I connected a resistive load, the current wave on a power analyzer was pure sinusoidal and in-phase to the voltage. When connected an inductive load instead, the current wave was still pure sinusoidal and delayed by an angle. But when replaced the inductive by a capacitor, or connected both the inductive load and the capacitor, or connect all three (resistive, inductive, and the capacitor), the wave becomes no longer sinusoidal.
Capacitors make indeed the existing voltage harmonics more visible. They can also resonate with an inductance in the grid and draw even more harmonic current. It might appear as a high harmonic current at the poit of common coupling. But capacitors remain passive, and they absorb still some harmonic power from the grid. In a classical kWh meter you pay also for that absorbed harmonic energy. The kWh meter should not bill the absorbed energy. I did write an article "fundamental tarification"
https://biblio.ugent.be/publication/913473
In a similar way, if you connect a retifier, you send also harmonic power into the grid, and your electricity bill is lowered by this (only a very little bit). If you look at the phase of voltage and current (the power) one can see if the connected load sends harmonics to the grid or is passive, absorbs power from the grid for that harmonic.
Resistance offered by circuit, is not frequency dependent, it depends on resistivity(property) of material, same for A.C(any frequency) and D.C.The reactance offered by capacitance or inductance of circuit depends on frequency, as Xl=2(pai)fL and Xc=1/2((pai)fC) if pure sinosoidal, generally the inductance or capacitance are having some impurity(resistive property), used in power system. The supply(generated) voltage wave form is also not pure sinusoidal, but are distorted having third harmonics and it's multiples, as voltage supply is from the source(Alternator/Transformer) working at higher flux density with flat top, flux wave form obtained by magnetizing current, and generates distorted supply voltage waveform responsible for distorted current wave(as reactance offered is different for different frequency for inductive or capacitive loading). More over inductive reactance, is directly praposnal to frequency(block higher harmonics), while capacitive reactance is inversely praposnal to frequency(pass higher harmonics), hence capacitive reactance offered would be less for higher frequency, and the distortion in current wave would be more in capacitive loading or can say capacitive loading has not taken care of higher harmonics, though has improved the power factor.
in case of a discharge load connected behide of Cap. it will create non sinusoidal current also.
Capacitors make indeed the existing voltage harmonics more visible. They can also resonate with an inductance in the grid and draw even more harmonic current. It might appear as a high harmonic current at the poit of common coupling. But capacitors remain passive, and they absorb still some harmonic power from the grid. In a classical kWh meter you pay also for that absorbed harmonic energy. The kWh meter should not bill the absorbed energy. I did write an article "fundamental tarification"
https://biblio.ugent.be/publication/913473
In a similar way, if you connect a retifier, you send also harmonic power into the grid, and your electricity bill is lowered by this (only a very little bit). If you look at the phase of voltage and current (the power) one can see if the connected load sends harmonics to the grid or is passive, absorbs power from the grid for that harmonic.
Thank you so much Prof. Alex.
Can we say that when capacitors are connected in a circuit that does not contain any harmonics source, and the voltage of the power supply is pure sinusoidal, the capacitor will not produce any distortion. And contrary, when there is a harmonics source (say an electronic dimmer) the capacitor will increase the current distortion?
Thank you again Prof.
If the capacitor is big enough, for instance a resonance between 3rd and 5rd harmonic, the harmonic currents will increase towards the load and decrease upstream. The capactor acts like a low pass filter. If the capacitor is small, it can resonate with the inductance of the grid. However, a diode rectifier stops also the amplitude of the resonance, the voltage gets flat topped, normally not often worse than that. This is often ignored in many linear analyses. What is the origin of the harmonics may also be a part of the solution, but standards do not take that in account. An amout of harmonics needs some oversizing of components which is a minor cost if taken into account.
Users have much more costs from other power quality aspects such as spikes, voltage dips and short interruptions. The interruptions may require storage, which makes the solution really expensive.
Time constant of the RC or RCL circuit will determine the output waveform. Usually we use 5RC to establish the time constant. If the input frequency of the waveform into the network is lower than the time constant then the rise time and decay of the output will tend to become markedly exponential, if faster then the time constant the signal will start to reduce and flatten because there is insufficient time for the capacitor to charge to full potential. These are the critically damped, over-damped and underdamped conditions. Any distortion of a pure sinusoidal waveform (even the slightest) creates harmonics and results in the Fourier signature arising as the fundamental and associated harmonics.
Interesting information dear Prof. Barrie. Thank you so much.
Yes, capacitors produce harmonics when connected at the load side. I have experienced many cases of polyester capacitor that even connected under a sinusoidal voltage sources, shown current wave forms with odd harmonics.
Dear Dr. Salah,
Ramdan Kareem! I came very late to your question but i think it needs a concepual answer. As the source is pure sinusoidal and the load is linear then the current waveform will be sinusoidal with only phase shift between the current and the voltage. It seems that your rististance is linear , your inductor is linear but you capacitor is slightly nonlinear which means that the capacitance of the capacitor depends on the terminal voltage. Expressed in an other way the relation between Q and C will not be a strict staight line.
In order to check the behavior of the capacitor you need only to measure its Q-V characteristics. The non-linearity is causes by nonlinear polarization of the medium.
Best wishes
Conference Paper Fundamental tarification of electricity
In fact if you put capacitors that absorb energy from harmonics (by their losses and wire losses), you pay for your absorbed damping power, as you pay for the real power... And if you inject harmonic power in the grid (present in both voltage and current), it lowers (very little) your energy bill. In fact one should pay for the fundamental power only. If you damp harmonics, you do a good thing. That is the aim of the article, or even be paid for the absorbed harmonic power.
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