Modeling Dynamic Spatial Correlations of Geographically Distributed Wind Farms and Constructing Ellipsoidal Uncertainty Sets for Optimization-Based Generation Scheduling

Abstract

The correlation information is very important for system operations with geographically distributed wind farms, and necessary for optimization-based generation scheduling methods such as the robust optimization (RO). The purpose of this paper is to provide the dynamic spatial correlations between the geographically distributed wind farms and apply them to model the ellipsoidal uncertainty sets for the robust unit commitment model. A stochastic dynamic system is established for the distributed wind farms based on a mesoscale numerical weather prediction (NWP) model, wind speed downscaling, and wind power curve models. By combining the observed wind generation measurements, a dynamic backtracking framework based on the extended Kalman filter is applied to predict the wind generation and the dynamic spatial correlations for the wind farms. In case studies, the new method is tested on actual wind farms and compared with the Gaussian copula method. The testing results validate the effectiveness of the new method. It is shown that the new method can provide more favorable interval forecasts for the aggregate wind generation than the Gaussian copula method in the entire forecast horizon, and by using the predicted spatial correlations, we can obtain more accurate ellipsoidal uncertainty sets than the Gaussian copula method and the frequently used budget uncertainty set (BUS).Index Terms-Dynamic backtracking, ellipsoidal uncertainty set, extended Kalman filter, mesoscale numerical weather prediction (NWP) model, spatial correlation, wind power. n, τIndexes of time. g m (n)Wind power generation of wind farm m at time t n . g m (n + τ |n) τ -step-ahead forecasted wind power generation of wind farm m at time t n . g(n + τ |n)Vector of τ -step-ahead forecasted wind power generation of M wind farm at time t n . e m (n)Prediction error of wind power generation of wind farm m at time t n . S(n + τ |n)Wind power prediction error covariance of overall wind farms. g(n)Vector of wind power generation of M wind farm at time t n . σ l,m,n+τ Covariance between the prediction error of wind farm l and wind farm m at time t n+τ . Ω Uncertainty set. γRobust parameter in the ellipsoidal and budget uncertainty sets (BUS). x(n)Vector of system state at time t n . χ(n)Vector of boundary conditions at time t n . ζ(n)Process noise. Q(n)Covariance of the process noise. η(n)Measurement noise. R(n)Covariance of the measurement noise. f (·)Vector-valued nonlinear function in the state equation. h(·)Vector-valued nonlinear function in the measurement equation. U m (n) Atmospheric wind velocity at 925 hPa pressure level over wind farm m at time t n . w sf m (n) Surface wind velocity of wind farm m at time t n . w sf m (n) Surface wind speed of wind farm m at time t n . a m , b m Regression coefficients in the linear regression model. ε m Residual error of the linear regression model. 1949-3029

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