Peak Current Detection Starting Based Position Sensorless Control of BLDC Motor Drive for PV Array Fed Irrigation Pump

ABSTRACT:

 The generation of exact commutation to start the permanent magnet brushless direct current (PMBLDC) motor in position sensorless control mode is the most challenging task. A peak current detection starting algorithm based wide speed range position sensorless control for solar photovoltaic array fed PMBLDC motor drive for the irrigation water pumping is presented here. This starting algorithm controls the exact starting commutation along with the peak staring current. An elimination of position sensor and current sensor for rotor position estimation makes the implemented drive compact and cost effective for agricultural application. The operation of the drive is first tested with simulation and the reliability is tested in the laboratory prototype as well as in compact industrial product prototype with cost-effective digital signal processor. The robustness of the system is verifiedwith different simulation and test results at various operating conditions. The compact cost-effective solution fits perfect for low cost, demanding both irrigation and domestic water pumping.

 KEYWORDS:

1.      Incremental conductance (INC) maximum power point tracking (MPPT) algorithm

2.      Peak current detection based starting

3.      Permanent magnet brushless direct current (PMBLDC) motor drive

4.      Position sensorless control

5.      Water pumping

SOFTWARE: MATLAB/SIMULINK

SCHEMATIC DIAGRAM:

Fig. 1. System configuration of position sensorless brushless dc motor drive.

 

EXPECTED SIMULATION RESULTS:

 

Fig. 2. Solar PV array performance. (a) Steady-state and starting performance at 1000 W/m2 insolation. (b) Dynamic performance varying from 500 to 1000 W/m2.

Fig. 3. BLDC motor performance at sensorless scheme. (a) Zero starting and steady-state performance at 1000 W/m2 irradiance. (b) Dynamic performance varying from 500 to 1000 W/m2 irradiance.

 

CONCLUSION:

A starting peak current controlled, smooth start, robust position sensorless control of a PMBLDC motor has been presented for solar powered pumping. The applied starting method takes care of the high starting inrush current to secure a good lifespan of the drive as well as the PMBLDC motor. The reduction of the position sensors makes the system compact and cost effective. The reliability and robustness of the developed drive are verified with both laboratory and industrial product prototype using d-SPACE (1104) and TMS320F28377S DSP. The performance and efficiency of the solar MPPT and PMBLDC motor are captured using DSO and the same is presented here. It is seen that the efficiency of the solarMPPT is more than 99%. It is also observed that the starting method is reliable and effective to keep the initial starting current within the desired limit. A fast settling stable dynamic performance of the drive is also observed.

 

REFERENCES:

 

[1] A. Sen and B. Singh, “Peak current detection starting based position sensorless control of BLDCmotor drive for PV array fed irrigation pump,” in Proc. IEEE Int. Conf. Environ. Elect. Eng. Ind. Commercial Power Syst. Europe (EEEIC /I&CPS Europe), 2019, pp. 1–6.

[2] S. Jain, A. K. Thopukara, R. Karampuri, and V. T. Somasekhar, “A single-stage photovoltaic system for a dual-inverter-fed open-end winding induction motor drive for pumping applications,” IEEE Trans. Power Electron., vol. 30, no. 9, pp. 4809–4818, Sep. 2015.

[3] L. An and D. D. Lu, “Design of a single-switch DC/DC converter for a PV-battery-poweredpumpsystem withPFM+PWMcontrol,” IEEE Trans. Ind. Electron., vol. 62, no. 2, pp. 910–921, Feb. 2015.

[4] J. V. M. Caracas, G. d. C. Farias, L. F. M. Teixeira, and L. A. d. S. Ribeiro, “Implementation of a high-efficiency, high-lifetime, and low-cost converter for an autonomous photovoltaic water pumping system,” IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 631–641, Jan./Feb. 2014.

[5] T.-H. Kim and M. Ehsani, “Sensorless control of the BLDC motors from near-zero to high speeds,” IEEE Trans. Power Electron., vol. 19, no. 6, pp. 1635–1645, Nov. 2004.

Maximum Power Point Tracking for Wind Turbine Using Integrated Generator-Rectifier Systems

ABSTRACT:

 Offshore wind is a rapidly growing renewable energy resource. Harvesting offshore energy requires multimegawatt wind turbines and high efficiency, high power density, and reliable power conversion systems to achieve a competitive levelized cost of electricity. An integrated system utilizing one active and multiple passive rectifiers with a multi-port permanent magnet synchronous generator is a promising alternative for an electro-mechanical power conversion system. Deployment of the integrated systems in offshore wind energy requires maximum power point tracking (MPPT) capability, which is challenging due to the presence of numerous uncontrolled passive rectifiers. This paper shows feasibility of MPPT based on a finding that the active rectifier d-axis current can control the total system output power. The MPPT capability opens up opportunities for the integrated systems in offshore wind applications.

