Consider a sinusoidal supply at fundamental frequency as shown, with a series inductive reactance leading to a bus. Let a diode rectifier load be connected to the bus. The switch Sw for resistive load be open. In this condition, the diode rectifier draws fundamental current from the source and also sends back harmonic current to it. Thus, the voltage drop in series reactance is distorted by the harmonic and so bus voltage is also correspondingly distorted. Now if switch Sw is closed, the resistive load draws both fundamental current as well as harmonic current from the distorted bus voltage. Both current components will lead to power dissipation in resistance as bus voltage contains both the corresponding voltage components. The question is from where is the harmonic power supplied to the resistor ? The sinusoidal source by basic understanding, cannot deliver any power corresponding to harmonic currents as its voltage remains sinusoidal, even though its current contains harmonics.
Dear Sujit,
Now i will give a conceptual answer and after that i may return again to share in the analysis of the give circuit.
The conceptual answer is that there is no ideal voltage source. A real voltage source has a resistance and may be also and inductance because of the wiring.
The ideal source voltage will remain sinusoidal. But assume that you have a voltage source Vs with a source resistance Rs,
A current i is passing through it, then its terminal voltage will be
v= Vs- iRs.
If i is distorted then v will be distorted.
In order to prevent the distortion you must make
either Rs=0
or I is pure sinusoidal.
Best wishes
Dear Sujit,
Now i will give a conceptual answer and after that i may return again to share in the analysis of the give circuit.
The conceptual answer is that there is no ideal voltage source. A real voltage source has a resistance and may be also and inductance because of the wiring.
The ideal source voltage will remain sinusoidal. But assume that you have a voltage source Vs with a source resistance Rs,
A current i is passing through it, then its terminal voltage will be
v= Vs- iRs.
If i is distorted then v will be distorted.
In order to prevent the distortion you must make
either Rs=0
or I is pure sinusoidal.
Best wishes
There is nothing supplying harmonic power loss directly. The non-linear load, intaking harmonic filled currents from the source -> bus, deteriorates the bus voltage to deviate from a pure 50-60Hz sinusoidal.
Your source inductance indicates a "weak" grid, in which it is not capable of keeping a perfectly fixed voltage. Therefore, your distorted voltage is supplying the resistor and the harmonic components will create power loss according to Ohm's law.
When ever conversion happens from AC to DC and DC to AC , there will be generation of harmonics. Simply when we disturb the AC waveform, there will be harmonics induced into the system.
While I thank all for their answers, what most are missing is that I am following the Law of Conservation of Energy and looking for the SOURCE of energy which is consumed by the resistor due to harmonic currents.
Even if I take Abdelhalim's answer, the "Source" is still sinusoidal and thus cannot supply power (or energy) corresponding to the harmonic current flowing through it. The presence of a series resistance may distort the terminal voltage and the resistance can "consume" power, but cannot "source" power.
I request all to think over again and help finding the answer.
Dear Sujit,
The source of energy is your voltage source/grid. The addition of voltage harmonics on your bus come from your non-linear load's current draw. This current is of course sourced from your energy source (ie your voltage source). So your voltage source is supplying power to your bus -> loads.
The term you might be missing is the distortion power (usually assigned as D). Active (P) and reactive (Q) powers are only defined on the fundamental harmonic. You have an expression for your distortion power of sqrt(V_1(50Hz) ^2*(sum of squared harmonic currents)).
Then define Q = sqrt(Q(fundamental)^2 + D^2)
This might give you good solutions to your problem.
Dear Sujit K. Biswas
I agree with Grigoris Sergentanis and Abdelhalim Zekry
All energy in the elctricity network is supplied by sources connected to it.
In your example network, load current drawn by a diode rectifier (i.e. non-linear load) is a short duration "pulse" of current during each half of a voltage cycle when diodes are conducting. This pulse of load current causes proportional voltage drop at the bus during the period of voltage cycle when the current is flowing. This voltage drop distorts the supply voltage because it is only occurring in part of the volatge cycle.
Only difference to linear load is that a linear load such as R or L or C draws current from the network in proportion to full cycle of voltage waveform. That is why they are called linear load i.e. V = ZI i.e. following the linear equation eqn y = mx + c.
If the supply voltage waveform is distorted, then current drawn by the linear loads would also be proportionally distorted because Z is constant. The energy to supply that current is still from the source.
The theory of harmonics allows us to analyse the "pulse" of current i.e. non-linear current as sum of multiple sinusoidal waves of different frequencies so that we can continue to apply phasor theory for network analysis.
Good books on harmonics in power systems were written by late Prof. Jos Arrillaga of Christchurch, New Zealand.
The harmonics power at resistor was came from the distorted signal contributes by the diode at point-of-common-coupling (PCC). See may calculation attached.
Bármely változó moduluszú erő vagy bármilyen függvénnyel kifejezett vektoriális menyiség, felbontható állandó moduluszú vektorokra, Fourier sór szerint amelyek frekvenciája vagy szögsebessége (omega), 1,2...n.
Please read my book
Power Electronics LABORATORY 1
you will have an idea how to go
from dc to ac.
What you have in the Lab is
a sin generator . This sin generator
use this book ideas to go from 110
or 220Volts 60 or 50Hz to the sin
wave we need in the Lab. For example:
5 sin (2 pi 1000 t).
Why to go for such reasoning like, nonlinear load, application of converter, etc, last one being in modern times; even with salient-pole hydro-generators it is always there. It is the second harmonic, owing to variation in reluctance of magnetic path and mathematically when evaluated depends on direct axis and quadrature axis reactance. In some cases, depending on design it is of significant value. It is a component of electric power and together with the fundamental power developed it comes from the conversion of input water power, depending upon rate of water flow in the turbine and effective head associated.
