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Power factor and displacement factor
When a sinusoidal voltage is connected to a linear load, the result is a sinusoidal current whose magnitude depends on the impedance of the electrical load. The flow of current normally results in power (kW) being consumed in the circuit of the electrical load.
With resistive loads, the current is in phase with the voltage and the total active power is essentially equal to the product of the RMS voltage and the RMS current, which is called the apparent power and is measured as volt-amperes. For resistive loads, the ratio between the active power and the total apparent power is equal to 1. With partially inductive loads, such as electric motors and transformers, the current lags behind the supply voltage by an angle between 0º to 90º, which results in a reduction in the total active power (useful work), which is transferred to the electrical load. The active power consumed is lower than the total RMS volt-amperes and the ratio between the active power and the total apparent power falls to a value less than 1.
With purely inductive loads, the current lags behind the supply voltage by 90º, which results in an active power of zero and the ratio between the active power and the total apparent power falls to zero.
The ratio between the active power and the total apparent power is known as the power factor and is defined as follows:
Amperes Volt RMS Total Power Average Total = Factor Power
The measurement of power is related to the product of the RMS voltage and RMS current, which is a function of the area under the respective waveforms. With purely sinusoidal voltages and currents, the power factor is a function of the phase displacement angle f between the voltage and the current. Since the phase displacement angle can readily be measured with simple instruments, it’s commonly used as a measure of the power factor. For purely sinusoidal voltages and currents, the power factor can be shown to be equal to the cosine of the phase displacement angle f.
Cos f is also referred to as the displacement factor, which has a value between 0 to 1.
f = Factor Displacement Cos
In those cases where both the voltage and the current are purely sinusoidal:
f = Factor Displacement = Factor Power Cos
Before the advent of power electronic converters, the power supply voltages, and load currents were sinusoidal and undistorted. The power factor was, in general equal to the displacement factor, with 1 indicating no lag. This is this quantity, which the manufacturers of AC converters correctly claim as being, '0.95 or better'. However, with non linear power electronic loads, the voltages and currents are distorted and displacement factor is not equal to power factor.
With non linear loads, with highly distorted currents, the total active power is no longer closely related to the displacement angle between the voltage and current. The harmonic components of the current don’t do any useful work and are lost as heat in various parts of the power system and the electrical load. By measuring the total RMS volt-amperes, all these harmonic components are taken into account, which results in a power factor that is much lower than would be calculated from simply measuring the displacement factor.
The distorted voltages and currents have to be measured by special true RMS reading instruments, which measure the 'area under the waveform'. In practice, the real power factor with diode converters can be as low as 0.65, even though the measured displacement factor is greater than 0.95.
The real power factor is also affected by circuit components such as the source impedance of the power system and the inductances in the power electronic circuit. In general, the more distorted the current waveform, the lower the real power factor will be.
Although it’s quite easy to measure the power factor of an existing circuit, it’s quite difficult to calculate the real power factor of a drive system at the design stage. To achieve an accurate figure in practice, it’s necessary to use a computer based circuit analysis program to model the electrical system and take into account the various impedances and the effect of harmonic frequencies on the inductive components of the electrical system.
Voltages and current on the motor side of PWM inverters
The principles of operation of AC squirrel cage induction motors and the frequency converters to control the speed of these motors are covered in detail in previous sections and won’t be repeated here. This section deals with how the motor responds to the distorted voltages and currents provided at the output terminals of the converter. The DC filter of the converter largely separates the AC input to the rectifier from the AC output from the inverter, so the harmonics on the motor side of the converter may be treated as a separate issue from the harmonics in the supply side. Users seldom pay much attention to the distorted currents in the motor, apart from applying some minor de-rating factors recommended by the manufacturer of the motor and converter. With the older current source (CSI) and voltage source inverters (VSI), the losses in the motor were significant and it was common practice to de-rate the motor output by as much as 20% to compensate for the harmonic heating in the motor.
With the introduction of inverters with special switching patterns at high switching frequencies, motor currents are almost perfectly sinusoidal and the harmonic losses in the motor are so small that they can usually be ignored. With the thermal margin built into most modern motors, it’s now seldom necessary to de-rate the motor for operation with a modern PWM converter.
As described, most modern AC converters use a voltage source inverter (VSI) to generate a pulse width modulated output voltage. With the introduction of high frequency switching above 1 kHz, the harmonics on the motor side are in the frequency spectrums from 10 kHz up to 20 MHz, which is well into the RFI spectrum (>100 kHz). Some of these can pass through the DC link and emerge on the supply side. RFI Filters are now commonly used to prevent this interference being conducted back into the mains.
Refer also to RFI Filters.
In contrast to the supply side of the converter, the motor side harmonics are mainly high frequency voltages (high dv/dt), which radiate an electric field. The mathematical analysis of these frequencies is complex and affected by many variables, certainly not as easy as the calculation of supply side harmonics.
