## 4 Renewable Energy Capacity Configuration Method
### Wind and PV Power Fluctuation Rate Calculation  
According to [PERSON]'s Sampling Theorem, wind speed and light intensity, among other uncertainties, are sampled for a typical day to obtain the measured output power of the wind and PV for that day. Discrete Fourier Transform (DFT) can transform the time domain signal into the frequency domain signal, and its expression is as follows [33]:  
\[Y(n)=\sum_{k=0}^{N-1}y_{k}\cdot e^{-\frac{2\pi j\mathrm{ik}}{N}} \tag{4}\]  
where \(Y\) is the frequency domain signal; \(n\) is the signal sampling number in the frequency domain; \(y\) is a time domain signal; \(k\) is the signal sampling serial number in the time domain; \(N\) is the total number of samples in the time domain.  
The measured output power sequence \(P_{w}\) of the wind and light is subjected to DFT transformation, and the measured output power amplitude sequence \(X_{w}\) of the wind and light and the corresponding frequency sequence \(f_{w}\) are obtained. The expressions are  
\[\left\{\begin{aligned} X_{w}&=[X_{w}[1],\cdots,X_{w} [n],\cdots,X_{w}[N]]^{\mathrm{T}}\\ f_{w}&=[f_{w}[1],\cdots,f_{w}[n],\cdots,f_{w}[N] ]^{\mathrm{T}}\end{aligned}\right. \tag{5}\]  
where \(X_{w}[n]\) is the amplitude corresponding to the \(n\)-th frequency; \(f_{w}[n]\) is the \(n\)-th frequency in the measured sequence; \(N\) is the total number of samples.  
In order to obtain the expected output power of the wind and PV, the low-frequency signals are intercepted from the sample amplitude sequence \(X_{w}\) with the cut-off frequency \(f_{L}\) and re-composed into the amplitude sequence. Based on the DFT characteristics and  
\begin{table}
\begin{tabular}{c c c} \hline
**Water Regimen** & **Utilization Hours (h)** &
\begin{tabular}{c} **Minimum/Maximum** \\ **Technical Output (MW)** \\ \end{tabular} \\ \hline Wet period & a\(A\) & \(P_{f,\min}/P_{f,\max}\) \\ Low water period & b\(A\) & \(P_{k,\min}/P_{k,\max}\) \\ \hline \end{tabular}
\end{table}
Table 1: Hydroelectric power station regulation capacity calculation table.  
Nyquist's Sampling Theorem, the amplitude sequence \(X_{L}\) intercepted by the cut-off frequency \(f_{L}\) is  
\[X_{L}=[X_{L}[1],\cdots,X_{L}[n_{L}],0,\cdots,X_{L}[N-n_{L}]\cdots,X_{L}[N]]^{ \mathrm{T}} \tag{6}\]  
where \(X_{L}[n_{L}]\) is the amplitude corresponding to the cut-off frequency.  
Inverse Discrete Fourier Transform (IDFT) is performed on the new sequence \(X_{L}\) to obtain the expected power output of wind and PV. The IDFT expression is [34].  
\[y_{k}=\sum_{k=0}^{N-1}Y(n)\cdot e^{\frac{2\pi\mathrm{j}nk}{N}} \tag{7}\]  
Wind and PV power exhibit significant volatility, so the expected output power of the wind and PV must comply with the specified range of power fluctuation rate to ensure the safety and stability of the power system operation. The power fluctuation rate in the period \(T_{r}\) is expressed as follows:  
\[F_{pr}=\frac{P_{\mathrm{max}t}-P_{\mathrm{min}t}}{P_{e}}\times 100\%\leq F_{pr, Tr} \tag{8}\]  
where \(F_{pr}\) is the active power fluctuation rate; \(F_{pr,Tr}\) is the maximum value of active power fluctuation rate; \(P_{e}\) is the rated power, kW; \(P_{\mathrm{max}t}\) and \(P_{\mathrm{min}t}\) are the maximum and minimum output power during the period, kW.  
The fluctuation index in Equation (8) is used to assess whether the expected power output of the wind and PV is within the fluctuation index. If it can be satisfied, the expected power output of wind and PV is \(P_{e}\). If it cannot be satisfied, the cut-off frequency \(f_{L}\) must be recursively adjusted until the expected value \(P_{e}\) satisfies the index.