February 2013 | Dimitris Bertsimas, Eugene Litvinov, Xu Andy Sun, Jinye Zhao, and Tongxin Zheng
This paper proposes a two-stage adaptive robust optimization model for the security constrained unit commitment (SCUC) problem in power systems. The model addresses the challenges posed by increasing uncertainty in load and generation due to the integration of variable renewable resources and price-responsive demand. Unlike traditional stochastic programming, the proposed model uses a deterministic uncertainty set rather than a probability distribution, making it more practical and robust against all possible realizations of uncertain nodal net injections. The model ensures that unit commitment decisions are robust and adaptive to uncertainty, incorporating key constraints such as network, ramp rate, and transmission security constraints.
The solution methodology combines Benders decomposition with outer approximation techniques to solve the two-stage adaptive robust SCUC problem. The model is tested on a real-world large-scale power system operated by the ISO New England, demonstrating its economic and operational advantages over the traditional reserve adjustment approach. The results show that the adaptive robust model achieves lower average dispatch and total costs, reduces the volatility of dispatch costs, and is more robust to different probability distributions of load uncertainty. The model also performs better under higher levels of load variation, showing significant cost savings and reduced penalty costs compared to the reserve adjustment approach. The study highlights the effectiveness of the adaptive robust model in improving the reliability and efficiency of power system operations under uncertainty.This paper proposes a two-stage adaptive robust optimization model for the security constrained unit commitment (SCUC) problem in power systems. The model addresses the challenges posed by increasing uncertainty in load and generation due to the integration of variable renewable resources and price-responsive demand. Unlike traditional stochastic programming, the proposed model uses a deterministic uncertainty set rather than a probability distribution, making it more practical and robust against all possible realizations of uncertain nodal net injections. The model ensures that unit commitment decisions are robust and adaptive to uncertainty, incorporating key constraints such as network, ramp rate, and transmission security constraints.
The solution methodology combines Benders decomposition with outer approximation techniques to solve the two-stage adaptive robust SCUC problem. The model is tested on a real-world large-scale power system operated by the ISO New England, demonstrating its economic and operational advantages over the traditional reserve adjustment approach. The results show that the adaptive robust model achieves lower average dispatch and total costs, reduces the volatility of dispatch costs, and is more robust to different probability distributions of load uncertainty. The model also performs better under higher levels of load variation, showing significant cost savings and reduced penalty costs compared to the reserve adjustment approach. The study highlights the effectiveness of the adaptive robust model in improving the reliability and efficiency of power system operations under uncertainty.