Stochastic Security-Constrained Unit Commitment

TLDR

The paper introduces a stochastic long‑term SCUC model. The approach models outages and load errors as Monte Carlo scenario trees, relaxes coupling constraints to decompose the problem into deterministic long‑term SCUC subproblems, then uses Lagrangian relaxation to split them into tractable short‑term MIP SCUC subproblems, and applies scenario reduction to trade speed for accuracy. Numerical simulations show the method is effective for stochastic SCUC and can be applied by utilities and ISOs.

Abstract

This paper presents a stochastic model for the long-term solution of security-constrained unit commitment (SCUC). The proposed approach could be used by vertically integrated utilities as well as the ISOs in electricity markets. In this model, random disturbances, such as outages of generation units and transmission lines as well as load forecasting inaccuracies, are modeled as scenario trees using the Monte Carlo simulation method. For dual optimization, coupling constraints among scenarios are relaxed and the optimization problem is decomposed into deterministic long-term SCUC subproblems. For each deterministic long-term SCUC, resource constraints represent fuel and emission constraints (in the case of vertically integrated utilities) and energy constraints (in the case of electricity markets). Lagrangian relaxation is used to decompose subproblems with long-term SCUC into tractable short-term MIP-based SCUC subproblems without resource constraints. Accordingly, penalty prices (Lagrangian multipliers) are signals to coordinate the master problem and small-scale subproblems. Computational requirements for solving scenario-based optimization models depend on the number of scenarios in which the objective is to minimize the weighted-average generation cost over the entire scenario tree. In large scale applications, the scenario reduction method is introduced for enhancing a tradeoff between calculation speed and accuracy of long-term SCUC solution. Numerical simulations indicate the effectiveness of the proposed approach for solving the stochastic security-constrained unit commitment