Abstract:  Power system restoration after a blackout can be speeded up by employing a parallel restoration strategy, while a reasonable zoning strategy is the basis of parallel restoration. The performances of most of the existing black-start zoning methods are highly dependent on the specified initial values, and it is hard to attain the global optimal solution by these methods. The semi-supervised spectral clustering algorithm is able to identify any shapes of sample spaces, and to attain the global optimal solution, which can be employed for black-start zoning. Given this background, this paper proposes the black-start zoning strategy based on the semi-supervised spectral clustering algorithm. Firstly, the reciprocal of electrical distance between nodes is used to determine the weight of the line, and then the undirected weighted graph of the power system concerned can be formed. On this basis, a black-start zoning strategy is presented based on the ratio cut set criterion. The proposed strategy consists of two steps. In the first step, a grouping optimization model of generators to be restored is presented for speeding the power system restoration, with both the maximization of the restored generation quantity in the given period and the minimization of the total capacitance of the restored transmission lines included in the objective function of the optimization problem. In the second step, the semi-supervised clustering algorithm is employed to solve the black-start zoning model based on the grouping information attained in the first step. In the the last step of semi-supervised spectral clustering algorithm, the k-means++ algorithm is employed to cluster the feature vectors, so as to avoid the  drawback of  the traditional k-means algorithm that the clustering result is sensitive to the specified initial cluster centers. Finally, the New England 10-unit 39-bus power system and IEEE 30-bus power system are employed to demonstrate the basic features of the developed model and method.

Key words:  power system restoration, black-start zone partitioning, semi-supervised clustering algorithm, k-means++ algorithm