⚡ electrical engineering

Productive Curtailment in Agrivoltaic Systems under Flexible Interconnection Agreements

This paper demonstrates that agrivoltaic systems can comply with flexible interconnection agreements by dynamically adjusting panel tilt to limit power exports, a strategy that simultaneously improves crop yields compared to the inverter curtailment used in conventional solar systems.

Original authors: Marcus Wu, Anna Stuhlmacher

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Marcus Wu, Anna Stuhlmacher

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a solar farm that doesn't just sit there soaking up the sun like a sunflower, but actually has a secret superpower: it can play "peek-a-boo" with the crops growing underneath it. That's the core idea behind this paper, which explores a clever way to solve a messy problem in the energy world.

The Problem: Too Much Power, Too Little Room
Think of the electrical grid like a busy highway. Right now, there are so many new solar farms (distributed generation) trying to merge onto this highway that traffic is getting jammed. Usually, when a new solar farm wants to connect, the utility company has to check if the road can handle the extra cars. If it can't, they have to build new lanes (grid upgrades), which costs a fortune.

To avoid these expensive construction projects, utilities are starting to offer "flexible interconnection agreements." It's like telling the solar farm, "You can join the highway, but you have to promise to slow down and not export more than a certain amount of electricity during rush hour."

The Old Way vs. The New Way
For a normal solar farm, slowing down means "curtailing" power. Imagine a solar farm that's generating 100 units of energy but is told to only send 60. The old way is to just turn off the inverter (the brain of the solar system) and waste the extra 40 units. It's like throwing away fresh bread because you can't fit it in the basket.

This paper suggests a much more creative solution for agrivoltaic systems—solar panels raised up high over agricultural land. Instead of just turning off the power, these systems can physically tilt their panels.

The Magic Tilt
Here's the analogy: Imagine the solar panels are like giant, adjustable umbrellas.

Normal Mode: The umbrellas tilt perfectly to catch the sun, making maximum electricity but casting a deep, dark shadow on the crops below.
The "Anti-Tracking" Mode: When the grid says, "Whoa, too much power!", the umbrellas tilt away from the sun. They stop chasing the sunbeam so aggressively.

Why do this? Because by tilting away, the panels let more sunlight (specifically the kind plants need to grow) filter through to the crops below. At the same time, the panels produce less electricity, which helps them stay within the grid's speed limit without wasting a single watt. It's a win-win: the grid gets its limit, the farmer gets more sun for their lettuce, and the solar owner doesn't have to pay for expensive road upgrades.

What the Computer Simulations Showed
The authors ran a computer simulation (a digital test drive) of a solar farm in Ames, Iowa, growing lettuce over a 60-day period in the summer of 2024. They didn't just guess; they used a complex math formula to figure out the perfect tilt angle for every single moment of the day to maximize energy while respecting the grid's limits.

Here is what their digital experiment found:

The Trade-off: As they forced the system to export less power (from 100% down to 40% of its capacity), the electricity generated dropped, but the crop yield went up.
The Numbers: When the power limit was set to 100% (no restrictions), the system produced 73,501 kWh of energy and grew 1.874 tons per hectare of lettuce.
The Sweet Spot: When they tightened the limit to 40%, the energy dropped to 42,257 kWh, but the lettuce harvest jumped to 2.455 tons per hectare. That is a 31% increase in crop yield just by tilting the panels!

The Catch and the Confidence
The paper is careful to point out that this isn't magic. If you try to limit the power too much (below 35%), the math says it becomes impossible to stay under the limit just by tilting the panels. This is because even when the panels are tilted away, the sky still sends down "diffuse" light (cloudy day light) and "reflected" light (light bouncing off the ground), which the panels can't completely block. In those extreme cases, you'd still need to turn off the inverter a little bit.

Also, the authors note that their computer model had tiny hiccups. In the simulation, when the limit was very strict (40% or 60%) on a cloudy day, the power sometimes accidentally went slightly over the limit (by about 0.93% to 1.88%). This happened because the math used to solve the problem was a simplified version of reality. In the real world, you'd likely use the inverter to make tiny adjustments to ensure you never break the rules.

The Bottom Line
This paper doesn't claim to have solved every problem in the world. It simply suggests, through a detailed simulation, that agrivoltaic systems have a unique superpower that regular solar farms don't: they can trade electricity for sunlight in a way that actually helps the crops grow. While a normal solar farm just wastes energy when the grid is full, an agrivoltaic farm can use that "wasted" energy potential to feed more people. It's a clever dance between the sun, the grid, and the soil.

Technical Summary: Productive Curtailment in Agrivoltaic Systems under Flexible Interconnection Agreements

Problem Statement
The rapid expansion of distributed solar photovoltaic (PV) generation has strained traditional interconnection processes, often necessitating costly grid upgrades to accommodate new capacity. To mitigate this, utilities are increasingly adopting flexible interconnection agreements, which allow distributed generators to connect by agreeing to operational constraints, such as limiting real power exports during specific grid conditions. Conventional PV systems typically comply with these limits through inverter curtailment, which simply discards energy and results in lost revenue without providing alternative benefits.

