Power Quality Improvement using Single-Phase Unified Power ...
Analysis and Evaluation of DC-Link Capacitors for High Power Density Electric Vehicle Drive Systems H. Wen1, W. Xiao1, and Xuhui Wen2, P.R. Armstrong1,31 Electrical Power Engineering Program, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates (Email: hwen@masdar.ac.ae).2 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China (e-mail: wxh@mail.iee.)3 Massachusetts Institute of Technology, Cambridge, MA 02139, USAAbstract - In electric vehicle (EV) inverter systems, dc-link capacitors, which are bulky, heavy and susceptible to degradation from self heating, can become a critical obstacle to high power density. This paper presents a comprehensive method for analysis and comparative evaluation of dc-link capacitor applications to minimize the volume, mass and capacitance. Models of equivalent series resistance (ESR) that are valid over a range of frequency and operating temperature are derived and experimentally validated. The RMS values and frequency spectra of capacitor current are analyzed with respect to three modulation strategies and various operating conditions over practical ranges of load power factor and modulation index in EV drive systems. The modeling and analysis also consider the self-heating process and resulting core temperature of the dc-link capacitors, which impacts their lifetimes. Based on an 80kW permanent-magnet (PM) motor drive system, the application of electrolytic capacitors and film capacitors has been evaluated by both simulation and experimental tests. The inverter power density is improved from 2.99 kW/L to 13.3 kW/L without sacrificing system performance in terms of power loss, core temperature, and lifetime. Index Terms - Electric Vehicle (EV); Power Density; Dc-Link Capacitor; Ripple Current Stress; Equivalent Series Resistance (ESR); Parasitic Inductance.INTRODUCTIONElectric Vehicle (EV) research has intensified recently due to the global warming and other environmental concerns surrounding the existing petroleum-based transportation infrastructure PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TYWxtYXNpPC9BdXRob3I+PFllYXI+MjAwNzwvWWVhcj48
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ADDIN EN.CITE PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TYWxtYXNpPC9BdXRob3I+PFllYXI+MjAwNzwvWWVhcj48
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ADDIN EN.CITE.DATA [1, 2]. In EVs, the most common power interface between batteries and traction motors is the voltage source inverter (VSI), as shown in Fig. 1. Current EV inverter research is concerned with aspects of compact design PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5OYW11ZHVyaTwvQXV0aG9yPjxZZWFyPjE5OTg8L1llYXI+
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ADDIN EN.CITE.DATA [8-10] and long lifetime ADDIN EN.CITE <EndNote><Cite><Author>Schaltz</Author><Year>2009</Year><RecNum>58</RecNum><record><rec-number>58</rec-number><foreign-keys><key app="EN" db-id="rx2v9vewpetsrnerefn5dxadaast990dta9t">58</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Schaltz, E.</author><author>Khaligh, A.</author><author>Rasmussen, P. O.</author></authors></contributors><titles><title>Influence of Battery/Ultracapacitor Energy-Storage Sizing on Battery Lifetime in a Fuel Cell Hybrid Electric Vehicle</title><secondary-title>Vehicular Technology, IEEE Transactions on</secondary-title></titles><periodical><full-title>Vehicular Technology, IEEE Transactions on</full-title></periodical><pages>3882-3891</pages><volume>58</volume><number>8</number><keywords><keyword>energy management systems</keyword><keyword>fuel cell vehicles</keyword><keyword>hybrid electric vehicles</keyword><keyword>supercapacitors</keyword><keyword>battery lifetime</keyword><keyword>fuel cell hybrid electric vehicle</keyword><keyword>ultracapacitor energy-storage</keyword></keywords><dates><year>2009</year></dates><isbn>0018-9545</isbn><urls></urls></record></Cite></EndNote>[11]. Several topologies and optimization strategies have been investigated to meet multiple objectives under the stringent operation requirements of EV inverters PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5NYXBlbGxpPC9BdXRob3I+PFllYXI+MjAxMDwvWWVhcj48
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ADDIN EN.CITE.DATA [12-15]. For example, overload conditions of 2-2.5 times rated capacity can last 1-3 minutes and power electronic components are expected to tolerate inlet coolant temperatures up to 105?C ADDIN EN.CITE <EndNote><Cite><Author>Infineon</Author><Year>2010</Year><RecNum>37</RecNum><record><rec-number>37</rec-number><foreign-keys><key app="EN" db-id="rx2v9vewpetsrnerefn5dxadaast990dta9t">37</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Infineon</author></authors></contributors><titles><title>IGBT4 Modules optimized for EV/HEV Drive Applications</title><secondary-title>Power Seminar</secondary-title></titles><periodical><full-title>Power Seminar</full-title></periodical><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>[16]. Other design requirements include high efficiency and high power density ADDIN EN.CITE <EndNote><Cite><Author>Xuhui</Author><Year>2007</Year><RecNum>37</RecNum><DisplayText>[17]</DisplayText><record><rec-number>37</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">37</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Xuhui, Wen</author><author>Wei, Hu</author><author>Tao, Fan</author><author>Jun, Liu</author></authors></contributors><titles><title>Lifetime model research of motor drive system for electric vehicles</title><secondary-title>Electrical Machines and Systems, 2007. ICEMS. International Conference on</secondary-title><alt-title>Electrical Machines and Systems, 2007. ICEMS. International Conference on</alt-title></titles><pages>129-132</pages><keywords><keyword>electric vehicles</keyword><keyword>induction motor drives</keyword><keyword>insulated gate bipolar transistors</keyword><keyword>invertors</keyword><keyword>higher power density</keyword><keyword>induction motor drive</keyword><keyword>insulated gate bipolar transistor</keyword><keyword>motor controller</keyword><keyword>power 160 kW</keyword><keyword>three phase inverter</keyword></keywords><dates><year>2007</year><pub-dates><date>8-11 Oct. 2007</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[17].Fig. 1 Schematic of a typical electric vehicle drive system including a battery bank, dc-link capacitors, VSI, and traction motor from left to right.Many efforts have been directed toward improving the power density, which may be quantified as the power density by weight (PDW) and the power density by volume (PDV). For example, the FreedomCAR and Vehicle Technologies (FCVT) program in the U.S. aims to develop energy efficient and environmentally friendly highway transportation systems ADDIN EN.CITE <EndNote><Cite><Author>FreedomCAR</Author><RecNum>29</RecNum><DisplayText>[18, 19]</DisplayText><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>FreedomCAR</author></authors></contributors><titles><title>FreedomCAR and Fuel Partnership, Electrical and Electronics Technical Team Roadmap</title></titles><dates><pub-dates><date>November, 2006</date></pub-dates></dates><urls><related-urls><url> app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">28</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>FreedomCAR</author></authors></contributors><titles><title>Electrical and electronics technical team roadmap</title></titles><dates><pub-dates><date>December 7, 2010</date></pub-dates></dates><urls><related-urls><url>;[18, 19]. The FCVT program reports that the PDW and the PDV of EV inverters have been increased from 4.08 to 10.04 kW/kg and from 2.03 to 8.82 kW/L, respectively ADDIN EN.CITE <EndNote><Cite><Author>Namuduri</Author><Year>1998</Year><RecNum>22</RecNum><DisplayText>[3]</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">22</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Namuduri, C. S.</author><author>Murty, B. V.</author></authors></contributors><titles><title>High power density electric drive for an hybrid electric vehicle</title><secondary-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</secondary-title><alt-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</alt-title></titles><pages>34-40 vol.1</pages><volume>1</volume><keywords><keyword>DC-AC power convertors</keyword><keyword>PWM invertors</keyword><keyword>brushless machines</keyword><keyword>electric vehicles</keyword><keyword>permanent magnet motors</keyword><keyword>traction motor drives</keyword><keyword>18 kHz</keyword><keyword>29 kW</keyword><keyword>32 kW</keyword><keyword>45 kW</keyword><keyword>9 kW</keyword><keyword>Freedom hybrid electric vehicle</keyword><keyword>IGBT inverters</keyword><keyword>PM brushless motor traction drives</keyword><keyword>PWM VSI</keyword><keyword>braking torque control</keyword><keyword>control strategy</keyword><keyword>machine performance</keyword><keyword>power density</keyword><keyword>surface mounted Magnaquench magnets</keyword><keyword>trapezoidal EMF</keyword></keywords><dates><year>1998</year><pub-dates><date>15-19 Feb 1998</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[3]. Further improvement is expected to achieve more than 14.1 kW/L in PDV of EV inverters according to the FCVT technology roadmap ADDIN EN.CITE <EndNote><Cite><Author>FreedomCAR</Author><RecNum>29</RecNum><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>FreedomCAR</author></authors></contributors><titles><title>FreedomCAR and Fuel Partnership, Electrical and Electronics Technical Team Roadmap</title></titles><dates><pub-dates><date>November, 2006</date></pub-dates></dates><urls><related-urls><url>;[18]. A corresponding technology roadmap has been defined in China in terms of cost, efficiency, and power density ADDIN EN.CITE <EndNote><Cite><Author>Earley</Author><RecNum>81</RecNum><record><rec-number>81</rec-number><foreign-keys><key app="EN" db-id="rx2v9vewpetsrnerefn5dxadaast990dta9t">81</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robert Earley </author><author>Liping Kang </author><author>Feng An </author><author>and </author><author>Lucia Green-Weiskel </author></authors></contributors><titles><title>Electric vehicles in the context of sustainable development in China </title><secondary-title>Commission on Sustainable Development, Nineteenth Session, New York</secondary-title></titles><periodical><full-title>Commission on Sustainable Development, Nineteenth Session, New York</full-title></periodical><pages>1-28</pages><dates><pub-dates><date>2-13, May, 2011</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[20]. In an example of high performance possibilities, the latest SiC JFETs-based inverter shows a potential 51 kW/L PDV while achieving 97.8% efficiency ADDIN EN.CITE <EndNote><Cite><Author>Hui</Author><Year>2011</Year><RecNum>24</RecNum><DisplayText>[21]</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hui, Zhang</author><author>Tolbert, L. M.