*5.1. Experimental Platform*

For the purpose of verifying the practicability of ONAC, a hardware experiment was carried out while the experimental platform is illustrated by Figure 5. A strong AC/DC power supply was used to provide stable three phase AC and DC voltages. The power supply was connected with the converter by an IGBT converter [27] with an inductive filter. IGBT converters can be driven by pulse width modulation (PWM) signals. Compared with the conventional PWM or sinusoidal pulse width modulation (SPWM) techniques, the space vector modulation (SVM) can increase 15% more of the maximum output voltage and reduce the switching times. The voltage/current isolators measured the voltages and currents, which were then sent to the dSPACE simulator through analogue/digital (A/D) blocks [28].

**Figure 5.** The experimental platform based on the dSPACE platform.

The dSPACE simulator had quad-core AMD (advanced micro devices) processors (DS1104) and operated with DS5202 ACMC board, which was capable of generating high-frequency PWM [29] signals and providing high-speed A/D interfaces. The IGBT converter, inductive filter, voltage/current isolators, and AC/DC power supply were all from the Lab-Volt company, which provides various equipment with the user-friendly interfaces, accurate system parameters, and reliable hardware protections. The DC bus of the IGBT converter was protected by adopting a 100 Ω damping resistor with 1 kW rated power connected to the damping circuit built in to the IGBT converter to avoid potential damages caused by overvoltage or overcurrent in the DC bus. Finally, Table 2 demonstrates the guaranteed measurement error of DS1104 board.


Offset drift 40 μV/K 130 μV/K Gain drift 25 ppm/K 25 ppm/K Signal-to-noise ratio Multiplexed channels: <sup>&</sup>gt;80 dB <sup>&</sup>gt;80 dB Parallel channels: >65 dB

**Table 2.** The error specification of quad-core AMD (advanced micro devices) processors (DS 1104) board [30].

The controller was embedded in the dSPACE platform (dSPACE Inc., Paderborn, Germany) shown in Figure 5, which measured the DC voltage, reactive power, and active power as inputs. Then, the PWM signals were generated with various duty cycles as controller outputs to the IGBT converter. Furthermore, the sampling frequency *f* <sup>s</sup> and the PWM frequency *f* PWM with SVPWM are given in Table 3. Here, sampling frequency was determined by the performance of industrial microprocessors of VSC, which usually ranges from 1 kHz to 3 kHz. Note that a lower sampling frequency might degrade the control precision while a higher sampling frequency might increase the computation burden. To make a trade-off between the control precision and computation burden, this paper adopted the median sampling frequency (2 kHz) to validate the controller implementation feasibility. MSSA was run 30 times and the optimal outcomes (the controller gains and observer gains leading to the lowest fitness function) were undertaken in ONAC. The parameters of the controller are provided in Table 4, while the control inputs were limited as |*u*d*i*| ≤ 50 V and |*u*q*i*| ≤ 50 V, *i* = 1,2, respectively. Based on SVPWM and ignoring the resistance in the steady state, the minimum DC voltage must satisfy the following inequality to ensure the converter is controllable and can work properly as [16]

$$V\_{\rm dci} \ge \sqrt{3} \sqrt{\left(u\_{\rm sdi} + \omega L \dot{u} \dot{q} \dot{i}\right)^2 + \left(u\_{\rm sqi} - \omega L \dot{u}\_{\rm di}\right)^2} \tag{37}$$

At last, the IGBT converter was used as the DC/AC converter, the antiparallel diodes were combined with the IGBT converters such that it could be operated as either a rectifier or an inverter.


**Table 3.** System parameters used in the experiment.

**Table 4.** Optimized controller gains and observer gains tuned by MSSA.


#### *5.2. Rectifier Controller Experiment*

The configuration of the rectifier controller experiment is illustrated by Figure 6, in which the DC bus was connected to a resistive load to achieve a specific evaluation of control performance when the active power flowed from the AC grid to the DC cable.

**Figure 6.** The configuration of the rectifier controller experiment.

The effectiveness of the ONAC-based rectifier controller was tested at first, in which the initial DC voltage *V*dc1 and reactive power *Q*<sup>1</sup> were adjusted to be 100 V and 0 Var, respectively. The DC voltage remained at 100 V for the whole period of the experiment. The reference of reactive power was set to be 15 Var, then dropped to 5 Var and was restored to 15 Var. After reactive power was stabilized at 15 Var, a resistive load *R*<sup>L</sup> was connected to the DC bus given in Figure 6 to represent the DC cable. Then a 50% voltage drop of the AC grid occured to evaluate the system transient performance.

The experiment results are provided in Figure 7. It demonstrates that both the reactive power and DC voltage were rapidly regulated, while the DC voltage was able to be restored after the AC grid voltage drop occurred, which validates the effectiveness of the ONAC-based rectifier controller.

**Figure 7.** System responses obtained in the rectifier controller experiment: (**a**) Average active power *P*1; (**b**) average active power *Q*1; (**c**) DC voltage *V*dc1; (**d**) control input *V*dq.

#### *5.3. Inverter Controller Experiment*

The configuration of the inverter controller experiment is shown in Figure 8, where a DC power supply was utilized to output a stable DC voltage (representing a constant DC voltage regulated by the rectifier controller) such that the IGBT converter could work properly.

