Fundamentals of 3-Phase Electricity | What Is 3-Phase Power?, Part 1
From the series: What Is 3-Phase Power?
In AC electrical systems, 3-phase power is commonly used due to the increased power density, efficiency, and operational flexibility compared with single-phase systems. Understanding how 3-phase electricity behaves in balanced and unbalanced systems is fundamentally important for AC electrical systems analysis, operation, and control.
You will learn:
- How 3-phase electricity is traditionally generated
- How 3-phase electricity can be described using vector representations
- The difference between balanced and unbalanced systems
- How balanced systems deliver constant, instantaneous 3-phase power
- How balanced and unbalanced systems affect neutral current
Published: 9 May 2022
Hello, everyone. My name is Graham Dudgeon. And welcome to the first of a series of videos that I'll be giving on three-phase power. The aim of the video series will be to build up our engineering knowledge on the design, analysis, and operation of three-phase electrical power systems. Today, we'll explore the fundamentals of three-phase electricity.
To set the context for three-phase, we'll begin with single-phase. What you see on the left is a representation of a magnet that we will ultimately rotate. In practice, the magnet is fitted on a rotor.
The orange dot and cross that you see is a representation of a wire coil that will remain stationary. In practice, the coil is wound on what we call the stator. The rotor will rotate. The stator remains stationary.
If we now rotate the magnet, you'll see that a voltage is generated as the magnetic field lines cut through the coil. We get maximum positive and negative voltage when the magnet is oriented at 90 degrees to the coil. When the magnet is aligned with the coil, voltage is 0.
In trigonometric form, the voltage is described as V equals V mag multiplied by cosine omega t, where V is instantaneous voltage, V mag is the peak magnitude of voltage, omega is rotational frequency in radians per second, and t is time in seconds.
For a three-phase system, we add two additional coils to the stator, each of which are separated by 120 degrees. We label the coils as A, B, and C. If we now start rotating the magnet, we see that the three voltages are formed. The voltages have equal magnitudes and are separated by 120 degrees.
The voltage of the coil B lags the voltage in coil A by 120 degrees. And the voltage in coil C lags the voltage in coil A by 240 degrees. As a circle is 360 degrees, we can also say that the voltage of coil C leads the voltage in coil A by 120 degrees.
Let's look at the voltages in vector form to gain more clarity on this observation. Here we see the instantaneous waveforms for voltage as time progresses and the associated vector representations. From the vector representations, we confirm that magnitude is equal and that the sinusoids are 120 degrees apart.
You can see that phase B is 120 degrees behind phase A, relative to the direction of rotation. And so we say that phase B lags phase A by 120 degrees. Phase C is 120 degrees ahead of phase A, relative to the direction of rotation. And so we say that phase C leads phase A by 120 degrees. We refer to this voltage profile as being balanced.
In trigonometric form, we see that phase A is our reference with 0 degrees phase shift. Phase B is shifted by minus 120 degrees. For radians, we multiply by pi divided by 180. Phase C is phase-shifted by plus 120 degrees. Notice that I am using the notation N, VAN, VBN, and VCN. N stands for neutral, which is the connection point of the vectors at the origin.
We'll now take a look at simple three-phase electrical network, which we will use to give more insight on network behavior. In this system, I have a three-phase voltage source connected to a three-phase load. The load consists of resistors in this case. Notice the neutral points at the source and loads, which are connected to ground.
The phase voltages are measured across the voltage sources from the terminal point of the source to the neutral point. The resistors are of equal value in this case. Because the voltage supply is balanced and the resistors are equal, we have balanced three-phase line current. When both voltage and current are balanced, we say we have a balanced three-phase system.
Instantaneous power of each phase is calculated by multiplying the phase voltage and the line current. Total instantaneous power delivered is the sum of the phase powers.
As we have resistive loads, each phase power in this case is strictly non-negative. You can see the powers are equal in terms of magnitude and are phase-shifted by 120 degrees. The total instantaneous power shown in purple is constant. Three phases is the minimum number of phases that can achieve constant instantaneous power.
We'll now consider what happens in the connection between the neutral points in a balanced system. Kirchhoff's current law dictates that the vector sum of all currents entering a node must equal the vector sum of all currents exiting that node. In other words, the neutral current is equal to the vector sum of the line currents.
Here's a visualization of the vector sum of the line currents. You can see they add to 0. And so in a balanced system, no neutral current will flow.
We'll now cause an imbalance in our system by reducing the resistance on phase A by 30% relative to phase B and phase C resistances. Notice that while the voltage remains balanced, we've now caused an imbalance in current with phase A current now being 30% larger in magnitude than phase B and phase C current.
In practice, imbalances in both voltage and current may occur. And imbalances can manifest as changes in magnitude as well as changes in phase.
The imbalance has caused oscillations in total instantaneous power. An unbalanced system is undesirable for a number of reasons. The oscillation in total delivered power is one of those reasons. For example, if we're driving a three-phase motor, the imbalance would cause mechanical oscillations and uneven heating of the motor coils.
If we now revisit neutral current, you can see that the imbalance means we now have a nonzero neutral current, which, in this case, is in phase with phase A current.
In summary, three-phase electricity is traditionally generated by rotating a magnetic field through three coils that are each separated by 120 degrees. Balanced three-phase voltage has equal voltage magnitudes in each phase, with phase B lagging phase A by 120 degrees and phase C leading phase A by 120 degrees. Balanced three-phase current has equal current magnitudes in each phase, with phase B lagging phase A by 120 degrees and phase C leading phase A by 120 degrees.
An unbalanced system is anything that does not meet the above criteria. A balanced three-phase system delivers constant instantaneous power. If neutral points are connected, no current will flow between the neutral points in a balanced system. If neutral points are connected, current will flow between the neutral points in an unbalanced system.
I hope you have found this information useful. In future videos, we'll build out more engineering detail on how three-phase systems are analyzed, designed, and operated. Thank you for listening.