We consider the optimal economic dispatch of power generators in a smart electric grid for allocating power between generators to meet load requirements at minimum total cost. We assume that each generator has a piece-wise linear cost function. We first present a polynomial time algorithm that achieves optimal dispatch. We then present a decentralized algorithm where, each generator independently adjusts its power output using only the aggregate power imbalance in the network, which can be observed by each generator through local measurements of the frequency deviation on the grid. The algorithm we propose exponentially erases the power imbalance, while eventually minimizing the generation cost.
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