Non-Linear Load
Related terms:
Reactor, Landing Gear, Transients, Voltage, Thyristors, Current Harmonic, Deflections, Harmonics, Transformers
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Learn more about Non-Linear Load
Motors, Generators, and Controls
Robert J. Alonzo P.E., in Electrical Codes, Standards, Recommended Practices and
Regulations, 2010
Harmonic Mitigation
There are several methods used for the mitigation of the harmonics produced by
non-linear loads such as variable frequency drives. Some methods are required
because of the type of rectifier used in the VFD, the type of DC to AC inverter used,
failure to utilize adequate harmonic filtering, etc. Some of the harmonic mitigation
methods include:
Use of 18 pulse VFD drives
AC drives with active front ends – transistor rectifiers with a microprocessor
controlled gate circuit
AC drives with active shunt filters
Use of AC input reactors
Use of phase shift transformers with the VFD rectifiers
Use of K-Factor transformers or derating transformers
Use of DC link reactors
Use of tuned LC (inductive/capacitive) or trap filters
Insertion of delta-wye transformers in the feeder to minimize harmonic currents
The use of K-Factor transformers or derating transformers for use with nonlinear
loads is not in itself a harmonic mitigation method. They are, however, a damage
mitigation method for transformers subjected to harmonic loading. ANSI/IEEE
C57.12.00, IEEE Standard for Standard General Requirements for Liquid-Immersed
Distribution, Power, and Regulating Transformers indicates:
that power transformers should not be expected to carry load currents with harmonic
factor in excess of 5% of rating. [40]
IEEE C57.12.01, IEEE Standard General Requirements for Dry-Type Distribution and
Power Transformers Including Those with Solid-Cast and/or Resin Encapsulated Windings
similarly provides recommendations for dry type transformers.
IEEE Standard C57.110, IEEE Recommended Practice for Establishing Liquid-Filled and
Dry-Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal
Load Currents was developed to deal with the problem of harmonic generating
nonlinear loads. The UL Standards used in association with K-Factor transformers
are UL 1561, Dry-Type General Purpose and Power Transformers and UL 1562, Standard
for Transformers, Distribution, Dry-Type – Over 600 Volts. Another standard associated
with harmonic generating loads for transformers is IEEE Standard C57.18.10, IEEE
Standard Practices and Requirements for Semiconductor Power Rectifier Transformers.
Transformer use with harmonic generating loads is also addressed in the IEEE
Emerald Book, IEEE 1100, IEEE Recommended Practice for Powering and Grounding
Electronic Equipment.
K-Factor is a mathematical representation to characterize a transformer's ability to
withstand overheating from harmonic loading without loss of normal life expectancy. UL 1561 and 1562 list two equations for determining K-Factors [41, 42]. The first
is as follows:
(Eq. 8.5)
where K is the unit-less weighing factor (K-Factor), Ih is the per unit harmonic current
component related to the fundamental frequency, and h is the harmonic order
number. A K-Factor value of 1.0 would indicate a liner load with no harmonics. As
the value of K increases, so does the effect of harmonic heating. The per unit current
Ih is expressed such that the total RMS current is one ampere, i.e.:
(Eq. 8.6)
The mathematical expression Ih could be determined for harmonic components
from the first harmonic to some very high harmonic value. It would be difficult
to perform this calculation without accepting some level of harmonic as the normally accepted maximum effective harmonic level above which harmonic order
components are very small in magnitude. The square of the harmonic component
number can become a large number. There have been suggestions limiting the
calculation to the 25th or 50th harmonic component. Many of the available harmonic
analyzer equipment produce harmonic current reading in the per unit format,
making insertion of any collected current data into the mathematical relationship
in Eq. 8.6 above very simple.
The second equation used by UL to establish the K-Factor for a transformer is shown
in Equation 8.7.
(Eq. 8.7)
where fh is the frequency in Hertz and h is the harmonic order component. Underwriters Laboratories recognizes K-Factors of 4, 9, 13, 20, 30, 40, and 50 as standard
transformer ratings.
