For the purpose of Monte Carlo scenario generation, we propose a graphical model for the joint distribution of wind power and electricity demand in a given region. To conform with the practice in the electric power industry, we assume that point forecasts are provided exogenously, and concentrate on the modeling of the deviations from these forecasts instead of modeling the actual quantities of interest. We find that the marginal distributions of these deviations can have heavy tails, feature which we need to handle before fitting a graphical Gaussian model to the data. We estimate covariance and precision matrices using an extension of the graphical LASSO procedure which allows us to identify temporal and geographical (conditional) dependencies in the form of separate dependence graphs. We implement our algorithm on data publicly available for the Texas grid as managed by ERCOT, and we confirm that the geographical dependencies identified by the algorithm are consistent with the geographical relative locations of the zones over which the data were collected.
翻译:为了蒙特卡洛情景生成的目的,我们为特定区域的风力和电力需求联合分配提出了一个图形模型。为了与电力工业的做法保持一致,我们假设点预报是外部提供的,并侧重于这些预测偏离的模型,而不是实际利息量的模型。我们发现这些偏差的边际分布可能有沉重的尾巴,在将图形高斯模型与数据相配之前我们需要处理这些特征。我们利用图形LASOS程序的一个延伸来估计共差和精确矩阵,该程序使我们能够以单独的依赖性图表的形式确定时间和地理(条件)依赖性。我们用ERCOT管理的德克萨斯电网公开可得的数据进行算法,我们确认算法所查明的地理依赖性与收集数据地区的相对位置相一致。