Polyphase circuits
When the neutral of a building is cut, some apartments receive more than 300 V and their appliances burn out. The phasor diagram of an unbalanced wye explains exactly why.
01Three voltages 120° apart
A three-phase generator has three windings spaced 120° apart in space, and produces three voltages of equal amplitude 120° apart in time. The entire electrical grid of the world is generated, transmitted and distributed this way, for three reasons that appear in this unit: with three conductors you transmit three times the power of a single phase with two conductors, the total instantaneous power is constant —and motors turn without vibrating— and two different voltages are obtained from the same grid.
02Wye and delta
The three phases can be connected in two ways. In wye (Y) each load goes between one phase and the common neutral; in delta (Δ), between two phases. The voltages between phases —line voltages— are \( \sqrt3 \) times the phase voltages:
| Wye | Delta | |
|---|---|---|
| Voltage across each load | \( V_f = V_L/\sqrt3 \) | \( V_L \) |
| Line current | Equal to that of each load | \( \sqrt3 \) times that of each load |
| Neutral | Available | Does not exist |
| Typical use | Residential distribution | Motors and industrial loads |
03The neutral and imbalance
If the three loads of a wye are equal, their currents add up to zero and the neutral carries nothing. But residential consumption is never balanced: in a building, each apartment is on a different phase and each one draws what it wants. The neutral then carries the sum of the three currents, and it also performs a function that is noticed only when it is missing: it holds the common point of the loads at zero volts.
If the neutral is cut, the common point of the loads is left floating and shifts toward the most heavily loaded phase. Its voltage comes directly from Millman’s theorem from the previous topic:
Three loads in wye on a 3 × 380/220 V grid, one per phase. You choose the power of each one and whether the neutral is connected. The phasor diagram shows the grid voltages, the common point of the loads and the voltage that reaches each one.
A neutral cut at the service entrance of a building is one of the most common causes of appliances burned out en masse: the apartments on the least loaded phase suddenly receive more than 300 V. That is why the regulations prohibit installing fuses or switches that interrupt only the neutral, and why overvoltage protection devices exist that disconnect the installation when the voltage goes out of range.
04Constant power
In a single phase the instantaneous power oscillates at twice the grid frequency and passes through zero a hundred times per second. In a balanced three-phase system, the three oscillations are out of phase and their sum is exactly constant. A three-phase motor then receives a constant torque and runs smoothly, whereas a single-phase one vibrates at twice the grid frequency. It is one of the reasons why industry uses three-phase even when the power could be transmitted in single-phase.
05Where it shows up in electronics
| Case | What is used from this unit |
|---|---|
| Motor variable-speed drive | Rectifies the three-phase supply and synthesizes it again at another frequency with transistors |
| Switched-mode power supplies in an office building | Their 3rd-order harmonics add up in the neutral instead of canceling, and overheat it |
| Inverter of a three-phase solar system | Generates the three phases at 120° synchronized with the grid |
| Three-phase energy meter | Measures power in the three phases, or in two with the two-wattmeter method |
06In the lab
With a three-phase practice panel and the appropriate protections, use a multimeter to measure the three phase voltages and the three line voltages. Verify the \( \sqrt3 \) relationship.
Using this page’s lab and the neutral connected, make the three powers equal and verify that the neutral current vanishes. Then leave a single load and verify that the neutral carries all its current.
For loads of 2000, 100 and 500 W with the neutral cut, calculate by hand the voltage of the common point and that of each load, and compare with the panel.
07Common mistakes
- Adding the phase voltages as plain numbers. They are phasors at 120°: the line voltage is \( \sqrt3 \) times the phase voltage, not double.
- Believing the neutral “carries nothing.” Only with perfectly balanced loads and no harmonics.
- Protecting the neutral with its own fuse. If only the neutral opens, the common point floats and overvoltages appear.
- Using \( P = 3VI\cos\varphi \) with line voltages. With line values it is \( \sqrt3\,V_L I_L\cos\varphi \).
- Thinking a neutral cut only switches things off. The voltage on the least loaded phase rises.
08Self-assessment
What is the line voltage of a grid with a 220 V phase voltage?
\( \sqrt3 \times 220 \approx 380 \) V.
When does no current flow through the neutral?
When the three loads are equal and linear: their currents add up to zero.
What happens to the least loaded phase if the neutral is cut?
The common point shifts toward the most loaded phase and the least loaded one receives a voltage higher than nominal.
Why does a three-phase motor run more smoothly than a single-phase one?
Because the instantaneous power of a balanced three-phase system is constant.
Which theorem gives the voltage of the common point with the neutral cut?
Millman’s.
09Further reading
- Charles K. Alexander and Matthew N. O. Sadiku. Fundamentals of Electric Circuits. 7th ed., McGraw-Hill, 2021. The chapter on three-phase circuits, with balanced and unbalanced loads.
- Argentine Electrotechnical Association (AEA). Reglamentación para la ejecución de instalaciones eléctricas en inmuebles (AEA 90364). AEA (in Spanish). The standard that governs installations in Argentina, including the prohibition on disconnecting the neutral separately.
- Stephen J. Chapman. Electric Machinery Fundamentals. 5th ed., McGraw-Hill, 2011 (Spanish edition, “Máquinas eléctricas”). The appendix on three-phase circuits, written for what motors later demand.