Modeling Urban–Rural Energy Mutual Assistance Through Photovoltaic–Carbon Sink Synergy: A System Dynamics Approach

China’s dual carbon goals and rural revitalization strategy necessitate innovative models that integrate energy transition with ecological conservation. However, a critical disconnect persists between photovoltaic (PV) promotion and forest carbon sink projects, limiting their collective potential for coordinated urban–rural emission reduction and common prosperity. To bridge this gap, this study pioneers an integrated “cooperation-mutual assistance” framework that synergizes PV and carbon sinks. A system dynamics model encompassing economic, energy, and environmental subsystems is developed to simulate the long-term evolution (2025–2050) of this synergy under multiple policy scenarios. The simulation results demonstrate that this integrated model can achieve substantial co-benefits: It enables a cumulative carbon emission reduction of 17.5 Gt (gigatons of CO2 equivalent) from 2025 to 2050, boosts regional GDP by 4.8% by 2050 compared to the baseline scenario, and narrows the urban–rural income gap by prioritizing rural resident income growth. The main contribution of this study is the novel integration of PV and carbon sinks into a unified analytical framework, quantitatively verifying its win–win potential. These findings provide a critical scientific basis for crafting integrated policies that combine carbon markets, green finance, and smart grid planning.