Abstract
•The multi-objective economic framework is proposed to maximize financial benefits.•Assessment of the distribution network at the optimal solution through exhaustive technical performance parameters is presented.•The effect of the ZIP model on economic and technical performance is evaluated.•An extension of the hiking algorithm for multi-objective problems is proposed.•The Pareto front quality is assessed by various performance indices and compared with other methods.
This work presents a multi-objective economic framework for the optimal allocation of distributed generators (DGs) and shunt capacitors (SCs), addressing a key limitation of earlier studies that optimized these economic objectives independently. Unlike conventional approaches, this study incorporates a practical ZIP (impedance–current–power) load model across multiple load levels, an aspect that remains largely unexplored in distribution system planning. Further, a comprehensive technical assessment under the most economical solution has not been sufficiently addressed in prior studies. To this end, this work evaluates key technical performance parameters, such as the voltage stability index (VSI), voltage deviation (VD), and line loading, under the best-compromised solution (BCS) and provides a comparative analysis. The proposed multi-objective hiking optimization algorithm (MOHOA) is applied to four case studies on a real-world 108-bus Indian distribution system. The result analysis provides critical insights, including the economic advantage of incorporating investment cost (IC) alongside the cost of annual energy loss (CAEL), and the necessity of upgrading existing distribution line infrastructure to ensure solution feasibility. Furthermore, challenges associated with SC allocation under low X/R ratio conditions are highlighted. The impact of the ZIP load model on economic performance is also examined by comparing it with the conventional constant-power (CP) load model. Notably, in Case 4, a 14.27% reduction in IC is achieved for a given CAEL when ZIP is used instead of the CP model. Pareto front quality indices, like inverse hypervolume (1/HV), overall spread (OS), and distribution metric (DM), are evaluated, and the comparison confirms MOHOA’s superiority.