</author><author>Ozpineci, B.</author></authors></contributors><titles><title>Impact of SiC Devices on Hybrid Electric and Plug-In Hybrid Electric Vehicles</title><secondary-title>Industry Applications, IEEE Transactions on</secondary-title></titles><periodical><full-title>Industry Applications, IEEE Transactions on</full-title></periodical><pages>912-921</pages><volume>47</volume><number>2</number><keywords><keyword>battery powered vehicles</keyword><keyword>fuel economy</keyword><keyword>hybrid electric vehicles</keyword><keyword>invertors</keyword><keyword>machine control</keyword><keyword>power electronics</keyword><keyword>power transmission (mechanical)</keyword><keyword>silicon compounds</keyword><keyword>PHEV</keyword><keyword>PSAT powertrain model</keyword><keyword>SiC</keyword><keyword>Toyota Prius</keyword><keyword>battery interface</keyword><keyword>motor controller</keyword><keyword>plug-in hybrid electric vehicle</keyword><keyword>silicon carbide device</keyword><keyword>thermal management system</keyword><keyword>vehicle simulation software powertrain system analysis toolkit</keyword></keywords><dates><year>2011</year></dates><isbn>0093-9994</isbn><urls></urls></record></Cite></EndNote>[21]. Table I summarizes main technical parameters and objectives corresponding to the road maps and timelines of EV drive system development programs in U.S. and China.Table SEQ Table \* ROMAN ISummary of technical Road map Targets for electric vehicle drive systemsSubsystemParametersFreedomCarphase I ADDIN EN.CITE <EndNote><Cite><Author>Namuduri</Author><Year>1998</Year><RecNum>22</RecNum><DisplayText>[3]</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">22</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Namuduri, C. S.</author><author>Murty, B. V.</author></authors></contributors><titles><title>High power density electric drive for an hybrid electric vehicle</title><secondary-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</secondary-title><alt-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</alt-title></titles><pages>34-40 vol.1</pages><volume>1</volume><keywords><keyword>DC-AC power convertors</keyword><keyword>PWM invertors</keyword><keyword>brushless machines</keyword><keyword>electric vehicles</keyword><keyword>permanent magnet motors</keyword><keyword>traction motor drives</keyword><keyword>18 kHz</keyword><keyword>29 kW</keyword><keyword>32 kW</keyword><keyword>45 kW</keyword><keyword>9 kW</keyword><keyword>Freedom hybrid electric vehicle</keyword><keyword>IGBT inverters</keyword><keyword>PM brushless motor traction drives</keyword><keyword>PWM VSI</keyword><keyword>braking torque control</keyword><keyword>control strategy</keyword><keyword>machine performance</keyword><keyword>power density</keyword><keyword>surface mounted Magnaquench magnets</keyword><keyword>trapezoidal EMF</keyword></keywords><dates><year>1998</year><pub-dates><date>15-19 Feb 1998</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[3]FreedomCarphase II ADDIN EN.CITE <EndNote><Cite><Author>Namuduri</Author><Year>1998</Year><RecNum>22</RecNum><DisplayText>[3]</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">22</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Namuduri, C. S.</author><author>Murty, B. V.</author></authors></contributors><titles><title>High power density electric drive for an hybrid electric vehicle</title><secondary-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</secondary-title><alt-title>Applied Power Electronics Conference and Exposition, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual</alt-title></titles><pages>34-40 vol.1</pages><volume>1</volume><keywords><keyword>DC-AC power convertors</keyword><keyword>PWM invertors</keyword><keyword>brushless machines</keyword><keyword>electric vehicles</keyword><keyword>permanent magnet motors</keyword><keyword>traction motor drives</keyword><keyword>18 kHz</keyword><keyword>29 kW</keyword><keyword>32 kW</keyword><keyword>45 kW</keyword><keyword>9 kW</keyword><keyword>Freedom hybrid electric vehicle</keyword><keyword>IGBT inverters</keyword><keyword>PM brushless motor traction drives</keyword><keyword>PWM VSI</keyword><keyword>braking torque control</keyword><keyword>control strategy</keyword><keyword>machine performance</keyword><keyword>power density</keyword><keyword>surface mounted Magnaquench magnets</keyword><keyword>trapezoidal EMF</keyword></keywords><dates><year>1998</year><pub-dates><date>15-19 Feb 1998</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[3]Chinese Goalsin 2006 ADDIN EN.CITE <EndNote><Cite><Author>Yonghua</Author><Year>2010</Year><RecNum>23</RecNum><DisplayText>[22]</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">23</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Yonghua, Song</author><author>Xia, Yang</author><author>Zongxiang, Lu</author></authors></contributors><titles><title>Integration of plug-in hybrid and electric vehicles: Experience from China</title><secondary-title>Power and Energy Society General Meeting, 2010 IEEE</secondary-title><alt-title>Power and Energy Society General Meeting, 2010 IEEE</alt-title></titles><pages>1-6</pages><keywords><keyword>hybrid electric vehicles</keyword><keyword>China</keyword><keyword>Chinese automobile industry</keyword><keyword>air pollution</keyword><keyword>electric vehicles</keyword><keyword>energy shortage</keyword><keyword>environmental protection</keyword><keyword>global energy crisis</keyword><keyword>greenhouse gas over emission</keyword><keyword>plug-in hybrid vehicles</keyword><keyword>status quo</keyword><keyword>sustainable development</keyword><keyword>technical researches</keyword></keywords><dates><year>2010</year><pub-dates><date>25-29 July 2010</date></pub-dates></dates><isbn>1944-9925</isbn><urls></urls></record></Cite></EndNote>[22]FreedomCarGoals in 2006 ADDIN EN.CITE <EndNote><Cite><Author>FreedomCAR</Author><RecNum>29</RecNum><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>FreedomCAR</author></authors></contributors><titles><title>FreedomCAR and Fuel Partnership, Electrical and Electronics Technical Team Roadmap</title></titles><dates><pub-dates><date>November, 2006</date></pub-dates></dates><urls><related-urls><url>;[18]FreedomCarGoals in 2020* ADDIN EN.CITE <EndNote><Cite><Author>FreedomCAR</Author><RecNum>28</RecNum><record><rec-number>28</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">28</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>FreedomCAR</author></authors></contributors><titles><title>Electrical and electronics technical team roadmap</title></titles><dates><pub-dates><date>December 7, 2010</date></pub-dates></dates><urls><related-urls><url>;[19]Sic JFET-basedConverter PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IdWk8L0F1dGhvcj48WWVhcj4yMDExPC9ZZWFyPjxSZWNO
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ADDIN EN.CITE.DATA [21, 23]InverterPDW (kW/kg)4.0810.042~5>12>14.1>51PDV (kW/L)2.038.82~>12>13.4>51Efficiency@maximum load80~88%80~88%90~92%92%94%97.8%MotorMotor typesIMIMPM, IM and SRMPMPMPMPDW (kW/kg)0.5~10.5~10.5~1>1.2>1.6>1,3PDV (kW/L)1.01~1.01~1.01~>3.7>5.7>5Efficiency909092~95%>93%>94%>93%SystemEfficiency72~84%76~86%90~92%92%94%>92%Cooling modeForced airLiquidLiquidLiquidLiquid or airNatural airAmbient Temp.-25~50 °C-25~50 °C~70 °C~105 °C105 °C120 °CCost($/kW)--70<105<62.7-Total Mileage (km)--241402 (15 yrs)241402 (15 yrs)241402 (15 yrs)241402 (15 yrs)* Based on a maximum coolant or air temperature of 105°CIn EV inverter systems, the dc-link capacitors are essential to provide reactive power, attenuate ripple current, reduce the emission of electro-magnetic interference, and suppress voltage spikes caused by leakage inductance and switching operations ADDIN EN.CITE <EndNote><Cite><Author>Jih-Sheng</Author><Year>2002</Year><RecNum>42</RecNum><DisplayText>[24]</DisplayText><record><rec-number>42</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">42</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Jih-Sheng, Lai</author><author>Kouns, H.</author><author>Bond, J.</author></authors></contributors><titles><title>A low-inductance DC bus capacitor for high power traction motor drive inverters</title><secondary-title>Industry Applications Conference, 2002. 37th IAS Annual Meeting. Conference Record of the</secondary-title><alt-title>Industry Applications Conference, 2002. 