<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">CS</journal-id><journal-title-group><journal-title>Circuits and Systems</journal-title></journal-title-group><issn pub-type="epub">2153-1285</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/cs.2016.712332</article-id><article-id pub-id-type="publisher-id">CS-71608</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Computer Science&amp;Communications</subject><subject> Engineering</subject><subject> Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Output Voltage Ripple (OVR) Reduction of Boost Converter Using Particle Swarm Optimization
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>K.</surname><given-names>Prithivi</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>M.</surname><given-names>Sathyapriya</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>L.</surname><given-names>Ashok Kumar</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib></contrib-group><aff id="aff1"><addr-line>Department of Electrical and Electronics Engineering, Kongu Engineering College, Erode, India</addr-line></aff><aff id="aff2"><addr-line>Department of Electrical and Electronics Engineering, PSG College of Technology, Coimbatore, India</addr-line></aff><author-notes><corresp id="cor1">* E-mail:<email>k.prthv@gmail.com(KP)</email>;</corresp></author-notes><pub-date pub-type="epub"><day>28</day><month>10</month><year>2016</year></pub-date><volume>07</volume><issue>12</issue><fpage>4009</fpage><lpage>4023</lpage><history><date date-type="received"><day>May</day>	<month>10,</month>	<year>2016</year></date><date date-type="rev-recd"><day>Accepted:</day>	<month>May</month>	<year>21,</year>	</date><date date-type="accepted"><day>October</day>	<month>28,</month>	<year>2016</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  KY
   
  Boost Converter, a modern invention in the field of non-isolated DC-DC boost converter is identified for minimum voltage ripple. KY boost converter is the com
  - 
  bination of KY converter and traditional boost converter. Such a converter has con
  - 
  tinuous input and output inductor current, different from the traditional boost con
  - 
  verter. And hence this converter is very suitable for very low-ripple applications.<b> </b>The Particle Swarm Optimization (PSO) based controller, FUZZY based controller and open loop KY boost converter are designed in MATLAB/Simulink model. The simu
  - 
  lated results show a reduction in output ripple from 1.18
   
  V of the existing open loop KY boost converter output to 0.54
   
  V in the FUZZY logic controlled converter out
  - 
  put. Further reduction in output ripple to 0.29
   
  V is achieved in the proposed PSO based converter. The simulated results also show the variation of switching pulses based on the different existing and proposed method.
 
</p></abstract><kwd-group><kwd>Boost Converter</kwd><kwd> Particle Swarm Optimization (PSO)</kwd><kwd> Output Voltage Ripple (OVR) Reduction</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>For the function of the power supply using the low voltage battery, analog circuits, such as radio-frequency (RF) amplifier, audio amplifier, often need very high voltage to obtain enough output power and voltage amplitude. This is done by boosting the minimum voltage to the required high voltage. For such applications, the output voltage ripple must be taken into account purposefully. Regarding the conventional non-iso- lated voltage-boosting converter, their output currents are pulsating; thereby the corresponding output voltage ripple tends to be large. As generally approved, to overcome this problem, one way is the usage and low equivalent series resistance (ESR), another way is to add inductance-capacitance (LC) filter. In [<xref ref-type="bibr" rid="scirp.71608-ref1">1</xref>] , the interleaved control scheme is employed in the dual buck-boost converters. In the literature [<xref ref-type="bibr" rid="scirp.71608-ref2">2</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref3">3</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref4">4</xref>] , the voltage- lift technique is utilized to boost the output voltage. Also several controlling techniques like coupling inductors [<xref ref-type="bibr" rid="scirp.71608-ref5">5</xref>] , sliding mode converter [<xref ref-type="bibr" rid="scirp.71608-ref6">6</xref>] and loop bandwidth control [<xref ref-type="bibr" rid="scirp.71608-ref7">7</xref>] were used for voltage ripple reduction. But these converters [<xref ref-type="bibr" rid="scirp.71608-ref2">2</xref>] - [<xref ref-type="bibr" rid="scirp.71608-ref7">7</xref>] have one right-half plane zero in CCM mode. So it is not easy to achieve required boosted output voltage. And hence the KY boost converter [<xref ref-type="bibr" rid="scirp.71608-ref8">8</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref9">9</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref10">10</xref>] is presented to overcome this problem. But these converters [<xref ref-type="bibr" rid="scirp.71608-ref8">8</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref9">9</xref>] [<xref ref-type="bibr" rid="scirp.71608-ref10">10</xref>] do not obtain the expected output voltage and also having large amount of output voltage ripple. The FUZZY logic controller based converter [<xref ref-type="bibr" rid="scirp.71608-ref11">11</xref>] is presented to overcome this problem. The FUZZY based converter [<xref ref-type="bibr" rid="scirp.71608-ref11">11</xref>] can produce the expected output voltage but the ripple reduction performance is not so good. To reduce the ripple in a very effective manner PSO based controller is used and the detailed illustration of the proposed converter is described herein, along with some experimental results to justify the effectiveness of such a converter.