Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance
<p>Structure and control scheme of a three-phase four-wire shunt active power filter system.</p> "> Figure 2
<p>Scheme of hybrid repetitive controller.</p> "> Figure 3
<p>Conventional model of a hybrid repetitive controlled shunt active power filter.</p> "> Figure 4
<p>Nyquist diagram of <span class="html-italic">H(z)</span> for shunt APF system.</p> "> Figure 5
<p>Simulated waveform of grid current under different conditions (parameters from <a href="#energies-12-02084-t001" class="html-table">Table 1</a>).</p> "> Figure 6
<p>Simulated waveform of grid current under different conditions (repeated simulation of [<a href="#B22-energies-12-02084" class="html-bibr">22</a>]).</p> "> Figure 7
<p>Modified model of shunt active power filter system.</p> "> Figure 8
<p>External circuit of shunt active power filter system.</p> "> Figure 9
<p>Sufficient stability criterion under resistor-inductor (RL) load. (<b>a</b>) Pole diagram of <span class="html-italic">T(z)</span> under RL load. (<b>b</b>) Nyquist diagram of <span class="html-italic">H(z)</span> under RL load.</p> "> Figure 10
<p>Sufficient stability criterion under resistor-inductor-capacitor (RLC) load. (<b>a</b>) Pole diagram of <span class="html-italic">T(z)</span> under RLC load. (<b>b</b>) Nyquist diagram of <span class="html-italic">H(z)</span> under RLC load.</p> "> Figure 11
<p>Poles of <span class="html-italic">T(z)</span> with change of capacitance load.</p> "> Figure 12
<p>Maximum values of moduli of poles of <span class="html-italic">T(z)</span> with certain <span class="html-italic">C<sub>load</sub></span> and variable RL load.</p> "> Figure 13
<p>Maximum values of moduli of poles of <span class="html-italic">T(z)</span> with different <span class="html-italic">GPI2(z)</span> controller parameters.</p> "> Figure 14
<p>Bode diagram of <span class="html-italic">P(z)</span> under different load conditions.</p> "> Figure 15
<p>Setting <span class="html-italic">Kp</span> of <span class="html-italic">G<sub>PI2</sub></span> to move poles of <span class="html-italic">T(z)</span> into the unit circle.</p> "> Figure 16
<p>Magnitude-frequency diagram of <span class="html-italic">S(z)P(z)</span> when controller is before or after modification.</p> "> Figure 17
<p>Phase correction effect of <span class="html-italic">z<sup>k</sup></span> to <span class="html-italic">S(z)P(z)</span>.</p> "> Figure 18
<p>Nyquist diagram of stability criterion <span class="html-italic">H(z)</span> of modified hybrid controller with capacitance load.</p> "> Figure 19
<p>Simulated grid current <span class="html-italic">i<sub>sys</sub></span> when shunt APF is compensating for RLC load and rectifier load.</p> "> Figure 20
<p>Simulated grid current <span class="html-italic">i<sub>sys</sub></span> when shunt APF is compensating for RL load and rectifier load.</p> "> Figure 21
<p>Experimental 75 kVA shunt active power filter prototype.</p> "> Figure 22
<p>Waveforms of grid current and its harmonic spectra carrying active load and three-phase rectifier load without shunt APF prototype.</p> "> Figure 23
<p>Waveforms of grid current and its harmonic spectra with common control strategy shunt APF prototype carrying active load and three-phase rectifier loads.</p> "> Figure 24
<p>Waveforms of grid current and its harmonic spectra with common control strategy shunt APF prototype after parallel capacitance load is connected at the point of common coupling (PCC).</p> "> Figure 25
<p>Waveforms of capacitor current.</p> "> Figure 26
<p>Waveforms of grid current and its harmonic spectra with modified strategy control shunt APF prototype after parallel capacitance load is connected at PCC.</p> "> Figure 27
<p>Waveforms of grid current and its harmonic spectra with modified strategy control shunt APF prototype carrying active load and three-phase rectifier load.</p> ">
Abstract
:1. Introduction
2. Problems of Conventional Model of Shunt APF
2.1. Review of Shunt Active Power Filter
2.2. Review of Hybrid Repetitive Controller
2.3. Conventional Model and Stability Problem of APF
- Transfer function T(z) does not have poles outside the unit circle.
