A Dual Approximate Dynamic Programming Approach to Multi-stage Stochastic Unit Commitment

TL;DR

This paper introduces a dual approximate dynamic programming method for multi-stage stochastic unit commitment, balancing bound strength and scalability by using demand-dependent multipliers, demonstrated on a complex 168-stage problem.

Contribution

It adapts the dual approximate dynamic programming approach to include demand-dependent multipliers, improving bounds and scalability in stochastic unit commitment.

Findings

Achieved effective bounds and policies for a 168-stage problem.

Balanced bound quality with scalability by demand-dependent multipliers.

Demonstrated applicability to complex constraints like ramping and minimum uptime/downtime.

Abstract

We study the multi-stage stochastic unit commitment problem in which commitment and generation decisions can be made and adjusted in each time period. We formulate this problem as a Markov decision process, which is "weakly-coupled" in the sense that if the demand constraint is relaxed, the problem decomposes into a separate, low-dimensional, Markov decision process for each generator. We demonstrate how the dual approximate dynamic programming method of Barty, Carpentier, and Girardeau (RAIRO Operations Research, 44:167-183, 2010) can be adapted to obtain bounds and a policy for this problem. Previous approaches have let the Lagrange multipliers depend only on time; this can result in weak lower bounds. Other approaches have let the multipliers depend on the entire history of past random observations; although this provides a strong lower bound, its ability to handle a large number of sample paths or scenarios is limited. We demonstrate how to bridge these approaches for the stochastic unit commitment problem by letting the multipliers depend on the current observed demand. This allows a good tradeoff between strong lower bounds and good scalability with the number of scenarios. We illustrate this approach numerically on a 168-stage stochastic unit commitment problem, including minimum uptime, downtime, and ramping constraints.