## 3 Case Study
### Establish Feature Sets of Each Component  
Photovoltaic output is affected by factors such as season, time, ambient temperature and solar irradiance. After the photovoltaic output is decomposed by VMD, each component contains the effects of the above factors of a different degree. Therefore, this section will study the effect of various factors on each component. Before establishing each component feature set, an original feature set \(F\) is established firstly, \(F\) includes time \(t\), season \(S\), ambient temperature \(T\), solar irradiance \(I\), and photovoltaic output history value \(P_{t}\). Among them, since the photovoltaic data takes a value every 15 min, the time is expressed as 0.0, 0.15, 0.30, 0.45, 1.0,..., 23.30, 23.45. In addition, the season \(S\) includes spring, summer, autumn and winter, which are represented by numbers 1, 2, 3, and 4 respectively; the photovoltaic output history value \(P_{t}\) represents the photovoltaic historical value before \(t\) minutes. In addition, the temperature of the photovoltaic panel is not considered in this paper because there are many solar panels in the photovoltaic power station, and the temperature of each photovoltaic panel is different due to the influence of factors such as the angle of illumination, so it is impossible to establish a characteristic factor uniformly. After the f is established, the mRMR is used to establish the feature set of each component. The specific process is shown in Figure 6.  
In Figure 6, \(N\) is the number of components after VMD decomposition. As can be seen from Figure 6, the selection step of the component feature set \(J_{n}\) is as follows:  
* Use an incremental search method to establish a candidate feature set of the component;
* Calculate the mRMR values of each feature in and arrange them in descending order according to the magnitude of the mRMR value, and then input them into error function one by one to obtain the error;
* Take the number of features corresponding to the minimum error to establish a component feature set. Figure 5: The image after being decomposed by VMD. The error function in Figure 6 uses the root mean square error (RMSE), which is calculated as shown in Equation (2). The errors obtained by inputting the feature factors, which is ordered in descending order according to the mRMR, of each component into the error function one by one are shown in Table 2.  
The letters in the Table 2 represent the names of each feature, the numbers are the error values, and the red numbers represent the smallest errors. The names of the features in the table are cumulative, for example, the \(P_{45}\) of IMF1 means that the error value obtained by inputting \(P_{45}\) and its previous \(t,P_{60}\) together into the error function is 0.0254. By observing Table 2, it can be seen that except for IMF8, for other component features, \(t\) are all ranked the front, it can be seen that time \(t\) has the greatest influence on the component, and it can be concluded that the photovoltaic output is greatly affected by the alternating day and night in one day, only in the daytime can a photovoltaic power station generate electricity and it cannot generate electricity at night. In addition, the effects of the irradiance intensity  
Figure 6: The flow chart of feature selection of components. and the temperature \(T\) on each component are also large. In comparison, the photovoltaic historical value seems to have a weak influence on each component. From Table 2 and the above discussion, it is found that the feature set of each component is as shown in Table 3.  
By observing Table 3, it can be clearly seen that the components containing the feature \(t\) are IMF1-IMF7 and IMF9-IMF10; the components containing the stochastic features as \(I\) or \(T\) are IMF1-IMF6 and IMF9-IMF10; the components containing the feature \(S\) are IMF3, IMF6 and IMF10.