Integrated high-quality rectifier-regulators - Semantic Scholar
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999
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Integrated High-Quality Rectifier–Regulators Michael T. Madigan, Member, IEEE, Robert W. Erickson, Senior Member, IEEE, and Esam Hamid Ismail, Member, IEEE
Abstract—A new family of ac–dc converters is derived which integrate the functions of low-harmonic rectification, low-frequency energy storage, and wide-bandwidth output voltage control into a single converter containing one, two, or four active switches. These converters utilize a discontinuous conduction mode input inductor, an internal energy storage capacitor, and transformer secondary circuits which resemble the bridge, forward, flyback, or Cuk ´ dc–dc converters. A large-signal equivalent circuit model for this family is presented, which uses the “loss-free resistor” concept. Design strategies and experimental results are given. High-performance regulation with satisfactory line-current harmonics is demonstrated with conventional duty-ratio control. Further improvements in line current are possible by simultaneous duty-ratio and switching-frequency control.
Fig. 1. Single-phase power converter using a high-quality rectifier (HQR), energy storage capacitor, and a dc–dc converter.
Index Terms— AC–DC power conversion, boost integrated with flyback rectifier/energy storage/dc-dc converter, buck rectifier/energy storage/dc-dc converter, low-harmonic rectifiers, power-factor correction.
I. INTRODUCTION
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WING TO THE growing concern regarding harmonic pollution of the power distribution system, and the adoption of standards such as IEC 1000-3-2 [1], there is a need for single-phase power supplies with ac line currents that are low in harmonic content and have power factor close to unity. A typical costly system which allays these concerns, shown in Fig. 1, involves the addition of a second converter for input current waveshaping at the ac line side of a conventional switching power supply. In this paper, a new family of converters is introduced which inherently draw line-current waveforms of high quality. As depicted in Fig. 2, it is possible to construct a single converter, containing a single transistor, which performs all of the functions performed by the system of Fig. 1. Integrated high-quality rectifier/dc regulator (IHQRR) topologies based on the flyback, buck, and other dc–dc converters are derived here, control strategies are developed, and the resulting systems are experimentally verified. The key to development of an IHQRR is the recognition that the low-frequency components of the input voltage the energy storage capacitor voltage and the load must all be independent and, hence, the converter voltage topology must possess sufficient degrees of freedom to allow these voltages to vary arbitrarily. Manuscript received October 25, 1997; revised January 14, 1999. Abstract published April 18, 1999. M. T. Madigan is with Unitrode Corporation, Cary, NC 27511 USA. R. W. Erickson is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425 USA. E. H. Ismail is with the Department of Electrical Engineering, College of Technological Studies, Al-Shaa’b, Kuwait 36051. Publisher Item Identifier S 0278-0046(99)05614-2.
Fig. 2. Single-phase power converter using a single converter which has the integrated functions of high-quality rectification, capacitive energy storage, and the wide-bandwidth output voltage regulation (an IHQRR).
There are two ways to accomplish this. First, we could place and which block the differences impedances between in the low-frequency components of these voltages. This is an undesirable approach because it requires large low-frequency reactances. The second approach is to place switching elements (highfrequency-switching transistors and/or diodes) between and , which block the difference in the low-frequency components of these voltages. This is the preferred approach. It requires that any network loop which contains at least and also contain at least one two of the elements diode or transistor. It is possible to construct such an IHQRR a diode, network which contains a loop comprised of and high-frequency reactive elements which filter only highfrequency switching harmonics, and which contains another a transistor, and high-frequency reloop comprised of active elements. and is obtained, Once the required independence of then it is possible to cause the input line current to be proportional to the input line voltage. Two approaches are commonly used here. First, feedback can be used to force where is the rectifier emulated input resistance. Second, certain converters are known to naturally
0278–0046/99$10.00 1999 IEEE
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(a)
(b)
(c) Fig. 3. (a) Integration of a DCM boost rectifier with a flyback converter results in (b) a BIFRED. (c) Schematic of a BIFRED which includes the bridge rectifier and the high-frequency EMI filter.
emulate a resistor, without active feedback. An example is the flyback and boost converters operating in discontinuous conduction mode (DCM) [2]–[4]. II. DERIVATION
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TOPOLOGIES
A. Boost Integrated with Flyback Rectifier/Energy Storage/DC–DC Converter (BIFRED) At low power levels (100 W), a conventional approach is to use a boost converter for input current waveshaping, and a flyback dc–dc converter for isolation and load voltage regulation. Hence, let us consider integration of a DCM boost HQR with a flyback dc–dc converter, as shown in Fig. 3. To preserve the nature of the input stage, the converters must be combined in such a way that the input inductor operates independently in the DCM. The resulting IHQRR is called a BIFRED. To understand how this can be accomplished, let us examine the operation of the two-converter system in Fig. 3(a). Each switching period contains three subintervals. Assume that and are synchronized and that the flyback switches converter operates in continuous conduction mode. and During the first subinterval, only switches conduct. During this subinterval, the DCM boost HQR inis energized by the rectified line voltage through ductor and coupled inductor is energized by energy switch through Load receives energy storage capacitor during this subinterval. During the only from capacitor and conduct. Energy second subinterval, only diodes receives all of the energy of through storage capacitor Inductor is completely deenergized at the end of this transfers some of its energy to interval. Coupled inductor and to filter capacitor through diode The the load becomes reverse third subinterval is initiated when diode
biased by the input current reaching zero. Diode conducts remains only in this interval. The energy state of capacitor continues to at a constant positive level. Coupled inductor transfer some of its energy to the load and to filter capacitor through diode as in the second subinterval. Now, combine the two converters in Fig. 3(a) into one must be converter, containing a single switch. Inductor in order to permit the input inductor in series with diode to operate in DCM. Also, diode cannot be eliminated because the coupled inductor does not necessarily operate in has two network DCM. Notice in Fig. 3(a) that switch functions; it controls the energy flow into the primary of and it aids in balancing the volt seconds of Switch can be replaced with a conductor by connecting the energy storage to the other capacitor in series with it and moving switch Also, the polarity of the primary of coupled side of diode must be reversed to preserve the states of diode inductor during each interval. The result of combining the two converters in Fig. 3(a) is the IHQRR in Fig. 3(b), which is called a BIFRED. The BIFRED of Fig. 3(b) bears a resemblance to a Sepic converter [5]. which is in series The most obvious difference is a diode Diode permits the BIFRED to with the input inductor operate in modes which are not possible with a Sepic. As a result, the BIFRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc–dc Sepic is not. falls to zero, diode stops When the current in conducting, regardless of the energy state of the coupled This permits to continue conducting and inductor to decrease. In allows the energy level of coupled inductor contrast, when a Sepic converter operates in DCM, neither the input inductor nor the coupled inductor can change their stored energy levels during the discontinuous subinterval, as seen by [6]. Hence, a BIFRED has an independence of inductive
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Fig. 4. Schematic of a BIBRED, which includes the bridge rectifier and the high-frequency EMI filter.
energy transfer which is not possible in a Sepic. The resulting differences in the line-current waveforms are demonstrated in Section V. B. Boost Integrated with a Buck Rectifier/Energy Storage/DC-DC Converter (BIBRED) The integration of a DCM boost HQR with a buck dc–dc converter results in a BIBRED, as shown in Fig. 4. The synthesis procedure of this IHQRR is similar to the procedure for a BIFRED. Isolation can also be obtained, in a manner similar to that used for the dc–dc C´uk converter [7]. , which is in series The most obvious difference is diode The additional diode permits the BIBRED to with operate in modes which are not possible with a C´uk converter, and the BIBRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc–dc C´uk converter is not. The additional diode of the BIBRED permits the input inductor current to remain at zero during the discontinuous subinterval, independent of the other reactive and capacitive states. In contrast, when a C´uk converter enters DCM, neither the input inductor nor the output inductor can change their energy levels during the discontinuous subinterval, as described by C´uk [8]. The resulting differences in the line-current waveforms are demonstrated in Section V. Other isolated BIBRED bridge topologies are also possible to derive as described in [9].
