Electrical supply issues

Updated on 25th November 2024

The basic parameters of 3-phase electrical supply may not all be perfect

Engineers, particularly Mechanical Engineers, often assume that the electrical supply to their equipment is at exactly the nominal voltage (eg 240 or 415 volts), and exactly the nominal frequency (eg 50 or 60Hz), with the current and voltage waveforms perfectly sinusoidal in shape (if they ever thought about them at all), with three phases all equal in magnitude, all similar in shape, and all at 120 degrees spacing from one another.

The truth is that the real world situation can be significantly different from this perfect world picture, and some of the differences can have consequences for the behaviour and reliability of your equipment.

In addition, your equipment can affect the power supply, particularly in areas such as the Power Factor for your site, and raised levels of harmonic distortion, put back onto your network.

Much of the time, you don’t actually know what the situation is – on a few assets you may have meters showing you overall voltage and current, but rarely do you have information on the actual frequency, phase balance, harmonic distortion or power factor, and even more rarely still do you get to see the shape of the voltage and current waveforms. When you install a Faraday Predictive system, suddenly this information is fully visible to you, and you can see not only what the values are, but how they can vary from day to day, and from minute to minute.

What does a three-phase electricity supply look like?

The image above shows the three-phase voltage and three-phase current being drawn by a small motor, powered by an inverter. The three voltage traces are the paler ones, slightly smaller in magnitude than the currents. The three-phase currents are the darker ones, with noticeably spikey distortion, particularly around the peaks. Note how they are different in shape from a pure sine wave.

Things to notice about this sort of three phase picture:

Voltage levels in a 3-phase supply:

The voltage traces on the plot have peaks that are approximately 170v above and below zero (left hand axis). As an AC system, the figure we normally quote (eg 240v) is an RMS value, which corresponds to the DC figure that would give the same energy level. If the traces were perfect sine waves, the ratio between the value of the RMS figure and the peak would be the square root of 2. So in this case, with a peak of around 170v, we’d expect an RMS value of around 170/1.4 = 121v. So why is the voltage figure in the table, detail shown below, 206v, which is more than the peak value, instead of 121v?

The answer is that the voltage figure reported in the table is the Line to line figure (L-L V) whereas the plot shows the individual phase to neutral values. On the plot, the line to line value is given by the vertical distance between one phase and another which is greater than the line to neutral value by a factor of Square Root of three, or approx. 1.7

Current levels in a 3-phase supply:

Note that the current measured in a phase is simply that, with no correction required for phase to phase – but it is an Alternating Current, so the ratio between the peaks on the plot – at about 0.90Amps – and the reported RMS value of 0.64 should be somewhere around square root of two, which it is.

Phase balance:

The three voltages should all be the same amplitude. In this case it’s a bit hard to tell visually because of the spikey distortion. Likewise the three currents should all be the same amplitude. In this case it looks as if the blue phase is of greater amplitude than the red and green phases. The figures on the right show that Voltage unbalance is 0.04% – which is good – and that current unbalance is 0.53%, which is also good.

Distortion:

The three phases should ideally all be perfectly smooth sinusoidal shapes. In this example, they are clearly not perfectly sinusoidal. The voltage waveforms are distorted in this case because they are created by an inverter, to give a variable speed control (note the frequency figure shown in the top right shows 45Hz – clearly not coming direct from the electricity supply grid). Inverters create a different frequency from the mains supply by first converting the AC supply to DC, and then synthesizing an AC supply of a different frequency by chopping up this DC into pulses of different duration, and by clever control of the width of these pulses, they create an overall shape approximating to a sinusoidal form. How close they get to a perfect sinusoid varies from one inverter to another, depending on the design, what filtering is fitted, and the situation they are working under.

The motor current is affected by the behaviour of the rotating equipment (both the motor and the driven equipment) – which is the basis for using the motor as a sensor for condition monitoring – so the current can often be more distorted than the voltage.

Any distorted waveform can be described mathematically as the sum of a series of perfect sinusoidal waveforms of multiple harmonic frequencies – ie a perfect sinusoidal waveform at the fundamental frequency plus a small amount of a perfect sinusoidal waveform of double the fundamental frequency (the 2nd harmonic), plus a small amount of the 3rd harmonic, etc. The total distortion can be described by the amount of energy in these higher harmonic frequencies and is referred to as the level of Total Harmonic Distortion, or THD. This is shown in the table above right, the relevant section of which is copied here:

We can see that the Voltage THD is 0.65%, which is good because it should ideally be below 1%.

The current THD is shown as 2.10%, and is shaded yellow, indicating it is at warning level.

