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Chance-constrained Solar PV Hosting Capacity Assessment for Distribution Grids Using Gaussian Process and Logit Learning

Sel Ly, Anshuman Singh, Petr Vorobev, Yeng Chai Soh, Hung Dinh Nguyen

TL;DR

This work addresses the challenge of safely scaling distributed solar PV by formulating a chance-constrained hosting capacity (HC) problem for distribution grids. It proposes a methodology that combines Gaussian Process regression (GPR) and logistic regression (LoR) to predict voltage violations as a function of PV penetration $X$, while accounting for load-PV correlation via copulas and control strategies (Q/PF droop and ESS). The key contributions include a GP-based framework for mean and uncertainty-aware HC (GP-WoCC-HC and GP-CC-HC) and a complementary LoR-based CC-HC approach, both enabling fast, scalable, and risk-tunable HC estimates, demonstrated on IEEE 33- and 123-bus systems with high predictive accuracy (≈90-93%). The results show that voltage-control measures substantially increase HC and that the proposed methods run in a few seconds, making them practical for planning and operation. These findings support risk-informed PV integration and grid resilience without excessive computational burden.

Abstract

Growing penetration of distributed generation such as solar PV can increase the risk of over-voltage in distribution grids, affecting network security. Therefore, assessment of the so-called, PV hosting capacity (HC) - the maximum amount of PV that a given grid can accommodate becomes an important practical problem. In this paper, we propose a novel chance-constrained HC estimation framework using Gaussian Process and Logit learning that can account for uncertainty and risk management. Also, we consider the assessment of HC under different voltage control strategies. Our results have demonstrated that the proposed models can achieve high accuracy levels of up to 93% in predicting nodal over-voltage events on IEEE 33-bus and 123-bus test-cases. Thus, these models can be effectively employed to estimate the chance-constrained HC with various risk levels. Moreover, our proposed methods have simple forms and low computational costs of only a few seconds.

Chance-constrained Solar PV Hosting Capacity Assessment for Distribution Grids Using Gaussian Process and Logit Learning

TL;DR

This work addresses the challenge of safely scaling distributed solar PV by formulating a chance-constrained hosting capacity (HC) problem for distribution grids. It proposes a methodology that combines Gaussian Process regression (GPR) and logistic regression (LoR) to predict voltage violations as a function of PV penetration , while accounting for load-PV correlation via copulas and control strategies (Q/PF droop and ESS). The key contributions include a GP-based framework for mean and uncertainty-aware HC (GP-WoCC-HC and GP-CC-HC) and a complementary LoR-based CC-HC approach, both enabling fast, scalable, and risk-tunable HC estimates, demonstrated on IEEE 33- and 123-bus systems with high predictive accuracy (≈90-93%). The results show that voltage-control measures substantially increase HC and that the proposed methods run in a few seconds, making them practical for planning and operation. These findings support risk-informed PV integration and grid resilience without excessive computational burden.

Abstract

Growing penetration of distributed generation such as solar PV can increase the risk of over-voltage in distribution grids, affecting network security. Therefore, assessment of the so-called, PV hosting capacity (HC) - the maximum amount of PV that a given grid can accommodate becomes an important practical problem. In this paper, we propose a novel chance-constrained HC estimation framework using Gaussian Process and Logit learning that can account for uncertainty and risk management. Also, we consider the assessment of HC under different voltage control strategies. Our results have demonstrated that the proposed models can achieve high accuracy levels of up to 93% in predicting nodal over-voltage events on IEEE 33-bus and 123-bus test-cases. Thus, these models can be effectively employed to estimate the chance-constrained HC with various risk levels. Moreover, our proposed methods have simple forms and low computational costs of only a few seconds.

Paper Structure

This paper contains 19 sections, 27 equations, 8 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Load flow model
  4. Problem formulation of the HC estimation
  5. Formulation of CC-HC estimation
  6. Proposed methods
  7. GPR-based HC estimation methods
  8. GPR-based HC estimation method for mean and confidence interval bounds
  9. GPR-based CC-HC estimation method
  10. A relationship between GP-WoCC-HC and GP-CC-HC estimation methods
  11. LoR-based CC-HC estimation method
  12. Results and discussions
  13. Test system
  14. Evaluating the proposed models
  15. Enhanced hosting capacity estimations with control techniques
  16. ...and 4 more sections

Figures (8)

  • Figure 1: Process Flowchart for the proposed HC estimation framework.
  • Figure 2: GPR used for predicting $V_{max}$ on IEEE 33-bus system, given different PV penetration levels, in comparison to Monte Carlo simulation (MCS).
  • Figure 3: Comparison between GPR and LoR used for predicting the risk index $R(x)$ on IEEE 33- and 123-bus systems, given different PV penetration levels (No control).
  • Figure 4: Risk curves by LoR for IEEE 33-bus system, considering the reactive power (Q) and power factor (PF) controls.
  • Figure 5: Risk curves by GPR for IEEE 123-bus system, considering the reactive power (Q), power factor (PF), and energy storage system (ESS) controls.
  • ...and 3 more figures