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Keywords = shunt capacitive compensation

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18 pages, 2622 KiB  
Article
Two-Way Power Flow Balancing in Three-Phase Three-Wire Networks by Unbalanced Capacitive Shunt Compensation
by Adrian Pană, Alexandru Băloi, Florin Molnar-Matei, Cristian Stănese, Andrei Jorza and David Stoica
Appl. Sci. 2024, 14(9), 3746; https://doi.org/10.3390/app14093746 - 27 Apr 2024
Viewed by 1467
Abstract
Developed to achieve the balancing of three-phase loads and improve their power factor, the BCC (Balancing Capacitive Compensator) is presented in this paper as having a broader capability, namely that of balancing the two-way power flow. BCCs are becoming useful in today’s distribution [...] Read more.
Developed to achieve the balancing of three-phase loads and improve their power factor, the BCC (Balancing Capacitive Compensator) is presented in this paper as having a broader capability, namely that of balancing the two-way power flow. BCCs are becoming useful in today’s distribution networks with a high content of DERs (Distributed Energy Resources), where unbalanced power transfers to the higher voltage network occur more and more frequently as a result of the excess power generated. The article contains a case study in which, by means of Matlab-Simulink 2021 modelling, such a network is studied by considering two regimes corresponding to the two-way power flow. The numerical analysis of phase components and sequence components confirms the validity of the mathematical model concerning the BCC and also for the case of changing the way of power flow in the section controlled by the compensator. This demonstrates the possibility of extending the load balancing function of the BCC to that of balancing the two-way power flow and is an additional argument in support of replacing, in the more or less near future, conventional shunt capacitive compensators with capacitive balancing compensators. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
Show Figures

Figure 1

Figure 1
<p>BCC (BRC) for load balancing in a three-phase three-wire network.</p>
Full article ">Figure 2
<p>ABCC used for power flow balancing in a three-phase three-wire network.</p>
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<p>The area of the three-phase distribution network containing a PV Power Supply System.</p>
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<p>The simplified network consists of equivalent elements.</p>
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<p>Regime 2—the voltage waveforms on the MV busbars of the substation, respectively, and the waveforms of the currents through the neighbouring sections.</p>
Full article ">
15 pages, 2584 KiB  
Article
Wideband SiGe-HBT Low-Noise Amplifier with Resistive Feedback and Shunt Peaking
by Ickhyun Song, Gyungtae Ryu, Seung Hwan Jung, John D. Cressler and Moon-Kyu Cho
Sensors 2023, 23(15), 6745; https://doi.org/10.3390/s23156745 - 28 Jul 2023
Cited by 5 | Viewed by 3203
Abstract
In this work, the design of a wideband low-noise amplifier (LNA) using a resistive feedback network is proposed for potential multi-band sensing, communication, and radar applications. For achieving wide operational bandwidth and flat in-band characteristics simultaneously, the proposed LNA employs a variety of [...] Read more.
In this work, the design of a wideband low-noise amplifier (LNA) using a resistive feedback network is proposed for potential multi-band sensing, communication, and radar applications. For achieving wide operational bandwidth and flat in-band characteristics simultaneously, the proposed LNA employs a variety of circuit design techniques, including a voltage–current (shunt–shunt) negative feedback configuration, inductive emitter degeneration, a main branch with an added cascode stage, and the shunt-peaking technique. The use of a feedback network and emitter degeneration provides broadened transfer characteristics for multi-octave coverage and a real impedance for input matching, respectively. In addition, the cascode stage pushes the band-limiting low-frequency pole, due to the Miller capacitance, to a higher frequency. Lastly, the shunt-peaking approach is optimized for the compensation of a gain reduction at higher frequency bands. The wideband LNA proposed in this study is fabricated using a commercial 0.13 μm silicon-germanium (SiGe) BiCMOS process, employing SiGe heterojunction bipolar transistors (HBTs) as the circuit’s core active elements in the main branch. The measurement results show an operational bandwidth of 2.0–29.2 GHz, a noise figure of 4.16 dB (below 26.5 GHz, which was the measurement limit), and a total power consumption of 23.1 mW under a supply voltage of 3.3 V. Regarding the nonlinearity associated with large-signal behavior, the proposed LNA exhibits an input 1-dB compression (IP1dB) point of −5.42 dBm at 12 GHz. These performance numbers confirm the strong viability of the proposed approach in comparison with other state-of-the-art designs. Full article
(This article belongs to the Special Issue Integrated Circuit Design and Sensing Applications)
Show Figures

Figure 1

Figure 1
<p>Conventional structures of wideband LNAs: (<b>a</b>) common-base stage with a feedforward amplifier; (<b>b</b>) common-emitter stage with a filter network; (<b>c</b>) common-emitter stage with a negative feedback loop.</p>
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<p>Schematic of the proposed wideband SiGe-HBT LNA.</p>
Full article ">Figure 3
<p>(<b>a</b>) Simplified small-signal equivalent circuit of the proposed LNA; (<b>b</b>) small-signal equivalent circuit with a broken loop for open-loop analysis.</p>
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<p>Simplified small-signal noise-equivalent circuit used for analysis.</p>
Full article ">Figure 5
<p>(<b>a</b>) Chip micrograph of the proposed wideband SiGe-HBT LNA. The core area of the LNA consumes 0.17 mm<sup>2</sup>. (<b>b</b>) On-wafer measurement setup.</p>
Full article ">Figure 6
<p>Simulated and measured (<b>a</b>) scattering parameters (s-parameters); (<b>b</b>) S<sub>11</sub>, S<sub>22</sub>, and S<sub>12</sub> (reverse isolation) versus frequency.</p>
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<p>Simulated and measured noise figure (NF) versus frequency. The measurement was conducted up to 26.5 GHz.</p>
