Two-stage data-driven adaptive robust bidding model for a virtual power plant in multi-market based on nonparametric method of LSSVM-AKDE under uncertainties

The virtual power plant (VPP) is increasingly used in power systems due to its benefits in promoting renewable energy consumption, reducing CO2 emissions and optimizing resource allocation. However, the uncertainties arising from renewable energy sources, varying energy demands, and multi-market interactions can pose significant challenges to system robustness and economic efficiency. To address this, we propose a two-stage data-driven adaptive robust bidding model (DDARBM) that integrates the day-ahead market (DAM), real-time market (RTM) and balancing market (BM). By incorporating bounded rationality responses of users, the model iteratively optimizes flexible resource dispatch through multi-round clearing in heterogeneous markets while providing individualized charging schedules to EV owners. Furthermore, using the non-parametric LSSVM-AKDE estimation framework, we construct a renewable energy output uncertainty set with dynamic bounds for DDARBM. Simulation results demonstrate that: 1) the proposed uncertainty set can effectively concentrate uncertainty information into narrow boundaries, while the AKDE curve based on 95 % confidence intervals can balance accuracy and selectivity while maintaining the original probability density function information. 2) By participating in the forward contract, DAM, RTM market clearing processes, VPP achieves a respective reduction in total cost by 0.442 %, 0.197 %, and 4.478 %. 3) By leveraging user-bounded rationality and resources like transferable load, interruptible load, and EV output, VPP can reduce bidding costs by 0.300 %, 0.155 %, 0.605 %, and 1.089 %, respectively. 4) Compared with stochastic optimization and robust optimization, adaptive robust models have both robustness and economy in resisting the influence of uncertainties. 5) By constraining paradigm variables, adjusting the confidence intervals, and increasing information from time-of-use tariff samples, the VPP's ability to handles uncertainties in DAM can be effectively improved.