(a)
III. DESIGN A. Modeling and Design of the BIFRED The modeling approach for the BIFRED converter is based on [2], [4], and [10]. The class of two-port lossless power processing networks are known as “loss-free resistors” (LFR’s) [11], and have been found to be a useful artifice for modeling and understanding low-harmonic rectifier circuits. The dynamic models contain an LFR to model the rectification process, and a dc transformer network [12] to model the output dc–dc conversion process of the network. The model is used to solve for the quiescent operating point, determine DCM boundaries, and derive converter design equations. Design of the BIFRED in Fig. 3(c) begins with ensuring the correct mode of operation, throughout the complete range of instantaneous line voltage. Relevant currents and voltages and are demonstrated in of network elements Fig. 5(a).
(b) Fig. 5. (a) Switching waveforms of various currents and voltages in the BIFRED of Fig. 3(c). (b) Large-signal nonlinear ac model of the BIFRED in Fig. 3(c).
1) DCM Definition: In the desired DCM, the switching cycle has three distinct intervals. During the first interval, only and diode conduct. During the second intertransistor and conduct. During the third interval, val, only diodes conducts. The motivation behind selecting this only diode particular mode is to guarantee that the energy in inductor is depleted before the energy in the coupled inductor is dewere depleted before in this topology, may pleted. If will become dependent on , which stop conducting and prevents this converter from functioning as an IHQRR. With this choice of mode, one avoids this possibility by designing never reaches the ground state. the converter such that
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The first interval of the switching cycle starts when tranturns on, causing the current in inductor to sistor ramp up from zero with a slope which is proportional to the conducts and diode instantaneous line voltage. Diode is reverse biased. At the end of this interval, an amount of which depends only on the input line energy is stored in voltage and is independent of the currents and voltages of the other inductors and capacitors of the converter. turns The second interval is initiated when transistor to ramp down with a slope off, which causes the current in proportional to the instantaneous line voltage minus the energy minus the output voltage reflected storage capacitor voltage and diode conduct. to the primary. Both diode The third interval commences when the current in reaches zero. Transistor remains off, is reverse biased, conducts. During this interval, the potential energy and and remain unchanged. Capacitor and the levels of and passes energy to the load. load receive energy from 2) A Large-Signal Model: Averaging over one switching cycle [13], [14] provides an analytic perspective of the overall action of the BIFRED. The resulting large-signal equations are given in (1) (2)
This equation implies that the input stage of the converter operates in the boost mode; the net voltage must be greater than the peak value of the ac line voltage. However, and the reflected load the energy storage capacitor voltage may individually be less than voltage 3) Steady-State Solution: Steady-state analysis can be performed by averaging the state equations over half of a line cycle. The nonlinear term must be averaged as a unit, since superposition does not apply to that term. Assuming that the and the switching period are constant and duty cycle the high-frequency neglecting the ripple of voltages and average state equations (2)–(4) are again averaged over a line half-cycle to give the steady state equations in (8) (9) (10) and requires the average Solution of the voltages value of the nonlinear term to be solved using the large-signal A nonseparable transcendental description of the voltage is formed by eliminating the current equation in from (8) and (10) and performing the averaging integral over a line half cycle. The result is
(3) (4) (11) where (5)
where and
and the nonlinear ratios of The equivalent resistance voltages in (1), (2), and (4) are energy related and can be modeled using a loss-free resistor with a dependent power or source [2], [4]. The power “consumed” by appears at the power source such that the network is lossless. This power source is connected between the converter input port and the remainder of the converter, such that its applied voltage is
Here, is the steady-state voltage conversion ratio of the effective boost input stage. The nonlinear relationship in (11) can be solved numerically for a specific case, or approximated for design by a ratio of a constant divided by a first-order polynomial as in
(6)
(12)
passing through the power source is Hence, the current divided by the voltage (6). Thus, equal to the power the nonlinear terms which are in (1), (2), and (4) describe the current from this dependent power source with the voltage described in (6) impressed upon it. It must be stressed that the dependent power source is neither a pure voltage source nor a pure current source, and is inherently a nonlinear element. A comparison between the waveform of in Fig. 5(a) and the input stage of Fig. 5(b) reveal that, in steady state, (6) must always be positive to maintain volt-seconds balance on , as shown in inductor (7)
(13)
(14) Equations (12)–(14) are accurate to within where between 1.4–3.0. Accuracy can 10% over the range of be improved with successive iterations of (11). The closedform (12)–(14) approximate the steady-state solution of the capacitor voltages in a BIFRED.
MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER–REGULATORS
4) Mode Boundaries: Steady-state (9) and the waveforms of Fig. 5(a) can be used to formulate the inequality (15), which completely deenergize before the requires that inductor next switch cycle begins (15)
Essentially, the second interval must always be less than the total switch period minus the duration of the first interval. The current waveform of in Fig. 5(a) relates the duration of the second interval with the capacitor voltages and the duration of the first interval. The length of the second interval is maximum when the instantaneous line voltage is at a maximum. The inequality in (15) describes the maximum duration for a given line-to-output transfer ratio which will allow the inductor to completely deenergize. Among the reasons to use the maximum duration is to reduce the rms currents in inductor Furthermore, the longer the first interval is relative to the second interval, the more resistive the BIFRED appears to the ac line. Equation (15) can be rearranged to the approximate form by as in (16), which includes the conduction coefficient the substitution of (14) (16) Equation (15) is used to solve for the duration of the first interval for a given turns ratio and a desired line-to-output can be determined as a function ratio. Then, the inductance of the previously given parameters, the switching period and the load resistance by use of (16) and the definition (11) of the conduction coefficient The dependence of the DCM boundaries on the value of is more subtle than that of because current inductor has large-signal variations during normal operation. These variations include a dc component and a twice-line-frequency component, the phase shift of which is 180 relative to the and capacitor are rectified line voltage. Since inductor chosen for filtering switching harmonics, and the switching and frequency is much higher than twice the line frequency, can be approximated as a short circuit and an open circuit, respectively. Solution of the resulting equivalent circuit yields
(17)
The current of the dependent power source in the equivalent circuit model in Fig. 5(b) can also be approximated as a function of known quantities as in
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The transfer ratio of (17) reveals a dc gain which can be different from the high-frequency gain. When the steady-state duty ratio is less than 1/2, the high-frequency gain is lower than the dc gain. The converse is also true. Since is very large, the shift in gain and the associated phase shift of 180 occurs at frequencies which are much lower than twice the line frequency. Thus, current is essentially minus plus a dc offset current. Current must always be positive in the to prevent an unwanted DCM, and maintain diode conducting state during the second and third intervals. Hence, for operation in the correct mode, we require that the dc gain of (17) be greater than the high-frequency gain, or (19) The restriction in (19) is further limited when considering the The minimum value of exact minimum value of current is given by (20) and it can be exactly solved using techniques similar to those used to find (11)
(20) Restrictions set by (19) and (20) neglect switching ripple because they are concerned with states which are averaged over a switch cycle. Equation (21) is an additional criterion which from completely deenergizing must be satisfied to prevent (21) must not completely deenergize during normal Capacitor and , operation. A transfer ratio can be formed between given in which leads to the lower limit for (22)
is the allowable proportion of ripple voltage where The limiting case for the smallest value of capacitor in is when the proportion of ripple in voltage is one. Typically, will be much larger than this limit, in that the capacitor proportion of ripple in voltage may be indirectly specified in terms of a holdup time of several line cycles. Capacitor is chosen to meet a switching ripple specification which is a fraction of the dc output voltage, as in (23). Thus, capacitor cannot completely deenergize unless the low-frequency output ripple is inadvertently too large (23)
(18) is a rectified sinusoid, varies between zero and Since can now some finite peak value. The minimum value of be estimated using (18) and the transfer ratio between and in (17).
