## 3 Materials and Methods
### Model Validation  
Firstly, verify the SD model's system boundary. After removing a variable from the system flow diagram, analyze whether the path where the variable is located can still run  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Number** & **Variables** & **Initial Value and Function Relation** & **Unit** \\ \hline \multirow{4}{*}{41} & \multicolumn{2}{c}{The utilization time of} & \multirow{4}{*}{300} & \multirow{4}{*}{Hour} \\  & & renewable energy power & & \\  & & generation equipment & & \\ \hline \multirow{2}{*}{42} & \multicolumn{2}{c}{Renewable energy power} & \multirow{2}{*}{MIN (SMOOTH (1 – “Technology—level} \\  & & production technology level & growth rate” \(\,\) * Time, 120), 1) & \\ \hline \multirow{4}{*}{43} & \multirow{4}{*}{Renewable energy power} & \multirow{4}{*}{\
\begin{tabular}{c} The utilization time of renewable energy power \\ generation equipment \(\times\) installed capacity of \\ renewable energy power generation + installed \\ capacity of renewable energy power generation \\ \(\times\) renewable energy power production \\ technology level \\ \end{tabular} } & \multirow{4}{*}{\(10^{8}\) KWh} \\  & & & & \\ \hline \multirow{4}{*}{44} & \multicolumn{2}{c}{Income from renewable} & \multirow{4}{*}{Electricity sale price \(\times\) Renewable energy} \\  & & energy power generation & \\ \cline{2-2} \multirow{3}{*}{45} & \multirow{2}{*}{
\begin{tabular}{c} Technology—level \\ growth rate \\ \end{tabular} } & \multirow{2}{*}{“R&\&D investment” \(\times\) Investment efficiency} & \% \\ \cline  
normally. Then, check each other variable in the model one by one to ensure the rationality of the model system boundary [45].  
Then, the \"Check Model\" function in Vensim PLE software 7.3.2 was used to inspect the model comprehensively. The results showed that all variables had been assigned values and had consistent dimensions. The functional equations between each variable had been correctly constructed, ensuring the model structure and logic's effectiveness and laying the foundation for subsequent simulation analysis.  
Finally, historical data verification will be conducted to check whether the model's simulation results match the actual situation. The results will be compared with historical data, simulation errors will be reduced by adjusting variable parameters reasonably, and the authenticity and effectiveness of the simulation results will be ensured. It is generally believed that if the error rate is within \(\pm\)10%, the model is effective and can be used for simulation analysis [30]. Considering that the electricity supply is involved in many impact paths in the system and the historical data of the electricity supply is easily accessible, it has been updated to 2022. Therefore, comparing the electricity supply values simulated by the system with the data from 2020 to 2022 in the Liaoning Statistical Yearbook, as shown in Table 2, the error rates are all less than \(\pm\)10%, indicating that the system dynamics model is authentic and can truly reflect the actual operating status of the impact of TGC and CET on the sustainable development of the power market.