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Implementing Dynamic Power Feed-In Limitations of Photovoltaic Systems in Distribution Grids for Generation Expansion Planning

Alexander Konrad, Robert Gaugl, Christoph Maier, Sonja Wogrin

TL;DR

The paper tackles PV expansion bottlenecks in Austrian distribution grids by introducing a dynamic feed-in limitation that caps grid-active PV feed-in while considering self-consumption, rather than merely limiting installed capacity. It formulates a mathematical extension to the LEGO optimization model, embedding a dynamic limit $FL$ and a uniform scaling factor $scal$ to maximize PV deployment while minimizing system costs, with constraints enforcing the feed-in limit via a binary decision variable. The approach is validated on four real-world grids (three MV, one LV), revealing that up to 32% more PV capacity can be installed, with curtailment remaining around 2% of annual energy in many cases; results vary by grid topology and bottlenecks, such as voltage limits and line capacities. The findings suggest that dynamic feed-in limitation can accelerate renewable integration and grid utilization, though limitations include not modeling storage and using a one-hour resolution; future work could explore day-ahead or real-time application and smart storage strategies to further reduce curtailment and enhance reliability.

Abstract

The rapid growth of photovoltaic (PV) systems in Austria's medium- and low-voltage grids has intensified challenges in grid access, with technical limits increasingly leading to restrictions on full feed-in power. This issue has sparked discussions about limiting PV feed-in power and the implications for both generated and curtailed PV energy. At the same time, expanding PV capacity remains critical to achieving future climate targets. However, there is a lack of robust methodologies of quantify the impact of PV feed-in limitations when implemented in an optimization model. This impact affects both the curtailed energy and the increase in maximum PV installation capacity and total energy production. To address this gap, we have developed a mathematical formulation of dynamic PV feed-in limitations and integrated it into an optimization model. This approach enables a comprehensive evaluation of its effects on PV integration potential and energy curtailment, validated through case studies on four representative real-world Austrian medium- and low-voltage grids. We analyzed maximum PV expansion, energy generation, and curtailment under feed-in constraints. The results highlight the potential for integrating up to 32% additional PV systems within existing infrastructure while keeping PV curtailment relatively low, i.e. at 2%. We provide actionable insights for grid operators and policymakers aiming to balance renewable energy expansion with grid reliability.

Implementing Dynamic Power Feed-In Limitations of Photovoltaic Systems in Distribution Grids for Generation Expansion Planning

TL;DR

The paper tackles PV expansion bottlenecks in Austrian distribution grids by introducing a dynamic feed-in limitation that caps grid-active PV feed-in while considering self-consumption, rather than merely limiting installed capacity. It formulates a mathematical extension to the LEGO optimization model, embedding a dynamic limit and a uniform scaling factor to maximize PV deployment while minimizing system costs, with constraints enforcing the feed-in limit via a binary decision variable. The approach is validated on four real-world grids (three MV, one LV), revealing that up to 32% more PV capacity can be installed, with curtailment remaining around 2% of annual energy in many cases; results vary by grid topology and bottlenecks, such as voltage limits and line capacities. The findings suggest that dynamic feed-in limitation can accelerate renewable integration and grid utilization, though limitations include not modeling storage and using a one-hour resolution; future work could explore day-ahead or real-time application and smart storage strategies to further reduce curtailment and enhance reliability.

Abstract

The rapid growth of photovoltaic (PV) systems in Austria's medium- and low-voltage grids has intensified challenges in grid access, with technical limits increasingly leading to restrictions on full feed-in power. This issue has sparked discussions about limiting PV feed-in power and the implications for both generated and curtailed PV energy. At the same time, expanding PV capacity remains critical to achieving future climate targets. However, there is a lack of robust methodologies of quantify the impact of PV feed-in limitations when implemented in an optimization model. This impact affects both the curtailed energy and the increase in maximum PV installation capacity and total energy production. To address this gap, we have developed a mathematical formulation of dynamic PV feed-in limitations and integrated it into an optimization model. This approach enables a comprehensive evaluation of its effects on PV integration potential and energy curtailment, validated through case studies on four representative real-world Austrian medium- and low-voltage grids. We analyzed maximum PV expansion, energy generation, and curtailment under feed-in constraints. The results highlight the potential for integrating up to 32% additional PV systems within existing infrastructure while keeping PV curtailment relatively low, i.e. at 2%. We provide actionable insights for grid operators and policymakers aiming to balance renewable energy expansion with grid reliability.

Paper Structure

This paper contains 18 sections, 7 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. General methodology
  4. Optimization model and mathematical formulation
  5. Case Study Description
  6. Data and general assumptions
  7. Description of the grids
  8. Results and Discussion
  9. Medium-voltage grids
  10. Rural medium-voltage grid
  11. Urban medium-voltage grid
  12. Hybrid medium-voltage grid
  13. Low-voltage grid
  14. Installable capacity
  15. Increase in energy generation
  16. ...and 3 more sections

Figures (13)

  • Figure 1: Stylized example of dynamic feed-in limitation of PV.
  • Figure 2: Schematic representation of the rural medium-voltage grid with existing and new generators, as well as the bottlenecks for further expansion.
  • Figure 3: Schematic representation of the urban medium-voltage grid with existing and new generators, as well as the bottlenecks for further expansion.
  • Figure 4: Schematic representation of the hybrid medium-voltage grid with existing and new generators, as well as the bottlenecks for further expansion.
  • Figure 5: Rural Grid
  • ...and 8 more figures