Analytical solution of stochastic real‐time dispatch incorporating wind power uncertainty characterized by Cauchy distribution

Real‐time power dispatch can coordinate wind farms, automatic generation control units and non‐automatic generation control units. In real‐time power dispatch, the probable wind power forecast errors should be appropriately formulated to ensure system security with high probability and minimize operational cost. Previous studies and the authors' onsite tests show that Cauchy distribution effectively fits the “leptokurtic” feature of small‐timescale wind power forecast errors distributions. In this paper, a chance‐constrained real‐time dispatch model with the wind power forecast errors represented by multivariate Cauchy distribution is proposed. Since the Cauchy distribution is stable and has promising mathematical characteristics, the proposed chance‐constrained real‐time dispatch model can be analytically transformed to a convex optimization problem considering the dependence among wind farms’ outputs. Moreover, the proposed model incorporates an affine control strategy compatible with automatic generation control systems. This strategy makes the chance‐constrained real‐time dispatch adaptively take into account both the potential power ramping requirement and power variation on transmission lines caused by the generation adjustment to offset the wind power forecast errors in real‐time power dispatch stage. Numerical test results show that the proposed method is reliable and effective. Meanwhile it is very efficient and suitable for real‐time application.