Many problems of recent interest in the design of sparse control for power grids can be posed in the structure optimization. Different performance indices and sparsity promoting penalty functions have been proposed for different control goals and structural constrains. We study the application of Lq norm as penalty function for sparse control optimization for bulk power networks. Our emphasis focus on identifying the sparsity patterns of feedback matrix under different value of q in Lq norm, by incorporating our design into the optimization framework of the alternating direction method of multipliers, which is well developed in recent researches on sparse control for power networks. The advantage of the alternating method allows us to exploit the penalty function by separating the function and quadratic performance in each iteration of solving the augmented Lagrangian. Case studies are provided to demonstrate the effectiveness of the proposed algorithm.
Alternating direction method of multipliers, Lq norm, Power networks, Sparse control
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