Self-adaptable hierarchical clustering analysis and differential evolution for optimal integration of renewable distributed generation

In a previous paper, we have introduced a simulation and optimization framework for the integration of renewable generators into an electrical distribution network. The framework searches for the optimal size and location of the distributed renewable generation units (DG). Uncertainties in renewable resources availability, components failure and repair events, loads and grid power supply are incorporated. A Monte Carlo simulation–optimal power flow (MCS–OPF) computational model is used to generate scenarios of the uncertain variables and evaluate the network electric performance with respect to the expected value of the global cost (ECG). The framework is quite general and complete, but at the expenses of large computational times for the analysis of real systems. In this respect, the work of the present paper addresses the issue and introduces a purposely tailored, original technique for reducing the computational efforts of the analysis. The originality of the proposed approach lies in the development of a new search engine for performing the minimization of the ECG, which embeds hierarchical clustering analysis (HCA) within a differential evolution (DE) search scheme to identify groups of similar individuals in the DE population and, then, ECG is calculated for selected representative individuals of the groups only, thus reducing the number of objective function evaluations. For exemplification, the framework is applied to a distribution network derived from the IEEE 13 nodes test feeder. The results show that the newly proposed hierarchical clustering differential evolution (HCDE) MCS–OPF framework is effective in finding optimal DG-integrated network configurations with reduced computational efforts.