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<front>
<journal-meta>
<journal-id journal-id-type="redalyc">3442</journal-id>
<journal-title-group>
<journal-title specific-use="original" xml:lang="es">TecnoLógicas</journal-title>
</journal-title-group>
<issn pub-type="ppub">0123-7799</issn>
<issn pub-type="epub">2256-5337</issn>
<publisher>
<publisher-name>Instituto Tecnológico Metropolitano</publisher-name>
<publisher-loc>
<country>Colombia</country>
<email>tecnologicas@itm.edu.co</email>
</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="art-access-id" specific-use="redalyc">344255453009</article-id>
<article-id pub-id-type="doi">https://doi.org/10.22430/22565337.781</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Artículos de investigación</subject>
</subj-group>
</article-categories>
<title-group>
<article-title xml:lang="en">Quasi-switched inverter using space vector pulse width modulation with triangular comparison for photovoltaic applications</article-title>
<trans-title-group>
<trans-title xml:lang="es">Inversor cuasi-conmutado
usando modulación de ancho de pulso del vector espacial con comparación
triangular para aplicaciones fotovoltaicas</trans-title>
</trans-title-group>
<alt-title alt-title-type="lt-running">TecnoLógicas,
ISSN-p 0123-7799 / ISSN-e 2256-5337, Vol. 21, No. 42, mayo-agosto de 2018, pp.
95-110</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Moran</surname>
<given-names>Iván F.</given-names>
</name>
<xref ref-type="aff" rid="aff1"/>
<email>ivan.moran@correounivalle.edu.co</email>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Restrepo</surname>
<given-names>José A.</given-names>
</name>
<xref ref-type="aff" rid="aff2"/>
<email>jarestrepo@utn.edu.ec</email>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Orozco-Gutierrez</surname>
<given-names>Martha L.</given-names>
</name>
<xref ref-type="aff" rid="aff3"/>
<email>martha.orozco@correounivalle.edu.co</email>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Ramirez-Scarpetta</surname>
<given-names>José M.</given-names>
</name>
<xref ref-type="aff" rid="aff4"/>
<email>jose.ramirez@correounivalle.edu.co</email>
</contrib>
</contrib-group>
<aff id="aff1">
<institution content-type="original">Electronic Engineer, Escuela de Ingeniería
Eléctrica y Electrónica, Universidad del Valle, Cali-Colombia,
ivan.moran@correounivalle.edu.co</institution>
<institution content-type="orgname">Universidad del Valle</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff2">
<institution content-type="original">PhD.
in Electrical Engineering and Electronics, Departamento de Electrónica y Circuitos, Universidad
Simón Bolívar, Caracas-Venezuela restrepo@usb.ve. Facultad de
Ingeniería en Ciencias Aplicadas, Universidad Técnica del Norte, Ibarra-Ecuador, jarestrepo@utn.edu.ec</institution>
<institution content-type="orgname">Universidad Técnica del Norte</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff3">
<institution content-type="original">PhD. in Engineering,
Escuela de Ingeniería Eléctrica y Electrónica, Universidad del Valle, Cali-
Colombia, martha.orozco@correounivalle.edu.co 

 </institution>
<institution content-type="orgname">Universidad del Valle</institution>
<country country="CO">Colombia</country>
</aff>
<aff id="aff4">
<institution content-type="original">PhD. in Control Systems, Escuela de
Ingeniería Eléctrica y Electrónica, Universidad del Valle, Cali-Colombia,
jose.ramirez@correounivalle.edu.co</institution>
<institution content-type="orgname">Universidad del Valle</institution>
<country country="CO">Colombia</country>
</aff>
<pub-date pub-type="epub-ppub">
<season>May-August 2019</season>
<year>2018</year>
</pub-date>
<volume>21</volume>
<issue>42</issue>
<fpage>95</fpage>
<lpage>110</lpage>
<history>
<date date-type="received" publication-format="dd mes yyyy">
<day>15</day>
<month>02</month>
<year>2018</year>
</date>
<date date-type="accepted" publication-format="dd mes yyyy">
<day>04</day>
<month>04</month>
<year>2018</year>
</date>
</history>
<permissions>
<copyright-statement>Los artículos publicados por la revista TecnoLógicas son obras literarias y científicas protegidas por las leyes de Derecho de Autor. Con la firma de la Declaración de Originalidad, así como con la entrega de la obra para su consideración o posible publicación, los autor autorizan de forma gratuita, al INSTITUTO TECNOLÓGICO METROPOLITANO –ITM- para la publicación, reproducción, comunicación, distribución y transformación de la obra e igualmente declaran bajo la gravedad del juramento que la obra es original e inédita de exclusiva autoría de los remitentes.</copyright-statement>
<copyright-year>2018</copyright-year>
<copyright-holder>Instituto Tecnológico Metropolitano</copyright-holder>
<ali:free_to_read/>
<license xlink:href="https://creativecommons.org/licenses/by/3.0/">
<ali:license_ref>https://creativecommons.org/licenses/by/3.0/</ali:license_ref>
<license-p>Esta obra está bajo una Licencia Creative Commons Atribución 3.0 Internacional.</license-p>
</license>
</permissions>
<abstract xml:lang="en">
<title>Abstract</title>
