Distributionally Robust Optimization Considering Moment Uncertainty Of Wind Generation

Real-time dispatch,which connects day-ahead generation planning and automatic generation control(AGC),is a significant part in the multi-time scale coordinated dispatch of power systems.On the one hand,it needs to determine the base points of online adjustable units in the next period.On the other hand,it also needs to determine the participation factors to optimize the AGC regulation process.Large-scale renewable energy(RE)sources,such as wind generation,have been integrated into modern power systems with ever-increasing penetration.The intermittent and randomness of RE have brought challenges to power systems.In this context,it is particularly important to quantitatively analyze the influence of wind power stochastic characteristics and thereby improve the anti-disturbance ability of power systems.To meet these challenges,a series of dispatching methods,such as stochastic programming(SP),interval programming(IP),chance constrained programming(CCP)and robust optimization(RO)have been proposed.SP and CCP rely on the predefined probability distributions of uncertainties.However,the probability distribution of wind power is difficult to obtain accurately in practice.RO describes the possible region of the uncertainties through an uncertainty set and seeks the best performance under the worst-case realization in the uncertainty set,but it is difficult to describe the probability distributions in the interval,hence,the result is inevitably conservative or aggressive.To remedy the gap between SP and RO,distributionally robust optimization(DRO)was introduced to power system operational optimization problems.DRO based approaches consider the statistical information of the uncertainties and the ambiguity set is applied to describe the uncertainties.Therefore,based on the DRO approaches,firstly,the ambiguity set,which is a critical part in DRO approaches,is described and illustrated.DRO assumes that the true distribution lies in an ambiguity set and does not limit the specific probability distributions of uncertainties.It is a set of all possible probability distributions that meet the given conditions,and is crucial to the solution of the optimization model.Secondly,based on the constructed ambiguity set,the objective function,which is the minimum sum of the generation costs,is presented and thereby a distributionally robust real-time dispatch model considering generalized moment uncertainty of wind power is investigated to realize the consideration of the randomness of wind power.Finally,this paper raised approximate linearization transformation methods of the proposed dispatching model and the effectiveness and high efficiency of the proposed method were verified by examples of a 6-bus and the IEEE 118-bus system.