# Droop Control Strategy of Utility-Scale Photovoltaic Systems Using Adaptive Dead Band
## 2 Reactive Power-Voltage Droop Control Method
### Proposed Reactive Power-Voltage Droop Control Method

Table 1: Nomenclature for reactive power-voltage droop control. Figure 3: Control block diagram of reactive power-voltage droop control. Figure 2: Simplified diagram of the proposed scheme. \[Q_{i}=|V_{i}|\sum_{j=1}^{N^{sys}}\left(G_{ij}\big{|}V_{j}\big{|}\sin\theta_{ij}-B_ {ij}\big{|}V_{j}\big{|}\cos\theta_{ij}\right) \tag{8}\]  
Equation (9) represents the relationship between the change in active and reactive injections at the bus and that in the voltage magnitude and phase angle through the Jacobian matrix. The size of the matrix in the equation is determined by the numbers of PV, PQ, and slack buses. The bus to which the generator is connected is called the PV bus, and considers the number of PV buses as \(N_{g}\). In the left term of Equation (9), one, the number of slack bus, is removed from each of the two matrices \(\Delta P\) and \(\Delta Q\), and the matrix \(N_{g}\) is extracted from the \(\Delta Q\) matrix. This is because PV buses do not consider the amount of voltage change because they prioritize a specific voltage. Therefore, the total number of equations becomes \(2N-N_{g}-2\), and the \(\partial Q_{bus}/\partial|V|\) equation representing the variation in the reactive power according to the voltage variation used in this paper has a \(N-N_{g}-1\times N-N_{g}-1\) matrix. \[\left[ \begin{array}{c}\Delta P_{1}\\ \vdots\\ \Delta P_{N}\\ \Delta Q_{1}\\ \vdots\\ \Delta Q_{N}\end{array} \right]=J\Delta\left[ \begin{array}{c}\Delta\theta\\ \Delta|V|\end{array} \right]=\left[ \begin{array}{cc}\frac{\partial P_{bus}}{ \partial\theta}&\frac{\partial P_{bus}}{\partial\theta[V]}\\ \frac{\partial Q_{bus}}{\partial\theta}&\frac{\partial Q_{bus}}{\partial \left|V\right|}\\ \vdots\\ \Delta|V_{N}|\end{array} \right]\right)\left(2N-N_{G}-2 \tag{9}\]  
The formula for each term in the Jacobian matrix is described in Appendix A. To calculate the amount of change in reactive power, the equation calculated through the relationship of each term in Equation (9) is shown as Equation (10). The information corresponding to the amount of reactive power output to the bus voltage change, which occurs due to the change in the output amount of the utility-scale PV connected to the transmission system, can be obtained using the voltage sensitivity approach. \[\left[ \begin{array}{c}\Delta Q_{1}\\ \vdots\\ \Delta Q_{N}\end{array} \right]=\left[ \begin{array}{cc}\frac{\partial Q_{ bus}}{\partial|V|}-\frac{\partial Q_{bus}}{\partial\theta}\Delta\frac{\partial P_{bus}}{ \partial\theta}^{-1}\Delta\frac{\partial P_{bus}}{\partial|V|}\end{array}  \right]\Delta\left[ \begin{array}{c}\Delta|V_{1}|\\ \vdots\\ \Delta|V_{N}|\end{array} \right] \tag{10}\]  
Corresponding to the system topology, daily solar generation, and daily load curve, the information applied to the reactive power output according to the voltage change in each bus connected to the utility-scale PV is obtained through the data of the proposed method and voltage sensitivity. The results are expressed through surface fitting, as shown in Figure 4. The 3D data obtained from all buses connected to renewable energy are transmitted to the transmission system operator to determine the dead band setting value for each period. For systems with connected RESs, the grid state changes frequently within a day. This is because the combination of the generator that balances the load as the load continues to change per day varies with the RES output. Therefore, it is important to derive the required reactive power by learning the situation in which the voltage will change for an event such as a specific accident or output change in an offline manner, and accordingly, an appropriate setting of the dead band value contributes to maintaining the voltage range. The required reactive power \(Q_{req}\) can be calculated using Equation (11), which indicates the relationship between the change in voltage magnitude and that in the reactive power obtained through voltage sensitivity analysis, and the values of the reference voltage and measured voltage, \(V_{POI,ref}\) and \(V_{POI,ma}\), at the POI.