A Model Predictive Control Approach to Dual-Axis Agrivoltaic Panel Tracking

Abstract

Agrivoltaic systems--photovoltaic (PV) panels installed above agricultural land--have emerged as a promising dual-use solution to address competing land demands for food and energy production. In this paper, we propose a model predictive control (MPC) approach to dual-axis agrivoltaic panel tracking control that dynamically adjusts panel positions in real time to maximize power production and crop yield given solar irradiance and ambient temperature measurements. We apply convex relaxations and shading factor approximations to reformulate the MPC optimization problem as a convex second-order cone program that determines the PV panel position adjustments away from the sun-tracking trajectory. Through case studies, we demonstrate our approach, exploring the Pareto front between i) an approach that maximizes power production without considering crop needs and ii) crop yield with no agrivoltaics. We also conduct a case study exploring the impact of forecast error on MPC performance. We find that dynamically adjusting agrivoltaic panel position helps us actively manage the trade-offs between power production and crop yield, and that active panel control enables the agrivoltaic system to achieve land equivalent ratio values of up to 1.897.

Figures (7)

• Figure 1: Block diagram of MPC approach to agrivoltaic panel tracking.
• Figure 2: (Left) The sun's position can be characterized by the solar azimuth $\phi_\text{s}^t$ and altitude $\beta_\text{s}^t$. (Right) PV panel position can be characterized by the panel azimuth $\phi_\text{pv}^t$ and tilt $\Sigma_\text{pv}^t$.
• Figure 3: Changes in shading factor as a function of the cosine of tilt angle adjustments away from the sun-tracking trajectory \ref{['eqn: ST tilt']}-\ref{['eqn: ST azimuth']}. Each line corresponds to a one-hour time step over the growing season, evaluated with $1^\circ$ resolution. The full range of feasible tilt angle adjustments were considered at each time step, i.e., $\Sigma_\text{pv}^t \in [\Sigma_\text{pv,st}^t \pm90^\circ \text{ s.t. } \ref{['eqn: PV tilt limit']}]$.
• Figure 4: Hourly $R^2$ values of the linear approximation \ref{['eqn: SF linear']}, averaged over the growing season.
• Figure 5: Standard deviation for temperature, DNI, and DHI Gaussian noise as a function of the forecast lead time $t-t_0$. The standard deviation increases with the forecast lead time and is capped at two weeks. In this example, the maximum standard deviation is capped at 10% of the expected range of each variable.