Maintaining a stable level of power quality in the distribution network is a growing challenge due to increased use of power electronics converters in domestic. In the present day deregulated power market electric power quality issues can be used on all reading devices; Immediate eBook download after download. Editorial Reviews. About the Author. Alexander Kusko is the corporate vice president of Failure eBook features: Highlight, take notes, and search in the book; Length: pages; Optimized for larger screens. Kindle e-Readers. Kindle (5th Generation).
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Free download of Power Quality by Andreas Eberhard. Available in PDF, ePub and Kindle. Read, write reviews and more. Read "Power Quality" by C. Sankaran available from Rakuten Kobo. Sign up today and get $5 off your first download. Frequency disturbances, transients. Due to the complexity of power systems combined with other factorssuch as increasing susceptibility of equipment, power quality (PQ)is apt to waver.
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Close Report a review At Kobo, we try to ensure that published reviews do not contain rude or profane language, spoilers, or any of our reviewer's personal information. Would you like us to take another look at this review? No, cancel Yes, report it Thanks! Shown in Table 1. The Scope of This Text We will address the significant aspects of power quality in the follow- ing chapters: Chapter 1, Introduction, provides a background for the subject, includ- ing definitions, examples, and an outline for the book.
Included are standards discussing harmonic distortion frequencies that are multiples of the line frequency as well as high-frequency interhar- monics caused by switching power supplies, inverters, and other high- frequency circuits. Chapter 3, Voltage Distortion, discusses line-voltage distortion, and its causes and effects.
Chapter 4, Harmonics, is an overall discussion of the manner in which line-voltage and line-current distortion are described in quantitative terms using the concept of harmonics and the Fourier series, and spectra of periodic waveforms. Chapter 5, Harmonic Current Sources, discusses sources of harmonic currents.
This equipment, such as electronic converters, creates fre- quency components at multiples of the line frequency that, in turn, cause voltage distortion. Chapter 6, Power Harmonic Filters, discusses power harmonic fil- ters, a class of equipment used to reduce the effect of harmonic cur- rents and improve the quality of the power provided to loads. These filters can be either passive or active. A means of transition is required.
Generators are used in cases of interruptions. Some success can also be achieved in instances of impulsive and oscillatory transients, long duration overvoltages and undervoltages, and noise.
Utilized for interruptions, and sags. Motor-Generator MG Equipment used in all cases except long duration outages. Surge Protective Device used to address impulsive transients. Shielded Isolation These devices are effective in cases of oscillatory transients and noise.
Line Reactors These devices are effective in cases of oscillatory transients. Fiberoptes Cable Alternative to copper cabling where communications may be susceptible to noise. Chapter 8, Methods for Correction of Power-Quality Problems, is a pre- liminary look at methods for design of equipment and supply sys- tems to correct for effects of poor power quality. Chapter 9, Uninterruptible Power Supplies, discusses the most widely employed equipment to prevent poor power quality of the supply system from affecting sensitive loads.
Chapter 10, Dynamic Voltage Compensators, is a description of low- cost equipment to prevent the most frequent short-time line-voltage dips from affecting sensitive equipment. Chapter 11, Power-Quality Events, discusses how power-quality events, such as voltage sags and interruptions affect personal com- puters and other equipment.
Chapter 12, Adjustable Speed Drives ASDs and Induction Motors, discusses major three-phase power-electronic equipment that both affect power quality and are affected by poor power quality. Chapter 13, Standby Power Systems, consisting of UPSs, discusses engine-generator and transfer switches to supply uninterrupted power to critical loads such as computer data centers. Chapter 14, Measurements, discusses methods and equipment for performing power-quality measurements.
As such, practically all of the electrical engineering literature bears on power quality. A group of pertinent references is given at the end of this chapter and in the following chapters of the book.
Two impor- tant early references that defined the field are the following: Clemmensen and R. Dougherty and W. Dugan, M. McGranaghan, S. Santoso, and H. Ise, Y. Hayashi, and K. Martzloff and T. Seymour and T. Available on the Web at http: Stones and A. Duffey and R. Hoevenaars, K.