<p> This work analyzes a prototype of a quasi-switched boost inverter (qSBI) feeding an isolated resistive load from a DC source. The use of spatial vector pulse width modulation (SPWM) with triangular comparison is proposed to increase the qSBI gain factor, and its performance is contrasted with other types of spatial vector modulations, such as discontinuous modulations. To verify the validity of the method for voltage range extension in the qSBI converter, a semi-customized test platform was developed. This platform uses a DSP floating point card (Analog Devices ADSP-21369) for processing and control strategies and an interface card that includes a programmable logic array (FPGA) from Xilinx (Spartan-3), which allows to develop the synchronized modulation qSBI needs. The experimental results show improvements in the performance of the qSBI converter in terms of gain factor, voltage reduction in the capacitor, and input current profiles. Discontinuous space vector modulation strategies do not perform well when compared to continuous SVPWM or SPWM modulations, because the ripple levels in the currents taken from the PV module are approximately twice as great as in continuous modulation techniques. Finally, the usefulness of a qSBI as PV microinverter is confirmed by two practical experimental cases of a PV photovoltaic system with a maximum power point adjustment algorithm (MPPT).  </p>
</abstract>
<trans-abstract xml:lang="es">
<title>Resumen</title>
<p> Este trabajo analiza un prototipo para un inversor elevador cuasi-conmutado (qSBI) alimentando una carga resistiva aislada desde una fuente de CC. Se propone el uso de una modulación de ancho de pulso de vectores espaciales (SPWM) con comparación triangular que genera un incremento en el factor de ganancia del qSBI, y se contrasta su desempeño con otro tipo de modulaciones de vectores espaciales, tales como las modulaciones discontinuas. Para verificar la validez de la extensión de rango de tensión en el convertidor qSBI, se desarrolló una plataforma de pruebas semi-personalizada. Esta plataforma utiliza una tarjeta DSP de punto flotante (Analog Devices ADSP-21369) para el procesamiento de las estrategias de control, y una tarjeta de interfaz que incluye un arreglo lógico programable (FPGA) de Xilinx (Spartan-3), que permite desarrollar la modulación sincronizada que el qSBI necesita. Los resultados experimentales demuestran mejoras en el desempeño del convertidor qSBI en cuanto al factor de ganancia, reducción del estrés de voltaje en el capacitor y los perfiles de corriente de entrada. Las estrategias discontinuas de modulación del vector espacial no presentan un buen desempeño cuando se compara con las modulaciones continuas SVPWM o SPWM, ya que los niveles de rizado en las corrientes tomadas del módulo PV son de aproximadamente el doble que en el caso de las técnicas de modulación continuas. Finalmente, el uso del convertidor qSBI como microinversor es puesto en evidencia por dos casos experimentales prácticos de un sistema fotovoltaico PV con un algoritmo de ajuste del máximo punto de potencia (MPPT).  </p>
</trans-abstract>
<kwd-group xml:lang="en">
<title>Keywords</title>
<kwd>Quasi-Switched Boost Inverter</kwd>
<kwd>Space Vector
Modulation</kwd>
<kwd>Sinusoidal Modulation</kwd>
<kwd>Embedded System</kwd>
<kwd>PV Microinverter</kwd>
</kwd-group>
<kwd-group xml:lang="es">
<title>Palabras clave</title>
<kwd>Inversor Elevador cuasi-Conmutado</kwd>
<kwd>Modulación del Vector
Espacial</kwd>
<kwd>Modulación Senoidal</kwd>
<kwd>Sistema Embebido</kwd>
<kwd>Microinversor PV</kwd>
</kwd-group>
<counts>
<fig-count count="15"/>
<table-count count="0"/>
<equation-count count="3"/>
<ref-count count="17"/>
</counts>
</article-meta>
</front>
<body>
<sec>
<title/>
<p>
<disp-quote>
<p> Cómo citar / How to cite </p>
<p> F. Moran, J. A. Restrepo, M. L. Orozco-Gutierrez, y J. M. Ramirez-Scarpetta, Quasi-switched inverter using space vector pulse width modulation with triangular comparison for photovoltaic applications. TecnoLógicas, vol. 21, no. 42, pp. 95-110, 2018.</p>
</disp-quote>
</p>
</sec>
<sec>
<title>1. INTRODUCTION</title>
<p> Voltage Source Inverters (VSIs) are an important part for power flow control in electrical vehicles, motor/generator drives, flexible power transmission, and integration of renewable generation units (photovoltaic panels, fuel cells, batteries, etc.) into the grid, among others. In the last two decades, the Z-source inverter (ZSI) and Switched boost inverters (SBI) began to appear in scientific literature for solving some drawbacks of VSIs. One of such drawbacks is that AC output voltage cannot be higher than the available DC source and thus extra power stages are needed for applications demanding higher voltage levels [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>]. In 2002 and 2003 Peng [<xref ref-type="bibr" rid="redalyc_344255453009_ref2">2</xref>], proposed the ZSI as a robust alternative to the VSI with the capacity to increase the output voltage. Some important advantages of ZSI include the ability to boost-buck voltage in a single-stage power conversion, allow tolerance to one-leg short circuit, minimize component count and reduce costs. Also, in ZSI converters, the output waveform presents less distortion, mainly because both power devices in a leg can turn on at the same time. Other authors [<xref ref-type="bibr" rid="redalyc_344255453009_ref3">3</xref>] have proposed alternative topologies based on ZSIs. For example, [<xref ref-type="bibr" rid="redalyc_344255453009_ref4">4</xref>] proposes