# Are more solar panels always better?

Assessing carbon impact at the community scale.

Are more solar panels always better? Assessing carbon impact at the community scale, Jonathan Coignard, Sacha Hodencq, Nana Kofi Twum-Duah, Mathieu Brugeron and Rémy Rigo-Mariani, TATuP 2022.

# Abstract

Are more solar panels always better in terms of carbon impact for a local energy community, and what is the influence of energy sufficiency? The answer is simple when the grid is considered as infinite storage. However, this answer becomes uncertain if we consider that exporting power to the larger grid at the national scale is not the desired option. Although this is a conservative assumption, it is considered for technical and social reasons. When taking this more conservative assumption, load profiles become a key to evaluating the carbon impact of hybrid systems with solar panels plus storage units. To summarize the impact of any load profiles on the optimal sizing of solar panels, we propose a novel index denoted “natural self-sufficiency”. Our results show that, not only reducing energy demand but also being more flexible, significantly impacts carbon emissions related to solar panels.

# Online supplementary materials

## Optimization problem to modify load profiles

To generate new load profiles, we start from an original real-world load profile and implement an optimization-based approach. The objective of the optimization is to make as little changes as possible from the original profile (i.e., minimum mean square error as an objective) to match a certain natural self-sufficiency target. Further, we impose that the energy consumption remains unchanged and that the previous maximum power demand is not exceeded as additional constraints. The problem results in a mixed integer quadratic programming problem.

\begin{alignat}{1} \text{minimize} \sum^T_t profile_{change}(t)^2 \\ profile(t) = load(t) + profile_{change}(t) \\ 0 \leq profile(t) \leq \max(load(t)) \\ \sum^T_t profile_{change}(t) = 0 \\ grid^+(t) - grid^-(t) = profile(t) - pv \times irradiance(t) \\ 0 \leq grid^+(t) \leq \delta (t) \times \max(load(t)) \\ 0 \leq grid^-(t) \leq (1 - \delta (t)) \times pv \times irradiance(t) \\ \frac{\sum^T_t grid^+(t)}{\sum^T_t load(t)} = 1 - target^{selfsufficiency} \end{alignat}

Where $$load(t)$$ represents the original load profile. The variables $$grid^+(t)$$ and $$grid^-(t)$$ have been added to calculate the self-sufficiency of the new load profile $$profile(t)$$. They represent respectively energy imports and energy exports. In order to ensure that power exports are zero when power imports are non-null and vice versa, we introduce the binary variable $$\delta (t)$$. Finally, $$target^{selfsufficiency}$$ represents the natural self-sufficiency to reach while minimizing the profile changes $$profile_{change}(t)$$. To solve those equations, we use the Gurobi solver.

French scenario.

German scenario.