An analytic probabilistic hosting capacity assessment method for low voltage distribution networks

There has been an increase in the capacity of distributed energy resources (DERs) integrated into distribution networks, in some cases even surpassing that of utility-scale systems. However, the integration of DERs is complicated by the inherent uncertainties related to their deployment and operations, termed as planning and operational uncertainties. Accurate modeling of these uncertainties is crucial for ensuring the precision of hosting capacity (HC) assessments and optimizing DER integration. State-of-the-art HC methods typically involve stochastic simulation of planning uncertainties through a Monte-Carlo simulation (MCS) and propagation of operational uncertainties using a probabilistic load flow method (PLF). This involves multi-tier iterations of the load flow, assessing the impacts of a range of input scenarios, including random DER placement, DER power variability, and penetration range. While the multi-scenario approach in the stochastic HC (SHC) methods enhances HC accuracy, they are computationally intensive, limiting their scalability and practical applicability. This study proposes a streamlined approach that replaces the stochastic simulation of planning uncertainties with an analytic approach. In this approach, planning uncertainty is characterized using a probability density function (PDF) and combined, as a product, with the PDF model of the operational uncertainties. The unified probabilistic function is thus used to represent the combined uncertainty, enabling a single-pass computation of the HC through an analytic PLF method. The proposed analytic HC (AHC) method is tested on a sample residential LV feeder, with a loading typical of suburban areas in South Africa. The resulting performance is compared to that of a state-of-the-art SHC method. The proposed AHC method records significant improvement in computational efficiency (>1000x) while maintaining comparable performance to the SHC method. This development enables fast, reliable, and scalable DER integration assessments by distribution network operators.