A Data-Driven Framework for Inferring the Income Calculation Method of AGC Service Using Adaptive p best Differential Evolution

Automatic generation control (AGC), as a critical regulation technology, plays a vital role in maintaining power system stability. However, in immature electricity markets, incomplete income calculation methods of AGC service in publicly relative rules introduce significant uncertainty for market participants in strategy formulations. To address this issue, this paper formalizes the AGC service income calculation methods inference problem (AGC-ICMIP) as a mixed-variable optimization problem (MVOP) and proposes a data-driven inference framework (IF-AI) based on historical market data. Additionally, a hybrid differential evolution (DE) algorithm designed for MVOPs, referred to as adaptive p best $\mathrm{DE}\left(\right.$ APDE $\left._{m v}\right)$, is proposed to effectively address the AGC-ICMIP within IF-AI. APDE ${ }_{m v}$ balances exploration and exploitation across distinct evolutionary stages of the population, with its superior performance validated on 28 artificial benchmarks. Experimental results demonstrate that the proposed framework effectively solves AGC-ICMIP, with $\boldsymbol{A} \boldsymbol{P D E}{ }_{m v}$ achieving optimal performance. Furthermore, experimental results indicate that the precise solution of AGCICMIP effectively guides an energy storage system (ESS)-assisted response strategy for AGC signals, thereby yielding higher income in real-world operations. This finding demonstrates that our approach helps bridge the gap between research on AGC service income optimization and its practical applications.