# Electricity market clearing price using fixed-MIP formulation?

Dual information of electricity markets clearing problem is required to calculate the marginal clearing price. As most electricity market problems are based on MIP (and dual information of MIP is not well-defined), fixed-MIP can be a potential strategy to obtain the dual prices.

I would like to ask if the fixed-MIP approach is used by electricity markets in practice? What could be its potential limitations except the one defined in an earlier post?

If it is not used, why?

I've gained sufficient information in last couple of weeks to write an answer myself.

As a prerequisite to the discussion, please note the difference between uniform vs non-uniform market clearing price. Non-convexities present in electricity market clearing models would lead to non-uniform prices, which would result in participants loosing money if no uplifts/side-payments are employed.

### Economic interpretation of dual prices obtained from fixed-MIP

The classical economic interpretation of dual price of power balance constraint in electricity market is "the total attained increase in objective cost if the electricity demand is increased by 1 MW"; Thus, the economic interpretation of dual price obtained from fixed-MIP concern the objective cost of fixed-MIP instead of the objective cost of original MIP problem.
Hence, if the desired market clearing price is supposed to be the one corresponding to the original MIP problem [in terms of economical interpretation], then, fixed-MIP approach to obtain dual price is not suitable. In other words, the dual price obtained from fixed-MIP does not represent the cost impact of 1 MW increase of demand in original MIP problem due to the fact that the original MIP could potentially find a completely different solution to binary/integer variable in response to 1 MW increase in demand.

### Additional non-convexities usually present in fixed-MIP model and their impact on dual prices

If the objective is to find a uniform market clearing price using fixed-MIP approach, one must make sure that fixed-MIP is free of all non-convexities. Most electricity market problems consist of various non-convexities in addition to already fixed binary/integer decision variables (startup/shutdown, mustrun etc.) making it impossible to find a uniform market clearing price using fixed-MIP. Such non-convexities include (non-exhaustive list):

1. Transmission congestion and losses
2. Minimum generation level
3. Ramping constraints
4. Co-optimization of energy and capacity etc.

### Fixed-MIP approach in practice

In practice, various market designs employ fixed-MIP to a certain degree but a special care is always required to clarify the impact of non-convexities. Below are some examples:

1. RTO/ISO type power pool markets: In this type of market, SCUC can be considered as original MIP problem and SCED can be considered equivalent to fixed-MIP. Some non-convexities such as transmission congestions and losses are handled using locational marginal pricing. Other non-convexities such as ramping, startup/shutdown etc. is handled using dedicated products which are settled via side-payments. However, even if the overall pricing mechanism is non-uniform, fixed-MIP (SCED) is used for driving the uniform part of price for energy and ancillary services products.
2. Pay-as-bid to manage non-convexities: Some markets settle the energy product at a uniform price [obtained from fixed-MIP] if the offer/bid is in-the-money and use pay-as-bid if the offer/bid is out of money (mostly due to non-convexities).
3. No fixed-MIP: Some other markets do not use fixed-MIP as they use alternate settlement mechanisms such as:
1. Pay-as-bid for all cleared offers/bids (+ side-payments for startup/shutdown).
2. Price of most expensive offer can be used if non-convexities are eliminated in the optimization algorithm by allowing sub-optimal solution.