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Industrial Electronics in renewable energy generation systems
Unit 4.- Dynamic modeling of electronic converters
Semester 2 – Industrial electronics in renewable energy generation systems
Lecturer: Jorge García, [email protected]
M.Sc. In Electrical Energy Conversion and Power Systems
4.3 AC-DC conversion. AC-DC conversion. The three-phase controlled rectifier
Industrial electronics in renewable energy generation systems
Industrial Electronics in renewable energy generation systems
2
Unit4.- Three-phaseconverters
4.1 DC-ACconversion.Thesingle-phaseinverterGeneralconceptsininverters.CharacteristicsandtypesHalf-bridgesquarewavesingle-phaseinverterFull-bridgesquarewavesingle-phaseinverterSine-waveformPWMmodulationOutputLCfilterandharmonicsanalysisInputfilterandDC-linkcurrent
4.2 DC-ACconversion.Thethree-phaseinverterGeneralconceptsininverters.6-pulsesinverter.Sine-waveformPWMmodulationOutputLCfilterandharmonicsanalysisInputfilterandDC-linkcurrentEffectofthedead-times.Limitations.Alternativemodulations,3rdharmonicinjection,SVPWM.
4.3 AC-DCconversion.Thethree-phasecontrolledrectifierReverseoperationofthethree-phaseinverterEquivalentsingle-phasecircuitControlofthefiltercurrentMainelectricalmagnitudesrelationsEvolutionofwaveforms
Industrial Electronics in renewable energy generation systems
3
Gearbox Grid
WT PMSG
BasicPower Schemes
Frequencyconverter
Industrial Electronics in renewable energy generation systems
GridPMSG
Frequencyconverter(BACKtoBACKinverter)
Filter+Transformer
BasicPower Schemes
4
Three-PhasePWMInverter
Industrial Electronics in renewable energy generation systems
GridPMSG
Frequencyconverter(BACKtoBACKinverter)
Filter+Transformer
BasicPower Schemes
5
Three-PhasePWMInverter
Three-PhasePWMRectifier
Industrial Electronics in renewable energy generation systems
6
uI
iI
u1
u2
u3ThePWMinverter
Industrial Electronics in renewable energy generation systems
7
ThePWMinverteruTRI 7.0=am 15=fmuTRI
uA
uB
uAB
uREFA uREFB uREFC
uI
iI
u1
u2
u3
Theappropriatecontrol,bymeansofsine-triangleorSVMalgorithmsprovideLFoutputsinewaveforms
Industrial Electronics in renewable energy generation systems
Overview:energyflowinDC/ACconversion
Inductive load
iS
uS
uR
uL
An inverter must be able to work in all
four quadrants
=+
-uE
iS
uS
L
R
Primary energysource
Inverter
Load
Inverter
Industrial Electronics in renewable energy generation systems
Rectifier operation
iS
uS
uM
uL=
+
-uE
iS
uS
L
R
Primary energysource
Inverter
Load
Overview:energyflowinDC/ACconversion
Inverter
Industrial Electronics in renewable energy generation systems
iIC
iIB
iIA
10
uO
iO
ugAuCuBuAuN
uAB
L
ugC
ugB
L
LOperation asacontrolled rectifier
C
Thesametopology,butwithoppositecurrentreferencesisarectifier.
Industrial Electronics in renewable energy generation systems
iIC
iIB
iIA
11
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
LOperation asacontrolled rectifier
C
Thesametopology,butwithoppositecurrentreferencesisarectifier.
EvenifallswitchesareOFF,thecircuitbehavesasathree-phasediodebridge.Thus,onstartup(ifthecontrolstageisnotoperating),thereisvoltageattheoutputoftheinverter!!!
Whichistheoperationwhenthesemiconductorareswitching?Thesinglephaseinverterwillbeconsideredfirstly
uCuB
Industrial Electronics in renewable energy generation systems
iIA
12
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
Single-PhasePWMRectifier
Industrial Electronics in renewable energy generation systems
iIA
13
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,D
Industrial Electronics in renewable energy generation systems
iIA
14
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,D• IfS1L ON,thecurrentflowschargingtheinductanceL.
Industrial Electronics in renewable energy generation systems
iIA
15
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,D• IfS1L ON,thecurrentflowschargingtheinductanceL.• IfS1H OFF,thecurrentflowstotheDClink.
Industrial Electronics in renewable energy generation systems
iIA
16
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
iDR
uCEuO
uI
iI iO
C
L DR
iL
iC
uL uDR
iT
ISTHEOPERATIONOFTHEBOOSTCONVERTER!!!
