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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

APPLICATION NOTE

AN-ART002BR1.1

Real-Time Simulation of Averaged Models of Power Converters

PART 2

Using the averaged model to study electromagnetic transients in external components

December 2000

OPAL-RT

REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

Table of Contents

1.0 Abstract ........................................................................................................1 2.0 Introduction..................................................................................................2 3.0 Electromagnetic transients induced by the control system.........................4 4.0 Electromagnetic transients caused by faults in the power circuit...............6 5.0 Conclusions..................................................................................................8 6.0 References ...................................................................................................8

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

1.0 Abstract

Application Note Part 1 [1] showed that the combination of RT-LAB with the Power System Blockset enhanced by the Artemis Plug-In allows for real-time simulation of complex powerelectronic energy conversion systems, using averaged models in place of detailed models for power-electronic bridges. This paper reports the results of a study conducted to see whether averaged models can be used to study electromagnetic transients, either caused by a large disturbance in the control system, or by faults in the power circuits. Experiment results show two main points: · As regards peaks over-voltages and over-currents, the averaged model can be used to study power component electromagnetic transients caused by disturbances in a control system. · Averaged models are not adequate for studying transient phenomena caused by faults in a power circuit external to power-electronic bridges. In addition, the results in [1] were confirmed-- that averaged models can be used for the design of control systems.

Inverter

Vdc1 Averaged model Or Switched model

LC Filter

RL Load

Duty cycle

1 z

Controller

fast -to- slow

slow -to -fast

Controller sampled at Ts2 = 1000µs

Figure 1.

Multi-rate simulation of a power converter. The model of the power converter illustrated in this figure is shown in Figure 2.

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

2.0 Introduction

In Application Note Part 1 [1], it was shown that combining RT-LAB and the Power System Blockset (PSB) enhanced by the Artemis Plug-In, allows real-time simulation of complex energy conversion systems, with averaged models used in place of detailed models of power-electronic bridges. This paper investigates the extent to which the averaged model can be used to predict the stresses on power components external to the power-electronic bridges. The system discussed in this investigation is illustrated in Figure 2. The same model is shown in two parts in Figure 3 and Figure 4. These figures, where Figure 3 relates to the top half of Figure 2and Figure 4 represents the bottom half, are shown separately solely for the purposes of this discussion.

Artemis Guide Continuous system

Continuous system

Vdc1

+ v

+ v Vab inverter + v A A B B B C C C B A B A C Vabc C Iabc Iabc C A B Vabc

Vab_inv 1 Vdc

+ A

Vab_load

L1

V+

C

V-

pulses

Measure

50 kW 380 V rms 50 Hz

PWM IGBT Inverter

LC Filter4

Subsystem 1 Vabc 2 Modindex OpComm

Signal(s) Pulses

3 Vabc1_s fast-to-slow1 2 ModIndex1

A=1 Discrete PWM Generator

1 Vabc (pu)

abc dq0 sin_cos

Demux PI Selector Vd Vq PI Controller 0 V0

hypot

mod index

2 m

Vd Vq inverter

dq0 abc sin_cos

abc_to_dq0 Transformation 2 Vd_ref (pu) 0

Freq Sin_Cos wt

1 Vabc_inv

dq0_to_abc Transformation

Vq_ref (pu)

Discrete Virtual PLL 50 Hz

Figure 2.

The power-electronic converter model under discussion in this Application Note.

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

Figure 3 shows the PSB diagram of the power-electronic system shown in Figure 2. The controller is shown in Figure 4. The rectifier is modeled with Simulink blocks, to avoid having numerous switching devices in the system. (This basic system is modified for the experiments reported hereafter.)

Artemis Guide Continuous system

Continuous system

Vdc1

+ v

+ v Vab inverter + v A A B B B C C C B A B A C Vabc C Iabc Iabc C A B Vabc

Vab_inv 1 Vdc

+ A

Vab_load

L1

V+

C

V-

pulses

Measure

50 kW 380 V rms 50 Hz

PWM IGBT Inverter

LC Filter4

Subsystem 1 Vabc 2 Modindex OpComm

Signal(s) Pulses

3 Vabc1_s fast-to-slow1 2 ModIndex1

A=1 Discrete PWM Generator

Figure 3.

The PSB model of a pulse-width modulation (PWM) power-electronic conversion system. This figure relates to the upper section of Figure 1 and Figure 2.