KEYWORDS:

1.      Power conversion

2.      Ac-dc power conversion

3.       Rectifiers

4.      Dc power systems

5.      Wind energy

6.      Maximum power point trackers

7.      Wind energy generation

SOFTWARE: MATLAB/SIMULINK

 BLOCK DIAGRAM:

 

Figure 1. (a) Wind turbine power-point tracking architecture: the prime mover is a variable-speed wind turbine. The turbine shares a common shaft with the multi-port PMSG. Ac power is converted to dc by an integrated generator-rectifier system. The dc output is connected to a stiff dc interface. The integrated generator-rectifier system performs maximum power-point tracking to extract the turbine maximum power.

 EXPECTED SIMULATION RESULTS:

 

Figure 2. (a) (Top plot) The active rectifier d-axis and q-axis currents track the reference command, presented by the dotted lines. The dc-bus current varies accordingly by changing the d-axis current, leading to a change in the dc-bus power (bottom plot). (b) The relationship between dc-bus power and active-rectifier d-axis current acquired from the simulation model (recorded by the markers) matches the theoretical analysis (plotted by the lines using equation (6)).

 

Figure 3. Waveforms to illustrate the system MPPT capability. (a) At each wind speed, the turbine speed (solid-blue line) successfully tracks the optimal speed to generate maximum power. (b) The dc-bus power and the turbine mechanical power versus time. (c) The d-axis and q-axis currents to achieve MPPT.

 

 

 

Figure 4. Generator phase-A back emf, phase-A current, and power of the passive and active rectifiers at different operating speeds. (a) Sinusoidal and phase-shifted back emfs at the rated generator speed. (b) The corresponding phase-A currents. (c) Sharing of PMSG input power between ac ports powering active versus passive rectifiers. (d) Back emfs at the minimum operating speed that is equal to 55% the rated speed. (e) Phase-A currents corresponding to the minimum speed. (f) Power sharing between the ac ports powering active and passive rectifiers at the minimum operating speed.

 

CONCLUSION:

This paper presents an MPPT methodology for an integrated generator-rectifier system. An analytical relationship between the dc-bus power and the active rectifier d-axis current is established and validated using both simulation and experiment. A cascaded control architecture is proposed for practical implementation. The inner loop comprises PI current controllers with feed-forward terms, while the outer loop is a PI power controller. Satisfactory power tracking performance has been accomplished. The power flow control enables the wind turbine MPPT through controlling the dc-bus power. This capability opens up opportunities for the integrated generator rectifier systems in wind energy applications.

REFERENCES:

[1] P. Huynh, S. Tungare, and A. Banerjee, “Maximum power point tracking for wind turbine using integrated generator-rectifier systems,” in 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Sep. 2019, pp. 13–20.

[2] D. S. Ottensen, “Global offshore wind market report,” Norweigian Energy Partner, Tech. Rep., 2018.

[3] C. Bak, R. Bitsche, A. Yde, T. Kim, M. H. Hansen, F. Zahle, M. Gaunaa, J. P. A. A. Blasques, M. Døssing, J.-J. W. Heinen et al., “Light rotor: The 10-MW reference wind turbine,” in EWEA 2012-European Wind Energy Conference & Exhibition. European Wind Energy Association (EWEA), 2012.

[4] P. Higgins and A. Foley, “The evolution of offshore wind power in the united kingdom,” Renewable and sustainable energy reviews, vol. 37, pp. 599–612, 2014.

[5] W. Musial, P. Beiter, P. Spitsen, J. Nunemaker, and V. Gevorgian, “2018 offshore wind technologies market report,” National Renewable Energy Laboratory, https://www.energy.gov/eere/wind/downloads/2018- offshore-wind-market-report, Tech. Rep., 2018.