</p></sec><sec id="s2"><title>2. System Overview</title><p><xref ref-type="fig" rid="fig1">Figure 1</xref> shows the overall block diagram of the controlled converter. Reduction of the output voltage ripple can be achieved by giving the proper switching pulse for the converter switch. The proper switching pulse is given by the proper controller design for PWM generator. Here the actual voltage (<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x2.png" xlink:type="simple"/></inline-formula>) and reference voltage (<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x3.png" xlink:type="simple"/></inline-formula>) are taken as a feedback parameters for controller design. The output of the controller is a control signal which is compared with the reference signal in the PWM generator for producing the proper switching pulse to operate the KY boost converter. Based on the controller design the switching pulse get vary and based on the switching pulse variation the output voltage ripple reduces and output voltage increases. Here the supply for KY converter is given by battery source.</p></sec><sec id="s3"><title>3. KY Boost Converter</title><p><xref ref-type="fig" rid="fig2">Figure 2</xref> shows the proposed positive-voltage KY boost converter composed of the KY converter combined with the traditional boost converter. The KY converter consist of</p><fig id="fig1"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref></label><caption><title> Block diagram of overall system</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x4.png"/></fig><fig id="fig2"  position="float"><label><xref ref-type="fig" rid="fig2">Figure 2</xref></label><caption><title> KY boost converter</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x5.png"/></fig><p>the switches <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x6.png" xlink:type="simple"/></inline-formula> and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x7.png" xlink:type="simple"/></inline-formula>, the diode<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x8.png" xlink:type="simple"/></inline-formula>, the energy-transferring capacitor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x9.png" xlink:type="simple"/></inline-formula>, the output inductor <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x10.png" xlink:type="simple"/></inline-formula> and the output capacitor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x11.png" xlink:type="simple"/></inline-formula>. The input of the KY converter is retrieved by the buffer capacitor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x12.png" xlink:type="simple"/></inline-formula>. On the other hand, the traditional boost converter consists of the switches <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x13.png" xlink:type="simple"/></inline-formula> and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x14.png" xlink:type="simple"/></inline-formula>, the input inductor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x15.png" xlink:type="simple"/></inline-formula>. The output of the conventional boost converter is replaced by the buffer capacitor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x16.png" xlink:type="simple"/></inline-formula>. The buffer capacitor <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x17.png" xlink:type="simple"/></inline-formula> is a buffer between the KY converter and the traditional boost converter. The output load is represented by the load resistor<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x18.png" xlink:type="simple"/></inline-formula>.</p><sec id="s3_1"><title>3.1. Mode 1 Operation of KY Boost Converter</title><p>In <xref ref-type="fig" rid="fig3">Figure 3</xref>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula>is turned off and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula> is turned on. In this case, the negative terminal of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula> is pulled to the ground and hence <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula> is forward biased and turned on. During this mode, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula>is discharged whereas <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula> is charged. Therefore, the voltage across <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula> is<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula>, thereby causing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula> to be magnetized, whereas the voltage across <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula> is <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula> subtracted from<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x30.png" xlink:type="simple"/></inline-formula>, thereby causing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x31.png" xlink:type="simple"/></inline-formula> to be demagnetized. Also, the current flowing through <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x32.png" xlink:type="simple"/></inline-formula> is equal to <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x33.png" xlink:type="simple"/></inline-formula> minus the current flowing through<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x19.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x20.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x21.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x22.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x23.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x24.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x25.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x26.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x27.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x28.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x29.