# Solutions to Increase PV Hosting Capacity and Provision of Services from Flexible Energy Resources
## 4 New Real-Time Adaptive Management Schemes
### Real-Time Frequency Adaptive PU-Droop  
In Section 3.2. the idea of frequency adaptive _PU_-droops for PVs and BESSs was presented. The implementation could be smoother without exact frequency (\(\geq\pm\) 0.2-0.5 Hz) and voltage limits for the activation of the frequency adaptive functionality. Therefore, in Figure 9 new'real-time frequency adaptive _PU_-droop' for PV and BESS units is proposed when frequency deviation is between \(\pm\) 1.0 Hz from the nominal frequency \(f_{\rm n}\). If frequency deviation is larger, then similar settings will be used as if the deviation would be 1.0 Hz from \(f_{\rm n}\). This approach enables constant and smoother frequency adaptive response from the DER units which is also more dependent on the real-time magnitude of frequency change. It should be noted from Figure 9 that different equations will be used for calculation of the _PU_-droop set-points X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\) depending on the situation (i.e., under- or over-frequency, \(f<\)\(f_{\rm n}\) or \(f>\)\(f_{\rm n}\)). In these Figure 9 equations for X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\):  
\(f\) = measured frequency (Hz)  
\(f_{\rm n}\) = nominal frequency (Hz)  
Figure 8: (a) PV 2 active power \(P_{\rm PV\_2}\), (b) BESS 3 active power \(P_{\rm BESS\_3}\), and (c) local voltage \(U_{\rm PV\_2}\) behavior at PV 2 connection point during simulated under-frequency (49.4 Hz) events in Cases 5a (_PU_-droop 1), 7b (_PU_-droop 2), and 7b (_PU_-droop 3), see also Figures 2 and 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \(\Delta P_{\rm PV\_2}\) & \(\Delta P_{\rm PV\_2}\) & \(\Delta P_{\rm BESS\_3}\) & \(\Delta P_{\rm BESS\_3}\) & \(\Delta P_{\rm TOTAL\_75s}\) & \(\Delta P_{\rm TOTAL\_95s}\) ***) \\  & **49.4 Hz,** & \(t=95\) s * (kW) & \(t=95\) s * (kW) & \(t=95\) s * (kW) & \(t=95\) s * (kW) & \(t=75\) s (kW) & \(t=95\) s * (kW) \\ \hline
2b & +3 & –31 & – & – & +3 & –31 \\
7a & +134 & +110 & – & – & +134 & +110 \\
7a & +134 & +100 & – & – & +134 & +100 \\
5a & –55 & –88 & +68 & +68 & +13 & \(-\)20 \\
7b & \(-\)50 & –74 & +237 & +228 & +187 & +154 \\
7b & \(-\)2 & –44 & +169 & +169 & +167 & +125 \\ \hline \hline \end{tabular}  
*) Part of the load also at PV\_2 connection point participates in demand response and disconnects from the LV network, **) \(\Delta P_{\rm TOTAL\_75s}=\Delta P_{\rm PV\_2}+\Delta P_{\rm BESS\_3}\) at \(t=75\) s, ***) \(\Delta P_{\rm TOTAL\_95s}=\Delta P_{\rm PV\_2}+\Delta P_{\rm BESS\_3}\) at \(t=95\) s.  
\end{table} 
Table 9: Provided frequency support by PV 2 and BESS 3 in different cases during simulated under-frequency (49.4 Hz) events (see also Tables 7 and 8). \(U_{\text{min\_ini}}\) = chosen initial minimum voltage set-point value when \(f\) = \(f_{\text{n}}\) (pu) \(U_{\text{max\_ini}}\) = chosen initial maximum voltage set-point value when \(f\) = \(f_{\text{n}}\) (pu) \(P_{\text{n}}\) = nominal active power (MW). Figure 10 shows example about calculated real-time frequency adaptive _PU_-droop values X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\) (Figure 9) for 200 kW BESS with different frequency values when \(f_{\text{n}}\) = 50 Hz, \(P_{\text{n}}\) = 0.2 MW, \(U_{\text{min\_ini}}\) = 0.955 pu, and \(U_{\text{max\_ini}}\) = 1.045 pu. Figure 10: Example of real-time frequency adaptive _PU_-droop values for 200 kW BESS with (**a**) \(f\) = 50 Hz, (**b**) \(f\) = 50.5 Hz, and (**c**) \(f\) = 49 Hz (\(f_{\text{n}}\) = 50 Hz, \(P_{\text{n}}\) = 0.2 MW, \(U_{\text{min\_ini}}\) = 0.955 pu, and \(U_{\text{max\_ini}}\) = 1.045 pu, Figure 9). Figure 9: Real-time smooth frequency adaptive _PU_-droop without specific frequency and voltage limits for activation e.g., for BESS unit. by cables (see Equation (1), Section 2.2), and therefore decreased need for voltage control support in MV and LV networks by the flexible energy resources. In addition, simultaneously the availability of, for example, demand response, for provision of system-wide frequency support could be increased.