Differential evolution using ancestor tree for service restoration in power distribution systems

Problems in power distribution system reconfiguration (PDSR), such as service restoration, power loss reduction, and expansion planning, are usually formulated as complex multi-objective and multi-constrained optimization problems. Several evolutionary algorithms (EAs) have been developed to deal with PDSR problems, but the majority of EAs still demand high running time when applied to large-scale distribution systems (thousands of buses and switches). This paper presents a new approach for service restoration in large scale distribution systems that employs a discrete differential evolution with ancestor tree (DE-Tree). We combine the node-depth encoding (NDE) to represent computationally the electrical topology of the system and the ancestor tree presented here to implement differential evolution for service restoration problems. The ancestor tree is used to build a list of elementary movements that maps one solution in the search space into another, thus capturing the “difference” between forests encoded with the NDE, which is essential in the search engine of differential evolution. The use of an ancestor tree is not only central to implement differential mutation in our algorithm but also can track the sequence of switching operations in the restoration of the system after the optimization process is finished. The proposed approach makes differential evolution suitable for treating combinatorial optimization problems related to PDSR. Results presented on distribution system reconfiguration problems suggest the benefits and fast convergence of the proposed approach