Peak-load pricing with different types of dispatchability

We extend the theory of peak-load pricing by considering that the production with different technologies can be adjusted within their capacity at different speeds. In the established analysis, all production decisions can be made after the random variables realize. In our setting, in contrast, some decisions are made before, others after. This is important, e.g., when increasing capacities of renewables are integrated in electricity systems worldwide. We consider fixed load and three types of capacities: partially dispatchable capacity (e.g., nuclear power-plants) needs to be scheduled ahead of actual production, non-dispatchable capacity (e.g., wind turbines) produces randomly, and highly-dispatchable capacity (e.g., gas turbines) can instantly adjust. If capacities differ in their dispatchability, some standard results of peak-load pricing break down. For example, less capacity types will be employed. Either a system with partially dispatchable technologies only, or a system dominated by non-dispatchable technologies and supplemented by highly-dispatchables occurs. Non- and highly dispatchable technologies can be substitutes or complements. The probability of outage does not rise if non-dispatchable capacity becomes cheaper. In a system with non-dispatchables, capacity decisions cannot be decentralized by conventional markets because cost recovery is not possible. Thus, the integration of renewable electricity generators requires alternative market designs.