Abstract-This paper proposes a method for choosing the best transmission system expansion plan considering a probabilistic reliability criterion LOLE . The method minimizes the investment budget for constructing new transmission lines subject to probabilistic reliability criteria, which consider the uncertainties of transmission system elements. Two probabilistic reliability criteria are used as constraints. One is a transmission system reliability criterion LOLE constraint, and the other is a bus/nodal reliability criterion LOLE constraint. The proposed method models the transmission system expansion problem as an integer programming problem. It solves for the optimal strategy using a probabilistic branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. Test results on an existing 21-bus system are included in the paper. They demonstrate the suitability of the proposed method for solving the transmission system expansion planning problem subject to practical future uncertainties.Index Terms-Branch and bound, probabilistic reliability criteria, transmission system planning.

This paper proposes a methodology for choosing the best transmission expansion plan considering various types of security (operating reliability) criteria. The proposed method minimizes the total cost that includes the investment cost of transmission as well as the operating cost and standby cost of generators. The purpose of the study is development of new methodology for solving transmission system expansion planning problem subject to (N ) contingency criteria which are essentially extensions of the (N-1) contingency criterion. The transmission expansion problem uses an integer programming framework, and the optimal strategy is determined using a branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. The characteristics of the proposed method are illustrated by applying it to a five-bus system and a 21-bus system. The results of these case studies demonstrate that the proposed method provides a practical way to find an optimal plan for power system expansion planning.Index Terms-Branch and bound method, investment cost, operating cost, security (reliability) criteria, standby cost, transmission expansion planning.

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This paper proposes a new method for choosing the best transmission system expansion plan for the highest satisfaction level of the decision maker. The proposed method considers the permissibility and ambiguity of the investment budget (economics) for constructing new transmission lines and the delivery marginal rate (reliability criterion) of the system. This is achieved by modeling the transmission expansion problem as a fuzzy integer programming one. The method solves for the optimal strategy (a reasonable and flexible plan that would not be significantly worsened by any assumed changes in the surrounding situations) using a fuzzy set theory-based branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. When only a very limited size database is available to evaluate probabilistic reliability indices, the proposed technique provides the decision maker with a valuable and practical tool to solve the transmission expansion problem, considering problem uncertainties. Test results on an existing 21-bus system show that the proposed method is suitable for solving the transmission expansion planning problem subject to practical ambiguities.Index Terms-Flexibility and ambiguity, fuzzy branch and bound, fuzzy integer programming, satisfaction level of decision maker, transmission expansion planning.