The interference generated by the PWM inverter on the motor side and radiated from the motor cable and the converter itself depends on:
• The inverter output frequency range
• The pulse width modulation (PWM) switching frequency (typically 2 kHz to 20 kHz)
• The architecture of the inverter, e.g. the internal screening, mechanical details, inductance in motor leads, etc
To comply with the latest EMI standards, it’s recommended that the power cable between the converter and the motor be shielded, with the shield connected to ground.
However, shielding can increase the cable shunt capacitance and leakage current.
Effect of the high PWM switching frequency on long motor cables
The high switching frequency of the inverter output voltage interacts with the shunt capacitance of the motor cable, which results in a high frequency leakage current. The higher the leakage current, the higher the losses in the inverter. The leakage current mainly affects the smaller sizes of AC converters (less than 11 kW) because the leakage current is of a similar magnitude as the motor current.
Therefore, modern PWM inverters are designed for a maximum cable length that is determined by the capacitive leakage current losses in the motor cable. Manufacturers can usually provide a de-rating table, which could be similar to the one shown in the ++++ below. The de-rating varies for different sizes of converter and also for different manufacturers.
The leakage current is dependent on the length of the cable and its capacitance. This problem is often aggravated by the use of shielded motor cables, which are installed to reduce the radiated EMI from the motor cable. Shielded cables have higher leakage capacitance per meter, almost double that of an unshielded cable. The AC converter needs to be de-rated for long motor cables as shown below.
++++ De-rating of the PWM converter for motor cable length
The capacitive leakage current can be reduced by installing a motor choke (inductance) at the output terminals of the converter. This series inductance introduces a high impedance between the HF voltage source and the cable capacitance, which reduces the high frequency currents to a relatively low magnitude. These motor chokes are seldom provided as part of the specification of a standard PWM inverter and, where required, are installed as a separate component.
Selection of PWM switching frequency
Many modern AC converters have a selectable output switching frequency and the tendency is to use the highest output frequency to reduce audible noise. The higher the switching frequency, the higher the leakage current losses.
The selection of the PWM switching frequency is a compromise between the losses in the motor and the losses in the inverter.
• When the switching frequency is low, the losses in the motor are higher because the current waveform becomes less sinusoidal
• When the switching frequency increases, motor losses are reduced but the losses in the inverter will increase because of the increased number of commutations. Losses in the motor cable also increase due to the leakage current through the shunt capacitance of the cable.
Manufacturers of converters usually provide a de-rating table or graph, which would be similar to the typical one.
++++ Typical de-rating of the PWM converter for high switching frequency
High rates of rise of voltage (dv/dt) at inverter output
High frequency switching, using modern IGBT devices in the inverter, achieves a relatively 'smooth' sinusoidal current and reduces the losses in the motor. While the smooth current reduces thermal losses and audible noise in the motor, the sharp rate of rise of the voltage at the inverter output can introduce several other problems. IGBTs have a rate of rise that is several orders of magnitude faster than a BJT. The rate of rise of voltage can be as high as 10 kV/µsec with an IGBT. Some of the problems that have emerged because of this high switching frequency are:
• High electrical stresses of the cable and motor insulation due to the high rate of rise of voltage (high dv/dt) and reflections at the end of the motor cable.
• High radiated electric field, due to the high dv/dt, can exceed the new EMC standards that have been implemented in Europe and U.S..
• As outlined above, the high dv/dt across the stray capacitance of cables results in leakage currents which flow into the cable shield (if provided) or alternatively via other conductive paths into the ground. These leakage currents generate additional heat in the inverter or exceed the current limit on smaller converters, which usually results in the converter tripping.
The most significant impact of the high rate of rise of voltage (high dv/dt) is the high voltage spikes that occur because of the reflected wave at the end of the long motor cable.
These voltage spikes can reach peaks of 2 to 2.5 times the inverter DC bus voltage. The phenomenon of reflected waves is quite well understood with communications cables, which operate at similar frequencies. On communications cables the main problem is the interference due to the reflected signal. The doubling of the voltage at the receiving end, due to the reflection, does not cause any physical damage because the signal voltage is usually low.
On modern AC variable speed drives, which use an IGBT inverter bridge, the high voltage spike due to the reflection at the motor end of the cable can damage the insulation of the motor and eventually lead to a short circuit. The mechanism of the failure is as follows:
• The cable between the IGBT inverter output terminals and the AC motor terminals represents an impedance, which comprises resistive, inductive and capacitive components. The cable presents a surge impedance to the voltage pulses generated by the PWM inverter and which travel down the cable. If the surge impedance of the cable does not match the surge impedance of the motor, a partial or full reflection occurs at the motor terminals.
