This paper proposes a new decentralized restoration scheme in order to realize efficient coordinated restoration of the coupled transmission and distribution (TS-DS) system. First, considering the separated operation of the TS operator (TSO) and DS operators (DSOs) and to avoid the TSO data processing burden, the TS-DS system is divided into several subsystems according to their physical connection. Then, in order to implement the independent but coordinated decision-making of the subsystems, a decentralized decision-making framework is constructed by model decoupling and iterative interaction between TS and DS. Furthermore, for the sake of the convergence of the iterative process with non-convex models, a new decentralized optimization method is developed to obtain the optimal coordinated restoration strategy of the TS-DS system. The proposed decentralized restoration scheme achieves independent decision-making of the TSO and DSOs in the coupled TS-DS system, and solves the non-convergence problem of the decentralized optimization method. The effectiveness of the proposed method is validated using two IEEE standard test systems and a real-world power system.

When power systems encounter outages and large-scale blackouts, system restoration is critical and should be carried out with dedicated schemes. In this past, most studies divided the power system restoration into three stages and deal with them separately. After that, few studies considering the three stages together were emerging while the support of multiple flexible resources, i.e., renewable energy source (RES), electric vehicle system (EVS) and energy storage system (ESS), were not considered comprehensively. Therefore, a bi-level coordinated power system restoration (BiCPSR) model is proposed in this work considering the support of multiple flexible resources. In the upper level, skeleton-network indexes and restoration characteristics of generators and loads are utilized for optimizing the start-up sequence of generators and network reconfiguration. In the lower level, the uncertainties of RES and EVS are considered by various scenarios and the support of multiple flexible resources is utilized cooperatively for accelerating the restoration process and maximizing the restorable load. Case studies on the revised IEEE-39, WECC-179 and the actual Zhejiang power systems are performed to illustrate the basic features of the proposed model and its availability in bulk power systems. The comparisons between the proposed model and other models are also performed to illustrate the strengths of the proposed model

Several parallel restored subsystems exist in the last stage of the build-up restoration process of bulk power systems. The whole system restoration is completed when these subsystems are re-connected and their internal loads are recovered. This paper pro-poses a robust distributed coordination scheme to achieve reconnection and load recovery of parallel restored subsystems in wind power penetrated transmission systems. First, robust distributed restoration models are constructed considering individual subsystems under uncertain conditions. Then, an inner-outer nested upper-lower (IOUL) iterative algorithm is developed to solve the constructed models. The robust distributed coordination can be realized according to convergence. The proposed algorithm solves the complex non-convex model with uncertain variables by iteratively solving the small-scale mixed-integer linear programming (MILP) problem. The robust distributed restoration scheme allows independent decision-making within subsystems and ensures the feasibility of the distributed restoration strategy under uncertain conditions. The effectiveness of the proposed method is validated using three interconnected 6-bus systems and the IEEE 118-bus system, showing improved computational efficiency and restoration acceleration.

This paper proposes a new distributed risk-limiting load restoration scheme for wind power penetrated interconnected bulk systems. The conditional value-at-risk (CVaR) is used as the risk-limiting index. The projection function based alternating direction method of multipliers algorithm (P-ADMM) is used to de-couple the CVaR integrated load restoration model into a distributed form. With the proposed algorithm, the risk-limiting constraints are decomposed and the complex non-convex load restoration model with the CVaR is transformed into small-scale scenario-based QP problems. The distributed risk-limiting load restoration scheme respects the individual decision-making of regional grids and reduces the security violation risk of the inter-connected bulk system under uncertain conditions. The CVaR integrated P-ADMM method can efficiently reduce the computation complexity of the load restoration optimization for the uncertain bulk system without loss of optimality. The effectiveness of the proposed method was validated using the IEEE-118 bus system connected with ten IEEE-33 bus systems.

This paper proposes a new scheme for bulk system restoration considering the available black-start resources (BSRs) in the distribution system (DS). The DS assisted generator start-up sequence (D-GSS) scheme is realized in a decentralized way, so that it does not only benefit the bulk system GSS by utilizing available BSRs in the DS, but also respects the independent operation of the transmission system operator (TSO) and distribution system operators (DSOs). First, the decentralized D-GSS scheme is presented including the interaction of the TSO and DSOs and the corresponding compact models. The models of the decentralized D-GSS scheme are built with the bulk system GSS modeled as a mixed-integer quadratic program (MIQP), the DS multi-step operation modeled as mixed-integer second-order conic programs (MISOCPs) and reliable power supply assessments of renewable energy sources as linear programs (LPs). Finally, a projection function based analytical target cascading (P-ATC) method is developed to iteratively solve the decentralized models with model complexity reduction. The P-ATC algorithm can handle integer variables and improve the computational efficiency of the iterative calculation process. The effectiveness of the proposed method is validated using the small-scale T6D2 system and large-scale T118D5 system, showing good GSS performance and computation efficiency.