Full article ">Figure 8
<p>Measured input 1-dB compression point (IP1dB) of the proposed LNA.</p>
Full article ">
16 pages, 6223 KiB  
Article
Current Ratio and Stability Issues of Electronically Enhanced Current Transformer Stimulated by Stray Inter-Winding Capacitance and Secondary-Side Disturbance Voltage
by Peter Zajec
Sensors 2022, 22(19), 7565; https://doi.org/10.3390/s22197565 - 6 Oct 2022
Cited by 1 | Viewed by 1665
Abstract
Electronically enhanced current transformers (EECT) have gained much interest in power quality assessment. Their magnitude and phase angle error, which mainly relates to the properties of the ferromagnetic materials used, the impedance of the secondary load, and the inter-turns capacitance, are thoroughly analyzed. [...] Read more.
Electronically enhanced current transformers (EECT) have gained much interest in power quality assessment. Their magnitude and phase angle error, which mainly relates to the properties of the ferromagnetic materials used, the impedance of the secondary load, and the inter-turns capacitance, are thoroughly analyzed. In contrast, the capacitance between the windings, i.e., inter-winding capacitances and their limiting effects on EECT operation, are rarely analyzed in detail—in particular, no details on the control design of the assisting electronic unit, its tuning recommendations, or both are provided. In this paper, the capacitive coupling between indication and compensating winding of EECT with simplified feedthrough construction is analyzed thoroughly in terms of current ratio error and stability of the implemented configuration of the trans-conductance amplifier. The preliminary assumption about the adverse effect of the inter-winding capacitance shunting both ends of the original amplifier, composed of two series-connected inverting amplifier stages, was confirmed and resolved within a modified amplifier with the help of a simplified simulation model and was experimentally proven with measurements on a custom-built EECT prototype. Furthermore, the analyzed phenomena were linked to trans-conductance amplifier parameters, explicitly with its compensating networks, and summarized in their design guidelines. Throughout the paper, the EECT features obtained with original and modified amplifier designs are compared with the plain composite current transformer to demonstrate the benefits of the modified amplifier, especially its robustness against inter-winding capacitance variations. Full article
(This article belongs to the Topic Power Quality)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>The EECT’s conceptual scheme.</p>
Full article ">Figure 2
<p>Cross-section view of cores with indicated windings.</p>
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<p>EECT’s equivalent circuit.</p>
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<p>EECT’s functional diagram: (<b>a</b>) drawn in accordance with (2), (3) and (4); (<b>b</b>) rearranged.</p>
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<p>The conceptual scheme for assisting electronics.</p>
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<p>Equivalent EECT scheme with simplified control and compensating networks of the original TC amplifier.</p>
Full article ">Figure 7
<p>Magnitude and phase of the current ratio <span class="html-italic"><span class="underline">H</span><sub>I</sub></span>—original circuit (magnitude-solid line, phase—dotted line); for varying <span class="html-italic">C<sub>eq</sub></span> = {5 pF, 1 nF, 50 nF} with detailed <span class="html-italic"><span class="underline">H</span><sub>I</sub></span> between 1 Hz and 200 Hz.</p>
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<p>Simulated frequency response <span class="html-italic"><span class="underline">Y</span></span> (magnitude-solid line, phase—dotted line) with original and modified amplifier for varying <span class="html-italic">C<sub>eq</sub></span>: (<b>a</b>) original amplifier; (<b>b</b>) modified amplifier.</p>
Full article ">Figure 9
<p>Magnitude (solid line) and phase (dotted line) of the current ratio <span class="html-italic"><span class="underline">H</span><sub>I</sub></span>—modified circuit for varying <span class="html-italic">C<sub>eq</sub></span> = {5 pF, 1 nF, 50 nF } with detailed <span class="html-italic"><span class="underline">H</span><sub>I</sub></span> between 1 Hz and 200 Hz.</p>
Full article ">Figure 10
<p>Disturbance rejection capability |<span class="html-italic"><span class="underline">H</span><sub>dist</sub></span>|<span class="html-italic"><sub>composite CT</sub></span> (blue line) vs |<span class="html-italic"><span class="underline">H</span><sub>dist</sub></span>|<span class="html-italic"><sub>EECT</sub></span> (red lines) for varying <span class="html-italic">C<sub>eq</sub></span> = {5 pF, 1 nF, 50 nF}: (<b>a</b>) original amplifier; (<b>b</b>) modified amplifier.</p>
Full article ">Figure 11
<p>EECT prototype during <span class="html-italic"><span class="underline">H</span><sub>dist</sub></span> measurement. Measuring set-up for |<span class="underline">ε</span><sub>I</sub>| (behind EECT).</p>
Full article ">Figure 12
<p>Current error |<span class="underline">ε</span><sub>I</sub>| in % at different frequencies and <span class="html-italic">PF</span>: 0.5 capacitive (blue), 1 (red), 0.5 inductive (black).</p>
Full article ">Figure 13
<p>Measured frequency response <span class="html-italic"><span class="underline">Y</span></span> with original and modified amplifier in regard to <span class="html-italic">C<sub>eq</sub></span>: (<b>a</b>) optimized Comp<sub>2</sub>; (<b>b</b>) non-optimized Comp<sub>2</sub>.</p>
Full article ">Figure 14
<p>Measured disturbance rejection—<span class="html-italic"><span class="underline">H</span><sub>dist</sub></span> of composite CT (grey) vs EECT with original amplifier with default <span class="html-italic">C<sub>eq</sub></span> (blue), original amplifier with increased <span class="html-italic">C<sub>eq</sub></span> (red) and modified amplifier with increased <span class="html-italic">C<sub>eq</sub></span> (green).</p>
Full article ">
15 pages, 3516 KiB  
Article
Multiple Quartz Crystals Connected in Parallel for High-Resolution Sensing of Capacitance Changes
by Vojko Matko
Sensors 2022, 22(13), 5030; https://doi.org/10.3390/s22135030 - 3 Jul 2022
Cited by 5 | Viewed by 2305
Abstract
