## 3 Proposed Methodology
### Hybrid AnFIS-SARIMA Model  
A composite algorithm comprising ensemble empirical mode decomposition (EEMD), ANFIS, and SARIMA can be utilized for short-term wind speed forecasting [43; 44]. Due to the stochastic nature of WD, deep insight into the actual wind speed series (WSS) is paramount to get accurate results. The original WSS contains periodic and nonperiodic series. Thus, a composite method with the capability of modeling periodic and nonperiodic series is an efficient choice for wind-speed forecasting. The EEMD decomposes the original WSS into a set of intrinsic mode functions (IMFs) of periodic and nonperiodic series. SARIMA forecasts the periodic WSS and ANFIS forecasts the nonperiodic WSS. The artificial neural network-based ANFIS-SARIMA constitutes better nonlinear ability, adaptivity, associative learning ability, and fault tolerance. To predict the WSS data of the \(n\)-th interval, the data of the \((n-1)\)-th interval are also taken into account for better results. The inputs taken into account are local time, temperature, pressure, and humidity, whereas the outputs are wind direction, wind speed, and WT output power. The step-by-step procedure from WD forecasting to FCL calculation is described below. 1. The WSS is decomposed into IMFs, and one residual series is given as \[\rm{S(t)}=\sum_{i=1}^{n}I_{i}(t)+R_{n}(t),\] (18) where S(t) is the wind speed series, \(I_{i}\)(t) represents the IMFs, and \(R_{n}\)(t) is the residual series. 2. The periodic and nonperiodic series of \(I_{i}\)(t) and \(R_{n}\)(t) are defined as \(P_{j}\)(t) and \(N_{i}\)(t), respectively. Thus, the original wind speed series can be given as \[\rm{S(t)}=\sum_{i=1}^{m}N_{i}(t)+\sum_{j=m+1}^{n}P_{j}(t)+R_{n}(t),\] (19) where \(N_{i}\)(t) is the nonperiodic WSS, and \(P_{j}\)(t) is the periodic WSS. 3. For \(P_{j}\)(t), the SARIMA model is implemented and the results are defined as \(\rm{\hat{P}_{j}}\)(t), Whereas, for \(N_{i}\)(t) and \(R_{n}\)(t), the ANFIS model is implemented and the results are defined as \(\rm{\hat{N}_{i}}\)(t) and \(\rm{\hat{R}_{n}}\)(t). The sum of results of ANFIS-SARIMA is the forecasted wind speed given as \[\rm{\hat{S}(t)}=\sum_{i=1}^{m}\hat{N}_{i}(t)+\sum_{j=m+1}^{n}\hat{P}_{j}(t)+ \rm{\hat{R}_{n}}(t).\] (20)
4. On the basis of the predicted wind speed in Equation (20), the wind power can be expressed in the form of wind power flux or kinetic energy flux given as \[\rm{P_{(WT)}}=\frac{1}{2}\rho_{(t)}C_{p}AS^{3}(t),\] (21)\[\rho_{(t)}=\frac{\mathrm{P}_{(t)}}{\mathrm{R}_{\mathrm{s}}\times\mathrm{T}_{(t)}}, \tag{22}\]  
where \(\rho_{(0)}\) is the density of air, \(\mathrm{P}_{(t)}\) is the atmospheric pressure, \(\mathrm{R}_{\mathrm{s}}\) is the specific gas density, and \(\mathrm{T}_{(t)}\) is the atmospheric temperature. A is the rotor swept area, \(\mathrm{C}_{\mathrm{P}}\) is the coefficient of maximum power, and \(\mathrm{S}(t)\) is the forecasted wind speed. If the wind hits the turbine at an angle \(\varphi_{(0)}\), as shown in Figure 2, then the azimuthal angle variation in the airflow can be considered as \(\cos\varphi_{(t)}\), and Equation (21) can be written as  
\[\mathrm{P}_{(WT)}=\frac{1}{2}\rho_{(t)}\mathrm{C}_{\mathrm{P}}\mathrm{A} \big{[}\mathrm{S}(t)\cos\varphi_{(t)}\big{]}^{3}. \tag{23}\]  
Usually, the quantity of interest is the temporal average of the power. In order to derive an expression for the temporal average of the power, we use [PERSON]'s decomposition [45]. \[S_{(t)}=\overline{S}_{(t)}+s_{(t)}\ \textit{and}\ \varphi_{(t)}=\overline{ \varphi}_{(t)}+\varphi_{(t)}, \tag{24}\]  
where \(\overline{S}_{(t)}\) and \(\overline{\varphi}_{(t)}\) are the temporal means of the wind speed and wind direction, respectively, while \(s^{\prime}_{(t)}\) and \(\varphi^{\prime}_{(t)}\) are perturbations or fluctuations about their respective means. Hereafter, for simplicity the notation \((t)\) is removed from all terms.