a bidirectional ZSI (BZSI), in which a bidirectional switch replaces the input diode. The BZSI admits bidirectional power exchange between AC and DC. Meanwhile, an improved ZSI (IZSI) [<xref ref-type="bibr" rid="redalyc_344255453009_ref5">5</xref>] uses the same elements found in the original ZSI, but in different positions, thus allowing a decrease in the capacitor’s voltage stress. On the other hand, the quasi-resonant soft-switching Z-source inverter (QRSSZSI) [<xref ref-type="bibr" rid="redalyc_344255453009_ref6">6</xref>] adds a quasi-resonant network for soft-switching and it increases the overall efficiency of the converter. Other extended topologies use switched inductor and/or capacitor circuits that increase the boost capacity and power density, which results in increased complexity. The ZSI converter has been the basic topology for other converters [<xref ref-type="bibr" rid="redalyc_344255453009_ref3">3</xref>] that always aim at single stage conversion and buck-boost characteristics. Another objective of ZSI-based converters is to decrease the size of passive components, reduce leakage current in the system, and improve output voltage quality, among others. On the other hand, the switched boost inverter (SBI) proposed in [<xref ref-type="bibr" rid="redalyc_344255453009_ref7">7</xref>] uses less passive components than the ZSI and one more active switch. Besides, it fits better in low power applications such as photovoltaic (PV) systems and micro grids. </p>
<p> Photovoltaic (PV) solar energy use has experienced an exponential increase in the last decade. The growing results of PV applications are mainly due to changes in energy and environmental policies, optimization of manufacturing processes of PV panels and power electronic devices, and new research on materials and electronic devices, among others. In PV systems, mismatching produced by shadows, aging and tolerances in manufacturing, result in large power losses. Recently, panel reconfiguration and distributed power processing (DPP) systems have shown promising results to overcome the limits imposed by mismatching [<xref ref-type="bibr" rid="redalyc_344255453009_ref8">8</xref>]. DPP systems use power electronics solutions dedicated to small portions of the PV array, usually a string or single panel (microinverter). In PV microinverters, there is a panel associated with a power converter. The converter must have a high boost factor because the voltage range in commercial PV panels is low, typically between 20V to 40V. An advantage of inverter-per-panel DC-AC power conversion is the capacity to extract the maximum available power from each panel by using a MPPT algorithm in the DC-to-DC stage. Moreover, PV microinverters allow for plug-and-play connectivity to the grid. Therefore, PV systems based on this technology are scalable and the impact of faults is lower than in centralized or string configurations. Additionally, the decrease in power management reduces the demands on the DC wire [<xref ref-type="bibr" rid="redalyc_344255453009_ref9">9</xref>]. However, a disadvantage of PV microinverters is the installation cost, as they require as many microinverters as panels. Also, the number of power converters with non-unitary efficiency affects the installation’s power harvesting. On the other hand, string configurations use a DC-to-DC converter for a group of PV panels, thus reducing the boost voltage factor in comparison with PV microinverter technology. The main weakness of string configuration is the reduced robustness under mismatching conditions. Additionally, typical string configurations provide a single phase solution on the AC side. A distribution of the control means that more power converters with higher efficiency and voltage boost are needed. For this type of applications, the previously mentioned ZSI and SBI converters seem to be suitable solutions.  </p>
<p> The Quasi-Switched Boost Inverter (qSBI) belongs to the class of SBI topologies. The qSBI has low capacitor voltage in a dc-linked type, with high boost voltage and continuous input current [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>]. Previous studies by other authors present complete analyses of the qSBI [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>],[<xref ref-type="bibr" rid="redalyc_344255453009_ref10">10</xref>]. This work implements a modulation technique for space vector PWM to increase the boost voltage factor of the qSBI converter, which makes it suitable to be used in PV microinverters. This paper is organized as follows: Section two explains the general performance of a qSBI. Section three details the PWM control techniques and describes the experimental prototype. Section 4 presents the experimental results using a fixed DC source as well as a DC source based on a single PV panel and string configuration. The paper ends with conclusions and future works.</p>
</sec>
<sec>
<title>2. qSBI
TOPOLOGY</title>
<p>The topology of a qSBI converter has higher efficiency and boost gain
than common boost converters (<xref ref-type="fig" rid="gf1">Fig.1</xref>) [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>]. Such topology uses one more active switch in comparison with others
boost inverters, such as the ZSI, but it requires less passive components.
