Analysis of future power grid loading considering uncertainties for application of risk based grid planning

可再生能源发电厂的整合、传统发电厂的同步拆除、由于部门耦合和能源市场的自由化而产生的新负荷，导致未来电力发电的巨大不确定性，从而也导致了能源网负荷的不确定性。由于电力线路和电缆的规划周期较长，电网扩建的投资必须在现有的不确定的未来发展情况下进行。在该项目的范围内，由Christian Rehtanz教授领导的能源系统、能源效率和能源经济研究所和由Gerardo Blanco教授领导的亚松森大学能源系统（GISE）研究小组将共同开发一个数学和技术整体模型，可用于规划不确定情况下的输电网。这使得未来电网负荷的确定，考虑到实际的不确定性，并从中扣除最优投资决策。因此，首先必须对不确定性进行随机分析和建模。利用情景技术对不同时间步长的发电局域化不确定性（第一阶段不确定性）进行了描述。第二阶段的不确定性是在发电定位确定后产生的，例如由于天气的不确定性，用多元分布函数表示。为此，使用了可以确定各个变量的边际概率分布之间的关系的函数copula。随后，导出了一个整体模型，该模型为第一阶段的每个场景分配了多元分布函数，从而通过概率密度函数（PDF）及其相关性对每个网格节点的输入变量进行建模。结果是确定线路负荷PDF的概率潮流计算的输入值。为此，进一步发展了点估计方法的方法，使该方法能够应用于实际网格。所开发的方法将通过蒙特卡罗模拟进行验证。为了对电网进行规划，需要一种基于预期线路负荷的不确定情况下的最优投资决策方法。为此，首先对网格分析的结果进行评估，然后进行集中。然后，扣除成本函数，作为实物期权分析应用的基础。路径积分的方法用于此目的。这个程序代表了一种全新的方法，与目前的状态相比，其中的不确定性几乎没有被考虑，概率潮流计算方法只在小的测试网格上工作。此外，概率潮流计算与实物期权分析的耦合也尚未出现，并提供了许多新的可能性。

The integration of renewable energy plants, the simultaneous dismantling of conventional power plants, the new loads because of sector coupling and the liberalization of energy markets lead to great uncertainties in the future generation of electrical energy and thus also in the load of energy grids. Due to long planning horizons for power lines and cables, investments for grid expansion must be made under existing uncertain future developments.Within the scope of the project, the institute of energy systems, energy efficiency and energy economics from Prof. Christian Rehtanz (ie³) and the research group energy systems (GISE) at the University of Asuncion from Prof. Gerardo Blanco will jointly develop a mathematical and technical overall model that can be used to plan the transmission grid under uncertainties. This enables the determination of future grid loads, taking into account real uncertainties, and the deduction of optimal investment decisions from these. Therefore, the uncertainties must be analyzed and modeled stochastically in a first step. The uncertainties resulting from the localization of the power generation (uncertainties of stage one) are represented using the scenario technique for different time steps. The uncertainties of the second stage, which result after the determination of the localization of the power generation, e.g. through weather uncertainties, are represented by multivariate distribution functions. For this purpose, the copula is used, a function which can determine the relationship between the marginal probability distribution of individual variables. Subsequently, an overall model is derived, which assigns multivariate distribution functions to each scenario of the first stage, so that the input variables for each grid node are modeled by probability density functions (PDF) and their correlations. The results are the input values for the probabilistic load flow calculations which determine the PDF of the line load. For this purpose, the approaches of the point-estimate method are developed further to enable the usage of the method for real grids. The developed method will be verified by Monte-Carlo-simulations. In order to plan the energy grid, a method is then required which makes optimal investment decisions under uncertainties based on the expected line loads. For this purpose, the results of the grid analysis are evaluated first and are concentrated afterwards. Subsequently, a cost function is deducted, which is used as the basis for the application of real option analysis. The approach of path integrals is used for this purpose.This procedure represents a completely new approach compared to the state of the art, where the uncertainties are hardly taken into account and the methods of probabilistic load flow calculations work only on small test grids. Also the coupling of the probabilistic load flow calculations with real option analysis has not taken place, yet, and offers a lot of new possibilities.