LeDoux, and M. Introduction 13 [1. Baran, J. Maclaga, A. Kelley, and K. Johnson and R. Redl and A. Chung, S. Hui, and K. Curatolo and S. Fink and H. Beaty, eds. Alves and T. Djokic, J. Desmet, G. Vanalme, J. Milanovic, and K. Kornick, and H. Lamoree, D. Mueller, P. Vinett, W. Jones, and M. De Koster, E. De Jaiger, and W. Emanuel, and L. Gallo, C. Landi, and N. Gallo, R. Langella, and A. Landi, R. Girgis, J. Stephens, and E.
Wang and M. Sakthivel, S. Das, and K. Salem and R. Chapter 2 Power-Quality Standards This chapter offers some details on various standards addressing the issues of power quality in electric systems. Standards are needed so all end users industrial, commercial, and residential and transmission and distribution suppliers the utilities speak the same language when discussing power-quality issues. Standards also define recommended limits for events that degrade power quality.
Both of these standards focus on AC systems and their harmonics that is, multiples of the line frequency. IEEE Standard [2. The standard covers limits to the various disturbances recommended to the power distribution system. The standard is a revision of an earlier IEEE work pub- lished in covering harmonic control. First, the utility has the responsibility to produce good quality voltage sine waves. The AC source is modeled as an ideal voltage source in series with a resistance Rs and a reactance jXs.
Secondly, end-use customers have the responsibility to limit the har- monic currents their circuits draw from the line.
Shown in Figure 2. The utility source has resistance R and line reactance jXs. The resist- ance and reactance model the impedances of the utility source, any transformers and switchgear, and power cabling.
Customer 1 on the line draws harmonic current Ih, as shown, perhaps by operating adjustable- speed drives, arc furnaces, or other harmonic-creating systems.
The voltage harmonic distortion limits apply to the quality of the power the utility must deliver to the customer. For instance, for systems of less than 69 kV, IEEE requires limits of 3 percent harmonic distortion for an individual frequency component and 5 percent for total harmonic distortion. Table High-voltage systems can have up to 2. Figure 2. Current distortions that result in a dc offset, e. The current harmonic distortion limits apply to limits of harmonics that loads should draw from the utility at the PCC.
Many different types of power-quality measurement devices exist and it is important for workers in different areas of power distri- bution, transmission, and processing to use the same language and measurement techniques. This range is allowable for infrequent use.
Note that voltage sags and surges go beyond these limits. The horizontal axis shows the duration of the sag or swell, and the vertical axis shows the percent change in line voltage.
This docu- ment includes measured power quality data taken from numerous sites. A similar curve has been proposed for semiconductor processing equipment: A comparison of these three curves is shown in Figure 2. Power-Quality Standards 19 Overvoltage condition Percent change in bus voltage 0. There are limits to the amount of harmonic pollution a power supply is allowed to inject onto the power line. These limits depend on the frequency of operation, and the power level of the power supply used.
Switching power supplies are discussed extensively in Chapter 7. The bus capacitor voltage will have Hz ripple due to the operation of the full-wave rectifier. The switching supply then chops the bus voltage at a very high frequency high, that is, compared to the Hz line frequency.
The line current is contains harmonics of the Hz line frequency, as well as high-frequency interharmonics from the switching power supply.
Through design combinations of switching methods and EMI filtering, we can reduce but never completely eliminate the high frequencies injected into the AC line. Another implementation that generates high-frequency harmonics on the line is the boost converter power factor correction circuit Figure 2.
This circuit is used in many high-power converters in the front end. This circuit draws high power factor current from the line, but the high-frequency switching of the MOSFET generates har- monics drawn from the line as well.
The Federal Communications Commission FCC , in their Rules, sub- part J, sets limits for the conducted emissions allowable on power lines injected from line-connected equipment [2. Class A covers indus- trial equipment, and class B covers residential equipment. When applying high- frequency switching supplies, one must be mindful of the various limits set forth by the regulating agencies [2.
For a power supply to comply with these limits, the peak of the spectral lines must fall below specified limits. Summary Power-quality standards address limits to harmonics and power-quality events at the point of common coupling in power systems.
Lee, M. Albu, and G. NW, Suite , Washington D. Djokic, G. Chapter 3 Voltage Distortion In this chapter, we shall discuss distortion of the line-voltage sine waves. Distortion to the line-voltage waveforms can be caused by transient or continuous disturbances. Examples of transient disturbances include lightning, motor starting and stopping, clearing faults, and other harmonic-generating occurrences.
