Stochastic allocation of photovoltaic energy resource and electric bus parking lot in distribution systems using an improved weighted average algorithm via sine–cosine strategy

This paper proposes a stochastic framework for the joint allocation of photovoltaic (PV) resources and electric bus parking lots (EBPLs) in radial distribution systems, aiming to minimize power losses, enhance voltage stability, and improve the voltage profile under uncertainties in PV generation and load. PV and EBPL siting and sizing are determined using an Improved Weighted Average Algorithm (IWAA) that incorporates a sine-cosine search to escape local minima and achieve a stronger exploration-exploitation balance. In the stochastic framework, PV output uncertainty is modeled via Monte Carlo simulation (MCS) using beta probability density functions (PDFs), while load uncertainty is represented with normal PDFs. The proposed methodology is evaluated across four cases-Case I: deterministic PV; Case II: deterministic PV + EBPL; Case III: stochastic PV; Case IV: stochastic PV + EBPL-on the IEEE 33- and 69-bus radial distribution systems. The outcomes show that the IWAA consistently outperforms the traditional WAA by yielding lower power losses, lower voltage deviations, and better voltage stability index in Cases I and II. Also, the results demonstrated that allocating the EBPL with PV (Case II) increases the net saving by 9.81% and 5.08% for the 33-bus and 69-bus systems, respectively, over Case I (without EBPL). Also, the stochastic model (Case III) outcomes showed that the net saving falls against the deterministic model (Case II), highlighting the effects of the uncertainties. Overall, these findings underscore that explicitly modeling uncertainty and co-locating EBPL with PV leads to more robust planning decisions and improved distribution-system performance under realistic operating conditions.