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,D• IfS1L ON,thecurrentflowschargingtheinductanceL.• IfS1H OFF,thecurrentflowstotheDClink.
Industrial Electronics in renewable energy generation systems
iIA
17
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
iDR
uCEuO
uI
iI iO
C
L
DRiL
iC
uL
uDR
iT
ISTHEOPERATIONOFTHEBIDIRECTIONALBOOST
CONVERTER!!!
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,D• IfS1L ON,thecurrentflowschargingtheinductanceL.• IfS1H OFF,thecurrentflowstotheDClink.• Thetwotransistorsimplybidirectionalcurrentflow(activepowerinbothdirections,reactivepower)
Industrial Electronics in renewable energy generation systems
iIA
18
uO
iO
uA
ug
L
Operation asacontrolled rectifier
C
Single-PhasePWMRectifier
uB
Considertheoperationofoneleg.
iDR
uCEuO
uI
iI iO
C
L
DRiL
iC
uL
uDR
iT
ISTHEOPERATIONOFTHEBIDIRECTIONALBOOST
CONVERTER!!!
• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,d• IfS1L ON,thecurrentflowschargingtheinductanceL.• IfS1H OFF,thecurrentflowstotheDClink.• Thetwotransistorsimplybidirectionalcurrentflow(activepowerinbothdirections,reactivepower)
• Ifug<0,theoperationisanalogous,butwiththeotherleg…
Industrial Electronics in renewable energy generation systems
iIA
19
uO
iO
uA
ug
L
Operation asacontrolled rectifier
CuB
iDR
uCEuO
uI
iI iO
C
L
DRiL
iC
uL
uDR
iT
ISTHEOPERATIONOFTHEBIDIRECTIONALBOOST
CONVERTER!!!
Thestudyofthesizeofcomponents,designofreactivecomponents,switchingscheme,dynamicmodeling,etc.hasalreadybeenseen.
Single-PhasePWMRectifierConsidertheoperationofoneleg.• Freq.switching>>freq.ug(t).• Ifug>0,S1L switchingatfs,d• IfS1L ON,thecurrentflowschargingtheinductanceL.• IfS1H OFF,thecurrentflowstotheDClink.• Thetwotransistorsimplybidirectionalcurrentflow(activepowerinbothdirections,reactivepower)
• Ifug<0,theoperationisanalogous,butwiththeotherleg…
Industrial Electronics in renewable energy generation systems
iIC
iIB
iIA
20
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
LOperation asacontrolled rectifier
CuCuB
Industrial Electronics in renewable energy generation systems
iIC
iIB
iIA
21
uO
iO
ugAuAuN
L
ugC
ugB
L
LOperation asacontrolled rectifier
CuCuB
Theper-phaseequivalentcircuitcanbeconsideredasaBOOSTconverter. iDR
uCEuO
uI
iI iO
C
L
DRiL
iC
uL
uDR
iT
However,itcanalsobeanalyzedconsideringthatthemid-pointofeachlegcanbecalculatedfromthePWMswitchingpatternoftheIGBTsatthatleg(asinaninverter)
Industrial Electronics in renewable energy generation systems
22
Operation asacontrolled rectifier.DCBusVoltageiIA
uO
iO
ugA
L
CuL
iIB
ugBiIC
ugC
Industrial Electronics in renewable energy generation systems
23
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
iIA
uO
iO
ugA
L
CuL
uA
Industrial Electronics in renewable energy generation systems
24
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
ugA
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern,
iIA
uO
iO
ugA
L
CuL
uA
Industrial Electronics in renewable energy generation systems
25
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
ugA
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the line circuit
iIA
uO
iO
ugA
L
CuL
uA
Industrial Electronics in renewable energy generation systems
26
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
ugA
uAφ
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the input line circuit
iIA
uO
iO
ugA
L
CuL
uA
Industrial Electronics in renewable energy generation systems
27
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
ugA
uAuLφ
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the line circuitThus, the inductor voltage, uL, can be fixed in a desired value.Therefore, the phase current, iIA, can be controlled as desired.
iIA
uO
ugA
L
CuL
uA
iO
Industrial Electronics in renewable energy generation systems
28
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
( )q·cos··23
PEAKgAPEAKIAIN uiP =
OOOUT iuP ·=
ugA
uAuL
iIA
º0=q
φ
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the line circuit
Suppose a iIA in phase with uA: There is ACTIVE power beingdrained from the grid.
