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# 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 Larsson Luleå University of Technology, Sweden Jean-Luc Schanen Grenoble Electrical Engineering Lab, France. What’s the problem?.

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## A SIMPLE MODEL FOR INTERACTION BETWEEN EQUIPMENT AT A FREQUENCY OF SOME TENS OF KHZ

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1. 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

2. 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

3. The emitter • 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

4. A simple model for the emitter • Current source + parallel capacitance • Grid: constant resistance Rönnberg – Sweden – RIF2….. – 206

5. Two emitters connected to the grid • Primary emission: from the device • Secondary emission: from another device Rönnberg – Sweden – RIF2….. – 206

6. Current and voltage (complex numbers) • Emission from one device and from both devices into the grid. • a =wRC Rönnberg – Sweden – RIF2….. – 206

7. 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

8. Multiple devices • Emission of one device: rather constant • Total emission: decreasing with frequency and with number of devices Rönnberg – Sweden – RIF2….. – 206

9. In time domain: two devices • Current shows amplitude modulation due to the difference in switching frequency between the two devices Rönnberg – Sweden – RIF2….. – 206

10. 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

11. Emission by each individual device Maximum in time domain Amplitude in frequency domain Minimum in time domain Rönnberg – Sweden – RIF2….. – 206

12. Total emission by the installation Maximum in time domain Amplitude in frequency domain Rönnberg – Sweden – RIF2….. – 206

13. Measurement in time domain (2 lamps) 1 ms Rönnberg – Sweden – RIF2….. – 206

14. 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 Rönnberg – Sweden – RIF2….. – 206

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