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A Novel Sectionalizing Method for Power System Parallel Restoration Based on Minimum Spanning Tree

Changcheng Li, Jinghan He, Pei Zhang, Yin Xu

2017
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Energies
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Parallel restoration is a way to accelerate the black-start procedure of power systems following a blackout. An efficient sectionalizing scheme can reduce the restoration time of a system, taking into account the black-start ability, generation-load balance of subsystems, restoration time of branches, start-up time of generating units, and effects of dispatchable loads and faulted devices. Solving the sectionalizing problem is challenging since it needs to handle a large number of Boolean
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... er of Boolean variables corresponding to the branches and nonlinear constraints associated with system topology. This paper investigates power system sectionalizing problem for parallel restoration to minimize the system restoration time (SRT). A novel sectionalizing method considering the restoration of generating units and network branches is proposed. Firstly, the minimum spanning tree (MST) algorithm is used to determine the skeleton network of a power system. Secondly, the number of subsystems is determined according to the number of black-start units. Based on the skeleton network, candidate boundary lines among subsystems are identified. Then, constraints are evaluated to identify feasible sectionalizing schemes. Except commonly used constraints on power balancing and black-start units, this paper also considers using dispatchable loads to meet the minimum output requirements of generating units. Finally, the sectionalizing scheme with the minimum SRT is selected as the final solution. The effectiveness of the proposed method is validated by the IEEE 39-bus and 118-bus test systems. The simulation results indicate that the proposed method can balance the restoration time of subsystems and minimize the SRT. Energies 2017, 10, 948 2 of 21 accelerates the system restoration process. The first step for parallel restoration is to determine a sectionalizing scheme. Some utilities and ISOs, including PJM (Pennsylvania-New Jersey-Maryland Interconnection) in United States [17] , National Grid Company in United Kingdom [18] and Chongqing Power of China State Grid [19] , have adopted parallel restoration plans for their systems. The sectionalizing schemes are designed mainly based on the operators' knowledge and experience. In recent years, theoretical investigations on sectionalizing methods for parallel restoration have attracted researchers' interests. The sectionalizing problem, which is usually determined by solving an optimization problem with constraints on black-start generators and generation-load imbalance, is proved to be a non-deterministic polynomial complete problem (NP-complete) [20] . There is no polynomial-time algorithm to solve it. Thus, it is difficult and time consuming to solve the sectionalizing problem for large-scale power systems. Wang, C. et al. applied the ordered binary decision diagram-based method (OBDD) to reduce the candidate sectionalizing schemes for determining optimal solution [20]. Afrakhte et al. applied genetic algorithm (GA) to find the subsystem boundaries and minimize the index of energy not supplied (ENS) [21]. Liang et al. also used GA to create subsystems with consideration of the start-up sequence of units [22]. Quiros-Tortos et al. put forward a sectionalizing methodology based on the cut-set matrix theory [23]. It was simple and useful for parallel restoration. Based on it, Sun et al. developed an optimal network sectionalizing strategy considering cranking generating units [24] . To minimize the time of units for getting cranking power is one of its objectives. These two methods are based on the recursive bisection and obtain two new subsystems by one iteration. After multiple iterations, multiple subsystems can be generated. Sarmadi et al. proposed a heuristic search algorithm to define an islands' matrix [25] . Considering the wide area measurement system (WAMS) information, the partitioning scheme for parallel restoration is determined by modifying the islands' matrix. A community detection algorithm was employed into the sectionalizing method for parallel restoration by Lin et al. [26] . The method can also generate the sequence for resynchronization of subsystems. The spectral graph clustering method was used in [27, 28] to design the optimal sectionalizing schemes. The sectionalized results depended on the eigenvalues of the Laplacian matrix of the system network, which were the impedance characteristics of branches. The aforementioned methods are focused on the topology of system without consideration of restoration time of the subsystems. A practical and efficient sectionalizing scheme can reduce the system restoration time (SRT) of a power system, which depends on the subsystem with the slowest restoration process, and enhance the efficiency of parallel restoration. Therefore, the restoration time of each subsystem is an important basis for determining sectionalizing schemes and should be estimated. Adibi discussed the estimation of the restoration duration [29] . The start-up time of generating units and the restoration time of branches are the main time consumption for restoring a power system. The time for the load pick up is ignored [30, 31] . The constraints, which should be considered in the sectionalizing problem, are summarized in references [20, 21, 23] . One important constraint is the minimum active power output of generating units, such as thermal units. To meet the minimum output constraint on generating units, researches generally take the total amount of load as the constraint but have not considered the effects of dispatchable loads [24, 25] . Since dispatchable loads can provide the variable power demand, they are widely used in power system operation, e.g., in demand side management [32, 33] . For power system restoration, they can be restored flexibly to balance the output of generating units [30, 34] . Especially, during the start-up process, a generator cannot be controlled effectively since its control system is designed for use between minimum and maximum load [12] . In this stage, dispatchable loads can be picked up to balance the output of restored units for system security. This paper proposes a novel sectionalizing method for parallel restoration based on the minimum spanning tree (MST). The objective is to minimize the SRT, considering the start-up time of generating units and the restoration time of branches. A power system can be abstracted as a weighted graph. The weight of each edge, representing a transmission line or a transformer, is specified with its Energies 2017, 10, 948 3 of 21

doi:10.3390/en10070948
fatcat:5i4s7weipzhczmjdxqdithmoze