Approximating expected marginal production cost with capacity commitment requirements

The authors consider methods for rapid computation of the cost function for a power system with no energy-limited units, but with capacity commitment constraints. Their goal is to embed such a computation in an optimization system for generation scheduling. The equivalent load method is unsuitable due to the commitment requirement. They compare crude Monte Carlo estimation, control variate estimation, direct approximation by orthogonal polynomials (“method of moments”), indirect approximation (approximation of an effective or linear-equivalent load function) by orthogonal polynomials, and indirect approximation by Chebyshev interpolation. They report computational results comparing the timing and accuracy of various methods. They find indirect approximation, in particular using the effective load, to be superior to moment methods