Gaussian Mixture Based Probabilistic Load Flow For LV-Network Planning

Abstract

Abstract-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 analysed. 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 modelling. Taking advantage of its radial nature and high R/X ratios, the LV-network can be analysed more efficiently from a computation viewpoint. By the application of simplifications defined in this paper, the backwards-forwards 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.

Data Analytics-Based Multi-Objective Particle Swarm Optimization for Determination of Congestion Thresholds in LV Networks

“…Nonetheless, detailed information is scarce at the LV network level, such as the particular phase where a single-end user or DER unit is connected [43], despite successful smart grid pilot projects such as Smartcity Malaga [44], INTEGRIS [5], IDE4L [45], or MONICA [46] have dedicated special efforts in distribution network digitalization and state estimation. Therefore, technical solutions are available today to address congestion in singular elements such as LV feeder phases, avoiding bottlenecks that may arise even earlier in the case of significant DER penetration or demand growth [47,48], since technical constraint violations may occur at an earlier stage [49].…”

Data-Driven Risk Analysis for Probabilistic Three-Phase Grid-Supportive Demand Side Management

“…The network sensitivity S t V can be calculated based on Equations (9) and (13). Similarly, ∆V t is easily derived using Equations (15) and (16).…”

“…In this case, state prediction of the network system states will be of high value to account for the probabilistic system states that will occur in the near future. For coping with the high stochasticity of DER and end user behaviour, a probabilistic approach is required to determine potential network risks [15][16][17]. On the down side, probabilistic approaches often require some form of probabilistic power flow (PPF) calculations to evaluate the probability of having operation limit violations at certain locations in the network.…”

MMSE-Based Analytical Estimator for Uncertain Power System With Limited Number of Measurements

“…In the case of unknown input PDF’s, a method for nonparametric probabilistic load flow analysis is developed in [5]. Other studies mainly use a Gaussian mixture model (GMM) to approximate the PDF of loads or a mix of DER’s, which cannot be approximated with a known shape PDF [6]–[8]. Furthermore, there has been tremendous effort towards real-time DSE in support of next generation power systems [14]–[23].…”

“…Therefore, the GMM, which is an approximate presentation of the PDF’s of NGRV’s, is utilized in the proposed estimator. As a weighted sum of several Gaussian components, GMM is widely used for NGRVs probability distribution [6]–[8], [37], [38]. More specifically, in many studies, GMM has been suggested to model the PDFs of load power and renewable energy sources [39]–[43].…”