双语建模与仿真实验九及答案.docx
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双语建模与仿真实验九及答案
EXAMPLE12
1-Phase,Bipolar-VoltageSwitchingInverter
1，Obtainthefollowingwaveformsusing1Phbsinv:
（a）voandio.
（b）voandid.
（c）vo,ioandpo.
Answer:
（a）vowaveform:
Or
Iowaveform:
（b）vowaveform:
Idwaveform:
（c）vowaveform:
Iowaveform:
Powaveform:
2,Obtainv01bymeansofFourieranalysisofthevowaveform.Comparev01withits
precalculatednominalvalue.
Answer:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEV（N00396,N00826）
DCCOMPONENT=-1.364900E+00
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO（HZ）COMPONENTCOMPONENT（DEG）PHASE（DEG）
14.000E+012.152E+021.000E+007.240E+010.000E+00
28.000E+018.215E-013.817E-03-1.373E+02-2.821E+02
31.200E+021.087E+005.052E-03-8.038E+01-2.976E+02
41.600E+026.943E-013.226E-03-8.213E+01-3.717E+02
52.000E+025.693E-012.645E-03-9.786E+01-4.599E+02
62.400E+026.443E-012.993E-038.586E+01-3.485E+02
72.800E+029.711E-014.512E-033.420E+01-4.726E+02
83.200E+021.027E+004.772E-039.653E+01-4.827E+02
93.600E+021.231E+005.722E-031.556E+02-4.960E+02
104.000E+021.534E+007.125E-033.867E+01-6.853E+02
114.400E+026.245E-012.902E-031.273E+02-6.690E+02
124.800E+023.197E-011.485E-03-3.498E+01-9.037E+02
135.200E+021.613E+007.495E-03-1.635E+02-1.105E+03
145.600E+021.071E+004.974E-03-1.276E+01-1.026E+03
156.000E+022.202E-011.023E-037.034E+01-1.016E+03
166.400E+021.064E+004.943E-03-4.897E+01-1.207E+03
176.800E+026.628E-013.079E-03-1.572E+02-1.388E+03
187.200E+021.169E+005.433E-03-8.197E+01-1.385E+03
197.600E+028.240E-013.828E-03-8.104E+01-1.457E+03
208.000E+021.059E+004.919E-031.142E+02-1.334E+03
218.400E+022.719E+001.263E-021.428E+02-1.378E+03
228.800E+023.061E-011.422E-031.006E+02-1.492E+03
239.200E+025.888E+012.735E-01-5.381E+01-1.719E+03
TOTALHARMONICDISTORTION=2.745429E+01PERCENT
JOBCONCLUDED
TOTALJOBTIME.88
V01（peak）=2.152E+02,thatis215.2V,V（rms）=152.17V,thephaseofV01is7.240E+01,thatis72.40
so2*pi*f=2*3.141592*40=251.33rad/s,soV01=152.17sin（251.33t+72.4*pi/180）
Whileitsprecalculatedominalvalue:
Vo1（rms）=153.33V,Vo1,peak=216.8V.
3,UsingtheresultsofProblem2,obtaintheripplecomponentVripplewaveformintheoutputvoltage.
Answer:
V01=152.17sin（251.33*time+72.4*pi/180）,theripplecomponentvrippleis
V0-V01=V0-152.17sin（251.33*time+72.4*pi/180）,thewaveformasfollow.
4,Obtaini01bymeansofFourieranalysisoftheiowaveform.Comparei01withits
precalculatednominalvalue.
