When three-phase motors are grouped on a line, things can get way out of balance. Bob Harper reports.

An electrician friend who works in a rural setting recently installed three identical single-phase motors.

They were intended to work together, so he wired them on three phases to balance the load, and ran a three-phase supply with neutral and earth. The motors were wired with individual control switches, not as a group.

Then the fun began

The motor capacitors began to fail, and one motor was replaced under warranty. The capacitors were replaced with the original values of capacitance and working voltage, but they still failed at odd times.

The electrician tested the terminal voltages and, typical of long runs, there was some dipping during start-up. But it didn’t seem significant.

The other issue with rural installations is the delay in obtaining parts, and travelling to and from the jobs. So this job quickly became a nuisance for the electrician and the client. Downtime, even allowing for the country location, was excessive.

After trying everything he could think of, and probably in a moment of frustration, he phoned to discuss the theory with me. To be honest, I was full of theories but thin on answers. We agreed that the neutral wasn’t meant to be downrated, as the three motors were not actually a three-phase load.

He was calling from the site, and wanted to fix things ASAP with what was on the truck, so he installed three individual circuits, all wired back to the sub-board on three separate breakers. Thankfully the issues have gone, for now at least.

Theory recap

Any three-phase load with exactly the same load on each phase will draw three equal currents from the three-phase lines.

That means you get the same value of current and the same phase angle supplied from identical phase voltages spaced 120º apart.

Most apprentices are taught according to the concept of an ‘infinite grid’, although they are not usually told that. The infinite grid simplifies the theory by assuming there is a concrete expectation of three equal phases of fixed (nominated) voltage, spaced 120º apart and of zero line impedance (ie: a perfect supply).

Those phase diagrams you used at TAFE started with three points of a perfect isosceles triangle, 415V between points and 240V to the centre, or 400/230V for recent graduates.

In such a perfectly balanced load, the neutral wire in any ‘star/wye’ connection would not be needed, as the balanced currents flow only in the phase wires or lines.

Figure 1 shows a phase diagram of a balanced three-phase system. Voltages are assumed to be 230/400V.

Perfection ends

Perfect worlds rarely remain perfect for long, as most contractors know.

To begin with, equal loads are rarely perfectly equal, especially when they are connected via three individual switches.

For example, if one motor is turned on first then it is a single-phase load that draws all of its current through the neutral. So the neutral must be at least fully rated to carry that load current and starting current.

When running, that motor improves its power factor depending on its mechanical load.

When another motor starts, depending on which one and which phase (leading or lagging phase), the added load can increase or decrease neutral current.

Without doing the phasor diagram, it seems that the maximum current might go as high as 150% of the single load current.

(That’s a guesstimate, so don’t send in your computer-generated calculations just yet.)

If both motors are running on an ‘infinite grid’ the calculations can be done by an electrician that passed the apprenticeship requirements honestly. However, I accept that it is somewhat more than the average electrician requires on the job.

Another scenario might be ‘loss of neutral’, where the neutral is somehow disconnected. (It does happen.) The two motors then appear ‘in series’ across the line voltage (400-415V), thus sharing the voltage equally. However, neither will start all by itself, only receiving current when a second motor is turned on (ie: both switches need to be closed to energise the two motors).

Spring model or analogy

As a TAFE teacher, I demonstrated the concepts using three strips of Meccano made into a triangle.

For those that didn’t grow up with Meccano, that’s three strips of metal with a threaded fastener on each corner.

Three equal-strength springs connected in the middle and stretched to the corners of the triangle should settle with the joint in the neutral position. Figure 2a shows the spring model or analogy for a balanced star/wye load without any neutral required. The term mechanical analogy would also fit.

This mechanical analogy is much easier to show students than phasor diagrams.

Figure 2b shows the spring model when one phase is open and there is no neutral. Figure 2c shows the spring model when three differed loads are represented by three unequal-strength springs, without a neutral.

Real world

In the real world, the power lines are not perfect.

They have impedance, which is not necessarily equal in the three phases. There are other implied loads, causing unbalanced and fluctuating voltage drop and therefore resulting in three-phase voltages that are neither equal nor consistent.