is the fraction of switching in where In summary, a BIFRED can be designed for a given line voltage, turns ratio, switching frequency, energy storage ripple, output voltage ripple, and output voltage using the following using (15). The duty ratio must be steps. First, select
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less than 1/2 per (19). Select using (16). Internal voltages and are then calculated using (12)–(14). The minimum in is calculated using (20). Current must current is then be positive for the design to be valid. Inductor and are then selected to selected using (21). Capacitors meet ripple specifications using (22) and (23), respectively. B. BIBRED and Other Topologies Design of a BIBRED, as well as other bridge topologies presented in [9], follows many of the steps as described in designing a BIFRED; limited space precludes a detailed description here. However, an equivalent circuit model for the BIBRED is described in [9], while a complete analysis of a full-bridge BIBRED is presented in [15]. IV. CONTROL
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A. Simple Duty-Ratio Control Scheme Duty-ratio variations result in variations in both the output voltage and the line current. The voltage conversion ratio between the energy storage capacitor and load and, hence, also the output voltage, is proportional to the duty ratio in (14). The line current is a function of equivalent resistance which, in turn, is a function of the duty ratio, as seen in (1) and (5). Thus, duty ratio can be used to control output voltage or line current. This family of IHQRR’s inherently produces line-current waveforms of low, but nonzero harmonic content, which, in most applications, can meet the harmonic limits in [1] without additional active control. Because of the low-frequency internal energy storage built into these converters, wide-bandwidth control of the output voltage is possible, without significantly degrading the line-current waveform quality. When the controller corrects for line harmonic disturbances in the output voltage, it affects line-current harmonics. This is because the line current is a function of duty ratio. Line-current distortion due to output voltage feedback can be minimized by increasing the size of the energy storage capacitor; in practice, however, such measures may be unnecessary. Laboratory results confirm that the total harmonic distortion of the line current for the closed-loop BIBRED is slightly lower than the total harmonic distortion during open-loop operation (21% compared to 19%). Thus, in this specific case, the output voltage feedback has a minimal effect on the line-current harmonic content. Regulation of output voltage using duty-ratio adjustments is also a method for controlling DCM flyback HQR’s [2]. However, the bandwidth of the IHQRR is much greater than the bandwidth of the simple HQR. This is because, in an IHQRR, the load is separated from the internal energy storage capacitor by reactive devices and semiconductor switching devices. To confirm this, output voltage regulation of a BIBRED and a DCM flyback HQR using duty-ratio control is demonstrated in Fig. 6, which shows the response of each of these converters to a sudden shift in load resistance. It is instructive to compare the response in Fig. 6 with that of a DCM flyback HQR under similar conditions [2]. The response time of the BIBRED is
(b) Fig. 6. Comparison of 2 : 1 load current transient response with output voltage duty ratio control. (a) BIBRED, 10-kHz crossover frequency. (b) DCM flyback HQR, 3.5-Hz crossover frequency.
Fig. 7. Block diagram of a variable switching period, fixed duty ratio modulator to reduce line-current harmonics.
many times faster than the DCM flyback HQR. The closedloop bandwidth of the BIBRED is approximately 10 kHz, compared to a bandwidth of 3.5 Hz for the DCM flyback HQR.
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TABLE I PARAMETER VALUES OF THE EXPERIMENTAL 40-W RECTIFIERS
(a)
(b) Fig. 8. Measured line voltage and current waveforms for 40-W BIFRED. (a) Open loop. (b) Using the switching frequency controller of Fig. 7.
B. Simultaneous Duty-Ratio and Switching-Frequency Control Returning to the nonlinear large-signal state equations in It is rearranged in (24) to demonstrate the (1), consider effects of variations in (24)
Fig. 9. Experimental switching frequency waveforms of the BIFRED described in Fig. 3(c) and Table I. These waveforms verify the mode of operation.
is given in (5). Incidentally, has the same form where is in both the BIFRED and the BIBRED topologies. If then the IHQRR presents a linear purely proportional to resistive load to the ac line. It can be seen that one method of eliminating harmonics in the line current is to vary such that it cancels the denominator of (24). Furthermore, the denominator of (24) is positive and less than one. Therefore, can be appropriately adjusted by variations in either duty or switching period or a combination of both. cycle A modulator which can independently vary the switching frequency and the duty cycle was constructed per the block diagram in Fig. 7, using an analog multiplier and a voltage controlled oscillator. Comparison of Fig. 8(a) and (b) reveals that line harmonics can be further reduced by use of the scheme described
above. Fig. 8(a) shows the line current of a 40-W BIFRED operating open loop with a fixed switching frequency and a fixed duty cycle. The total harmonic distortion of the line current in Fig. 8(a) is approximately 20%. Fig. 8(b) is the line current of the same 40-W BIFRED, operating with a variable switching period which is adjusted to correct line harmonics. The total harmonic distortion of the line current in Fig. 8(b) is approximately 4%. It is possible to use both duty-ratio adjustments and switchperiod adjustments to simultaneously regulate the output voltage and control the line-current harmonics. Equation (14) shows that the output voltage is directly proportional to duty Under ratio and a function of the switching period through the condition of the inequality in (25), it is found that the output voltage is not sensitive to changes in the switching
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Comparison of the line-current waveforms of (a) BIFRED, (b) Sepic converter, (c) BIBRED, and (d) C´uk converter.
period (25) However, the line current is proportional to the switching period. Thus, it is possible to regulate the output voltage with the duty cycle and reduce line harmonics with switch frequency variations. Phase control is a third method of control which can be used by the full-bridge BIBRED. Reference [15] addresses this issue in more detail. V. EXPERIMENTAL RESULTS A 40-W BIFRED and a 40-W BIBRED were designed and implemented to operate from a 110-V line to produce 20output voltage. The schematic for the BIFRED is given in Fig. 3(c), while the schematic for the BIBRED is given in Fig. 4. The component values are given in Table I. These values were chosen to assure that the modes of each IHQRR are the same as the modes which are described in Section III.