Simulink model of the controller

1 Vabc (pu)

abc dq0 sin_cos

Demux PI Selector Vd Vq PI Controller 0 V0

hypot

mod index

2 m

Vd Vq inverter

dq0 abc sin_cos

abc_to_dq0 Transformation 2 Vd_ref (pu) 0

Freq Sin_Cos wt

1 Vabc_inv

dq0_to_abc Transformation

Vq_ref (pu)

Discrete Virtual PLL 50 Hz

Figure 4.

The control system associated with the power-electronic conversion system in Figure 3. This figure relates to the lower section of Figure 1 and Figure 2.

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

3.0 Electromagnetic transients induced by the control system

In order to study the extent to which an averaged model can be used to determine the electromagnetic transients induced by the control system, a stair-shaped reference voltage (Vd_ref (pu)) has been applied to the reference input of the control system. The results of this experiment are shown in Figure 5 and Figure 6.

Varstep c o n t 2 µ s v s . a v e r a g e d m o d e l 2 0 0 µ s , D C V o l t a g e 1100 1000 900 800 700 Vdc (Volts) 600 500 400 300 200 CASE WITHOUT TRANSFORMER AND CLOSED LOOP CONTROL 100 0 0 0.02 0.04 0.06 0.08 T ime (s) 0.1 0.12 0.14 0.16 Reference Tustin and Art5 in the Artemis Plug - In, 200 µs

Varstep c o n t 2 µ s , s w i t c h e d m o d e l v s . a v e r a g e d m o d e l , M o d u l a t i o n I n d e x 1 Tustin and Art5 in the Artemis Plug - In, 200 µs 0.8 Modulation Index

0.6

0.4 Reference 0.2

0 CASE WITHOUT TRANSFORMER AND CLOSED LOOP CONTROL 0 0.02 0.04 0.06 0.08 T ime (s) 0.1 0.12 0.14 0.16

Figure 5.

DC voltage and modulation index for large perturbation from the control system. 200µs fixed time step simulation for the averaged model.

Figure 5 shows that the modulation index waveforms from both the averaged and the switched models have the same profile. From this observation, we can project that the use of the averaged model is suitable for the design of control systems. The averaged model is simulated with a fixed time step of 200µs, which is of benefit to the user since an integration time step that large is more than enough for real-time simulation. This is the same conclusion as was drawn in Part 1 of this Application Note [1].

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

Figure 6 shows the filter current and the line-to-line load voltage. The filter current waveform shows that the system loading the inverter has a natural mode at the third harmonic. The peaks in the current filter and the load voltage are well reproduced by the fixed time step integration algorithms (Tustin in the Power System Blockset, and Art5 in the Artemis Plug-In). This suggests that the averaged model can also be used to study the stresses (over-voltages and over-currents) in the external power component for protection sizing.

Varstep cont 2µs, switched model vs. averaged model, Filter Current 50 40 30 20 Ifilt (Amps) 10 0 -10 -20 -30 -40 0 CASE WITHOUT TRANSFORMER AND CLOSED LOOP CONTROL 0.02 0.04 0.06 0.08 T ime (s) 0.1 0.12 0.14 0.16 Reference Tustin and Art5 in the Artemis Plug -In, 200 µs

Varstep cont 2µs, switched model vs. averaged model, Load Voltage

600 400

Vab (Volts) Tustin and Art5 in the Artemis Plug -In, 200 µs

200 0 -200

Reference

-400

CASE WITHOUT TRANSFORMER AND CLOSED LOOP CONTROL

0

0.02

0.04

0.06

0.08

T ime (s)

0.1

0.12

0.14

0.16

Figure 6.

Filter current and load voltage perturbation from the control system. 200µs fixed time step simulation for the averaged model.

While the filter current and load voltage show similar shapes with the three simulation methods discussed (Simulink variable step size integration, Tustin, and Art5), the waveforms resulting from the fixed step size integration method depart significantly from the reference waveform. As the third harmonic (150Hz) is considerably less than the PWM switching frequency (2kHz), the fact

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

that the averaged model fails to accurately reproduce the third harmonic seems to go against the observations made in the Part 1 of this Application Note [1]. This requires further investigation.

Note: The Tustin method in PSB and the Art5 method in the Artemis Plug-In give approximately the same results because the system is well damped. Figure 6 in [2] shows that when the circuit is very well damped, the Tustin and Art5 methods are both quite accurate.