• It’s important to understand that this reflection occurs regardless of the type of switching device (IGBT, BJT, MOSFET, GTO, etc) in the inverter. The maximum amplitude of the reflected voltage depends on the velocity of the voltage pulse, its rise time and the length of the cable between the converter and the motor. The rise time of the pulse is related to the switching device.
With IGBTs, which have a short rise time (50-500 ns), the length of cable at which voltage doubling occurs is much shorter than for a BJT (0.2-2 µs) or a GTO (2-4 µs), which have longer rise times.
• Under worst case conditions, the amplitude of the reflected voltage pulse can be 2 to 2.5 times the inverter DC bus voltage. For a nominal 415 V AC supply voltage to a converter, the DC Bus voltage will be approximately 600 V, which means that the voltage spike at the motor terminals can be as high as 1.5 kV.
(a) Inverter output voltage (4 kHz) | (b) Motor input voltage (100m cable)
++++ Comparison of voltage at each end of the motor cable
These voltage spikes could have the following effects on the AC induction motor:
• The first turn of the motor winding is likely to be the worst affected because it’s estimated that 60-80% of the voltage spike is likely to be distributed across it.
• The voltage spikes could be greater than the basic insulation level of the electrical phases in the motor, causing dielectric stress of the insulation and eventual failure.
• The voltage spikes could exceed the breakdown voltage of the air separating a winding from the frame at certain points and a partial discharge can occur.
These discharges will degrade the insulation slowly and lead to insulation failure.
• Even if the peak voltage is not high enough to cause a breakdown of the insulation, localized peak capacitive currents heat up the windings. These hot spots may aggravate the insulation degradation process. This problem particularly affects older motors, which used insulation materials of a lower temperature rating.
Although the problem of motor insulation stress due to voltage reflections has been present for some time, even with older generations of PWM converters, a few motor insulation failures since the introduction of IGBT inverters has highlighted the problem.
On VS drive applications where long motor cables are required, some form of protection should be installed to protect the motor from insulation stress.
While we are not aware of any definitive study that has been done on how these voltage spikes affect the cable insulation, it’s felt that the substantial insulation of most cables can withstand these voltage stresses.
Inverter Type Rated Motor Surge Voltage Withstand Level
1,000V Peak 1,200V Peak 1,600V Peak IGBT (0.1µs)
++++ Recommended maximum motor cable lengths
Protection of motors against high PWM switching frequency
The use of high frequency PWM switching techniques in modern IGBT inverters has been developed to synthesize a sinusoidal current, thereby reducing the harmonic current losses in the motor and reducing audible noise. These are both desirable features of modern AC variable speed drives.
The new problems due to the leakage currents in the cables and insulation stress in the motor, which have arisen as a result of the high frequency PWM switching techniques, can usually be fairly easily solved.
From point of view of the motor, the best solution is to provide a motor whose insulation can withstand the amplitudes of the reflected voltage spikes. Many motor manufacturers have recognized that motor insulation levels should be increased and have responded with motors that are designed to operate with IGBT inverters. The addition of insulating paper in the motor slots and between phases, can provide additional protection to the most vulnerable areas of the motor windings. This reinforces the benefit of using better quality induction motors for variable speed drive applications.
Since the amplitude of the reflected voltage spike is dependent on the length of the motor cables, these should be kept as short as possible and installations should be planned to minimize the length of motor cables. The table below gives a rough guide to acceptable cable lengths for various inverter types and 415 volt induction motor insulation levels.
If motor cable lengths need to be longer than the above recommended values, or when retro-fitting a modern IGBT converter to an existing motor of unknown insulation level, there are a number of solutions which can be used to reduce the effect of the reflected voltage spike on the insulation and thereby extending the life of the drive system. Output reactors (chokes)
A choke may be installed on the output side of the PWM inverter to increase the inductance of the circuit. While this may introduce a small additional volt drop at motor running frequencies, it also reduces the high rate of rise of voltage, which effectively limits the amplitude of the reflected voltage and extends the permissible length of the motor cable. A choke located at the converter output has the additional advantage that it reduces the leakage current flowing into the capacitance of the cable and reduces the losses in the inverter. Locating the choke at the motor end does nothing to reduce the cable leakage current or the losses in the inverter. Obviously, the insulation of the choke should itself be designed to withstand the high rates of rise of voltage.
Output motor filters:
Special harmonic filters, comprising R, L and C components, may also be used in a similar way to the output reactor described above to protect both the cable and the motor. The filter can also be designed to reduce the EMI in the motor cable. The filter achieves this by changing the impedance conditions so that the EMI is diverted into the ground and directed back to the source. The filter mainly comprises a low value series inductance (choke), similar to the choke above, and provides a high impedance to the flow of high frequency current, with some additional shunt components. However, the use of shunt capacitance on the inverter side of these filters is restricted due to the effect on inverter performance.