Additionally, the qSBI can provide a continuous input current.</p>
<p>
<fig id="gf1">
<label>Fig. 1.</label>
<caption>
<title>One-line diagram of the Three-Phase quasi-Switched
Boost Inverter.</title>
</caption>
<alt-text>Fig. 1. One-line diagram of the Three-Phase quasi-Switched
Boost Inverter.</alt-text>
<graphic xlink:href="344255453009_gf1.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p>As shown in <xref ref-type="fig" rid="gf1">Fig.1</xref>, a qSBI converter is essentially formed by two
cascaded power stages, a boost DC/DC stage and a Voltage-Source Inverter (VSI)
stage. When the VSI outputs space vectors zero (<inline-graphic xlink:href="344255453009_gi2.png"/> or <inline-graphic xlink:href="344255453009_gi3.png"/> in <xref ref-type="fig" rid="gf2">Fig.2</xref>), the voltage in the DC
bus ( <italic>V<sub>pn</sub>
</italic>) has no effect on these vectors’
value. This opens the possibility of using the VSI to establish a path for
energy storage in the boost inductance <italic>L<sub>a</sub>
</italic>, an operating condition known as
shoot-through state. While the VSI puts out space vectors zero, the
shoot-through state uses any VSI leg while switching <italic>S<sub>0 </sub>
</italic>to feed the boost inductance from the PV
generator. This stores energy in inductance<italic> L<sub>a</sub>
</italic>, as described above, and at the
same time capacitor <italic>C<sub>a</sub>
</italic> discharges into the load. The other state
(non-shoot-through state) occurs when switch <italic>S<sub>0</sub>
</italic>
<sub/>opens while removing the VSI short-circuit.
During the non-shoot-through state, inductor<italic> L<sub>a</sub>
</italic> transfers energy from the DC voltage source (<italic>V<sub>pn</sub>
</italic>)to the load and to capacitor <italic>C<sub>a</sub>
</italic>.</p>
<p>
<fig id="gf2">
<label>Fig. 2.</label>
<caption>
<title>Space vectors in the voltage source inverter
(VSI).</title>
</caption>
<alt-text>Fig. 2. Space vectors in the voltage source inverter
(VSI).</alt-text>
<graphic xlink:href="344255453009_gf2.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p>
<xref ref-type="fig" rid="gf3">Fig.3</xref> shows the equivalent circuits for the two qSBI’s stable states,
where <italic>r<sub>s</sub>
</italic> is the power devices’ resistance; <italic>r<sub>L</sub>
</italic>    and <italic>r<sub>C</sub>
</italic>, the parasitic resistance of the
inductor and the equivalent series resistance (ESR) of the capacitor; i<italic>
<sub>0</sub>
</italic>, the current in the load; R, the
load; and<italic> r<sub>D</sub>
</italic>, the diode’s resistance. Diodes <italic>D<sub>1</sub>
</italic> and <italic>D<sub>2</sub>
</italic>    do not conduct during the shoot-through state,
while switch <italic>S<sub>0</sub>
</italic> turns on and the VSI closes the path by
turning on all its (high side and low side) power devices, which results in the
equivalent circuit shown in <xref ref-type="fig" rid="gf3">Fig.3a</xref>. On the other hand, diodes <italic>D<sub>1</sub>
</italic> and <italic>D<sub>2</sub>
</italic>
<sub/>conduct during the non-shoot-through state,
while the VSI does not close the path and switch <italic>S<sub>0</sub>
</italic> is off, which results in the
equivalent circuit shown in <xref ref-type="fig" rid="gf3">Fig. 3b</xref>.</p>
<p>
<fig id="gf3">
<label>Fig. 3. </label>
<caption>
<title>qSBI stable operating states.</title>
</caption>
<alt-text>Fig. 3.  qSBI stable operating states.</alt-text>
<graphic xlink:href="344255453009_gf3.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>]</attrib>
</fig>
</p>
<p> The two stable operating states provide the equations describing the circuit's operation and the capacitor’s voltage <italic>V<sub>ca</sub>
</italic> as a function of the input voltage <italic>V<sub>ph</sub>
</italic> and duty cycle<italic> D</italic>    [<xref ref-type="bibr" rid="redalyc_344255453009_ref1">1</xref>][<xref ref-type="bibr" rid="redalyc_344255453009_ref10">10</xref>]: </p>
<p> The voltage ratio between V<sub>ca</sub> and V<sub>pℎ </sub>indicates the converter's voltage gain. Since the overall circuit operation, shoot-through and non-shoot-through states depend on the duration of the VSI’s zero state, the duty cycle in (<xref ref-type="disp-formula" rid="e1">1</xref>) bounds the VSI modulation index <italic>M</italic>. Therefore, the time allotted for the non-zero space vectors plus the time for the shoot-trough state should not exceed the modulator’s carrier period. According to (<xref ref-type="disp-formula" rid="e1">1</xref>), the ideal converter's gain becomes undetermined for <italic>D</italic> = 0.5. This imposes a practical low limit for the modu-lation index value of <italic>M<sub>BL</sub>
</italic> = 0.5.</p>
<p>
<disp-formula id="e1">
<label>(1)    </label>
<graphic xlink:href="344255453009_ee1.png" position="anchor" orientation="portrait"/>
</disp-formula>
</p>
</sec>
<sec>
<title>3.  PWM CONTROL
OF qSBIs</title>
<p>This work uses the triangular comparison method for implementing the
