A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

In this paper, we study the risk-limiting dispatch (RLD) of power system in the case that the distribution information of random variable is ambiguous. Under an ellipsoidal moment uncertainty of the mean and the covariance matrix, we develop the distributionally robust optimization approach to set up a new RLD model, named robust RLD (RRLD for short). The RRLD considers simultaneously the risk of unsafe operation limit by conditional Value-at-Risk management. We further convert the RRLD model into a solvable convex optimization for a special case that the operation constraint is addressed on the overloading transmission current. The new RRLD model is a development and generalization of the traditionary economic dispatch and the RLD approach. Meanwhile, our research extends the distributionally robust optimization application in portfolio problems to a security economic operation of power system. The IEEE-14 and IEEE-30 bus system are chosen as numerical test systems. Preliminary numerical examples show the validity of the model and its reformulation.