Non-convex myopic electricity markets : the AC transmission network and interdependent reserve types

Electricity markets are particularly complex because they must accommodate the underlying physics that govern the electric power system. These physics present non-convexities in the social welfare maximization problem, also called the economic dispatch problem, solved by the Independent System Operator (ISO), which is the social planner in this context. The non-convexity of this problem presents difficulties in computing the social welfare maximizing dispatch as well as difficulties in deriving a pricing structure that satisfies certain economic requirements such as revenue adequacy of the ISO and non-negative operating profits for market participants. This dissertation analyzes two sources of non-convexity that pertain to two separate market changes that have been recently proposed in Texas. Both proposals pertain to the real-time electricity market, which clears every 5-minutes and is myopic in the sense that only the demand at the end of the upcoming 5-minute interval is considered and no future time intervals are considered in the social welfare maximization problem.

The Electric Reliability Council of Texas (ERCOT) is the ISO in Texas and currently neglects resistive losses along transmission lines when formulating the economic dispatch problem. The first part of this dissertation regards a proposed market change to incorporate transmission losses into the economic dispatch problem. Two general approaches are considered to accommodate associated non-convexity. Similar to current practice, the first approach is based on a marginal pricing structure and uses convex approximations that facilitate efficient computation. By utilizing various approximations, the aforementioned economic requirements are proven to be satisfied approximately. The second approach is based on an alternative pricing structure in which prices are chosen to explicitly minimize the worst-case violation of these economic requirements. For example the prices may be chosen to minimize the potential revenue shortfall of the ISO. These alternative prices are termed convex hull prices and can be approximated by use of convex relaxations.

The economic dispatch problem currently used by ERCOT does not endogenously represent operating reserves to handle contingencies that may occur. Instead, operating reserves are currently optimized separately from the electric power generation dispatch. The second part of this dissertation regards a proposed market change to co-optimize reserve and generation dispatch in a social welfare maximization problem called a co-optimization problem. Implementation of the real-time co-optimization problem is being pursued simultaneously with a new definition of the primary frequency responsive reserve types considered in the market. One of these reserve types intends to accommodate standard droop control. Another of these reserve types is newly introduced and intends to facilitate participation of fast-acting batteries in primary frequency response. This dissertation derives reserve requirements from first principles that capture the coupling of these two reserve types as well as their ramping abilities. The newly proposed non-convex requirements represent limits on the ramp-constrained primary frequency responsive reserve procurement. Placing these non-convex requirements into a co-optimization problem is proven to result in the satisfaction of the aforementioned economic requirements.