generalized space vector modulation [<xref ref-type="bibr" rid="redalyc_344255453009_ref11">11</xref>],[<xref ref-type="bibr" rid="redalyc_344255453009_ref12">12</xref>],[<xref ref-type="bibr" rid="redalyc_344255453009_ref13">13</xref>]. <xref ref-type="fig" rid="gf4">Fig.4</xref> shows an example of the PWM pulses generated by test duty cycle
demands in phases <italic>a,b</italic> and <italic>c</italic>, where <italic>V<sub>cc</sub>
</italic> is approximately equal to the capacitor’s
voltage <italic>v<sub>c</sub>
</italic>. The zero vectors in<xref ref-type="fig" rid="gf4"> Fig.4</xref> appear
spread in three different regions. From the start of the switching period to<italic> t<sub>1</sub>
</italic>, they are associated with zero
vector <inline-graphic xlink:href="344255453009_gi1.png"/> ; from <italic>t<sub>3</sub>
</italic> to <italic>t<sub>4</sub>
</italic>, with <inline-graphic xlink:href="344255453009_gi2.png"/>; and from <italic>t<sub>6</sub>
</italic> to the end of the switching period, with <inline-graphic xlink:href="344255453009_gi3.png"/>. It is clear from <xref ref-type="fig" rid="gf4">Fig. 4</xref> that
nonzero space vectors <inline-graphic xlink:href="344255453009_gi4.png"/>    are active between instants<italic> t<sub>1</sub>
</italic> and <italic>t<sub>3</sub>
</italic> and between <italic>t<sub>4</sub>
</italic> and <italic>t<sub>6</sub>
</italic>. The extreme duty cycles <italic>D<sub>max</sub>
</italic>and <italic>D<sub>min</sub>
</italic> define the previous time slices, employed later by the qSBI modulation
method.</p>
<p>
<fig id="gf4">
<label>Fig. 4.</label>
<caption>
<title>PWM pulses generated using the triangle
comparison method.</title>
</caption>
<alt-text>Fig. 4. PWM pulses generated using the triangle
comparison method.</alt-text>
<graphic xlink:href="344255453009_gf4.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: [<xref ref-type="bibr" rid="redalyc_344255453009_ref13">13</xref>].</attrib>
</fig>
</p>
<p>
<xref ref-type="fig" rid="gf5">Fig. 5</xref> shows the time distribution of the PWM carrier signal. The
duty cycle requires sinusoidal modulation for the three phases of the VSI and
the duty cycle, for the shoot-though states (<italic>D<sub>L</sub>
</italic> and <italic>D<sub>H</sub>
</italic>). The references of the duty cycle
for the shoot-through states also provide a visual representation of the VSI’s
maximum modulation index.</p>
<p>
<fig id="gf5">
<label>Fig. 5.</label>
<caption>
<title>Modulation and Carrier signals in PWM by
triangle comparison for sinusoidal modulation and boost references.</title>
</caption>
<alt-text>Fig. 5. Modulation and Carrier signals in PWM by
triangle comparison for sinusoidal modulation and boost references.</alt-text>
<graphic xlink:href="344255453009_gf6.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<sec>
<title>3.1 Experimental
qSBI test rig</title>
<p> The carrier for the PWM synchronizes the acquisition (current and voltage) and the controller’s execution cycle. For the qBSI, this synchronization allows the correct operation of the shoot-through and non-shoot-through states, as shown in <xref ref-type="fig" rid="gf4">Figs. 4</xref> and <xref ref-type="fig" rid="gf5">5</xref>. Hence, a prototype board housing an FPGA provides the means to integrate the PWM module and the temporal synchronization with the qSBI’s shoot-through pulses. There are other tasks incorporated in the FPGA, such as AD controlling and allowing data exchange between sensor boards and the processing unit (digital signal processor, DSP). </p>
<p> This work proposes a noninvasive change in the existing PWM hardware for producing the "on-off" commands feeding the power switches. The original PWM pulse generation remains unchanged, while new pulses are synthesized for controlling the shoot-through states. To this end, two extra duty cycle demands <italic>D<sub>L</sub>
</italic> and <italic>D<sub>H</sub>
</italic> generate extra gating signals <italic>g<sub>L</sub>
</italic> and <italic>g<sub>H</sub>
</italic> used to control switch <italic>S<sub>0</sub>
</italic> and to change the signals going to the VSI’s power switches, as shown in <xref ref-type="fig" rid="gf4">Fig. 4</xref>. The conventional PWM puts out the trigger signals <italic>g<sub>1</sub>
</italic> to <italic>g<sub>2</sub>
</italic>, plus <italic>g<sub>L</sub>
</italic> and <italic>g<sub>H</sub>
</italic> used to change the gate signals going to the VSI in<xref ref-type="fig" rid="gf1"> Fig.1</xref>. The new gate signals <inline-graphic xlink:href="344255453009_gi5.png"/> follow the logic rule described in (<xref ref-type="disp-formula" rid="e2">2</xref>) and (<xref ref-type="disp-formula" rid="e3">3</xref>). <xref ref-type="fig" rid="gf6">Fig. 6</xref> shows the modified gate signals, created with the original gated signal and the boost duty cycle demands, in accordance with (<xref ref-type="disp-formula" rid="e2">2</xref>) and (<xref ref-type="disp-formula" rid="e3">3</xref>):</p>
<p>
<fig id="gf6">