The white boxes below show how these Total harmonic distortion figures are built up from the levels of distortion at each of the odd harmonics up to 13th. The reason for only showing odd harmonics not even ones will be explained elsewhere on this site.

Active Power/Reactive Power & Phase Angle / Power Factor

Looking at the plots, the peak on the pink trace, the phase 1 voltage, occurs some time before the peak on the red trace, the corresponding phase 1 current. The voltage is said to be leading the current. You may remember from school days the mnemonic, CIVIL:

CIVIL: in a Capacitor, (C) current (I) comes before voltage (V); whereas voltage (V) comes before current (I) in an inductor (L)

So the voltage leading current indicates that this is an inductive system – which you would expect, because the motor windings are inevitably inductive, comprising lots of windings deliberately creating a magnetic field which is magnified by the windings being wrapped around an iron core.

A pure inductive load would be 90° out of phase between current and voltage – but since power is voltage multiplied by current in phase with the voltage, there would be no power consumed – and our motor would not be doing any useful work.

The work done by a motor is effectively measured by voltage multiplied by the current in phase with it. If we had a phase angle of zero, it would mean all of the current drawn by the motor was doing useful work. In practice this is never possible, as it takes a significant amount of current to magnetise the core, and so a phase angle of around 30o is typical. The figures are shown on the table, the relevant extract of which is here:

The Phase Angle is given by Phi – in this case 48.32°

The Active Power (A pwr) is given as 0.15 kW; this is real work, driving the pump round and pumping water along the pipe;

The Reactive Power (R pwr) is given as 0.17 kVAR; this is energy flowing in and out of the system, but not contributing to useful work.

The Power Factor (P Factor) is given as 0.665;

(not shown is the Apparent Power, which is simply the figure you would get if you multiplied voltage x current – as if there were no phase angle)

These figures are related, in that Reactive Power / Active Power = Tan Phi.

Active Power / Apparent Power = Cos Phi. Or to put it the other way,

Active Power = Apparent Power x Cos Phi – since we can readily measure Apparent Power and phase angle, so we can use this to calculate the Active Power.

Low power factor is to be avoided if possible, since the reactive current does no useful work but still represents current flowing in the windings, resulting in resistive losses in the windings (“copper losses”) and reactive losses in the core (“iron losses”) which represent wasted energy, and raise the temperature of the motor, which can be bad for reliability.

Why should I worry about the quality of the mains power supply?

Phase balance can be important for two reasons

Firstly, an unbalanced supply to a motor results in the motor creating an oscillating torque output.

If you were to plot the torque as the motor rotates on a polar plot, in an ideal world, with a perfectly balanced 3-phase supply, the torque plot would be a perfect circle, because the three phases, each at 120^o apart, create a rotating magnetic field of constant strength, rotating at constant speed.

However, if the three phases are not perfectly balanced, the magnetic field will be stronger in the windings corresponding to the stronger phase, and weaker in the windings corresponding to the weaker phase. So the torque will be stronger or weaker as each of the phases in turn pass through their alternating cycle. Note that this effect occurs on both the positive and negative parts of the cycle, so it will occur at twice line frequency. On a two pole motor, this means the torque plot will be elliptical rather than circular. On a four pole machine (which rotates at half the speed) the torque plot will be a somewhat squared-off circle.

This variation in torque puts additional (fatigue) stresses on elements such as shafts and couplings.

Secondly, an unbalanced supply leads to motor heating which reduces the motor life (and wastes energy).

As a rule of thumb, a 1% voltage unbalance leads to a 5% current unbalance; and a 5% current unbalance leads to a 10^oC rise in motor temperature; and a 10^oC rise in motor temperature halves the life of the motor windings (through more rapid ageing of the insulation). So unbalance is to be avoided if possible. AND heating indicates wasted energy, so it represents an opportunity for energy saving if we can eliminate it.

Harmonic distortion is important for two reasons

Firstly it creates motor heating:

the distortions represent current flowing in and out of the motor, which don’t contribute to driving the rotation forward. However, they incur resistance in the windings (copper losses) and create eddy currents in the core (iron losses) which waste energy, which appears as heat. So as with unbalance supply, a 10^oC rise in motor temperature halves the life of the windings and wastes energy.

Secondly, it can contribute to shaft currents

which in turn can lead to electric currents flowing through bearings, causing arcing between the balls and the races, and resulting in rapid damage to bearings, with some characteristic “fluted” damage patterns.

Power Factor can be important

to the extent that your electricity supplier may charge you extra for your power if you have a low power factor. This is because although you only use energy in the real power, the supply system has to be rated to carry the maximum current you draw, and with a low power factor, the current is increased by the factor of 1/cos phi.

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Tags: Technical education