Gaussian Mixture Based Probabilistic Load Flow For LV-Network Planning

Due the many uncertainties present in the evolution of loads and distributed generation, the use of probabilistic load flow in low voltage (LV) networks is essential for the evaluation of the robustness of these networks from a planning perspective. The main challenge with the assessment of LV-networks is the sheer number of networks which need to be analyzed. Moreover, most loads in the LV-network have a volatile nature and are hard to approximate using conventional probability distributions. This can be overcome by the use of a Gaussian mixture distribution in load modeling. Taking advantage of its radial nature and high R/X ratios, the LV-network can be analyzed more efficiently from a computation viewpoint. By the application of simplifications defined in this paper, the backward-forward load flow can be solved analytically. This allows for the direct computation of the load flow equations with a Gaussian mixture distribution as load. When using this new approach, the required calculation time for small networks can be decreased to 3% of the time it takes to generate a similar accuracy with a Monte Carlo approach. The practical application of this load flow calculation method is illustrated with a case study on PV penetration.