Switching waveforms of the BIFRED are shown in Fig. 9. These waveforms depict currents and near the peak of the line voltage. At that instant, the magnetizing is at a minimum, nonzero value, as discussed current of in Section III-A-4. The experimental waveforms agree with those of Fig. 5(a). Thus, the BIFRED operates in the desired mode. Comparable waveforms are also found for the BIBRED. of the BIBRED begins and ends each switch cycle Inductor at ground state, and it is the only reactive component in the BIBRED to do so. The switching waveforms of Fig. 9 demonstrate the difference between a BIFRED and a Sepic converter; the energy in a BIFRED returns to ground state, level of inductor even though the magnetizing inductance maintains a level of energy. Fig. 10(a) and (b) demonstrates the resulting difference in the line current of a BIFRED and a Sepic converter. The of the Sepic converter maximum current level in inductor and an output was reached at a line voltage of 50 V voltage of 8.8 V Under these conditions, the Sepic converter operates in continuous conduction mode. It can be seen that
MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER–REGULATORS
the BIFRED emulates a resistive load, while the Sepic linecurrent waveform resembles peak detection. These waveforms are not qualitatively changed when the Sepic operates in its DCM. Fig. 10(c) and (d) shows a similar comparison between a BIBRED and a C´uk converter. For this demonstration, the Sepic and C´uk converters were constructed simply by shorting in the respective BIFRED and BIBRED. The slow diode bridge rectifier diodes do not switch in the same manner , owing to the presence of input filter elements as and and, hence, the circuit input behavior is radically different. In the Sepic and C´uk converters, peak detection occurs is small in value, and has small impedance because inductor at the line frequency. As a result, the low-frequency comis very small. The remaining ponent of voltage across components, i.e., the energy storage capacitor and the four ac rectifier diodes, operate as a peak detection circuit. In the is able to support the lowBIBRED and BIFRED, diode frequency components of the voltage difference between the energy capacitor voltage and the rectified line voltage, such that peak detection need not occur. Thus, it has been demonstrated that the BIFRED and BIBRED naturally yield low-harmonic line-current waveforms which are distinctly different from Sepic and C´uk converters. VI. CONCLUSION A new family of converters has beem presented in this paper which exhibit low-harmonic line currents, internal energy storage, and wide-bandwidth output voltage response. These converters are derived by the integration of a DCM boost converter, energy storage capacitor, and a cascaded dc–dc converter. The function of the switches in each individual converter is examined under synchronized conditions, and redundant switch functions are integrated together. A valid integration preserves the low-frequency independence of the energy storage capacitor voltage. Steady-state and dynamic operation of this new family of IHQRR’s were analyzed with large-signal LFR models [Fig. 5(b)]. This modeling technique preserves the large-signal nonlinearities which affect steady-state and ac operation. Moreover, a step-by-step design procedure example using the BIFRED topology was presented. The other topologies in this family can be designed in a similar manner, [15]. Output voltage regulation using duty-ratio variations and a fixed switching period is the simplest method of control. Experimental results demonstrate that it is possible for these converters to have fast response and low line-current harmonic content. The harmonic content of the line current is low enough to satisfy typical IEC1000-3-2 specifications. Further reduction of line-current harmonics is possible with variable-switching-frequency control, as demonstrated in Fig. 8. The comparison of the BIBRED IHQRR with the DCM flyback HQR in Fig. 6 distinguishes this family as IHQRR’s, rather than simple low-bandwidth HQR’s. The comparison of the BIFRED
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and BIBRED line currents with the line currents of their respective dc–dc Sepic and C´uk converter counterparts, in Fig. 10, distinguishes these IHQRR’s from simple dc–dc converters. REFERENCES [1] Electromagnetic Compatibility (EMC)—Part 3: Limits Section II: Limits for Harmonic Current Emissions (Equipment Input Current 16A per Phase), IEC 1000-3-2, 1st ed., 1995. [2] R. Erickson, M. Madigan, and S. Singer, “Design of a simple highpower-factor rectifier based on the flyback converter,” in Proc. IEEE APEC’90, 1990, pp. 792–801. [3] S. Freeland, “Input current shaping for single-phase AC-DC power converters,” Ph.D. dissertation, pt. II, Elect. Eng. Dep., California Inst. Technol., Pasadena, Oct. 1987. [4] S. Singer and R. W. Erickson, “Canonical modeling of power processing circuits based on the POPI concept,” IEEE Trans. Power Electron., vol. 7, pp. 37–43, Jan. 1992. [5] R. P. Massey and E. C. Snyder, “High voltage single-ended DC-DC converter,” in Proc. IEEE PESC’77, 1977, pp. 156–159. [6] J. Sebastian, J. Uceda, J. A. Cobos, J. Aaru, and F. Aldana, “Improving power factor correction in distributed power supply systems using PWM and ZCS-QR Sepic topologies,” in Proc. IEEE PESC’91, 1991, pp. 780–791. [7] R. D. Middlebrook and S. C´uk, “Isolation and multiple output extensions of a new optimum topology switching DC-DC converter,” in Proc. IEEE PESC’78, 1978, pp. 256–264. [8] S. C´uk, “Discontinuous inductor current mode in the optimum topology switching converter,” in Proc. IEEE PESC’78, 1978, pp. 105– 123. [9] M. Madigan, R. W. Erickson, and E. Ismail, “Integrated high quality rectifier-regulators,” in Proc. IEEE PESC’92, 1992, pp. 1043– 1051. [10] S. Singer, “Canonical approach to energy processing network synthesis,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 767–774, Aug. 1986. , “The application of loss-free resistors in power processing [11] circuits,” IEEE Trans. Power Electron., vol. 6, pp. 595–600, Oct. 1991. [12] R. D. Middlebrook and S. C´uk, “A general unified approach to modeling switching-converter power stages,” in Proc. IEEE PESC’76, 1976, pp. 18–34. [13] S. C´uk and R. D. Middlebrook, “A general unified approach to modeling switching DC-DC converters in discontinuous conduction mode,” in Proc. IEEE PESC’77, 1977, pp. 160–179. [14] R. W. Erickson, “Large signals in switching converters, Part I: Distortion in switching amplifiers, Part II: Transients in switching regulators,” Ph.D. dissertation, Elect. Eng. Dep., California Inst. Technol., Pasadena, Nov. 1982. [15] M. A. Johnston and R. W. Erickson, “Reduction of voltage stress in the full-bridge BIBRED by duty ratio and phase shift control,” in Proc. IEEE APEC’94, 1994, pp. 849–854.
Michael T. Madigan (S’75–M’77) received the B.S. degree from the University of Colorado, Denver, in 1977 and the M.S. and Ph.D. degrees from the University of Colorado, Boulder, in 1988 and 1992, respectively, all in electrical engineering. He is currently an Applications Engineer with Unitrode Corporation, Cary, NC. Between 1992–1997, he served as a Power Electronics Consultant to Sony, Unique Mobility, and Echostar. Between 1977–1987, he designed control systems and power electronics for industrial and aerospace companies, such as Martin-Marietta and Honeywell. His research interests include power processing topologies, modeling, and control.
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Robert W. Erickson (S’82–M’82–SM’97) received the B.S., M.S., and Ph.D. degrees from California Institute of Technology, Pasadena, in 1978, 1980, and 1983, respectively. In 1982, he joined the faculty of the University of Colorado, Boulder, where he is currently a Professor of Electrical and Computer Engineering. He is the author of Fundamentals of Power Electronics (New York: Chapman & Hall, 1997), as well as more than 50 papers in power electronics conference proceedings and journal transactions. He teaches courses in power electronics, energy conversion, circuits, and control. His current research interests include low-harmonic rectification technology, modeling of converter systems and power components, low-voltage converters, and wind energy systems. Prof. Erickson received an IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award for 1996.
Esam Hamid Ismail (S’84–M’85) was born in Kuwait in 1962. He received the B.S. and M.S. degrees in electrical engineering from the University of Dayton, Dayton, OH, in 1983 and 1985, respectively, and the Ph.D. degree from the University of Colorado, Boulder, in 1993. From 1985 to 1988, he was with the Electrical Engineering Department, College of Technological Studies, Al-Shaa’b, Kuwait, where he is currently an Assistant Professor. His research interests include low-harmonic rectification, high-frequency power conversion, and the development of new converter topologies. Dr. Ismail is a member of Tau Beta Pi.