We present a new highly sensitive, low-value capacitance sensor method that uses multiple quartz crystals connected in parallel inside the oscillator. In the experimental setup, the measured (sensible) reactance (capacitance) is connected in parallel to the total shunt capacitance of the quartz crystals, [...] Read more.
We present a new highly sensitive, low-value capacitance sensor method that uses multiple quartz crystals connected in parallel inside the oscillator. In the experimental setup, the measured (sensible) reactance (capacitance) is connected in parallel to the total shunt capacitance of the quartz crystals, oscillating in the oscillator. Because AT-cut crystals have a certain nonlinear frequency–temperature dependence, we use the switching mode method, by which we achieve a temperature compensation of the AT-cut crystals’ frequency–temperature characteristics in the temperature range between 050 °C. The oscillator switching method also compensates for any other influences on the frequency of the oscillator, such as ageing of the crystals and oscillator elements, supply voltage fluctuations, and other parasitic impedances in the oscillating circuit. Subsequently using two 50-ms-delayed switches between the measuring and reference capacitors, the experimental error in measuring the capacitance is lowered for measurements under a dynamic temperature variation in the range of 050 °C. The experimental results show that the switching method, which includes a multiple quartz connection and high-temperature compensation improvement of the quartz crystals’ characteristics, enables a sub-aF resolution. It converts capacitance changes in the range 10 zF200 fF to frequencies in the range 4 kHz100 kHz. Full article
(This article belongs to the Section Physical Sensors)
Show Figures

Figure 1

Figure 1
<p>The impedance curves for one, two, and three quartz crystals connected in parallel without (line and symbols) and with (symbols) the load capacitor with capacitance <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> in parallel. <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>r</mi> </msub> </mrow> </semantics></math> is the frequency ratio. The quartz crystal parameter values are <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi>fF</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>158.314</mn> <mo> </mo> <mi>mH</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> </mrow> </semantics></math> Ω, and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi>MHz</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 2
<p>The imaginary part of impedance as a function of the frequency ratio <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>r</mi> </msub> </mrow> </semantics></math> close to the antiresonant frequency of a single crystal (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1.0012499</mn> </mrow> </semantics></math> ). The dependencies are shown for one (Q), two (2Q), and three (3Q) crystals in series with and without the addition of the load capacitor with capacitance (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>Experimental setup for switching one, two, or three crystals (<math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>3</mn> </msub> </mrow> </semantics></math> ) connected in parallel and for switching of the reference (<math display="inline"><semantics> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mi>j</mi> <mi>ω</mi> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>) and measured (<math display="inline"><semantics> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mi>j</mi> <mi>ω</mi> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math>) reactance. For switching the crystals and realization of the switching method, a microcontroller is used. For measuring the frequency, a programable counter and LabVIEW software are used. A prototype of a low value reactance sensor includes the red-encircled elements.</p>
Full article ">Figure 4
<p>The frequency (<math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> and load capacitance (<math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </semantics></math> characteristics for one (Q), two (2Q), and three (3Q) quartz capacitors connected in parallel, with <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math> μH, <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>v</mi> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> = 1, and <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>25</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> </mrow> </semantics></math> is the shunt capacitance of one quartz crystal.</p>
Full article ">Figure 5
<p>Extended temperature dynamic frequency stability for <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>n</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>f</mi> <mi>r</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mrow> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>n</mi> </mrow> </msub> </mrow> <mo stretchy="true">¯</mo> </mover> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>f</mi> <mi>r</mi> </msub> </mrow> </semantics></math> if three quartz crystals are connected in parallel, where <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>v</mi> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>70</mn> <mo> </mo> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">H</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>3.459</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>3.450</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and the quartz crystal parameters <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi>fF</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>158.314</mn> <mo> </mo> <mi>mH</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> </mrow> </semantics></math> Ω. <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> </semantics></math> are the initial and final temperatures, respectively, and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> are the corresponding frequency differences <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Output frequency dynamic error, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>±</mo> <mrow> <mo>(</mo> <mrow> <mo>Δ</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>Δ</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, measured at <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> during the change in temperature from 24 °C to 29 °C, as shown in <a href="#sensors-22-05030-f005" class="html-fig">Figure 5</a>, for three quartz crystals connected in parallel, where <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>v</mi> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>70</mn> <mo> </mo> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">H</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>3.459</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mrow> <mi>l</mi> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>3.450</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and the quartz crystal parameters <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi>fF</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>158.314</mn> <mo> </mo> <mi>mH</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>4</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> </mrow> </semantics></math> Ω.</p>