A chart summarizing voltage distortion and its causes is shown at the end of this chapter. Voltage Sag 1 A voltage sag is an event where the line rms voltage decreases from the nominal line-voltage for a short period of time. Figure 3. This type of vari- ation can occur if a large load on the line experiences a line-to-ground fault, such as a short in a three-phase motor or a fault in a utility or plant feeder.
In Figure 3. Note that the line impedances cause a voltage drop when currents are drawn from the line. When the motor is energized, the motor current Im causes a voltage drop to other loads in the system at the point of common coupling PCC.
This average dip clearing time of roughly 6 cycles milliseconds is attributable to the circuit breaker switching time for clearing a fault. Example 3. Motor starting. This corresponds to a sag of roughly 15 percent. Voltage sag analysis. We shall next do a voltage sag analy- sis on a V line-line system.
The system is modeled as shown in Figure 3. With a line-line volt- age of V, the source presents a line-neutral voltage of V. The line reactance is 0. Systems [3. Voltage Distortion 29 R jXL 0. Top trace is line-neutral voltage with peak value The bottom trace is the voltage drop across the line impedance. We see that the inductive reactance results in a phase shift of: The rms value of the voltage drop across the line impedance is 51 V.
A capacitor can be added on the load end to help the power factor, as shown in Figure 3. The reactive power provided by the added capacitor —jXc can improve the power factor. The top trace is the instantaneous rms value of the voltage. The bottom trace is the line-voltage [3. Shown in Figure 3. The most common sources of impulsive tran- sients are lightning strikes Figure 3. Impulsive transients due to lightning strikes6 can occur because of a direct strike to a power line, or from magnetic induction or capacitive coupling from strikes on adjacent lines.
The frequency and amplitude of lightning-induced transients vary geographically, as shown in Figure 3. Voltage impulse due to a lightning strike. Note that the line impedance is 0. At high frequencies, the line impedance is dominated by the line inductance. In this case, the inductance is XL XL 0. The lightning strike then decays to zero in approximately microseconds.
The lightning strike is mod- eled as a triangular pulse of current injected onto the line. Voltage Distortion 33 example, we assume there are no lightning arresters or insulation break- down to limit the transient voltages. These transients can occur due to res- onances during switching. A circuit capable of exhibiting this phenom- enon is shown in Figure 3.
A power supply bus is shown with the bus having inductance L. A capacitor bank labeled C1 is connected at one end of the bus. This capacitor bank may be in place, for instance, for power factor improvement or for voltage sag improvement. The resultant resonance will be underdamped, and the cur- rent in the capacitor bank may look something like that in Figure 3.
Capacitor bank switching. The capac- itor bank may be for power factor correction, or for some other reason.
We see in Figure 3. The top trace is the instantaneous line-voltage, while the bottom trace is the current in the capac- itor. Voltage Distortion 35 capacitor bank is switched. The ripple in the load voltage is due to the capac- itor current that rings at the resonant frequency of the LC circuit. Interruptions can be a result of control malfunction, faults, or improper breaker tripping.
The top trace is the rms line-voltage.
The bottom trace is the first mil- liseconds of the interruption. With a finite line inductance, there is a finite switchover time from diode pair to diode pair. If we assume the line inductance is zero, how will this circuit operate? Looking at the rectifier output voltage Figure 3. In this circuit, D1 and D4 are on for the positive half-wave of the sine wave, and D2 and D3 are on for the negative half-wave.
At the sine wave zero crossing, the switchover from diode pair to diode pair occurs instantaneously. The effect of the inductor is to introduce a finite switchover time from one pair of diodes turning off to the other pair turning on.
During this switchover time, all four diodes are on and the output of the rectifier is zero. This effect is shown in Figure 3. This notching adds unde- sirable harmonics to the load voltage, and also reduces the average value of the load voltage. Note the notching in the output voltage wave- form. Welders Rolling Residences Internal A. A varying source of harmonic cur- rents includes welders and capacitor banks.
Voltage variation created by this setup couples to residential lighting through the distribution system. The harmonics produced by an arc furnace are unpredictable due to the variation of the arc during metal melting.
We see that during ini- tial melting, the harmonic content both even and odd harmonics of the line-voltage are relatively high. During the latter part of the arc furnace melt cycle, the arc is more stable and the harmonic current has dimin- ished.