<label>Fig. 6. </label>
<caption>
<title>Gate signal modified with the boost duty cycle
demands.</title>
</caption>
<alt-text>Fig. 6.  Gate signal modified with the boost duty cycle
demands.</alt-text>
<graphic xlink:href="344255453009_gf7.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p>
<disp-formula id="e2">
<label>(2)    </label>
<graphic xlink:href="344255453009_ee2.png" position="anchor" orientation="portrait"/>
</disp-formula>
</p>
<p>
<disp-formula id="e3">
<label>(3)                        </label>
<graphic xlink:href="344255453009_ee3.png" position="anchor" orientation="portrait"/>
</disp-formula>
</p>
<p>Where + denotes the logic or operator. This way,
all the power devices turn on during the shoot-through state.</p>
</sec>
<sec>
<title>3.2 PWM control
techniques for the qSBI</title>
<p> The boost gain versus the maximum modulation index in the qSBI topology sets a limit to its use. In turn, such limit imposes a compromise between modulation index and boost gain to supply maximum voltage to the load. Once the user fixes the boost stage gain, any extra gain for the qSBI should come from the modulation technique used in the voltage source inverter (VSI). For three-phase systems, sinusoidal and space vector PWM are the most widely-used modulation techniques. However, the qSBI needs a coordinated switching of the boost stage and the VSI, as previously described. SV PWM allows the SVI to synthesize space vectors 15.47% larger than the ones from sinusoidal PWM. </p>
<p> The use of standard triangular comparison SV PWM solves the synchronization problem. From <xref ref-type="fig" rid="gf5">Figs 5</xref> and <xref ref-type="fig" rid="gf7">7</xref>, it is clear that standard SV PWM does not need any change in the duty cycle demand for the shoot-through states.</p>
<p>
<fig id="gf7">
<label>Fig. 7.</label>
<caption>
<title>Modulation and Carrier signals in PWM by
triangle comparison for space vector modulation  

and boost references.</title>
</caption>
<alt-text>Fig. 7. Modulation and Carrier signals in PWM by
triangle comparison for space vector modulation  

and boost references.</alt-text>
<graphic xlink:href="344255453009_gf8.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p> However, there are more possible candidates for SV PWM [<xref ref-type="bibr" rid="redalyc_344255453009_ref14">14</xref>]. Among them, the discontinuous form is a special type [<xref ref-type="bibr" rid="redalyc_344255453009_ref15">15</xref>],[<xref ref-type="bibr" rid="redalyc_344255453009_ref12">12</xref>]. <italic>DPWM<sub>max</sub>
</italic>, <italic>DPWM<sub>min</sub>
</italic>, <italic>DPWM<sub>0</sub>
</italic>, <italic>DPWM<sub>1</sub>
</italic>, <italic>DPWM<sub>2</sub>
</italic>, <italic>DPWM<sub>3</sub>
</italic> comprise the most commonly-used discrete space vector modulation techniques. Modulation methods (<italic>DPWM<sub>0-3</sub>
</italic>) need a complex switching selection to synchronize the boost stage with the VSI stage, while the <italic>DPWM<sub>min</sub>
</italic> and <italic>DPWM<sub>max</sub>
</italic> with the VSI stage, while the <italic>DPWM<sub>min</sub>
</italic> and <italic>DPWM<sub>max</sub>
</italic> methods use a simpler duty cycle demand. For example, when the <italic>DPWM<sub>min</sub>
</italic>method is adopted, the <italic>S<sub>0</sub>´s</italic> commutation frequency halves. This means that the current charge and discharge cycle takes more time and the inductance current ripple increases, as shown in <xref ref-type="fig" rid="gf8">Fig.8.</xref> As a result, the ripple current is higher for discrete modulations, while the continuous modulation methods result in smaller ripple in the inductor current, shown in <xref ref-type="fig" rid="gf8">Fig. 8.</xref> Therefore, it is more likely that a converter starts working in a discontinues zone. In the discontinuous operation equation (<xref ref-type="disp-formula" rid="e1">1</xref>), it is not valid to evaluate the boost voltage gain or the capacitor voltage. No experimental test will be presented for discontinuous modulation methods.</p>
<p>
<fig id="gf8">
<label>Fig. 8.</label>
<caption>
<title>Inductance current comparison for operation
using SVM vs   .</title>
</caption>
<alt-text>Fig. 8. Inductance current comparison for operation
using SVM vs   .</alt-text>
<graphic xlink:href="344255453009_gf9.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
</sec>
</sec>
<sec>
<title>4. EXPERIMENTAL VALIDATION</title>
<p>
<xref ref-type="fig" rid="gf9">Fig.9 </xref>shows the experimental prototype used in this work. The power stage uses seven switches and two diodes mounted on four heat-sink columns. The driver for the IGBT switches sits on top of the heat-sinks to minimize the cable’s length. The DC link is located in the middle of the equipment, with the capacitor placed on the left. The sensor board, placed in the lower part of the setup, allows to record the control variables for the inverter and quasi-boost converter.  </p>
<p>
<fig id="gf9">
<label>Fig.
