1SINTEF Energy Research
Project memo AN 03.12.103
Average model of PWM converter
2SINTEF Energy Research
ObjectiveImplement and test an averaging model of a three-phase
pulse-width modulated (PWM) converter.
The purpose of the model is less complexity and faster time domain simulation studies of grid connected converters,
while still maintaining sufficient converter dynamic accuracy.
(converter interaction phenomena, stability, short circuit analysis)
3SINTEF Energy Research
Description of implemented modelThe model has the same average V-I terminal relationship on AC and DC side as a full switched model (averaged over one switching period).Simulation time steps larger than the switching period can be used since the switches are not modelled.The control circuit is modelled in the same way as if a full switched model were used except that modelling of gate-pulse generation is not needed.Over-modulation, saturation effects and other non-linearity's are also modelled correctlyThe model is not suited for analysis were consequences of switching frequency ripple phenomena are focused.
4SINTEF Energy Research
Full switched model of 3-phase PWM-converter
V_DC
DC N
DC_P
222
2 2
R
S
T
I_DC
IR
IS
IT
2
Implemented averaging model of the same converter
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5SINTEF Energy Research
Example of use
The case used to illustrate the model performance is a step reversal of the reactive power reference to a grid connected PWM converter.The converter is connected to a DC-link capacitor on the DC-side. A LC-filter is included on the AC-sideNo load or source is connected to the DC-side. The converter is controlled such that the DC-link voltage is kept constantSimulation results using both switched model and average model are shown on the following slides
6SINTEF Energy Research
Full switched model (control circuit not shown)
g_Rm
g_Sp g_Tp
g_Tm
I_S
I_S
I_T
A
B
C
A
B
C
2T3
2T6
2T5
2T2
*
V_DC
V_DC
I_DC *1E3
P_DC I_DC
I_R
I_PWM
VTR
Power
AB
PQ
I_R
2T4
VS
VT
Power calculation
6600.06600.0 V_DC_P
V_DC_P
VS
V_R_G
V_DC_N
V_R_G
V_R_0
0.0064
0.0064
0.00330.0033
P
Q
V_DC
R=0V
g_Sm
Active front end PWM converterDC-link
DC_ref
I_DC
Load / SourcePre-charge
*0.
001
I_T
Char
ge_b
g_Rp
0.0064
VRS
*
VT
VR
I_C_T
B1B2
VR
I_C_R
B10
0.001587
0.001587
I_mainS
I_mainT
I_mainR
I_mainS
I_mainT
B1 A B C
B3
VST
I_C_S
I_C_R
0.001
0.001
0.001
B11
B12
B15
I_mainR
VRS0.001587
52.0
52.0
52.0
B2
A
B
C
2T1 D1 D3 D5
D2D6D4
VST
VTR
V_DC*1E3
*-1
V_R_0
I_PWMVPWM_RS
VPWM_RS
VPWM_ST
VPWM_TR
64.0
64.0
64.0
VPWM TR
VPWM_ST
VR_B
VS_B
VT_B
VR_B
Transformer
0.013
0.013
0.013
4.2E-005
4.2E-005
4.2E-005
0.00042
0.00042
0.00042
0.0013A
B
C
VFPh
1E3
Averaging model (control circuit not shown)
I_S
I_S
I_T
A
B
C
I_R
I_PWM
VTR
I_R
6600.06600.0 V_DC_P
VS
V_DC_N
0.0064
0.0064
0.0033
V_DC
R=0V
Active front end PWM converterDC-link
DC_ref
I_DC
Load / SourcePre-charge
*0.