Flicker is the human perception of light intensity variation. Table 4. October 24, A voltage imbalance can cause a reverse-rotating airgap field in induc- tion machines, increasing heat loss and temperature rise. Summary To summarize voltage distortion types and causes, see Figure 3. Disturbance type Description Causes Narrow pulse with fast rise and Load switching, fuse clearing, utility Impulse exponential or damped oscillatory switching, arcing contacts, lightning decay; 50 V to 6 kV amplitude, 0.
Cornick and H. Redl, R. Chapter 4 Harmonics and Interharmonics In this chapter, we shall discuss harmonics frequency components that are integer multiples of the fundamental line frequency and interharmonics high-frequency components.
For most of what we shall do in this chapter, the fundamental frequency used will be 60 Hz. Background As we mentioned in previous chapters, harmonics can adversely affect the operation of cables, capacitors, metering, and protective relays. To summarize, a brief listing of some systems and the effects of harmon- ics is shown in Table 4. Periodic Waveforms and Harmonics The notion that any periodic waveform can be broken up into a series of sine waves at the proper amplitudes and phase relationships was first worked out by Joseph Fourier, the French mathematician and physicist [4.
For instance, a square wave Figure 4. Also, note that the square wave has only odd harmonics that is, harmonics of the order 1, 3, The spectrum of the square wave is shown in Figure 4. Likewise, a triangle wave Figure 4. The square wave has only odd harmonics. This makes sense since the triangle wave more closely resembles a pure sine wave than a square wave, and therefore has fewer harmonics than the square wave.
Shown are the first har- monic at 60 Hz top trace , third and fifth harmonics, and the total waveform bottom trace that is the sum of the three harmonics.
Shown in Figure 4. Another waveform often encountered in power systems is the trape- zoidal waveform Figure 4. This waveform models a switching wave- form with a finite risetime and falltime.
The Fourier series for this waveform is given by [4. It can be shown that the two corner frequencies f1 and f2 are found by [4. The power dissipation in both cases is the same. For a sine wave of peak value Vpk, the rms value is Vpk Vrms 5! The rms value of a waveform can be interpreted by considering power dissipation. Looking at Figure 4. The power dissipation in both loads is the same at W. Remember that the rms value of a periodic waveform is the square root of the average value of the square of the waveform over a period.
Irms 5 I Pure sine wave A pure sine wave Figure 4. The rms value of this waveform is Irms 5 Ipk i t Ipk t Figure 4. In this case, i t is the inductor current. In this case, the rms value of the current is ipp Irms 5 2! In this case, i t is the capacitor current. Pulsating waveform The rms value of a pulsating waveform Figure 4. The rms value of the total waveform made up of the sum of i t Ipk Figure 4. Irms 5 2I1,rms 2 1 I2,rms 2 1 I3,rms 2 1???
Total Harmonic Distortion Total harmonic distortion or THD is a measure of how much harmonic content there is in a waveform. Crest Factor Crest factor is another term sometimes used in power systems analysis, and represents the ratio of the peak value to the rms value of a waveform.
For a sine wave Figure 4. Thus, the crest factor is 1. For a square wave Figure 4. Example 4. A truncated square wave. The total waveform for this example is 4 4 4 4 vstd 5 a b sinsvtd 1 a b sins3vtd 1 a b sins5vtd 1 a b sins7vtd p 3p 5p 7p The rms value of the first harmonic is 4 V1,rms 5 5 0.
Harmonics and Interharmonics 55 Truncated square wave 1. The THD is Neutral current in three-phase systems. The three-phase voltages have the form: The phase currents are: V ia 5 a b sinsvtd R V ib 5 a b sinsvt 2 d R V ic 5 a b sinsvt 2 d R The neutral current is the vector sum of the three-phase currents. Referring to the phase current phasor diagram Figure 4. Nonlinear loads. Power-line harmonics are created when nonlinear loads draw nonsinusoidal current from a sinusoidal volt- age source.
These har- monics can result in neutral current that exceeds the individual phase current. Therefore, the magnitudes of the current in each phase are equal to one another.
Mathematically, we can express the current in phases a, b, and c as: We see that I1 is the amplitude of the fundamen- tal, and the Ins are the amplitudes of the odd harmonics. There are phase shifts, denoted by un, for each of the harmonics as well. In many three-phase circuits, the third harmonic is the dominant harmonic. In three-phase systems where there are third-harmonic currents, the degree phase shift for the funda- mental results in a degree phase shift for the third harmonic.