Thus, the inductor voltage, uL, can be fixed in a desired value.Therefore, the phase current, iIA, can be controlled as desired.
iIA
uO
ugA
L
CuL
uA
iO
Industrial Electronics in renewable energy generation systems
29
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
OOOUT iuP ·=
2··21
OuCE =
ugA
uAuL
iIA
φ
( )q·cos··23
PEAKgAPEAKIAIN uiP =
º0=q
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the line circuit
Suppose a iIA in phase with uA: There is ACTIVE power beingdrained from the grid. If this input power, PIN, is smaller than theoutput power, POUT, then the DC bus voltage will decrease.
Thus, the inductor voltage, uL, can be fixed in a desired value.Therefore, the phase current, iIA, can be controlled as desired.
iIA
uO
ugA
L
CuL
uA
iO
Industrial Electronics in renewable energy generation systems
30
Operation asacontrolled rectifier.DCBusVoltage
Considerthesinglephaseequivalent
Suppose a iIA in phase with uA: There is ACTIVE power beingdrained from the grid. If this input power, PIN, is smaller than theoutput power, POUT, then the DC bus voltage will decrease.On the other hand, if PIN is greater than POUT, the DC voltage willincrease, yielding to the destruction of the capacitor/switches
OOOUT iuP ·=
2··21
OuCE =
º0=q
( )q·cos··23
PEAKgAPEAKIAIN uiP =
Thus, the inductor voltage, uL, can be fixed in a desired value.Therefore, the phase current, iIA, can be controlled as desired.
Given a fixed value of uO, the amplitude and phase of the uAvoltage can be controlled with the PWM pattern, and the controlscheme can be understood looking at the line circuit
iIA
uO
ugA
L
CuL
uA
iO
ugA
uL
iIA
φuA
Industrial Electronics in renewable energy generation systems
31
Operation asacontrolled rectifier.DCBusVoltage
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
ugA
uA
uL
iIA
φ
Industrial Electronics in renewable energy generation systems
32
Operation asacontrolled rectifier.DCBusVoltage
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
ugA
uA
uL
iIA
φ
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
33
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φ
ugAiIA
iIA
iIA-iIA(1ST-HARM)
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
34
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φ
ugAiIA
iIA
iIA-iIA(1ST-HARM)
iIA
iIA-iIA(1ST-HARM)
iIA(1ST-HARM)
ugAiIA
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
θ’
35
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φiIA’
( )q·cos··23
PEAKgAPEAKIAIN uiP =
Additionally, provided that the DC voltage is controlled, the ACTIVE poweris fixed, but the REACTIVE power can be selected to be any desired value.
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
36
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φiIA’’θ’’
( )q·cos··23
PEAKgAPEAKIAIN uiP =
Additionally, provided that the DC voltage is controlled, the ACTIVE poweris fixed, but the REACTIVE power can be selected to be any desired value.
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
θ’’’
37
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φiIA’’’
( )q·cos··23
PEAKgAPEAKIAIN uiP =
Additionally, provided that the DC voltage is controlled, the ACTIVE poweris fixed, but the REACTIVE power can be selected to be any desired value.
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
θ’’’
38
Operation asacontrolled rectifier.DCBusVoltage
ugA
uA
uL
iIA
φiIA’’’
( )q·cos··23
PEAKgAPEAKIAIN uiP =
Additionally, provided that the DC voltage is controlled, the ACTIVE poweris fixed, but the REACTIVE power can be selected to be any desired value.
A reference for the input current must be generated in a loop thatmeasures and controls the DC bus. Controlling the DC busmeans controlling the ACTIVE power drained from the grid
However, the PWM voltage uA depends on the DC bus voltage,that depends on the load (iO). Therefore, the construction of thePWM pattern to create uAmust consider this output power.
iIA
uO
ugA
L
CuL
uO(MEASURE)
PWMAT
PWMAB
uA
iO
Industrial Electronics in renewable energy generation systems
39
Operation asacontrolled rectifier.DCBusVoltage
iIC
iIB
iIA
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
L
CuCuB
PSIM Simulations, for a 1100 VDC NominalDC bus voltage.What situations can be present, consideringthe input current control?
