Learn about Harmonics in Power system(2024) -

Contents

Harmonics
What is Fundamental Frequency?
How to Find Fundamental Frequency

How to Calculate Harmonics

Difference Between Harmonics and Overtones

Harmonics

Harmonics in Power system or any other system are a series of sinusoidal waveforms that are integer multiples of a fundamental frequency. Harmonics are defined as an unwanted higher frequency component which create distortion in the fundamental waveform.

Harmonics typically have a lower amplitude than the fundamental frequency.

Fundamental Frequency: This is the lowest frequency of a periodic waveform. It determines the pitch of a sound in acoustics or the base signal in electrical systems.

Harmonics: These are frequencies that are integer multiples of the fundamental frequency. For example, if the fundamental frequency is f the harmonics will be 2f2, 3f, 4f, and so on.

Types of Harmonics

First Harmonic: This is the fundamental frequency itself ( f ).

Second Harmonic: This is twice the fundamental frequency ( 2f ).
Third Harmonic: This is three times the fundamental frequency ( 3f ), and so on.

Sources of Harmonics

Harmonics in power systems are primarily caused by non-linear loads, which draw current in abrupt pulses rather than in a smooth sinusoidal manner. Common sources include:

Electronic Devices: Computers, printers, and other office equipment.
Power Electronics: Variable frequency drives (VFDs), rectifiers, inverters, and other devices used in industrial applications.

Lighting: Fluorescent lights and other lighting systems with electronic ballasts.
Transformers: Saturated transformers can also produce harmonics.

Harmonics are produced by non-linear loads like iron-cored inductor, rectifiers, electronic ballasts in fluorescent lights, switching transformers, discharge lighting, and other highly inductive loads.

Harmonics are also due to the most powerful electronic switching circuits such as a silicon controlled rectifier (SCR), the power transistors, the power converters, and an electronics drive such as the variable frequency drive (VFD) or variable voltage variable frequency drive (VFD). These switching circuits draw a current only at the peak values of the AC supply and since the switching current is non-linear in behavior the load current is non-sinusoidal in nature and it contains the harmonics.

What Are the Effects of Harmonics?

Overheating: Transformers, motors, and cables can overheat due to increased losses caused by harmonic current.

Voltage Distortion: Harmonic currents flowing through the impedance of the power system can cause distortion in the voltage waveform, leading to poor power quality.

Equipment Malfunction: Sensitive electronic equipment can malfunction or suffer reduced lifespan due to voltage distortion and harmonic interference.

Increased Losses: Harmonic currents increase the resistive losses in power system components, reducing overall efficiency.

Resonance: Harmonics can cause resonance in power systems, amplifying their effects and leading to potential damage to system components.

What is Fundamental Frequency?

The lowest or base frequency produced by any particular instrument which we hear the sound at is known as the fundamental frequency. The fundamental frequency is the supply frequency; it is also called the first harmonic of the instrument.

The number of cycles completed by an alternating quantity per second is known as a frequency. It is denoted by f and expressed in hertz (Hz) or cycles/second.

\begin{align*} f= \frac{1}{T} \end{align*}

How to Find Fundamental Frequency

In a simple 2-pole generator, one cycle of the alternating current or voltage is generated in one revolution. In the case of 4 poles, two cycles would have been produced in each revolution. So, the frequency of the alternating voltage or current is given by

Where:

f = Frequency

P = No. of poles of the alternator
N= Speed of the alternator in rpm

The standard frequency of generation adopted in India is 50Hz while in the USA, it is 60Hz.

How to Calculate Harmonics

Harmonics are the sinusoidal voltage or current that is an integer (whole number) at a multiple of the fundamental frequency at which the supply system is designed to operate.

It can be expressed as a 2f, 3f, 4f, 5f,….……,nf, etc.

So if 50Hz fundamental is the first harmonic then 2nd harmonic would be 100Hz (250), a 3rd harmonic would be 150Hz (350), a 5th harmonic at 250Hz, a 7th at 350Hz and so on.

Harmonics Calculation Formula

1st Harmonic: It is a fundamental frequency.

\begin{align*} V_1= V_m_a_x sin(\omega t) &= V_m_a_x sin(2\pi f t) \end{align*}

2nd Harmonic: It is two times the fundamental frequency.

\begin{align*} V_2 = V_2_m_a_x sin(2\omega t) = V_2_m_a_x sin(2*2\pi f t) = V_2_m_a_x sin(4\pi f t) \end{align*}

nth Harmonic: It is n times the fundamental frequency.

\begin{align*} V_n = V_n_m_a_x sin(n\omega t) = V_n_m_a_x sin(n*2\pi f t) = V_n_m_a_x sin(m\pi f t) \end{align*}

So the value of complex waveform (i.e. fundamental plus harmonics) will be:

\begin{align*} V_T_o_t_a_l = V_1 + V_2 +V_3 + V_4+.............+ V_n \end{align*}

\begin{align*} V_T_o_t_a_l = V_1_m_a_x sin(2\pi f t) + V_2_m_a_x sin(4\pi f t) + V_3_m_a_x sin(6\pi f t) + .............. + \\ V_n_m_a_x sin(m\pi f t) \end{align*}

Classifications of harmonics are generally based on their name and frequency. For example, at a fundamental frequency, the 2nd harmonic frequency is 100Hz. Harmonic sequence related to the phasor rotation of the harmonics voltages and currents to the fundamental waveform in a balanced system.

