Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter
<p>Single-stage grid-tied PV-fed differential boost AC module.</p> "> Figure 2
<p>Time-domain waveforms of the sampled extracted power <math display="inline"><semantics> <msub> <mi>p</mi> <mi>pv</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 3
<p>The sampled inductor currents <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and capacitor voltages <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 4
<p>Time-domain waveforms of the sampled grid voltage <math display="inline"><semantics> <msub> <mi>v</mi> <mi>g</mi> </msub> </semantics></math> and sampled grid current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>g</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 5
<p>Time-domain waveforms of the sampled extracted power <math display="inline"><semantics> <msub> <mi>p</mi> <mi>pv</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 6
<p>The sampled inductor currents <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and capacitor voltages <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 7
<p>Time-domain waveforms of the grid voltage <math display="inline"><semantics> <msub> <mi>v</mi> <mi>g</mi> </msub> </semantics></math> and grid current <math display="inline"><semantics> <msub> <mi>i</mi> <mi>g</mi> </msub> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> in steady-state operation. <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>M</mi> </msub> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> V.</p> "> Figure 8
<p>The feedback signal <math display="inline"><semantics> <mi>σ</mi> </semantics></math> and the control signal <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>s</mi> </msub> <mi>ref</mi> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>v</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p> "> Figure 9
<p>The time varying duty cycle calculated from (<a href="#FD12-applsci-11-02106" class="html-disp-formula">12</a>) (<math display="inline"><semantics> <mrow> <mi>D</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) and obtained from numerical simulation (<math display="inline"><semantics> <mrow> <mi>d</mi> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </semantics></math>) for <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> W/m<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math>.</p> "> Figure 10
<p>The eigenvalue <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </semantics></math> as the phase angle is varied within <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>π</mi> <mo>)</mo> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <msub> <mi>V</mi> <mi>M</mi> </msub> </semantics></math>.</p> "> Figure 11
<p>The eigenvalue <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </semantics></math> as the phase angle is varied within <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>π</mi> <mo>)</mo> </mrow> </semantics></math> with an adaptive compensation scheme using <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>r</mi> </msub> <mo>=</mo> <mo>−</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>m</mi> <mn>0</mn> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>.</p> "> Figure 12
<p>The block diagram (<b>top</b>) and the equivalent schematic circuit representation (<b>bottom</b>) of the adaptive compensating slope signal generator.</p> "> Figure 13
<p>The time varying duty cycle calculated from (<a href="#FD12-applsci-11-02106" class="html-disp-formula">12</a>) (<math display="inline"><semantics> <mrow> <mi>D</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) obtained from numerical simulation (<math display="inline"><semantics> <mrow> <mi>d</mi> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </semantics></math>) for guaranteeing stability within the complete duty cycle range.</p> "> Figure 14
<p>The time varying duty cycle calculated from (<a href="#FD12-applsci-11-02106" class="html-disp-formula">12</a>) (<math display="inline"><semantics> <mrow> <mi>D</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) obtained from numerical simulation (<math display="inline"><semantics> <mrow> <mi>d</mi> <mo>(</mo> <mi>n</mi> <mi>T</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </semantics></math>) for guaranteeing a <span class="html-italic">deadbeat</span> response within the complete duty cycle range.</p> ">
Abstract
:1. Introduction
2. Differential Boost AC Module under Three-Loop Control
3. Nonlinear Behavior and Fast-Scale Instability in the Differential Boost Inverter
3.1. Test 1: W/m and C
3.2. Test 2: W/m and C
4. Approximate Prediction of Fast-Scale Instability and Adaptive Slope Compensation
4.1. Reduced-Order Discrete-Time Model for Predicting the Fast-Scale Instability in the DC-AC Inverter
4.2. Fast-Scale Stability Analysis
4.3. Adaptive Slope Compensation Circuit
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
and | 100 μH and 5 mH |
22 μF | |
2 mF | |
50 kHz | |
50 Hz | |
V |
Parameter | Value |
---|---|
and | 0.1 and 1 |
0.0247 s | |
0.2 | |
50 Hz | |
and | 500 Hz and 50 kHz |
2 |
Parameter | Value |
---|---|
Number of series-connected cells in a module | 72 |
Open-circuit voltage | 46.5 V |
Short-circuit current | 9.60 A |
Maximum power voltage | V |
Maximum power current | A |
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El Aroudi, A.; Debbat, M.; Al-Numay, M.; Abouloiafa, A. Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter. Appl. Sci. 2021, 11, 2106. https://doi.org/10.3390/app11052106
El Aroudi A, Debbat M, Al-Numay M, Abouloiafa A. Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter. Applied Sciences. 2021; 11(5):2106. https://doi.org/10.3390/app11052106
Chicago/Turabian StyleEl Aroudi, Abdelali, Mohamed Debbat, Mohammed Al-Numay, and Abdelmajid Abouloiafa. 2021. "Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter" Applied Sciences 11, no. 5: 2106. https://doi.org/10.3390/app11052106