On the Convexity of Common Resource Adequacy and Capacity Accreditation Metrics

Many emerging capacity expansion optimization formulations implicitly presume the convexity (or concavity) of power system adequacy risk (or capacity accreditation) metrics. These assumptions have yet to be formally justified. We present concise mathematical proofs validating the claim for certain metrics (expected unserved energy and effective load carrying capability), but also provide simple invalidating counterexamples for others (loss-of-load expectation and equivalent firm capacity). Formulations built on non-convex (non-concave) metrics structurally undervalue candidate portfolio adequacy, and so cannot claim to produce least-cost expansion plans.