Optimal dispatch in Smart Power Grids with partially known deviation

We consider the optimal economic dispatch of power generators in a smart electric grid for allocating power between generators to meet load requirements at a minimum total cost. The first algorithm presented, is a distributed algorithm for frequency control and optimal dispatch, where, each generator independently adjusts its power-frequency set-point to erase power imbalance and load fluctuations by using the aggregate power imbalance in the grid, observed by local measurements of the frequency deviation. We also present a second decentralized consensus based algorithm where, we assume each generator, in addition to the measured frequency deviation in the grid, has minimal information exchange with its neighbors. Existing algorithms assume that frequency deviation is proportional to the load imbalance. In practice this is seldom exactly correct. We assume in both cases, that the only thing known about this relationship is that it is an unknown, odd, strictly increasing function. By simulations and mathematical proof of convergence, we provide verification of the efficiency of the algorithm.