Phase shift transformers are sometimes used in variable frequency drive rectifier
sections to minimize harmonic effects. IEEE C57.153, IEEE Guide for the Application,
Specification, and Testing of Phase-Shifting Transformers and IEC 62032 Ed. 1, Guide for
the Application, Specification, and Testing of Phase-Shifting Transformers (IEEE Standard
C57.135) provide guidance with the utilization of phase shift transformers.
Long cables, connecting a power source to a motor/VFD, contain a series of natural
self-inductive components and shunt distributed natural capacitive components.
Natural resonant conditions can develop from those inductive and capacitive components, should the proper excitement conditions develop. Resonant conditions
development can occur as a result of the presence of 5th, 7th, 11th, 13th, etc.
harmonic components feeding the motor load. The only natural damping factor
for the created resonant voltage and current waveforms is the resistance of the
line conductors feeding the motor. Resonant conditions can produce insulation
damaging voltage levels and overheat motor connections.
The introduction of a series connected inductive choke is one method to attenuate or
eliminate the resonant waveform. The choke will act as a low-pass filter, attenuating
the higher harmonic components and passing the lower fundamental frequency
components to the motor. Three percent and 5% line reactors are commonly used
to accomplish that task.
VFD generated harmonic waveform components can also cause motor winding and
bearing heating problems. Because of that potential, the use of motors with a 1.15
service factor, energy efficient motors, or VFD rated motors is recommended.
Alternating current VFD-driven excited motors, operating with large inertia loads,
can in some circumstances act as an induction generator, causing the voltage on
the DC bus to rise above normal operating levels. To protect the VFD rectifier section
from damage a braking resistor, can be inserted in parallel with the line to ground
capacitor filter in that section. The braking resistor can be activated by an electronic
component called a brake chopper. That component will conduct, tying the braking
resistor to the circuit neutral when DC Bus voltage levels reach a predetermined
point. That action will divert motor generated current from the DC bus, preventing
damage to the VFD.
PWM VFDs can also cause current flow into motor rotor bearings by capacitive
coupling. It can induce a rotor shaft voltage of up to 30 Volts [43]. The high
switching frequency of an IGBT inverter can result in inducing current pulses in
the motor bearings, if the rotor is not properly grounded. Large motors can develop
circulating current between the rotor, shaft bearings, and the stator frame because of
motor stator winding capacitive leakage current. The leakage current will eventually
overcome the impedance of the bearing lubrication film in a process called bearing
fluting. That process will result in a rhythmic pattern of pitting and gouges on the
bearing race. Current flow through the bearings can eventually result in bearing
overheating and failure.
There are several methods to minimize VFD induced motor bearing failures. They
include:
Proper selection of motor feeder cable and minimizing its length
Insertion of a filter at the motor terminal end of the cable
Use of motor insulated bearings
Use of non-conductive mechanical couplings in the motor
Addition of a motor shaft grounding device
Ensure proper grounding of a motor and VFD
Selection of VFD-rated motors manufactured with insulation meeting the
requirements of NEMA Standard MG1 Part 31; Paragraph 40.4.2
In situations where single-phase to ground connected harmonic generating nonlinear loads are fed over a three-phase, four-wire feeder circuit, IEEE 1100 [44]
recommends the use of a delta-wye three-phase transformer on that feeder. The
triplen harmonics from the nonlinear loads will be trapped in the transformer
primary (delta) windings, reducing the introduction of those harmonics to other
parts of the electrical distribution system. The delta-wye transformer selected for
that task must be listed or certified for that service.
> Read full chapter
Power Quality – Harmonics in Power
Systems
DrC.R. Bayliss CEng FIET, B.J. Hardy CEng FIET, in Transmission and Distribution
Electrical Engineering (Fourth Edition), 2012
24.3.1 General
Harmonic distortion needs to be defined as either ‘current distortion’ or ‘voltage distortion.’ Non-linear loads, unlike linear loads, draw a non-sinusoidal current from a
sinusoidal voltage supply. The distortion to the normal incoming sinusoidal current
wave can be considered to result from the load emitting harmonic currents that
distort the incoming current. These emitted harmonic currents, like any generated
current, will circulate via available paths and return to the other pole of the non-linear
load. In doing so, they cause harmonic voltage drops in all the impedances through
which they pass which distort the normal supply sinusoidal voltage. The aim must
therefore be to shunt the emitted harmonic currents into low impedance paths as
close to the non-linear load as possible to minimize the resulting voltage distortion,
as the voltage distortion will cause harmonic currents to flow in other linear and
non-linear connected loads, such as motors, with deleterious effects. Zero-sequence
triplen harmonic currents present a further problem as they are constrained to
zero-sequence paths such as neutral conductors which can then become overloaded
and present a serious risk as neutral conductors are not normally protected against
overloading.