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x30.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x31.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x32.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x33.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x34.png" xlink:type="simple"/></inline-formula>. And hence, the corresponding differential equations are given by (1) to (4).</p><disp-formula id="scirp.71608-formula44"><label>(1)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x35.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula45"><label>(2)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x36.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula46"><label>(3)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x37.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula47"><label>(4)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x38.png"  xlink:type="simple"/></disp-formula></sec><sec id="s3_2"><title>3.2. Mode 2 Operation of KY Boost Converter</title><p>In <xref ref-type="fig" rid="fig4">Figure 4</xref>, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x39.png" xlink:type="simple"/></inline-formula>is turned on and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x39.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x40.png" xlink:type="simple"/></inline-formula> is turned off. In this case, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x39.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x40.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x41.png" xlink:type="simple"/></inline-formula>is in the on-state</p><fig id="fig3"  position="float"><label><xref ref-type="fig" rid="fig3">Figure 3</xref></label><caption><title> Power flow of mode 1 operation</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x42.png"/></fig><fig id="fig4"  position="float"><label><xref ref-type="fig" rid="fig4">Figure 4</xref></label><caption><title> Power flow of mode 2 operation</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x43.png"/></fig><p>and hence <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula> is reverse biased and turned off. During this mode, C<sub>m</sub> is charged whereas <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula> is discharged. Therefore, the voltage across <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula> is <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula> subtracted from<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula>, thereby causing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula> to be demagnetized, whereas the voltage across <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula> is <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula> subtracted from sum of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x52.png" xlink:type="simple"/></inline-formula> and<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x53.png" xlink:type="simple"/></inline-formula>, thereby causing <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x54.png" xlink:type="simple"/></inline-formula> to be magnetized. Also, the current flowing through Co is equal to <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x55.png" xlink:type="simple"/></inline-formula> minus the current flowing through<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x44.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x45.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x46.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x47.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x48.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x49.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x50.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x51.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x52.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x53.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x54.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x55.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x56.png" xlink:type="simple"/></inline-formula>. And hence, the corresponding differential equations are given by (5) to (8).</p><disp-formula id="scirp.71608-formula48"><label>(5)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x57.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula49"><label>(6)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x58.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula50"><label>(7)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x59.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula51"><label>(8)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x60.png"  xlink:type="simple"/></disp-formula><p>The average equations which are obtained from Equation (1) to Equation (8), are given by (9) to (13).</p><disp-formula id="scirp.71608-formula52"><label>(9)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x61.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula53"><label>(10)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x62.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula54"><label>(11)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x63.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula55"><label>(12)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x64.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula56"><label>(13)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x65.png"  xlink:type="simple"/></disp-formula><p>where,</p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x66.png" xlink:type="simple"/></inline-formula>= 2% of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x66.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x67.png" xlink:type="simple"/></inline-formula></p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x68.png" xlink:type="simple"/></inline-formula>= 2% of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x68.