This means that the third-harmonic currents from each phase conductor are in phase with one another, and that the neutral current is equal to the sum of the third-harmonic amplitudes from each of the phases, or: Note that the peak of the 60 Hz fundamental is 1.
Shown in the bottom trace of Figure 4. Next, we add up the sum of the phase currents to get the total neutral current. The top traces show the fundamental and third harmonic currents. The bottom trace is the vector sum. Note that the vector sum of the fundamental of the neutral current is zero. The vector sum of the third-harmonic neutral current is three times that of the third-harmonic amplitude of each phase.
Total harmonic distortion. The THD for this waveform is found simply by: Effects of load current harmonics on load voltage and THD. Figure 4. VLOAD 0. Next, we add a load current that draws a fifth-harmonic current of 50 A Figure 4. The fifth-harmonic current results in significant load volt- age distortion.
The resultant waveform Figure 4. Harmonics cause many detrimental effects in equipment. References [4. New York: Dover Publications, Inc. Mardiguian, M. Erickson and D.
Maksimovic, Fundamentals of Power Electronics, 2nd ed, Springer, Harmonics are generated by rectifiers, line-frequency converters, and nonlinear magnetics. Interharmonics are created by high-frequency switching power supplies.
Background A typical setup that shows how harmonic currents can affect power quality is shown in Figure 5. An AC voltage source is displayed, with its associated line reactance, Xs, and resistance, Rs. This AC source can be single-phase or three-phase. The line inductance depends on the length of the line and the geometry of the conductors.
The line resist- ance, on the other hand, depends on the length of the wire and the wire gauge used. The AC source voltage then supplies a nonlinear load that draws harmonic current. Typically, this harmonic source is a rectifier or other converter. In Figure 5. Note that the voltage labeled Vpcc for voltage at the point of common coupling or PCC has harmonic components due to the harmonic current Ih drawn by the load running through the line impedance.
If this voltage at the PCC feeds additional equipment other than the harmonic generating cir- cuit, the resulting voltage distortion can disrupt operation of the equip- ment if the harmonic distortion is too high. In low-power applications using single-phase power, rectifiers are used as the front-end of switch- ing power supplies and small motor drives. A single-phase, full-wave rectifier with current source load is shown in Figure 5.
This circuit is an idealized model of systems where the load draws approximately constant current. In this simplified model, the line current is a square wave. Note that the line current drawn by this rectifier circuit is very harmonic-rich, with a THD of Another rectifier is the full-wave rectifier with capacitive filter Figure 5.
In this type of circuit, the diodes are only on for a frac- tion of a 60 Hz cycle, and the capacitor charges near the peaks of the input sine wave voltage.
Example 5. Line-current harmonics. Line current is a square wave. With a F bus capacitor, the load voltage ripple is about V peak-peak Figure 5. Note that the line current waveform has significant harmonic distortion Figure 5.
As shown in Figure 5. In Table 5. The THD for the rectifier with a F capacitive filter is approximately per- cent, and the peak-peak output ripple is 25 V. This result illustrates one trade-off with this type of rectifier. Three-phase power labeled phases a, b, and c is full-wave rectified by the six-pulse rectifier.
The rectified voltage is filtered by the high-voltage bus capacitor, Cbus, generating a DC voltage, which is used by the subsequent inverter. The three-phase inverter generates the three-phase currents necessary to drive the motor. A six-pulse rectifier is shown in Figure 5. Assuming that the load approximates a current source with very large load inductance , the line current drawn from the rectifier shows a THD of 31 percent, and an absence of a third-harmonic and all triplen harmonics Figure 5.
We can show that the harmonic amplitudes of the phase currents of the ideal six-pulse rectifier with current source load, IL, are [5. The resultant phase current waveform Figure 5. This is because the pulse topology elimi- nates the 5th, 7th, 17th, and 19th harmonics, leaving the 11th, 13th, 23rd, and 25th harmonics. The line waveform is rectified by a power-factor corrected boost converter. The power factor correction circuit switches at a frequency much higher than line frequency.
Usually, the line side has passive filter- ing to help reduce the high-frequency harmonics drawn from the AC line. Figure 5. The induc- tor has N turns; a mean path length, lc; core permeability, mc; and a core cross- sectional area, Ac. From magnetic circuit analysis, we can find the inductance of this structure as: Equivalently, saturation means the permeability of the core decreases with a corresponding decrease in the inductance at high current levels.