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16 pages, 3710 KiB  
Article
Coordinated Reactive Power Control with a Variable Shunt Reactor and an Inverter-Based Wind Power Plant
by Seung-Ho Song and Soo-Bin Kim
Energies 2022, 15(13), 4739; https://doi.org/10.3390/en15134739 - 28 Jun 2022
Cited by 7 | Viewed by 2549
Abstract
Underground or submarine cables have a higher capacitance component than overhead lines, and they inject a large amount of capacitive reactive power into the system. A separate reactive power compensation device is required in order for a wind power plant (WPP) connected to [...] Read more.
Underground or submarine cables have a higher capacitance component than overhead lines, and they inject a large amount of capacitive reactive power into the system. A separate reactive power compensation device is required in order for a wind power plant (WPP) connected to the public network with a cable to meet the reactive power requirements required by the grid code. In this paper, a reactive power control using a variable shunt reactor (VSR) was proposed to satisfy the reactive power requirement required by the grid code for a WPP connected to the grid through a cable. The proposed reactive power control method compensates for the capacitive reactive power of the cable by using a VSR, and it follows the reactive power command through the reactive power control of a WPP. In the section where it is difficult to follow the WPP reactive power command only with the reactive power capacity of a WPP due to cable losses or a cable reactive power compensation error of the VSR, the reactive power control is additionally supported through the hysteresis control of the VSR. The proposed method satisfies the grid codes, and it enables fast and accurate reactive power control. The performance of the proposed method was verified through simulation using MATLAB/Simulink. Full article
(This article belongs to the Section F: Electrical Engineering)
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<p>Reactive power capability requirements in various grid codes [<a href="#B7-energies-15-04739" class="html-bibr">7</a>,<a href="#B8-energies-15-04739" class="html-bibr">8</a>,<a href="#B9-energies-15-04739" class="html-bibr">9</a>,<a href="#B10-energies-15-04739" class="html-bibr">10</a>].</p>
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<p>Configuration and reactive power control of wind power plant with HV cable and VSR.</p>
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<p>Block diagram for reactive power control of wind power plant [<a href="#B16-energies-15-04739" class="html-bibr">16</a>,<a href="#B17-energies-15-04739" class="html-bibr">17</a>].</p>
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<p>Effects of power transmission cable; (<b>a</b>) Equivalent π Circuit for a long transmission line and (<b>b</b>) WPP power capability curve at the PoC considering power losses due to the impedance of the transmission line.</p>
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<p>Winding arrangement of a VSR [<a href="#B5-energies-15-04739" class="html-bibr">5</a>].</p>
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<p>Block diagram of reactive power control of a VSR.</p>
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<p>Set–point change of reactive power control using a VSR.</p>
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<p>Block diagram of proposed reactive power control of a WPP with a VSR.</p>
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<p>Hysteresis control concept diagram; (<b>a</b>) Hysteresis control setting when cable reactive power compensation error of the VSR is capacitive; (<b>b</b>) Hysteresis control setting when cable reactive power compensation error of the VSR is inductive.</p>
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<p>Hysteresis control concept diagram; (<b>a</b>) Hysteresis control setting when cable reactive power compensation error of the VSR is capacitive; (<b>b</b>) Hysteresis control setting when cable reactive power compensation error of the VSR is inductive.</p>
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<p>Simulation model of wind power plant with HV cable and VSR using MATLAB/Simulink.</p>
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<p>Reactive power capability by reactive power control method.</p>
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<p>Reactive power capability by the reactive power control method.</p>
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<p>Set–point change control response of reactive power using only a VSR.</p>
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<p>Set–point change control response of reactive power using proposed method.</p>
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16 pages, 12385 KiB  
Article
Receiver Analog Front-End Cascading Transimpedance Amplifier and Continuous-Time Linear Equalizer for Signals of 5 to 30 Gb/s
by Pragada Venkata Satya Challayya Naidu and Chih-Wen Lu
Electronics 2022, 11(10), 1546; https://doi.org/10.3390/electronics11101546 - 12 May 2022
Cited by 1 | Viewed by 3880
Abstract
A 5–30 Gb/s receiver analog front-end (AFE) cascading transimpedance amplifier (TIA) and continuous-time linear equalizer (CTLE) were implemented using a Taiwan Semiconductor 180 nm process. The system comprises a two-stage differential input pair CTLE, TIA, and a differential termination resistor Rm. [...] Read more.
