Mathematics – Optimization and Control
Scientific paper
2011-06-28
Mathematics
Optimization and Control
Scientific paper
We consider the problem of optimal reactive power compensation for the minimization of power distribution losses in a smart microgrid. We first propose an approximate model for the power distribution network, which allows us to cast the problem into the class of convex quadratic, linearly constrained, optimization problems. Then, we design a randomized, gossip-like optimization algorithm based on that model. We show how a distributed approach is possible, where agents have a partial knowledge of the problem parameters and state, and can only perform local measurements. For the proposed algorithm, we provide conditions for convergence together with an analytic characterization of the convergence speed. The analysis shows that the best performance can be achieved when we command cooperation among agents that are neighbors in the electric topology. Numerical simulations are included to validate the proposed model and to confirm the analytic results about the performance of the proposed algorithm.
Bolognani Saverio
Zampieri Sandro
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