[Paper Review] A Control-variable Regression Monte Carlo Technique for Short-term Electricity Generation Planning

Magnus Perninge|arXiv (Cornell University)|Dec 30, 2015

Electric Power System Optimization3 citations

TL;DR

This paper proposes a control-variate regression Monte Carlo method to solve high-dimensional short-term electricity generation planning problems with delayed reactions and stochastic network constraints. By using lower-bound approximations of the value function as control variates, the method significantly reduces variance in Monte Carlo simulations, enabling efficient computation of optimal re-dispatch strategies for power systems under operational risk and cost trade-offs.

ABSTRACT

In the day-to-day operation of a power system, the system operator repeatedly solves short-term generation planning problems. When formulating these problems the operators have to weigh the risk of costly failures against increased production costs. The resulting problems are often high-dimensional and various approximations have been suggested in the literature. In this article we formulate the short-term planning problem as an optimal switching problem with delayed reaction. Furthermore, we proposed a control variable technique that can be used in Monte Carlo regression to obtain a computationally efficient numerical algorithm.

Motivation & Objective

• Address the computational challenge of solving high-dimensional optimal switching problems in short-term electricity generation planning under network constraints and delays.
• Develop a numerically efficient algorithm for real-time power system operation that balances economic efficiency with security constraints.
• Improve Monte Carlo regression efficiency for optimal switching problems by introducing a control variate derived from lower-dimensional approximations of the value function.
• Enable tractable computation of optimal generation re-dispatch strategies in realistic power systems with multiple controllable generators and stochastic load variations.

Proposed method

• Formulate the short-term generation planning problem as an optimal switching problem with delayed execution and high-dimensional stochastic noise.
• Construct lower and upper bounds on the value function using dimensionally reduced approximations of the original problem.
• Use the lower bound as a control variate in regression Monte Carlo simulations to reduce variance in the estimation of the value function.
• Apply state-space partitioning and basis functions (e.g., polynomial and neural network-based) to approximate the value function and control policies.
• Implement a hybrid approach combining value function approximation and policy approximation to enhance computational efficiency.
• Utilize linear interpolation and Markov chain approximations to extend bounds across the state space and enable Monte Carlo sampling.

Experimental results

Research questions

• RQ1 How can high-dimensional optimal switching problems in short-term electricity generation planning be solved efficiently under network constraints and execution delays?
• RQ2 Can lower-dimensional approximations of the value function serve as effective control variates in regression Monte Carlo for such problems?
• RQ3 What is the impact of using control variates on the variance and convergence rate of Monte Carlo estimations in power system operation planning?
• RQ4 How does the method scale with increasing numbers of controllable generators and system complexity?
• RQ5 Can tighter bounds on the value function be derived through iterative sampling and policy evaluation to improve solution accuracy?

Key findings

• The proposed control-variate regression Monte Carlo method significantly reduces variance in value function estimation, leading to faster convergence and more accurate results compared to crude Monte Carlo.
• For a 39-bus system with 16 load buses and 10 controllable generators, the method achieved estimated optimal costs of 7,472 k¤/MW at 1 k¤/MW disruption cost using 100,000 trajectories.
• The use of the lower bound as a control variate reduced estimated costs by up to 30% compared to baseline Monte Carlo without control variates.
• The method demonstrated improved performance with increasing sample size, with costs stabilizing at 7,472 k¤/MW for 100,000 samples under low disruption cost (1 k¤/MW).
• The upper bound on the value function at t=0 was estimated at 94,865 k¤/MW for a 100 k¤/MW disruption cost, indicating the method can handle high-cost scenarios.
• The numerical complexity scales linearly with the number of operating modes (|Γ|), which grows exponentially with the number of controllable generators, posing a challenge for large-scale systems.