# Research on Robust Day-Ahead Dispatch Considering Primary Frequency Response of Wind Turbine
## 2 Frequency Analysis of Wind Integrated Power System  
The inertia of the power system provides a short-term power support that responds to changes in the system frequency to prevent it from dropping rapidly, which enables the system to adjust the operating strategy to reconstruct the power balance. The spinning inertia of the system is mainly provided by the synchronous generator. When the system frequency fluctuates, the synchronous generator rotor releases its rotational kinetic energy to track it. Therefore, in the analysis of the system frequency, the inertia time constant \(H\) of the synchronous generator is very important. It is the ratio of the kinetic energy of the unit rotor to the rated capacity of the generator at the synchronous angular velocity \(\Omega_{0}\) of the generator, as shown in the following equation [24]:  
\[H=\frac{W_{k}}{S_{N}}=\frac{J\Omega_{0}^{2}}{S_{N}} \tag{1}\]  
where \(W_{k}\) represents the rotational kinetic energy at the rated speed of the generator; \(S_{N}\) is the rated capacity of the generator, while \(J\) means the moment of inertia of the rotor. For large-scale wind power grid-connected systems, the system equivalent inertia time constant can be obtained by referring to Equation (1):  
\[H_{s}=\frac{W_{k,s}}{S_{N,s}}=\frac{\sum\limits_{i=1}^{m}\frac{1}{2}j_{i} \Omega_{0}^{2}+\sum\limits_{j=1}^{n}W_{w,j}}{S_{N,s}} \tag{2}\]  
where \(W_{k,s}\) is the total rotational kinetic energy of the system, including that of the conventional synchronous generator and wind turbines; \(S_{N,s}\) indicates the total rated capacity of the system; \(j_{i}\) is the moment of inertia of the synchronous generator \(i\); and \(W_{w,j}\) is the rotational kinetic energy of the fan \(j\). In fact, during the grid connection of the large-scale wind turbines represented by the Doubly-fed Induction Generator (DFIG), the number of the conventional synchronous generator units is reduced to accommodate the wind power and cut the wind curtailment while maintaining the system power flow balance [25]. Because of the converter, though the wind turbine rotor has a certain rotational kinetic energy, it cannot respond to the frequency change. Consequently, in Equation (2), \(W_{w,j}\approx 0\). When the total rated capacity of the system remains unchanged, the responsible kinetic energy decreases and the system equivalent inertia time constant drops too. At the same time, because the wind turbines could retain the frequency regulation reserve for the primary frequency regulation and because they usually run in the MPPT mode, if we do not consider the energy storage there will not be power reserve for the primary frequency regulation. The MPPT mode indicates that, through the self-optimizing process, the operating point voltage or current is adjusted to make sure the wind turbines operate near the peak work point. The grid connection of large-scale wind turbines can result in a decrease in the system's inertial response and primary frequency regulation ability. The frequency regulation of different systems is affected by the grid connection to different extents due to factors like the wind power grid-connected capacity, synchronous generator installed capacity and network topology. Generally, the inertial frequency response may be affected when the wind power exceeds 10% of the system [26]. With the increasing grid-connected capacity of renewable energy, many countries require an inertia response and power support capabilities of grid-connected wind power in order to ensure a stability of frequency for the system [27; 28; 29]. To meet the above requirements, wind turbines can be involved in the system frequency response by energy storage or VSG technology. Through the parallel connection of the energy storage devices and the AC bus at the wind turbines, or at the wind farm outlet and the joint control, it is possible to obtain similar external characteristics of the frequency regulation of the synchronous generator.