defined in terms of the system-failure criteria. The FT construction along the series of branches is terminated whenever a component-failure event is reached.

The FT construction will be illustrated here by the example of the bridge-circuit shown in Fig A13 in Appendix B. For the sake of simplicity, the branches are denoted by numbers 1 . . . . ,5, instead of ll . . . . . Is.

The states of the network are listed in Table 2, where the numbers denote the components in an outage state and the successful states are all those in which the load point supply is guaranteed.

The top event in the VI' represents a failure of the

452 ISTVAN MATIJEVICS and LAIOS JOZSA: ANALYSIS OF ELECTRIC POWER NETWORKS

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Fig. 2. State-space diagram for second-order minimal cut, including all stochastic dependencies.

A,

entire system, which has been defined for the example network as "Station n4 unsupplied". Based on this definition and the physical network diagram, the FT in Fig. 4 can be constructed downwards from the top event. The first subtree is denoted by A, where the event "Station n4 unsupplied" is caused by the failure of the supply from nodes n2 AND n3. These two sub-

events are the top events for subtrees B and C. Continuing the process...