37th IAS Annual Meeting. Conference Record of the</alt-title></titles><pages>955-962 vol.2</pages><volume>2</volume><keywords><keyword>AC motor drives</keyword><keyword>capacitors</keyword><keyword>invertors</keyword><keyword>secondary cells</keyword><keyword>traction motor drives</keyword><keyword>AC motor drive</keyword><keyword>DC-bus capacitor sizing</keyword><keyword>battery-powered traction motor drive</keyword><keyword>device switching</keyword><keyword>electrolytic bulk capacitors</keyword><keyword>high current</keyword><keyword>high power traction motor drive inverters</keyword><keyword>high temperature environment</keyword><keyword>high-frequency pulsating current</keyword><keyword>inverter DC bus</keyword><keyword>inverter design</keyword><keyword>low-inductance DC bus capacitor</keyword><keyword>low-inductance high-current film capacitor</keyword><keyword>performance improvement</keyword><keyword>traction motor drive inverter</keyword><keyword>voltage ripple</keyword></keywords><dates><year>2002</year><pub-dates><date>13-18 Oct. 2002</date></pub-dates></dates><isbn>0197-2618</isbn><urls></urls><electronic-resource-num>10.1109/ias.2002.1042673</electronic-resource-num></record></Cite></EndNote>[24]. DC-link capacitors are bulky, heavy and expensive ADDIN EN.CITE <EndNote><Cite><Author>Liutanakul</Author><Year>2008</Year><RecNum>9</RecNum><DisplayText>[25]</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">9</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Liutanakul, P.</author><author>Pierfederici, S.</author><author>Meibody-Tabar, F.</author></authors></contributors><titles><title>Application of SMC With I/O Feedback Linearization to the Control of the Cascade Controlled-Rectifier/Inverter-Motor Drive System With Small dc-Link Capacitor</title><secondary-title>Power Electronics, IEEE Transactions on</secondary-title></titles><periodical><full-title>Power Electronics, IEEE Transactions on</full-title></periodical><pages>2489-2499</pages><volume>23</volume><number>5</number><keywords><keyword>feedback</keyword><keyword>induction motor drives</keyword><keyword>invertors</keyword><keyword>linearisation techniques</keyword><keyword>machine control</keyword><keyword>power capacitors</keyword><keyword>rectifying circuits</keyword><keyword>robust control</keyword><keyword>variable structure systems</keyword><keyword>voltage control</keyword><keyword>dc-link capacitor</keyword><keyword>dc-link voltage</keyword><keyword>induction motor</keyword><keyword>input-output feedback linearization</keyword><keyword>power balance equation</keyword><keyword>robust control strategy</keyword><keyword>sliding mode controller</keyword><keyword>system parameter uncertainties</keyword><keyword>voltage controlled-rectifier-inverter-motor drive system</keyword></keywords><dates><year>2008</year></dates><isbn>0885-8993</isbn><urls></urls></record></Cite></EndNote>[25]. One typical design comprises five electrolytic capacitors, which are connected in parallel with the battery bank to supply a 80 kW motor drive system ADDIN EN.CITE <EndNote><Cite><Author>Jun</Author><Year>2008</Year><RecNum>12</RecNum><record><rec-number>12</rec-number><foreign-keys><key app="EN" db-id="rx2v9vewpetsrnerefn5dxadaast990dta9t">12</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Jun, Liu</author><author>Huiqing, Wen</author><author>Xuhui, Zhang</author></authors></contributors><titles><title>Analysis of the VSI with small DC-link capacitor for Electric Vehicles</title><secondary-title>Electrical Machines and Systems, 2008. ICEMS 2008. International Conference on</secondary-title><alt-title>Electrical Machines and Systems, 2008. ICEMS 2008. International Conference on</alt-title></titles><pages>1401-1405</pages><keywords><keyword>battery powered vehicles</keyword><keyword>electric drives</keyword><keyword>invertors</keyword><keyword>power capacitors</keyword><keyword>DC-link capacitor</keyword><keyword>PSpice model</keyword><keyword>VSI analysis</keyword><keyword>electric vehicle drive</keyword><keyword>film capacitor</keyword><keyword>power 80 kW</keyword><keyword>voltage source inverter</keyword></keywords><dates><year>2008</year><pub-dates><date>17-20 Oct. 2008</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[26]. Each capacitor is 9.4 cm in diameter and 14.6 cm in height. Since the five dc-link capacitors occupy more than 40% of the volume, the achievable PDV is limited to 2.99 kW/L. Furthermore, the height of dc-link capacitors is higher than most IGBT modules and requires a crooked busbar to make the connection. The resulting parasitic inductance may exceed 100 nH causing voltage spikes, which are a major factor in the failure of power electronic devices. For the above-mentioned reasons, an optimum design of dc-link capacitor is critical to achieve the goals shown in Table I. Some basic requirements for choosing and comparing different capacitors for EV inverter applications include the following.The dc-link capacitors should be able to handle the ripple current under all VSI operating conditions for EV applications. The AC ripple current should never exceed 10% of the rated battery current to avoid significant degradation on the lifetime of battery.The ripple voltage across the dc bus should be limited to 10% of the rated voltage for all expected load conditions. Low inductance capacitors are preferred to avoid overvoltage failure of IGBTs.Hot spot temperature should be below 105°C under maximum ambient temperature for any expected load condition.Ripple current is one of the main considerations in sizing and selecting dc-link capacitors. Approaches have been proposed to reduce the capacitor current ripple and minimize the capacitor size without violating other constraints by coordinating the modulation strategies between the active rectifier and the PWM inverter stages PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Cb24tR3dhbjwvQXV0aG9yPjxZZWFyPjIwMDY8L1llYXI+
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ADDIN EN.CITE.DATA [27, 28]. The coordinating modulation method has been shown to cancel most of the dc-link capacitor ripple current in Hybrid EV DC-DC converters and inverter system applications ADDIN EN.CITE <EndNote><Cite><Author>Xi</Author><Year>2011</Year><RecNum>40</RecNum><DisplayText>[29]</DisplayText><record><rec-number>40</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">40</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Xi, Lu</author><author>Wei, Qian</author><author>Dong, Cao</author><author>Fang Zheng, Peng</author><author>Jianfeng, Liu</author></authors></contributors><titles><title>A carrier modulation method for minimizing the dc link capacitor current ripple of the HEV DC-DC converter and inverter systems</title><secondary-title>Applied Power Electronics Conference and Exposition (APEC), 2011 Twenty-Sixth Annual IEEE</secondary-title><alt-title>Applied Power Electronics Conference and Exposition (APEC), 2011 Twenty-Sixth Annual IEEE</alt-title></titles><pages>800-807</pages><keywords><keyword>DC-DC power convertors</keyword><keyword>PWM invertors</keyword><keyword>PWM power convertors</keyword><keyword>hybrid electric vehicles</keyword><keyword>power capacitors</keyword><keyword>power factor</keyword><keyword>reliability</keyword><keyword>AC-DC-AC pulse-width modulation converter</keyword><keyword>DC link capacitor current ripple</keyword><keyword>DC-DC-AC PWM converter</keyword><keyword>HEV DC-DC converter</keyword><keyword>bidirectional DC-DC converter</keyword><keyword>carrier modulation method</keyword><keyword>close-loop control method</keyword><keyword>energy storage system</keyword><keyword>low-cost hybrid electric vehicle converter-inverter system</keyword></keywords><dates><year>2011</year><pub-dates><date>6-11 March 2011</date></pub-dates></dates><isbn>1048-2334</isbn><urls></urls></record></Cite></EndNote>[29]. However, the implementation of coordinating control strategies is infeasible for the EV drive system shown in REF _Ref309885527 \h Fig. 1, where the dc-link capacitors are connected directly in parallel with the battery bank without any power stages in between PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5HcmluYmVyZzwvQXV0aG9yPjxZZWFyPjIwMDU8L1llYXI+
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ADDIN EN.CITE.DATA [31-34]. Most analysis has been based on an ideal capacitor model, which cannot accurately predict power loss and capacitor lifetime. The ideal capacitor model does not properly account for the effects of variation of load power factor and modulation index in a practical EV system. Models that include equivalent series resistances (ESR) and show the effects of temperature and frequency are investigated and applied to electrolytic capacitors in PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5HYXNwZXJpPC9BdXRob3I+PFllYXI+MjAwNTwvWWVhcj48