Answer:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI（R_R1）
DCCOMPONENT=-4.719698E-01
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO（HZ）COMPONENTCOMPONENT（DEG）PHASE（DEG）
14.000E+011.354E+011.000E+004.403E+010.000E+00
28.000E+013.947E-022.916E-03-1.560E+02-2.441E+02
31.200E+027.786E-025.752E-03-1.118E+02-2.439E+02
41.600E+022.435E-021.799E-03-1.555E+02-3.317E+02
52.000E+022.570E-021.899E-03-1.064E+02-3.265E+02
62.400E+021.252E-029.249E-041.561E+02-1.081E+02
72.800E+022.285E-031.688E-041.474E+02-1.609E+02
83.200E+024.269E-033.154E-041.430E+02-2.092E+02
93.600E+024.284E-033.165E-041.701E+02-2.262E+02
104.000E+029.197E-036.794E-04-1.136E+02-5.539E+02
114.400E+021.157E-028.546E-041.496E+02-3.348E+02
124.800E+026.981E-035.157E-041.585E+02-3.699E+02
135.200E+021.201E-028.870E-041.259E+02-4.466E+02
145.600E+028.194E-036.053E-04-1.427E+02-7.591E+02
156.000E+025.535E-034.089E-04-1.350E+02-7.956E+02
166.400E+024.930E-033.642E-04-1.476E+02-8.522E+02
176.800E+024.122E-033.045E-041.635E+02-5.851E+02
187.200E+027.549E-035.577E-041.583E+02-6.343E+02
197.600E+024.627E-033.418E-04-1.707E+02-1.007E+03
208.000E+021.062E-037.843E-051.569E+02-7.238E+02
218.400E+023.030E-022.238E-037.941E+01-8.453E+02
228.800E+022.964E-032.190E-04-1.272E+02-1.096E+03
239.200E+021.030E+007.612E-02-1.418E+02-1.155E+03
TOTALHARMONICDISTORTION=7.650194E+00PERCENT
JOBCONCLUDED
TOTALJOBTIME.86
I
（peak）=1.354E+01,thatis13.54A,I（rms）=9.574A,thephaseis4.403E+01
Whileitsprecalculatedominalvalue:
Io1（rms）=10Aata0.866pf（lagging）,I
（peak）=14.14A.
5,UsingtheresultsofProblem4,obtaintheripplecomponentIrippleintheoutputcurrent
Answer:
I
=9.574sin（2*pi*f*time+44.03*pi/180）=9.574sin（2*pi*40+44.03*pi/180）
theripplecomponentirippleis（I
-I
）,itswaveformisasfollow
6,ObtainId（avg）andid2（thecomponentatthe2ndharmonicfrequency）bymeansofthe
Fourieranalysisoftheidwaveform.Comparethemwiththeirprecalculatednominal
values.
Answer:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI（V_V1）
DCCOMPONENT=-4.893025E+00
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO（HZ）COMPONENTCOMPONENT（DEG）PHASE（DEG）
14.000E+014.692E-011.000E+006.937E+010.000E+00
28.000E+015.423E+001.156E+01-1.554E+02-2.942E+02
31.200E+026.118E-021.304E-013.030E+01-1.778E+02
41.600E+028.395E-021.789E-015.346E+01-2.240E+02
52.000E+024.896E-021.043E-01-9.629E+00-3.565E+02
62.400E+023.820E-028.141E-02-5.784E+00-4.220E+02
72.800E+024.377E-029.328E-02-1.139E+02-5.995E+02
83.200E+025.191E-021.106E-017.187E+01-4.831E+02
93.600E+023.148E-026.709E-02-1.697E+02-7.940E+02
104.000E+025.119E-021.091E-01-7.545E+01-7.691E+02
114.400E+023.731E-027.952E-02-1.656E+02-9.287E+02
124.800E+021.236E-022.634E-026.434E+01-7.681E+02
135.200E+024.233E-029.020E-02-1.740E+02-1.076E+03
145.600E+022.151E-024.585E-02-9.854E+01-1.070E+03
156.000E+023.325E-027.085E-021.731E+02-8.674E+02
166.400E+024.631E-029.869E-023.875E+01-1.071E+03
176.800E+024.390E-029.355E-021.430E+02-1.036E+03
187.200E+025.532E-021.179E-01-8.981E+01-1.338E+03
197.600E+023.294E-027.020E-023.511E+01-1.283E+03
208.000E+021.153E-012.458E-017.638E+00-1.380E+03
218.400E+022.876E-026.129E-02-4.330E+00-1.461E+03
228.800E+021.266E+002.698E+001.513E+02-1.375E+03
239.200E+021.669E-013.556E-01-5.120E+01-1.647E+03
TOTALHARMONICDISTORTION=1.188283E+03PERCENT
JOBCONCLUDED
TOTALJOBTIME.86
Id=4.893025E+00,thatis4.893A,
Id
（peak）=5.423E+00,Id
（rms）=3.835A,itsphaseis-1.554E+02,thatis-155.4
theirprecalculatednominalvalues:
Id=
*cosΦ=
=4.656A
Id
=
=
=3.801A
7,UsingtheresultsofProblem6,obtainthehighfrequencyripplecomponentid,ripplein
theinputdccurrent.Calculateitsrmsvalue
answer:
Io1（peak）=4.692E-01,thatis0.4692A,itsrmsvalueis0.3318A,TOTALHARMONICDISTORTION=1.188283E+03PERCENT,%THD=1188.283%,thehighfrequencyripplecomponentofid,ripple=0.3318*11.88283=3.942A,soitsrmsvalueis3.942A
EXAMPLE16
Three-PhasePWMInverter
Obtainthefollowingwaveformsusing:
（a）vANandiA.
