Distributionally robust hydro-thermal-wind economic dispatch

With the penetration of wind energy increasing, uncertainty has become a major challenge in power system dispatch. Hydro power can change rapidly and is regarded as one promising complementary energy resource to mitigate wind power fluctuation. Joint scheduling of hydro, thermal, and wind energy is attracting more and more attention nowadays. This paper proposes a distributionally robust hydro-thermal-wind economic dispatch (DR-HTW-ED) method to enhance the flexibility and reliability of power system operation. In contrast to the traditional stochastic optimization (SO) and adjustable robust optimization (ARO) method, distributionally robust optimization (DRO) method describes the uncertain wind power output by all possible probability distribution functions (PDFs) with the same mean and variance recovered from the forecast data, and optimizes the expected operation cost in the worst distribution. Traditional DRO optimized the random parameter in entire space, which is sometimes contradict to the actual situation. In this paper, we restrict the wind power uncertainty in a bounded set, and derive an equivalent semi-definite programming (SDP) for the DR-HTW-ED using S-lemma. A delayed constraint generation algorithm is suggested to solve it in a tractable manner. The proposed DR-HTW-ED is compared with the existing ARO based hydro-thermal-wind economic dispatch (AR-HTW-ED). Their respective features are shown from the perspective of computational efficiency and conservativeness of dispatch strategies.