**2. What are harmonics?**

In electrical power engineering the term harmonics refers to a sinusoidal waveform that is a multiple of the frequency of system. Therefore, the frequency which is three times the fundamental is known as third harmonics; five times the fundamental is fifth harmonic; and so on. The harmonics of a system can be defined generally using the eq. 1

$$\mathbf{f\_h} = \mathbf{h f\_{ac}}\tag{1}$$

Harmonics Generation, Propagation and Purging Techniques in Non-Linear Loads 5

(2)

  (3)

the most troublesome harmonics are thus 3rd, 5th, 7th, 9th, 11th and 13th. The general expression

V V sin n t n rn

The harmonics that are odd multiples of fundamental frequency are known as Odd harmonics and those that are even multiples of fundamental frequency are termed as Even harmonics. The frequencies that are in between the odd and even harmonics are called inter-

Although, the ideal demand for any power utility is to have sinusoidal currents and voltages in AC system, this is not for all time promising, the currents and voltages with complex waveforms do occur in practice. Thus any complex waveform generated by such devices is a mixture of fundamental and the harmonics. Therefore, the voltage across a

fp 1 2p 2 3p 3 np n V V sin t V sin 2 t V sin 3 t V sin n t

Similarly, the expression for current through a given circuit in a harmonically polluted

fp 1 2p 2 3p <sup>3</sup> np <sup>n</sup> I I sin( t ) I sin(2 t ) I sin(3 t ) I sin n t

Harmonic components are also termed as positive, negative and zero sequence. In this case the harmonics that changes with the fundamental are called positive and those that have phasor direction opposite with the fundamental are called negative sequence components. The zero components do not take any affect from the fundamental and is considered neutral in its behavior. Phasor direction is pretty much important in case of motors. Positive sequence component tends to drive the motor in proper direction. Whereas the negative

 

  (4)

 

Where, Vrn is the rms voltage of any particular frequency (harmonic or power line).

harmonically polluted system can be expressed numerically in eq. 3,

  of harmonics waveforms is given in eq. 2

φ = Angle of the respected frequency

Vfp = Peak value of the fundamental frequency Vnp= Peak value of the nth harmonic component

**Figure 1.** Fundamental and harmonics frequency waveforms

 

system is given by the expression given in eq. 4

harmonics.

Where,

Where fh is the hth harmonic and fac is the fundamental frequency of system.

Harmonics follow an inverse law in the sense that greater the harmonic level of a particular harmonic frequency, the lower is its amplitude as shown in Fig.1. Therefore, usually in power line harmonics higher order harmonics are not given much importance. The vital and the most troublesome harmonics are thus 3rd, 5th, 7th, 9th, 11th and 13th. The general expression of harmonics waveforms is given in eq. 2

$$\mathbf{V\_n = \ V\_m \sin \left( n \text{ot} \right)}\tag{2}$$

Where, Vrn is the rms voltage of any particular frequency (harmonic or power line).

The harmonics that are odd multiples of fundamental frequency are known as Odd harmonics and those that are even multiples of fundamental frequency are termed as Even harmonics. The frequencies that are in between the odd and even harmonics are called interharmonics.

Although, the ideal demand for any power utility is to have sinusoidal currents and voltages in AC system, this is not for all time promising, the currents and voltages with complex waveforms do occur in practice. Thus any complex waveform generated by such devices is a mixture of fundamental and the harmonics. Therefore, the voltage across a harmonically polluted system can be expressed numerically in eq. 3,

$$\mathbf{V} = \mathbf{V}\_{\text{fp}}\sin(\alpha \mathbf{t} + \boldsymbol{\phi}\_1) + \mathbf{V}\_{2\mathbf{p}}\sin(2\alpha \mathbf{t} + \boldsymbol{\phi}\_2) + \mathbf{V}\_{3\mathbf{p}}\sin(3\alpha \mathbf{t} + \boldsymbol{\phi}\_3) + \mathbf{V}\_{\text{np}}\sin(\alpha \mathbf{t} + \boldsymbol{\phi}\_n) \tag{3}$$

Where,

4 An Update on Power Quality

Waveform distortion

approaches include:

engineers in particular.

