I h is the magnitude of h order harmonic current
I f is the magnitude of the fundamental current
h is harmonic order
are the presence of multiple frequencies superimposed on the fundamental frequency of voltage or current or both. The definition as per IEEE 1159 is harmonics are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate.
The fundamental system frequency is either 50 or 60 Hz. Due to the presence of harmonics, a system fundamental frequency of 50 or 60 Hz is added with multiple frequency ranges of 150, 250, 350, etc.
These multiple ranges of frequencies are also called harmonic frequencies, and are related to harmonic order. The harmonic order increases from lower frequencies to higher frequencies. The 50 Hz fundamental frequencies have harmonic frequencies of 100, 150, 200, and 250 Hz. Corresponding harmonic order is second order for 100 Hz frequency, third order for 150 Hz frequency, fourth order for 200 Hz frequency, and fifth order for 250 Hz frequency.
Generally, harmonics are represented by their frequency in Hz or harmonic order. Plotting multiple harmonic orders or frequencies to their magnitude is called harmonic spectrum.
The typical harmonic spectrum with harmonic order from second to 15th for voltage distortion is shown in Fig. 1.47.
Theoretically, the magnitude of individual harmonic order can be obtained through Eq. (1.5):
Harmonic is caused by :
1. Converter or Rectifiers
2. Arc Furnace
3. Static var compensator
4. Inverter for Dispersed Generator
5. Electronic Phase Control
7. Switching Power Supply
8. Pulse Width Modulation(PWM) Drives
Motors and generatorsA major effect of harmonic voltages and currents in rotating machinery (induction and synchronous) is increased heating due to iron and copper losses at the harmonic frequencies. The harmonic components thus affect the machine efficiency, and can also affect the torque developed.
TransformersWith the exception that harmonics applied to transformers may result in increased audible noise, the effects on these components usually are those arising from parasitic heating. The effect of harmonics on transformers is two fold: Current harmonics cause an increase in copper losses and stray flux losses, and Voltage harmonics cause an increase in iron losses. The overall effect is an increase in the transformer heating, as compared to purely sinusoidal (fundamental) operation.
Power CablesCables involved in system resonance may be subjected to voltage stress and corona, which can lead to dielectric (insulation) failure Cables that are subjected to “ordinary” levels of harmonic current are prone to heating. The flow of non sinusoidal current in a conductor will cause additional heating over and above what would be expected for the rms value of the wave form. This is due to two phenomena known as “skin effect” and “proximity effect,” both of which vary as a function of frequency as well as conductor size and spacing. As a result of these two effects, the effective ac resistance, Rac, is raised above the de resistance, Rdc, especially for larger conductors. When a current waveform that is rich in high-frequency harmonics is flowing in a cable, the equivalent Rae for the cable is raised even higher, amplifying the I2Rac loss.
CapacitorsA major concern arising from the use of capacitors in a power system is the possibility of system resonance. This effect imposes voltages and currents that are considered higher than would be the case without resonance. The reactance of a capacitor bank decreases with frequency, and the bank, therefore, acts as a sink for higher harmonic currents. This effect increases the heating and dielectric stresses. Frequent switching of nonlinear magnetic components (e.g. iron core), such as transformers and reactors, can produce harmonic currents that will add to the loading of capacitors. IEEE Std 18-1992 gives limitations on voltage, current, and reactive power for capacitor banks. These can be used to determine the maximum allowable harmonic levels. The result of the increased heating and voltage stress brought about by harmonics is a shortened capacitor life.
Electronic equipmentA major concern arising
InterharmonicsInterharmonics are not integral multiples of a fundamental frequency. Multiple har- monic frequencies are added with a fundamental frequency whose frequencies are not integral multiples of a fundamental frequency. The integral multiples of the fundamental frequency are 100, 150, 200, etc. Interharmonic frequencies are not integral multiples of frequencies 100, 150, 200, etc.
DC offset is the presence of DC current or voltage in an AC power system.
The notch depth in a voltage wave shape is shown in Fig. 1.49.
From Fig. 1.49, notch depth in a voltage wave shape is 71.037 V.
Notch width in a voltage wave shape is shown in Fig. 1.50. From Fig. 1.50, notch width in a voltage wave shape is 304.937 μs.
At any point in the system, the notch depth can be determined by the magnitude of current flow, source inductance, and isolating inductance between the converter and monitoring point.
An unwanted signal added to the fundamental frequency of voltage or current in
the phase or neutral conductor is called noise.
Noise in the current wave shape
is shown in Fig. 1.51 and the neutral conductor is shown in Fig. 1.52.
Basically, noise cannot be classified as transients or harmonic distortion. This
problem is frequently increased by improper or poor grounding in the system.
Noise magnitude and frequency range generally depend on the source and system
Typically, magnitude is less than 1% of voltage magnitude and
spectral content is less than 200 kHz.
A UPS is a reliable solution to prevent damage to electronic equipment from power fluctuations or outages. It provides stable and uninterrupted power, protecting sensitive equipment like PLC and microcomputers. A UPS also ensures optimal performance and longevity of electronic equipment by delivering a consistent and reliable power source. We strongly recommend considering a UPS as a preventative measure to mitigate the risk of damage to sensitive equipment.
Voltage fluctuation is
A continuous change in the instantaneous voltage (cycle to cycle) due to variation in load resistance in every cycle.
Continuous voltage changes are called voltage fluctuation.
The definition of voltage fluctuation by IEC 61000-3-3 is a series of changes of RMS voltage evaluated as a single value for each successive half period between zero crossings of the source voltage.
The major cause of voltage fluctuation is arc furnaces in industrial plant. Voltage fluctuations have an impact on illumination intensity from the lamp. That is, continuous variation in voltage has an impact on illumination density resulting in a noticeable change in illumination by the normal human eye.
This phenomenon is called flicker or voltage flicker.
The definition of flicker by IEC 61000-3-3 is the impression of unsteadiness of visual sensation induced by a light stimulus whose luminance or spectral distribution fluctuates with time.
- Short-term flicker (Pst)
- Long-term flicker (Plt).
The expression for short-term flicker is given in Eq. (1.3):
The expression for long-term flicker is given in Eq. (1.4):
SL is rated apparent power of the connected load
STR is rated apparent power of the feeding transformer
Limits of Flicker
Frequently, the degree of susceptibility is not readily determinable. Figure 10-3 (IEEE Std.519-1992) is offered as a guide for planning for such applications. This curve is derived from empirical studies made by several sources. There are several such curves existing that have approximately the same vertical scale.