ارزیابی قابلیت اطمینان سیستم کامپوزیت با استفاده از برنامه ریزی خطی فازی

Composite power system reliability evaluation refers to assessment that considers both, generation and transmission facilities. The conventional dc load flow-based crisp linear programming (CLP) model used in composite power system reliability evaluation is modified as a fuzzy linear programming (FLP) model including fuzzy constraints and objective functions. This fuzzy linear programming model can include uncertainties that exist in certain variables and overcome the limitations of minor constraint violations in crisp linear programming model. This fuzzy optimization model is employed to test the system outage contingencies and to determine the degree of difficulty due to these contingencies. Fuzzy-based adequacy indices are obtained after all the selected contingencies have been analyzed using contingency enumeration approach. The effectiveness of the developed model is tested on the IEEE-14 bus system.

The conventional dc flow-based crisp linear programming (CLP) model [1] used in composite system reliability evaluation method is formulated as an optimization problem with crisp constraints. The CLP is often insufficient in real life situation. In reality, certain coefficients that appear in CLP problems may not be assessed precisely or only qualitative estimates of these coefficients are available. In addition, the given fixed values of constraint limits have to be met all the times. Any violation of a single constraint by even a small amount renders the solution infeasible or it may lead to over-conservative solutions. In many of the real life problems, there are situations where small violations of these limits are sometimes acceptable. In this regard, the constraints may be classified either as ‘hard’ or ‘soft’. For example, generation output is a ‘hard’ constraint whereas transmission line flow is a ‘soft’ one. Fuzzy linear programming (FLP) [2] is an extension of CLP and deals with such imprecise coefficients and ‘soft’ constraints by using fuzzy variables. In fuzzy environment, the decision maker could accept small violations of the constraints and attach different degrees of importance to the violations of different constraints. Saraiva et al. [3] use fuzzy numbers to define loads in composite power system reliability evaluation using Monte-Carlo simulation. The authors propose a set of new indices reflecting the integration of probabilistic models and fuzzy concepts and discuss the application of variance reduction techniques (a simulation approach) if fuzzy numbers define loads. Saraiva and Sousa [4] extend this work with some new developments. The two main new developments are: fuzzy load duration curve and modeling of failure and repair rates using trapezoidal fuzzy number (TrFN). Saman and Singh [5] develop a Genetic Algorithm-based method for composite system state evaluation where the system constraints are represented by fuzzy membership functions. Choi et al. [6] propose a new fuzzy effective load duration curve (ELDC) model for reliability evaluation of composite power system using fuzzy set theory considering the flexibility and ambiguity of capacity limitation and over load of transmission lines which are subjective matter characteristics. A number of papers on bibliographic review of the applications of fuzzy set theory in power systems are found in literature [7], [8], [9] and [10]. In the present study, the conventional dc load flow-based CLP model is modified into a FLP model including fuzzy constraints and fuzzy objective functions. The FLP is then converted into an equivalent crisp optimization model using the concept of fuzzy mathematical programming [2]. The developed equivalent crisp optimization model is used in contingency enumeration approach to evaluate adequacy indices [11]. The effectiveness of the developed model is tested using a 14-bus system and the results are compared with the conventional one.

In this paper, a dc load flow-based fuzzy optimization model is proposed. The model is used in contingency enumeration method of composite system reliability for evaluating the outage contingencies of the system. Fuzzy-based load point and system reliability indices are calculated for an IEEE-14 bus system using the proposed model and the conventional dc load flow-based linear programming model. Various studies have been conducted to examine the effect of increased load and generation on reliability indices. Effect of fuzzy parameters on the reliability indices and on the satisfaction levels has also been studied. The effects are quite significant while load demand and generation capacities are increased in proportion to the given system peak load level and generation capacities. The flexibility in considering crisp system parameters, such as load and transmission line flow, as fuzzy parameters helps to study a system with uncertain loading conditions and transmission flow. The decision maker could accept small violations of the constraints and attach different degrees of importance to the violations of different constraints.