A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads
<p>Diagram of unbalanced load power supply system.</p> "> Figure 2
<p>Topology of the three phase four-leg converter.</p> "> Figure 3
<p>Average model of the four-leg inverter.</p> "> Figure 4
<p>Diagram of the existing VSG control strategy for a four-leg inverter.</p> "> Figure 5
<p>Problems of the existing control strategy under load variation.</p> "> Figure 6
<p>Equivalent sequential network model of VSG with an unbalanced load.</p> "> Figure 7
<p>Improved VSG control block diagram.</p> "> Figure 8
<p>Diagram of a four-leg inverter transitioning from off-grid to grid-connected operation.</p> "> Figure 9
<p>Improved VSG pre-synchronization control block diagram.</p> "> Figure 10
<p>Schematic diagram of a PLL.</p> "> Figure 11
<p>Pole map of the current control loop with varying <span class="html-italic">k</span><sub>c</sub>.</p> "> Figure 12
<p>Pole map of the voltage control loop with varying <span class="html-italic">k</span><sub>r</sub>.</p> "> Figure 13
<p>Simulation model of the main circuit and proposed control strategy.</p> "> Figure 14
<p>Simulation results with an unbalanced load. (<b>a</b>) Traditional VSG for a conventional converter [<a href="#B40-symmetry-16-01116" class="html-bibr">40</a>]; (<b>b</b>) traditional VSG [<a href="#B38-symmetry-16-01116" class="html-bibr">38</a>] for a four-leg converter; (<b>c</b>) improved VSG for a four-leg converter.</p> "> Figure 15
<p>Simulation results of voltages of the power grid and four-leg converter under pre-synchronization control.</p> "> Figure 16
<p>Photograph of a down-scaled prototype of the four-leg inverter.</p> "> Figure 17
<p>Single-line diagram of the experimental setup.</p> "> Figure 18
<p>Steady-state waveforms with an unbalanced load. (<b>a</b>) Voltages of a traditional VSG for a conventional inverter; (<b>b</b>) currents of a traditional VSG for a conventional inverter; (<b>c</b>) voltages of a traditional VSG for a four-leg inverter; (<b>d</b>) currents of a traditional VSG for a four-leg inverter; (<b>e</b>) voltages of an improved VSG for a four-leg inverter; (<b>f</b>) currents of an improved VSG for a four-leg inverter.</p> "> Figure 19
<p>Waveforms of frequency with an unbalanced load.</p> "> Figure 20
<p>Waveforms under load being turned on.</p> "> Figure 21
<p>Waveforms of voltages of the power grid and four-leg converter.</p> "> Figure 22
<p>Waveforms of the pre-synchronization process.</p> "> Figure 23
<p>Waveforms under the system turned on with different control parameters. (<b>a</b>) Parameters I; (<b>b</b>) parameters II; (<b>c</b>) proposed optimized parameters.</p> "> Figure 24
<p>Active power waveforms under a system turned on with different control parameters.</p> ">
Abstract
:1. Introduction
- (1)
- An improved VSG control strategy for a four-leg inverter is proposed. The improved virtual impedance control and power calculation method are used to keep the output voltages symmetrical and stable in the case of load symmetry. The results show that the voltage unbalance ratio can be reduced by 89%.
- (2)
- A pre-synchronization control strategy is put forward. The control loops for voltage amplitude and phase are developed according to the proposed VSG control strategy. Results indicate that the difference in amplitude and phase angle between the inverter output voltages and the grid voltage decreases.
- (3)
- An optimized design method for control parameters is presented. Considering the stability margins, the parameters of the voltage and current control loop are independently optimized to obtain faster dynamic performance. From the experimental results, the response time can be shortened by 50%.
2. Mathematical Model of Four-Leg Inverter
3. Improved VSG Control Strategy for a Four-Leg Inverter
3.1. Problems in the Existing Control Strategy
3.2. Improved VSG Control Strategy
3.2.1. Improved Virtual Impedance Method
3.2.2. Power Calculation Method
3.2.3. Control Block Diagram
4. Improved VSG Pre-Synchronization Control Strategy for a Four-Leg Inverter
4.1. Analysis of a VSG Control Strategy from Isolated Mode to Grid-Connected Mode under Unbalanced Loads
4.2. Design of Improved VSG-Based Pre-Synchronization Control Strategy
4.2.1. Phase Pre-Synchronization
4.2.2. Amplitude Pre-Synchronization
5. Optimized Parameters Design Method
5.1. Parameters Design for Current Control Loop
5.2. Parameters Design for Voltage Control Loop
6. Simulation Verifications
7. Experimental Verifications
7.1. Verifications of Improved VSG Control Strategy
7.2. Verifications of Improved VSG Pre-Synchronization Control Strategy
7.3. Verifications of Optimized Parameters Design Method
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Abbreviations | |
VSG | Virtual synchronous generator. |
PSO | Particle swarm optimization. |
PWM | Pulse width modulation. |
MPC | Model predictive control. |
3D-SVM | Three-dimensional space vector modulation. |
PI | Proportional-integral. |
PR | Proportional-resonant. |
PCC | Point of common coupling. |
P | Proportional. |
RMS | Root mean square. |
SOGI | Second order generalized integrator. |
GM | Gain margin. |
PM | Phase margin. |
