| In this dissertation, we propose a novel distributed approach to the control of generators in the electric grid. Specifically, we consider the problem of the optimal economic dispatch of generator; we present a simple, distributed algorithm, which adjusts the power-frequency set-points of generators to correct for power imbalances arising from generation and load fluctuations. In this algorithm each generator independently adjusts its real-power output based on its estimate of the aggregate power imbalance in the network; such as an estimate can be independently obtained by each generator through local measurements of the frequency deviation on the grid. Eventually, over the course of network operation, the distributed algorithm achieves the equal-marginal-cost power allocation among generators while driving the power imbalance exponentially to zero. In the absence of power losses, we prove the eventual optimality of the distributed algorithm under mild assumptions (strict convexity and positivity of cost functions) and present simulation results to compare its performance with traditional (centralized) dispatch algorithms. Furthermore, we present numerical simulation results that show that the distributed algorithm performs well even in the presence of power losses and other constraints. We argue that distributed control methods are especially attractive for electric grids with smart meters and other advanced capabilities at the end node and grids with high penetration of alternative energy generators and we identify interesting open problems for future work in this area. |