Investigation of Voltage Sags Effects on ASD and Mitigation using ESRF theory-based DVR

ABSTRACT:

 Voltage sag is a frequently occurring power quality disturbance in the industries equipped with adjustable speed drives (ASD). A detailed investigation of voltage sag effects on ASD performance with the novel mathematical analyses to estimate the ASD parameters during different types of voltage sag is discussed in this article. The effects of voltage sags are mitigated using an enhanced synchronous reference frame (ESRF) theory-based dynamic voltage restorer (DVR). The working principle of the ESRF theory-based DVR during sag is also described. The investigation of the effects of type A, type B and type F voltage sags on ASD parameters are verified using the simulation and the experimental studies. Further, these effects are mitigated by the ESRF theory-based DVR using the developed simulation and experimental models. The ESRF controller of DVR is working effectively during voltage sags by improving its transient response, which tightly regulates the DC link voltage of ASD around its reference value. Also, the steady state response of DVR is enhanced during severe voltage sag, which further validates the ability of the ESRF theory-based DVR. This type of improved performance of ASD during voltage sags cannot be obtained using other existing SRF theories of the DVR.

KEYWORDS:

1.      Adjustable speed drives

2.      DC-link voltage

3.      Symmetrical sag

4.      Unsymmetrical sag

5.      Dynamic voltage restorer

 SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:

 

 

Fig. 1. Circuit diagram of DVR with ASD system.

 EXPECTED SIMULATION RESULTS:

Fig. 2. Simulation results of ASD during TAVS, TBVS and TFVS.

 

Fig. 3. Simulation results (a) ASD performance during severe TBVS and (b) RMS input line current.

Fig. 6. Comparison of the simulation results of the SRF [24,26] and the ESRF controller. (a) DC-link voltage of ASD and (b) Speed of the motor.

 

Fig. 7. Simulation results of the ESRF theory-based DVR during voltage swell. (a) PCC, DVR and ASD R-phase RMS voltages and (b) DC-link voltage of ASD.

CONCLUSION:

A detailed investigation of ASD performance under TAVS, TBVS and TFVS is presented in this article. A novel mathematical analysis to evaluate the ASD parameters during different types of voltage sag with various sag magnitudes is presented in this article. The initial effect of any voltage sag occurs on ASD is a drop in the DC-link voltage, which results in the fluctuation of stator current, torque and speed of the motor. From the mathematical analyses, simulation results and experimental results, it is observed that the ASD performance affects more severely due to TAVS. However, the most frequently occurring TBVS can also halt the operation of ASD. It can be inferred from the experimental study that the effects of voltage sag on ASD performance depend on its loading condition, type of sag and sag magnitude. The ESRF theory-based DVR is used to regulate the DC-link voltage of ASD to its reference value during the sag period, which results in the constant speed of the motor. Moreover, the ESRF controller enhanced the transient response compared to the other SRF theories. Also, the steady-state response of the DVR is improved during severe voltage sag (TAVS), which further validates the ability of the ESRF theory-based DVR to regulate the DC-link voltage of the ASD. The obtained simulation and experimental results proved that the ESRF theory-based DVR is able to regulate the speed of the motor around its reference value during 0.5 p.u. voltage sag for a minute. This proves the effectiveness of the ESRF controller technique over the existing SRF control theories of the DVR.

REFERENCES:

[1] N. Khatri, A. Jain, V. Kumar and R. R. Joshi, “Voltage sag assessment with respect to sensitivity of adjustable speed drives in distributed generation environment,” in proc. IEEE Int. Conf. on Computer, Communication and Control, Indore, India, 2015, pp. 1-6.

[2] Y. Liu, X. Xiao, X. Zhang and Y. Wang, “Multi-Objective Optimal STATCOM Allocation for Voltage Sag Mitigation,” in IEEE Trans. Pow. Del., vol. 35, no. 3, pp. 1410-1422, June 2020.

[3] Y. Wang, L. Deng, M. H. J. Bollen and X. Xiao, “Calculation of the Pointon- Wave for Voltage Dips in Three-Phase Systems,” in IEEE Trans. Pow. Del., vol. 35, no. 4, pp. 2068-2079, Aug. 2020.

[4] S. Jothibasu and M. K. Mishra, “A Control Scheme for Storageless DVR Based on Characterization of Voltage Sags,” in IEEE Trans. Pow. Del., vol. 29, no. 5, pp. 2261-2269, Oct. 2014.

