a simple model for interaction between equipment at a frequency of some tens of khz

A SIMPLE MODEL FOR INTERACTION BETWEEN EQUIPMENT AT A

FREQUENCY OF SOME TENS OF KHZ

Math Bollen, Sarah Rönnberg, Anders LarssonLuleå University of Technology, Sweden

Jean-Luc SchanenGrenoble Electrical Engineering Lab, France

Frankfurt (Germany), 6-9 June 2011

What’s the problem?

Modern equipment emits disturbances in the range 2 to 150 kHz.

We do not know how this spreads. Measurements indicate that it mainly

spreads between devices. A model is needed to understand the

measurements.

Rönnberg – Sweden – RIF2….. – 206


The emitter

A typical device with active power-factor correction circuit

Small emission below 2 kHz Switching frequency is emitted into the grid

C3

L1

C4

Active PFC

C1 Grid

L2

Active PFC

C1

GRID

L1

C3 C4

L2



C4 C1? R

Iem

IL1

C1R IL1

Iem

A simple model for the emitter

Current source + parallel capacitance Grid: constant resistance



Two emitters connected to the grid

Primary emission: from the device Secondary emission: from another device

C IL1 R IL2 C

Iem Igrid

Primary emission

Secondary emission

Int. emission

Internalemission

Primaryemission

Secondaryemission

Iem

IL1 IL2

Igrid

RC C



Current and voltage (complex numbers)

Emission from one device and from both devices into the grid.

=RC



Current and voltage (magnitude)

The internal emissions are independent from each other

Use Parseval’s theorem to add primary and secondary emission



Multiple devices

Emission of one device: rather constant Total emission: decreasing with frequency and

with number of devices



In time domain: two devices

Current shows amplitude modulation due to the difference in switching frequency between the two devices



Numerical example

Grid impedance: R = 50 Device capacitance: C = 220 nF Switching frequency: = 2 x 40 kHz

Typical values for high-frequency ballast with fluorescent lamps.



Emission by each individual device

2 4 6 8 10 12 140

0.5

1

1.5

2

Number of devices

Em

issi

on

by

on

e d

evi

ce

Amplitude in frequency domain

Maximum in time domain

Minimum in time domain



Total emission by the installation

2 4 6 8 10 12 140

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Number of devices

Em

issi

on

by

the

wh

ole

inst

alla

tion

Amplitude in frequency domain

Maximum in time domain



Vgrid

Igrid

Iem1

Iem2

Measurement in time domain (2 lamps)


1 ms


Conclusions

The simple model shows that Emission per device increases with frequency towards

an upper bound Total emission of the installation decreases with

frequency towards zero The currents and voltages are amplitude modulated

This has been confirmed by various measurements

Further comparison between simulations and measurements is needed


a simple model for interaction between equipment at a frequency of some tens of khz

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