Proactive Robust Hardening of Resilient Power Distribution Network: Decision-Dependent Uncertainty Modeling and Fast Solution Strategy

To address the power system hardening problem, traditional approaches often adopt robust optimization (RO) that considers a fixed set of concerned contingencies, regardless of the fact that hardening some components actually renders relevant contingencies impractical. In this paper, we directly adopt a dynamic uncertainty set that explicitly incorporates the impact of hardening decisions on the worst-case contingencies, which leads to a decision-dependent uncertainty (DDU) set. Then, a DDU-based robust-stochastic optimization (DDU-RSO) model is proposed to support the hardening decisions on distribution lines and distributed generators (DGs). Also, the randomness of load variations and available storage levels is considered through stochastic programming (SP) in the innermost level problem. Various corrective measures (e.g., the joint scheduling of DGs and energy storage) are included, coupling with a finite support of stochastic scenarios, for resilience enhancement. To relieve the computation burden of this new hardening formulation, an enhanced customization of parametric column-and-constraint generation (P-C&CG) algorithm is developed. By leveraging the network structural information, the enhancement strategies based on resilience importance indices are designed to improve the convergence performance. Numerical results on 33-bus and 118-bus test distribution networks have demonstrated the effectiveness of DDU-RSO aided hardening scheme. Furthermore, in comparison to existing solution methods, the enhanced P-C&CG has achieved a superior performance by reducing the solution time by a few orders of magnitude. Note to Practitioners - This paper presents a robust-stochastic optimization method for enhancing power system resilience considering endogenous and exogenous uncertainties. A resilience-based network hardening model is formulated under the trilevel RSO framework incorporating the DDU set. Compared to the traditional RO built upon the static uncertainty sets, the DDU-RSO formulation has a dynamic and stronger modeling capability, which captures the endogenous nature of contingency uncertainties associated with proactive hardening decisions. Also, the exogenous uncertainty of power loads and available storage levels is considered by introducing a scenario-based SP formulation in the innermost level problem. Note that the real shape and size of DDU set are changeable depending on the proactive decisions, which makes our problem very challenging to compute. To exactly and efficiently solve the DDU-RSO model, we design and implement a customized P-C&CG algorithm. Also, the enhancement strategy based on resilience importance indices is applied, which helps address the multi-solution dilemma widely existing in network optimization problems. It is worthy noting that the resilience importance indices can be attained not only using numerical calculation, but also through the prior knowledge of system operators. The probability information of contingency events is also helpful for determining the resilience importance indices to reduce the conservatism of RO decisions. By exploiting the "deep knowledge"contained in power systems, the customized P-C&CG algorithm has demonstrated a superior scalable capability over existing methods (e.g., the basic C&CG and a type of Benders decomposition algorithm). With this advanced analytical tool, the proposed optimization framework can be readily implemented for resilient planning and operation of large-scale real-world power systems.