Risk-averse co-optimization of virtual power plants in multi-markets considering scheduling costs and uncertainties of controllable loads

Multiple uncertainties, stemming from high distributed energy resource penetration and coupled multiple markets, pose significant risks to the economic dispatch and profitability of virtual power plants. A risk-averse optimization framework is developed to mitigate these risks and maximize total profit. The framework aggregates diverse urban flexible resources and extends the uncertainty set beyond renewables and market prices to include controllable load-side factors: schedulable potential bounds of two controllable-load classes and agents’ willingness to comply with dispatch. A scheduling-cost model maps dispatch intensity to user cost (discomfort, degradation) via a nonlinear function, while a time-varying, fair incentive mechanism is indexed to energy prices. Building on this, a coordinated co-optimization framework enables arbitrage across capacity, energy, and ancillary service markets, explicitly differentiating normal and emergency states. Under emergency conditions, the model determines the optimal strategy between honoring capacity contracts and defaulting for short-term market participation. Simulation studies show that omitting controllable load uncertainties inflates profit estimates; the proposed model increases profit by 11.31% over traditional models; and capacity market bidding (using 2025 prices) increases virtual power plant profit by 48.50%. The results highlight both the validity of the proposed co-optimization model and the critical necessity of integrating controllable load-side uncertainties for secure and profitable virtual power plant operation. • A risk-averse optimization framework for virtual power plants is proposed. • Uncertainties in controllable load boundaries and willingness are considered. • A scheduling-cost model for controllable loads is established. • A multi-market coordinated arbitrage model is developed.