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

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I_DC

IR

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IT

2

Implemented averaging model of the same converter

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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)

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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 olve.mo@sintef.no 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