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Integrated High-Quality Rectifier–Regulators Michael T. Madigan, Member, IEEE, Robert W. Erickson, Senior Member, IEEE, and Esam Hamid Ismail, Member, IEEE
Abstract—A new family of ac–dc converters is derived which integrate the functions of low-harmonic rectification, low-frequency energy storage, and wide-bandwidth output voltage control into a single converter containing one, two, or four active switches. These converters utilize a discontinuous conduction mode input inductor, an internal energy storage capacitor, and transformer secondary circuits which resemble the bridge, forward, flyback, or Cuk ´ dc–dc converters. A large-signal equivalent circuit model for this family is presented, which uses the “loss-free resistor” concept. Design strategies and experimental results are given. High-performance regulation with satisfactory line-current harmonics is demonstrated with conventional duty-ratio control. Further improvements in line current are possible by simultaneous duty-ratio and switching-frequency control.
Fig. 1. Single-phase power converter using a high-quality rectifier (HQR), energy storage capacitor, and a dc–dc converter.
Index Terms— AC–DC power conversion, boost integrated with flyback rectifier/energy storage/dc-dc converter, buck rectifier/energy storage/dc-dc converter, low-harmonic rectifiers, power-factor correction.
I. INTRODUCTION
O
WING TO THE growing concern regarding harmonic pollution of the power distribution system, and the adoption of standards such as IEC 1000-3-2 [1], there is a need for single-phase power supplies with ac line currents that are low in harmonic content and have power factor close to unity. A typical costly system which allays these concerns, shown in Fig. 1, involves the addition of a second converter for input current waveshaping at the ac line side of a conventional switching power supply. In this paper, a new family of converters is introduced which inherently draw line-current waveforms of high quality. As depicted in Fig. 2, it is possible to construct a single converter, containing a single transistor, which performs all of the functions performed by the system of Fig. 1. Integrated high-quality rectifier/dc regulator (IHQRR) topologies based on the flyback, buck, and other dc–dc converters are derived here, control strategies are developed, and the resulting systems are experimentally verified. The key to development of an IHQRR is the recognition that the low-frequency components of the input voltage the energy storage capacitor voltage and the load must all be independent and, hence, the converter voltage topology must possess sufficient degrees of freedom to allow these voltages to vary arbitrarily. Manuscript received October 25, 1997; revised January 14, 1999. Abstract published April 18, 1999. M. T. Madigan is with Unitrode Corporation, Cary, NC 27511 USA. R. W. Erickson is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425 USA. E. H. Ismail is with the Department of Electrical Engineering, College of Technological Studies, Al-Shaa’b, Kuwait 36051. Publisher Item Identifier S 0278-0046(99)05614-2.
Fig. 2. Single-phase power converter using a single converter which has the integrated functions of high-quality rectification, capacitive energy storage, and the wide-bandwidth output voltage regulation (an IHQRR).
There are two ways to accomplish this. First, we could place and which block the differences impedances between in the low-frequency components of these voltages. This is an undesirable approach because it requires large low-frequency reactances. The second approach is to place switching elements (highfrequency-switching transistors and/or diodes) between and , which block the difference in the low-frequency components of these voltages. This is the preferred approach. It requires that any network loop which contains at least and also contain at least one two of the elements diode or transistor. It is possible to construct such an IHQRR a diode, network which contains a loop comprised of and high-frequency reactive elements which filter only highfrequency switching harmonics, and which contains another a transistor, and high-frequency reloop comprised of active elements. and is obtained, Once the required independence of then it is possible to cause the input line current to be proportional to the input line voltage. Two approaches are commonly used here. First, feedback can be used to force where is the rectifier emulated input resistance. Second, certain converters are known to naturally
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(a)
(b)
(c) Fig. 3. (a) Integration of a DCM boost rectifier with a flyback converter results in (b) a BIFRED. (c) Schematic of a BIFRED which includes the bridge rectifier and the high-frequency EMI filter.
emulate a resistor, without active feedback. An example is the flyback and boost converters operating in discontinuous conduction mode (DCM) [2]–[4]. II. DERIVATION
OF
TOPOLOGIES
A. Boost Integrated with Flyback Rectifier/Energy Storage/DC–DC Converter (BIFRED) At low power levels (100 W), a conventional approach is to use a boost converter for input current waveshaping, and a flyback dc–dc converter for isolation and load voltage regulation. Hence, let us consider integration of a DCM boost HQR with a flyback dc–dc converter, as shown in Fig. 3. To preserve the nature of the input stage, the converters must be combined in such a way that the input inductor operates independently in the DCM. The resulting IHQRR is called a BIFRED. To understand how this can be accomplished, let us examine the operation of the two-converter system in Fig. 3(a). Each switching period contains three subintervals. Assume that and are synchronized and that the flyback switches converter operates in continuous conduction mode. and During the first subinterval, only switches conduct. During this subinterval, the DCM boost HQR inis energized by the rectified line voltage through ductor and coupled inductor is energized by energy switch through Load receives energy storage capacitor during this subinterval. During the only from capacitor and conduct. Energy second subinterval, only diodes receives all of the energy of through storage capacitor Inductor is completely deenergized at the end of this transfers some of its energy to interval. Coupled inductor and to filter capacitor through diode The the load becomes reverse third subinterval is initiated when diode
biased by the input current reaching zero. Diode conducts remains only in this interval. The energy state of capacitor continues to at a constant positive level. Coupled inductor transfer some of its energy to the load and to filter capacitor through diode as in the second subinterval. Now, combine the two converters in Fig. 3(a) into one must be converter, containing a single switch. Inductor in order to permit the input inductor in series with diode to operate in DCM. Also, diode cannot be eliminated because the coupled inductor does not necessarily operate in has two network DCM. Notice in Fig. 3(a) that switch functions; it controls the energy flow into the primary of and it aids in balancing the volt seconds of Switch can be replaced with a conductor by connecting the energy storage to the other capacitor in series with it and moving switch Also, the polarity of the primary of coupled side of diode must be reversed to preserve the states of diode inductor during each interval. The result of combining the two converters in Fig. 3(a) is the IHQRR in Fig. 3(b), which is called a BIFRED. The BIFRED of Fig. 3(b) bears a resemblance to a Sepic converter [5]. which is in series The most obvious difference is a diode Diode permits the BIFRED to with the input inductor operate in modes which are not possible with a Sepic. As a result, the BIFRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc–dc Sepic is not. falls to zero, diode stops When the current in conducting, regardless of the energy state of the coupled This permits to continue conducting and inductor to decrease. In allows the energy level of coupled inductor contrast, when a Sepic converter operates in DCM, neither the input inductor nor the coupled inductor can change their stored energy levels during the discontinuous subinterval, as seen by [6]. Hence, a BIFRED has an independence of inductive
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Fig. 4. Schematic of a BIBRED, which includes the bridge rectifier and the high-frequency EMI filter.
energy transfer which is not possible in a Sepic. The resulting differences in the line-current waveforms are demonstrated in Section V. B. Boost Integrated with a Buck Rectifier/Energy Storage/DC-DC Converter (BIBRED) The integration of a DCM boost HQR with a buck dc–dc converter results in a BIBRED, as shown in Fig. 4. The synthesis procedure of this IHQRR is similar to the procedure for a BIFRED. Isolation can also be obtained, in a manner similar to that used for the dc–dc C´uk converter [7]. , which is in series The most obvious difference is diode The additional diode permits the BIBRED to with operate in modes which are not possible with a C´uk converter, and the BIBRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc–dc C´uk converter is not. The additional diode of the BIBRED permits the input inductor current to remain at zero during the discontinuous subinterval, independent of the other reactive and capacitive states. In contrast, when a C´uk converter enters DCM, neither the input inductor nor the output inductor can change their energy levels during the discontinuous subinterval, as described by C´uk [8]. The resulting differences in the line-current waveforms are demonstrated in Section V. Other isolated BIBRED bridge topologies are also possible to derive as described in [9].
