Getting prices right on electricity spot markets: On the economic impact of advanced power flow models

As the share of variable renewable energy increases, adequate prices on electricity spot markets become increasingly important as they set signals for scarcity, investment, or demand response. Market prices are derived from the underlying welfare maximization problem. On electricity spot markets, this optimization problem is based on the non-convex and non-linear Alternating Current Optimal Power Flow (ACOPF) model. Since the ACOPF is intractable, electricity markets around the world use a linear approximation, the Direct Current Optimal Power Flow (DCOPF) model. Recent research has led to better non-linear relaxations of the ACOPF. We show that these non-linear relaxations increase welfare and imply significantly lower redispatch costs and side-payments. Most importantly, we show that the price signals obtained from non-linear relaxations are much improved. The DCOPF often yields high price differences between nodes when there is no line congestion in the AC-feasible solution or vice versa. Such biased price signals pose a significant problem in practice as they lead to inefficient demand response, distorted investment signals, and incorrect congestion incomes. The use of non-linear relaxations mitigates this problem and provides an important advantage of the resulting prices over prices based on the DCOPF.