[5] M. R. Alam, K. M. Muttaqi and T. K. Saha, “Classification and Localization of Fault-Initiated Voltage Sags Using 3-D Polarization Ellipse Parameters,” in IEEE Trans. Pow. Del., vol. 35, no. 4, pp. 1812-1822, Aug. 2020.SSSSSSSSSSS

Partial Power Conversion and High Voltage Ride-Through Scheme for a PV-Battery Based Multiport Multi-Bus Power Router

ABSTRACT:

 With the development of renewable energy technology, distributed power supply mode with multi energy and multi-directional power flow including utility grid, renewable energy and energy storage unit has gradually become a research hotspot. An AC/DC hybrid multi-port power routing (MPPR) system which based on partial power conversion (PPC) of dual DC buses is proposed in this paper. The photovoltaic (PV) port, the battery port and two DC voltage buses form a power router. PV maximum power point tracking (MPPT) and high-voltage ride through (HVRT) of the grid-tied inverter are implemented by the same auxiliary port voltage modulation. The PPC based PV conversion features that only the power determined by voltage difference between PV panel and the series connected DC bus is dealt with, which significantly reduces the loss compared to the full power conversion (FPC) for PV. The detailed control schemes of all converters and energy transmit are given. The simulation and experimental results verify the effectiveness of the proposed scheme.

 KEYWORDS:

1.      Partial power conversion

2.      Multi-port power routing

3.      High voltage ride-through

4.      PV-battery

5.      Grid-connected system

SOFTWARE: MATLAB/SIMULINK

 BLOCK DIAGRAM:

 

 

Figure 1. The MPPR Topology Of PV-Battery Grid-Connected System.

 

EXPECTED SIMULATION RESULTS:

 

Figure 2. Simulation Result Of Case I.

Figure 3. The Steady-State Waveform In 0-1s.

Figure 4. Simulation Result Of Case II.

CONCLUSION:

This article proposes a PV-battery based multi-port power routing. Compared with the traditional PV-battery grid-connected system, the proposed MPPR in this paper has two main characteristics implemented by one auxiliary port simultaneously: first is the partial power conversion of the DC/DC stage, which significantly improves the power transfer efficiency. Secondary, MPPR realizes HVRT on the premise of maintaining normal PV output, and auxiliary port is adaptive to the grid-side voltage swell by adjusting its voltage so as to improve the voltage level of three phase converter DC bus. The system can flexibly realize the power exchange between three ports, two DC buses and the grid.

REFERENCES:

 

[1] A. Sangwongwanich, Y. Yang, and F. Blaabjerg, ``High-performance con- stant power generation in grid-connected PV systems,'' IEEE Trans. Power Electron., vol. 31, no. 3, pp. 1822_1825, Mar. 2016.

[2] C. Zhong, Y. Zhou, X. Zhang, and G. Yan, ``Flexible power-point-tracking- based frequency regulation strategy for PV system,'' IET Renew. Power Gener., vol. 14, no. 10, pp. 1797_1807, Jul. 2020.

[3] H. Fathabadi, ``Improving the power ef_ciency of a PV power generation system using a proposed electrochemical heat engine embedded in the system,'' IEEE Trans. Power Electron., vol. 34, no. 9, pp. 8626_8633, Sep. 2019.

[4] Y. Liu, S. You, and Y. Liu, ``Study of wind and PV frequency control in U.S. power grids_EI and TI case studies,'' IEEE Power Energy Technol. Syst. J., vol. 4, no. 3, pp. 65_73, Sep. 2017.

[5] H. Sugihara, K. Yokoyama, O. Saeki, K. Tsuji, and T. Funaki, ``Economic and ef_cient voltage management using customer-owned energy storage systems in a distribution network with high penetration of photovoltaic systems,'' IEEE Trans. Power Syst., vol. 28, no. 1, pp. 102_111, Feb. 2013.

Parameter Adjustment for the Droop Control Operating a Discharge PEC in PMG-Based WECSs With Generator-Charged Battery Units

ABSTRACT: 

Permanent magnet generator (PMG)-based wind energy conversion systems (WECSs) with battery units, have become a popular class of distributed generation units. These distributed generation units are typically operated using various types of controllers, including droop controllers. Existing droop controllers are designed to operate grid-side dc-ac power electronic converters (PEC) to ensure stable and reliable power production by a PMG-based WECS. The employment of battery storage units (to mitigate fluctuations in the power produced by a PMG-based WECS) introduces additional considerations for the design of droop controllers. Such considerations are due to the power available from battery units that is dependent on the state-of-charge (SOC). This paper proposes adjustments in the parameters (droop constants) of the droop control (operate the the discharge PEC) based on the SOC of the battery units. These adjustments are made to further support stable and reliable power delivery of the PMG-based WECS into the point-of-common-coupling (PCC). The proposed adjustments of droop constants are evaluated using a 7.5 kW grid-connected PMG-based WECS with 3.52 kW generator-charged battery storage units. Performance tests are carried out for step changes in the active and reactive power demands, changes in the wind speed, and grid-side disturbances. Test results show that the proposed correction of the droop constants is critical for maintaining a stable, effective, and accurate power delivery by the battery units, thus supporting the voltage/frequency stability at the PCC under different operating conditions.

