BY **Cecilia Maya**, Chief Market Operations, Colombian Power Independent System and Market Operator

ON **June 1, 2022**

Originally published in APEx Newsletter Volume XXI – June 2022

*Since the early waves of electricity market liberalizations, pricing in day-ahead markets has raised challenging questions rooted in economics and optimization theory. In general, finding uniform paid-as-cleared market prices, i.e. clearing prices that uniformly apply to bids such that all price-compatible bids are accepted and price-incompatible bids are rejected, is mathematically impossible in day-ahead (or more generally closed-gate) electricity markets, due to the presence of indivisibility constraints.*

We discuss here how that pricing challenge is addressed currently in the EU Single Day-Ahead Coupling (SDAC), in the US, and why Non-uniform Clearing prices may potentially be a key enabler leading to more welfare and better algorithm scalability. The question of obtaining meaningful price signals is also briefly discussed.

Uniform pricing means that in the market outcome, every market participant of the same market segment (location and hour of the day) will pay or receive the same electricity price and no other transfers or payments are considered. Uniform prices correspond to the classic pay-as-clear design.

Competitive equilibrium is a market outcome where the market clears (balance of supply and demand), and where market prices are such that no one (buyers or suppliers) has an incentive to deviate from the accepted quantities satisfying the power balance. Equivalently, for these market prices, there is no paradoxical acceptance (in which case the market participant would rather prefer its order not to be matched), or paradoxical rejection (in which case the market participant would rather prefer its order to be accepted).

When only demand and offer curves are in scope, classic economics teaches us that the intersection of the supply and demand curves determines a competitive equilibrium and its market-clearing price.

In day-ahead electricity markets, additional more advanced bids than simple demand and offer curves are used to take into account technical-economic constraints such as minimum power output levels or start-up costs for generation assets. In such a case, it is in general not possible to find a “single price fits all” supporting a competitive equilibrium and ensuring that every market player is perfectly fine with the market outcome. A simple example is demonstrated in the full version of this article is available here.

In the current design in the EU Single Day-ahead Coupling and in India, the welfare optimal allocation would most of the time be discarded, in case it is not possible to find uniform prices avoiding that some orders are paradoxically accepted. A concrete example can be found in the full version of this article here.

An advantage of this design is for example that there is no need to organize compensations (also called sidepayments) to bids losing money because they are paradoxically accepted, as those solutions are forbidden.

Regarding fairness of the outcome, on one hand, every accepted order will be cleared at the same prices without relying on anonymous discriminatory side-payments, but on another hand, some (block) orders are paradoxically rejected, which can be perceived by some market participants as an unfair or at least undesirable market outcome. Paradoxical rejection of orders is however in general unavoidable in (“non-convex”) day-ahead electricity markets.

Such a design requires checking specific price conditions every time an order-matching candidate solution is found, and to discard such a solution if paradoxical acceptance of some so-called block orders cannot be avoided. Technically speaking, this implies that the market-clearing algorithm needs to “iterate” between a volume problem (which a.o. determines the acceptance of bids), and a price problem (which verifies that prices are compatible with the accepted bids actually exist).

Non-uniform pricing essentially consists in dropping price conditions in the welfare optimization stage, and purely focusing on finding the welfare optimal order matching, i.e. the optimal allocation, optimizing the value of the accepted demand and of the supply costs (while taking into account all sorts of the market and network constraints, but without checking explicitly the market-clearing prices).

Because the problem is less constrained, solutions with more welfare are allowed. It also eases calculations of the market results, since there is no need to iterate anymore between the search for optimal bid acceptance and the calculation of clearing prices when a candidate solution is found.

On another hand, to ensure that all market participants are cleared at least at the price of their bids, compensations should be paid to so-called “out-of-the-money” orders that are losing money (i.e. those which are paradoxically accepted). This results in side-payments that differ among the impacted market participants.

The most extreme example of a non-uniform pricing scheme is pay-as-bid, as pay-as-bid settlement outcomes can be seen as resulting from some market-clearing prices, and (in general high) side-payments. However, in practice, pricing schemes such as Convex Hull pricing or Extended Locational Marginal Pricing, used by leading Independent

System Operators in the US (MISO, PJM, …) aim at being as close as possible to a uniform pricing scheme, and as far away from a pay-as-bid scheme.

Several questions arise with non-uniform pricing, and pricing rules in day-ahead electricity markets are still subject to active research in academia and in the industry. For the pricing stage aimed at computing market prices and sidepayments, several requirements or objectives could be imposed.

For example, Convex Hull Pricing aims at minimizing actual losses and lost opportunity costs of market participants and on the network side (congestion rent). With Convex Hull Pricing (or variants aimed at minimizing make-whole payments), some classic network price requirements enforced by strict Locational Marginal Pricing are usually not

met, for example, the fact that prices must be equal in different locations if there is no congestion in the network do not necessarily hold under Convex Hull Pricing.

Another property not guaranteed with Convex Hull Pricing is fractionally accepted orders set the clearing prices. For those two reasons, Convex Hull Pricing may not be seen as a good candidate for implementation in EU or Indian markets.

On another hand, Convex Hull Pricing and variants generally focus on making market prices as significant as possible, by minimizing deviations from a competitive equilibrium and minimizing the discretionary payments complementing the settlements purely based on these market prices.

The non-uniform pricing is by design leading to higher welfare and lowers computational complexity compared to pure uniform pricing. On another hand, non-uniform pricing implies side-payments, which in turn mean an additional complexity in terms of settlements. How market participants would behave under various pricing schemes is also an interesting question.

Non-uniform pricing is currently studied in the R&D program of Euphemia under the supervision of the Single Day-ahead Coupling Market & System Design body, as a promising avenue to improve market and algorithmic efficiency [1]. Further research will be needed in the future to have a complete understanding of the advantages and disadvantages of the pricing paradigms in scope for (European) day-ahead electricity markets.

CACM Annual Report 2020, All NEMO Committee in collaboration with ENTSO-E, available online here: https://www.nemo-committee.eu/assets/files/NEMO_CACM_Annual_Report_2020_deliverable_2_313_01_AT.pdf