A General Sensitivity Analysis Approach for Demand Response Optimizations

In this work, we build upon existing literature on the demand response (DR) market, which consists of price-taking prosumers each with various appliances, an electric utility company and a social welfare optimizing distribution system operator, to design a general sensitivity analysis approach (GSAA) that can quantitatively estimate the potential of each consumer's contribution to the social welfare when given more resource capacity, such as allowing net-selling behavior. GSAA is based on existence of an efficient competitive equilibrium, which we establish in the paper. When prosumers’ utility functions are quadratic, GSAA can give closed forms characterization on social welfare improvement based on duality analysis. Furthermore, we extend GSAA to a general convex settings, i.e., utility functions with strong convexity and Lipschitz continuous gradient. Even without knowing the specific forms the utility functions, we can derive upper and lower bounds of the social welfare improvement potential of each prosumer, when extra resource is introduced. For both settings, several applications and numerical examples are provided: including extending AC comfort zone, ability of EV to discharge and net-selling behavior. The estimation results show that GSAA can be used to decide how to allocate potentially limited DR market resources in a more impactful way.