(a)
III. DESIGN A. Modeling and Design of the BIFRED The modeling approach for the BIFRED converter is based on [2], [4], and [10]. The class of two-port lossless power processing networks are known as “loss-free resistors” (LFR’s) [11], and have been found to be a useful artifice for modeling and understanding low-harmonic rectifier circuits. The dynamic models contain an LFR to model the rectification process, and a dc transformer network [12] to model the output dc–dc conversion process of the network. The model is used to solve for the quiescent operating point, determine DCM boundaries, and derive converter design equations. Design of the BIFRED in Fig. 3(c) begins with ensuring the correct mode of operation, throughout the complete range of instantaneous line voltage. Relevant currents and voltages and are demonstrated in of network elements Fig. 5(a).
(b) Fig. 5. (a) Switching waveforms of various currents and voltages in the BIFRED of Fig. 3(c). (b) Large-signal nonlinear ac model of the BIFRED in Fig. 3(c).
1) DCM Definition: In the desired DCM, the switching cycle has three distinct intervals. During the first interval, only and diode conduct. During the second intertransistor and conduct. During the third interval, val, only diodes conducts. The motivation behind selecting this only diode particular mode is to guarantee that the energy in inductor is depleted before the energy in the coupled inductor is dewere depleted before in this topology, may pleted. If will become dependent on , which stop conducting and prevents this converter from functioning as an IHQRR. With this choice of mode, one avoids this possibility by designing never reaches the ground state. the converter such that
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The first interval of the switching cycle starts when tranturns on, causing the current in inductor to sistor ramp up from zero with a slope which is proportional to the conducts and diode instantaneous line voltage. Diode is reverse biased. At the end of this interval, an amount of which depends only on the input line energy is stored in voltage and is independent of the currents and voltages of the other inductors and capacitors of the converter. turns The second interval is initiated when transistor to ramp down with a slope off, which causes the current in proportional to the instantaneous line voltage minus the energy minus the output voltage reflected storage capacitor voltage and diode conduct. to the primary. Both diode The third interval commences when the current in reaches zero. Transistor remains off, is reverse biased, conducts. During this interval, the potential energy and and remain unchanged. Capacitor and the levels of and passes energy to the load. load receive energy from 2) A Large-Signal Model: Averaging over one switching cycle [13], [14] provides an analytic perspective of the overall action of the BIFRED. The resulting large-signal equations are given in (1) (2)
This equation implies that the input stage of the converter operates in the boost mode; the net voltage must be greater than the peak value of the ac line voltage. However, and the reflected load the energy storage capacitor voltage may individually be less than voltage 3) Steady-State Solution: Steady-state analysis can be performed by averaging the state equations over half of a line cycle. The nonlinear term must be averaged as a unit, since superposition does not apply to that term. Assuming that the and the switching period are constant and duty cycle the high-frequency neglecting the ripple of voltages and average state equations (2)–(4) are again averaged over a line half-cycle to give the steady state equations in (8) (9) (10) and requires the average Solution of the voltages value of the nonlinear term to be solved using the large-signal A nonseparable transcendental description of the voltage is formed by eliminating the current equation in from (8) and (10) and performing the averaging integral over a line half cycle. The result is
(3) (4) (11) where (5)
where and
and the nonlinear ratios of The equivalent resistance voltages in (1), (2), and (4) are energy related and can be modeled using a loss-free resistor with a dependent power or source [2], [4]. The power “consumed” by appears at the power source such that the network is lossless. This power source is connected between the converter input port and the remainder of the converter, such that its applied voltage is
Here, is the steady-state voltage conversion ratio of the effective boost input stage. The nonlinear relationship in (11) can be solved numerically for a specific case, or approximated for design by a ratio of a constant divided by a first-order polynomial as in
(6)
(12)
passing through the power source is Hence, the current divided by the voltage (6). Thus, equal to the power the nonlinear terms which are in (1), (2), and (4) describe the current from this dependent power source with the voltage described in (6) impressed upon it. It must be stressed that the dependent power source is neither a pure voltage source nor a pure current source, and is inherently a nonlinear element. A comparison between the waveform of in Fig. 5(a) and the input stage of Fig. 5(b) reveal that, in steady state, (6) must always be positive to maintain volt-seconds balance on , as shown in inductor (7)
(13)
(14) Equations (12)–(14) are accurate to within where between 1.4–3.0. Accuracy can 10% over the range of be improved with successive iterations of (11). The closedform (12)–(14) approximate the steady-state solution of the capacitor voltages in a BIFRED.
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4) Mode Boundaries: Steady-state (9) and the waveforms of Fig. 5(a) can be used to formulate the inequality (15), which completely deenergize before the requires that inductor next switch cycle begins (15)
Essentially, the second interval must always be less than the total switch period minus the duration of the first interval. The current waveform of in Fig. 5(a) relates the duration of the second interval with the capacitor voltages and the duration of the first interval. The length of the second interval is maximum when the instantaneous line voltage is at a maximum. The inequality in (15) describes the maximum duration for a given line-to-output transfer ratio which will allow the inductor to completely deenergize. Among the reasons to use the maximum duration is to reduce the rms currents in inductor Furthermore, the longer the first interval is relative to the second interval, the more resistive the BIFRED appears to the ac line. Equation (15) can be rearranged to the approximate form by as in (16), which includes the conduction coefficient the substitution of (14) (16) Equation (15) is used to solve for the duration of the first interval for a given turns ratio and a desired line-to-output can be determined as a function ratio. Then, the inductance of the previously given parameters, the switching period and the load resistance by use of (16) and the definition (11) of the conduction coefficient The dependence of the DCM boundaries on the value of is more subtle than that of because current inductor has large-signal variations during normal operation. These variations include a dc component and a twice-line-frequency component, the phase shift of which is 180 relative to the and capacitor are rectified line voltage. Since inductor chosen for filtering switching harmonics, and the switching and frequency is much higher than twice the line frequency, can be approximated as a short circuit and an open circuit, respectively. Solution of the resulting equivalent circuit yields
(17)
The current of the dependent power source in the equivalent circuit model in Fig. 5(b) can also be approximated as a function of known quantities as in
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The transfer ratio of (17) reveals a dc gain which can be different from the high-frequency gain. When the steady-state duty ratio is less than 1/2, the high-frequency gain is lower than the dc gain. The converse is also true. Since is very large, the shift in gain and the associated phase shift of 180 occurs at frequencies which are much lower than twice the line frequency. Thus, current is essentially minus plus a dc offset current. Current must always be positive in the to prevent an unwanted DCM, and maintain diode conducting state during the second and third intervals. Hence, for operation in the correct mode, we require that the dc gain of (17) be greater than the high-frequency gain, or (19) The restriction in (19) is further limited when considering the The minimum value of exact minimum value of current is given by (20) and it can be exactly solved using techniques similar to those used to find (11)
(20) Restrictions set by (19) and (20) neglect switching ripple because they are concerned with states which are averaged over a switch cycle. Equation (21) is an additional criterion which from completely deenergizing must be satisfied to prevent (21) must not completely deenergize during normal Capacitor and , operation. A transfer ratio can be formed between given in which leads to the lower limit for (22)
is the allowable proportion of ripple voltage where The limiting case for the smallest value of capacitor in is when the proportion of ripple in voltage is one. Typically, will be much larger than this limit, in that the capacitor proportion of ripple in voltage may be indirectly specified in terms of a holdup time of several line cycles. Capacitor is chosen to meet a switching ripple specification which is a fraction of the dc output voltage, as in (23). Thus, capacitor cannot completely deenergize unless the low-frequency output ripple is inadvertently too large (23)
(18) is a rectified sinusoid, varies between zero and Since can now some finite peak value. The minimum value of be estimated using (18) and the transfer ratio between and in (17).