A 5–30 Gb/s receiver analog front-end (AFE) cascading transimpedance amplifier (TIA) and continuous-time linear equalizer (CTLE) were implemented using a Taiwan Semiconductor 180 nm process. The system comprises a two-stage differential input pair CTLE, TIA, and a differential termination resistor Rm. A source-degenerated transconductance stage was adopted in the CTLE, and source follower and shunt feedback resistor stages were adopted in the TIA. The proposed CTLE could achieve high frequencies by altering the tail current with fixed degenerate capacitance CS and resistance RS. The proposed AFE achieved high bandwidth, and the use of a feedback resistor Rf and inductor Lf improved its high-frequency performance. Simulation results revealed that the CTLE can compensate for 16 dB of channel loss at a 3 GHz Nyquist frequency and can open closed eyes in a 6 Gb/s non-return-to-zero signal with a bit error rate of 0.16 × 10−12 for a 231 − 1 pseudorandom binary sequence input. The AFE could compensate for 12 dB of channel loss at a 15 GHz Nyquist frequency and can open closed eyes in a 30 Gb/s PAM4 signal from a pseudorandom binary sequence input; it consumed 27 mW of power at 1.8 V. Full article
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<p>Block Diagram of a Receiver with an AFE.</p>
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<p>Schematic of Conventional CTLE.</p>
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<p>Single-ended Bode Plot of the CTLE.</p>
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<p>Schematic of Proposed CTLE.</p>
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<p>Single-ended Bode Plot of the Proposed CTLE.</p>
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<p>Simple TIA Topology with feedback resistor <span class="html-italic">R</span><sub>f</sub>.</p>
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<p>Schematic of Single-ended TIA.</p>
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<p>Single end of the TIA.</p>
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<p>Receiver AFE Architecture.</p>
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<p>Variations in Channel Characteristics for Lengths of 2 m–8 m at 1.5 GHz.</p>
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<p>Simulated Frequency Response for the CTLE.</p>
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<p>Simulated AC response of the CTLE with and without the Channel.</p>
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<p>Simulated Output Eyes (<b>a</b>) with CTLE Enabled and (<b>b</b>) with CTLE Disabled.</p>
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<p>Simulated Eye Diagram. (1) 0 level at 1.33 V; (2) 1 level at 1.52 V; (3) and (4) rise and fall time of 102.2 and 95.1151 ps, respectively; (5) and (6) eye height and width of 118.882 mV and 196.79 ps, respectively.</p>
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<p>(<b>a</b>) Horizontal Histogram and (<b>b</b>) Vertical Histogram of eye diagrams for the 0 and 1 levels.</p>
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<p>Simulated BER(t) bathtub curves for the 6 Gb/s NRZ signal.</p>
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<p>Simulated frequency response for the AFE. (<b>a</b>) 12 dB by tuning <span class="html-italic">V<sub>bias</sub></span> from −80, 0, and 80 mV and (<b>b</b>) from −80 to 160 mV.</p>
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<p>Eye diagram AFE for PAM4 signal.</p>
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<p>(<b>a</b>) Histogram of the eye diagram reveals eye widths for levels 0, 1, 2, and 3. (<b>b</b>) Threshold histogram of the eye diagram reveals the bit period of levels 0/1, 1/2, and 2/3.</p>
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<p>(<b>a</b>) Histogram of the eye diagram reveals eye widths for levels 0, 1, 2, and 3. (<b>b</b>) Threshold histogram of the eye diagram reveals the bit period of levels 0/1, 1/2, and 2/3.</p>
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19 pages, 7055 KiB  
Article
Research on Oscillation Suppression Methods in Shunt Active Power Filter System
by Rui Hou, Pengfei Wang, Jian Wu and Dianguo Xu
Energies 2022, 15(9), 3125; https://doi.org/10.3390/en15093125 - 25 Apr 2022
Cited by 5 | Viewed by 1686
Abstract
The shunt active power filter (SAPF) system oscillation is a massive threat to the security and stability of the power grid. This study classifies SAPF oscillation into two categories according to the difference in mechanisms. The SAPF oscillation in one category is caused [...] Read more.
