## 5 Case Studies Analysis
### Calculation and Analysis of Scheduling Potential  
Calculate the (35) correlation degree of the data in Table 3 using Equations (28) and (40), calculate the entropy weight using Equation (36), and finally calculate the weighted correlation degree. Among them, \(\rho=0.5\) represents the traditional grey correlation theory, and the selection of dynamic \(\rho\) is an improved grey correlation theory.  
(1) Comparative analysis of grey relational theory.  
According to Table 4, the improved grey correlation theory effectively weakens the influence of the maximum value of the difference matrix in the calculation of the correlation coefficient by redefining the selection of the resolution coefficient \(\rho\). Meanwhile, as shown in Table 4, the application of the improved algorithm effectively highlights the correlation between the initial investment cost and environmental governance cost with the total operating cost of the microgrid, thereby reflecting the high correlation between the volatility of new energy output and the initial investment cost and environmental governance cost.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  
(2) Analysis of the correlation between fluctuations in new energy output and various cost indicators.  
According to Table 4, the ranking of the degree of correlation between new energy and the initial investment cost, equipment maintenance cost, and environmental governance cost of the local microgrid is as follows: distributed photovoltaic power station > wind turbine. By comparing and analyzing the differences in various cost indicators, the correlation between wind turbines and equipment maintenance costs and environmental governance costs is significantly higher than that of distributed photovoltaic power plants. Therefore, in areas with heavy environmental pollution, the impact of wind turbines in new energy should be fully considered. The correlation between initial investment cost and new energy of wind turbines is slightly greater than that of distributed photovoltaic power plants, so wind turbines should be given special consideration on the basis of similar local photovoltaic and wind energy resources.  
(3) Weighted correlation analysis.  
According to Table 4, after comprehensive weighting of the cost indicators of new energy and various power grid operations, they are sorted by size as follows: wind turbines > distributed photovoltaic power plants. Therefore, it can be seen that when there is an equal fluctuation in the output of new energy in the region, the cost of wind turbines is greater than that of distributed photovoltaic power plants. Therefore, in the process of long-term planning for new energy in this area, emphasis should be placed on considering the impact of wind turbines on overall operating costs.  
(4) Comparative analysis of weighted correlation degree with other algorithms.  
According to Table 4, compared to other correlation analysis algorithms, the improved grey correlation theory proposed in this paper can better consider the correlation between initial investment costs and environmental governance costs, resulting in a better initial investment cost, equipment maintenance cost, and environmental governance cost. The weighted correlation degrees of the improved grey correlation theory in this article are 0.738 and 0.798 in the photovoltaic power station and wind turbine unit, respectively.