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x69.png" xlink:type="simple"/></inline-formula></p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x70.png" xlink:type="simple"/></inline-formula>= 2% of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x70.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x71.png" xlink:type="simple"/></inline-formula></p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x72.png" xlink:type="simple"/></inline-formula>= 2% of <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x72.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x73.png" xlink:type="simple"/></inline-formula></p><p>According to the small-ripple approximation and the voltage-second balance, the voltage ratio can be obtained to be</p><disp-formula id="scirp.71608-formula57"><label>(14)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x74.png"  xlink:type="simple"/></disp-formula><p>where,</p><p>d = Duty cycle.</p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x75.png" xlink:type="simple"/></inline-formula>= Output voltage in Volts.</p><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x76.png" xlink:type="simple"/></inline-formula>= input voltage in Volts.</p><p>From Equations (9) to (14), we can obtain the specification values for KY boost converter. Here 2% of ripple will be taken for finding the specification values for KY boost converter.</p></sec><sec id="s3_3"><title>3.3. KY Boost Converter Specifications</title><p><xref ref-type="table" rid="table1">Table 1</xref> gives a detailed specification adopted for analyzing the performance of KY boost converter.</p></sec><sec id="s3_4"><title>3.4. KY Boost Converter Simulink Modeling</title><p>The KY boost converter realized in Simulink model is represented by <xref ref-type="fig" rid="fig5">Figure 5</xref>, in which switches are represented by <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x77.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x77.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x78.png" xlink:type="simple"/></inline-formula> with interrelated body diodes <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x77.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x78.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x79.png" xlink:type="simple"/></inline-formula> and</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Specifications adopted for KY boost converter</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Parameter</th><th align="center" valign="middle" >Symbol</th><th align="center" valign="middle" >Value</th><th align="center" valign="middle" >Unit</th></tr></thead><tr><td align="center" valign="middle" >Input voltage</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x80.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >12</td><td align="center" valign="middle" >V</td></tr><tr><td align="center" valign="middle" >Rated output voltage</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x81.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >36</td><td align="center" valign="middle" >V</td></tr><tr><td align="center" valign="middle" >Rated load current</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x82.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >10.36</td><td align="center" valign="middle" >A</td></tr><tr><td align="center" valign="middle" >Output inductance</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x83.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >3.623</td><td align="center" valign="middle" >mH</td></tr><tr><td align="center" valign="middle" >Buffer capacitance</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x84.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >31.24</td><td align="center" valign="middle" >mF</td></tr><tr><td align="center" valign="middle" >Energy transferring capacitor</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x85.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >62.2</td><td align="center" valign="middle" >mF</td></tr><tr><td align="center" valign="middle" >Output capacitance</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x86.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >470</td><td align="center" valign="middle" >μF</td></tr><tr><td align="center" valign="middle" >Load</td><td align="center" valign="middle" >Separately excited motor</td><td align="center" valign="middle" >0.5</td><td align="center" valign="middle" >Hp</td></tr><tr><td align="center" valign="middle" >Switching frequency</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x87.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >195</td><td align="center" valign="middle" >kHz</td></tr><tr><td align="center" valign="middle" >Input inductance</td><td align="center" valign="middle" ><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x88.png" xlink:type="simple"/></inline-formula></td><td align="center" valign="middle" >0.402</td><td align="center" valign="middle" >mH</td></tr></tbody></table></table-wrap><fig id="fig5"  position="float"><label><xref ref-type="fig" rid="fig5">Figure 5</xref></label><caption><title> KY boost converter Simulink model</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x89.png"/></fig><p><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula>. L<sub>i</sub> represents input inductor; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula>represent output inductor; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x92.png" xlink:type="simple"/></inline-formula>represent buffer capacitance; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x92.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x93.png" xlink:type="simple"/></inline-formula>represent energy transferring capacitor; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x92.