is the fraction of switching in where In summary, a BIFRED can be designed for a given line voltage, turns ratio, switching frequency, energy storage ripple, output voltage ripple, and output voltage using the following using (15). The duty ratio must be steps. First, select
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less than 1/2 per (19). Select using (16). Internal voltages and are then calculated using (12)–(14). The minimum in is calculated using (20). Current must current is then be positive for the design to be valid. Inductor and are then selected to selected using (21). Capacitors meet ripple specifications using (22) and (23), respectively. B. BIBRED and Other Topologies Design of a BIBRED, as well as other bridge topologies presented in [9], follows many of the steps as described in designing a BIFRED; limited space precludes a detailed description here. However, an equivalent circuit model for the BIBRED is described in [9], while a complete analysis of a full-bridge BIBRED is presented in [15]. IV. CONTROL
(a)
A. Simple Duty-Ratio Control Scheme Duty-ratio variations result in variations in both the output voltage and the line current. The voltage conversion ratio between the energy storage capacitor and load and, hence, also the output voltage, is proportional to the duty ratio in (14). The line current is a function of equivalent resistance which, in turn, is a function of the duty ratio, as seen in (1) and (5). Thus, duty ratio can be used to control output voltage or line current. This family of IHQRR’s inherently produces line-current waveforms of low, but nonzero harmonic content, which, in most applications, can meet the harmonic limits in [1] without additional active control. Because of the low-frequency internal energy storage built into these converters, wide-bandwidth control of the output voltage is possible, without significantly degrading the line-current waveform quality. When the controller corrects for line harmonic disturbances in the output voltage, it affects line-current harmonics. This is because the line current is a function of duty ratio. Line-current distortion due to output voltage feedback can be minimized by increasing the size of the energy storage capacitor; in practice, however, such measures may be unnecessary. Laboratory results confirm that the total harmonic distortion of the line current for the closed-loop BIBRED is slightly lower than the total harmonic distortion during open-loop operation (21% compared to 19%). Thus, in this specific case, the output voltage feedback has a minimal effect on the line-current harmonic content. Regulation of output voltage using duty-ratio adjustments is also a method for controlling DCM flyback HQR’s [2]. However, the bandwidth of the IHQRR is much greater than the bandwidth of the simple HQR. This is because, in an IHQRR, the load is separated from the internal energy storage capacitor by reactive devices and semiconductor switching devices. To confirm this, output voltage regulation of a BIBRED and a DCM flyback HQR using duty-ratio control is demonstrated in Fig. 6, which shows the response of each of these converters to a sudden shift in load resistance. It is instructive to compare the response in Fig. 6 with that of a DCM flyback HQR under similar conditions [2]. The response time of the BIBRED is
(b) Fig. 6. Comparison of 2 : 1 load current transient response with output voltage duty ratio control. (a) BIBRED, 10-kHz crossover frequency. (b) DCM flyback HQR, 3.5-Hz crossover frequency.
Fig. 7. Block diagram of a variable switching period, fixed duty ratio modulator to reduce line-current harmonics.
many times faster than the DCM flyback HQR. The closedloop bandwidth of the BIBRED is approximately 10 kHz, compared to a bandwidth of 3.5 Hz for the DCM flyback HQR.
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TABLE I PARAMETER VALUES OF THE EXPERIMENTAL 40-W RECTIFIERS
(a)
(b) Fig. 8. Measured line voltage and current waveforms for 40-W BIFRED. (a) Open loop. (b) Using the switching frequency controller of Fig. 7.
B. Simultaneous Duty-Ratio and Switching-Frequency Control Returning to the nonlinear large-signal state equations in It is rearranged in (24) to demonstrate the (1), consider effects of variations in (24)
Fig. 9. Experimental switching frequency waveforms of the BIFRED described in Fig. 3(c) and Table I. These waveforms verify the mode of operation.
is given in (5). Incidentally, has the same form where is in both the BIFRED and the BIBRED topologies. If then the IHQRR presents a linear purely proportional to resistive load to the ac line. It can be seen that one method of eliminating harmonics in the line current is to vary such that it cancels the denominator of (24). Furthermore, the denominator of (24) is positive and less than one. Therefore, can be appropriately adjusted by variations in either duty or switching period or a combination of both. cycle A modulator which can independently vary the switching frequency and the duty cycle was constructed per the block diagram in Fig. 7, using an analog multiplier and a voltage controlled oscillator. Comparison of Fig. 8(a) and (b) reveals that line harmonics can be further reduced by use of the scheme described
above. Fig. 8(a) shows the line current of a 40-W BIFRED operating open loop with a fixed switching frequency and a fixed duty cycle. The total harmonic distortion of the line current in Fig. 8(a) is approximately 20%. Fig. 8(b) is the line current of the same 40-W BIFRED, operating with a variable switching period which is adjusted to correct line harmonics. The total harmonic distortion of the line current in Fig. 8(b) is approximately 4%. It is possible to use both duty-ratio adjustments and switchperiod adjustments to simultaneously regulate the output voltage and control the line-current harmonics. Equation (14) shows that the output voltage is directly proportional to duty Under ratio and a function of the switching period through the condition of the inequality in (25), it is found that the output voltage is not sensitive to changes in the switching
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(a)
(b)
(c)
(d)
Comparison of the line-current waveforms of (a) BIFRED, (b) Sepic converter, (c) BIBRED, and (d) C´uk converter.
period (25) However, the line current is proportional to the switching period. Thus, it is possible to regulate the output voltage with the duty cycle and reduce line harmonics with switch frequency variations. Phase control is a third method of control which can be used by the full-bridge BIBRED. Reference [15] addresses this issue in more detail. V. EXPERIMENTAL RESULTS A 40-W BIFRED and a 40-W BIBRED were designed and implemented to operate from a 110-V line to produce 20output voltage. The schematic for the BIFRED is given in Fig. 3(c), while the schematic for the BIBRED is given in Fig. 4. The component values are given in Table I. These values were chosen to assure that the modes of each IHQRR are the same as the modes which are described in Section III.