 KEYWORDS:

1.      Permanent magnet generators

2.      Wind energy conversion systems

3.      Battery storage systems

       Droop control

 B   Distributed generation

SOFTWARE: MATLAB/SIMULINK

 SCHEMATIC DIAGRAM:

 

Figure 1. A Schematic Diagram For A Grid-Connected Pmg-Based Wecs With Generator-Charged Battery Units [2]. The Notation Mchb Denotes Modified Cascaded H-Bridge.

 

EXPECTED SIMULATION RESULTS:

 

Figure 2. Test Case 1: Changes In The Wind Speed And Power Delivery To The Grid: (A) The Wind Speed, (B) The Frequency As Measured At The Pcc, (C) The Voltage As Measured At The Pcc, (D) The Command And Actual Active And Reactive Powers Injected Into The Grid, (E) The Command And Actual Active And

Reactive Powers Delivered By The Gs-Pec, (F) The Command And Actual Active And Reactive Powers Delivered By The Ds-Pec, (G) The 3_ Currents Flowing From The Gs-Pec, (H) The 3_ Currents Flowing From The Ds-Pec, And (I) The Soc, Mp2, And Mq2.

 

Figure 3. Test Case 2: Voltage And Frequency Disturbance At The Pcc: (A) The Wind Speed, (B) The Frequency As Measured At The Pcc, (C) The Voltage As Measured At The Pcc, (D) The Command And Actual Active And Reactive Powers Injected Into The Grid, (E) The Command And Actual Active And Reactive Powers Delivered By The Gs-Pec, (F) The Command And Actual Active And Reactive Powers Delivered By The Ds-Pec, (G) The 3_ Currents Flowing From The Gs-Pec, (H) The 3_ Currents Flowing From The Ds-Pec, And (I) The Soc, Mp2, And Mq2.

CONCLUSION:

This paper has presented a method to adjust the constants of a droop controller operating a discharge PEC of battery units based on their SOC. The proposed adjustments in droop constants are developed for battery storage systems that are deployed in grid-connected PMG-based WECSs. Adjustments of droop constants are intended to ensure that the power delivered by a storage system is maintained close to its command as the SOC decreases. In addition, the correction of droop constants improves the ability of the PMG-based WECS and its battery storage system to meet their command power delivery, while ensuring the frequency and voltage stability at the PCC. The performance and responses of the pro- posed corrected droop constants have tested using a 7.5 kW grid-connected PMG-based WECS that has a 3.52 kW bat- tery storage system under different operating conditions. Test results for the PMG-based WECS with its battery storage system have shown an encouraging ability to adjust the power delivered by the grid-side and discharge PECs in response to changes in wind speed, power delivery to the grid, and grid-side disturbances. These abilities have been found insensitive to the wind speed, levels of power delivery to the grid, and/or nature of disturbances on the grid side. Such features of the droop control support its applicability.

REFERENCES:

 

[1] IEEE Application Guide for IEEE Standard for Interconnecting Distributed Resources With Electric Power Systems, IEEE Standard 1547.2- 2008, 2008.

[2] S. A. Saleh and X. F. S. Onge, ``A new structure for PMG-based WECSs with battery storage systems,'' IEEE Access, vol. 8, pp. 190356_190366, 2020.

[3] S. Lakshminarayana, Y. Xu, H. V. Poor, and T. Q. S. Quek, ``Cooperation of storage operation in a power network with renewable generation,'' IEEE Trans. Smart Grid, vol. 7, no. 4, pp. 2108_2122, Jul. 2016.

[4] Y. Geng, L. Zhu, X. Song, K. Wang, and X. Li, ``A modi_ed droop control for grid-connected inverters with improved stability in the _uc- tuation of grid frequency and voltage magnitude,'' IEEE Access, vol. 7, pp. 75658_75669, 2019.

