Reliability Assessment for Distribution Optimization Models: A Non-Simulation-Based Linear Programming Approach

The advent of smart grids and active distribution networks has boosted the relevance of reliability in the operation and planning of distribution systems. As is customary, reliability is assessed analytically through several standard indices. Unfortunately, analytical reliability assessment relies on simulation, thereby requiring the use of inexact heuristic- or metaheuristic-based solution methods to operate and plan distribution systems when economic and reliability criteria are jointly considered. In order to overcome this shortcoming, this paper presents a new optimization-based approach to compute the standard network-dependent reliability indices that are widely used in reliability-constrained distribution optimization models. As a major salient feature over the conventional simulation-based method, reliability indices are equivalently determined by an efficient approach based on linear programming, where the network topology is explicitly represented by decision variables of the optimization process. The proposed approach has been tested on several benchmarks including a 1080-node system. Numerical simulations show that the proposed approach yields the same results as the conventional algorithm. Moreover, the moderate computational effort is suitable for the subsequent integration of the proposed equivalent formulation in reliability-constrained optimization models for distribution operation and planning. Such successful numerical experience backs the potential of the proposed formulation to enable the use of sound techniques different from the available heuristics and metaheuristics to solve reliability-constrained operational and planning optimization models for distribution systems.