A source‑load joint scenario generation method for distributed photovoltaic hosting capacity assessment considering tail risk

High penetration of distributed photovoltaic generation increases the complexity of source‑load temporal characteristics in distribution networks. The mismatch between photovoltaic output and load demand， together with extreme operating scenarios， poses challenges to distributed photovoltaic hosting capacity （PVHC） assessment. To address this issue， a source‑load joint PCA‑K‑means clustering scenario generation method was proposed considering tail risk. First， a source‑load joint feature model integrating photovoltaic output， load， and net load was established， and principal component analysis （PCA） was used to reduce the dimensionality of high-dimensional source‑load conditions. Second， conditional value at risk （CVaR） was used to calculate the tail-risk weights of source‑load samples， and the weights of low-frequency high-risk samples， such as high-photovoltaic and low-load conditions， were increased during K-means clustering， thereby reducing the computational scale while maintaining scenario representativeness. Then， a PVHC assessment model considering power-flow constraints， node-voltage limits， and reverse-power-flow constraints was developed based on the typical scenarios. Finally， case studies on the IEEE 33-bus distribution system compare the proposed method with source‑load independent K‑means clustering and source‑load joint PCA‑K‑means clustering without tail-risk consideration， demonstrating its effectiveness.