（b）vAnandiA.
（c）vANandid.
Answer（a）vANwaveform:
IAwaveform:
（b）vAnwaveform:
IAwaveform:
（c）vANwaveform:
Idwaveform:
2,ObtainvAn1bymeansofFourieranalysisofthevAnwaveform.ComparevAn1with
itsprecalculatednominalvalue.
Answer:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEV（VA,VNEUTRAL）
DCCOMPONENT=-2.239930E-02
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO（HZ）COMPONENTCOMPONENT（DEG）PHASE（DEG）
14.762E+011.491E+021.000E+001.372E+020.000E+00
29.524E+014.832E-013.240E-03-8.232E+01-3.568E+02
31.429E+024.600E-023.085E-04-1.106E+02-5.222E+02
41.905E+024.246E-012.848E-031.929E+01-5.296E+02
52.381E+026.052E-014.059E-033.124E+00-6.830E+02
62.857E+024.407E-022.955E-04-1.323E+02-9.557E+02
73.333E+027.786E-015.222E-031.476E+02-8.130E+02
83.810E+026.795E-014.557E-031.786E+02-9.192E+02
94.286E+024.730E-023.172E-04-1.491E+02-1.384E+03
104.762E+029.098E-016.101E-031.662E+02-1.206E+03
115.238E+021.551E-011.040E-03-7.099E+01-1.580E+03
125.714E+024.816E-023.230E-04-1.729E+02-1.820E+03
136.190E+021.455E+009.758E-031.256E+02-1.658E+03
146.667E+028.385E-015.623E-03-9.956E+01-2.021E+03
157.143E+024.384E-022.940E-041.718E+02-1.887E+03
167.619E+022.030E-011.361E-03-9.822E+01-2.294E+03
178.095E+021.799E+001.207E-02-9.840E+01-2.431E+03
188.571E+024.842E-023.247E-041.518E+02-2.318E+03
199.048E+024.585E+013.075E-011.751E+02-2.432E+03
209.524E+027.544E-015.059E-037.145E+01-2.673E+03
211.000E+034.487E-023.009E-041.273E+02-2.754E+03
221.048E+036.855E-014.597E-031.205E+02-2.898E+03
231.095E+034.598E+013.084E-014.126E+00-3.152E+03
TOTALHARMONICDISTORTION=4.359678E+01PERCENT
JOBCONCLUDED
TOTALJOBTIME2.80
vAn1（peak）=1.491E+02,vAn1（rms）=105.43V,itsphaseis1.372E+02,thatis137.2
itsprecalculatednominalvalue:
vLL1（rms）=
*230=182.54V,vAn1（rms）=
=105.39V
3,UsingtheresultsofProblem2,obtaintheripplecomponentvripplewaveforminthe
outputvoltage
Answer:
vAn1=105.43sin（2*pi*47.619time+137.2*pi/180）
theripplecomponentvripplewaveformintheoutputvoltageis
（vAn-vAn1）,itswaveform:
4,ObtainiA1bymeansofFourieranalysisofiAwaveform.CompareiA1withits
precalculatednominalvalue.
Answer:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI（R_R1）
DCCOMPONENT=-1.633990E-02
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO（HZ）COMPONENTCOMPONENT（DEG）PHASE（DEG）
14.762E+011.417E+011.000E+001.076E+020.000E+00
29.524E+011.690E-021.193E-03-1.546E+02-3.698E+02
31.429E+028.724E-036.157E-041.718E+02-1.510E+02
41.905E+027.686E-035.424E-041.213E+02-3.090E+02
52.381E+021.073E-027.575E-04-1.011E+02-6.390E+02
62.857E+023.529E-032.491E-041.441E+02-5.014E+02
73.333E+024.672E-033.297E-043.53
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