# Research on Robust Day-Ahead Dispatch Considering Primary Frequency Response of Wind Turbine
## 3 Optimization Model Considering Primary Frequency Response
### Primary Frequency Response
From Equation (9), we can see that between \(t_{N}\) to \(t_{d}\), assuming that the power variation of the unit \(i\) is \(\Delta P\), \(C_{i}=\frac{\Delta P}{t_{N}-t_{d}}\), whereas if we consider the power imbalance of \(P_{\text{loss}}\) after the fault in the unit, \(C_{MIN}=\frac{P_{\text{loss}}}{t_{N}-t_{d}}\) is the minimum required ramp rate of the governor; so, \(\Delta P=C_{i}\frac{P_{i}}{C_{MIN}}\). Therefore, in order to meet the demand of the reserve (8) without causing any waste, the primary reserve of unit \(i\), \(R_{i}^{F}\leq\Delta P=C_{i}(t_{N}-t_{d})=P_{MIN}\) where \(P_{MIN}\) is the adjustment power of \(i\). In fact, the primary reserve of unit \(i\) shall be within the range of the upper limit of the unit's output and comply with the constraint \(P_{MIN}\), while releasing before \(t_{N}\). Readers can read it in [13] for ease of understanding. The above discussion demonstrates the PFR constraint for the economic dispatch (ED) based on the synchronous generator parameters. In this paper, we also consider the grid connection of large-scale wind power. In order to ensure a sufficient frequency response of the grid, it is necessary to involve wind power in the primary frequency control. Research into the frequency considers mainly the real-time time scale. The scenario of the wind power output during the real-time operation is fixed; based on this, the work in [15] proposes the constant power reserve mode of the wind power, as shown in Figure 2a. And we propose primary reserve constraint of the wind power, as shown in Figure 2b. Figure 2a shows that when the wind power output is below a certain level, the wind power could not provide the primary reserve. When it is above that, the reserve capacity is fixed. This is a technically reliable mode and has been applied [34]. However, it is undeniable that this mode is not flexible enough in the ED, especially when it joins other synchronous generators in the frequency response. The primary reserve in wind power indicates some wind curtailment, so the fixed reserve capacity  
Figure 2: Primary reserve of wind power; (**a**): constant power reserve of the wind power, (**b**): primary reserve constraint of the wind power. does not prove to be an effective approach considering the dispatch strategy and costs. Therefore, a better form of constraint is needed within the framework of the optimal dispatch. As we have mentioned, the VSG control technology enables the wind turbine to share similar external frequency regulation characteristics to the synchronous generator. When the system frequency deviation is above \(f_{d}\) and the active output of the VSG is greater than 20% of the rated capacity, the VSG active output can be adjusted to participate in the PFR of the system. When the system frequency drops, the VSG active output rises, and the maximum active output increase will be at least 10% of the rated capacity. However, in order to ensure a sufficient power generation of the wind farm, the number should not be too large. In this paper, assuming that it is 20%, when the real-time wind power output scene is determined, the question of whether to retain the primary reserve depends on whether the output power is more than 20% of the rated capacity. The primary reserve constraint is shown in Figure 2b in the following form:  
\[0\leq R_{W}^{F}\leq\min\left(\varepsilon P_{N},2C_{W}\frac{M_{H}(f_{0}-f_{M}- f_{d})}{P_{loss}}\right) \tag{10}\]  
\[M_{H}\frac{df(t)}{dt}=-\Delta P=P_{m}(t)-P_{e}(t) \tag{4}\]0  
where \(R_{W}^{F}\) indicates the primary reserve of the wind power unit \(i\), and \(P_{N}\) is its rated installed capacity; \(C_{W}\) represents the ramp rate of the governor after the simulation of the virtual synchronous generator units; \(\varepsilon\) is the upper limit for the active output increase greater than 10%; and \(P_{W}^{r}\) and \(P_{W}^{m}\) indicate the actual wind power output and the wind power output in the MPPT mode.