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ADDIN EN.CITE.DATA [35-37]. Their modeling approach concentrates on only the characteristic analysis for electrolytic capacitors. A systematic comprehensive evaluation of the benefits and drawbacks of film capacitors for EV inverter applications has not been reported. The basic requirements, system constraints, and performance metrics have not been fully and systematically addressed. In EV inverter systems, the capacitor ripple current consists of various frequency components corresponding to different pulse width modulation (PWM) strategies. Therefore, the frequency spectrum analysis of the capacitor current and an accurate model of ESR with consideration of the temperature and frequency response are important to properly account for the self-heating process of dc-link capacitors. Further, the electro-thermal coupling dynamics must be evaluated to estimate the true core temperature of the dc-link capacitors, which is critical to predict capacitor lifetime. This paper presents a comprehensive analysis and evaluation of dc-link capacitors in EV inverter systems to improve the power density. The analysis starts with ESR models of both electrolytic and film capacitors. The derived mathematical models are verified by experiments. The voltage and current stresses are analyzed with respect to three common modulation strategies including sinusoidal PWM (SPWM), space vector modulation (SVM) and third harmonics injection (THI). The frequency spectrum of the capacitor ripple current is also investigated corresponding to these modulation strategies over the practical ranges of load power factor and modulation index. Based on the above analysis, the self-heating process and the resulting core temperature are modeled and analyzed. Two design schemes using electrolytic and film capacitors are compared through simulation and experiments in terms of power loss, core temperature, lifetime and battery current harmonics. The proposed design has been tested in an 80kW permanent-magnet (PM) motor drive system. CAPACITOR CHARACTERISTICSThis section investigates the ESR models of electrolytic and film capacitors and shows the characteristics of frequency and self heating. Electrolytic capacitorElectrolytic capacitors are commonly used as the dc-link capacitors due to their large capacitance per unit volume. The ESR model of an electrolytic capacitor is illustrated in Fig. 2 ADDIN EN.CITE <EndNote><Cite><Author>Rendusara</Author><Year>1999</Year><RecNum>21</RecNum><DisplayText>[38]</DisplayText><record><rec-number>21</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">21</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Rendusara, D.</author><author>Cengelci, E.</author><author>Enjeti, P.</author><author>Lee, D. C.</author></authors></contributors><titles><title>An evaluation of the DC-link capacitor heating in adjustable speed drive systems with different utility interface options</title><secondary-title>Applied Power Electronics Conference and Exposition, 1999. APEC '99. Fourteenth Annual</secondary-title><alt-title>Applied Power Electronics Conference and Exposition, 1999. APEC '99. Fourteenth Annual</alt-title></titles><pages>781-787 vol.2</pages><volume>2</volume><keywords><keyword>AC motor drives</keyword><keyword>PWM power convertors</keyword><keyword>capacitors</keyword><keyword>heating</keyword><keyword>inductors</keyword><keyword>rectifying circuits</keyword><keyword>variable speed drives</keyword><keyword>DC-link capacitor heating</keyword><keyword>DC-link inductor</keyword><keyword>active PWM rectifier</keyword><keyword>adjustable speed drive systems</keyword><keyword>auto-connected 12-pulse rectifier</keyword><keyword>capacitor heating factor</keyword><keyword>capacitor operating life reduction</keyword><keyword>nearly sinusoidal current</keyword><keyword>ripple currents</keyword><keyword>self-heating</keyword><keyword>six-pulse diode rectifier</keyword><keyword>utility interface options</keyword></keywords><dates><year>1999</year><pub-dates><date>14-18 Mar 1999</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[38], where the resistance R0 accounts for the sum of resistances of foil, tabs, and terminals, R1 represents the electrolyte resistance, C1 represents the terminal capacitance, and the parallel combination of R2 and C2 represents the dielectric dynamics. The ESR of the capacitor in terms of the frequency responses is derived accordingly. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (1)For electrolytic capacitors, a rise in temperature causes a decrease in ESR because the resistance R1 is reduced by the increased conductivity of electrolyte. The effect of temperature on R1 is described by GOTOBUTTON ZEqnNum666575 \* MERGEFORMAT REF ZEqnNum666575 \* Charformat \! \* MERGEFORMAT (2) PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5HYXNwZXJpPC9BdXRob3I+PFllYXI+MjAwNTwvWWVhcj48
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ADDIN EN.CITE.DATA [35, 39]. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (2)where R1b represents the value of R1 at the base temperature Tbase (27 oC), T is the capacitor core temperature (oC), and F is a temperature sensitivity factor ADDIN EN.CITE <EndNote><Cite><Author>Gasperi</Author><Year>2005</Year><RecNum>8</RecNum><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="z0st2rta5tedtjed0wa50txo5pt2xtxrrz50">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Gasperi, M. L.</author></authors></contributors><titles><title>Life prediction modeling of bus capacitors in AC variable-frequency drives</title><secondary-title>IEEE Trans. Ind. Appl.</secondary-title></titles><periodical><full-title>IEEE Trans. Ind. Appl.</full-title></periodical><pages>1430-1435</pages><volume>41</volume><number>6</number><keywords><keyword>AC motor drives</keyword><keyword>capacitor storage</keyword><keyword>electrolytic capacitors</keyword><keyword>remaining life assessment</keyword><keyword>AC line impedance</keyword><keyword>AC variable frequency drives</keyword><keyword>aluminum electrolytic capacitors</keyword><keyword>bus capacitor life prediction modeling</keyword><keyword>bus filters</keyword><keyword>capacitor banks</keyword><keyword>heat transfer characteristics</keyword><keyword>motor drive simulation</keyword><keyword>ripple current waveform</keyword></keywords><dates><year>2005</year></dates><isbn>0093-9994</isbn><urls></urls></record></Cite></EndNote>[40].Fig. SEQ Fig. \* ARABIC 2 ESR model of an electrolytic capacitor. Film capacitor A R-L-C series equivalent circuit that includes the equivalent inductance Lc, capacitance Cc and resistance Rc is used to model film capacitors. When the operating frequency is higher than 1 kHz, the ESR value can be modeled as a function of frequency based on ADDIN EN.CITE <EndNote><Cite ExcludeYear="1"><Author>AVX</Author><RecNum>34</RecNum><record><rec-number>34</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">34</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>AVX</author></authors></contributors><titles><title>AVX Medium power film capacitors for power applications</title></titles><pages>2-18</pages><dates></dates><urls><related-urls><url>;[41]. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (3)where Rs is the base resistance, f represents the frequency, and As is a given value depending on the capacitor size. K(f) is the predefined function showing the effect of frequency, which is usually given by plots in manufacturer datasheets. In this analysis, K(f) is mathematically expressed as a cubic polynomial function, as shown in (4), in which the coefficients k0-3 can be established by using least square curve fitting. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (4)In contrast with the electrolytic capacitor, the ESR value of film capacitors increases with the frequency. Its temperature-sensitivity is less than that of electrolytic capacitors ADDIN EN.CITE <EndNote><Cite ExcludeYear="1"><Author>AVX</Author><RecNum>34</RecNum><record><rec-number>34</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">34</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>AVX</author></authors></contributors><titles><title>AVX Medium power film capacitors for power applications</title></titles><pages>2-18</pages><dates></dates><urls><related-urls><url>;[41] because the ESR of film capacitors results mainly from the tabs and contact resistances, but not from the electrolyte ADDIN EN.CITE <EndNote><Cite><Author>Buiatti</Author><Year>2007</Year><RecNum>14</RecNum><record><rec-number>14</rec-number><foreign-keys><key app="EN" db-id="rx2v9vewpetsrnerefn5dxadaast990dta9t">14</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Buiatti, G. M.</author><author>Cruz, S. M. A.</author><author>Cardoso, A. J. M.</author></authors></contributors><titles><title>Lifetime of Film Capacitors in Single-Phase Regenerative Induction Motor Drives</title><secondary-title>Diagnostics for Electric Machines, Power Electronics and Drives, 2007. SDEMPED 2007. IEEE International Symposium on</secondary-title><alt-title>Diagnostics for Electric Machines, Power Electronics and Drives, 2007. SDEMPED 2007. IEEE International Symposium on</alt-title></titles><pages>356-362</pages><keywords><keyword>induction motor drives</keyword><keyword>invertors</keyword><keyword>machine vector control</keyword><keyword>polymer films</keyword><keyword>rectifying circuits</keyword><keyword>thin film capacitors</keyword><keyword>MPPF</keyword><keyword>indirect rotor field oriented control</keyword><keyword>inverter</keyword><keyword>lifetime analysis</keyword><keyword>metallized polypropylene film capacitors</keyword><keyword>single-phase active rectifier</keyword><keyword>single-phase regenerative induction motor drives</keyword></keywords><dates><year>2007</year><pub-dates><date>6-8 Sept. 2007</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[42].Ripple current multiplier Since the ESR values of electrolytic and film capacitors show frequency-dependent characteristics, a ripple current multiplier Mf is defined in GOTOBUTTON ZEqnNum575314 \* MERGEFORMAT REF ZEqnNum575314 \* Charformat \! \* MERGEFORMAT (5) to characterize the ripple current that capacitors can absorb at a given frequency. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (5)where I100 and ESR100 are defined as the rated ripple current and the ESR value at 100Hz, which are usually given by manufacturers. If and ESRf represent ripple current and ESR at a specific frequency. Electrolytic capacitors are characterized as absorbing more high-frequency ripple current than the low-frequency component. Conversely, the film capacitors usually handle less high-frequency ripple current because the ripple current multiplier drops with increasing ESRf. CAPACITOR RIPPLE Current AND voltageThe battery current (ibat) is the sum of capacitor current (icap) and dc-link current (iinv), as shown in Fig. 1. These current waveforms are greatly affected by the load power factor, which determines the current flowing into IGBT devices or free-wheeling diodes of the VSI. As a result, the practical EV operating conditions, expressed in terms of load power factor and modulation index, must be considered in evaluating the capacitor ripple current and voltage. Capacitor ripple current analysisBased on the synthesis of the inverter input current modulation by SVM ADDIN EN.CITE <EndNote><Cite><Author>Kolar</Author><Year>2006</Year><RecNum>18</RecNum><record><rec-number>18</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">18</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kolar, J. W.