## 4 Validation of General ESS-Based VSM Control
### Simulation Test of Hybrid ESS-Based VSM under Renewable Generation Fluctuation  
The power network under test is sketched in Figure 17. This case considers AC-coupled hybrid ESS in Figure 4c, with parameters in Table 2. The connecting impedances are also set at 0.05 p.u. The parameters of FAESS is identical to the lithium titanite battery used in Section 4.1. The energy capacity of SAESS is 320 kWh and the DC voltage is 960 V. This is realized by assembling 80 cells of 12 V lead-acid batteries and then having three groups in parallel. The photovoltaic generator is synchronized with the grid using PLL and operating in MPPT control mode. Comparison of traditional power system control with ESS-based VSM control is conducted. Figure 16: Simulation results after adding the single ESS-based VSM. (**a**) Energy recovery control \(k_{p,e}=0.4\) and \(k_{i,e}=0.002\). The waveforms show the dynamics of synchronous generator power (\(\mathrm{P_{SG}}\)), the power component of VSM in inertial and damping support (\(\mathrm{P_{HD}}\)), virtual governor control (\(\mathrm{P_{Gov}}\)) and the total power (\(\mathrm{P_{VSM}}\)). The energy is restored in steady state. (**b**) Energy recovery control \(k_{p,e}=1\) and \(k_{i,e}=0.5\). There are oscillations in all the waveforms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Devices and Key Control Parameters**} & \multicolumn{2}{c}{**Frequency Nadir after the Disturbance**} & \multicolumn{2}{c}{**Oscillation Behavior**} & \multicolumn{2}{c}{**Steady-State SoC**} \\  & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{**Variation of ESS**} \\ \hline SG only & 57.98 Hz, 0.19 s after & Period: 0.94 s; Cycles: 2 & N/A \\ \hline \multirow{3}{*}{SG and ESS, without SoC recovery} & \(H_{\mu}=5\) s, \(D_{\mu}=10\) p.u., & 59.35 Hz, 0.39 s after & Trivial & 0.066 p.u. \\  & \(k_{i,e}=5\) p.u. & 59.35 Hz, 0.39 s after & Trivial & 0.013 p.u. \\ \hline \multirow{3}{*}{SG and ESS, with SoC recovery} & \(H_{\mu}=5\) s, \(D_{\mu}=10\) p.u., & 59.34 Hz, 0.38 s after & Trivial & 0 p.u. \\  & \(k_{p,e}=0.4\), \(k_{i,e}=0.002\) & 59.34 Hz, 0.38 s after & Period: 12 s; Undamped & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control performance for different control of a single ESS and synchronous generator. First, FAESS adopting constant voltage and frequency (or short for \"VF\") control under the master-slave control scheme is tested [35]. As illustrated in Figure 18, the FAESS picks up all the power mismatch, and frequency is controlled to be constant. Although the SAESS and SG have frequency support capability, their power is fixed around their references. The power reference of the FAESS is set to zero and implicitly managed by a higher-level dispatch, but the renewable power fluctuation will make the FAESS discharge in the given case, which will soon drain its energy given the small energy capacity (\(E_{\text{nom}}=6.8\) p.u.-s) selected. Therefore, VF control under master-slave scheme requires the ESS have a high response speed and large energy capacity. In Figure 19 where the ESS adopts grid-following control and the SG adopts PI frequency control, there is a large fluctuation in frequency and SG power. This also reflects the worsened frequency performance in the practical power system, with more uptakes of renewable generators and higher pressure placed on SG for frequency regulation. Figure 17: Power network to test the VSM based on AC-coupled hybrid ESS. Figure 18: Power, frequency and SoC dynamics when FAESS adopts VF control. The waveforms show that the frequency is fixed near 60 Hz, but the SoC of FAESS keeps increasing. In Figure 20a, we first consider FAESS with conventional VSM control parameters set as \(H_{\beta\mu}=5\) s and \(D_{\beta\mu}=10\) p.u., yet without energy recovery control. The rate of frequency fluctuation becomes smaller (59.9-60.1 Hz), but the SoC of FAESS deviates from its reference value 0.5 and continues increasing. In Figure 20b, both VSM control and SoC recovery control are adopted.