## 3 Advanced Control Functionalities for Power-Frequency Regulation  
In order to enable the ST to provide active power-frequency regulation services to the main power system, a set of advanced functionalities based on droop controllers is proposed to be incorporated in the ST. The aforementioned droop controllers are intended to provide active power-frequency support to the main power system by regulating the active power exchanged between the ST and the main power system as a function of frequency deviations in the main power system. The droop controllers proposed to be incorporated in the ST are described in Section 3.1. The aforementioned droop controllers aim to trigger a response of the hybrid distribution network according to the relationships generally represented in Figure 11, namely, by inducing a power response in the controllable DER units through its embedded droop-based controllers (described in Section 3.2) and by exploiting an indirect active power response of non-controllable resources through its power-voltage sensitivity.  
Figure 10: Equivalent computational model for the Upstream AC power system.  
The implemented droop controllers follow the general functional relation represented in Figure 12 and expressed according to Equation (20), where the X axis represents the controlling quantity, the Y axis represents the quantity to be controlled (output of the droop controller), \(Y_{min}/Y_{max}\) is the minimum/maximum output of the droop controller, \(Y_{os}\) is the offset of the droop controller, \(m_{d}\) is the slope of the droop controller, \(X_{min}/X_{max}\) is the minimum/maximum value of X at which the droop controller responds, \(X_{db}^{-}/X_{db}^{+}\) is the dead-band interval at which the droop controller holds at the offset value and \(\Delta Y^{-}/\Delta Y^{+}\) is the maximum negative/positive variation of Y provided by the droop controller around the offset value. \(m_{d}\) is an input parameter which is applied to both intervals defined by \([X_{min},\,X_{db}^{-}]\) and \([X_{db}^{+},\,X_{max}]\). Further, \(Y_{min}/Y_{max}\) are input parameters, which means that \(X_{min}\) and \(X_{max}\) are defined as a function of \(Y_{min}\), \(Y_{max}\), \(X_{db}^{-}\), \(X_{db}^{+}\), \(m_{d}\) and \(Y_{os}\) according to Equation (20).  
\[Y=\begin{cases}Y_{min}&\text{if }X\in\,\,]-\infty,X_{min}]\\ m_{d}(X-X_{db}^{-})+Y_{os}&\text{if }X\in\,\,]X_{min},X_{db}^{-}[\\ Y_{os}&\text{if }X\in\,\,[X_{db}^{-},X_{db}^{+}]\\ m_{d}(X-X_{db}^{+})+Y_{os}&\text{if }X\in\,\,]X_{db}^{+},X_{max}[\\ Y_{max}&\text{if }X\in\,\,[X_{max},\infty[\end{cases}\qquad\qquad X_{min} = \frac{Y_{min}-Y_{os}}{m_{d}}+X_{db^{-}} \tag{20}\]  
The reaction chain that triggers the combined actuation of the implemented droop controllers in face of the occurrence of frequency deviations in the main power system is represented in Figure 13. As shown in this figure, a frequency disturbance in the MV AC network will trigger the actuation of a set of droop controllers sensitive to the frequency in the MV AC network. Consequently, the DC voltage in the DC networks, the voltage and frequency in the LV AC network and the active power in the local ESS are modulated accordingly. As a result, the resources available in the hybrid distribution network will change their power output, due to voltage sensitivity in non-controllable loads and to the actuation of the droop controllers embedded in the controllable DER units. These power changes will propagate to the ST's MV inverter (given the relationship expressed in Equation (15)), thus adjusting the ST active power exchange with the upstream AC power system.  
Figure 11: Advanced functionalities to be exploited by the ST.