- H(z) = |Q(z) − S(z)P(z)| < 1, z = ejωTs, ω ⸦ [0, π/Ts].
2.4. Flaws of Conventional Model of Shunt APF
3. Modified Model of Shunt APF and its Stability Analysis
3.1. Modeling Shunt Active Power Filter
3.2. Stability Analysis of Shunt APF System
- Transfer function T(z) does not have poles outside the unit circle.
- H(z) = |Q(z) – S(z)P(z)| <1, z = ejωTs, ω ⸦ [0, π/Ts].
3.3. Mechanism of Resonance Under Capacitance Load
3.4. Stability of External Circuit: T(z)
3.5. Stability of Hybrid Controller: H(z)
4. System Stabilization Strategies
5. Simulation and Experimental Results
5.1. Simulation Results
5.2. Experimental Results
6. Conclusions
- The dynamic characteristics of input signals of active power filter were taken into account.
- The external circuit (power grids and the loads) were modelled.
- The stability problem of the system could be reflected more accurately.
Author Contributions
Funding
Conflicts of Interest
References
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Circuit Parameters | Controller Part | |||
---|---|---|---|---|
Symbol | Parameter | Physical Meanings | Control Unit | Illustration |
Usys | 220 V | System phase voltage (RMS) | N = 256 | fs/f0 |
Lvs | 50 μH | System reactance | Q(z) = 0.95 | Attenuation coefficient |
Udc | 700 V | DC bus voltage of APF | GPI1(z) = 1 | Proportion unit |
f0 | 50 Hz | Frequency of distribution network | GPI2(z) = 1 | Proportion unit |
fs | 12.8 kHz | Sample frequency | S(z) | Corrector |
Lf | 0.375 mH | Inductance of inverter side of LCL | ||
Lg | 0.075 mH | Inductance of grid side of LCL | ||
Cf | 30 μF | Capacitor of LCL | ||
Rload | 4.4 Ω | Parallel active load | ||
Lload | 15 mH | Parallel inductance load | ||
Cload(Y) | 90 μF | Y connecting parallel capacitance load | ||
Cload(Δ) | 276.5 μF | Δ connecting parallel capacitance load | ||
3 ph rectifier load | Represents harmonics | |||
Rline | 0.05 Ω | Represents line resistance | ||
Usys | 220 V | System phase voltage (RMS) |
Dynamic characteristics of input signals are ignored |
External circuits (power grids and loads) are ignored |
Some stability problems cannot be reflected |
Before Modification | |
Control unit | Values |
GPI2(z) | Kp = 1; Ki = 0.0001 |
GLP(z) 2nd Butterworth low-pass filter | Cut–off frequency = 500 Hz |
After Modification | |
GPI2(z) | Kp = 0.5; Ki = 0.0001 |
GLP(z) 2nd Butterworth low-pass filter | Cut–off frequency = 1000 Hz |
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Bing, Y.; Jiang, D.; Liang, Y.; Jiang, C.; He, T.; Yang, L.; Hu, P. Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance. Energies 2019, 12, 2084. https://doi.org/10.3390/en12112084
Bing Y, Jiang D, Liang Y, Jiang C, He T, Yang L, Hu P. Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance. Energies. 2019; 12(11):2084. https://doi.org/10.3390/en12112084
Chicago/Turabian StyleBing, Yuqi, Daozhuo Jiang, Yiqiao Liang, Chongxi Jiang, Tianxiang He, Lei Yang, and Pengfei Hu. 2019. "Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance" Energies 12, no. 11: 2084. https://doi.org/10.3390/en12112084
APA StyleBing, Y., Jiang, D., Liang, Y., Jiang, C., He, T., Yang, L., & Hu, P. (2019). Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance. Energies, 12(11), 2084. https://doi.org/10.3390/en12112084