A cloud-fuzzy multi-objective optimization framework for allocation of bidirectional energy storage based electric bus charging station and renewable resources in distribution network incorporating carbon trading and technical-operational flexibility

The coordinated integration of a bidirectional energy storage system (BESS)-based electric bus charging station (EBCS) with photovoltaic (PV) and wind turbine (WT) in distribution networks is critical for decarbonizing power and transportation. However, this integration faces three major challenges. First, conflicting economic, environmental, and technical objectives inherently. Second, there is no unified robustness measure that combines voltage stability and loss minimization. Third, inadequate management of the stochasticity and associated uncertainty in the renewable generation, load, and availability of BESS-based EBCS. To address these gaps, this paper presents a multi-objective fuzzy stochastic optimization framework that simultaneously minimizes the overall cost (OC), maximizes the revenue from carbon trading (RCT), and maximizes a novel decentralized voltage and loss robustness (DVLR) index. The first innovation is the DVLR index itself. Unlike traditional approaches that consider voltage and losses separately, DVLR embeds a mutual penalty function that jointly normalizes voltage deviations and power losses, forcing the optimizer to simultaneously achieve improved voltage profiles and reduced line losses. The second innovation is an improved Newton-Raphson-based multi-objective optimizer (MO-INRBO). It integrates a sine-cosine chaotic map to replace deterministic decay with controlled randomness and a nonlinear adaptive weighting factor for balancing exploration and exploitation. The third innovation is a multidimensional cloud model (MDCM) for stochastic optimization. It uses three features (expectation, entropy, hyper-entropy) to capture uncertainty interdependencies while dynamically adapting hyper-entropy to the system operational state. A distance-preserving scenario reduction technique condenses the uncertainty space without losing probabilistic and fuzzy features. Simulation on a 33-bus IEEE distribution network quantifies the causal impact of each innovation. BESS-based EBCS integration reduces OC by 10.1% and increases DVLR by 12.8%, proving that flexible storage buffers renewable variability. Explicit optimization of DVLR improves robustness by 11.75% and increases OC and RCT by only 2.81% and 3.79%, respectively – an acceptable trade-off for network robustness. Compared to deterministic solutions, the stochastic MDCM approach increases OC by 4.63% while reducing RCT by 5.36% and DVLR by 6.76%, representing the cost of robustness under real-world uncertainties. Most importantly, MDCM saves 94.5% of the computational cost compared to MCS, while maintaining the same accuracy and enabling large-scale practical deployment. Overall, this framework provides an efficient, theoretically sound, and practically deployable computational solution for low-carbon and robust distribution networks.