The parallel connected loads are services all along the supply and distribution network, via transformers and other complications.

The loads are potentially unbalanced and may even pass through unbalanced transformers, affecting the supply your circuit runs on.

My mechanical analogy should have some complex levers and springs added to make it approximate the real world accurately, and that is all possible if you want to try it.

Without boring you with a full description, please feel free to experiment with a handful of tension springs, and perhaps some phasor diagrams as clues.

Figure 3a shows a spring analogical model of a balanced three-phase system without a neutral pinned to earth or balanced by a second set of springs.

The three Meccano points represent the alternator, which is assumed to be regulated to fine tolerance in an attempt to present the best standard phase/voltage/frequency relationship to the system being fed.

Three springs are attached to a triangle of three more springs, representing the supply and distribution network.

Then three more springs are attached to this supply, and joined at a common point to represent the three-phase star/wye load.

Figure 3b shows a badly balanced load having no effect on the almost ‘infinite grid’.

Figure 3c shows a large load, unbalanced, having an effect on a smaller grid, eg: starting a large unbalanced motor on the end of a lossy distribution line.

Mathematical method

To find a mathematical solution to such a problem, especially using pencil and paper and a good scientific calculator, is time consuming to say the least.

Remembering the step from simple Ohm’s Law to Ohm’s Law involving impedances, and complex impedances if you have experienced them, will alert you to the thinking required to solve the circuit from alternator to load.

It is not expected that electricians would ever set out to solve such a problem.

Engineers do, but even then only those that perform such maths regularly would attempt it without grabbing for their textbooks. There has to be a simpler way of determining, or at least estimating, the neutral current.

A simple method

One way of estimating the current in the neutral, assuming all currents are in phase, is given by the formula N² = A² + B² + C² –AB –AC –BC.

Do not try this in an engineering exam. The lecturer probably expects more.

Back to the problem

I have spent a few hours trying to explain the problem, at least to myself.

The capacitors may have been failing due to over-voltage. Not a constant over-voltage, but a short duration at start-up of one of the motors while another was running.

One motor on normal load suddenly has another motor on starting current dragging the neutral away from the centre voltage, therefore pulling the line voltage above the rated working voltage.

To test this would require three meters to read the voltage on each motor or, preferably, a three-phase power monitor.

Unless the circuit is always balanced, it’s not reasonable to assume that three identical motors will form a balanced load.

Not only do the motors have mechanical independence, but the three motors also have three independent mechanical loads that may fluctuate.

They have three independent switches, so they will start and stop independently. Starting currents will exceed the normal rated current of the cable, which is typically chosen for cost, not robustness. A slim neutral conductor in particular will suddenly have a high voltage drop.

It may also be that the voltages have dropped for a period longer than the normal starting cycle, so the motor was in start mode for longer than expected.

Capacitors have dielectric losses, which cause dielectric heating. Too much for too long will cause them to melt. Even before that happens, most will find a weak spot in the melting insulation and burn through, short out and launch their lunch.

The neutral for most of the time might be able to have a reduced CSA, but the CSA certainly should be at least that required for one circuit, ie: equal to the active conductor size.

The savings on downsizing the neutral have in this case been outweighed by the replacement capacitors and return visits. Never forget the potential cost of a return visit, especially to remote sites.

Finally, a reminder on starting capacitors, which are commonly 350-400V maximum voltage – that’s DC working voltage. But we have been using them on 240V, which has a peak voltage of 339V, assuming the line voltage is kept at 240 and below.

Rural voltage has always been a wanderer, often higher or lower than the old +/- 5% tolerance.

Modern capacitors are most likely made for 220V motors and deemed ‘near enough’ for those of us that use 240V AC. Hence the change towards a 220V system at some point in the future.

The second issue is that capacitors are often rated at a maximum temperature of 40ºC. I have had jobs where the award allowed us to knock off if the temperature went over 42ºC – and I don’t see why a capacitor wouldn’t join us.

Let’s face it, Australia has some of the highest temperatures in the world, and we are using capacitors made in cold countries, presumably for their own conditions.