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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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**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?**• 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 Rönnberg – Sweden – RIF2….. – 206**A simple model for the emitter**• Current source + parallel capacitance • Grid: constant resistance Rönnberg – Sweden – RIF2….. – 206**Two emitters connected to the grid**• Primary emission: from the device • Secondary emission: from another device Rönnberg – Sweden – RIF2….. – 206**Current and voltage (complex numbers)**• Emission from one device and from both devices into the grid. • a =wRC Rönnberg – Sweden – RIF2….. – 206**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**Multiple devices**• Emission of one device: rather constant • Total emission: decreasing with frequency and with number of devices Rönnberg – Sweden – RIF2….. – 206**In time domain: two devices**• Current shows amplitude modulation due to the difference in switching frequency between the two devices Rönnberg – Sweden – RIF2….. – 206**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**Emission by each individual device**Maximum in time domain Amplitude in frequency domain Minimum in time domain Rönnberg – Sweden – RIF2….. – 206**Total emission by the installation**Maximum in time domain Amplitude in frequency domain Rönnberg – Sweden – RIF2….. – 206**Measurement in time domain (2 lamps)**1 ms Rönnberg – Sweden – RIF2….. – 206**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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