**2. What are harmonics?** 

 Identification of harmonics sources Measurement of harmonics level Possible purging techniques

Failure of insulation co-ordination system

 Fuzzy logic based active harmonics filters Wavelet techniques for analysis of waveforms

To follow the above scheme the power utilities have R&D sections that are involved in continuous research to keep the harmonics levels within the allowed limits. Power

De-rating of transformer, cables, switch-gears and power factor correction capacitors

The above mentioned research challenges are coped with the help of regulatory bodies that are focused much on designing and implementing the standards for harmonics control. Engineering consortiums like IEEE, IET, and IEC have designed standards that describe the allowable limits for harmonics. The estimation, measurement, analysis and purging techniques of harmonics are an important stress area that needs a firm grip of power quality engineers. Nowadays, apart from the traditional methods like Y-∆ connection for 3rd harmonic suppression, modern methods based on artificial intelligence techniques aids the utility engineers to suppress and purge the harmonics in a better fashion. The modern

frequency harmonics problems that have been a constant area of research are:

Sophisticated PWM techniques for switching of power electronics switches

so on. The harmonics of a system can be defined generally using the eq. 1

Where fh is the hth harmonic and fac is the fundamental frequency of system.

The focus of this chapter is to explain all the possible sources of harmonics generation, identification of harmonics, their measurement level as well as their purging/suppression techniques. This chapter will be helpful to all electrical engineers in general and the utility

In electrical power engineering the term harmonics refers to a sinusoidal waveform that is a multiple of the frequency of system. Therefore, the frequency which is three times the fundamental is known as third harmonics; five times the fundamental is fifth harmonic; and

h ac

Harmonics follow an inverse law in the sense that greater the harmonic level of a particular harmonic frequency, the lower is its amplitude as shown in Fig.1. Therefore, usually in power line harmonics higher order harmonics are not given much importance. The vital and

f hf (1)

Power factor correction in harmonically polluted environment

Vfp = Peak value of the fundamental frequency Vnp= Peak value of the nth harmonic component φ = Angle of the respected frequency

**Figure 1.** Fundamental and harmonics frequency waveforms

Similarly, the expression for current through a given circuit in a harmonically polluted system is given by the expression given in eq. 4

$$\mathbf{I} = \mathbf{I}\_{\mathrm{fp}} \sin(\alpha \mathbf{t} + \phi\_1) + \mathbf{I}\_{2\mathbf{p}} \sin(2\alpha \mathbf{t} + \phi\_2) + \mathbf{I}\_{3\mathbf{p}} \sin(3\alpha \mathbf{t} + \phi\_3) \dots + \mathbf{I}\_{\mathrm{np}} \sin(\mathrm{not} + \phi\_\mathbf{n}) \tag{4}$$

Harmonic components are also termed as positive, negative and zero sequence. In this case the harmonics that changes with the fundamental are called positive and those that have phasor direction opposite with the fundamental are called negative sequence components. The zero components do not take any affect from the fundamental and is considered neutral in its behavior. Phasor direction is pretty much important in case of motors. Positive sequence component tends to drive the motor in proper direction. Whereas the negative

sequence component decreases the useful torque. The 7th, 13th, 19th etc. are positive sequence components. The negative sequence components are 5th, 11th, 17th and so on. The zero component harmonics are 3rd, 9th, 15th etc. As the amplitude of harmonics decreases with the increase in harmonic order therefore, in power systems the utilities are more concerned about the harmonics up to 11th order only.

Harmonics Generation, Propagation and Purging Techniques in Non-Linear Loads 7

any non-linearity in the circuit will give rise to harmonics in the current waveform. Harmonics can also be generated due to the iron cores in the transformers. Such transformer

Harmonically polluted system has many threats for its stability. It not only hampers the power quality (PQ) but when a current is rich in harmonics, is drawn by some device, it overloads the system. For example third harmonic current has a property that unlike other harmonic component it adds up into the neutral wire of the system. This results in false tripping of circuit breaker. It also affects the insulation of the neutral cable. Overloading of the cables due to harmonically polluted current increases the losses associated with the wires. It should also be kept in mind that only the power from fundamental component is the useful power, rest all are losses. These additional losses make the power factor poor that results in more power losses. The overall summarized effects of harmonics in the power

Harmonic frequencies can cause resonant condition when combined with power factor

The distribution transformers have a ∆-Y connection. In case of a highly third harmonic current the current that is trapped in the neutral conductor creates heat that increases the heat inside the transformer. This may lead to the reduced life and de-rating of transformer. The different types of harmonic have their own impact on power system. For instance let us

Increased losses in system elements including transformers and generating plants

cores have a non-linear B-H curve [37].

**Figure 2.** Voltage distortion due to non-linear current

**4. Problems associated with harmonics** 

system include the following [9, 18, 39]

 Interruption in communication system False tripping of circuit breakers Large currents in neutral wires

correction capacitors

Ageing of insulation