This nonlinear property of the magnetic core requires that the current has harmonic distortion, as shown in Figure 5. Other Systems that Draw Harmonic Currents High-frequency switch-mode power supplies are covered extensively in Chapter 7. Other sources of harmonic currents are adjustable speed drives ASDs , motors, and arc furnaces. Harmonics can cause many detrimental effects, including resonances with power factor correction capacitors, the heating of neutral conductors, the false tripping of relaying equipment, and the heating of capacitors.
References [5. Maksimovic, Fundamentals of Power Electronics, second edi- tion, Springer, Chapter 6 Power Harmonic Filters In this chapter, we will discuss methods of reducing harmonic distortion in line voltages and currents through the use of filters. Filters can be implemented with either passive components capacitors and magnetics or active filters. Introduction Industrial and commercial power systems usually incorporate power capacitors to improve the power factor and provide reactive power for voltage support [6.
When the system includes sources of harmonic cur- rent, such as power electronic converters or adjustable speed drives ASDs , the capacitors may be used in power harmonic filters to mini- mize the harmonic voltage applied to the system load at the point of common coupling PCC.
The current harmonics produced by power converters, usually polyphase rectifiers, can be reduced in one of three ways: When these measures do not reduce the current harmonics to an acceptable level, power harmonic filters can be introduced to obtain further reduction.
The current harmonics, of themselves, are seldom the problem, such as when the third harmonic produces overheating in the three-phase feeder neutral conductor. The problem occurs when a higher-order current harmonic is resonant with the capacitors and system reactance to pro- duce excessive voltages at the point of common coupling PCC. A model of a distribution system powering a nonlinear load is shown in Figure 6.
The utility is modeled as a source with impedance con- sisting of line resistance and line inductance. The source is then stepped down with a transformer. The resulting voltage typically V line-to- line in three-phase systems drives nonlinear loads such as motors and other equipment. Shown in Figure 6. The power-factor correction capacitor has been converted to a series-tuned passive filter. In the nonlinear load, for example, an ASD requires a fun- damental frequency current for operation, but can be represented as the source of harmonic currents into the system.
The harmonic cur- rents and voltages are described as follows: A motor load, nonlinear load, and a filter reactor are part of a power factor correction circuit. The standard does this by means of the Tables A very large load has an SCR of 10 and maximum harmonic volt- ages of 2.
A very small load has an SCR of and max- imum harmonic voltages of 0. In order to achieve the voltage harmonic limits of Table The har- monic current is shown in Figure 6. The current is the resultant of the converter current Ih and the filter current Ihf. In addition, the TDD total demand distortion1 must be less than Figure 6. Line reactor One of the simplest harmonic filters is the line reactor2 shown as the three-legged inductor in Figure 6. This magnetic component is often used in the line in series with motor controllers and other converters that draw significant harmonic current.
The reactor presents high impedance to high frequency currents while passing the fundamental. The theoretical waveform of the line current of the six-pulse con- verter rectifier is shown in Figure 6. This first figure assumes no line inductance. When we add a line reactor, the inductance of the reac- tor causes the converter to exhibit a significant commutation time. The 2 The line reactor is basically a series inductor. The reactor does not reduce the 5th and 7th harmonics significantly, but does reduce the 11th harmonic and higher— for example, the 11th is reduced from 9.
The reactor will also reduce the magnitude of the short-circuit current within the converter. In Figure 6. For line reactor applications, the reac- tor is usually rated in the percent voltage drop at the rated load current. The diagram illustrates the typical reduction in harmon- ics and total harmonic distortion THD that can be accomplished through the use of line reactors.
Without the reactor, we see a THD of The filter is usually placed as shown in Figure 6. The capacitors of the filter also provide reactive power at the fundamental frequency 60 Hz for power factor correction. The filter is usually made up of one or more sections, as shown in Figure 6. The single-tuned RLC filter for each harmonic frequency is the most common.
The impedance Z of the single-tuned section shown in Figure 6. The resistance R is due to the winding loss and the core loss of the inductor. The quality factor, or Q of an inductor, is given by: The series resonant circuit has a dip in its series impedance at resonance at the frequency where the inductive impedance and capacitive impedance exactly cancel each other out.
For other than resonance, the magnitude of Z is given by: The impedances of the L and C at resonance are selected for the example as 0. Example 6. A series resonant filter used on an AC line is shown in Figure 6.