</author><author>Round, S. D.</author></authors></contributors><titles><title>Analytical calculation of the RMS current stress on the DC-link capacitor of voltage-PWM converter systems</title><secondary-title>Electric Power Applications, IEE Proceedings -</secondary-title></titles><periodical><full-title>Electric Power Applications, IEE Proceedings -</full-title></periodical><pages>535-543</pages><volume>153</volume><number>4</number><keywords><keyword>PWM invertors</keyword><keyword>PWM power convertors</keyword><keyword>capacitors</keyword><keyword>digital simulation</keyword><keyword>insulated gate bipolar transistors</keyword><keyword>DC-link capacitor</keyword><keyword>RMS current stress</keyword><keyword>analytical expression</keyword><keyword>low-frequency IGBT inverter system</keyword><keyword>modulation depth</keyword><keyword>output current amplitude</keyword><keyword>output-current ripple</keyword><keyword>phase angle</keyword><keyword>voltage-PWM converter system</keyword></keywords><dates><year>2006</year></dates><isbn>1350-2352</isbn><urls></urls></record></Cite></EndNote>[34], the RMS capacitor ripple current Icap can be expressed by GOTOBUTTON ZEqnNum552453 \* MERGEFORMAT REF ZEqnNum552453 \* Charformat \! \* MERGEFORMAT (6). MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (6)where, M is the modulation index, IN is the output phase current amplitude, and is the phase delay of inverter output current with respect to the voltage fundamental. REF _Ref305223130 \h Fig. 3 illustrates the dependence of Icap/IN on modulation index M and load power factor. The modulation index corresponding to the maximum RMS value of capacitor ripple current is denoted as MIcap(max), and it depends somewhat on modulation strategy. The SPWM and SVM share the same expression GOTOBUTTON ZEqnNum127517 \* MERGEFORMAT REF ZEqnNum127517 \* Charformat \! \* MERGEFORMAT (7) for MIcap(max), and for THI MIcap(max) is given by GOTOBUTTON ZEqnNum115716 \* MERGEFORMAT REF ZEqnNum115716 \* Charformat \! \* MERGEFORMAT (8). MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (7) MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (8) Fig. SEQ Fig. \* ARABIC 3 Ratio of Icap/Il is a function of modulation index M and load power factor .Shown in Fig. 3, the blue line illustrates the maximum RMS value of capacitor ripple current corresponding to the THI modulation strategy, under which the modulation index can range from 0 to 1.15. The black line indicates the upper bound (M = 1) of MIcap(max) when modulation is by SPWM or SVM . In order to address typical operation conditions, the distribution of MIcap(max) in relation to the load power factor is plotted in a two-dimensional space, which is shown in Fig. 4. When the is lower than a certain value of the power factor , the ratio increases with M and reaches to the maximum at the upper bound of modulation range. When is larger than , MIcap(max) is located in the middle of the modulation range, no longer at the upper bound. It is noticeable that THI shows a different value from SPWM and SVM since the modulation index is up to 1.15. In the case of THI, the threshold value of the load power factor cos is 0.43, while the corresponding threshold value of load power factor is 0.49 in the cases of SPWM and SVM. Based on the above analysis, five typical operating conditions denoted by P1-P5 are defined in Table II.Table SEQ Table \* ROMAN IIPredefined Typical Operating conditions P1-P5Operating conditionModulation index MLoad power factor P11.150.43P210.49P31.150.23P410.23P50.6250.954Fig. 4 The distribution of MIcap(max) corresponding to power factor .The maximum current stress on a dc-link capacitor can be estimated by applying GOTOBUTTON ZEqnNum552453 \* MERGEFORMAT REF ZEqnNum552453 \* Charformat \! \* MERGEFORMAT (6) over a wide variety of load conditions for a specific motor, modulation method, and battery. Here we consider an 80kW permanent-magnet (PM) motor is supplied by a 312V battery pack. The capacitor maximum current stress is calculated as 105A, which is used as the base value for capacitor ripple current evaluation. Capacitor voltage ripple analysisTable III summarizes the expressions for dc-link capacitor RMS ripple voltage (in per unit) for different modulation strategies ADDIN EN.CITE <EndNote><Cite><Author>Dahono</Author><Year>1996</Year><RecNum>30</RecNum><record><rec-number>30</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">30</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dahono, P. A.</author><author>Sato, Y.</author><author>Kataoka, T.</author></authors></contributors><titles><title>Analysis and minimization of ripple components of input current and voltage of PWM inverters</title><secondary-title>Industry Applications, IEEE Transactions on</secondary-title></titles><periodical><full-title>Industry Applications, IEEE Transactions on</full-title></periodical><pages>945-950</pages><volume>32</volume><number>4</number><keywords><keyword>PWM invertors</keyword><keyword>power factor</keyword><keyword>input current ripple</keyword><keyword>input voltage ripple</keyword><keyword>load power factor</keyword><keyword>ripple components minimisation</keyword><keyword>three-phase</keyword><keyword>voltage-source PWM inverters</keyword></keywords><dates><year>1996</year></dates><isbn>0093-9994</isbn><urls></urls></record></Cite></EndNote>[43]. The base value is given by GOTOBUTTON ZEqnNum494955 \* MERGEFORMAT REF ZEqnNum494955 \* Charformat \! \* MERGEFORMAT (9), where Cd is the dc-link capacitance and f1 is the inverter switching frequency. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (9)Table SEQ Table \* ROMAN IIIdc-link capacitor Voltage ripple expressions for SPWM, SVM and THIModulation StrategiesVoltage ripple of dc-link capacitor (p.u.) ADDIN EN.CITE <EndNote><Cite><Author>Dahono</Author><Year>1996</Year><RecNum>30</RecNum><record><rec-number>30</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">30</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dahono, P. A.</author><author>Sato, Y.</author><author>Kataoka, T.</author></authors></contributors><titles><title>Analysis and minimization of ripple components of input current and voltage of PWM inverters</title><secondary-title>Industry Applications, IEEE Transactions on</secondary-title></titles><periodical><full-title>Industry Applications, IEEE Transactions on</full-title></periodical><pages>945-950</pages><volume>32</volume><number>4</number><keywords><keyword>PWM invertors</keyword><keyword>power factor</keyword><keyword>input current ripple</keyword><keyword>input voltage ripple</keyword><keyword>load power factor</keyword><keyword>ripple components minimisation</keyword><keyword>three-phase</keyword><keyword>voltage-source PWM inverters</keyword></keywords><dates><year>1996</year></dates><isbn>0093-9994</isbn><urls></urls></record></Cite></EndNote>[43]SPWMSVMTHIFig. 5 illustrates the characteristic of dc-link ripple voltage in per unit with regard to the modulation index M, the load power factor for the three modulation strategies. When the load power factor is zero, the ripple voltage levels are the same for all three modulation strategies SPWM, SVM and THI. When the load power factor is non-zero, the SPWM shows the largest voltage ripple, the THI gives the lowest voltage ripple and the SVM demonstrates relatively low voltage ripple. Fig. 5 Characteristics of the voltage ripple across the dc link as a function of modulation index M and power factor for the three modulation strategies SPWM, SVM, and THI.Frequency Spectrum of Capacitor Ripple CurrentThe frequency spectra of capacitor current icap for the predefined operating conditions, Pi, and modulation methods are illustrated in REF _Ref309913050 \h Fig. 6 and are summarized in Table IV to demonstrate the interaction of modulation strategy and operating condition. The current spectra contain significant switching frequency f1 multiples and their sidebands (sbs). At low, switching frequency sidebands are usually the biggest harmonic components and the current spectrum is more or less evenly distributed among f1 sbs, 3f1 sbs and 2f1. At high (larger than 0.49 for SVM), 2f1 is the dominant component and its amplitude increases with . For instance, the largest harmonic component is nearly 21% of output current amplitude at =0.49, while the corresponding harmonic component reaches as high as 48.8% at =0.954. Moreover, the impact of modulation strategy on current spectrum distribution is obvious at high and the major harmonics for SVM will extend to higher frequency such as 6f1. One can see that the ESR characteristic of the dc-link capacitor is highly affected by frequency for both electrolytic and film capacitors. The FFT results shown in REF _Ref309913050 \h Fig. 6 and Table IV provide information essential to proper sizing of the dc-link capacitors.P5 (M=0.625, =0.954), SVMP5 (M=0.625, =0.954), SPWMP5 (M=0.625, =0.954), THIP1 (M=1.15, =0.43), THIP2 (M=1, =0.49), SVMP3 (M=1.15, =0.23), THIP4 (M=1, =0.23), SVMP4 (M=1, =0.23), SPWMFig. SEQ Fig. \* ARABIC 6 Frequency spectra of capacitor current based on modulation strategy and predefined operating condition: load power factor and modulation index.Table SEQ Table \* ROMAN IVComparison of spectral distribution For the Three modulation Strategies and five operating conditionsOperating conditionModulationMajor three components sorted by magnitude (% of IN)frequencymagnitudefrequencymagnitudefrequencymagnitudeP4SPWM3f1 sbs19.2f1 sbs17.22f110.2P4SVMf1 sbs16.63f1 sbs15.92f111.7P1THIf1 sbs20.23f1 sbs12.32f17.3P1THIf1 sbs19.72f113.63f1 sbs11.4P2SPWM2f121.7f1 sbs15.43f1 sbs14.7P2SVM2f121.73f1 sbs17.4f1 sbs17P5SPWM2f149.24f113.13f1 sbs11.1P5SVM2f1524f1146f19.9P5THI2f148.83f1 sbs9.94f18.7 PERFORMANCE MetricsBased on the above analysis, four metrics are proposed to evaluate the performance of dc-link capacitors: power loss, core temperature, capacitor life, and battery ripple current. Power Loss and Core TemperatureThe power loss of dc-link capacitors is the sum of the power dissipation of ESR from individual frequency current components that can be calculated by using the ripple current multiplier Mf. The expression is shown in GOTOBUTTON ZEqnNum483468 \* MERGEFORMAT REF ZEqnNum483468 \* Charformat \! \* MERGEFORMAT (10), where represents the ESR value corresponding to the specific frequency fi and is the RMS current absorbed by the capacitor at a certain frequency fi. