Download A simple model for interaction between equipment at a

A SIMPLE MODEL FOR INTERACTION
BETWEEN EQUIPMENT AT A
FREQUENCY OF SOME TENS OF KHZ
Math Bollen, Sarah Rönnberg, Anders Larsson
Luleå University of Technology, Sweden
Jean-Luc Schanen
Grenoble 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
Frankfurt (Germany), 6-9 June 2011
The emitter
Active PFC
Active
PFC
Iem
L2
G
R
Grid
C1
C1
I
D



L2
L1
L1
C3
C3
C4
C4
A typical device with active power-factor
correction circuit
Small emission below 2 kHz
Switching frequency is emitted into the grid
Rönnberg – Sweden – RIF2….. – 206
R
ive PFC
Frankfurt (Germany), 6-9 June 2011
A simple model for the emitter
IIem
em
IL1
C4
R
R
C1
C1?
IL1
Current source + parallel capacitance
 Grid: constant resistance

Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Two emitters connected to the grid
Primary
Primary
emission
emission
Internal
Int.
emission
emission
em
IIem
IIL1
L1


Secondary
Secondary
emission
emission
C
C
IIgrid
grid
RR
C
C
IL2
IL2
Primary emission: from the device
Secondary emission: from another device
Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Current and voltage (complex numbers)
Emission from one device and from both
devices into the grid.
 a =wRC

Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Current and voltage (magnitude)


The internal emissions are independent from
each other
Use Parseval’s theorem to add primary and
secondary emission
Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Multiple devices


Emission of one device: rather constant
Total emission: decreasing with frequency and
with number of devices
Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
In time domain: two devices

Current shows amplitude modulation due to the
difference in switching frequency between the
two devices
Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Numerical example
Grid impedance: R = 50 W
 Device capacitance: C = 220 nF
 Switching frequency: w = 2p x 40 kHz


Typical values for high-frequency ballast with
fluorescent lamps.
Rönnberg – Sweden – RIF2….. – 206
Frankfurt (Germany), 6-9 June 2011
Emission by each individual device
Emission by one device
2
Maximum in time domain
1.5
1
Amplitude in frequency domain
0.5
Minimum in time domain
0
2
4
6
8
Number of devices
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10
12
14
Frankfurt (Germany), 6-9 June 2011
Total emission by the installation
Emission by the whole installation
0.4
0.35
Maximum in time domain
0.3
0.25
0.2
0.15
0.1
0.05
0
2
4
6
8
Number of devices
Rönnberg – Sweden – RIF2….. – 206
10
12
14
Frankfurt (Germany), 6-9 June 2011
Measurement in time domain (2 lamps)
Vgrid
Igrid
Iem1
Iem2
1 ms
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Frankfurt (Germany), 6-9 June 2011
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
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