Inductor Ls models the inductance of the source. A harmonic filter designed to attenuate fifth-harmonic components for an adjustable speed drive4 application is shown in Figure 6. In 4 In the power world, capacitors are often specified not by the capacitance value, but by the VAr rating. VAr stands for volt-amperes reactive. Power Harmonic Filters 87 Figure 6. Harmonic filters have also been used to reduce har- monic interference with telephone systems.
The filter is designed to attenuate higher-order harmonics such as the 5th, 7th, and 11th that are generated by the nonlinear load. Generally, the filter components are tuned a few percent below the harmonic frequency [6. In this design example, each filter section is tuned 4 percent below the filtered harmonic.
The series resonant frequencies of the three series resonant circuits are 1 1 f1 5 5 5 Hz 2p 2L1C1 2p 2s 3 ds 3 d 1 1 f2 5 5 5 Hz 2p 2L2C2 2p 2s 3 ds 3 d 1 1 f3 5 5 5 Hz 2p 2L3C3 2p 2s 3 ds 3 d These are the frequencies at which we expect significant attenua- tion, as evidenced in the PSPICE plot of Figure 6. We also see peak- ing at frequencies below the three series-resonant frequencies.
The harmonic generating load is modeled as a current source of value Ih. This filter provides mimima at the 5th, 7th, and 11th harmonics. Note the circuit of Figure 6. First, we need to determine what the IEEE limits are for line har- monic currents, using Table From Table Therefore, both the 5th and 7th harmonics violate this standard. We also violate the TDD specification, which is 12 percent.
The line current is shown in Figure 6. A spectrum of the line current Figure 6. A hypothetical nonlinear load draws fundamental 60 Hz and harmonic currents from an AC source. The AC source is modeled as an ideal V source in series with a H inductance and a line resistance of 0. The load draws harmonic currents with the strength shown in Table 6.
We can calculate the expected total harmonic distortion of the load volt- age using the calculated values shown in Table 6. We have found the magnitude of the line impedance at each harmonic frequency, and then the voltages at the harmonics are calculated. So, the THD of the load voltage is In the frequency domain, we see harmonic distortion, as expected, at the 5th, 7th, and 11th harmonics, as shown in the Fourier spectrum of Figure 6.
We can reduce the harmonic distortion in the load voltage using the circuit of Figure 6. The three series-resonant circuits are tuned 4 percent below the 5th, 7th, and 11th harmonics. Looking at the spectrum Figure 6. TABLE 6.
There is no unique solution to the design problem, so in each case a careful trade-off analysis must be performed. Practical con- siderations include the following: The harmonic filter sections are tuned below the harmonic frequency to prevent the filter frequency from shifting upward if one or more capacitors fail and their fuses blow.
Typical orders are 4. Capacitors are protected by fuses in small groups to minimize the effect of fuse blowing. The whole filter can be divided into assemblies, each protected by a circuit breaker. Filters provide fundamental frequency reactive power vars. Portions of the filter can be switched off at times of light load to limit overvoltage.
Capacitors and inductors must be specified so that the combination of ratings L and C does not result in resonance at an undesired frequency. In other words, we do not want positive peaks in the filter impedance curves to correspond with harmonic frequencies. The current rating of the inductors and the voltage rating of the capacitors must include the fundamental and harmonic com- ponents.
Filters should be located electrically close to the nonlin- ear load that produces the harmonic currents. A change in system impedance or component variations due to aging or temperature can result in some detuning of the har- monic filter. Especially at high power levels, the cost of magnetic and capacitive components can be high. High- frequency switching devices, including the metal-oxide semiconductor field-effect transistor MOSFET and insulated gate bipolar transistor IGBT have emerged in recent years with high current and voltage ratings.
These devices switch on and off with fast switching speeds. Thus, high-frequency converters can be designed with good power deliv- ery efficiency using them. An alternative to passive filters are active filters, where power electronics components are used to actively inject harmonics to cancel harmonics in the line current.
This method has been used in the past in lower power electronics applications [6. The diagram of one type of active harmonic filter is shown in Figure 6. Note that the nonlinear load draws harmonic current, Ih, from the power source. The active compensator senses the harmonic current and injects a compensation current, Ic, which cancels the harmonic current.
The net supply current, Is, contains only the fundamental.