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (10)The self-heating process of dc-link capacitors can be numerically evaluated by using the coupled electrothermal method. Fig. 7 depicts the iterative solution process. The computation starts with a given ambient temperature Ta. The capacitor core temperature Tj_C is initially calculated by using the capacitor power loss and the equivalent thermal model ADDIN EN.CITE <EndNote><Cite ExcludeYear="1"><Author>AVX</Author><RecNum>34</RecNum><record><rec-number>34</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">34</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>AVX</author></authors></contributors><titles><title>AVX Medium power film capacitors for power applications</title></titles><pages>2-18</pages><dates></dates><urls><related-urls><url> ExcludeYear="1"><Author>BHC</Author><RecNum>36</RecNum><record><rec-number>36</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">36</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>BHC</author></authors></contributors><titles><title>Aluminum Electrolytic Capacitors - Application Notes</title></titles><pages>10-11</pages><dates></dates><urls></urls></record></Cite></EndNote>[41, 44]. Thermal resistances are denoted by Rhc, from hot spot to can, Rca from can to ambient, Rbp, from can base to mounting plate, and Rha from mounting plate to ambient air. The equivalent thermal resistance from the core of capacitor to the ambient is given by: MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (11)The values of ESR and ripple current are updated repeatedly using the previous value of Tc for each update. The iterative corrections are repeated until the process converges to within a given tolerance. The core temperature Tj_C and the temperature rise are used for predicting the capacitor lifetime.Fig. SEQ Fig. \* ARABIC 7 Flowchart for iterative solving process of core temperature and ESR.Capacitor Lifetime The capacitor lifetime is influenced by the capacitor core temperature and the ripple current and is given [17] for both kinds of capacitors by: MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (12)where Lb is the capacitor lifetime under its maximum temperature and commonly given by manufacturer datasheets. I0 denotes the allowable maximum ripple current at a given frequency, also given in data sheets, and I denotes the actual ripple current value. The K is a constant, which is typically assigned a value of 2 ADDIN EN.CITE <EndNote><Cite><Author>Xuhui</Author><Year>2007</Year><RecNum>37</RecNum><DisplayText>[17]</DisplayText><record><rec-number>37</rec-number><foreign-keys><key app="EN" db-id="rerws9wvqtv090esrwt5par2patzazaa9zav">37</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Xuhui, Wen</author><author>Wei, Hu</author><author>Tao, Fan</author><author>Jun, Liu</author></authors></contributors><titles><title>Lifetime model research of motor drive system for electric vehicles</title><secondary-title>Electrical Machines and Systems, 2007. ICEMS. International Conference on</secondary-title><alt-title>Electrical Machines and Systems, 2007. ICEMS. International Conference on</alt-title></titles><pages>129-132</pages><keywords><keyword>electric vehicles</keyword><keyword>induction motor drives</keyword><keyword>insulated gate bipolar transistors</keyword><keyword>invertors</keyword><keyword>higher power density</keyword><keyword>induction motor drive</keyword><keyword>insulated gate bipolar transistor</keyword><keyword>motor controller</keyword><keyword>power 160 kW</keyword><keyword>three phase inverter</keyword></keywords><dates><year>2007</year><pub-dates><date>8-11 Oct. 2007</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[17]. Battery ripple current analysisStudies show that ripple current affects battery lifetime due to the internal temperature rise ADDIN EN.CITE <EndNote><Cite><Author>Hilmy</Author><Year>2010</Year><RecNum>54</RecNum><record><rec-number>54</rec-number><foreign-keys><key app="EN" db-id="z0st2rta5tedtjed0wa50txo5pt2xtxrrz50">54</key></foreign-keys><ref-type name="Conference Proceedings">10</ref-type><contributors><authors><author>Hilmy, M.</author><author>Ahmed, M. E.</author><author>Orabi, M.</author><author>Sayed, M. A.</author><author>El-Nemr, M.</author></authors></contributors><titles><title>Optimum design of high efficiency power conditioning wind energy system</title><secondary-title>Power and Energy (PECon), 2010 IEEE International Conference on</secondary-title><alt-title>Power and Energy (PECon), 2010 IEEE International Conference on</alt-title></titles><pages>611-616</pages><keywords><keyword>maximum power point trackers</keyword><keyword>permanent magnet generators</keyword><keyword>synchronous generators</keyword><keyword>wind power</keyword><keyword>MPPT</keyword><keyword>PMSG</keyword><keyword>bidirectional power flow link</keyword><keyword>high efficiency power conditioning</keyword><keyword>maximum power point tracking</keyword><keyword>permanent magnet synchronous generator</keyword><keyword>wind energy conversion system</keyword></keywords><dates><year>2010</year><pub-dates><date>Nov. 29 2010-Dec. 1 2010</date></pub-dates></dates><urls></urls></record></Cite></EndNote>[45]. Therefore, the battery ripple current should be maintained under a certain limit to avoid the harmful effect. The dc-link capacitor is represented by an equivalent circuit including Rc, Lc and Cc, as shown in Fig. 8. The switching frequency is 20 kHz, and that the ESR of battery pack and interconnects can be neglected since the impedance of interconnects is dominated by the inductance component, shown as L1 in Fig. 8. It includes the inductance introduced by the battery pack and interconnects between the battery pack and the inverter. The battery ripple current can be obtained as GOTOBUTTON ZEqnNum987289 \* MERGEFORMAT REF ZEqnNum987289 \* Charformat \! \* MERGEFORMAT (13) according to the equivalent circuit shown in REF _Ref309886612 \h Fig. 8. Fig. SEQ Fig. \* ARABIC 8 Equivalent AC circuit of the EV inverter for the battery ripple current analysis. MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (13) MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (14)The reference values of inductance (L1b) are assigned to 10 ?H considering the practical component layout and the parameters of interconnects. The RMS battery ripple current in percentage can be defined by the division of AC RMS value (Ibat, ac) over the DC RMS current (Ibat, dc), as shown in GOTOBUTTON ZEqnNum505804 \* MERGEFORMAT REF ZEqnNum505804 \* Charformat \! \* MERGEFORMAT (15). MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT (15)EVALUATION Results and discussionThis section includes the validations of the derived capacitor ESR models by experimental tests and the analysis of dc-link capacitor current. Then two configurations of dc-link capacitors are comparatively investigated through simulation and experiment for an 80 kW PM motor drive system in terms of the previously defined performance metrics.The parameters of two dc-link capacitor designs, Scheme I and Scheme II, are listed in Table V. Scheme I uses five 3300?F electrolytic capacitors (ALS332QP500) and Scheme II includes two 220?F film capacitors (AVX FFVE6K0227K). The capacitor specifications are given in the Appendix. Both Schemes meet the base requirements shown in section I and are comparable considering product availability, effect of ripple frequency, temperature, etc. Table SEQ Table \* ROMAN VMain parameters for two design schemesParametersScheme IScheme IIQuantity52Manufacturer PartALS332QP500FFVE6K0227KTotal Capacitance(?F)16500440Volume (LWH, cm)38×7.7×1516.8×8.2×8Ripple current limit (A)132200Cost($)*566176 * Source: , Date: Feb. 20, 2012Validation of Capacitors ModelThe ESR values using the derived model are plotted together with the experimental results as shown in Fig. 9. The ESR values are measured using a HP4263B LCR meter. The mathematical model shown in GOTOBUTTON ZEqnNum675419 \* MERGEFORMAT REF ZEqnNum675419 \* Charformat \! \* MERGEFORMAT (1) matches the experiment evaluation regarding to the frequency effect. Table VI summarizes the model parameters for the electrolytic capacitor. Fig. SEQ Fig. \* ARABIC 9 Comparison of measured and modeled ESR for the electrolytic capacitor ALS332QP500 at 300°K.Table SEQ Table \* ROMAN VIModel parameters of the electrolytic capacitor ALS332QP500ParametersValueResistance of foil, tabs, and terminals R0 (m?)5.03Resistance of electrolyte R1b @ 300oK (m?)6Temperature sensitivity factor F (oK-1)21Dielectric loss resistance R2 (m?)38.35Terminal capacitance C1 (?F)3300Dielectric loss capacitance C2 (?F)11.6The modeling process of