This paper investigates whether agrivoltaic systems—where PV panels are installed over agricultural land—can offer a more productive form of curtailment. Unlike static PV systems, agrivoltaic systems with dynamic tracking capabilities can adjust panel tilt angles away from optimal sun-tracking positions. This adjustment reduces power output to meet export limits while simultaneously increasing the Photosynthetically Active Radiation (PAR) reaching the crops below. The core problem addressed is how to optimize the time-varying tilt of a single-axis tracking agrivoltaic system over a growing season to maximize energy production while strictly adhering to a real power export limit, thereby quantifying the trade-offs between energy generation and crop yield.

Methodology
The authors propose a framework linking an optimization problem with shading analysis and crop modeling (illustrated in Fig. 1 of the paper).

PV System Modeling: The study models a single-axis tracking system where the tilt angle ( $\Sigma_{pv}^t$ ) is the control variable. The power generation is calculated based on direct, diffuse, and reflected irradiance components, which are functions of the panel tilt, sun position, and ground reflectance.
Optimization Formulation: The authors formulate an optimization problem to maximize total energy production over a growing season ( $t=1..T$ $t = 1.. T$ ) subject to a static real power export limit ( $P^t \leq \bar{P}$ $P^{t} \leq \overset{ˉ}{P}$ ).
- Challenge: The problem is non-convex due to trigonometric relationships in the irradiance and power equations.
- Solution: The authors reformulate the problem into a Second-Order Cone Program (SOCP). They introduce auxiliary variables representing the deviation from a pre-specified sun-tracking algorithm and relax the non-convex constraints (specifically the unit circle constraint for sine/cosine deviations) into inequalities. This allows for efficient solution over seasonal time horizons.
Crop and Shading Evaluation: The optimal tilt schedule derived from the optimization is fed into a shading analysis to determine the field shading factor. This factor is then input into the EPIC crop model, a widely used growth model, to simulate crop yield based on accumulated heat units, temperature stress, and light availability.

Case Study and Results
The methodology was tested using data from the Alliant Energy Solar Farm in Ames, Iowa, simulating a 60-day growing season (June 1 – July 31) with a 150 kW system and lettuce crops.

Trade-off Analysis: Table I demonstrates a clear inverse relationship between export limits and crop yield. As the export limit decreased from 100% to 40% of rated capacity:
- Energy Production: Decreased from 73,501 kWh to 50,382 kWh.
- Crop Yield: Increased from 1.874 t/ha to 2.276 t/ha (a 31% increase).
Operational Behavior: Under lower export limits, the optimizer shifts panels further from sun-tracking to curtail power, allowing more PAR to reach the crops.
Feasibility Limits: The study notes that below a 35% export limit, the optimization becomes infeasible without supplemental inverter curtailment. This is because mechanical reorientation alone cannot sufficiently reduce output when diffuse and reflected irradiance components dominate.
Constraint Violations: The SOCP relaxation resulted in minor violations of the export limit (0–0.13% for limits >50%; up to 1.88% for limits ≤50%), particularly on cloudy days where diffuse light makes tilt adjustments less effective at curtailment.

Key Contributions

Optimization Framework: The paper formulates the first optimization-based framework for agrivoltaic operation specifically under flexible interconnection agreements with real power export limits.
Quantification of Dual Outcomes: It provides a quantitative assessment of how interconnection constraints impact both PV energy production and crop yield, demonstrating that agrivoltaic systems can comply with grid limits through operational adjustments that benefit agriculture.
SOCP Reformulation: The authors present a specific reformulation of the non-convex agrivoltaic operation problem into a solvable SOCP, accounting for single-axis tracking, seasonal horizons, and reflected irradiance.

Significance and Claims
The paper claims that agrivoltaic systems offer a distinct advantage over conventional PV systems when operating under flexible interconnection agreements. While conventional systems rely solely on inverter curtailment (a "zero-sum" loss of energy), agrivoltaic systems can achieve "productive curtailment." By adjusting panel orientation to meet grid limits, these systems simultaneously increase crop yields, thereby offsetting the economic trade-off of reduced energy production.

The authors conclude that this approach highlights a key distinction in the food-energy nexus: agrivoltaics can reduce the pressure for grid upgrades by providing a mechanism to manage export limits that generates agricultural value. The paper positions this work as a step toward understanding the interactions between agrivoltaics and the power grid, suggesting that future deployment practices should consider these operational synergies. The study remains modest in its scope, noting that it focuses on a single case study and that future work will need to address more detailed crop models, uncertainty, and panel tilt rate limits.

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