Helping to find the ”missing money”: Semi-lagrangean approach applied to electricity markets with payments for engaged capacity

One peculiarity of the wholesale electricity market that seems persistent across some market designs is the ”missing money” problem. This problem appears when generators do not recover their costs given the market price of electricity. The ”missing money” problem may be in part due to the pricing and payment mechanisms set in place. Competitive forces should set the price of a commodity to the marginal cost of the marginal unit producing the good if the functions are convex. However, electricity markets are characterised for having non-convex function due to the generators' minimum and maximum outputs constraints, start up and shut down costs, amongst other characteristics. Therefore, uniform marginal price schemes will not always create market-clearing price. Under this scheme, not all the generators will cover the costs incurred in production. Different recovery mechanisms have been proposes, but the case of the ”missing money” is still a challenge these days, especially in pool-based markets. A possible solution is to price for capacity as well as for the electricity. Capacity markets have developed, and they still are in progress. And although some authors are not supporters of capacity payments and capacity markets, some others have shown the need for capacity payments and suggested a design for its market. This paper contributes to the growing literature in capacity pricing by suggesting a new approach to obtain electricity prices and capacity prices for the plants engaged into production. This approach applies the semi-Lagrangean methodology to an expanded Unit Commitment and Dispatch Problem. The expanded problem includes an extra constraint that sets the total capacity engaged to its optimal value. The new semi-Lagrangean problem is solved by using a subgradient approach. We obtain a set of prices for electricity and capacity that are high enough to cover the generators' costs, as well as sending the right signals to the market, and producing efficiently at a minimum costs. We believe that the excess revenue obtained with this approach can be used as a guide to future investment, and as a consequence, can help to find the ”missing money”.