A discussion on electricity prices, or the two sides of the coin

We examine how different pricing frameworks deal with non-convex features typical of day-ahead energy prices when the power system is hydro-dominated, like in Brazil. For the system operator, requirements of minimum generation translate into feasibility issues that are fundamental to carry the generated power through the network. When utilities are remunerated at a price depending on Lagrange multipliers computed for a system with fixed commitment, the corresponding values sometimes fail to capture a signal that recovers costs. Keeping in mind recent discussions for the Brazilian power system, we analyse mechanisms that provide a compromise between the needs of the generators and those of the system operator. After characterizing when a price supports a generation plan, we explain in simple terms dual prices and related concepts, such as minimal uplifts and bi-dual problems. We present a new pricing mechanism that guarantees cost recovery to all agents, without over-compensations. Instead of using Lagrange multipliers, the price is defined as the solution to an optimization problem. The behaviour of the new rule is compared to two other proposals in the literature on illustrative examples, including a small, yet representative, hydro-thermal system. This article is part of the theme issue 'The mathematics of energy systems'.