> Read full chapter
Computer-Aided Method NTVPM for
Evaluating the Performance of Vehicles
with Flexible Tracks
J.Y. Wong Ph.D., D.Sc., in Terramechanics and Off-Road Vehicle Engineering (Second Edition), 2010
The characteristics of roadwheel suspensions are fully taken into consideration in
NTVPM. Pivot-arm suspensions, such as torsion bar suspensions and hydro-pneumatic suspensions, and translational spring suspensions, with linear or non-linear
load–deflection characteristics, can be simulated. The non-linear behaviour of the
suspension may be characterized using a polynomial up to the fifth order. On
highly deformable terrain, such as deep snow, track sinkage may be greater than
vehicle ground clearance. Thus, the vehicle belly (hull) may be in contact with the
terrain surface. This would induce additional drag due to belly–terrain interaction.
It may also reduce vehicle traction due to the belly supporting part of the vehicle
weight which causes the reduction of the load applied on the track. The effects
of belly–terrain interaction on vehicle performance have been taken into account.
All pertinent terrain characteristics, including the pressure–sinkage and shearing
characteristics and the response to repetitive loading, measured by the bevameter
technique described in Chapters 3, 4 and 5Chapter 3Chapter 4Chapter 5, are taken
into consideration. The basic features of the computer-aided method have been validated by means of full-scale vehicle tests on various types of terrain. Thus, NTVPM
provides the engineer with a comprehensive and realistic tool for performance and
design evaluation of vehicles with flexible tracks, from a traction perspective. It has
been successfully employed by off-road vehicle manufacturers in the development of
new products and by governmental agencies in the evaluation of vehicle candidates
in North America, Europe and Asia.
> Read full chapter
Hybrid wind–diesel energy systems
G. Bhuvaneswari, R. Balasubramanian, in Stand-Alone and Hybrid Wind Energy
Systems, 2010
6.5.4 Loads
As mentioned earlier, the loads have been categorized into three types in accordance
with their priorities. The loads can be passive loads such as lighting and heating
loads; they can be active loads consisting of industrial drives; they can be non-linear
loads drawing harmonic-rich currents such as rectifier-fed DC motors, fluorescent
lamps with electronic ballasts or power supply systems feeding computers or other
medical electronic systems. Depending upon the studies that are undertaken for
the system, the loads can be modelled suitably. If simple domestic loads have to be
modelled, they are represented by a constant power lumped load. If power quality at
the distribution level has to be studied for industrial drive kind of loads, a detailed
model of the drive unit has to be adopted. The generator should be in a position to
supply all these loads and still maintain a power factor of unity. This will be made
possible by making use of power quality conditioners.
> Read full chapter
Buckling of a Column with Non-Linear
Lateral Supports
H.S. Tsien, in Collected Works of H.S. Tsien (1938–1956), 2012
During the investigation of the buckling phenomenon of thin spherical shells [1] and
thin cylindrical shells[2], it was found that for these structures the load sustained is
not a linear function of the deflection even when the stresses are below the elastic
limit and are proportional to the corresponding strains. This non-linear load vs.
deflection relation gives a buckling phenomenon entirely different from that of the
classical theory. However, the exact solution of these problems involves a pair of
non-linear partial differential equations. It is difficult to obtain an exact solution.
