Stochastic Analysis of Transformer Loading Due to Single-Phase Distributed Energy Resources

The escalating penetration of single-phase distributed energy resource (DER) systems has far-reaching implications for electric distribution systems. Existing studies have extensively explored the effects of these DERs on parameters such as voltage levels and conductor loading. However, the impacts on transformer loading are often overlooked, as assessments typically focus on aggregate loading without considering individual phase loading. This paper proposes a probabilistic method based on a dis aggregate approach, assessing the loading of individual phases of the transformer. This allows for the accounting of the impacts of unbalanced allocation due to DER planning uncertainties. Furthermore, the method addresses operational uncertainties related to both load and DERs through probabilistic characterization. Through a case study focused on solar photovoltaic (PV) penetration in low-voltage residential feeders, the results demonstrate that the proposed methodology enables a comprehensive assessment of transformer loading, mitigating risk for undetected overloads in individual transformer phases. Within the context of the case study, the conventional aggregate method is found to be conservative in its depiction of transformer loading, leading to overly relaxed penetration limits. Further sensitivity studies highlight the necessity of modelling operational uncertainty and ensuring proper output interpretation through risk assessment. These elements are critical for accurate impact assessment, which is essential in hosting capacity studies for system planning and operations.