Optimal allocation of distributed generators and capacitor banks considering load models under stochastic load levels

Optimal allocation of distributed generators (DGs) and capacitor banks (CBs) is crucial for enhancing both the technical performance and environmental sustainability of distribution systems. Uncertainties arising from consumer behaviour, climatic conditions, and time-of-use introduce variability in load demands. Therefore, accounting for load demand uncertainty is essential for effective and sustainable distribution system planning. In this study, a novel fuzzified random number approach is employed to model the uncertainty in voltage-dependent non-linear load (VDL) models. An improved particle swarm optimization (IPSO) algorithm is then applied for the simultaneous allocation of DGs and CBs in radial distribution networks under both constant (CL) and stochastic VDL scenarios. The IPSO method is validated on the IEEE 33-bus system to evaluate the technical, economic, and environmental benefits of DG and CB allocation. Key results indicate that DGs operating at an optimal power factor (OPF-DGs) combined with CBs outperform unity-power-factor (UPF-DGs) and CBs under the CL model, achieving superior outcomes in terms of reduced power loss, lower voltage deviation, and enhanced voltage stability. Specifically, power loss reductions of 94.36% are achieved for UPF-DGs + CBs, compared to 94.89% for OPF-DGs + CBs under CLs. For defuzzified mixed VDLs, a power loss reduction of 93.92% is observed under OPF-DGs + CBs. The proposed approach also demonstrates significant economic benefits, including high net present values and cost savings, alongside substantial reductions in environmental emissions. Furthermore, sensitivity analysis highlights that considering different load mixes, rather than static or single-load configurations, is critical for optimal planning and economic dispatch of distribution systems with DGs and CBs. Incorporating load uncertainty provides a more realistic representation of system performance, emphasizing its importance in sustainable distribution network planning.