the film capacitor is described in Section 2B, which includes the polynomial expression of the frequency dependent parameter K(f) and the parameter extraction through the comparison with the measured impedance. Fig. 10 shows that the mathematical model matches the experimentally measured frequency response for the 500V/220?F film capacitor AVX FFVE6K0227K. Table VII summarizes the equivalent circuit parameters of film capacitors. (a)(b)Fig. 10 Comparison of measured and modeled impedance for the film capacitor AVX FFVE6K0227K at 300°K; (a) Amplitude characteristic; (b) Phase characteristic.Table SEQ Table \* ROMAN VIIModel parameters of the film capacitor AVX FFVE6K0227KParameters ValueParametersValueEquivalent series inductance Lc (nH)40Coefficient of K expression f30.0000003173Equivalent series capacitance Cc (?F)210Coefficient of K expression f2-0.000124Base resistance Rs (m?)1Coefficient of K expression f10.02369Parameter defined by height As (m?)0.24Coefficient of K expression f01.014The ESR characteristics of two schemes are compared in Fig. 11. It shows the ESR of scheme II is always lower than that of the scheme I through the frequency span. Furthermore, the ESR of scheme I decreases remarkably when the temperature increases from 27°C to 70°C. Fig. SEQ Fig. \* ARABIC 11 ESR comparison of the two design schemes for dc-link capacitors with respect to the operating frequency and temperature.The capacitor ripple current multiplier Mf was defined in GOTOBUTTON ZEqnNum575314 \* MERGEFORMAT REF ZEqnNum575314 \* Charformat \! \* MERGEFORMAT (5) and used to evaluate the capacitor power loss by using GOTOBUTTON ZEqnNum483468 \* MERGEFORMAT REF ZEqnNum483468 \* Charformat \! \* MERGEFORMAT (10). Based on the verified mathematical models, the estimated Mf values are summarized in Table VIII corresponding to both design schemes.Table SEQ Table \* ROMAN VIIIripple current multiplier Mf of two design schemes for dc-link capacitorsFrequency (kHz)Mf for Scheme IMf for Scheme IIFrequency (kHz)Mf for Scheme IMf for Scheme II0.11152.040.980.21.081102.050.970.51.391202.050.9511.741502.060.9021.950.991002.060.86Validation of Ripple Current AnalysisThe RMS value of the capacitor ripple current is evaluated by Pspice simulation. The load is a 0.2? resistor connected with a variable inductor, which can be used to effect different load power factors. The inverter is modulated by the SVM algorithm and the switching frequency is 20 kHz. One test case, which corresponds to the constant power operation mode of motors, maintains constant output current and the constant input voltage. The test condition is designed such that IN is constant at 84A and Vin = 312V with a adjusted modulation indexes, M. The simulated capacitor current RMS value is compared with the value estimated from the mathematical model in GOTOBUTTON ZEqnNum552453 \* MERGEFORMAT REF ZEqnNum552453 \* Charformat \! \* MERGEFORMAT (6). Table IX presents the results, which include the simulated capacitor current RMS value (Icap), the estimated capacitor RMS current (Icap_est), and the estimation error () under different operating conditions. The root-mean-square deviation (RMSD) is used to evaluate the differences between the mathematical modeling results and the simulation results. This indicates that the RMSD value is 0.36 A, which is small relative to the average capacitor current RMS value 22.77 A.Table SEQ Table \* ROMAN IXCapacitor Current Comparison Between the simulation and Model estimation for constant output current (84A) and Input voltage (312V)L (mH)MIcap (A)Icap_est (A) (A)40.160.72927.7426.970.772.70.230.49723.3423.110.2310.540.21119.7219.78-0.060.50.790.14520.9720.9700.20.950.11922.1022.040.06Table SEQ Table \* ROMAN XCapacitor Current Comparison Between the simulation and THE Model estimation for constant output current (84A) and Modulation Index (0.84)L (mH)Vin (V)Icap (A)Icap_est (A) (A)40.16261.726.7927.44-0.652.70.23184.829.5228.990.5310.5477.531.5430.830.710.50.7953.133.9233.320.600.20.9543.435.7635.220.54The second test case keeps the output current and modulation index constant, where IN = 84A and M = 0.84. The input voltage is tuned according to the variation of the load power factor. Table X presents the comparison between the simulation results and the model estimation. The RMSD result is 0.61A and the average capacitor ripple current RMS value is 31.51 A. The simulation verified the proposed mathematical models and indicated a 1.85% relative modeling error based on the two cases. Furthermore, it exhibits the same trends as the analysis derived in Section 2A and illustrated in Fig. 3.Evaluation of Performance MetricsThe power loss and core temperature are calculated and illustrated in REF _Ref307753562 \h Fig. 12. The main parameters of two design schemes are defined in Table V. As shown in Fig. 12a, the capacitor power loss of the Scheme II is significantly lower than the scheme I due to the reduction of ESR value. It shows that the capacitor power loss increases with the load power factor and decreases with the ambient temperature Ta in Scheme I. The power loss is nearly constant when Ta varies from 45°C to 85°C in Scheme II due to the insensitive temperature factor of film capacitors. The estimated core temperature of both schemes is illustrated in Fig. 12b. Scheme II shows a lightly higher core temperature considering the volume difference of dc-link capacitors. The thermal resistance is calculated to be 1.02 K/W for both electrolyte and film capacitors considering the outer diameters and air flow rate. (a)(b)Fig. SEQ Fig. \* ARABIC 12 Performance comparison between two schemes; (a) Power loss; (b) Core temperature.The impact of modulation strategy on the capacitor power loss is illustrated in Fig. 13, where the load power factor is constant (= 0.23). Among three modulation strategies, the THI modulation shows the highest power loss due to the frequency spectrum distribution of the capacitor current, which is about 10% higher than that of the SVM. The SVM shows moderate impact on the power loss of dc-link capacitors, which is roughly 3% higher than the SPWM. Shown in Fig. 13a, the power loss decreases with the increased temperature, which is the characteristic of electrolyte capacitors. For scheme II, the power loss of dc-link capacitors is lower as shown in Fig. 13b and the temperature variation shows insignificant impact to the power loss, which is the characteristic of film capacitors. (a)(b)Fig. SEQ Fig. \* ARABIC 13 Power loss of dc-link capacitors among three switching modulation strategies. (a) Scheme I – five 3300?F electrolytic capacitors; (b) Scheme II – two 220?F film capacitors.The lifetime of the two design schemes can be predicted using the mathematical models of capacitor ESR and ripple current. The lifetime estimation is based on the expression GOTOBUTTON ZEqnNum312129 \* MERGEFORMAT REF ZEqnNum312129 \* Charformat \! \* MERGEFORMAT (12), where the key parameters are derived from the product datasheet and shown in Appendix. Apparently, the temperature and its variation significantly affect the lifetime of dc-link capacitors, as shown in REF _Ref307040240 \h Fig. 14. Moreover, the life expectancy of the film capacitor is about 180 kilo hours and times longer than that of the electrolytic capacitor when the operating ambient temperature is constant at 65°C. (a)(b)Fig. 14 Life expectancy of the two design schemes for dc-link capacitors with the ambient temperature spanning from 45°C to 85°C. (a) Scheme I – five 3300?F electrolytic capacitors; (b) Scheme II – two 220?F film capacitors.Twenty-six valve-regulated lead-acid (VRLA) batteries are series connected to form the battery pack, of which the DC bus voltage is rated as 312V. The battery model is 6-DM-150 VRLA, which is specially designed for EV applications and manufactured by FENGFAN Co. Ltd.. The product specification is shown in Table A-I. The battery internal resistance is a nonlinear function of the states of charge (SOC). The measured internal resistance of the battery pack ranges from 46 m? to 182 m?. Battery current harmonics are analyzed for the two design schemes. An upper bound on AC ripple current is defined as 10% of the rated battery current to avoid degradation of battery life. The main parameters of the two schemes are defined in Table V. The RMS battery ripple current in percentage is calculated by using the expression in GOTOBUTTON ZEqnNum505804 \* MERGEFORMAT REF ZEqnNum505804 \* Charformat \! \* MERGEFORMAT (15) and the equivalent circuit shown in REF _Ref309886612 \h Fig. 8. REF _Ref307040254 \h Fig. 15 shows the analysis results of battery ripple current, where the symbol α is predefined in GOTOBUTTON ZEqnNum797391 \* MERGEFORMAT REF ZEqnNum797391 \* Charformat \! \* MERGEFORMAT (14) and determined by the equivalent circuit shown in REF _Ref309886612 \h Fig. 8. The battery ripple current in scheme II is higher than the ripple current in scheme I due to the vast reduction of capacitance. The capacitance in scheme II is 440?F, which is about 2.6% of the capacitance in scheme I. Therefore, to meet the 10% upper bound, α must be larger than 0.6 in scheme II with consideration of various combinations of modulation index and load power factor. In practical EV system, the cable interconnect provides enough impedance to guarantee α larger than 0.6 since the inverter and the battery bank are located at some distance. (a)(b)(c)(d)Fig. 15 Battery ripple current analysis for two design schemes (five 3300?F electrolytic capacitors and two 220?F film capacitors). (a) ΔIbat with and α in scheme I; (b) ΔIbat with M and α in scheme I; (c) ΔIbat with and α in scheme II; (b) ΔIbat with M and α in scheme II.Experiment with 80kW PM MotorThe EV drive system is now tested with an 80kW permanent magnet AC motor, of which the parameters