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x94.png" xlink:type="simple"/></inline-formula>is output diode; <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x92.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x95.png" xlink:type="simple"/></inline-formula>is forward diode. The switching signal is fed through the connector M and the output voltage taken to Matlab workspace by connector<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x90.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x91.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x92.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x93.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x94.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x95.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x96.png" xlink:type="simple"/></inline-formula>.</p></sec></sec><sec id="s4"><title>4. Modeling of Fuzzy</title><p>Fuzzy controller is designed to control the output voltage ripple of the KY boost converter. The input to the Fuzzy controller is error (e) and change in error (ce), where the error (e) is the deviation of output voltage <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x97.png" xlink:type="simple"/></inline-formula> and reference voltage<inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x97.png" xlink:type="simple"/></inline-formula><inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/2-7601017x98.png" xlink:type="simple"/></inline-formula>. The output of Fuzzy controller is duty cycle (d). To generate the switching signal for KY boost converter, the duty cycle (d) is given to a PWM generator. <xref ref-type="fig" rid="fig6">Figure 6</xref> shows the Simulink model of the Fuzzy controller for KY boost converter which subsists of Fuzzy controller, PWM generator block with KY boost converter block with reference output voltage of 36 V. The switching frequency generated by the PWM generator block is 195 kHz which is fed to the KY boost converter switches.</p>Fuzzy Controller Simulink Modeling<p>The Fuzzy logic controller consists of Mamdani fuzzy inference system. The fuzzifier consists of two inputs (i.e.) error (e) and change in error (ce). The triangular membership function is used to represent the inputs and the output. The defuzzifier consists of output duty cycle (d). The Fuzzy rule base consists of 8 fuzzy rules which are used to produce duty cycle (d) for KY boost converter switches.</p><fig id="fig6"  position="float"><label><xref ref-type="fig" rid="fig6">Figure 6</xref></label><caption><title> KY fuzzy controller Simulink model</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x99.png"/></fig></sec><sec id="s5"><title>5. Modeling of PSO</title><p>Particle Swarm Optimization (PSO) comes from the research on the bird and fish flock movement behavior which is used to find the global minimum of the proposed objective function. In this method a swarm of particles describe a candidate solution move in the search space. Each particle position represents the objective function which is depending on the variables defined by the optimization problem. It is simple and easy to implement. It does not require any specific information about the converter model as well as the system parameters. And the calculation is very simple but the step for the calculation is high. <xref ref-type="fig" rid="fig7">Figure 7</xref> shows the steps to be adapted for PSO.</p><fig id="fig7"  position="float"><label><xref ref-type="fig" rid="fig7">Figure 7</xref></label><caption><title> Flow chart for PSO</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x100.png"/></fig>PSO Controller Simulink Modeling<p>The aim of the present work is to find out the optimized vector of the switching angles, for which the ripple components are limited to acceptable low level or even to be eliminated. On the other side, the obtained average value has to be equal or closer to the reference or desired output voltage. To fulfill these requirements an objective function which has to be minimized is proposed as follows:</p><disp-formula id="scirp.71608-formula58"><label>(15)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x101.png"  xlink:type="simple"/></disp-formula><p>where,</p><disp-formula id="scirp.71608-formula59"><graphic  xlink:href="http://html.scirp.org/file/2-7601017x102.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula60"><graphic  xlink:href="http://html.scirp.org/file/2-7601017x103.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.71608-formula61"><graphic  xlink:href="http://html.scirp.org/file/2-7601017x104.png"  xlink:type="simple"/></disp-formula><p>This function contains two terms, the error between the desired average voltage and the obtained output average voltage and the output voltage ripple which is to be eliminated. For reducing the output voltage ripple the output voltage should satisfy the following Constrain.</p><disp-formula id="scirp.71608-formula62"><label>(16)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/2-7601017x105.png"  xlink:type="simple"/></disp-formula></sec><sec id="s6"><title>6. Simulation Results and Discussion</title><p>The simulated results of the KY boost converter with input voltage 12 V and the rated output voltage of 36 V for a load current of 10.36 A is simulated with Matlab/Simulink R2013a as shown in <xref ref-type="fig" rid="fig8">Figure 8</xref>. <xref ref-type="fig" rid="fig9">Figure 9</xref> shows the switching pulse of KY boost converter for S1 and S2. The inverted switching pulse of S1 is given to S2.</p><p><xref ref-type="fig" rid="fig1">Figure 1</xref>0 shows the output voltage for 12 V input voltage in open loop condition of KY boost converter. It clearly shows that the output voltage ripple for an output voltage of 32.18 V in open loop condition is about 1.18 V.