In industrial settings, the primary sources of #harmonic generation include static converters, arc furnaces, lighting systems, saturated reactors, and other devices, such as rotating machines that produce slot harmonics, which are usually considered insignificant.
Let's discuss each of the listed harmonic #generators, their #calculations, and their impact on the industrial network.
The Table of Contents:
1| Harmonics Generators
Harmonic generators are devices or systems that produce harmonic frequencies, which are integer multiples of a fundamental frequency. These harmonics can have a significant impact on electrical systems, often leading to inefficiencies and the possibility of damage. The following are some common sources of harmonics and their effects:
1.1 Static Converters on 3-Phase Networks
Rectifier bridges and static converters, which consist of #diodes and #thyristors, generate harmonics. For instance, a Graetz bridge requires a rectangular pulsed AC current to provide an ideal DC current, especially when the load is highly #inductive (as shown in Figure 1).
For guidance on scenarios where a #bridge is succeeded by a capacitor, please see Figure 2.
Despite their differing #waveforms, the currents before and after passing through a delta-star-connected transformer possess identical characteristic harmonic components.
The characteristic harmonic components of the current pulses that supply rectifiers are defined by harmonic orders n, which follow the formula n = kp ± 1, where:
k = 1, 2, 3, 4, 5…
p = number of rectifier arms, for example:
Graetz bridge (p=6)
6-pulse bridge (p=6)
12-pulse bridge (p=12)
Using the formula, rectifiers with p = 6 produce harmonics of 5, 7, 11, 13, 17, 19, 23, 25, and so on, while rectifiers with p = 12 yield harmonics of 11, 13, 23, 25, and beyond.
The characteristic harmonics are exclusively odd-numbered, and their currents approximate the amplitude relation In = I1 / n, where I1 represents the amplitude of the fundamental, particularly when approaching the ideal scenario depicted in figure 5. Consequently, I5 and I7 will exhibit the highest amplitudes. It's noteworthy that employing a 12-pulse bridge (p = 12) can eliminate these harmonics.
In practical terms, the current spectrum exhibits some variations.
New even and odd harmonics, known as non-characteristic harmonics with low amplitudes, emerge, and the amplitudes of the characteristic harmonics are altered by various factors, including:
Asymmetry,
Inaccuracy in thyristor firing times,
Switching times,
Imperfect filtering.
In thyristor bridges, one may also observe a shift in harmonics relative to the phase angle of the thyristor.
Mixed thyristor-diode bridges are known to produce even harmonics. They are typically utilized at low #power ratings due to the difficulty in eliminating the second harmonic, which can cause significant disturbances. In contrast, other power #converters like cyclo-converters and dimmers exhibit a richer and more varied harmonic spectrum compared to rectifiers.
It's worth noting that rectifiers can be substituted by devices utilizing Pulse Width Modulation (PWM) techniques. These devices function at high chopping frequencies, typically around 20 kHz, and are usually engineered to produce minimal harmonic levels.
The harmonic currents from multiple converters merge vectorially at the common supply busbars. Typically, their phases are indeterminate, with the exception of diode #rectifiers where they are known.
Thus, it is feasible to reduce the 5th and 7th current harmonics by employing two equally loaded 6-pulse diode bridges, provided that the couplings of the two power supply transformers are selected with precision.
1.2 Lighting
Lighting systems consisting of discharge or fluorescent lamps generate harmonic currents. In some instances, modern compact fluorescent lamps can produce a 3rd harmonic ratio exceeding 100%. As a result, the neutral conductor carries the total of the 3rd harmonic current from all three phases, which can lead to dangerous overheating if it is not properly sized.
1.3 Electric Arc Furnaces (EAFs)
An electric arc furnace (EAF) heats materials using an electric arc, enhanced by the chemical energy from oxygen and fuel. In these furnaces, the electric arc directly contacts the charged materials, allowing current from the electrodes to pass through them. This method is distinct from induction furnaces, where the material is heated by induced eddy currents.
Electric Arc furnaces used in the steel industry may be of the AC or DC type.
Advancements in technology have enabled a higher utilization of power, thereby enhancing the productivity of the melting unit. Concurrently, Tenova has leveraged its extensive experience to improve the equipment's design, rendering the Electric Arc Furnace (EAF) highly efficient and adaptable.
The electric arc furnace is currently a versatile piece of equipment capable of melting a variety of charge mixes, ranging from 100% scrap to 100% DRI/HBI, and encompassing all intermediate combinations, including the incorporation of hot metal.
1.3.1 AC Arc Furnaces (Figure 4)
The arc exhibits non-linearity, asymmetry, and instability. It produces a spectrum that encompasses both odd and even harmonics, as well as a continuous spectrum, which manifests as background noise across all frequencies.
The spectrum is influenced by the furnace type, its power rating, and the specific #operation being performed, such as melting or refining. Consequently, precise measurements are necessary to ascertain the exact spectrum (refer to Figure 5).
1.3.2 DC Arc Furnaces (Figure 6)
The #arc, supplied through a rectifier, is more stable than that in AC furnaces. The drawn current can be broken down as follows:
A spectrum similar to that of a rectifier,
A continuous spectrum lower than that of an AC arc furnace.
1.4 Saturated Reactors
The impedance of a saturable #reactor varies with the current passing through it, leading to significant distortion of the current.
This is, for instance, the case for transformers at no load, subjected to a continuous overvoltage.
1.5 Rotating Machines (which generate slot harmonics)
Rotating machines produce high-order slot harmonics, typically with minimal amplitude. However, small synchronous machines can generate 3rd order voltage harmonics that may lead to detrimental effects such as continuous heating of #earthing resistors in generator neutrals.