The shunt active power filter (SAPF) system oscillation is a massive threat to the security and stability of the power grid. This study classifies SAPF oscillation into two categories according to the difference in mechanisms. The SAPF oscillation in one category is caused by the resonant characteristics of a switching noise filter and is called external loop amplification. The SAPF oscillation in the other category is induced by the presence of a capacitor in the load current for SAPF and is called self-excited oscillation. Unlike previous studies, this study tried to reveal the internal relationship between the two kinds of SAPF oscillation, present a general shunt virtual-damping-based SAPF oscillation suppression strategy covering the previous resonant damping method, and provide the discrete domain stability criterion of the control system. The sampling frequency was at least six times the resonant frequency. The stability region was enlarged with an increase in the sampling frequency and narrowed with a rise in the resonant frequency. As to the harmful self-excited oscillation problem, this study proposes a composite control strategy combining selective harmonic compensation and grid-side current feedback. Moreover, this study considers the more general resistance–inductance–capacitance load situations and analyzes the stability of the SAPF–Thyristor Switched Capacitor (TSC) hybrid compensation system. Simulations and experiments demonstrated that the proposed compound control method can reduce the primary harmonics of the system by more than 90% and has a better oscillation suppression performance than previous suppression methods. In particular, if we selected the TSC series reactance rate following more than 6%, self-excited oscillation could usually be avoided. Full article
(This article belongs to the Special Issue Smart Grids and Renewables)
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<p>Positions of a virtual resistor.</p>
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<p>Bode diagram of various values of <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>pc</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Frequency response characteristics: (<b>a</b>) magnitude; (<b>b</b>) phase.</p>
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<p>Block diagram of the digital current controller.</p>
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<p>Variation of <math display="inline"><semantics> <mrow> <msub> <mi>K</mi> <mrow> <mi>max</mi> </mrow> </msub> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Diagram of poles and zeros.</p>
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<p>The system’s single-phase equivalent circuit (<b>a</b>) without virtual damping; (<b>b</b>) with virtual damping.</p>
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<p>Control block diagrams of the system (<b>a</b>) without virtual damping; (<b>b</b>) with virtual damping.</p>
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<p>Magnitude characteristic of the resonance damping system.</p>
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<p>Block diagram of the compound control system.</p>
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<p>Bode diagram of the compound control system.</p>
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<p>Analysis of hybrid system: (<b>a</b>) single-phase equivalent circuit; (<b>b</b>) control diagram.</p>
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<p>Bode diagram of the hybrid system.</p>
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<p>Grid current waveforms with different values of <span class="html-italic">K</span> (<b>a</b>) when <span class="html-italic">K</span> = 0; (<b>b</b>) when <span class="html-italic">K</span> = 0.4; (<b>c</b>) when <span class="html-italic">K</span> = 1.3; (<b>d</b>) when <span class="html-italic">K</span> = 1.6.</p>
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<p>Variation of grid current with <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi mathvariant="normal">r</mi> </msub> </mrow> </semantics></math> and <span class="html-italic">T</span> (<b>a</b>) when <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>270</mn> <mrow> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">F</mi> </mrow> </mrow> </semantics></math>; (<b>b</b>) when <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>32</mn> <mrow> <mtext> </mtext> <mi>kHz</mi> </mrow> </mrow> </semantics></math>.</p>
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<p>Photo of laboratory prototype.</p>
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<p>Experimental waveforms of virtual damping (CH1—SAPF current before LCL filter; CH2—SAPF current after LCL filter; CH3—grid current) (<b>a</b>) without virtual damping; (<b>b</b>) with virtual damping.</p>
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<p>The filtered grid current performance in different cases with a capacitive load: (<b>a</b>) case I, full harmonic compensation; (<b>b</b>) case II, selective harmonic compensation; (<b>c</b>) case III, combining selective harmonic compensation and resonance damping strategies; (<b>d</b>) case IV, the proposed compound control; (<b>e</b>) comparison of grid current harmonic in three cases.</p>
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<p>Effects on compound control (CH1—load current containing capacitor; CH2—SAPF current; CH3—grid current) (<b>a</b>) when <span class="html-italic">K</span><sub>p</sub> = 0; (<b>b</b>) when <span class="html-italic">K</span><sub>p</sub> = 1.5.</p>
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<p>Grid current of hybrid system (<b>a</b>) when <span class="html-italic">β</span> = 2%; (<b>b</b>) when <span class="html-italic">β</span> = 6%.</p>
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<p>Experimental waveforms of hybrid system (CH1—SAPF current; CH2—TSC current; CH3—load current; CH4—grid current).</p>
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11 pages, 30056 KiB  
Article
Maximizing Transfer Efficiency with an Adaptive Wireless Power Transfer System for Variable Load Applications
by Jung-Hoon Cho, Byoung-Hee Lee and Young-Joon Kim
Energies 2021, 14(5), 1417; https://doi.org/10.3390/en14051417 - 4 Mar 2021
Cited by 4 | Viewed by 2690
Abstract
Electronic devices usually operate in a variable loading condition and the power transfer efficiency of the accompanying wireless power transfer (WPT) method should be optimizable to a variable load. In this paper, a reconfigurable WPT technique is introduced to maximize power transfer efficiency [...] Read more.
