## 2 Analysis of the Operating Mechanism of a Hybrid Plant Station Primary Frequency Regulation
### Research on EEMD Algorithms Suitable for Power Frequency Division  
Empirical Mode Decomposition (EMD) is a new time domain analysis method of signal decomposition that decomposes the signal adaptively according to its intrinsic properties. The intrinsic-mode functions (IMFs) with frequencies from high to low are obtained. EEMD is an improvement on EMD. It improves the mode aliasing problem of EMD by adding a white noise processing signal. The addition of white noise can provide a relatively consistent reference scale distribution for EMD and ensure the time-domain continuity of each mode function to reduce mode aliasing. At the same time, compared with the short-time Fourier transform, EEMD is more suitable for processing non-stationary data. Compared with wavelet transform, EEMD has better adaptability and is a frequency division algorithm that is very suitable for the application scenarios of this article. The steps of the EEMD algorithm to achieve power instruction decomposition are as follows:  
1. Add \(m\) random white noise sequences \(n_{i}(t)\) with zero mean and equal variance to the power instruction signal \(p(t)\), and set their sum as \(P_{i}(t)\): \[P_{i}(t)=p(t)+n_{i}(t)\ (i=1,2,\ldots,m)\] (15)
2. The EMD algorithm decomposes \(P_{i}(t)\). The specific process is as follows: 1. All local maximum values and local minimum values are connected by the cubic spline interpolation method to form upper and lower envelope curves \(y_{\max}(t)\) and \(y_{\min}(t)\) of the signal, and the average \(y_{j}(t)\) is calculated. \[y_{j}(t)=\frac{y_{\max}(t)+y_{\min}(t)}{2}\] (16)
2. Subtract the average value \(y_{j}(t)\) from the power instruction signal to be decomposed \(P_{i}(t)\): \[h_{ij}(t)=P_{i}(t)-y_{j}(t)\] (17)
3. The calculated difference \(h_{j}(t)\) is taken as the data to be decomposed, and steps 1 and 2 are repeated until the standard deviation of the calculated difference is less than the pre-set value \(\sigma\): \[SD=\sum_{t=0}^{T}\left[\frac{\left|h_{i(j-1)}(t)-h_{ij}(t)\right|^{2}}{h_{i(j- 1)}^{2}(t)}\right]<\sigma\] (18)
4. At this point, the first IMF component of \(P_{i}(t)\) is obtained, and the high-frequency component \(h_{i1}(t)\) is separated from \(P_{i}(t)\) to obtain the remaining signal. \[r_{i1}(t)=P_{i}(t)-h_{i1}(t)\] (19)  
\(r_{i1}(t)\) is taken as the original signal, and steps 1 to 2 are repeated to obtain the second IMF component \(h_{i2}(t)\) of \(P_{i}(t)\) and the remaining signal \(r_{i2}(t)\). This cycle is repeated to obtain \(n\) IMF components of frequency from high to low and a residual signal \(r_{\text{in}}(t)\) representing the center trend of \(P_{i}(t)\). The power instruction signal can be expressed as: \[P_{i}(t)=\sum\limits_{j=1}^{n}h_{ij}(t)+r_{\text{in}}(t)\] (20)
3. Repeat step (2) for the EMD decomposition of the power instruction signal of each white noise sequence \(P_{i}(t)\) to obtain the IMF signal of the \(m\) group and the margin of the \(m\) group: \[H= \begin{bmatrix}h_{11}&h_{12}&\cdots&h_{1n}\\ h_{21}&h_{22}&\cdots&h_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ h_{m1}&h_{m2}&\cdots&h_{mm}\end{bmatrix} ,\ r= \begin{bmatrix}r_{1n}\\ r_{2n}\\ \vdots\\ r_{mm}\end{bmatrix} \] (21)
4. Calculate the average value of the IMF component of the \(m\) group and the margin of the \(m\) group: \[\left\{ \begin{aligned} H_{1}&=\frac{1}{m}\sum\limits_{i=1}^{m}h_{ i1}\\ H_{2}&=\frac{1}{m}\sum\limits_{i=1}^{m}h_{i2}\\ &\vdots\\ H_{n}&=\frac{1}{m}\sum\limits_{i=1}^{m}h_{\text{in}}\end{aligned} ,\ R=\frac{1}{m}\sum\limits_{i=1}^{m}r_{\text{in}}\right.\] (22)  
Step (4): Eliminate the influence of the white noise sequence added at the beginning, and then the original signal \(p(t)\) can be expressed as:  
\[p(t)=\sum\limits_{i=1}^{n}H_{i}+R \tag{23}\]  
The primary frequency regulation power command signal is divided into \(n\) Intrinsic Mode Function (IMF) components with frequencies ranging from high to low and a residual component using the EEMD algorithm.