9.</label>
<caption>
<title>Experimental prototype for the qSBI.</title>
</caption>
<alt-text>Fig.
9. Experimental prototype for the qSBI.</alt-text>
<graphic xlink:href="344255453009_gf10.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p> The processing unit is based on a digital signal processor (DSP) that provides the necessary processing power to execute complex computational tasks. The test rig in this work uses an Analog Devices DSP of the SHARC family (ADSP-21369). </p>
<p> This section shows the qSBI experimental validation for three practical cases. The first test uses a DC source to show the qSBI’s basic performance. The other two tests use a PV source controlled with an MPPT algorithm. One uses a single PV panel, which reveals the need for high boost factor and high efficiency in distributed applications. The other PV test uses a PV string feeding the qSBI and has the advantages of using SVPWM instead of the common SPWM.</p>
<sec>
<title>4.1 Experimental
test using a DC Source</title>
<p>
<xref ref-type="fig" rid="gf10">Fig.10</xref> shows the steady state behavior of the capacitor, inductor and DC bus of the qSBI converter. When switch    of <xref ref-type="fig" rid="gf1">Fig.1</xref> is turned OFF, the voltage in the DC bus of the inverter (CH-2 in <xref ref-type="fig" rid="gf10">Fig.10</xref>) is equal to the capacitor’s voltage (CH-1 in <xref ref-type="fig" rid="gf10">Fig.10</xref>). At that instant, the inductor current (CH-3 in <xref ref-type="fig" rid="gf10">Fig.10</xref>) has a negative slope, so the current flows to the load. On the other hand, when switch <italic>S<sub>0</sub>
</italic> is turned ON, the DC bus voltage (CH-2 in <xref ref-type="fig" rid="gf10">Fig.10</xref>) is zero. The inductor current (CH-3 in <xref ref-type="fig" rid="gf10">Fig.10</xref>) has a positive slope that corresponds to the shoot-through state. In this experiment, the boost factor was 3.3, which corresponds to D equal to 0.35, and the modulation index in the VSI was 0.6. </p>
<p>
<fig id="gf10">
<label>Fig. 10.</label>
<caption>
<title>Experimental waveforms of qSBI (ch1:
Capacitor voltage, ch2: DC bus voltage, ch3: Inductor current).</title>
</caption>
<alt-text>Fig. 10. Experimental waveforms of qSBI (ch1:
Capacitor voltage, ch2: DC bus voltage, ch3: Inductor current).</alt-text>
<graphic xlink:href="344255453009_gf11.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: Author</attrib>
</fig>
</p>
<p>
<xref ref-type="fig" rid="gf11">Figure 11</xref> shows the results for a test using a DC source with higher
voltage. The blue signal is the inductor current, the cyan signal is the
capacitor voltage and the magenta signal is the output voltage. The qSBI is
controlled using a sinusoidal PWM. To avoid high current and voltage overshoots
in the converter, the duty cycle is increased in six steps. For measuring
purposes, the <italic>V<sub>ab</sub>
</italic> output voltage is taken from a passive RC
filter with a 1/3 gain. This results in a peak output voltage close to 120 V.<xref ref-type="fig" rid="gf12">
Figure 12</xref> shows the results when using the previous conditions in DC source and
duty cycle steps, but with space vector PWM (SVPWM). As shown by the cursor
position in <xref ref-type="fig" rid="gf11">Figs. 11</xref> and <xref ref-type="fig" rid="gf12">12</xref>, the SV PWM technique improves the total boost
factor of the qSBI converter. The output voltage increased from 120 V (SVPWM) to
150 V (SPWM).</p>
<p>
<fig id="gf11">
<label>Fig.
11.</label>
<caption>
<title>Experimental waveforms of qSBI for sinusoidal modulation (ch1: Inductor
current, ch2: Capacitor voltage,  

ch3:
Low-pass filter voltage).</title>
</caption>
<alt-text>Fig.
