Risk-Sensitive Security-Constrained Economic Dispatch: Pricing and Algorithm Design

TL;DR

The paper addresses risk-aware security-constrained economic dispatch by embedding the CVaR risk measure ${\rm CVaR}_{\alpha}$ into a forward-looking ED framework, balancing dispatch cost with resilience to line outages. It develops a convex, linear-program formulation (R-SCED) that co-optimizes nominal generation, reserves, and contingent recourse actions across multiple outage scenarios, and proves two market-clearing pricing schemes (N-LMP and S-LMP) with ex-ante payments. The authors establish revenue adequacy and lost opportunity cost properties, showing that S-LMP ensures nonnegative merchandising surplus while N-LMP can fail to do so, especially under higher risk aversion. A Benders' decomposition algorithm is proposed to scale R-SCED to large networks, and numerical experiments on the IEEE 24-bus RTS network illustrate how risk aversion shapes load shedding, pricing signals, and computational performance. The work demonstrates that incorporating contingency costs into pricing via S-LMP yields more reliable and economically sound market outcomes and provides a scalable solution approach for risk-aware security-constrained operation.

Abstract

We propose a risk-sensitive security-constrained economic dispatch (R-SCED) formulation capturing the tradeoff between dispatch cost and resilience against potential line failures, where risk is modeled via the conditional value at risk (CVaR). In the context of our formulation, we analyze revenue adequacy and side payments of two pricing models, one based on nominal generation costs, and another based on total marginal cost including contingencies. In particular, we prove that the system operator's (SO) merchandising surplus (MS) and total revenue are nonnegative under the latter, while under the former the same does not hold in general. We demonstrate that the proposed R-SCED formulation is amenable to decomposition and describe a Benders' decomposition algorithm to solve it. In numerical examples, we illustrate the differences in MS and total revenue under the considered pricing schemes, and the computational efficiency of our decomposition approach.

Figures (5)

• Figure 1: A description of CVaR over the cost distribution induced by a set of fixed decision variables
• Figure 2: A 3-bus network example.
• Figure 3: The impact of varying line 1-3 failure probability on nominal generation cost and load shed in the 3-bus example when $\alpha = 0$ (solid) and $\alpha=0.9$ (dotted).
• Figure 4: Simulation results on the IEEE 24-bus RTS test network with \ref{['fig:24bus.cost.load']} load shed (average and total) and dispatch cost (nominal and total including reserve), \ref{['fig:24bus.ms.uplift']} merchandising surplus and uplift payments under N-LMP and S-LMP schemes, and S-LMP for \ref{['fig:24bus.lmp.alpha06']}$\alpha = 0.6$, and \ref{['fig:24bus.lmp.alpha09']}$\alpha = 0.9$.
• Figure 5: The KKT conditions for \ref{['eq:RSCED.lp']}.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Theorem 1
• Theorem 2