4.0 Electromagnetic transients caused by faults in the power circuit

Figure 7 and Figure 8 show the results for a three-phase short-circuit to ground across the load. In this experiment, the voltage command reference is a step function starting at 0.01s, with a final value of 0.8pu. The three-phase to ground is applied across the load at 0.04 and removed at 0.06. Figure 7 shows the DC voltage and the Modulation Index, while Figure 8 shows the filter current and the load voltage.

1200 Varstep cont 2µs, switched model vs. average model, DC Voltage Art5 in the Artemis Plug -In, 2 µs 1000

800 Vdc (Volts)

600 Reference 400

200

CASE WITHOUT TRANSFORMER T H R E E -P H A S E S H O R T -C I R C U I T O N T H E L O A D S I D E

0

0

0.01

0.02

0.03

0.04

0.05 T ime (s)

0.06

0.07

0.08

0.09

0.1

1.8 1.6 1.4 Modulation Index 1.2 1 0.8 0.6 0.4 0.2 0 0

Varstep cont 2µs, switched model vs. averaged model, Modulation Index

Art5 in the Artemis Plug -In, 2 µs

Reference

CASE WITHOUT TRANSFORMER T H R E E -P H A S E S H O R T -C I R C U I T O N T H E L O A D S I D E 0.01 0.02 0.03 0.04 0.05 T ime (s) 0.06 0.07 0.08 0.09 0.1

Figure 7.

DC Voltage and Modulation Index for a three-phase short-circuit on the load side.

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

100 80 60 40 Ifilt (Amps) 20 0 -20 -40 -60

Varstep cont 2µs, switched model vs. averaged model, Filter Current

Art5 in the Artemis Plug -In, 2 µs

CASE WITHOUT TRANSFORMER -80 THREE -P H A S E S H O R T -C I R C U I T O N T H E L O A D S I D E -100 0 0.01 0.02 0.03 0.04 0.05 T ime (s) 0.06 0.07 0.08 0.09 0.1

1000 800 600 400 Vab (Volts) 200 0 -200 -400 -600 -800 -1000 -1200 0

Varstep cont 2µs, switched model vs. averaged model, Load Voltage Art5 in the Artemis Plug -In, 2 µs

CASE WITHOUT TRANSFORMER THREE -P H A S E S H O R T -C I R C U I T O N T H E L O A D S I D E 0.01 0.02 0.03 0.04 0.05 T ime (s) 0.06 0.07 0.08 0.09 0.1

Figure 8.

Filter Current and Load Voltage for a three-phase short-circuit on the load side.

In this case, both the switched model and the averaged model were simulated using a variable step size integration algorithm with a maximum step-size of 2µs. Since the behavior of the averaged model was quite different from that of the reference, we wanted to make sure no effects were related to fixed time step integration. Figure 7 and Figure 8 show that prior to applying the short circuit, the averaged model and the switched model gave almost the same results. The transients following the clearing of the short circuit are quite different, however. This indicates that the averaged model used in this experiment is not adequate for studying the transients caused by faults in the power circuit. Better averaged models can be developed as reported in [3].

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REAL-TIME SIMULATION OF AVERAGED MODELS OF POWER CONVERTERS, PART 2

5.0 Conclusions

From the experiments related in this paper, the aim of which was to complement the experiments related in [1], we can draw the following conclusions: · As far as peak over-voltages and over-currents are concerned, the averaged model can be used to study the power component stresses caused by disturbances in the control system. · Averaged models are adequate for the design of control systems. · Averaged models are not appropriate for studying transient phenomena caused by faults in the power circuit external to the power-electronic bridges. · The accuracy of more complex averaged methods as reported in [3] should be further investigated.

6.0 References

[1] Nicolas Léchevin, Guillaume Murere, Jean Bélanger. "Real-Time Simulation of Averaged Models of Power Converters, Part 1: Overview and Computing Efficiency", Opal-RT Technologies Inc. (October 2000). Guillaume Murere. "The Artemis Plug-In improves the Accuracy of the Power System Blockset", Opal-RT Technologies Inc. (September 2000). Seth Saunders, J. Mark Noworolski, Xiaojun Z. Liu, George C. Verghese. "Generalized Averaging Method for Power Conversion Circuits", IEEE Transactions on Powerelectronics 6.2 (April 1991).

[2]

[3]

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