## 1 Introduction
### Objective Function  
Under the premise of a given carbon quota budget for the power industry at each planning horizon year, and relying on key low-carbon technology support, it is assumed that the carbon emissions of the power industry in each planning horizon year are exactly equal to the power carbon quota, achieving a supply-demand balance of carbon quotas between coal-fired enterprises within the power industry. Overall, the power industry does not need to purchase or sell carbon quotas to other industries. Therefore, the cost objective function of the power industry's \"dual carbon\" path optimization model mainly includes three parts: power generation investment cost I, key low-carbon technology investment cost D, and operational cost F, as shown in the following formula:  
\[\text{Min C}=\text{I}+\text{D}+\text{F} \tag{4}\]  
In the formula, C represents the total cost of electricity supply within the planning period. 1. Power Generation Investment Cost The power generation investment cost I mainly includes the investment and construction costs of typical power sources such as coal power, gas power, nuclear power, biomass power generation, wind power, solar power, hydropower, and pumped storage. \[\text{I}=\sum_{t\in\Gamma}\sum_{i\in\Phi}K_{i,t}.\Delta R_{i,t}.\mathit{Fint}\] (5)  
In the formula, \(K_{i,t}\) represents the unit capacity investment cost of power source \(i\) in the \(\mathbf{t}-\mathbf{th}\) planning year. \(\Delta R_{i,t}\) represents the newly added installed capacity of power source \(\mathbf{I}\) in the \(\mathbf{t}-\mathbf{th}\) planning year. \(\Phi\) represents the set of generator groups for eight types of typical power sources. \(T=\{2025,2030\ldots 2060\}\) represents the set of planning horizon years. \(\Delta R_{i,t}>0\) represents the newly added generator groups. \(\mathit{Fint}_{t}\) represents the discount factor for the \(\mathbf{t}-\mathbf{th}\) year. 2. Key Low-Carbon Technology Investment Cost The key low-carbon technology investment cost \(\mathbf{D}\) mainly includes the investment and construction costs of new energy storage, CCUS retrofitting and upgrading, and hydrogen energy technology. \[D=\sum_{i\in\Gamma}\left(\sum_{i=1}^{N1}K_{i,t}^{stor}\Delta R_{i,t}^{stor}+ \sum_{i=1}^{N2}\sum_{j=1}^{3}K_{i,j,t}^{CCUS}\Delta R_{i,j,t}^{stor}+\sum_{i=1 }^{N3}\sum_{j=1}^{2}K_{i,j,t}^{P2H}\Delta R_{i,j,t}^{P2H}\right)\mathit{Fint}_ {t}\] (6)  
In the formula, \(K_{i,t}^{stor}\), \(K_{i,j,t}^{CCUS}\), and \(K_{i,j,t}^{P2H}\) represent the unit capacity investment costs of new energy storage power station \(i\), the \(\mathbf{j}-\mathbf{th}\) type of CCUS upgrading station \(\mathbf{i}\), and the \(\mathbf{j}-\mathbf{th}\) type of hydrogen energy application station \(\mathbf{i}\) in the \(\mathbf{t}-\mathbf{th}\) planning horizon year, respectively. In the formula, the subscript \(\mathbf{j}=1,2\), \(3\) in \(K_{i,j,t}^{CCUS}\), respectively, indicates that the types of thermal power units undergoing CCUS retrofitting and upgrading are coal-fired power, gas-fired power, and biomass power generation. The subscript \(\mathbf{j}=1,2\), in \(K_{i,j,t}^{P2H}\), respectively, indicates that the technologies are electrolytic hydrogen production and hydrogen energy storage. \(\Delta R_{i,t}^{stor}\), \(\Delta R_{i,t}^{stor}\), and \(\Delta R_{i,t}^{P2H}\), respectively, represent the newly added installed capacities of new energy storage, CCUS, and hydrogen energy technology application stations \(\mathbf{i}\) in the \(\mathbf{t}-\mathbf{th}\) planning year. \(\mathbf{N1}\), \(\mathbf{N2}\), and \(\mathbf{N3}\) represent the number of new energy storage, CCUS, and hydrogen energy technology application stations, respectively. The operating cost \(F\) mainly includes the following: fuel and operation and maintenance (O&M) costs for various types of power sources, among which the fuel cost for renewable energy generation is zero, and the operation and maintenance costs for key low-carbon technology application stations such as new energy storage, CCUS, and hydrogen energy. \[