## Tuesday, 28 August 2018

### Basics of Harmonics...

Harmonic is multiple order of the fundamental frequency and it can be voltage and current in an electric power system are a result of non-linear electric loads. Harmonic frequencies in the power grid are a frequent cause of power quality problems. Harmonics in power systems result in increased heating in the equipment and conductors, misfiring in variable speed drives, and torque pulsations in motors. Reduction of harmonics is considered desirable. CURRENT HARMONICS:
In a normal alternating current power system, the current varies sinusoidally at a specific frequency, usually 50 or 60 hertz. When a linear electrical load is connected to the system, it draws a sinusoidal current at the same frequency as the voltage (though usually not in phase with the voltage)
Current harmonics are caused by non-linear loads. When a non-linear load, such as a rectifier is connected to the system, it draws a current that is not necessarily sinusoidal. The current waveform can become 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, as described through Fourier series analysis, it is possible to deconstruct it into a series of simple sinusoid, which start at the power system fundamental frequency and occur at 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.
In power systems, harmonics are defined as positive integer multiples of the fundamental frequency. Thus, the third order harmonic is the third multiple of the fundamental frequency. This type of harmonics is generated in non-linear loads. Examples of nonlinear loads include transistors, electrical motors, and the non-ideal transformer. Non-linear loads create disturbances in the fundamental harmonic, which produce all types of harmonics. However, in this section we focus on the 3rd order harmonic due to its certain special characteristics in the context of powers systems

Power is supplied by a three phase system, where each phase is 120 degrees apart. This is done for two reasons: Firstly it is because generators/motors that use three phases are more efficient due to the constant torque the phases supply, and secondly it is because after power is supplied to a load, the three phases can theoretically be added onto a neutral wire and cancel each other out. This saves the utility from creating return wiring to the power plant. However, if the 3 phases contain 3rd order harmonics, the currents will not fully add to zero. As seen in the figure, the 3rd harmonic will add constructively with the 3rd harmonics within the other phases. This leads to an oscillating current in the neutral wire, which can be dangerous since it is designed (i.e. small-size conductors) to carry minimal current.

### VOLTAGE HARMONICS:

Voltage harmonics are mostly caused by current harmonics. The voltage provided by the voltage source will be distorted by current harmonics due to source impedance. If the source impedance of the voltage source is small, current harmonics will cause only small voltage harmonics. It is typically the case that voltage harmonics are indeed small compared to current harmonics. For that reason, the voltage waveform can usually be approximated by the fundamental frequency of voltage. 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). What can be observed is that for every period of voltage, there is equal area above the horizontal axis and below the current harmonic wave as there is below the axis and above the current harmonic wave. This means that the average real power contributed by current harmonics is equal to zero. However, if higher harmonics of voltage are considered, then current harmonics do make a contribution to the real power transferred to the load.

### HARMONICS FUNDAMENTALS:

Harmonics are caused by distortions to the underlying sinusoid of any signal, be it power, audio, radio frequency, even mechanical vibrations. Harmonic behaviour is defined by the Bullard Laws Of Harmonics
1. Harmonic amplitudes are proportional to the area of the distortion.
2. The Harmonic Signature is the result of the angle where the sinusoid impacts the distortion as predicted by the Bullard Harmonic Solution.
3. Even harmonics don't appear in symmetrical distortion because they cancel each other out.
4. When a portion of a sinusoid is removed (such as in clipping), the Harmonic Signature mirrors the harmonic signature of the feature removed from the sinusoid.
5. Square waves, triangle waves and all other kinds of waveforms obey these rules and their harmonic behaviour can be predicted with simple mathematical formulas.
Harmonics are caused by steady-state distortions to current and voltage waves and repeat every cycle. They are different from transient distortions such as spikes, dips and impulses.

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