Department of Mathematics

McCleer Power, Inc.

Designing a quieter pulse-width-modulation algorithm*

Future automotive electrical systems will be operating at 42 Volts DC, rather than the present nominal 13.8 Volts. Advanced applications in the modern automobile require this rise in operating voltage, such as active suspensions, hemetically sealed air-conditioning motor/compressors, hybrid Diesel/electric power trains, and other advanced intelligent systems.

The electric motors of these applications will require 3-phase AC current at 42 Volts. The conversion from the 42 Volt DC bus to 3-phase AC  is done by  power inverters, processor driven FET switches (usually 6 in number) that synthesize the AC voltage.

Let us look at the simplest possible case --- let us synthesize some nonnegative voltage wave form v(t) < 42 using one switch:

We partition time into small intervals of length T whereupon  the desired signal v(t) is more or less constantly v. The processor then closes the switch for only a portion dt of this interval T so that  the energy drawn from the battery during dt equals the energy that would be supplied during the whole interval T were the voltage to be v, i.e.,       T  v^2 = dt 42^2.

In other words, the switch doles out average current as if the voltage were v. This is  pulse-width-modulation (PWM). The switch is intelligently driven by a processor that monitors the smoothed voltage across the load R and varies the width dt of the pulse so as to synthesize the desired voltage v(t).

But the 42 Volt DC bus will suffer from such abuse --- it is being asked to deliver current in a train of square waves. These waves induce voltage drops across the inductance of the wires coming from the battery, create radio noise,  stress the alternator, and generally degrade the power quality of the DC bus, affecting the performance or even damaging other components at other locations in the automobile. The standard remedy is to hang large electrolytic capacitors across the DC bus as it enters the power inverter to serve as current sources or sinks,  thus smoothing the train of current demands. These capacitors are large, expensive, and cannot endure well the 120C temperatures found in an engine compartment.

The problem is to redesign the PWM algorithm to minimize the number of electrolytic capacitors.

In more detail, the inverter supplies 3-phase AC  (three 42 Volt sinusoidal voltages shifted in phase 0, 120, and 240 degrees) by pulse-width modulating 6 field effect transistors (FET):
These 6 FETs are to be switched according to some algorithm to be designed by the team. McCleer Power will specify the response of the load and the required bus power quality. With the load response in hand,  one can predict the current waveform demanded from the DC bus. Using the standard description of electrolytics it is then possible to model the improvement in demand from adding each electrolytics in turn across the bus. Conceivably a large automated search will find an algorithm for which the specified power quality is reached with the minimum number of electrolytic capacitors. Such a switching algorithm would be of deep interest to the automobile industry.

A proof-of-concept for a simple two FET, single-phase inverter would be a sufficient (and significant) deliverable.

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