Fairness-aware Dynamic Hosting Capacity and the Impacts of Strategic Solar PV Curtailment

TL;DR

The paper tackles the challenge of determining hosting capacity (HC) for distribution grids with high distributed solar generation while ensuring fair access across nodes and over time. It extends the previous convex inner approximation (CIA) of AC optimal power flow by deriving tighter branch-current envelopes using a SOC-based epigraph relaxation, enabling a larger admissible region for DER injections. A fairness framework based on epsilon-fairness constraints and entropy-like metrics is integrated, showing that equal- or demand-proportional allocations can reduce inequities and improve utilization when PV curtailment is allowed. Through a case study on a modified IEEE-37 feeder with time-varying demand and solar data, the approach demonstrates that modest PV curtailment can substantially increase total PV hosting capacity, reduce curtailment in fair allocations, and yield higher net profits driven by carbon-revenue opportunities, with benefits varying by regional MOER and energy mix.

Abstract

Rapid deployment of distributed energy resources (DERs), such as solar photovoltaics (PV), poses a risk to the distribution grid under high penetration. Therefore, studying hosting capacity (HC) limits considering grid physics and demand variability is crucial. This paper introduces an improved framework for determining the HC of radial distribution networks by enhancing an existing convex inner approximation (CIA) approach. The proposed method achieves a more accurate and larger inner approximation, resulting in better HC limits. We also consider time-varying demand and the design of objective functions to ensure equitable access to grid resources. A case study with solar PV integration is conducted using a modified IEEE-37 radial network to examine the impact of increased PV capacity, demonstrating that with no more than 5% annual solar PV energy curtailed, it is possible to increase solar PV hosting capacity by at least 50% with no negative grid impacts and a net positive economic impact when accounted for the cost of carbon. Results show that fair allocation methods can lead to higher net profits and reduced PV curtailment and CO2.

Figures (19)

• Figure 1: Representative radial network and notation.
• Figure 2: 4-bus radial network with power injections at buses 3 and 4.
• Figure 3: (Top) Admissible set of power injections with admissible (dark blue) and inadmissible (red) trajectories. Voltages at nodes 3 and 4: (Bottom Left) red trajectory passing through a hole (Bottom Right) vs. blue trajectory without hole passage.
• Figure 4: Comparing the MAE between \ref{['eq: branch_current_eq']} and the conservative upper bound $l_{ij,\text{from~}NAWAF2021}^+$ (blue), and MAE between \ref{['eq: branch_current_eq']} and the proposed upper proxy variable $l_{ij, \text{SOC}}^+$ (red) across all $l_{ij} \in \mathcal{L}$.
• Figure 5: Comparison of the branch currents: the upper bound proxy variable from NAWAF2021 ($l_{ij}^+ \text{ from~}NAWAF2021$), the second order Taylor expansion (STE) of \ref{['eq: branch_current_eq']} ($l_{ij, \text{STE}}$), the proposed upper bound ($l_{ij, \text{SOC}}^+$) obtained via epigraph relaxation using a SOC formulation, the actual branch current ($l_{ij}$) from \ref{['eq: branch_current_eq']}, and the lower bound proxy ($l_{ij}^-$) from \ref{['eq:lower_bound']}.

Theorems & Definitions (2)

• Definition 1
• Remark