Extended Long-Run Incremental Cost Pricing for Distribution Networks Based on Extreme Value Statistics

As a key to distribution use-of-system pricing, network utilization has become increasingly difficult to predict with growing penetration of distributed renewable energy (DRE), flexible loads, and modern operation schemes. Conventional pricing approaches, such as long-run incremental cost (LRIC) pricing, generally focus on the forecasted value of users' maximum network utilization and overlook its probability, leading to overly conservative network charges. To tackle this challenge, this paper integrates extreme value statistics into the network pricing framework and introduces an extended LRIC (ELRIC) method. Specifically, the generalized Pareto distribution (GPD) is employed to model the tail probability distribution of nodal power injections, while a linearized power flow model is used to derive the tail distributions of branch flows. Pricing and reinforcement decisions are then driven by the branch flow exceedance probability in the future and associated curtailment costs. Compared to traditional schemes, the ELRIC method offers a more robust and analytically transparent pricing framework under uncertainty, enabling differentiated use-of-system charges for users exhibiting various tail distributions. A 59-bus case study demonstrates that the ELRIC approach effectively captures uncertainties stemming from DREs and loads via extreme value theory and provides differentiated price signals to users with distinct tail behaviors.