Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

Abstract

Abstract-Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.Index Terms-Bilevel mixed-integer optimization, power system control and reliability, robust and adaptive optimization, security constrained unit commitment.

Two‐Stage Robust Security‐Constrained Unit Commitment with Optimizable Interval of Uncertain Wind Power Output

“…where Δ u and Δ d are up and down power generation adjusting amounts for generator under the worst-case scenarios (10) and (12), respectively, during period . The generators may be in off schedule in UC during periods − 1 and ; hence it assumes in (18) and (19) that the power output of generator will reach the minimum value once the generator starts up and the power output of generator is required to be the minimum value before it shuts down.…”

“…Because the bounded uncertainty set considered in robust optimization method with a high solving efficiency is easy to be obtained in reality and the robust optimization strategies can consider the worst case to guarantee the security of power systems operation under all possible scenarios within a given uncertainty set, the robust optimization method applied to UC with uncertain wind power output has become the current research hotspots [9][10][11][12][13][14]. A contingency-constrained UC with an -security criterion based on robust optimization is proposed in [9], 2 Mathematical Problems in Engineering where a single-level equivalent robust counterpart of the original problem is formulated.…”

“…A contingency-constrained UC with an -security criterion based on robust optimization is proposed in [9], 2 Mathematical Problems in Engineering where a single-level equivalent robust counterpart of the original problem is formulated. Bertsimas et al [10] and Jiang et al [11], respectively, propose a two-stage adaptive robust UC model with adjustable uncertainty budget to reduce the conservativeness of conventional robust optimization. Hu et al [12] proposes an effective method to acquire robust solutions to the security-constrained UC (SCUC) problem, which takes wind and load uncertainties into account via interval numbers.…”

“…In [14], a new concept recourse cost defining the upper bound of redispatch cost when uncertainties are revealed is proposed to reduce the conservativeness of robust optimization. All these works [9][10][11][12][13][14] indicate that robust optimization can ensure system security under the worst-case scenario, and, therefore, it is an effective approach for solving optimization problems with uncertainties.…”

“…However, in the existing works [9][10][11][12][13][14], the robust optimization approaches applied to solve UC problem mainly focus on the adjustment of conservativeness of uncertain parameters including wind power output and load as well as demand response. Wind power spillage which is also called "wind power curtailment" is rarely considered in these robust UC models which have a premise that wind power generation can be completely accommodated no matter how much wind power output and its uncertainty are.…”