The source voltage at fundamental frequency can't supply harmonic power as the harmonic currents and the source voltage are orthogonal. A voltage at the same frequency as the harmonic current is responsible for harmonic power drawn by the resistor and that should be present in distorted bus voltage. Now to generate a voltage of the same frequency as the harmonic current sent back by the non-linear load, the current should go through a linear operator something like Ls*di/dt. Hence, the source should be the back emf across the source reactance due to harmonic current that actually adds to the source voltage and injects the harmonic component in it i.e reflected in the bus voltage.
Harmonics take place in steady state and are integer multiple of the fundamental frequency.Non linear loads are major sources of harmonics,UPS,Arc or discharge loads PV inverters etc
Dear Sujit K. Biswas ,
perhaps the simplest circuit with current harmonics in which the generation of harmonic power can be easily observed is
- an ideal voltage source, V(t) = V0 * sin(omega * t), connected to
- a time dependent resistor as non-linear element, R1(t) = Rx * (1 - cos(2 * omega * t)) and
- a constant resistor R2, in series to R1(t).
The resulting current I(t) comprises odd harmonics, of course. For the sake of simplicity, Rx = R2 = 1 Ohm, and V0 = 2.17533 V which results in P = 1 W.
For the nth harmonic (resp. the fundamental), naming the current component In(t), the power component in R1 P1n, and the power component in R2 P2n, the spectral components of the power dissipated in the resistors can be calculated by
P1n = Integral(In(t) * (V(t) - I(t) * R2), t from 0 to T) / T
P2n = Integral(In(t) * I(t) * R2, t from 0 to T) / T
Please note that the voltage implicitely used in the integrals is the real voltage, not an artefact based on a spectral current component, as would be In(t) * R2.
The sum of all these power components is 1 W, of course, and P11 + P21 = 1 W, as expected. The interesting point is:
All harmonic power components in R1 are negative, all harmonic power components in R2 are positive, and P1n + P2n = 0, for n >= 3.
Obviously, the harmonic power is generated in R1 (the nonlinear element) and dissipated in R2. Accordingly,
P1tot = P11 + P13 + P15 + ... P21,
i. e. the power used to generate the harmonic power is taken from P11 (and P11 + P21 is supplied directly by the source, of course).
Your circuit is more complicated but the principle is the same. I simulated your circuit with an ideal diode and a resistor in series as nonlinear element, and again, the harmonic power is negative in the nonlinear element, and positive in the parallel resistor.
Further analysis (conditions inside the nonlinear element) fails in this case because of the ideal diode which doesn't convert any power at all.
Transformers, rotating machines, power converters, fluorescent lamps and Arcing Devices are the main source of harmonic in power system. Harmonic current is produced by harmonic. Harmonic currents can cause overload in wiring and transformers, can produce heat, and in extreme cases, fire.
https://www.iosrjournals.org/iosr-jeee/Papers/Vol7-issue3/A0730103.pdf?id=6829
Harmonics are created by electronic equipment with nonlinear loads drawing in current in abrupt short pulses. The short pulses cause distorted current waveforms, which in turn cause harmonic currents to flow back into other parts of the power system.
https://www.grainger.com/content/safety-electrical-power-system-harmonics
Wikipedia
In an electric power system, a harmonic is a voltage or current at a multiple of the fundamental frequency of the system, produced by the action of non-linear loads such as rectifiers, discharge lighting, or saturated magnetic devices. 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.
https://en.m.wikipedia.org/wiki/Harmonics_(electrical_power)
Harmonics cannot be avoided in today's electric Power Supply-Utilization System, more so, because of usage of power electronics devices & systems in large scale and in decentralized way, be it transmission (including HVDC & FACTS Devices) or distribution, and then devices used for utilization of electricity causing electrical pollution in terms of harmonics with frequency in multiple order of fundamental (super) or in fractional one (sub). However, as it is a part of the scenario, depending upon the tolerance level of Total Harmonic Distortion (THD) in order not to severely jeopardize the Electric Power System, and the most predominant ones, necessary filtration is called for, either with passive or active elements.
The major cause of power system harmonics is power electronics especially switched mode power supplies. The rapid switching of the incoming ac power feeding the unit creates chopped or square wave pulses in the incoming current creating distortion. Per Fourier any periodic waveform can be represented as the sum of harmonic related sinusoidal functions. When a fourier analysis is performed the harmonics or multiples of fundamental frequency with their magnitudes are revealed. There are other industrial non-linear load such as arc furnaces, but mostly the nonlinear load include variable frequency drives, server and network switch power supplies, electronic ballast or drivers, and copier power supplies to name a few. Depending on the electronic circuit used the harmonics present will vary from device to device. Even harmonics and the fundamental frequency currents on 3 phase systems tend to cancel in the neutral odd harmonics tend to combine increasing the neutral which creates localized heating of the common neutral and transformer neutrals.
Precisely to the point and yet explicitly Daniel Pohnert has answered the question of source of harmonic power.
The main source of harmonics in any power system is the power electronics installed (mainly SMPS) and nonlinear loads.
An Overview of Harmonic Sources in Power System
https://www.iosrjournals.org/iosr-jeee/Papers/Vol7-issue3/A0730103.pdf?id=6829#:~:text=Transformers%2C%20rotating%20machines%2C%20power%20converters,and%20in%20extreme%20cases%2C%20fire.
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