The method adopted in these investigations is the so-called energy method, where a
plausible form of deflection of the shell is assumed, first with certain undetermined
parameters, and then these parameters are determined by the condition that the
first variation of the strain energy of the system must be zero. Although this method
yields quite satisfactory results for the cases investigated, it is felt that due to the
novel nature of the problem, an exact solution is very desirable. Experiments on a
column with non-linear lateral supports[3] show that the essential characteristics of
the buckling of curved shells can be reproduced by this structure. The problem of a
column with non-linear lateral supports is, however, much simpler than the problem
of curved shells, and an exact solution can be obtained without any mathematical
difficulty. In the present paper, an exact solution of the column problem will be
carried out.
> Read full chapter
The power supply
Ben Duncan A.M.I.O.A., A.M.A.E.S., M.C.C.S, in High Performance Audio Power
Amplifiers, 1996
Power factor
To discover either the overall efficiency of a power amplifier, or just that of its PSU,
we first need to measure the current drawn off the AC supply when driving a known
number of watts into a defined load. Excepting those amplifiers fitted with ‘unity’
PFC both 50/60HZ passive and switching power supplies present a highly non-linear
as well as reactive load to the AC power line; the periodic AC current generally leads
the AC voltage. PSUs using certain ‘smart’ electronic techniques (effectively now
outlawed for sale in Europe) may present even more complex non linear loads.
For these reasons alone, power input requires careful definition, to screen out the
effects of non-unity Power Factor (a perfectly resistive load has a power factor of 1.0;
for many amplifiers, PF is around 0.8 to 0.6) and associated high peak currents.
The latter aggravate losses in cables, leading to voltage droop, hence power and
efficiency losses. For the most part, these effects are essentially external to the
amplifier. They're also liable to be significant only if the incoming line power cabling
has too high a resistance; or the socketry in line is dirty or loose. But, with high
peak currents, the cable gauge needed may be many times that suggested on the
basis of safe current rating alone. The efficiency comparisons that follow assume
a competent, low resistance installation. An audit of the accuracy of power input
measurements would need to take account of auxiliary circuitry, subtracting the
power drawn by fans, lamps, LEDs and relays.
> Read full chapter
IGBT Applications
B. Jayant Baliga, in The IGBT Device, 2015
17.4.1 Fuji Electric 200-kVA UPS
In 1990, the Fuji Electric Company reported the development of a 200-kVA UPS using IGBTs for use by financial institutions [9]. The goal of this UPS is to provide power
to computers that are sensitive to power source voltage fluctuations and prevent
halting operations. The authors state [9]: “As compared with the conventional type
UPS using bipolar junction transistors, this UPS utilizing IGBT provides an equivalent
efficiency in spite of having an approximately 10-times higher switching frequency. As
a result, the new UPS has realized a compact, lightweight, low acoustic noise and high
performance design resulting in a reduced input harmonic current (less than 5% THD), and
also a reduced output voltage distortion (less than 8% THD) under non-linear load.” The
specifications for this 200-kVA UPS equipment are provided in Table 17.3. These
results demonstrate that IGBTs became the chosen power device technology for UPS
systems by 1990.
Table 17.3. Fuji Electric Insulated-Gate Bipolar Transistor-Based 200-kVA UPS from
1990
Item
Specification
Input voltage
200 V ±10%
Input frequency
50 or 60 Hz ±5%
Input phases/wires
3 phases/3 wires
Capacity
220 kVA; 160 kW
Input power factor
Over 95%
THD input current
Under 5%
Output voltage
200 V
Voltage accuracy
±1.5%
Output frequency
50 or 60 Hz
Output frequency accuracy
±0.1%
Output phases/wires
3 phases/3 wires
Load power factor
0.7 lagging to 1.0
Transient output voltage fluctuation
(a) 100% sudden load change—±8%
(b) 10% input voltage sudden change—±5%
(c) Major power interruption and recovery—±5%
(d) UPS bypass switching—±8%
Response time
100 ms
Output waveform THD
100% linear load—under 5%
100% nonlinear load—under 8%
Voltage imbalance between phases
100% unbalanced load—±3%
The topology for the Fuji Electric 200-kVA UPS is shown in Fig. 17.5. Two 100-kVA
units are configured in parallel here [9]. Each unit consists of a converter with high
power factor, a PWM inverter, an inverter transformer, and AC filters. The converters
make use of IGBT modules operated at 8 kHz to achieve a high input power factor
to reduce harmonics introduced into the input power line. The inverters are also
built using IGBT modules operated at a PWM carrier frequency of 8 kHz. This allows
delivering AC sinusoidal output waveforms with low distortion using small AC filters.
