Modeling the Stackelberg regulatory game between government and grid corporation for transmission expansion investment under permitted rate of return: Impacts of diverse carbon abatement pathways

Against the global energy transition toward high Variable Renewable Energy (VRE) penetration and active efforts toward carbon abatement, transmission network expansion is critical for VRE integration and reducing emissions. However, transmission investments' capital intensity and inherent uncertainty create conflicts between governments' emission reduction goals and grid companies' financial return requirements. The conventional unified Permitted Rate of Return (PRR) mechanism lacks the flexibility to accommodate regional disparities and evolving low-carbon demands, causing investment misallocation and inefficiencies in VRE utilization. To address this issue, this study explores the coordination between transmission expansion and low-carbon pathways through a government-grid company game. A bi-level model is formulated: the upper-level government sets PRR to minimize the Social Cost of Electricity per MWh (SCEM) with adhering to carbon constraints; the lower-level grid company optimizes the capacity and location of new and expanded transmission lines to maximize full-cycle net profit. The resulting non-convex model is transformed into a Mixed-Integer Linear Programming problem using a combined KKT-BigM-McCormick approach to ensure global optimality. Numerical experiments on China's provincial power system under four PRR mechanisms and three carbon abatement scenarios show: ① The Non-game scenario achieves theoretical “first-best” solution outcome but is impractical for real-world implementation; ② The unified PRR causes economic and operational inefficiencies; ③ The proposed Zonal PRR, as a feasible “second-best” solution, reduces SCEM, improves national VRE penetration, and adapts to different emission reduction stages. This study provides a quantitative decision-support tool for transmission infrastructure planning and offers policy insights for reforming electricity transmission pricing in China.