Conditional Value at Risk-Sensitive Solar Hosting Capacity Analysis in Distribution Networks

TL;DR

This paper introduces a risk-sensitive approach to solar hosting capacity analysis in distribution networks using CVaR, optimizing solar capacity while managing constraint violation risks through SOCP and incremental algorithms.

Contribution

It develops a novel CVaR-based framework for risk-aware solar hosting capacity analysis, including an SOCP formulation and an incremental feasibility algorithm.

Findings

Risk parameters significantly affect hosting capacity.

The framework scales with scenario number and network size.

Incremental algorithm efficiently assesses configuration acceptability.

Abstract

Solar hosting capacity analysis (HCA) assesses the ability of a distribution network to host distributed solar generation without seriously violating distribution network constraints. In this paper, we consider risk-sensitive HCA that limits the risk of network constraint violations with a collection of scenarios of solar irradiance and nodal power demands, where risk is modeled via the conditional value at risk (CVaR) measure. First, we consider the question of maximizing aggregate installed solar capacities, subject to risk constraints and solve it as a second-order cone program (SOCP) with a standard conic relaxation of the feasible set with power flow equations. Second, we design an incremental algorithm to decide whether a configuration of solar installations has acceptable risk of constraint violations, modeled via CVaR. The algorithm circumvents explicit risk computation by incrementally constructing inner and outer polyhedral approximations of the set of acceptable solar installation configurations from prior such tests conducted. Our numerical examples study the impact of risk parameters, the number of scenarios and the scalability of our framework.