Switching waveforms of the BIFRED are shown in Fig. 9. These waveforms depict currents and near the peak of the line voltage. At that instant, the magnetizing is at a minimum, nonzero value, as discussed current of in Section III-A-4. The experimental waveforms agree with those of Fig. 5(a). Thus, the BIFRED operates in the desired mode. Comparable waveforms are also found for the BIBRED. of the BIBRED begins and ends each switch cycle Inductor at ground state, and it is the only reactive component in the BIBRED to do so. The switching waveforms of Fig. 9 demonstrate the difference between a BIFRED and a Sepic converter; the energy in a BIFRED returns to ground state, level of inductor even though the magnetizing inductance maintains a level of energy. Fig. 10(a) and (b) demonstrates the resulting difference in the line current of a BIFRED and a Sepic converter. The of the Sepic converter maximum current level in inductor and an output was reached at a line voltage of 50 V voltage of 8.8 V Under these conditions, the Sepic converter operates in continuous conduction mode. It can be seen that
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the BIFRED emulates a resistive load, while the Sepic linecurrent waveform resembles peak detection. These waveforms are not qualitatively changed when the Sepic operates in its DCM. Fig. 10(c) and (d) shows a similar comparison between a BIBRED and a C´uk converter. For this demonstration, the Sepic and C´uk converters were constructed simply by shorting in the respective BIFRED and BIBRED. The slow diode bridge rectifier diodes do not switch in the same manner , owing to the presence of input filter elements as and and, hence, the circuit input behavior is radically different. In the Sepic and C´uk converters, peak detection occurs is small in value, and has small impedance because inductor at the line frequency. As a result, the low-frequency comis very small. The remaining ponent of voltage across components, i.e., the energy storage capacitor and the four ac rectifier diodes, operate as a peak detection circuit. In the is able to support the lowBIBRED and BIFRED, diode frequency components of the voltage difference between the energy capacitor voltage and the rectified line voltage, such that peak detection need not occur. Thus, it has been demonstrated that the BIFRED and BIBRED naturally yield low-harmonic line-current waveforms which are distinctly different from Sepic and C´uk converters. VI. CONCLUSION A new family of converters has beem presented in this paper which exhibit low-harmonic line currents, internal energy storage, and wide-bandwidth output voltage response. These converters are derived by the integration of a DCM boost converter, energy storage capacitor, and a cascaded dc–dc converter. The function of the switches in each individual converter is examined under synchronized conditions, and redundant switch functions are integrated together. A valid integration preserves the low-frequency independence of the energy storage capacitor voltage. Steady-state and dynamic operation of this new family of IHQRR’s were analyzed with large-signal LFR models [Fig. 5(b)]. This modeling technique preserves the large-signal nonlinearities which affect steady-state and ac operation. Moreover, a step-by-step design procedure example using the BIFRED topology was presented. The other topologies in this family can be designed in a similar manner, [15]. Output voltage regulation using duty-ratio variations and a fixed switching period is the simplest method of control. Experimental results demonstrate that it is possible for these converters to have fast response and low line-current harmonic content. The harmonic content of the line current is low enough to satisfy typical IEC1000-3-2 specifications. Further reduction of line-current harmonics is possible with variable-switching-frequency control, as demonstrated in Fig. 8. The comparison of the BIBRED IHQRR with the DCM flyback HQR in Fig. 6 distinguishes this family as IHQRR’s, rather than simple low-bandwidth HQR’s. The comparison of the BIFRED
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and BIBRED line currents with the line currents of their respective dc–dc Sepic and C´uk converter counterparts, in Fig. 10, distinguishes these IHQRR’s from simple dc–dc converters. REFERENCES [1] Electromagnetic Compatibility (EMC)—Part 3: Limits Section II: Limits for Harmonic Current Emissions (Equipment Input Current 16A per Phase), IEC 1000-3-2, 1st ed., 1995. [2] R. Erickson, M. Madigan, and S. Singer, “Design of a simple highpower-factor rectifier based on the flyback converter,” in Proc. IEEE APEC’90, 1990, pp. 792–801. [3] S. Freeland, “Input current shaping for single-phase AC-DC power converters,” Ph.D. dissertation, pt. II, Elect. Eng. Dep., California Inst. Technol., Pasadena, Oct. 1987. [4] S. Singer and R. W. Erickson, “Canonical modeling of power processing circuits based on the POPI concept,” IEEE Trans. Power Electron., vol. 7, pp. 37–43, Jan. 1992. [5] R. P. Massey and E. C. Snyder, “High voltage single-ended DC-DC converter,” in Proc. IEEE PESC’77, 1977, pp. 156–159. [6] J. Sebastian, J. Uceda, J. A. Cobos, J. Aaru, and F. Aldana, “Improving power factor correction in distributed power supply systems using PWM and ZCS-QR Sepic topologies,” in Proc. IEEE PESC’91, 1991, pp. 780–791. [7] R. D. Middlebrook and S. C´uk, “Isolation and multiple output extensions of a new optimum topology switching DC-DC converter,” in Proc. IEEE PESC’78, 1978, pp. 256–264. [8] S. C´uk, “Discontinuous inductor current mode in the optimum topology switching converter,” in Proc. IEEE PESC’78, 1978, pp. 105– 123. [9] M. Madigan, R. W. Erickson, and E. Ismail, “Integrated high quality rectifier-regulators,” in Proc. IEEE PESC’92, 1992, pp. 1043– 1051. [10] S. Singer, “Canonical approach to energy processing network synthesis,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 767–774, Aug. 1986. , “The application of loss-free resistors in power processing [11] circuits,” IEEE Trans. Power Electron., vol. 6, pp. 595–600, Oct. 1991. [12] R. D. Middlebrook and S. C´uk, “A general unified approach to modeling switching-converter power stages,” in Proc. IEEE PESC’76, 1976, pp. 18–34. [13] S. C´uk and R. D. Middlebrook, “A general unified approach to modeling switching DC-DC converters in discontinuous conduction mode,” in Proc. IEEE PESC’77, 1977, pp. 160–179. [14] R. W. Erickson, “Large signals in switching converters, Part I: Distortion in switching amplifiers, Part II: Transients in switching regulators,” Ph.D. dissertation, Elect. Eng. Dep., California Inst. Technol., Pasadena, Nov. 1982. [15] M. A. Johnston and R. W. Erickson, “Reduction of voltage stress in the full-bridge BIBRED by duty ratio and phase shift control,” in Proc. IEEE APEC’94, 1994, pp. 849–854.
Michael T. Madigan (S’75–M’77) received the B.S. degree from the University of Colorado, Denver, in 1977 and the M.S. and Ph.D. degrees from the University of Colorado, Boulder, in 1988 and 1992, respectively, all in electrical engineering. He is currently an Applications Engineer with Unitrode Corporation, Cary, NC. Between 1992–1997, he served as a Power Electronics Consultant to Sony, Unique Mobility, and Echostar. Between 1977–1987, he designed control systems and power electronics for industrial and aerospace companies, such as Martin-Marietta and Honeywell. His research interests include power processing topologies, modeling, and control.
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Robert W. Erickson (S’82–M’82–SM’97) received the B.S., M.S., and Ph.D. degrees from California Institute of Technology, Pasadena, in 1978, 1980, and 1983, respectively. In 1982, he joined the faculty of the University of Colorado, Boulder, where he is currently a Professor of Electrical and Computer Engineering. He is the author of Fundamentals of Power Electronics (New York: Chapman & Hall, 1997), as well as more than 50 papers in power electronics conference proceedings and journal transactions. He teaches courses in power electronics, energy conversion, circuits, and control. His current research interests include low-harmonic rectification technology, modeling of converter systems and power components, low-voltage converters, and wind energy systems. Prof. Erickson received an IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award for 1996.
Esam Hamid Ismail (S’84–M’85) was born in Kuwait in 1962. He received the B.S. and M.S. degrees in electrical engineering from the University of Dayton, Dayton, OH, in 1983 and 1985, respectively, and the Ph.D. degree from the University of Colorado, Boulder, in 1993. From 1985 to 1988, he was with the Electrical Engineering Department, College of Technological Studies, Al-Shaa’b, Kuwait, where he is currently an Assistant Professor. His research interests include low-harmonic rectification, high-frequency power conversion, and the development of new converter topologies. Dr. Ismail is a member of Tau Beta Pi.
