# 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  
In this section, the proposed reactive power-voltage droop control method is described. A novel droop control strategy is proposed to control the voltage variation caused by the daily change in the output of the renewable sources and disturbance in the grid. Several plants, which are PVs, are connected to the POI to form a utility-scale source. The magnitude of the voltage measured at the POI is continuously provided to the plant controller, and the dead band information per hour provided by the TSO is received to control the amount of reactive power output of the PV inverter. The dead band information is studied offline by the TSO using information such as system topology, bus voltage magnitude, and historical PV output. The plant controller shown in Figure 2 provides information regarding the reactive power output by time to the PV system. The control type of the plant controller increases the reliability of the application by using a proven model--called the PV power-plant generic dynamic model, developed by WECC. Among all WECC models, the REPC_A model, which is a plant controller, has a control in the form shown in Figure 3. For reactive droop control, the dead band information is included in the controller structure. The required reactive power is executed through the PI controller according to the reference voltage, measured voltage, and dead band data to control the voltage. The values corresponding to the plant controller are expressed in nomenclature form in Table 1. The adaptive dead band of the proposed scheme changes the setting of the dead band information in the REPC_A controller by hour. The voltage sensitivity method is used to set the dead band value for each hour of the plant controller. In systems whose values change with time, such as PV output and load data, setting a different dead band for each hour improves stability against disturbances. The voltage sensitivity equation is defined through modeling of the system including utility-scale PV. Let us consider that the number of buses in the AC system is \(N\) and express it in the form of set \(N^{sys}\). The information on voltage sensitivity is obtained through the Newton-Raphson equation, which is a solution of the power flow calculation. The equation corresponding to the active/reactive power injection of bus \(i\) in the system is expressed as Equations (7) and (8). The magnitude and phase angle of the voltage appear in the form of \(|V|,\theta\). In addition, the conductance and susceptance of admittance matrix are shown in the forms of \(G\) and \(B\), respectively, and take the real and imaginary parts of the Y matrix. All values comprise \(\{1,\ldots,N\}\in N^{sys}\), which is a subset of buses in the AC system. For example, the voltage magnitude has the following form: \(\{|V_{i}|,\ldots,|V_{N}|\}\). All buses comprise generator and load buses, and in the case of utility-scale PV, they are connected to the load buses. \[P_{i}=|V_{i}|\sum_{j=1}^{N^{sp}}\bigl{(}G_{ij}\big{|}V_{j}\bigr{|}\cos\theta_{ ij}+B_{ij}\big{|}V_{j}\bigr{|}\sin\theta_{ij}\bigr{)} \tag{7}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Nomenclature** & **Description** \\ \hline \(Q_{branch}\) & Regulated branch initial reactive power flow (p.u) \\ \(K_{c}\) & Reactive droop (p.u) \\ \(V_{reg}\) & Regulated bus voltage (p.u) \\ \(T_{fltr}\) & Voltage and reactive power filter time constants (s) \\ \(V_{ref}\) & Regulated bus initial voltage (p.u) \\ \(e_{max}\) & Maximum Volt/VAR error (p.u) \\ \(e_{min}\) & Minimum Volt/VAR error (p.u) \\ \(K_{p}\) & Volt/VAR regulator proportional gain \\ \(K_{i}\) & Volt/VAR regulator integral gain \\ \(Q_{max}\) & Maximum plant reactive power command (p.u) \\ \(Q_{min}\) & Minimum plant reactive power command (p.u) \\ \(T_{ft}\) & Plant controller Q output lead time constant (s) \\ \(T_{ft}\) & Plant controller Q output lag time constant (s) \\ \(Q_{ext}\) & Reactive power command from plant controller (p.u) \\ \hline \hline \end{tabular}
\end{table}