11. Experimental waveforms of qSBI for sinusoidal modulation (ch1: Inductor
current, ch2: Capacitor voltage,  

ch3:
Low-pass filter voltage).</alt-text>
<graphic xlink:href="344255453009_gf12.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors</attrib>
</fig>
</p>
<p>
<fig id="gf12">
<label>Fig. 12.</label>
<caption>
<title>Experimental waveforms of the qSBI for space
vector modulation (ch1: Inductor current, ch2: Capacitor voltage,  

ch3: Low-pass filter voltage).</title>
</caption>
<alt-text>Fig. 12. Experimental waveforms of the qSBI for space
vector modulation (ch1: Inductor current, ch2: Capacitor voltage,  

ch3: Low-pass filter voltage).</alt-text>
<graphic xlink:href="344255453009_gf13.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: author’s</attrib>
</fig>
</p>
<sec>
<title>4.2 Experimental
practical test: Extracting Maximum Power from a PV panel</title>
<p> The improved gain factor of the qSBI and the adoption of a MPPT algorithm are two of the main features of the converter that make it appropriate for PV microinverters. Those characteristics are confirmed in the following two experimental cases. In the first test, the experimental qSBI prototype extracts the maximum power from a PV panel. A basic perturb and observe algorithm (P&amp;O) [<xref ref-type="bibr" rid="redalyc_344255453009_ref16">16</xref>] implemented in the DSP unit extracts the maximum power from a commercial ERDM85 PV panel. The P&amp;O continually changes the duty cycle of the qSBI to reach the maximum power point of the PV panel. </p>
<p> The modulation in this experiment is the standard SPWM, the maximum duty cycle is 0.49, and the modulation index is 0.5 for maximum voltage swing. The changes in D, named   in the P&amp;O algorithm [17], were set to 0.01, and the perturbation period Tp was 50 ms. Fig.13 shows the experimental results extractedfrom the DSP’s external memory. In this figure, the red line corresponds to the duty cycle D of the boost stage. The first part of that curve shows the starting operation, where D increases from 0.125 to 0.31 to avoid current and voltage overshoots in the converter. At 0.7 s, the algorithm reaches the MPP and maintains typical variations in 𝐷 around the maximum power. The variation in 𝐷 produces oscillations in the input power and input voltage of the qSBI, which is evident in the blue and green curves, respectively. Such variations are propagated to the VSI’s output voltage, shown in the magenta curve. However, the total boost factor is close to 2.2. </p>
<p>
<fig id="gf13">
<label>Fig. 13. </label>
<caption>
<title>Experimental results of the qSBI with MPPT
algorithm for a PV panel. </title>
</caption>
<alt-text>Fig. 13.  Experimental results of the qSBI with MPPT
algorithm for a PV panel. </alt-text>
<graphic xlink:href="344255453009_gf14.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: Author’s own work.</attrib>
</fig>
</p>
</sec>
</sec>
<sec>
<title>4.3 Experimental
practical test: Extracting maximum power from a String PV System</title>
<p>The second test with a PV system uses a PV string comprised of four
ERDM85 PV panels connected in series feeding the qSBI. This test uses the same
basic P&amp;O algorithm employed in the single PV panel test. However, since
the MPP occurs at lower duty cycles, <italic>D</italic> is limited to 0.39 and the modulation index (using sinusoidal PWM
modulation in the VSI) is increased to 0.6. <xref ref-type="fig" rid="gf14">Fig.14</xref> shows the experimental
results under these conditions. The red curve shows that the MPP algorithm has
faster convergence, in 0.3 s. Also, the duty cycle required to reach the MPP (0.35)
is lower than in the case of the single panel. The green curve corresponds to
the PV string voltage and the magenta curve, to the output voltage, which results
in a 1.7 boost factor.</p>
<p>
<fig id="gf14">
<label>Fig. 14.</label>
<caption>
<title>Experimental results of the qSBI with MPPT
algorithm for a PV String.</title>
</caption>
<alt-text>Fig. 14. Experimental results of the qSBI with MPPT
algorithm for a PV String.</alt-text>
<graphic xlink:href="344255453009_gf15.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
<p>The final test uses SVPWM, and <xref ref-type="fig" rid="gf15">Fig.15</xref> shows the results. In this case,
the duty cycle needed to reach the MPP is around 0.36, as shown by the red
curve. The string voltage, depicted by the green curve, is close to 62.5 V,
while the output voltage represented by the magenta curve is 130 V. This shows
an increase in the boost factor resulting from the use of the SVPWM in the VSI.</p>
<p>
<fig id="gf15">
<label>Fig. 15</label>
<caption>
<title>Experimental results of the qSBI with MPPT
algorithm for a PV String and using SV PWM Modulation. </title>
</caption>
<alt-text>Fig. 15 Experimental results of the qSBI with MPPT
algorithm for a PV String and using SV PWM Modulation. </alt-text>
<graphic xlink:href="344255453009_gf16.jpg" position="anchor" orientation="portrait"/>
<attrib>Source: authors.</attrib>
</fig>
</p>
</sec>
</sec>
<sec>
<title>5.  CONCLUSIONS</title>
<p>In this paper a qSBI experimental prototype has been implemented. Space
Vector Pulse Width Modulation (SV PWM) with triangular comparison has been
proposed to increase the total boost factor of the converter, which is needed for
recent applications such as PV microinverters in distributed PV systems where a
single or few PV panels feed the converter. The qSBI prototype employed in this
work uses a DSP and FPGA technology that enables the synchronization needed by
the modulation method. In PV applications, when MPPT algorithms are used for
harvesting power, some oscillations are present in the output voltage.
Therefore, more complex MPP algorithms are required to mitigate this
undesirable behavior. That will be the aim of future works.</p>
</sec>
</body>
<back>
<ack>
<title>Acknowledgements</title>
<p>This work was supported by Universidad del Valle under Project 2823, and
Departamento Administrativo de Ciencia, Tecnología e Innovación-Colciencias
(Colombia) under contract FP-501-2014.</p>
</ack>
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