Multi-objective optimization for short-term peak shaving in multi-grid energy systems with uncertainty and aggregated constraints

Rapidly developing power transmission channels effectively alleviate the spatial mismatch between power supply and demand by delivering diverse electricity to other regions. However, reasonably allocating limited electricity among multiple power grids, avoiding curtailment caused by wind and solar generation forecast errors, and accelerating the solution speed of models with complex cascade hydropower constraints remain challenges for such transmission models. To address these issues, a short-term peak shaving scheduling model is proposed, in which hydropower-dominated multi-energy is delivered to multiple power grids through multiple high-voltage direct current transmission channels. First, a bi-level objective function is constructed to address the multi-objective problem of multi-grid peak shaving, prioritizing the minimization of sequential penalty difference based on absolute first-order differences and supplemented by the minimization of peak valley difference. Second, non-parametric Gaussian kernel density estimation is used to characterize error confidence intervals of wind and solar power, and a novel transmission channel reserve capacity mechanism is proposed to directly accommodate their output uncertainty, reducing reliance on hydropower flexibility. Finally, the conventional hydropower operational equality constraints aggregated formulation is enhanced through the incorporation of inequality bounds constraints to substantially cut redundant constraints and variables, while structural comparisons elucidate acceleration mechanisms that broaden applicability across optimization algorithms. A case study involving five transmission channels delivering hydropower, wind, and solar power to three power grids demonstrates the proposed model's efficacy, reducing the sequential penalty difference by 88.2% and the peak valley difference by 68.3%, with a 91.2% faster solution speed than the traditional model.