001
I_T
VT
VR
B1B2
VR_B
VS_B
VT_B
B10
VR_B
0.001587
0.001587
I_mainS
I_mainT
B3
VST
Transformer
B11
B12
B15
I_mainR
VRS 0.013
0.013
0.013
4.2E-005
4.2E-005
4.2E-005
0.001587 0.00042
0.00042
52.0
52.0
52.0
B2
A
B
C
REF_T
REF_R
REF_S
0.0013A
B
C
VFPh
0.0064VPWM_RS
VPWM_ST
A
B
C
VPWM_TR 0.00042
VS
VT
I_C_T
VR
I_C_R64.0
64.0
64.0
I_mainR
I_mainS
I_mainT
B1 A B C
I_C_S
I_C_R
0.001
0.001
0.001
*1E3
*1E3
VRS
VST
VTR
VPWM_RS
VPWM_ST
VPWM_TR
Power
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PQ
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V_DC
V_DC
I_DC P_DC I_DC*
1E3
Power calculation
V_DC_P
0.0033Char
ge_b
I_PWM
VS_PWM
VT_PWM
VR_PWM
7SINTEF Energy Research
Untitled
Time (sec)
no name
0.13 0.142 0.154 0.166 0.178 0.19-0.05
-0.028
-0.006
+0.016
+0.038
+0.06IR IS I_R_AV I_S_AV IT I_T_AV Filter inductor
currents (kA) for switched model and for average model just before and after the reactive power reversal
(switched model and average model)
Untitled
Time (sec)
no name
0.158 0.16 0.162 0.164 0.166 0.168-0.05
-0.028
-0.006
+0.016
+0.038
+0.06IR IS I_R_AV I_S_AV IT I_T_AV
8SINTEF Energy Research
Untitled
Time (sec)
no name
0.158 0.16 0.162 0.164 0.166 0.168-0.05
-0.03
-0.01
+0.01
+0.03
+0.05I_PWM I_PWM_av
Current (kA) in DC-link capacitor just before and after the reactive power reversal
(switched model and average model)
9SINTEF Energy Research
Untitled
Time (sec)
no name
0.158 0.16 0.162 0.164 0.166 0.168-0.03
-0.016
-0.002
+0.012
+0.026
+0.04I_C_R I_C_R_AV
Current (kA) in phase R filter capacitor just before and after the reactive power reversal
(switched model and average model)
10SINTEF Energy Research
Untitled
Time (sec)
no name
0.158 0.16 0.162 0.164 0.166 0.168-0.5
-0.3
-0.1
+0.1
+0.3
+0.5VPWM_TR_AV VPWM_TR
Converter TR line output voltage (kV) just before and after the reactive power reversal
(switched model and average model)
PROJECT MEMO MEMO CONCERNS
Average model of PWM converter
DISTRIBUTION
SINTEF Energy Research Address: NO-7465 Trondheim, NORWAY Reception: Sem Sælands vei 11 Telephone: +47 73 59 72 00 Telefax: +47 73 59 72 50 www.energy.sintef.no Enterprise No.: NO 939 350 675 MVA
Magnar Hernes Kjell Ljøkelsøy Tormod Kleppa Olve Mo
AN NO. CLASSIFICATION REVIEWED BY
AN 03.12.103 Tormod Kleppa ELECTRONIC FILE CODE AUTHOR(S) DATE
2003-12-04 PROJECT NO.
Olve Mo NO. OF PAGES
12X127.02 [email protected] 17 DIVISION LOCATION LOCAL FAX
Energy Systems Sem Sælands v. 11 +47 73597250 This memo present results of the Strategic Institute Programme (SIP) “Power electronics and energy storage technologies for cost- and energy efficient power systems” funded by The Research Council of Norway.
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Described is a new model developed for the PSCAD/EMTDC simulation program. The new model is an average model of a three phase, two-level, PWM converter. The model performs as a PWM-converter, except that switching frequency phenomena’s are averaged over the switching period. Voltages and currents on both AC- and DC-side is therefore smooth and without switching frequency ripple. The typical application of such a model is in analysis were several converters are connected to an AC-grid. The model makes it possible to run the simulation with much larger time steps. The consequence is that the simulation can be run much faster and/or that larger time-spans can be simulated. The phases can be controlled individually. The models also perform correct in over-modulation. It is possible to use it to model PI-current control, tolerance band control and other control schemes.
This memo is an informal internal document containing information and/or preliminary results which may serve as a basis for final report(s). SINTEF Energy Research accepts no responsibility for the contents, and results and data presented in the final report(s) may deviate from information contained in this memo without special notification. The present documentation and its basic ideas may not be used by anyone without SINTEF Energy Research's prior approval.
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12X127.02 AN 03.12.103
TABLE OF CONTENTS
Page
1 MODELLING PRINCIPLE.............................................................................................. 3 1.1 The average principle............................................................................................ 3 1.2 The PWM average model...................................................................................... 3
2 PSCAD/EMTDC MODEL ............................................................................................... 5 2.1 Circuit symbol and model code............................................................................. 5 2.2 Electric node connections ..................................................................................... 5 2.3 Signal inputs.......................................................................................................... 5 2.4 Configuration / Input parameters .......................................................................... 6 2.5 Internal output variables........................................................................................ 6 2.6 Important observations.......................................................................................... 7
3 EXAMPLE OF USE ......................................................................................................... 8
APPENDIX A : FORTRAN CODE......................................................................................... 15
APPENDIX B : BRANCH CODE........................................................................................... 17