# Droop Control Strategy of Utility-Scale Photovoltaic Systems Using Adaptive Dead Band
## 2 Reactive Power-Voltage Droop Control Method  
### Conventional Reactive Power-Voltage Droop Control Method  
Generators connected to a transmission system typically perform voltage regulation to maintain the network voltage. According to NERC's VAR-004-2 standards [28], which deal with the generation operation for maintaining the network voltage schedules, each generator is connected to an interconnected transmission system in the automatic voltage control mode (with its automatic voltage regulator in service and controlling voltage) or in a different control mode, as instructed by the transmission operator. Although this standard is limited to synchronous generators, various control functions can be added to inverter-based resources (e.g., solar PV and wind power resources) due to the development of modern technology, and accordingly, RESs must cooperate to maintain the network voltage. A large-scale RES directly connected to the transmission system comprises several plants connected to the same bus. This bus corresponds to the POI and controls the voltage at this point. The voltage droop assigns control to each resource as it sets a set-point of reactive power equal to the deviation from the nominal operating voltage. Equation (1) expresses the reactive power reference as a piecewise equation and describes the reactive power control in response to the voltage measured at the POI [29; 30]. Figure 1 shows a characteristic curve for the reactive power-voltage droop control, where \(Q\) is the reactive power reference of the inverter-based resource (IBR), \(V\) is the voltage magnitude measured at the POI, \(V_{\text{op}}\) is the operating voltage, and \(Q_{\text{max}},\ Q_{\text{min}}\) are the limits of reactive power at a specific time that can be controlled by the plant controller. The voltage at the beginning of the reactive limit is expressed as \(V_{\text{H}},\ V_{\text{L}}\), and when \(Q_{\text{min}}\) represents a negative value, the reactive power is absorbed. \(V_{\text{dbd,high}},\ V_{\text{dbd,low}}\) indicate the voltage range in which the reactive power reference is 0, \"dbd\" represents the dead band,and reactive control for the voltage is not executed in the voltage deviation within the dead band for efficient operation of the system including IBR. \[Q_{ref}=\left\{ \begin{array}{ccc}Q_{max}&,(V<V_{L})\\ Q_{max}*\big{(}V_{dd,low}-V\big{)}\big{/}\big{(}V_{dd,low}-V_{L}\big{)}&,(V_{L}<V <V_{dd,low})\\ 0&,(V_{dd,low}<V<V_{dd,high})\\ Q_{min}*\big{(}V-V_{dd,high}\big{)}/(V_{H}-V_{dd,high})&,(V_{dd,high}<V<V_{H}) \\ Q_{min}&,(V>V_{H})\end{array} \right. \tag{1}\]  
The formula representing the droop in the reactive power-voltage droop control method is expressed as Equation (2). The reciprocal value of the droop coefficient indicates the droop slope. Because Equation (2) does not include the dead band information, the difference between \(V_{H}\) and \(V_{L}\) is substituted for the voltage deviation term. \(\Delta Q_{c}\), which represents the difference value of the reactive power capability, is expressed as Equation (3) using the term of time, because it is related to the active power value at a specific point in time. \[\frac{1}{\textit{Droop}}=\frac{\Delta Q_{c}}{\Delta V/V_{op}} \tag{2}\]  
In Equations (3) and (4), the reactive power output of the plant controller is expressed as a time phrase. A finite set T comprises 24 subsets because it contains data per hour and the data size can be increased or decreased according to the user settings. The maximum and minimum values of the reactive power output at a specific time, in relation to the apparent capacity of a utility-scale RES and the amount of active power output at a specific time, can be expressed as Equation (4). \[\Delta Q_{c,i}=Q_{max,i}-Q_{min,i}\,\ \forall i\in T \tag{3}\]  
\[Q_{max,i}=-Q_{min,i}=\sqrt{S_{max}^{2}-P_{PV,i}^{2}}\,\forall i\in T \tag{4}\]  
The droop slope including the dead band information can be expressed as Equation (5).