A bypass path with thyristors is included to handle the situations when the UPS may
fail and need servicing.
Figure 17.5. Configuration of the Fuji electric uninterruptible power supplies.
IGBT modules with ratings of 600 V and 150 A were used for this UPS application.
In order to reach the 200-kVA UPS capability, six IGBT modules were connected in
parallel to create the IGBT stack shown in Fig. 17.6. Each stack includes the gate
drive circuits, the electrolytic DC bus capacitors, and fuses. The snubber circuit was
sufficiently small to fit directly on top of each IGBT module.
Figure 17.6. Insulated-gate bipolar transistor (IGBT) stack for the Fuji electric uninterruptible power supplies.
The UPS configuration described above with IGBTs was able to achieve an efficiency
of 90% over a range of 20–100% of the total output power. It delivered a compact,
light weight UPS unit with low acoustic noise for use of customers in the financial
sector.
> Read full chapter
Harmonic Models of Transformers
Mohammad A.S. Masoum, Ewald F. Fuchs, in Power Quality in Power Systems and
Electrical Machines (Second Edition), 2015
2.4.3 Time-Domain Simulation of Power Transformers
Time-domain techniques use analytical functions to model transformer primary and
secondary circuits and core characteristics [17–25]. Saturation and hysteresis effects,
as well as eddy-current losses, are included with acceptable degrees of accuracy.
These techniques are mostly used for the electromagnetic transient analysis (such as
inrush currents, overvoltages, geomagnetically induced currents, and out-of-phase
synchronization) of multiphase and multilimb core-type power transformers under
(un)balanced (non)sinusoidal excitations with (non)linear loads. The main limitation
of time-domain techniques is the relatively long computing time required to solve
the set of differential equations representing transformer dynamic behavior. They
are not usually used for steady-state analyses. Harmonic modeling of power transformers in the time domain are performed by some popular software packages and
circuit simulators such as EMTP [24] and DSPICE (Daisy’s version of circuit simulator
SPICE [25]). The electromagnetic mathematical model of multiphase, multilimb
core-type transformer is obtained by combining its electric and the magnetic cir-
cuits [35–37]. The principle of duality is usually applied to simplify the magnetic
circuit. Figure 2.22 illustrates the topology and the electric equivalent circuit for the
general case of a five-limb transformer, from which other configurations such as
three-phase, three-limb, and single-phase ones can be derived. The open ends of
the nonlinear multiport inductance matrix L (or its inverse, the reluctance matrix )
allow the connection for any electrical configuration of the source and the load at
the terminals of the transformer.
Figure 2.22. Time-domain harmonic model of power transformers; (a) general
topology for the three-phase, five-limb structure, (b) equivalent circuit [23].
Most time-domain techniques are based on a set of differential equations defining
transformer electric and magnetic behaviors. Their computational effort involves
the numerical integration of ordinary differential equations (ODEs), which is an
iterative and time-consuming process. Other techniques use Newton methodology
to accelerate the solution [22,23]. Transformer currents and/or flux linkages are
usually selected as variables. Difficulties arise in the computation and upgrading of
magnetic variables (e.g., flux linkages), which requires the solution of the magnetic
circuit or application of the nonlinear hysteresis characteristics, as discussed in
Section 2.4.2.
In the next section, time-domain modeling based on state-space formulation of
transformer variables is explained. Either transformer currents and/or flux linkages
may be used as the state variables. Some models [22,23] prefer flux linkages since
they change more slowly than currents and more computational stability is achieved.
2.4.3.1 State-Space Formulation
The state equation for an m-phase, n-winding transformer in vector form is [19]
(2-40)
where , , , , and are the terminal voltage vector, the current vector, the resistance
matrix, the leakage inductance matrix, and the flux linkage vector, respectively.
