On the difference between 'load-flow' and 'phasor' studies

A loadflow (power-flow) simulation is a phasor simulation. It is a phasor simulation of a power system at nominal frequency (50Hz or 60Hz.) It assumes that the system is at sinusoidal steady state and that nothing is changing.

The distinction between a 'load flow' study and a 'phasor study' is that a phasor study can be performed at any arbitrary frequency, say 50Hz, 100Hz, 150Hz, whereas a load-flow study is nearly always performed at the power system nominal frequency (50 or 60Hz.)

The generalised 'phasor study' is useful in the study of power system harmonics, which requires simulation of the power system at 50Hz and its harmonic frequencies 100Hz, 150Hz, 200Hz, 250Hz, ... and so on. This is done by running one separate 'phasor study' for each harmonic frequency of interest.

On the difference between load-flow/phasor and dynamic/transient studies

A load-flow study evaluates steady state operation of a power system. We do load-flow studies to check that elements like transformers, overhead lines, and cables won't be overloaded, and that system voltage regulation is within acceptable limits (-6%, +10% for Australian domestic power supply.)

The time scale of interest is hours to days.

The loadflow study is just an exercise in solving a lot of simultaneous linear equations. There is no time dependent element, no differential equations, or anything exciting. You multiply some big matrices together and that's it.

A dynamic/transient study evaluates the behaviour of the power system when a change occurs. The change could be an increase or decrease in load, a line fault, a change in generator output, or a big motor starting.

The objective is to determine if there will be any detrimental effects on the scale of milliseconds to minutes. Detrimental effects might include - voltage spikes/dips, generator frequency slip, protection relay operation.

A dynamic/transient study must take account of the time-dependent response of the electrical and mechanical parts of the power system.

• Generators and motors have a mechanical inertia
• Capacitors and inductors have energy storage
• Iron-cored transformers have remanence/hysteresis
• Protection relays are digital signal processors which decide whether the power system is healthy or not, based on the history of the signals they see.
• Generators have control systems with sophisticated transfer functions for calculating output voltage set point and governor (throttle) set point

Therefore a transient study involves simulating a system of differential equations evolving over time, with a typical time step of 1 millisecond.

The electrical quantities are still voltages and currents, but there are also a lot of variables in things like 'generator inertial energy' and 'motor rotational speed'.

PS: I do power system studies for a living.

To measure the power consumption of each motor, you'd need to measure the voltage and current, before the motor driver.

(the 3 phase power after the driver will be very hard to measure).

Both voltage and current measurements will need to be filtered to remove the 40 kHz signal, which will otherwise cause all sorts of trouble, as you correctly anticipate.

Fortunately, 40 kHz is far away from your likely sample rate of about 50 Hz. A first order RC filter with its knee at 40 Hz will attenuate the 50 kHz ripple voltage by about 30 times, which might be enough. An inductor and two capacitors will be much better.

Voltage is fairly easy to measure - as a nice low impedance source, you can build a simple filter and feed it to your ADC. You only need one voltage measurement after the 24 V power supply. The ripple in the voltage should be fairly small anyway.

Current is a bit more tricky. You could use a sense resistor in the ground wire, and an op-amp to amplify the small voltage, then the filter. At some torque settings, the current might really be a square wave at 40 kHz, it'll be hard to measure and filter. It might be an idea to filter the power line itself with one LC, just to remove some of the ripple, and then filter the sense output again before the ADC.

One last digital idea would be to sample faster than you need to, perhaps at 1 kHz, and average these in the Arduino. The aliasing will still be a problem, however if you randomise the time of the samples, you may be able to average out the 40 kHz signal, preventing it from being properly aliased into your band of interest. Some experiments here would be valuable.