Welfare optimal reliability and reserve provision in electricity markets with increasing shares of renewable energy sources

We develop an analytical model to derive the competitive market equilibrium for electricity spot and reserve markets under uncertain demand and renewable electricity generation. The first-best market equilibrium of the model resembles the result of a centralized co-optimization of the markets involved. We then derive the welfare-optimal provision of reserves. At first-best, cost of reserve capacity is balanced against expected cost of outages. Comparative statics and a numerical application based on German secondary reserve provision imply an increase of reserve provision with a growing share of renewable generation. Furthermore, a growing share of renewable generation decreases the level of reliability as measured in energy not served since required reserves to balance higher expected deviations will be more expensive, resulting in a trade-off between higher reserve costs and costs of energy not served.