Multi-dimensional scenario forecast for generation of multiple wind farms

J. Mod. Power Syst. Clean Energy ( Multi-dimensional scenario forecast for generation of multiple wind farms Ming YANG You LIN Simeng ZHU Xueshan HAN Hongtao WANG A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed. In the proposed approach, support vector machine (SVM) is applied for the spot forecast of wind power generation. The probability density function (PDF) of the SVM forecast error is predicted by sparse Bayesian learning (SBL), and the spot forecast result is corrected according to the error expectation obtained. The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression (DCCMR) model to describe the correlation among the errors. And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function. Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach. Wind power generation forecast; Multidimensional scenario forecast; Support vector machine (SVM); Sparse Bayesian learning (SBL); Gaussian copula; Dynamic conditional correlation matrix - 1 Introduction The wind power has been developing very fast in China since 2006. Within the mainland, the total installed capacity of wind power had reached up to 91424 MW by the end of 2013 [ 1 ]. Since many wind farms are centrally constructed in the wind-rich zones, some regional power grids in China have already had a relatively high wind power penetration [ 2 ]. To improve the operating security and economics of the power grid which is integrated with large-scale wind power, a project named as collaborative optimization of the thermal power, hydro power and wind power in extremely cold areas was carried out by Shandong University and Heilongjiang Electric Power Company. Developing a short-term wind power forecast program is the main and fundamental research objective of this project. Heilongjiang power grid has 45 integrated wind farms, and the installed capacity reaches up to 3153 MW which accounts for 14.8% of the total installed capacity in that region. Because of the rapid growth of wind power and relatively slow expansion of the transmission networks, transmission congestion happens from time to time in the grid. To consider the transmission constraints during the scheduling process, forecast is required to be performed for each single wind farm as well as the whole region. Moreover, the cross-correlation among the outputs of multiple wind farms is expected to be estimated to make full use of the adjustable capacity of the power grid. Although great efforts have been made to improve the forecast accuracy, it is still hard to predict the wind power generation precisely. As a result, estimating the uncertainty of the forecast result is believed to be crucial for the operation of power systems [ 3, 4 ]. By now, several parametric or non-parametric approaches, e.g., the quantile regression approaches [5], the interval estimation approaches [ 6, 7 ], and the probability density forecast approaches [ 8, 9 ], have been proposed to achieve this aim. These approaches can provide end-users with forecast uncertainty information in various ways. Temporal-spatial dependence relation among the outputs of wind farms is the valuable information for the power system operation [ 10, 11 ]. In [12], a short-term joint probability density function (JPDF) forecast approach was proposed to include the temporal correlation of forecast errors into the distribution forecast results. The errors were assumed to follow a joint Gaussian distribution and the correlation matrix was estimated by the recursive statistic estimation. Reference [ 13 ] introduced an approach to consider the temporal interdependence structure in the quantile regression based probabilistic forecast approach. In the approach, the interdependence structure was summarized by a unique covariance matrix through the conversion of the prediction errors to a multivariate Gaussian random vector. The approaches mentioned in [ 12, 13 ] are instructive. However, the spatial dependence structure is ignored in the approaches. In this paper, a novel multi-dimensional scenario forecast approach which can capture the dynamic temporalspatial interdependence relation among the outputs of multiple wind farms is proposed. The advantages of the proposed approach are as follows. 1) The temporal-spatial dependence relation of the forecast errors is included into the probabilistic forecast result, and the approach can provide more useful information for the system operation. 2) By using the kernel based sparse learning approaches and the error correction strategy, the accuracy of the spot and probabilistic forecast results is guaranteed. 3) The dependence structure of the forecast errors is well represented by the Gaussian copula, and (...truncated)