Microgird (MG) can operate in islanded mode and serve as black-start resource for power system restoration (PSR). In this work, a model predictive control based generator start-up optimization strategy for PSR is proposed utilizing MGs as black-start resources. Firstly, the generator start-up sequence (GSUS) optimization is formulated as a mixed integer linear programming. Then the uncertainties of microgrid black-start resources (MBSRs) are modeled by discretizing the probability distribution of the forecast errors, and representative scenarios for MBSRs extracted by formulating the probability mass transportation problem. Thirdly, the generator start-up optimization strategy considering MBSRs is formulated utilizing the model predictive control (MPC) technique, in which the optimization objective is to maximize the energy capability of the power systems and minimize the load curtailment of the MGs in each looking-ahead interval. Simulations on the IEEE 118 bus system with MGs and Zhejiang provincial power system in China verify that the proposed strategy for PSR can successfully restore the power system and effectively determine the optimal GSUS.

Power system restoration comprises of three stages, i.e. the preparation stage, system restoration stage, and load restoration stage. This paper addresses the first two stages by a new skeleton-network restoration strategy considering the generator start-up sequence and load pickup. The proposed restoration strategy consists of three mathematical models: generator start-up sequence (GSUS) model, transmission line restoration (TLR) model and load pickup (LDP) model. The GSUS model aims to maximize the overall system generated energy considering the actual power system topology. The TLR model is to attain an optimal skeleton-network by identifying the restoration sequence of transmission lines. Critical loads are restored to keep the voltage within a specified respective threshold, and the load amounts are optimized in the LDP model. The proposed GSUS model and TLR model are both solved by the branch-and-bound method, while the LDR model is solved by the interior point method as well as the branch-and-cut method. Finally, the performance of the proposed method is demonstrated by two case studies on the New England 10-unit 39-bus system and an actual power system in Guangdong, China, respectively.

This paper presents a coordinated islanding partition and scheduling strategy for service restoration of active distribution networks (ADNs) to maximize weighted restored energy considering the minimum sustainable duration (MSD) of controllable islands (CIs). To avoid the forming of uncontrollable islands, the concept of dominated buses is proposed and integrated into the topological model of ADNs for islanding partition. The co-optimization of mobile distributed generator (MDG) dispatch and dominated bus identification is carried out to accelerate the restoration process. The MSD of CIs is explicitly modeled, and the CIs are scheduled in a risk-adjusted way, whose conservatism can be adjusted by controlling the predefined risk confidence level. Interruptible loads are considered as flexible resources in the islanding partition strategy considering the effects of the MSD of CIs. To improve the practicability of the presented method, time-varying power demands and distributed renewable generation outputs are incorporated into the presented framework. The studied problem is formulated as a mixed-integer second-order cone programming model, which can be efficiently solved by commercial solvers. Finally, a modified version of the Pacific Gas and Electric Company 69-bus distribution system, a practical medium-voltage distribution system in Denmark, and a modified IEEE 123-bus distribution system are employed to demonstrate the performance of the developed model.

This paper proposes a restorability improvement strategy to accelerate system restoration through the implementation of a wind farm-battery energy storage system (WF-BESS) system. The concept of restorability is introduced and a restorability improvement model (RIM) is proposed and formulated as a mixed integer linear programming problem. To simulate the cylinder temperature drop during outages, the cranking time of a unit is modeled as a stepwise function of its startup time in the RIM. The WF might fail to meet its scheduled generation outputs optimized by the RIM due to the intermittency of wind. To tackle this problem, a linearized control strategy for the BESS (CSBESS) is proposed to minimize the difference between the scheduled wind power outputs and the combined power of the WF-BESS system. An iterative method is employed to efficiently solve the RIM and CSBESS by introducing optimality cuts. An actual power system case is employed to illustrate the effective performance of the proposed approach.

This article proposes a two-layer optimal scheduling strategy to handle the overvoltage problem in high photovoltaic (PV) power-penetrated distribution networks. The voltage regulators can be classified as the power utility and PV owners, which are referred to as stakeholders. The proposed scheduling strategy includes autonomous optimization layer and coordination optimization layer. In the autonomous optimization layer, a min-max robust game model and a mixed-integer second-order cone programming-based model are respectively proposed to minimize the operating costs of PV stakeholders and the power utility stakeholder. A parallel optimization is employed to solve the two models in the autonomous optimization layer. In the coordination optimization layer, a noncooperative game-based model is presented to coordinate scheduling solutions of each stakeholder. Finally, an actual 10 kV, 106-bus feeder in Zhejiang Province, China, and a modified IEEE 123-bus distribution system are employed to verify the feasibility and effectiveness of the proposed approach.

One of the major functions of a smart substation is to restore power supply to interrupted customers as quickly as possible after an outage. The high cost of a smart substation limits its widespread utilization. In this paper, a smart substation allocation model (SSAM) to determine the optimal number and allocation of smart substations in a given distribution system is presented, with the upgrade costs of substations and the interruption costs of customers taken into account. Besides, the reliability criterion is also properly considered in the model. By linearization strategies, the SSAM is simplified into a mixed integer linear programming problem which could be solved efficiently with commercial solvers. Finally, the performance of the proposed methodology is demonstrated by the standard RBTS-BUS 4 test system and a medium voltage power distribution system in Denmark.