Continuous heating (without faults) of earthing resistors of generator neutrals;
The malfunctioning of current relays is designed to protect against insulation faults.
2| Calculation Model
In the calculation of #disturbances, static converters and arc furnaces are regarded as generators of harmonic currents (refer to Figure 7).
The harmonic currents produced by disruptive equipment are largely independent of other loads and the total #network #impedance.
Thus, these currents may be regarded as being injected into the network by the disruptive equipment. It is merely required to change the sign arbitrarily, so that the disruptive equipment can be treated as sources of current for computational purposes.
The approximation becomes less precise for arc furnaces. For these, the current source model needs adjustment by incorporating a specifically chosen parallel impedance. Additionally, it's feasible to account for existing voltage harmonics at the connection point to the upstream network by employing the Norton equivalent model (refer to figure 8).
For every UH order, the corresponding IH is determined by considering Z and the impedance of the downstream network.
3| Calculation Method
When the phase shifts of harmonic currents are established, vector processing can be utilized. Unbalanced modelling may be beneficial for analyzing multiple single-phase disturbance sources.
When only the amplitudes of harmonic currents from disruptive sources are known, the technical report IEC 61000-3-6 recommends a method for summing the effects of these sources.
Interesting readings on this subject (PDF):
4| Principal Disturbances Caused by Harmonic Currents and Voltages
Harmonic currents and voltages, when superimposed on the fundamental frequency, have cumulative effects on the equipment and devices connected to the #powersupply network.
The adverse effects of harmonics vary depending on the type of load and can include:
Instantaneous effects and
Long-term effects due to heating
4.1 Instantaneous Effects
Harmonic voltages may interfere with controllers in electronic systems. For instance, they can influence the switching conditions of thyristors by altering the zero-crossing point of the voltage waveform.
Harmonics may introduce additional inaccuracies in induction-disk electricity meters. For instance, a class 2 meter's error margin could increase by 0.3% if there is a 5th harmonic present at a 5% ratio in both current and voltage.
Ripple control receivers, like the relays utilized by electrical utilities for centralized remote control, may experience interference from voltage harmonics with frequencies close to the control frequency. Additional sources of disturbances that impact these relays, associated with the network's harmonic impedance, will be addressed later.
4.1.1 Vibrations and Noise
The electrodynamic forces generated by instantaneous currents, which are linked to harmonic currents, result in vibrations and acoustic noise, particularly in electromagnetic devices such as #transformers and #reactors.
Pulsating mechanical torque, caused by harmonic rotating fields, can induce vibrations in rotating machinery.
4.1.2 Interference on communication and control circuits (Telephone, control and monitoring)
Disturbances occur when #communication or #controlcircuits are installed alongside power distribution circuits that carry distorted currents.
Parameters that must be taken into account include:
The length of parallel running,
The distance between the two circuits and
The harmonic frequencies (coupling increases with frequency).
4.2 Long-term Effects
In addition to mechanical fatigue caused by vibrations, the primary long-term effect of harmonics is increased heating.
4.2.1 Capacitor Heating
Heating losses are attributed to two phenomena: conduction and dielectric hysteresis.
As an initial estimate, the effects are proportional to the square of the root mean square (rms) current. Consequently, capacitors are sensitive to overloads, whether these are caused by an excessively high fundamental frequency or by the presence of voltage harmonics.
The losses in a capacitor are characterized by the loss angle δ, which is the angle whose tangent is the ratio of the power losses to the reactive power generated (refer to Figure 9). Values for tanδ are commonly cited as being around 10^-4.
The generated heat can result in dielectric breakdown.
4.2.2 Heating due to additional losses in machines and transformers
Additional losses occur in the stators (copper and iron) and primarily in the rotors (damping windings, magnetic circuits) of machines due to significant speed differences between the harmonic inducing rotating fields and the rotor. It should be noted that measurements of the rotor (such as temperature and induced currents) are challenging, if not impossible.
Transformers experience additional losses due to the skin effect, which increases the resistance of copper with frequency, as well as hysteresis and eddy currents within the magnetic circuit.
4.2.3 Heating of Cables and Equipment
Increased losses in cables carrying harmonic currents lead to a rise in temperature. The factors contributing to these additional losses encompass:
An increase in the RMS value of the current results in an equal active power consumption.
The apparent resistance of the core increases with frequency due to the skin effect.
Dielectric losses in insulation increase with frequency when the cable experiences significant voltage distortion.
The phenomena associated with the proximity of conductors to metal cladding and shielding, which are earthed at both ends of the cable, are significant. Steady-state calculations can be performed following the guidelines outlined in IEC 60287.
In general, electrical equipment, including switchboards, that is subject to voltage harmonics or carries harmonic currents, will experience elevated energy losses and may require derating to ensure safe and efficient operation..
For instance, the design of a capacitor feeder cubicle should account for a current that is 1.3 times the reactive compensation current. However, this safety factor does not consider the additional heating caused by the skin effect in the conductors.
Harmonic distortion in currents and voltages is assessed with spectrum analyzers, which determine the amplitude of each harmonic component. It is crucial to employ current or voltage sensors that possess adequate bandwidth to capture the frequencies being measured.
The RMS value of distorted current or voltage can be evaluated using one of three methods:
Measurement using a device designed to give the true RMS value,
Reconstitution based on the spectrum provided by spectral analysis,
Estimation from an oscilloscope display.
Reference: | Harmonic disturbances in networks, and their treatment by Schneider Electric |
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