PLL | Phase-locked loop. |
THD | Total harmonic distortion. |
Parameters | |
Lf, Ln | Inductor of LC filter, neutral inductor. |
Cf | Capacitor of LC filter. |
Udc | Voltage at the DC side of the four-leg inverter. |
uA, uB, uC, uG | Arm voltages relative to the negative terminal on the DC side. |
uAG, uBG, uCG | Arm voltages relative to the fourth leg (G). |
da, db, dc, dg | Duty cycles of each upper arm switch. |
uan, ubn, ucn | Load voltages. |
iLa, iLb, iLc | Currents of the filter inductor. |
ia, ib, ic | Currents of the loads. |
in | Currents of the neutral inductor. |
uαG, uβG, uγG | Arm voltages relative to the fourth leg (G) in the αβγ reference frame. |
uαn, uβn, uγn | Load voltages in the αβγ reference frame. |
iLα, iLβ, iLγ | Filter currents inductor in the αβγ reference frame. |
iα, iβ, iγ | Load currents of the in the αβγ reference frame. |
Pref, Qref | Reference active power and reactive power at PCC points. |
Pe, Qe | Calculated active power and reactive power at PCC points. |
D1 | Damping coefficient. |
D2 | Voltage regulation coefficient. |
J | Virtual inertia constant. |
K | Integral regulation coefficient. |
ωn, ω | Reference angular frequency and output angular frequency. |
em | Internal electric potential of VSG. |
Em | Magnitude of em. |
Uref, Um | Magnitude voltages of the output reference and measurement. |
Zv | Virtual impedance of VSG. |
urefabc | Reference of uan, ubn, ucn. |
urefαβγ | Reference of uan, ubn, ucn in the αβγ reference frame. |
iabc | Three-phase currents of the loads. |
I, U | RMS of ia, ib, ic, RMS of uan, ubn, ucn. |
Za, Zb, Zc | Impedances of the load. |
Sequence components of uan, ubn, ucn. | |
Sequence components of ia, ib, ic. | |
Za_pp, Za_nn, Za_00 | Sequence components of Za, Zb, Zc. |
Za_ij | Coupling impedance between sequence i and sequence j of Za, Zb, Zc. |
Sequence components of em. | |
Sequence components of Zv. | |
Pm | RMS of oscillating power at PCC points. |
Average active and reactive power at PCC points. | |
Ts | Sampling period. |
ZLine | Line impedance. |
uU, uV, uW | Voltages of power grid. |
uα, uβ | Voltages of power grid in the αβγ reference frame. |
ud, uq | Voltages of power grid in the dq reference frame. |
θg | Voltage phase of the power grid. |
uqn | uan, ubn, ucn in the dq reference frame. |
Δω | Difference phase between the voltages of grid and converter output. |
Ug | RMS of uU, uV, uW. |
ωr | |
ωi | Frequency band where the error of z transformation is reduced. |
kc | Proportional parameter of current control loop. |
kc_O | Optimized parameter of the current control loop on the α and β axis. |
kc_Oγ | Optimized parameter of the current control loop on the γ axis. |
kv, kr | Proportional and resonant parameters of voltage control loop. |
kr_O | Optimized parameter of the voltage control loop on the α and β axis. |
kr_Oγ | Optimized parameter of the voltage control loop on the γ axis. |
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Control Strategies | Implementation Process | Dynamic Performance | Voltages Unbalance Ratio | Affected by Mismatch | Can Provide Inertia and Damping |
---|---|---|---|---|---|
[29,30] | Easy | Low | Low | Low | No |
[31,32,33,34,35] | Complex | High | Low | Medium | No |
[36] | Easy | Low | High | Low | Yes |
Proposed method | Easy | Medium | Low | Low | Yes |
Parameters | Value |
---|---|
Rated phase voltage (RMS value) Um | 60 V |
Rated phase current I | 6 A |
DC-side voltage Udc | 200 V |
Filter inductance Lf | 2 mH |
Neutral inductance Ln | 1 mH |
Filter capacitance Cf | 30 μF |
Fundamental frequency fn | 50 Hz |
Sampling period Ts | 0.0001 s |
Switching frequency fPWM | 10 kHz |
Parameters | Value |
---|---|
Rated power | 13 kW |
Rated phase voltage (RMS value) Um | 220 V |
DC-side voltage Udc | 750 V |
Filter inductance Lf | 2.5 mH |
Neutral inductance Ln | 1.25 mH |
Filter capacitance Cf | 80 μF |
Fundamental frequency fn | 50 Hz |
Sampling period Ts | 0.0001 s |
Switching frequency fPWM | 10 kHz |
Items | Parameters I | Parameters II | Optimized Parameters |
---|---|---|---|
Parameters on the αβ axis | kc = 5 | kc = 7.8 | kc = 6.7 |
kv = 0.05 | kv = 0.04 | kv = 0 | |
kr = 3 | kr = 10 | kr = 190 | |
Parameters on the γ axis | kc = 10 | kc = 14.6 | kc = 13.8 |
kv = 0.01 | kv = 0.02 | kv = 0 | |
kr = 1 | kr = 2 | kr = 40 |
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Huang, Z.; Liu, Z.; Shen, G.; Li, K.; Song, Y.; Su, B. A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads. Symmetry 2024, 16, 1116. https://doi.org/10.3390/sym16091116
Huang Z, Liu Z, Shen G, Li K, Song Y, Su B. A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads. Symmetry. 2024; 16(9):1116. https://doi.org/10.3390/sym16091116
Chicago/Turabian StyleHuang, Zhenshan, Zhijie Liu, Gang Shen, Kejun Li, Yuanzong Song, and Baihe Su. 2024. "A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads" Symmetry 16, no. 9: 1116. https://doi.org/10.3390/sym16091116
APA StyleHuang, Z., Liu, Z., Shen, G., Li, K., Song, Y., & Su, B. (2024). A Virtual Synchronous Generator-Based Control Strategy and Pre-Synchronization Method for a Four-Leg Inverter under Unbalanced Loads. Symmetry, 16(9), 1116. https://doi.org/10.3390/sym16091116