These filters have thermal losses, so the filter losses should be added to the converter losses when determining enclosure cooling requirements. In addition, the filter must be earthed to the same ground bar in the enclosure.
Terminator at the motor terminals:
On communications cables, reflected voltages can be attenuated by connecting a terminator at the end of the cable. A similar solution can be used with the motor cable. A terminator, comprising mainly an R-C circuit, connected at the motor terminals can be designed to keep the voltage spike below a potentially destructive level. In comparison to output chokes and filters, terminators occupy only a small space, dissipate minimal power and their cost is less than 10% of a filter. In addition, terminators can be used at each motor in multi-motor drive installations.
The following table illustrates the typical maximum motor cable lengths with IGBT converters and the alternative solutions discussed above. The variations in the cable lengths depend on the rated voltage withstand levels of the motor.
Protection System Maximum Motor Cable Length No Compensation Reactor at Inverter Reactor at Motor Terminator at Motor 10 - 50 meters 30 - 100 meters 60 - 200 meters 120 - 300 meters
++++ Maximum motor cable lengths with IGBT inverters
Compliance with EMC standards
Various levels of electromagnetic interference (EMI) are generated by all electrical and electronic equipment. EMI is sometimes also referred to as radio frequency interference (RFI). The latter is an 'old-fashioned' term and its continued use is being discouraged in the standards. With the expanded use of variable speed drives (VSDs) throughout industry, the level of EMI generated by this equipment can put at risk the reliable operation of many other electronic devices, such as instrumentation and control devices.
However, VSDs are not the only source of EMI, other devices such as fluorescent lamps, switch-mode power supplies, rectifiers, UPS, hand-held radios, mobile phones, etc also generate quite a high level of EMI.
In most industrialized countries, regulating authorities have introduced a framework of EMC standards, which introduce limits for emissions from all electrical/electronic products. At the same time, thresholds of immunity to interference that electrical/electronic products must be able to withstand have also been defined. Products are said to be electromagnetically compatible when they can operate together in the same environment, with limits imposed on those devices that radiate interference and higher levels of immunity for the equipment, which is susceptible being above these limits.
To establish compliance with the EMC framework, manufacturers need to comply with the published standards relevant to the products they supply. In U.S., those items of electrical equipment that comply with the EMC standards can use the compliance mark to signify their compliance. The supplier must take responsibility to ensure that the products comply with the EMC standards. In Europe, the CE mark represents compliance to the similar European standards.
To achieve compliance with the EMC framework in U.S., the supplier must satisfy four basic requirements:
• The supplier must establish sound technical grounds for the product's compliance
• The supplier must make a declaration of conformity
• The supplier must prepare a compliance folder including test reports or a technical construction file
• The supplier must label the product accordingly
From 1st January 1997, products had a 2 year period of grace in which to achieve compliance with the EMC framework. From 1st January 1999, it’s mandatory for all electrical products offered for sale in the commercial, residential, and industrial environment to comply with the EMC framework.
The relevant generic standards are as follows:
U.S. | Europe Generic emission standards
Generic Immunity standards
These generic standards call up the tests specified in the relevant IEC-1000 standards.
EMI (or RFI) filters for PWM inverters
When properly designed and used, EMI (RFI) filters connected to the input terminals (line side) of a modern PWM inverter can substantially attenuate the flow of conducted high frequency electromagnetic interference into the power supply cables and into the mains. The best location for the filter is close to the VSD terminals.
In general, a PWM type variable speed drive won’t comply with the EMC framework unless it’s fitted with a correctly installed RFI filter. Shielding and grounding should be in accordance with the installation instructions supplied with the VSD and/or RFI filter. To achieve EMC compliance, the installation procedure is important. To overcome this dependence on correct installation, many modern VSDs now have the RFI filter built into the VSD as standard equipment.
The line-side filter usually comprises a combination of series inductance and shunt capacitance. This filter diverts the harmonic currents away from the power cable and into the local ground connection. Care should be taken to ensure that the ground return cable is installed in such a way that the radiated field does not couple with signal and communications cables.
++++ Typical line-side filter for a variable speed drive
Concluding comments about high PWM switching frequency
Although the issue of reflected voltage spikes with IGBT inverters is an important one, clearly there are many drives operating successfully without additional protection. This does not mean that voltage reflections are not taking place, they are below the damage level because either the motor cable is not too long or the cable shunt capacitance is low or the motor insulation level is adequately high. It’s not the purpose of this section to over-state the rate of occurrence of this problem. Not all IGBT inverter drive applications will experience a problem. However, users of VSDs should be aware of the potential for this problem to occur and to design the VSD system to minimize its effects.
The following figure summarizes some of the protection features that can be used to improve the harmonic and EMI performance of an AC variable speed drive system.
++++ An AC drive fitted with line-side and motor-side filters
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Updated: Monday, 2013-01-07 16:01 PST