of which are summarized in the Appendix. REF _Ref307040614 \h Fig. 16 shows a corner of the inverter assembly with the two film capacitors. Fig. 16 Photo of the EV inverter assembly with two film capacitors.The experimental switching frequency is 20 KHz and the output current frequency is 93 Hz. Fig. 17 shows the experimentally measured waveforms with respect to the proposed schemes II. Shown in the oscilloscope screen, the CH1 and CH2 represent the output current (upper waveform) and capacitor current (lower waveform), respectively. Fig. 17b illustrates a detailed look of the output current and the capacitor current, of which the overall views are shown in Fig. 17a. The current signals are sensed by Rogowski coils, which are transducers for measuring alternating current (AC) or high frequency current pulses. The current waveforms are represented voltage signals and shown in the oscilloscope screen. Considering that the scale factors are 2 mV/A and 1 mV/A for the CH1 and CH2, respectively, the actual current scales are 100A/div for both channels.The experiment shows that the ripple current spectrum contains significant switching frequency multiples and their sidebands, as predicted by the analysis of Section 3C. Each film capacitor absorbs 38A ripple current, as shown in Fig. 17a and Fig. 17b. Thus, the test shows the total ripple current through the film capacitor banks is 76A, when the inverter output current is 135ARMS. Considering the high load power factor (cos?> 0.9) of the PM motor and the modulation index (M = 0.6), the measured ratio Icap/IN was 0.4 consistent with GOTOBUTTON ZEqnNum552453 \* MERGEFORMAT REF ZEqnNum552453 \* Charformat \! \* MERGEFORMAT (6), as illustrated in Fig. 3. (a)(b)Fig. SEQ Fig. \* ARABIC 17 The experimental waveforms of scheme II using two film capacitors. (a) the output phase current (upper scale factor: 2mV/A) and film capacitor current (upper scale factor: 1mV/A) in scheme II with current scale of 100A/div; (b) Zoom-in detailed look of the output phase current (upper scale factor: 2mV/A) and film capacitor current (upper scale factor: 1mV/A) in scheme II with current scale of 100A/div.Fig. 18 shows the experimentally measured waveforms with respect to the schemes I. Shown in the oscilloscope screen, the CH1 and CH2 represent the high frequency capacitor current (upper waveform) and output current (lower waveform), respectively. Considering that the correspondingly scale factors are 5 mV/A and 2 mV/A for the CH1 and CH2, the actual current scales are 20A/div and 100A/div for CH1 and CH2. The individual electrolytic capacitor ripple current is 16.2A. Thus, the five electrolytic capacitors share the total 81A ripple current through the parallel interconnected capacitor bank. It demonstrates that each film capacitor can handle more ripple current due to the low ESR characteristics. Fig. SEQ Fig. \* ARABIC 18 The experimental dc-link capacitor current (upper scale factor: 5mV/A) and output phase current (lower scale factor: 2mV/A) waveforms of scheme I using five electrolytic capacitors for 80kW PM motor.The DC bus voltage ripple is recorded and shown in REF _Ref307753807 \h Fig. 19 at the rated capacity of 80kW. In order to analysis the fluctuation of the DC bus voltage, the measured voltage ripple is zoomed and displayed in the center of in the oscilloscope screen. The zero axes are far from the trigger level indictor because the ripple voltage is far below the dc bus voltage. The scale of 0.2V/div showing in the Fig. 19 represents the actual voltage scale of 35V/div considering the voltage division network parameter. The oscilloscope screen shows the measured RMS and the peak value is 1.81V and 1.925V respectively, which represents the actual 317V RMS DC voltage and the actual 337V peak voltage. Therefore, the ripple magnitude is recorded as the 6.31% of the dc bus voltage. Fig. SEQ Fig. \* ARABIC 19 Measured DC bus voltage ripple for EV inverter with proposed design scheme with the scale of 35V/div.Summary of Experimental Results. Table XI summarizes performance comparison between the two design schemes. Main parameters of two schemes are defined in Table V. The scheme II show the significant advantages regarding to the small size, low parasitic inductance, long lifetime, reduced bus voltage spikes, and improved power density. It is shown that the power density is increased to 13.3 kW/L by applying scheme II in contrast of 2.99 kW/L by using the scheme I. For battery ripple current, the constraint of α 0.6 is required for the scheme II. This is achievable by considering the practical layout of electric vehicles.Table SEQ Table \* ROMAN XIPerformance comparison of two design schemesParametersScheme IScheme IICapacitance (mF)16500440Capacitor typeElectrolyticFilmMeasured parasitic inductance (nH)12434Measured ripple current (A)8176Power loss (W)**40.820.6 Core temperature (oC)** =0.954 73.375.5Life expectancy (Hours) for Ta=65 oC16092181530ΔIbat for α=0.61.8%8.7%Switching voltage spike across IGBT (V)*5735PDW(kW/kg)4.6711PDV (kW/L)2.9913.3 * With 2?F snubber capacitor; **for Ta = 65 ?C and cos(?) = 0.954 CONCLUSIONThis paper presents a comprehensive analysis and comparative evaluation of dc-link capacitors to meet EV system requirements of long lifetime, high reliability, low cost, and high power density. The main findings and contributions of the research are summarized as follows:Modulation strategy: regarding the dc-link capacitor ripple current, three modulation strategies of SPWM, SVM and THI show approximately the same RMS values. Considering the ripple voltage, THI modulation shows the lowest value across the dc-link capacitors followed closely by SVM modulation. However, THI results in the highest capacitor power loss, which is 10% higher than that of SVM. Capacitor power losses correspond to the ripple frequency spectrum, which is different among modulation strategies. The SVM shows moderate impact on the capacitor power loss, which is roughly 3% more than that of the SPWM. Influence of operating conditions: operating conditions of EV inverters may be expressed in terms of the practical ranges of load power factor () and modulation index M. When is less than 0.43, the peak ripple current always results from the upper bound of M. After the threshold (0.43), increasing of load power factor causes a decreasing of MIcap(max), which is the modulation index referring to the maximum RMS value of capacitor ripple. Furthermore, the power factor has great impact on the frequency spectrum of the dc-link capacitor ripple current. For low , the ripple current spectrum is fairly evenly distributed along the switching frequency (f1) sidebands (sbs), 3f1 sbs and 2f1. For high (larger than 0.49 for SVM), 2f1 is the dominant component and its amplitude increases with . The largest harmonic component is nearly 21% of output current amplitude at low , while the corresponding harmonic component reaches as high as 48.8% at the high .Modeling of ESR and self-heating characteristics: the ESR models of electrolytic and film capacitors are derived and experimentally validated. Two dc-link capacitor designs are used for the comparative evaluation. The ESR of scheme II (film capacitor) is always lower than that of scheme I (electrolytic) throughout the frequency spectrum. The ESR value of scheme I decreases with increasing temperature, which is more significant than that of the scheme II. Furthermore, the RMS values and frequency spectra of the dc-link capacitor current are analyzed. The self-heating effect is subsequently considered and numerically evaluated by using the iterative simultaneous solution for core temperature and ESR by electro-thermal coupling method to predict the core temperature. Lifetime estimates are based on core temperature. Experimental evaluation of two design schemes: The applications and performance of electrolytic capacitors (scheme I) and film capacitors (scheme II) were tested and compared and evaluated in terms of power loss, core temperature, lifetime and battery current harmonics based on a practical 80kW permanent-magnet motor drive system. The comparison verifies that the film capacitor application shows significant advantages shown by the improved power density, low power loss, low parasitic inductance, and long lifetime. The capacitor power loss introduced by the scheme II is roughly half of the value of scheme I due to the lower ESR value. The analysis shows that the values of capacitor core temperature are close to each other in both schemes. At the rated ambient temperature of 65 oC, the lifetime of the film capacitors is ten times longer than that of scheme I. Regarding to the battery ripple current, both schemes meet the 10% upper bound limit considering the practical EV system layout. Further, the parasitic inductance is reduced to 34 nH in contrast with the value of 100 nH for scheme I. The power density of 13.3 kW/L was achieved by applying the proposed scheme II, which is compared to the PDV of 2.99 kW/L for scheme I.AppendixTABLE a-ISpecification of the vrla battery (6-DM-150)ParametersValueC20(Ah)150Cold Cranking Amperes defined by BCI (A)300Rated voltage (V)12Weight (kg)32.5TABLE A-IISpecification of Evox Rifa ALS332QP500and AVX FFVE6K0227KComparison ItemsMax ESR(mΩ)at 20 oC/ 100hzMax Impedance (mΩ) at 20oC / 10 khzRipple current(A) at 85°C & 10 khzLife time Lb at 85°C (hrs)Expected ambient temperature Ta(oC)ALS332QP500513226.4400065FFVE6K0227K1-1003000065TABLE A-IIIMain parameters of AC induction motorParametersValueStator resistor (m?)6.8Stator leakage inductance (mH)0.071789Rotor resistor (m?)4.23Rotor leakage inductance (mH)0.0921067Mutual inductance (mH)2.2857359Pairs of poles3Rated speed(rpm)1860Reference ADDIN EN.REFLIST ADDIN EN.REFLIST [1]F. R. 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