Analysis of installed photovoltaic capacity in Mexico: A systems dynamics and conformable fractional calculus approach

This study develops a new estimation method within the system dynamics (SD) framework, incorporating fractional calculus (FC) to conduct a sensitivity analysis on photovoltaic capacity growth in Mexico. The primary goal is to address the need to model energy transitions accurately and realistically, considering Mexico's advantages in renewable energy, particularly solar power. The study explores the use of FC to improve the precision of simulations and provide valuable insights into the growth of photovoltaic installations under different market conditions and policies.

The methodology is structured in three phases. Initially, an exponential growth model is developed to simulate the early stage of photovoltaic capacity expansion, incorporating key variables such as public investment, subsidies, and the effects of rural loss on the adoption of renewable technologies. In the second phase, a sigmoidal growth model is applied to represent more realistic capacity limits, considering market saturation and structural limitations. The differential equations governing the growth were solved using the conformable derivative, which captures the complexity of the system's dynamics, including memory effects.

The sensitivity analysis performed on both the exponential and sigmoidal models reveals that the fractional parameter $\alpha =0.8652$ provides the best fit to the actual data from 2015 to 2023, reducing the average error to 16.52%. Projections for the period from 2023 to 2030 suggest that Mexico's installed photovoltaic capacity could range between 23,000 and 25,000 MW, with $\alpha$ values varying between 0.8 and 1, aligning with the expected market dynamics and national energy goals.

This study emphasizes the importance of using system dynamics combined with FC as an innovative tool for energy planning in Mexico. The ability to simulate multiple scenarios and perform sensitivity analyses is crucial for optimizing energy resources, designing policies that promote renewable technologies, and ensuring a successful transition to a sustainable energy future.