The flux linkage vector can be expressed in terms of the core flux vector by
(2-41)
where is the transformation ratio matrix (number of turns) and is the core-flux
vector.
In general, the core fluxes are nonlinear functions of the magnetomotive forces (),
therefore, can be expressed as
(2-42)
where is a m × m Jacobian matrix. The magnetomotive force vector can be expressed
in terms of the terminal current vector by
(2-43)
where is a matrix that can be determined from matrix and the configuration of the
transformer.
Substituting Eqs. 2-42 and 2-43 into Eq. 2-40, we obtain
(2-44)
Defining the nonlinear incremental (core) inductance
(2-45)
the transformer state equation is finally expressed as follows:
(2-46)
Equations 2-45 and 2-46 are the starting point for all modeling techniques based
on the decoupling of magnetic and electric circuits. The basic difficulty is the
calculation of the elements of the Jacobian at each integration step. The incorporation of nonlinear effects (such as magnetic saturation and hysteresis) and the
computation of are performed by appropriate modifications of the differential and
algebraic equations (Eqs. 2-40 to 2-46). As discussed in Section 2.4.2, numerous
possibilities are available for accurate representation of transformer saturation and
hysteresis. However, there is a trade-off between accuracy and computational speed
of the solution. Figure 2.23 shows the flowchart of the nonlinear iterative algorithm
for transformer modeling based on Eqs. 2-40 to 2-46, where elements of can be
derived from the solution of transformer magnetic circuit with a piecewise linear
(Fig. 2.16b) or an incremental (Fig. 2.16c) magnetizing characteristic [19].
Figure 2.23. Flowchart of the time-domain iterative algorithm for transformer modeling [19].
2.4.3.2 Transformer Steady-State Solution from the Time-Domain Simulation
Conventional time-domain transformer models based on the brute force (BF) procedure [22,23] are not usually used for the computation of the periodic steady-state
solution because of the computational effort involved requiring the numerical integration of ODEs until the initial transient decays. This drawback is overcome with the
introduction of numerical differentiation (ND) and Newton techniques to enhance
the acceleration of convergence [22,23].
> Read full chapter
Inverter-fed Induction Motor Drives
Austin Hughes, Bill Drury, in Electric Motors and Drives (Fourth Edition), 2013
5.1 Harmonic currents
Harmonic current is generated by the input rectifier of an a.c. drive. The essential
circuit for a typical a.c. variable-speed drive is shown in Figure 8.1. The utility supply
is rectified by the diode bridge, and the resulting d.c. voltage is smoothed by the
d.c. link capacitor and, for drives rated typically at over 2.2 kW, the d.c. current is
smoothed by an inductor in the d.c. circuit. The d.c. voltage is then chopped up in the
inverter stage, which uses PWM to create a sinusoidal output voltage of adjustable
voltage and frequency.
While small drive ratings may have a single-phase supply, we will consider a 3-phase
supply. We see from Figure 8.5 that current flows into the rectifier as a series of
pulses that occur whenever the supply voltage exceeds that of the d.c. link, which is
when the diodes start to conduct. The amplitude of these pulses is much larger than
the fundamental component, which is shown by the dashed line.
Figure 8.5. Typical current from utility supply for a 1.5 kW 3-phase drive.
Figure 8.6 shows the spectral analysis of the current waveform in Figure 8.5.
Figure 8.6. Harmonic spectrum of the current waveform shown in Figure 8.5.
Note that all currents shown in spectra comprise lines at multiples of the 50 Hz utility
frequency. Because the waveform is symmetrical in the positive and negative half-cycles, apart from imperfections, even-order harmonics are present only at a very low
level. The odd-order harmonics are quite high, but they diminish with increasing
harmonic number. For the 3-phase input bridge there are no triplen harmonics, and
by the 25th harmonic the level is negligible. The frequency of this harmonic for a
50 Hz supply is 1250 Hz, which is in the audio frequency part of the electromagnetic
spectrum and well below the radio-frequency part, which is generally considered to
begin at 150 kHz. This is important, because it shows that supply harmonics are
low-frequency effects, which are quite different from radio-frequency EMC effects.
