_applied_  
_sciences_  
_Article_  
A Two-Stage Stackelberg Game Wind-Storage Planning Model Considering a Bus Carbon Intensity Incentive Mechanism  
**[PERSON] \({}^{1}\)\({}^{\copyright}\)**, [PERSON] \({}^{1}\)\({}^{\copyright}\)**, [PERSON] \({}^{2}\)**, [PERSON] \({}^{3}\)**, [PERSON] \({}^{4}\)\({}^{\copyright}\)** and [PERSON] \({}^{1,*}\)\({}^{\copyright}\)  
\({}^{1}\) College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China  
\({}^{2}\) National Power Dispatpatching and Control Center, State Grid Corporation of China, Beijing 100031, China  
\({}^{3}\) State Grid Zhejiang Electric Power Co., Ltd., Hangzhou 310007, China  
\({}^{4}\) School of Electric Power Engineering, South China University of Technology, Guangzhou 510641, China  
\({}^{*}\) Correspondence: [EMAIL_ADDRESS]  
**Abstract:** In the trend of power system decarbonization, wind power and energy storage planning studies are in full swing. Incentives for wind power and energy storage development are important research topics. However, most studies have proposed incentives from an energy perspective, and few focus directly on incentives from a carbon perspective. To this end, this paper proposes a novel unified bus carbon intensity incentive mechanism from the carbon perspective. A two-stage Stackelberg game wind storage planning model that considers the proposed carbon incentive mechanism is constructed. In the first stage, the carbon flow of the entire system is obtained following economic dispatch based on the carbon emission flow theory. In the second stage, a Stackelberg game wind-storage planning model is constructed to model the game between the power generation company and the power grid company. Through simulation analyses of these cases, the proposed incentive mechanism can effectively guide the construction of wind turbines and energy storage at the best buses. Additionally, by comparing the proposed incentive with the existing incentive mechanisms, this paper finds that the proposed incentive mechanism can achieve a higher carbon reduction effect with a similar total investment in wind turbines and energy storage. **Keywords:** bus carbon intensity incentive mechanism; carbon emission flow theory; Stackelberg game; power system; wind storage planning  
**1. Introduction**  
The UN Sustainable Development Goals (SDGs) and the Paris Agreement jointly indicated the urgency of reducing global carbon emissions [1, 2, 3]. More than 80% of global carbon emissions are closely related to energy production, transmission, and consumption [4]. Since the Second Industrial Revolution, the power system has become a key part of the energy field. Represented by wind and photovoltaic power, renewable energy has emerged in the context of the low-carbon development of the power system [5, 6]. Most renewable energy sources draw directly from natural resources and experience a large intermittency. Therefore, it is difficult for them to meet the requirements and load demand of the power system operation. As a result, the development of renewable energy has also greatly driven the development of energy storage (ES) [7, 8]. At present, renewable energy and energy storage planning research have become hot spots for international scholars in the field. [PERSON] et al. [9] focused on the portfolio planning of the renewable energy industry with energy storage technologies and proposed a two-stage planning framework based on fuzzy, multi-criteria decision-making techniques to select the most promising renewable energy within the energy storage portfolio from the perspectives of energy generation, transmission, and terminal application. [PERSON] et al. [10] proposed a hybrid, shared energy storage planning framework in which the private energy storage of power suppliers and independent energy storage operators jointly provided shared energy storage services for users. [PERSON] et al. [11] established a wind-photovoltaic battery-thermal energy storage hybrid power system and investigated its multi-objective planning-operation co-optimization.