Analytical Solution for Stochastic Unit Commitment Considering Wind Power Uncertainty with Gaussian Mixture Model

TL;DR

This paper presents an analytical approach using Gaussian mixture models to efficiently solve stochastic unit commitment problems with wind power uncertainty, ensuring operational constraints with specified probabilities.

Contribution

It introduces a novel Newton method-based procedure to transform chance constraints into deterministic forms within a GMM framework for CCUC.

Findings

Efficient solution of CCUC as a mixed-integer quadratic programming problem.

Demonstrated scalability and efficiency through numerical tests.

Accurately models wind power uncertainty with Gaussian mixture models.

Abstract

To capture the stochastic characteristics of renewable energy generation output, the chance-constrained unit commitment (CCUC) model is widely used. Conventionally, analytical solution for CCUC is usually based on simplified probability assumption or neglecting some operational constraints, otherwise scenar-io-based methods are used to approximate probability with heavy computation burden. In this paper, Gaussian mixture model (GMM) is employed to characterize the correlation between wind farms and probability distribution of their forecast errors. In our model, chance constraints including reserve sufficiency and branch power flow bounds are ensured to be satisfied with pre-determined probability. To solve this CCUC problem, we propose a Newton method based procedure to acquire the quantiles and transform chance constraints into deterministic constraints. Therefore, the CCUC model is efficiently solved as a mixed-integer quadratic programming problem. Numerical tests are performed on several systems to illustrate efficiency and scalability of the proposed method.