*4.1. Single ES Control*

Proper operation of the microgrid with multiple ESs rests on the correct control of a single ES. In order to examine a single ES, *L*2 and *L*3 are cut out from the circuit in Figure 8 and only the first ES is activated. The correctness of the control is evaluated by testing the ES behavior under voltage and frequency excursions.

Figure 9 shows the simulation results of voltage control for a single ES. The figure contains three channels, namely the predefined Root Mean Square (RMS) value of the CL voltage, the measured RMS value of the CL voltage and the RMS value of the grid voltage designated as *VG*. In the time interval from 0 to 0.5 s, the grid voltage is 209 V, the ES is deactivated, and the CL voltage is significantly less than the expected value of 220 V.

**Figure 9.** Simulation results of voltage control for a single ES.

From 0.5 s to 1 s, the ES starts to work, and the CL voltage reaches the predefined value of 220 V gradually. Between 1–2 s and 2–3 s, the RMS value of grid voltage is steeply increased to 220 V and then to 231 V, respectively. Under the ES voltage control, after a short and restrained transient, the CL voltage quickly stabilizes at the predefined value of 220 V, ensuring the power quality of the CL supply in agreemen<sup>t</sup> with the requirements.

Figure 10 shows the simulation results under frequency control of a single ES. The figure has two channels, namely the predefined and measured values of frequency. At the beginning of the simulation, ES is deactivated. Due to the lack of active power, the microgrid frequency is decreased to about 49.7 Hz, which is lower than the maximum frequency excursion of ±0.2 Hz stipulated in the national standards. At 0.5 s, the ES starts to work and quickly compensates for the active power lack of the microgrid by both reducing the active power consumption of the NCL and providing active power from the ES, thus recovering the microgrid frequency at the default value of 50 Hz. At 4 s, a switch is closed to emulate a further loading of the microgrid; its active power balance is broken again and produces a consequent fall of the microgrid frequency. The ES takes an immediate action and restores the frequency to 50 Hz at 5 s. The results above are evidence of the soundness of the designed frequency control for a single ES.

**Figure 10.** Simulation results of frequency control for a single ES.

#### *4.2. Hierarchical Control of Multiple ESs*

This subsection validates the effectiveness of the proposed hierarchical control by simulating the microgrid with three ESs of Figure 8 at first without any coordinated control and then by introducing the coordinated control. In the simulations, the predefined voltages at the nodes with ESs are set to 220 V.

Figure 11 reports the waveforms of the RMS value of the node voltages, and the active and reactive powers P and Q entering the nodes under the voltage control without the coordinated control. During the first 1 s-long time interval of the simulation, none of the three ESs is activated. Due to the line impedance, the CL voltages at the three PCCs greatly deviate from 220 V. At 1 s, the ES is activated. Under the action of the ESs, the CL voltages start to ge<sup>t</sup> closer to the predefined value of 220 V. However, as it emerges from the magnified waveforms in the central part of Figure 11(a), the three CL voltages are not able to reach the predefined value but settle on a different value. At 4 s and then at 7 s, two steeply increases of the microgrid voltage are emulated. Although the three CL voltages are close to 220 V within a certain range, they do not replicate exactly the preset value, exhibiting a steady-state error.

At 7 s, when the RMS value of the grid voltage is set to 228 V, the integral term of the voltage regulator goes saturated at 7.45 s due to the persisting voltage error, which results in a larger voltage deviation of *VS*1. Although *VS*2 and *VS*3 are regulated at the predefined value since the integral term of their voltage regulators do not saturate, the microgrid nodes with the tied ESs are unable, on the whole, to reach the expected steady-state operation. The simulation results confirm the shortcoming arising from the combined action of the voltage drop along the microgrid line and the gradual winding up of the integral term of the voltage regulators of some ESs. The latter ESs do no longer exert the regulating action of the node voltage, as outlined in Figure 11a, while causing a rise of the ES reactive power, as outlined in Figure 11b, which is limited by either control or device protections. This behavior is against the motivations for the usage of multiple ESs, which is intended for the existing ESs to share the microgrid fluctuations in a favorable manner.

 **Figure 11.** *Cont*.

**Figure 11.** Simulation results of multiple ESs operating without coordinated control: (**a**) RMS value of point of common coupling (PCC) voltage; (**b**) active power; (**c**) reactive power.

As can be seen from the above section, it is far from enough for a single ES to ensure voltage deadness-free tracking, and it is necessary to have a coordinated control strategy to achieve reasonable setting of the reference values for multiple ESs. This section mainly carries out simulations under hierarchical control using droop control as the secondary control and power decoupling control with filter capacitor voltage control as the primary control for multiple ESs. Both voltage and frequency regulations are included.

Figure 12 shows the simulation results of reference voltage and measured voltage of ES when multiple ESs are distributed along the transmission line based on droop control. Within the first second during simulation, ES is deactivated at each PCC. In order to monitor the effectiveness of reference value change by each ES with the proposed droop control, all the reference values are initialized to 221 V. At 1 s, the ESs at the three PCC start to work and the reference voltage values of the ESs at three PCC are modified dynamically along with the sudden change of grid voltage. At the moments of 4 s and 7 s, when grid voltages are set to 220 V and 228 V respectively, it is seen that reference voltage value of each ES has been modified to new values and been tracked quickly.

Figure 13 shows the results of the three ESs under the action of the proposed control, showing the steady state and dynamic responses of the ESs under the case of grid voltage fluctuations. Figure 13a shows that the reference values of PCC voltages are different and tracked quickly with droop control. Figure 13b,c show the active and reactive power of each ES under the proposed control. It is seen that the ESs are three PCC operate at a dynamically stable state, which withstand the power fluctuation of the whole system in a harmony manner.

Finally, the frequency responses are verified with three sets of ESs by simulations, as shown in Figure 14. The figure contains two channels, namely the predefined value and the measured value of frequency. Within the first second, the ESs were not activated, and the system frequency was offset due to the imbalance between the active load and the active power supply, and thus the difference

was about 0.05 Hz. At 1 s, the ESs start to work, and the active power sag of the whole system is compensated gradually due to the participation of multiple ESs, and the frequency of the system is kept stable at 50 Hz. At 5 s, the load demand in the system suddenly increases, leading to an increase in the power shortage of the system. At this time, the system frequency decreases to about 49.8 Hz, which violates the requirement that the maximum frequency deviation of the system should not exceed ±0.2 Hz. However, under the regulation of three ESs with the proposed control, the newly added active load of the system will achieve the purpose of sharing that partial active power are absorbed by the battery inside the ESs and meanwhile partial power fluctuations are passed to the NCLs. As a result, the system frequency is finally seen to stabilize at 50 Hz. The simulation verifies that the proposed control can enhance the stability of system frequency with the help of multiple ESs.

**Figure 12.** Reference versus measured voltages with the proposed control of multiple ESs.

(**b**) **Figure 13.** *Cont*.

**Figure 13.** Simulation results of multiple ESs operating with the proposed control: (**a**) RMS value of PCC voltage; (**b**) active power; (**c**) reactive power.

**Figure 14.** Simulation results of frequency responses with three ESs under the proposed control.
