Power dispatch and load control with generation uncertainty

In this paper, we focus on the problem of joint load scheduling and generation management to better match supply and demand. We formulate an optimization problem to jointly minimize the generation cost and discomfort cost of the users subject to the voltage and power balance equations for the equivalent circuit of the power system. The optimal power flow (OPF) equations are solved using semidefinite programming (SDP) relaxation technique. In our system model, we assume that users can exploit renewable energy resources (RERs). RERs are random in nature and may cause voltage variations in different nodes of the system. To minimize the risk of having high voltage values, a barrier term is added to the objective function. This term is calculated based on the concept of conditional value-at-risk (CVaR). Simulation results show that compared to the case where there is no control over the load, our proposed algorithm reduces the generation cost by better matching the generation and demand. Moreover, the proposed algorithm reduces the voltage variations at different nodes of the system.