They are not sensitive to fine details of layout and screening of circuits, and any
remedial measures which are required use conventional electrical power techniques
such as tuned power-factor capacitors and phase-shifting transformers. This should
not be confused with the various techniques used to control electrical interference
from fast switching devices, sparking electrical contacts, etc.
The actual magnitudes of the current harmonics depend on the detailed design of
the drive, specifically the values of d.c. link capacitance and, where used, d.c. link
inductance, as well as the impedance of the utility system to which it is connected,
and the other non-linear loads on the system.
We should make clear that industrial problems due to harmonics are unusual,
although with the steady increase in the use of electronic equipment, they may
be more common in the future. Problems have occurred most frequently in office
buildings with a very high density of personal computers, and in cases where most
of the supply capacity is used by electronic equipment such as drives, converters and
uninterruptible power supplies (UPS).
As a general rule, if the total rectifier loading (drives, UPS, PCs, etc.) on a power
system comprises less than 20% of its current capacity then harmonics are unlikely
to be a limiting factor. In many industrial installations the capacity of the supply
considerably exceeds the installed load, and a large proportion of the load is not a
significant generator of harmonics – uncontrolled (direct-on-line) induction motors
and resistive heating elements generate minimal harmonics.
If rectifier loading exceeds 20% then a harmonic control plan should be in place.
This requires some experience and guidance can often be sought from equipment
suppliers. The good news is that if it is considered that a problem will exist with the
estimated level of harmonics then there are a number of options available to reduce
the distortion to acceptable levels.
A.C. drives rated over 2.2 kW tend to be designed with inductance built into the d.c.
link and/or the a.c. input circuit. This gives the better supply current waveform and
dramatically improved spectrum as shown in Figures 8.7 and 8.8, respectively, which
are again for a 1.5 kW drive for ease of comparison with the previous illustrations. (In
this case the inductance in each line is specified as ‘2%’, which means that when rated
fundamental current flows in the line, the volt-drop across the inductor is equal to
2% of the supply voltage.) Note the change of vertical scale between Figures 8.5 and
8.7, which may tend to obscure the fact that the pulses of current now reach about
5 A, rather than the 17 A or so previously, but the fundamental component remains
at 4 A because the load is the same. (Remember that while we have just demonstrated
the tremendous improvement in supply harmonics achieved by adding d.c. link
inductance to a 1.5 kW drive, standard drives would rarely be manufactured with
any inductance because while the harmonic spectrum looks worrying, the currents
are at such a low level that they would rarely cause practical problems.)
Figure 8.7. Input current waveform for the 3-phase 1.5 kW drive with d.c. and 2%
a.c. inductors.
Figure 8.8. Harmonic spectrum of the improved current waveform shown in Figure
8.7.
Standard 3-phase drives rated up to about 200 kW tend to use conventional 6-pulse
rectifiers. At higher powers, it may be necessary to increase the pulse number to
improve the supply-side waveform, and this involves a special transformer with two
separate secondary windings, as shown for a 12-pulse rectifier in Figure 8.9.
Figure 8.9. Basic 12-pulse rectifier arrangement.
The voltages in the transformer secondary star and delta windings have the same
magnitude but a relative phase shift of 30°. Each winding has its own set of six
diodes, and each produces a 6-pulse output voltage. The two outputs are generally
connected in parallel, and, because of the phase shift, the resultant voltage consists
of 12 pulses of 30° per cycle, rather than the six pulses of 60° shown, for example,
in Figure 2.13.
The phase shift of 30° is equivalent to 180° at the fifth and seventh harmonics
(as well as 17, 19, 29, 31, etc.), so that flux and hence primary current at these
harmonics cancels in the transformer, and the resultant primary waveform therefore
approximates well to a sinusoid, as shown for the 150 kW drive in Figure 8.10.
Figure 8.10. Input current waveform for 150 kW drive with 12-pulse rectifier.
The use of drive systems with an input rectifier/converter using PWM which generates negligible harmonic current in the utility supply is becoming increasingly
common. This also permits the return of power from the load to the supply, and is
discussed later in section 7.
> Read full chapter
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