What is a Three-Phase Power System

A three-phase power system distributes three alternating currents (AC) simultaneously along a three-wire conductor to a load. The wires are configured so each current phase is offset by 120 degrees. This allows power to be delivered more efficiently than a single-phase power system while requiring less construction material, reducing cost and energy loss.

To understand what a three-phase power system is, we must first discuss a single-phase system and how it relates to the concept of a phase.

What is a Single-Phase Power System

A single-phase alternating current is induced by a coil positioned between a pair of permanent magnets. When the coil rotates, the magnetic field moves relative to that coil. Faraday’s law tells us that a changing magnetic field creates an electromotive force, which generates a current.

When the coil moves from 0 to 180 degrees and then comes back to 0 degrees, this generates a single alternating current in the coil with a sinusoidal waveform, as shown in the diagram.

As the coil rotates, the induced current starts from 0 and moves to its peak, then drops to its negative peak and finally returns to 0. This is referred to as a full cycle, which takes 360 degrees to complete. Most of the household appliances operate on single-phase power, including lights, refrigerators, and televisions. Single-phase power delivers consistent voltage and is easy to distribute, making it ideal for home and small-scale loads.

A second generator can be added with a current of equal magnitude and frequency, but with a 120-degree phase shift relative to the first, as shown in the following plot.

Introducing the Three-Phase Power System

A three-phase power system works similarly to single-phase, except it consists of three alternating currents that are phase-shifted by 120 degrees.

This system consists of a three-phase generator, several three-phase transformers along the transmission line, and a final step-down transformer that drops the voltage to the appropriate level based on the specific application.

The final output can power large motors, commercial facilities, and data centers, or it can be split into single-phase power for household use, as shown in the diagram below.

How to Generate Three-Phase Power

Three-phase generators are the key components in a three-phase power system, as illustrated in the following diagrams:

As opposed to a single-phase generator, a three-phase generator features a rotating magnet, the rotor, which is surrounded by three separate wires located on the stator. The three wires correspond to the three phases. The wires are precisely positioned to generate current at exactly 120 degrees out of phase to each other.

The speed at which the rotor rotates is synchronized with the frequency of the power system, which is either 50Hz or 60Hz in North America, Europe, Australia, and most other countries. When generators operate in sync with the grid it is referred to as a synchronous generator.

Two Connection Methods for Three-Phase Power

Inside a generator, the three phases can be wired differently as either a wye or delta configuration.

Wye Connection

In a wye (Y) connected system, the three phases are connected to a common junction point, and an optional neutral wire can be connected at that junction.

The neutral wire is optional, but it does help prevent potential problems if an element fails and the system becomes unbalanced. The neutral wire also enables the load to be connected from line to neutral, effectively using the system as three single-phases, making it more suitable for residential or commercial buildings.

When the load is connected between line to neutral, the voltage across the load is called line-to-neutral voltage:

Since the neutral is 0V, the line-to-neutral voltage equals phase voltage:

The current flows from the source, passes through the load, and flows back to the neutral, so line current equals phase current.

In this case, the power delivered to the load is single-phase, which can be calculated as:

Where PF stands for power factor, which is the ratio between real and apparent power, whereas real power is the power consumed by the load, and apparent power is the power generated by the source, including real and reactive power.

When the load is connected between two lines, the voltage across the load is called line-to-line voltage (V_LL), as shown in the diagram below:

The relation between V_LL and phase voltage (V_P) can be expressed as:

The current can then be calculated according to Ohm’s law:

Finally, the power delivered to the load is:

Delta Connection

For a delta-connected system, the power sources are connected to each other on both ends, forming a triangle. There is no neutral in a delta connection. The current flows from one phase and returns from the other two phases.

When the load is connected from line to line, the voltage across equals phase voltage.

The line current, on the other hand, is √3 times the phase current.

Finally, the power is calculated as

Notice that both connection methods, wye and delta, deliver the same amount of power to the load.

Three-Phase Power Transmission and Distribution

Once power is generated, there are a few challenges that must be solved before it is transmitted and distributed.

Transmission systems incur a power loss while traveling over cables. Power stations equipped with transformers step up the voltage to a suitable level to mitigate loss from transmission. This is because power loss is directly proportional to the square of current.

When increasing the voltage and lowering the current, the power loss during transmission will be minimized.

Another factor is that due to the impedance of the transmission lines, the voltage naturally drops across long distances. As a result, transformers must be installed along the transmission lines in order to maintain and stabilize the voltage at the appropriate level.

Lastly, before the power is delivered to the end user, whether it is large industrial motors, commercial facilities, or residential households, a final transformer must be installed to lower the voltage.

Similar to generators, these transformers are also three-phase, which have a structure shown in the following diagrams .

This can complicate the power system because the primary and secondary sides of the transformer can have different wiring configurations.

Delta-Wye Transformer

The delta-wye configuration is usually used by transformers installed at the power station to step up the voltage before the power gets transmitted, as shown in the diagram below:

The delta connection on the primary side can handle the high current output from generators, while the wye connection allows for higher voltage on the secondary side.

This is due to the delta connection not requiring a neutral, and the current flows back through the other two phases. And because the three currents are out of phase to each other by 120 degrees, the net current in each line is zero.

For the wye connection on the secondary side, the line-to-line voltage is higher than the line-to-neutral voltage by a factor of √3, allowing it to deliver a higher voltage compared to the delta side.

Wye-Wye Transformer

The wye-wye configuration is often used for high-voltage, low-current systems, such as those along the transmission lines to maintain the voltage.

The main advantage of this configuration is the neutral terminal on both sides, which enables grounding on both sides to improve safety and removes possible distortion from the waveform.

Wye-Delta Transformer

The wye-delta configuration is the opposite of the delta-wye transformer. It is typically used for step-down transformers, often installed before the power is delivered to the end user.

Delta-Delta Transformer

The delta-delta configuration is commonly used for low-voltage high-current systems, such as motors and large machinery, where high-current is required to provide a large initial torque.

Unbalanced Three-Phase Power Systems

Thus far, each scenario has assumed three phases do not encounter any issues, but a condition can arise when a power failure occurs, and the system becomes unbalanced.

Wye-Wye System

For example, for a wye-connected system, when a phase fails, the corresponding line-to-neutral voltage drops to 0V. If a neutral is connected, the other two phases will not be affected, and the system operates as a two-phase system.

This is because the remaining power sources are connected in parallel, and the voltage on the remaining two loads will stay balanced with respect to the neutral.

However, if a neutral wire is not connected, the voltage delivered to the loads will drop.

In this case, the two power sources will be connected in series, and the net voltage delivered to the loads will be the vector sum of the voltages of the remaining two phases. The exact reduction in voltage depends on the phase angle and the configuration of the system.

For the example above, the vector sum of 120V ∠0° and -120V ∠120° gives 208V ∠-30°. This can be verified using the vector calculator below: