Probabilistic Load Flow Approach Considering Dependencies of Wind Speed, Solar Irradiance, Electrical Load and Energy Exchange with a Joint Probability Distribution Model

The modelling of stochastic feed-ins and demands becomes essential for transmission grid operation and planning due to the extension of renewable energy sources (RES). Neglecting the correlation between uncertain variables and/or oversimplifying the distribution through the assumption of Normal distributions leads to the inaccurate determination of future network states. Therefore, the uncertainties need to be accurately modelled in order to be used in a probabilistic load flow approach. This paper analyses the characteristics of wind speed and solar irradiance for different locations throughout countries and models the dependencies between them. In addition, the total electrical load and the energy exchange between neighbouring countries are analysed. All of these uncertainties are modelled together in a high-dimensional joint probability distribution using pair-copula constructions. The model is applied to generate samples and determine the probability of extreme events, e.g. high RES production and low demand. The probability for rather high load (>65 GW) and low RES production with wind speed less than 3 m/s and solar irradiance less than 100 W m ² at 90% of all stations is e.g. 0.064%. In addition, the model is integrated in a probabilistic load flow approach in order to analyse the German transmission grid for a future scenario of the year 2025. With the copula, samples are generated as an input for the Monte Carlo simulation approach. The approach enables the assessment of planned HVDC lines. When considering the HVDC lines, the load on the AC lines can be significantly reduced.