Harmonics (electrical power)
Harmonic frequencies are produced by the action of non-linear loads such as rectifiers, discharge lighting, or saturated electric machines.
They are a frequent cause of power quality problems and can result in increased equipment and conductor heating, misfiring in variable speed drives, and torque pulsations in motors and generators.
Harmonics are usually classified by two different criteria: the type of signal (voltage or current), and the order of the harmonic (even, odd, triplen, or non-triplen odd); in a three-phase system, they can be further classified according to their phase sequence (positive, negative, zero).
When a non-linear load, such as a rectifier is connected to the system, it draws a current that is not sinusoidal.
The current waveform distortion can be quite complex, depending on the type of load and its interaction with other components of the system.
Regardless of how complex the current waveform becomes, the Fourier series transform makes it possible to deconstruct the complex waveform into a series of simple sinusoids, which start at the power system fundamental frequency and occur at integer multiples of the fundamental frequency.
In power systems, harmonics are defined as positive integer multiples of the fundamental frequency.
Further examples of non-linear loads include common office equipment such as computers and printers, fluorescent lighting, battery chargers and also variable-speed drives.
Non-linear load currents create distortion in the pure sinusoidal voltage waveform supplied by the utility, and this may result in resonance.
The even harmonics do not normally exist in power system due to symmetry between the positive- and negative- halves of a cycle.
Further, if the waveforms of the three phases are symmetrical, the harmonic multiples of three are suppressed by delta (Δ) connection of transformers and motors as described below.
If this approximation is used, current harmonics produce no effect on the real power transferred to the load.
An intuitive way to see this comes from sketching the voltage wave at fundamental frequency and overlaying a current harmonic with no phase shift (in order to more easily observe the following phenomenon).
This means that the average real power contributed by current harmonics is equal to zero.
takes negative and positive integer values (not including zero, since the DC component is usually not considered as a harmonic).
Certain distorted (non-sinusoidal) periodic signals only possess harmonics that are neither even nor triplen harmonics, for example the output voltage of a three-phase wye-connected AC voltage controller with phase angle control and a firing angle of
and with a purely resistive load connected to its output and fed with three-phase sinusoidal balanced voltages.
[5] In the case of balanced three-phase systems (three-wire or four-wire), the harmonics of a set of three distorted (non-sinusoidal) periodic signals can also be classified according to their phase sequence.
[6]: 7–8 [7][3] The positive sequence harmonics of a set of three-phase distorted (non-sinusoidal) periodic signals are harmonics that have the same phase sequence as that of the three original signals, and are phase-shifted in time by 120° between each other for a given frequency or order.
The negative sequence harmonics of a set of three-phase distorted (non-sinusoidal) periodic signals are harmonics that have an opposite phase sequence to that of the three original signals, and are phase-shifted in time by 120° for a given frequency or order.
This effect can require special consideration in the design of an electric system to serve non-linear loads.
[10] In addition to the increased line current, different pieces of electrical equipment can suffer effects from harmonics on the power system.
The 5th harmonic causes a CEMF (counter electromotive force) in large motors which acts in the opposite direction of rotation.
In the United States, common telephone lines are designed to transmit frequencies between 300 and 3400 Hz.
Since electric power in the United States is distributed at 60 Hz, it normally does not interfere with telephone communications because its frequency is too low.
Since neither the winding distribution nor the magnetic field are uniform in a working AC machine, voltage waveform distortions are created, and the voltage-time relationship deviates from the pure sine function.
In non-linear and/or time-variant loads, such as an amplifier with a clipping distortion, the voltage swing of the applied sinusoid is limited and the pure tone is polluted with a plethora of harmonics.
However, in most cases where the power delivery system is functioning correctly under normal conditions, the voltage distortions will be quite small and can usually be ignored.
Waveform distortion can be mathematically analysed to show that it is equivalent to superimposing additional frequency components onto a pure sinewave.
Other examples of nonlinear loads are battery chargers, electronic ballasts, variable frequency drives, and switching mode power supplies.