</p><disp-formula id="scirp.71608-formula63"><graphic  xlink:href="http://html.scirp.org/file/2-7601017x106.png"  xlink:type="simple"/></disp-formula><p><xref ref-type="fig" rid="fig1">Figure 1</xref>1 shows the switching pulse of closed loop KY boost converter using fuzzy logic controller for S1 and S2. The inverted pulse of S1 is given to S2. From this it is observed that the duty cycle will be varied based on error and change in error of output voltage.</p><p><xref ref-type="fig" rid="fig1">Figure 1</xref>2 shows the output voltage for 12 V input voltage in closed loop condition of KY boost converter using FUZZY controller. It clearly shows that the output voltage ripple for an output voltage of 36 V is about 0.54 V.</p><p><xref ref-type="fig" rid="fig1">Figure 1</xref>3 shows the switching pulse of KY boost converter using PSO algorithm based controller for S1 and S2. The inverted pulse of S1 is given to S2. From this it is observed that the duty cycle will be varied based on the updating of position and velocity.</p><p><xref ref-type="fig" rid="fig1">Figure 1</xref>4 shows the output voltage for 12 V input voltage in closed loop condition of KY boost converter using PSO based controller. It clearly shows that the output</p><fig id="fig8"  position="float"><label><xref ref-type="fig" rid="fig8">Figure 8</xref></label><caption><title> KY PSO controller Simulink model</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x107.png"/></fig><fig id="fig9"  position="float"><label><xref ref-type="fig" rid="fig9">Figure 9</xref></label><caption><title> Switching pulse for KY boost converter in open loop condition</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x108.png"/></fig><p>voltage ripple for an output voltage of 36 V is about 0.29 V.</p><disp-formula id="scirp.71608-formula64"><graphic  xlink:href="http://html.scirp.org/file/2-7601017x109.png"  xlink:type="simple"/></disp-formula></sec><sec id="s7"><title>7. Conclusion</title><p>The problem of the KY Boost converter output voltage ripple is presented in this paper. The Particle Swarm Optimization PSO algorithm is used to solve this problem using an objective function. This objective function contains a defined number of switching angles pattern depending on the degree of ripple reduction. The resulting output values of the proposed PSO Controller are compared with the existing FUZZY logic controller</p><fig id="fig10"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref>0</label><caption><title> Output voltage waveform of open loop KY boost converter</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x110.png"/></fig><fig-group id="fig11"><label><xref ref-type="fig" rid="fig1">Figure 1</xref>1</label><caption><title> Switching pulse for KY boost converter in closed loop condition using FUZZY logic controller.</title></caption><fig id ="fig11_1"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x111.png"/></fig><fig id ="fig11_2"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x112.png"/></fig></fig-group><fig id="fig12"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref>2</label><caption><title> Output voltage waveform of closed loop KY boost converter using FUZZY logic controller</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x113.png"/></fig><p>output and the open loop system. The minimization of output voltage ripple from 1.18 V in open loop system to 0.54 V in FUZZY based converter and further minimization to 0.29 V in PSO based converter is proved by the simulation results comparison shown in <xref ref-type="table" rid="table2">Table 2</xref>. And the future work could be continued by using various renewable sources as an input voltage source instead of constant voltage source like battery and can be</p><fig id="fig13"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref>3</label><caption><title> Switching pulse for KY boost converter in closed loop condition using PSO based controller</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x114.png"/></fig><fig id="fig14"  position="float"><label><xref ref-type="fig" rid="fig1">Figure 1</xref>4</label><caption><title> Output voltage waveform of closed loop KY boost converter using PSO based controller</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/2-7601017x115.png"/></fig><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Comparison of existing and proposed technique output</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Parameter</th><th align="center" valign="middle" >Existing open loop system</th><th align="center" valign="middle" >Existing FUZZY logic controller</th><th align="center" valign="middle" >Proposed PSO based controller</th></tr></thead><tr><td align="center" valign="middle" >Output voltage ripple</td><td align="center" valign="middle" >1.18 V</td><td align="center" valign="middle" >0.54 V</td><td align="center" valign="middle" >0.29 V</td></tr></tbody></table></table-wrap><p>compared in hybrid condition.</p></sec><sec id="s8"><title>Cite this paper</title><p>Prithivi, K., Sathyapriya, M. and Kumar L.A. (2016) Output Voltage Ripple (OVR) Reduction of Boost Converter Using Particle Swarm Opti- mization. Circuits and Systems, 7, 4009- 4023. http://dx.doi.org/10.4236/cs.2016.712332</p></sec></body><back><ref-list><title>References</title><ref id="scirp.71608-ref1"><label>1</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Giral</surname><given-names> R.</given-names></name>,<name name-style="western"><surname> Arango E.</surname><given-names> Calvente</given-names></name>,<name name-style="western"><surname> J. and Martinez-Salamero</surname><given-names> L. </given-names></name>,<etal>et al</etal>. 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