[5] M. Farhadi and O. Mohammed, ``Energy storage technologies for high- power applications,'' IEEE Trans. Ind. Appl., vol. 52, no. 3, pp. 1953_1961, Jun. 2016

Multi-Mode Operation and Control of a Z-Source Virtual Synchronous Generator in PV Systems

 ABSTRACT:

 

The increasing penetration of power electronics-based distributed energy resources (DERs) displacing conventional synchronous generators is rapidly changing the dynamics of large-scale power systems. As the result, the electric grid loses inertia, voltage support, and oscillation damping needed to provide ancillary services such as frequency and voltage regulation. This paper presents the multi-mode operation of a Z-source virtual synchronous generator (ZVSG). The converter is a Z-source inverter capable of emulating the virtual inertia to increase its stability margin and track its frequency. The added inertia will protect the system by improving the rate of change of frequency. This converter is also capable of operating under normal and grid fault conditions while providing needed grid ancillary services. In normal operation mode, the ZVSG is working in MPPT mode where the maximum power generated from the PV panels is fed into the grid. During grid faults, a low voltage ride through control method is implemented where the system provides reactive power to reestablish the grid voltage based on the grid codes and requirements. The proposed system operation is successfully validated experimentally in the OPAL-RT real-time simulator.

 

KEYWORDS:

1.      Impedance-source inverter

2.      Virtual synchronous generator

3.      Photovoltaic (PV) systems

4.      Low voltage ride through

SOFTWARE: MATLAB/SIMULINK

SCHEMATIC DIAGRAM:

Figure 1. Proposed ZVSG Converter Equipped With VSG And LVRT Control Algorithms.

 

EXPECTED SIMULATION RESULTS:

 

Figure 2. Rocof Curves With Different Amounts Of (A) Inertia (H) And (B) Damping Constant (Dp ).

Figure 3. Comparison In Zvsg Current Increase While (A) The Converter Is Directly Connected (100(Ma)_3:2_10000 D 3200a) And (B) A Pre-Synchronizing Control Method Is Hired To Decrease The Current Increment (200(Ma)_1_5000 D 1000a).

 

Figure 4. Multi-Mode Operation Of The Zvsg During (A) Normal Operation (C) Voltage Sage Occurrence At T1 And Switching To Lvrt Mode And (D) Returning To Normal Mode At T2.

 

CONCLUSION:

This paper studied the multi-mode operation of an impedance-source virtual synchronous generator which is comprised of a single-stage ZSI, equipped with VSG control algorithm and is capable of providing grid ancillary services. Since the PLL may fail to detect the correct angle in case of harmonic distorted voltage, a virtual flux orientation control method is hired which can select the correct angle to be fed to Park transformation. The operation of the system has been tested while transitioning from islanded to grid-connected mode where, to protect the system against inrush current while connecting to the grid, a pre-synchronizing control method is used to minimize the phase difference between grid and converter. In addition, a solution to survive the system against voltage faults is embedded in the system which can regulate the reactive power based on the grid codes. Hence, the control paradigm will switch from MPP generation to LVRT mode after detecting voltage sag in the system. In this method, the peak of the grid current is kept constant during LVRT operation mode and ensures over current protection limit is not violated then. The ZVSG has been implemented in the OPAL-RT real-time digital simulator and its validity have been verified by conducting several case studies. The proposed seamless control frame- work helps to smoothly switch between normal and faulty conditions.

REFERENCES:

 

[1] K. Jiang, H. Su, H. Lin, K. He, H. Zeng, and Y. Che, ``A practical secondary frequency control strategy for virtual synchronous generator,'' IEEE Trans. Smart Grid, vol. 11, no. 3, pp. 2734_2736, May 2020.

[2] K. Shi, W. Song, H. Ge, P. Xu, Y. Yang, and F. Blaabjerg, ``Transient analysis of microgrids with parallel synchronous generators and virtual synchronous generators,'' IEEE Trans. Energy Convers., vol. 35, no. 1, pp. 95_105, Mar. 2020.

[3] J. Chen and T. O'Donnell, ``Parameter constraints for virtual synchronous generator considering stability,'' IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2479_2481, May 2019.

[4] H. Cheng, Z. Shuai, C. Shen, X. Liu, Z. Li, and Z. J. Shen, ``Transient angle stability of paralleled synchronous and virtual synchronous generators in islanded microgrids,'' IEEE Trans. Power Electron., vol. 35, no. 8, pp. 8751_8765, Aug. 2020.

[5] H. Nian and Y. Jiao, ``Improved virtual synchronous generator control of DFIG to ride-through symmetrical voltage fault,'' IEEE Trans. Energy Convers., vol. 35, no. 2, pp. 672_683, Jun. 2020.