Based on a sequence there are three types of sequence harmonics.

Positive sequence harmonic: A positive sequence harmonic would rotate in the forward (same) direction as that of the fundamental frequency. i.e. 4th, 7th, 10th, 13th, 16th …etc

Negative sequence harmonic: A negative sequence harmonic rotates in the reverse (opposite) direction of the fundamental frequency. i.e. 2nd, 5th, 8th, 11th …etc

Zero sequence harmonics: A zero sequence harmonic does not rotate with the fundamental hence it has zero rotational sequences and they are in phase with each other. It is a set of special harmonics called “triplens” (multiple of three). Triplens are multiples of the third harmonic. i.e. 3rd, 6th, 9th, 12th, 15th …etc

Effects of Positive, Negative and Zero Sequence Harmonics

Due to a positive sequence harmonic the overheating of conductors, power lines and transformer takes place because of addition to the fundamental as it’s rotating in forward (same) direction as the fundamental frequency.

Negative sequence harmonic circulates negative sequence current between the phases which causes the opposite phasor rotation and due to that the rotating magnetic field may be weakened and thus mechanical torque is reduced especially in the induction motors.

Zero sequence currents circulate between the phase and neutral which add up arithmetically in the common neutral wire and the neutral current becomes three times the phase current causing it to become less efficient and overheat.

Current Harmonics

In the AC system, the alternating current varies sinusoidally at a particular frequency called the fundamental frequency, usually 50Hz or 60Hz.

Current Harmonics are caused by the non-linear loads such as switching transformers, discharge lighting, saturated magnetic devices, electronic ballasts in fluorescent lights, computer and data-processing loads, laser printers, half-wave rectifiers, SMPS, PLC, refrigerators, IGBTs, MOSFETs, etc.. in which current is not proportional to the applied voltage.

The effect of these loads is the distortion of the fundamental sinusoidal current waveform and the current waveform becomes quite complex.

What is Linear Load?

A Linear electrical load is one in which the current at any time is proportional to the applied voltage. It draws the current at the same frequency as the voltage.

What is Non-Linear Load?

A non-linear load is one where the current is not proportional to the applied voltage and does not draw current at the same frequency as the voltage.

Effects of Current Harmonics

Harmonic currents increase I²R heat losses in the transformer winding. If harmonic current has supplied to the transformer, the less fundamental current it can provide for powering the loads because harmonic current doesn’t deliver any power so it reduces the number of loads that can be powered.

Due to the additive nature of the 3rd harmonic (triplens) the currents in a phase-to-neutral connected load cause a sharp increase in the zero-sequence current and therefore increases the current in the neutral conductor, being three times the fundamental frequency.

Current harmonics are mostly caused by the non-linear loads but the linear load will also generate current harmonics if the supply voltage waveform is significantly distorted.

Another major effect of current harmonics on an electrical system is the creation of voltage harmonics.

Voltage Harmonics

Voltage harmonics are generated by the current harmonics which distort the voltage waveform. Current distortion interacts with the system impedance creating the voltage distortion.

The non-linear loads generate currents that are rich in harmonic frequency components that generate harmonic voltages.

Effects of Voltage Harmonics

The harmonic voltage causes increased eddy current losses in the motors and transformers and it has a significant effect on the operating temperature. Harmonic voltages in a stator induce high-frequency currents in the rotor further increase losses.

The negative sequence 5th harmonic voltage when supplied to an induction motor produces a negative torque which drives the motor in a reverse direction and slows down its rotation. The result is overcurrent in the motor.

Harmonic voltages can produce excessive vibration in both the single and three-phase motors. Vibration leads to higher than normal wear and tear on the bearings.

Odd and Even Order Harmonics

The harmonics occurring at a frequency 3f, 5f, 7f, 9f…etc are called the odd-order harmonics. The harmonics occurring at a frequency 2f, 4f, 6f, 8f…etc are called the even-order harmonics.

In even order harmonics there is an equal number of positive and negative half-cycles so they cancel out and not significant in power system. While in case of odd harmonics there is a positive half cycle left in each order (e.g. in 3rd order odd harmonics contains two positive cycles and one negative cycle, 5th order odd harmonic contains three positive cycles and two negative cycles) which does not cancel the negative half cycle, therefore it is significant in power system which add up and increase the neutral current and temperature rises.

The odd-order harmonics are mostly produced by the non-linear loads. The even-order harmonics are produced when the uneven current is drawn between the positive and negative half cycle of the fundamental frequency.

The electric arc furnaces, arc welders generate non-integer harmonics. Transformer magnetizing currents contain even order harmonic.

Difference Between Harmonics and Overtones

The differences between harmonics and overtones have been summarised the table below:

Harmonics	Overtones
A harmonic is an integral multiplication of the fundamental frequency.	An overtone is defined as any frequency which is greater than the fundamental frequency.
Harmonics starts counting from the fundamental frequency.	Overtones start counting after the fundamental frequency and starts counting from the harmonics.
All harmonics are stationary waves.	Overtones may be stationary not stationary waves. Those overtones which match the frequencies of the harmonic acts as a stationary wave.
Harmonics are a resonant frequency.	Overtones are also a resonant frequency.
Example. The first harmonic is a Fundamental frequency (f). Second harmonic is two times the fundamental frequency (2f).	Example. Second harmonic (2f) is the first overtone. Third harmonic (3f) is the second overtone.