Competitive Equilibrium Analysis for Renewables Integration in Dynamic Combined Heat and Power Trading Market

With the increasing interdependence among the electricity and district heating systems in economy and physics, this study focuses on the equilibrium analysis of the combined heat and power market (CHPM). Based on the gradient method in game theory, a dynamic model characterizing renewables uncertainty and negotiation process among dominant participants is established. Inspired by modern control theory, the dynamic model can be viewed as state equations in which the actions of participants are control signals, and the system states, such as nodal price and bus voltages, are treated as system state variables. A detailed proof for asymptotic stability around the market equilibrium is derived, and its region of attraction is quantified. The resulting sufficient conditions can also be used to quantify the impact of renewable energy uncertainty and congestion constraints on market stability. The whole trading process is designed to be implemented by distributed algorithms to reduce the computation burden of central authority. Numerical tests on two cases with different scales are conducted to demonstrate the theoretical analysis and the application of the proposed sufficient conditions for market stability.