# Coordinated Control of Virtual Power Plants to Improve Power System Short-Term Dynamics
## 2 Control of VPPs
### Proposed Coordinated Control  
Figure 1 shows the proposed coordinated control of the resources that compose a VPP. This control is similar to a conventional secondary frequency control. However, it is aimed at improving the fast frequency response of the VPP and, thus, it operates in the same time scale as the primary frequency control.  
It is assumed that in normal operating conditions and in a given period, the VPP power set-point is defined by the Transmission System Operator (TSO) based on the solution of an electricity market problem such as the unit commitment. Hence, before the occurrence of any contingency, \(p_{\text{inj}}\) is the set-point of the VPP as scheduled by the TSO.  
The proposed approach consists of measuring the total active power injected (\(p_{\text{inj}}\)) into the transmission grid by the VPP as well as the frequency variation (\(\Delta\omega_{\text{POC}}\)) and then transmitting the following signal:  
\[y_{p}=H(s)\,\Delta\omega_{\text{POC}}\,p_{\text{inj}} \tag{1}\]  
to the DERs and ESSs that compose the VPP. In (1), \(H(s)\) is the transfer function of the coordinated control. \(H(s)\) includes a proper gain that adjusts the magnitude of \(y_{p}\) and makes it consistent and compatible with the primary frequency controllers of the resources of the VPP. Apart from the proportional controller considered in (1), other controllers such as Proportional-Integral (PI) and lead-lag can also be used. The case study in Section 4 compares and discusses the performance of different controllers.  
The rationale of the proposed coordinated controller is as follows. In steady-state conditions, \(\Delta\omega_{\text{POC}}=0\) and hence the primary controllers of the resources that form the VPP are decoupled. For practical implementation issues, a small dead-band is then included on the signal \(\Delta\omega_{\text{POC}}\), to avoid unnecessary communications of the signal \(y_{p}\) when the frequency deviations are negligible. The dead-band is used only to make the coordinated control insensitive to noise.  
After the occurrence of a major contingency in the transmission grid, e.g., a fault or the outage of a large load/generator, the frequency of the system varies. This event leads to \(\Delta\omega_{\text{POC}}\
eq 0\) and thus triggers the coordinated feedback control.  
The effect of \(y_{p}\) is, in turn, to \"amplify\" the sensitivity of the primary control with respect to the local frequency deviation by a coefficient that is proportional to the power generated by the VPP. In fact, assuming that \(\Delta\omega_{\text{POC}}\) measured at the POC is the same as the  
Figure 1: Control diagram of the proposed coordinated control of VPPs.  
local frequency deviation measured by the DERs, one has that the overall signal entering the primary frequency controllers is:  
\[\epsilon_{i} =(\omega_{\text{ref}}-\omega_{i})+u_{i} \tag{2}\] \[\approx\left[1+K_{i}H(s)\,p_{\text{inj}}\right]\Delta\omega_{\text {POC}}\,,\]  
where \(\omega_{\text{ref}}-\omega_{i}\) is the local frequency error as measured by the ESS or DER controller; and \(u_{i}=K_{i}y_{p}\).  
Figure 1 shows that timers are included in the signals sent to the DERs. These timers are triggered by a threshold value of \(u_{i}\) and allows improving the coordination of the DERs and ESSs. This point is duly discussed and illustrated in the case study.