Electronic devices usually operate in a variable loading condition and the power transfer efficiency of the accompanying wireless power transfer (WPT) method should be optimizable to a variable load. In this paper, a reconfigurable WPT technique is introduced to maximize power transfer efficiency in a weakly coupled, variable load wireless power transfer application. A series-series two-coil wireless power network with resonators at a frequency of 150 kHz is presented and, under a variable loading condition, a shunt capacitor element is added to compensate for a maximum efficiency state. The series capacitance element of the secondary resonator is tuned to form a resonance at 150 kHz for maximum power transfer. All the capacitive elements for the secondary resonators are equipped with reconfigurability. Regardless of the load resistance, this proposed approach is able to achieve maximum efficiency with constant power delivery and the power present at the load is only dependent on the input voltage at a fixed operating frequency. A comprehensive circuit model, calculation and experiment is presented to show that optimized power transfer efficiency can be met. A 50 W WPT demonstration is established to verify the effectiveness of this proposed approach. Full article
(This article belongs to the Special Issue Research on Wireless Power Transfer System)
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<p>(<b>a</b>) The circuit model of a conventional wireless power transfer (WPT) system. (<b>b</b>) Equivalent circuit model of the secondary resonator represented by a reflected impedance, <math display="inline"><semantics> <mrow> <msub> <mi>Z</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>The power transfer efficiency of a conventional WPT system with a variable loading condition at different coupling coefficient values.</p>
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<p>WPT characteristics respect to load resistance. (<b>a</b>) The required inductance of the secondary resonator for maximum efficiency. (<b>b</b>) Power transfer efficiency is displayed for different secondary inductance values.</p>
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<p>Schematic of the proposed WPT system.</p>
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<p>Power transfer efficiency as a function of frequency with different <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </semantics></math> condition. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>100</mn> <mrow> <mtext> </mtext> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>500</mn> <mrow> <mtext> </mtext> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>.</p>
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<p>Calculated efficiency and normalized output power (w.r.t. its maximum value) as a function of frequency when <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </semantics></math> is optimized to a 100 Ω load.</p>
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<p>Design process of the proposed work.</p>
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<p>A plot of the transfer efficiency as a function of load. Solid line and the dot represent calculation and measurement, respectively. Note that the solid black dot is measured using manually optimized capacitors and the empty black dot is measured using 4-channel relay capacitor network.</p>
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<p>The output power at the load respect to load variation with different direct current (DC) voltage at inverter. The solid and empty dot denotes measurement using manually optimized capacitor and 4-channel relay capacitor network, respectively. Note that the amount of power delivered to the load does not depend on the load resistance.</p>
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<p>Proposed reconfigurable WPT system in this work.</p>
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<p>Photograph of the measurement setup.</p>
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19 pages, 17222 KiB  
Article
Modified Modeling and System Stabilization of Shunt Active Power Filter Compensating Loads with μF Capacitance
by Yuqi Bing, Daozhuo Jiang, Yiqiao Liang, Chongxi Jiang, Tianxiang He, Lei Yang and Pengfei Hu
Energies 2019, 12(11), 2084; https://doi.org/10.3390/en12112084 - 31 May 2019
Cited by 8 | Viewed by 3031
Abstract
The interactions between shunt active power filter (APF) and capacitance load tend to result in stability problems and resonance. The conventional model of a shunt APF is not precise enough to reflect this phenomenon. To address it, this paper proposes a modified shunt [...] Read more.
The interactions between shunt active power filter (APF) and capacitance load tend to result in stability problems and resonance. The conventional model of a shunt APF is not precise enough to reflect this phenomenon. To address it, this paper proposes a modified shunt APF system model to accurately reflect various stability problems. This paper also studies the mechanism of positive feedback resonance brought by capacitance load and proposes a modified hybrid controller to improve the stable margin of the system, making the shunt APF work stably under different working conditions where there are μF capacitors on the demand side. The correctness and validity of the proposed strategy are verified by simulation analysis and prototype experiments. Full article
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Figure 1

Figure 1
<p>Structure and control scheme of a three-phase four-wire shunt active power filter system.</p>
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<p>Scheme of hybrid repetitive controller.</p>
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<p>Conventional model of a hybrid repetitive controlled shunt active power filter.</p>
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<p>Nyquist diagram of <span class="html-italic">H(z)</span> for shunt APF system.</p>
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<p>Simulated waveform of grid current under different conditions (parameters from <a href="#energies-12-02084-t001" class="html-table">Table 1</a>).</p>
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<p>Simulated waveform of grid current under different conditions (repeated simulation of [<a href="#B22-energies-12-02084" class="html-bibr">22</a>]).</p>
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<p>Modified model of shunt active power filter system.</p>
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<p>External circuit of shunt active power filter system.</p>
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<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>
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<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>
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<p>Poles of <span class="html-italic">T(z)</span> with change of capacitance load.</p>
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<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>
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<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>
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<p>Bode diagram of <span class="html-italic">P(z)</span> under different load conditions.</p>
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<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>
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<p>Magnitude-frequency diagram of <span class="html-italic">S(z)P(z)</span> when controller is before or after modification.</p>
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<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>
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<p>Nyquist diagram of stability criterion <span class="html-italic">H(z)</span> of modified hybrid controller with capacitance load.</p>
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<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>
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<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>
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<p>Experimental 75 kVA shunt active power filter prototype.</p>
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<p>Waveforms of grid current and its harmonic spectra carrying active load and three-phase rectifier load without shunt APF prototype.</p>
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<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>
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<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>
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<p>Waveforms of capacitor current.</p>
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<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>
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<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>
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Article
High Resolution Switching Mode Inductance-to-Frequency Converter with Temperature Compensation
by Vojko Matko and Miro Milanović
Sensors 2014, 14(10), 19242-19259; https://doi.org/10.3390/s141019242 - 16 Oct 2014
Cited by 22 | Viewed by 6365
Abstract
This article proposes a novel method for the temperature-compensated inductance-to-frequency converter with a single quartz crystal oscillating in the switching oscillating circuit to achieve better temperature stability of the converter. The novelty of this method lies in the switching-mode converter, the use of [...] Read more.