The compensator switches at a very high frequency compared to the fundamental fre- quency—hence, the VA rating of the energy storage devices in the com- pensator can be minimized. Purported advantages of active filters are [6. The goal is to have the supply current be the only fundamental harmonic. The load draws har- monic current, Ih, and the active compensator injects a current, Ic, to cancel the harmonic content in the line current.
The filter can be tuned under microprocessor control if, for instance, the system impedance changes. The high switching speed of devices allows energy storage elements capacitors and inductors to be of smaller weight and volume.
They are more flexible in application compared to pas- sive filters. Of course, the purported advantages of active filters must be weighed against extra design time and cost. In this method, harmonic reduction and reactive power compensation is shared between a passive filter and a modest active filter. Typically, the active filter section is rated at a few percent of load kVA.
Summary In this chapter, we have discussed power harmonic filters, both passive and active. Passive filters can be as simple as a line reactor, or as complicated as a multisection filter with individual sections tuned to resonant fre- quencies.
Active filters afford design flexibility and smaller physical size. In all cases, filters are designed so that IEEE limits are met. McGranaghan and D. Gonzales and J. LaWhite and M. Chen, F. Blaabjerg, and J. Rivas, L. Moran, J. Dixon, and J. Fujita and H. Bhattacharya, P.
Cheng, and D. Chapter 7 Switch Mode Power Supplies In this chapter, we shall examine high-frequency switching power supplies. Typically, switching frequencies are in the few-kiloHertz range to upwards of a megahertz or higher. Due to the high switching speed of these power supplies, and also due to the fast rising and falling edges of voltages and currents, these converters create significant high-frequency harmonics.
Background Switch mode power supplies are used extensively in consumer and industrial equipment such as personal computers and battery chargers. These fast switching frequencies have a detrimental effect on electromagnetic compatibility EMC because of conducted electromagnetic interference EMI to the power line.
In each case, there is switching going on at frequencies much higher than the line frequency. In recent years, the United States and Europe have placed stringent requirements on the harmonic pollution injected into power lines. In this chapter, we will discuss high-frequency power supply issues and other technical chal- lenges related to harmonic injection and EMI. The input AC source is rectified, and the resultant rectified voltage is chopped at a high fre- quency to produce the desired DC output s.
The load presented by the input rectifier is a large capacitor, so the line current is therefore highly discontinuous, as shown in the typical waveform of Figure 7. A typ- ical spectrum of the input current is shown in Figure 7. Numerous types of switching power supplies are used in offline appli- cations, and we will discuss some representative examples.
Figure 7. The switch is ON for a fraction of a switching cycle of D percent. A full-wave rectifier at the front end of the flyback converter converts the AC input waveform to a DC waveform, which is filtered by the bus capac- itor, CBUS. The voltage across the bus capacitor is used to periodically ener- gize the primary side of the isolation transformer. When the switch turns off, energy is dumped to the output capacitor. This process repeats itself over and over at the switching frequency, fsw.
This switching action gen- erates frequency components at multiples of the switching frequency fsw to be drawn from the line through the full-wave rectifier. The bus capacitor will have some series inductance, and at high frequencies some of the switch current can bypass the bus capacitor and enter the utility line. By properly controlling the high-frequency switch, the first harmonic of the line current is forced to be sinusoidal and in-phase with the line voltage, improving power factor to be near percent.
The push-pull and forward converters are shown in Figure 7. Also note that the characteristic drain current risetime and falltime is tR and that TD is the pulse width of the drain current. The spectrum of the drain current includes a number of impulses at multiples of the switching frequency.
In Chapter 4, we showed that f1 and f2 are found by: The switching period is T, the pulse width is TD, and the risetime of the current pulse is tr. Example 7. Spectrum of boost converter current. The spectral lines occur at multiples of kHz. From kHz to Above Note that the fundamental switching frequency is kHz, and that the overall spectrum of the switch current is as shown in Figure 7. Boost current spectrum with slower risetime and falltime.
Above 6. Slower switching of the MOSFET causes the higher frequency harmonics to roll-off faster, but incurs a penalty in power supply efficiency. Testing for conducted EMI Conducted EMI is the terminology used for the harmonic pollution that high-frequency circuits put onto the utility line. These standards are discussed in Chapter 2. The LISN provides a controlled impedance in this case 50 ohms through which we measure the harmonic current injected onto the util- ity line by the device-under-test D.
We then measure the voltage across the resistor using a spectrum ana- lyzer.