**Figure 8.** The configuration of the inverter controller experiment.

The effectiveness of the ONAC-based inverter controller was then tested, the initial value of reactive power and active power were zero. The DC voltage *V*dc2 was maintained at 60 V for the whole period of the experiment. The controller was activated to increase the reactive power *Q*<sup>2</sup> to be 20 Var at first; after reactive power *Q*<sup>2</sup> was stabilized the active power *P*<sup>2</sup> was increased to be 10 W, then the reactive power *Q*<sup>2</sup> was decreased to be 10 Var. At last a 33.3% voltage drop of the AC grid occurred to evaluate the system transient performance.

The experiment outcomes are given in Figure 9. Obviously, the reactive power and active power were able to be regulated independently, and the system could also be restored after the voltage drop, which verified the effectiveness of the ONAC-based inverter controller.

**Figure 9.** System responses obtained in the inverter controller experiment. (**a**) Average active power *P*2; (**b**) average active power *Q*2; (**c**) DC voltage *V*dc2; (**d**) control input *V*dq.

#### *5.4. Set point Tracking*

In order to evaluate the set point tracking performance of ONAC, both the simulation (set point curve) and experiment are compared in Figure 10. One can clearly observe that the experiment can closely track the set point, while their tiny difference resulted from the transmission delay of control signals or measurement noises during the experiment.

**Figure 10.** System responses obtained under set point tracking. (**a**) DC voltage *V*dc1 of rectifier; (**b**) average reactive power *Q*<sup>1</sup> of rectifier; (**c**) DC voltage *V*dc2 of inverter; (**d**) average reactive power *Q*<sup>2</sup> of inverter.

#### *5.5. Disturbance Rejection*

Disturbances are very common in many industrial processes which often have a malignant impact on the predesigned control performance of the studied system. As a result, disturbance rejection performance is a very crucial property for advanced controller design in industries [31–33]. This test aimed to evaluate the disturbance rejection performance of ONAC, while the perturbation estimation performance of HGPO under 20% voltage drop lasting for 15 ms (t = 0.1 s–0.115 s) of VSC under rectifier mode was recorded and illustrated in Figure 11. As shown in Figure 11, both perturbations Ψr1 and Ψr2 could be rapidly estimated by HGPO s under the voltage drop of VSC as the perturbation estimation error could be efficiently converged to 0. As a result, the disturbance was able to be effectively rejected as its real-time estimate could be rapidly obtained and then fully compensated by ONAC. Here, only the rectifier results are provided as it involved both the second-order HGPO (Figure 11a) and third-order HGPO (Figure 11b), while similar results could be found in inverter mode. Note that the transient relatively large variation of perturbation when the disturbance occurred was due to the high gains used in HGPO.

**Figure 11.** Disturbance rejection performance obtained under 20% voltage drop of rectifier. (**a**) Perturbation Ψr1 and (**b**) perturbation Ψr2.

#### *5.6. Robustness to Parameter Uncertainties*

Lastly, the robustness to parameter uncertainties was investigated in this section. Here, a series of plant model mismatches of equivalent resistance *R*<sup>1</sup> and inductance *L*<sup>1</sup> within ±20% variation around their nominal value were undertaken. Then, a 50% voltage drop lasting 100 ms at VSC was applied, in which the peak value of output power |*P*| was recorded. Figure 12 shows that the variation of peak value of active power |*P*| obtained by FLC [10] and ONAC were 73.4% and 26.5%, which clearly demonstrated that ONAC provided the highest robustness against VSC parameter uncertainties thanks to the real-time compensation of perturbation, while FLC was vulnerable to parameter uncertainties as it required an accurate VSC system model.

**Figure 12.** Peak value of active power |*P*| obtained under a 50% voltage drop lasting 100 ms at VSC with 20% variation of the equivalent resistance *R*<sup>1</sup> and inductance *L*<sup>1</sup> of FLC and ONAC. (**a**) FLC and (**b**) ONAC.

#### **6. Conclusions**

This paper designed an ONAC-based rectifier controller and ONAC based inverter controller. It can provide significant robustness as various modelling uncertainties were aggregated into a perturbation, which was rapidly evaluated by HGPO and then compensated for by the proposed controller. Besides, ONAC merely needs the active power and reactive power, as well as DC voltage need to be measured, while a precise VSC system model is not required, thus the proposed controller can be readily implemented in practice. Moreover, the controller gains and observer gains are optimally tuned by an emerging and promising biology based metaheuristic algorithm called MSSA, which can effectively achieve an appropriate trade-off between global exploration and local exploitation, thus a satisfactory control performance and perturbation estimation performance could be guaranteed. Finally, for the sake of verifying the practicability of the proposed controller, a hardware experiment utilizing dSPACE platform was undertaken. The experiment results showed that ONAC could achieve satisfactory control performance.

Future studies will apply ONAC-based VSC on renewable energy systems, e.g., PV inverter, wind energy conversion systems, as well as electric energy storage systems.

**Author Contributions:** Preparation of the manuscript has been performed by Y.J., X.J., H.W., Y.F., W.G., B.Y., and T.Y.

**Funding:** The authors gratefully acknowledge the support of National Natural Science Foundation of China (51777078), and Yunnan Provincial Basic Research Project-Youth Researcher Program (2018FD036).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


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