At first, the switches are turned off (operation as an uncontrolled diodebridge).At a certain instant, a fixed PWM pattern is applied (open loop)
Industrial Electronics in renewable energy generation systems
40
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VL
VDCnominal(1100VDC)
PWMSwitching,Controlled Rectifier
VGRID
VPWMVL
IPHASEφ
Noswitching,Uncontrolled Rectifier
1100VDC
θ=0º
φ=1º
620VDC
ActivePower Control
Step-upvoltage effect !!(boost converter)
Industrial Electronics in renewable energy generation systems
41
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VL
VDCSmaller than nominal(750VDC)
PWMSwitching,Controlled Rectifier
VGRID
VPWM VL
IPHASEφ
Noswitching,Uncontrolled Rectifier
750VDC
θ=0º
φ=0.5º
620VDC
ActivePower Control
Industrial Electronics in renewable energy generation systems
42
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VL
VDCnominal(1100VDC)
PWMSwitching,Controlled Rectifier
VGRID
VPWMVL
IPHASEφ
Noswitching,Uncontrolled Rectifier
1100VDC
θ=0º
φ=1º
620VDC
ActivePower Control
Step-upvoltage effect !!(boost converter)
Industrial Electronics in renewable energy generation systems
PWMSwitching,Controlled Rectifier
43
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VLVGRID
VPWM
VL
IPHASE
φ
Noswitching,Uncontrolled Rectifier
1500VDC
θ=0º
φ=2º
620VDC
VDCgreater than nominal(1500VDC)
ActivePower Control
Industrial Electronics in renewable energy generation systems
44
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VL
VDCnominal(1100VDC)
PWMSwitching,Controlled Rectifier
VGRID
VPWMVL
IPHASEφ
Noswitching,Uncontrolled Rectifier
1100VDC
θ=0º
φ=1º
620VDC
Reactive Power Control
Industrial Electronics in renewable energy generation systems
45
Operation asacontrolled rectifier.DCBusVoltage
VBUS
VGRID IPHASE
VGRID VPWM
VL
VDCnominal(1100VDC).Current LAG
PWMSwitching,Controlled Rectifier
VGRID
VPWMVL
IPHASE
φ
Noswitching,Uncontrolled Rectifier
1100VDC
θ=85º
φ=1.2º
620VDC
Reactive Power Control
Industrial Electronics in renewable energy generation systems
46
Operation asacontrolled rectifier.
iIC
iIB
iIA
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
L
CuCuB
• Control of the DC bus means control of the ACTIVE power• REACTIVE power is independent of the DC bus voltage, and hence ACTIVE and
REACTIVE power are fully decoupled
In addition…• At start-up, with no control of the topology, the circuit behaves like a uncontrolled
rectifier, and thus there is voltage at the capacitor.• The dynamic modeling must consider the grid inductance (and resistance, if present)
and the output capacitor, plus the load itself
CONCLUSIONS
Industrial Electronics in renewable energy generation systems
47
Comparison with uncontroled rectifier +boost
iIC
iIB
iIA
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
L
CuCuB
Full reactive power control.The current may flow back to thegrid, even delivering activepower towards the input.BIDIRECTIONALACTIVEPOWERFLOW.
Industrial Electronics in renewable energy generation systems
48
Comparison with uncontroled rectifier +boost
iIC
iIB
iIA
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
L
CuCuB
Full reactive power control.The current may flow back to thegrid, even delivering activepower towards the input.BIDIRECTIONALACTIVEPOWERFLOW.
iIC
iIB
iIA
uO
iO
ugAuN
uAB
L
ugC
ugB
L
L
C
The diode bridge does not allowthe current to flow back to thegrid.UNIDIRECTIONALACTIVEPOWERONLY.
L DR
S
Industrial Electronics in renewable energy generation systems
49
Comparison with uncontroled rectifier +boost
iIC
iIB
iIA
uO
iO
ugAuAuN
uAB
L
ugC
ugB
L
L
CuCuB
In addition…• At start-up, with no control of the topology, the circuit behaves like a uncontrolled
rectifier, and thus there is voltage at the capacitor.• The dynamic modeling must consider the grid inductance (and resistance, if present)
and the output capacitor, plus the load itself• It could also be used as a inverter, delivering active power BACK to the grid (and
this cannot be done by the diode bridge+DC-DC boost topology!!!)
• Control of the DC bus means control of the ACTIVE power• REACTIVE power is independent of the DC bus voltage, and hence ACTIVE and
REACTIVE power are fully decoupled
Industrial Electronics in renewable energy generation systems
References:“PowerElectronicsHandbook,SecondEdition:Devices,CircuitsandApplications”Editor:MuhammadH.Rashid, Ed.ElsevierInc.,2007.ISBN-10:0120884798
“PowerElectronics:Converters,ApplicationsandDesign,3rd edition”.Mohan,undeland,Robbns.JohnWiley&Sons,Inc.2003.ISBN:978-0-471-22693-2
“FundamentalsofPowerElectronics”Secondedition.RobertW.Erickson,DraganMaksimovic,Ed.SpringerScience+BusinessMedia,LLC,2001.ISBN:978-0-7923-7270-7
“Switch-ModePowerSupplies.SPICEsimulationsandPracticalDesigns”.ChristopheP.Basso.Mc Graw Hill,2008.ISBN:978-0-07-150858-2