Control and Optimization of Power Systems with Renewables: Voltage Regulation and Generator Dispatch

Control and Optimization of Power Systems with Renewables:Voltage Regulation and Generator DispatchbyBaosen ZhangDoctor of Philosophy in Engineering-Electrical Engineering and Computer SciencesUniversity of California, BerkeleyProfessor David Tse, Chair The electric power system is undergoing dramatic transformations due to the emergence ofrenewable resources. However, integrating these resources into the electric grid has provento be difficult for two main reasons: these resources are uncertain and distributed. Thisthesis discusses how uncertainty and distributedness of the new resources are manifested aschallenges in time and spatial scales, and how we can optimally control the power grid toovercome these challenges.The theme of this thesis is that in order to control the new resources, we need a betterunderstanding of the physical power flow in the system. To illustrate the spatial-scale chal-lenge, we consider the voltage regulation problem for distribution networks. With a deeppenetration of distributed energy resources the voltage magnitudes in a distribution systemcan fluctuate significantly. To control these resources such that voltage profiles remain flat,we need to coordinate the tens of thousands of households in the distribution network. Bystudying the geometry of power flows in the network, we show that even though the volt-age regulation problem is non-convex, it can be convexified exactly through a semidefiniterelaxation . Based on this insight, we an optimal and decentralized algorithm for this prob-lem. Only communication between electrical neighbors are required in the algorithm, thusallowing it to scale to problem of large sizes.The second problem we consider is dispatching generators in the transmission networkunder deep penetration of wind power. Because of on/off and ramp-rate constraints, tradi-tional generators need to be dispatched before the actual time of delivery of energy. On theother hand, wind power cannot be dispatched and is difficult to predict in advance. Thiscreates a mismatch in time-scale between the controls (traditional generators) and the ran-domness in the system (wind). We capture this challenge as a two-stage stochastic dispatchproblem. In contrast to the standard Monte Carlo solutions, we show that the dimensional ofthe problem can be reduced dramatically by using forecast informations. This dimensionalreduction is based on a better understanding of congested DC optimal power flow problems.Using this reduction, we show how to calculate the optimal reserve margin for the system in