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Stochastic Optimization for Resource Adequacy in Capacity Markets with Storage and Renewables

Baptiste Rabecq, Andy Sun, Feng Zhao, Tongxin Zheng, Xiaochu Wang, Yufan Zhang

Abstract

The integration of storage and renewable resources fundamentally alters resource-adequacy analysis. Because storage couples decisions across time, it invalidates the traditional reliability models that are based on time-independent capacity demand curves. Moreover, renewables introduce temporally correlated intermittency. To address this, we formulate the capacity procurement problem as a two-stage stochastic program, where the capacity decision is made in the first stage, while the expected unserved energy is evaluated by a second-stage dispatch problem that considers uncertainties such as generator failures via Markov chains, temporally correlated renewable output, and stochastic load. We implement the resulting stochastic capacity procurement (SCP) model on a New England system with 305 generators, including conventional, renewable, and storage units. Using the stochastic decomposition (SD) algorithm, we solve the SCP with up to 20,000 Monte Carlo samples, each representing a six-month trajectory of more than 4,300 hours of uncertainty across all units. We analyze the convergence behavior of SD and show that convergence for the stochastic program happens faster than reliable estimation of the reliability metrics, which require more samples than are used in typical stochastic programs. These results show that chronologically detailed Monte Carlo sampling can be integrated into capacity procurement optimization in a computationally tractable manner, enabling reliability evaluation with controlled statistical accuracy at realistic system scales.

Stochastic Optimization for Resource Adequacy in Capacity Markets with Storage and Renewables

Abstract

The integration of storage and renewable resources fundamentally alters resource-adequacy analysis. Because storage couples decisions across time, it invalidates the traditional reliability models that are based on time-independent capacity demand curves. Moreover, renewables introduce temporally correlated intermittency. To address this, we formulate the capacity procurement problem as a two-stage stochastic program, where the capacity decision is made in the first stage, while the expected unserved energy is evaluated by a second-stage dispatch problem that considers uncertainties such as generator failures via Markov chains, temporally correlated renewable output, and stochastic load. We implement the resulting stochastic capacity procurement (SCP) model on a New England system with 305 generators, including conventional, renewable, and storage units. Using the stochastic decomposition (SD) algorithm, we solve the SCP with up to 20,000 Monte Carlo samples, each representing a six-month trajectory of more than 4,300 hours of uncertainty across all units. We analyze the convergence behavior of SD and show that convergence for the stochastic program happens faster than reliable estimation of the reliability metrics, which require more samples than are used in typical stochastic programs. These results show that chronologically detailed Monte Carlo sampling can be integrated into capacity procurement optimization in a computationally tractable manner, enabling reliability evaluation with controlled statistical accuracy at realistic system scales.
Paper Structure (9 sections, 6 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 9 sections, 6 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Model
  3. Methods
  4. Experiments
  5. Results
  6. Convergence of the algorithm
  7. Statistical validation of the solution
  8. Solution and seasonal mix
  9. Conclusion

Figures (3)

  • Figure 1: Convergence diagnostics of the SD algorithm: (a) model gap $\Delta_k$, (b) incumbent objective value, and (c) expected cost of unserved energy, all as functions of the number of iterations for the summer and winter capacity auction, at aggregation level $10$ ($5$ hours) MW and $100$ MW ($2$ hours).
  • Figure 2: Comparison between summer and winter capacity mix of $x^*$ (MW). The blue and pink bars represent the cleared capacity and total available capacity, respectively.
  • Figure 3: Load Shedding Distribution for the summer and winter auction (MWh)