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

Abstract

Summary 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.

SR‐based chance‐constrained economic dispatch for power systems with wind power

“…To improve the security level and the economic performance of power system operations with high penetration of wind power, significant work has been performed on the operation methods for power systems under uncertainties [5] such as scenario-based stochastic optimisation methods [1,[6][7][8], robust optimisation methods [9][10][11][12] and chance-constrained programming methods [13][14][15][16][17][18][19][20][21]. In scenario-based stochastic optimisation methods, several scenarios or scenario trees of possible wind power outputs are usually generated through sampling methods such as Monte Carlo simulation to model the uncertainty of wind power.…”

Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

“…In the field of power systems, the moment-based DRO method has been applied to solve some problems. Reference [19] studied the economic dispatch problem of power systems under the distribution information of random variable as ambiguous, the ambiguity set was constructed as an ellipsoidal by using the mean and the covariance matrix, and conditional value-at-risk management is used to reformulate the proposed DRO model into a solvable convex optimization. Reference [20] presented a chance-constrained programming approach to deal with the distribution expansion planning problem under uncertain renewables and loads, and a DRO model was applied to solve the uncertainty variables.…”