This article proposes a novel method for the temperature-compensated inductance-to-frequency converter with a single quartz crystal oscillating in the switching oscillating circuit to achieve better temperature stability of the converter. The novelty of this method lies in the switching-mode converter, the use of additionally connected impedances in parallel to the shunt capacitances of the quartz crystal, and two inductances in series to the quartz crystal. This brings a considerable reduction of the temperature influence of AT-cut crystal frequency change in the temperature range between 10 and 40 °C. The oscillator switching method and the switching impedances connected to the quartz crystal do not only compensate for the crystal’s natural temperature characteristics but also any other influences on the crystal such as ageing as well as from other oscillating circuit elements. In addition, the method also improves frequency sensitivity in inductance measurements. The experimental results show that through high temperature compensation improvement of the quartz crystal characteristics, this switching method theoretically enables a 2 pH resolution. It converts inductance to frequency in the range of 85–100 µH to 2–560 kHz. Full article
(This article belongs to the Special Issue Smart Materials for Switchable Sensors)
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<p>Schematic representation of the inductance-to-frequency converter.</p>
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<p>Experimental circuit and final inductance-to-frequency converter design with connection pins for industrial use.</p>
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<p>Inductive frequency characteristics <span class="html-italic">f</span><sub>0</sub> (for different values of capacitance <span class="html-italic">C</span><sub>10</sub> in parallel to the crystal at T = 25 °C).</p>
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<p>Non-compensated oscillator frequency <span class="html-italic">Δf</span><sub>0</sub>/<span class="html-italic">f</span><sub>0</sub> characteristics variation depending on the temperatures <span class="html-italic">T</span><sub>1</sub>, <span class="html-italic">T</span><sub>2</sub> and <span class="html-italic">T</span><sub>3</sub> and on <span class="html-italic">L</span><sub>x</sub> (<span class="html-italic">C</span><sub>10</sub> = 8 pF).</p>
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<p>Switching mode compensated oscillator` s frequency <span class="html-italic">Δ</span>(<span class="html-italic">f</span><sub>01</sub> − <span class="html-italic">f</span><sub>02</sub>)/<span class="html-italic">f</span><sub>02</sub> characteristics variation depending on the temperatures <span class="html-italic">T</span><sub>1</sub>, <span class="html-italic">T</span><sub>2</sub> and <span class="html-italic">T</span><sub>3</sub> and on <span class="html-italic">L</span><sub>x</sub> (<span class="html-italic">C</span><sub>10</sub> = 8 pF, <span class="html-italic">L</span><sub>ref</sub> = 85 μH, <span class="html-italic">f</span><sub>Syn</sub> = 1 Hz).</p>
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<p>Compensated frequency characteristics for two different values of <span class="html-italic">C</span><sub>10</sub> at <span class="html-italic">L</span><sub>ref</sub> = 85 μH.</p>
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<p>(<b>A</b>) Extended temperature dynamic frequency instability for <span class="html-italic">f</span><sub>01</sub> and <span class="html-italic">f</span><sub>02</sub>; (<b>B</b>) temperature shock (25 °C–37 °C). <span class="html-italic">f</span><sub>Syn</sub> = 1 Hz.</p>
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<p>Output frequency dynamic variation of <span class="html-italic">f</span><sub>out</sub> during the change of temperature from 25 °C to 37 °C and back to 25 °C (measurement time: 0–100 s, <span class="html-italic">f</span><sub>out</sub> = <span class="html-italic">f</span><sub>02</sub> − <span class="html-italic">f</span><sub>01</sub>, <span class="html-italic">L</span><sub>x</sub> = 85.001 μH, <span class="html-italic">L</span><sub>ref</sub> = 85 μH).</p>
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<p>Output frequency dynamic error <span class="html-italic">Δf</span><sub>out</sub> (ppm) during the change of temperature from 25 °C to 37 °C and back to 25 °C (<a href="#f7-sensors-14-19242" class="html-fig">Figures 7</a> and <a href="#f8-sensors-14-19242" class="html-fig">8</a>).</p>
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