## 1 Introduction
### Constraints  
#### 3.2.1 Planning Capacity Constraints  
The future expansion of hydropower and nuclear power is mainly constrained by the availability of suitable sites, and existing units will continue to operate beyond their economic life cycle without unit retirement being considered. The scale of new renewable energy generation is primarily constrained by national policies and industry production capacity, and existing renewable energy stations will be replaced with an equivalent capacity after reaching their economic life cycle, with unit retirement effectively not being considered. The scale of new gas-fired power installations is influenced by local policies and gas prices, while the scale of new coal-fired power installations is mainly constrained by national policy planning. For existing coal-fired power units, some will continue to operate after reaching their economic life cycle through life extension or equivalent capacity replacement, while others will be retired as planned. Overall, the new installed capacity and retirement capacity of various types of power sources should meet the constraints as shown in the following formula:  
\[\left\{\begin{array}{l}\Delta R_{i,t}^{\min}\leq\Delta R_{t,t}\leq\Delta R_{i, t}^{\max}\\ \Delta R_{i,t}^{dw,\min}\leq\Delta R_{t,t}^{dw}\leq\Delta R_{i,t}^{dw,\max} \end{array}\right. \tag{8}\]  
In the formula, \(\Delta R_{i,t}^{\max}\), \(\Delta R_{i,t}^{\min}\) represent the lower and upper limits of the newly added installed capacity for power source \(i\) in the \(\mathbf{t}-\mathbf{th}\) planning year, respectively.\(\Delta R_{i,t}^{dw,\max}\), \(\Delta R_{i,t}^{dw,\min}\) represent the upper and lower limits of the retired installed capacity for power source \(i\) in the \(\mathbf{t}-\mathbf{th}\) planning year, respectively.  
To meet the system capacity adequacy requirements, especially electricity supply guarantee issues under extreme weather conditions, the installed capacities of various types of power sources and new energy storage technologies must meet the following constraints:  
\[\sum_{i\in\Phi}\beta_{i,t}\left(R_{i,t}+\sum_{l=1}^{t}\left(\Delta R_{i,l}- \Delta R_{i,l}^{dw}\right)\right)+\sum_{i=1}^{N1}\beta_{i,t}^{stor}\left(R_{ i}^{stor}+\sum_{l=1}^{t}\Delta R_{i,l}^{stor}\right)\leq(1+\alpha_{t})P_{t}^{ load,\max} \tag{9}\]  
In the formula, \(\beta_{i,t}\), \(\beta_{i,t}^{stor}\) represent the effective capacity coefficients of power source \(i\) and new energy storage \(i\) in the \(\mathbf{t}-\mathbf{th}\) planning year, respectively. \(\alpha_{t}\) represents the system reserve capacity coefficient in the \(\mathbf{t}-\mathbf{th}\) planning year. \(P_{t}^{load,\max}\) represents the maximum load of all of society in the \(\mathbf{t}-\mathbf{th}\) planning year.  
The future scale of new low-carbon technologies such as new energy storage, CCUS, and hydrogen energy is mainly limited by factors such as the development status of technology, national policy planning, and industry production capacity. In addition, the scale of CCUS technology application is also closely related to the scale of existing thermal power units and the demand for electricity carbon emission reduction.