IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 47 Predicted (On-Time) Equal-Charge Criterion Scheme for Constant-Frequency Control of Single-Phase Boost-Type AC–DC Converters Ramesh Oruganti, Member, IEEE, Kannan Nagaswamy, and Lock Kai Sang Abstract—A new constant switching frequency control method for single-phase boost-type ac–dc converters is presented. The on times of the converter switches in each switching period is determined such that the average input current tracks the reference template in every switching cycle. The problems encountered in achieving smooth and stable operation and the modifications made to overcome them are discussed. The simulation studies done on the converter controlled with this method, which is given the name predicted (on-time) equal-charge criterion (PECC) method, indicate stable operation at different input-current and voltage levels and power factors. The method was implemented on an insulated gate bipolar transistor (IGBT) converter rated for 1 kVA using a 80 386 processor system for computations. The experimental results are presented and discussed in this paper. Index Terms—Boost ac–dc converters, constant-frequency power converters, equal-charge criterion control, microprocessor control of converters. Fig. 1. Single-phase boost-type ac–dc converter with current control. I. INTRODUCTION T HE DRAWBACKS due to harmonic-rich currents drawn by the conventional ac–dc converters have been well documented in literature. Considerable research has been done in the recent past to improve the quality of input-current waveforms. Of the many schemes and topologies which have been proposed to address the problem, single- and three-phase boost-type ac–dc power converters are popular [1]–[11]. Fig. 1 shows a single-phase boost-type converter with bidirectional power-flow capability. By switching the appropriate pair of devices (1, 4) or (2, 3), the input-current waveform is controlled to keep close to a sinusoidal template, which is derived from the input-voltage waveform and whose phase and magnitude can be set as desired. Single-phase ac–dc converters [10]–[12] find application in areas such as traction drives, low-power-rated induction motor drives, low-power uninterruptible power supply (UPS) systems, and battery chargers. The converter in Fig. 1 is of particular interest in traction drives, where its bidirectional power-transfer capability can be used to recover energy when the motors are braked. Manuscript received June 13, 1996; revised January 31, 1997. Recommended by Associate Editor, R. Steigerwald. R. Oruganti and L. K. Sang are with the Center for Power Electronics, Department of Electrical Engineering, National University of Singapore, 119260, Singapore. K. Nagaswamy is with Hewlett-Packard, Singapore. Publisher Item Identifier S 0885-8993(98)00484-0. Fig. 2. Reference and actual current waveforms in HCC. Many methods for input-current waveshaping have been reported [1], [3], [5], [6], [8], and [9]. The most common method is the hysteresis current control (HCC) [1], [2], [7], [10], and [11]. Here, the input current is kept to within a band about the reference current wave. The waveform of the input current and reference current along with the hysteresis band for part of a line cycle are shown in Fig. 2. This method has the advantages of simple implementation, fast current dynamics, and inherent peak-current limiting capability. However, the scheme has a major drawback in that the switching frequency varies over a wide range. As a result, issues such as design of input filter and switching losses of the semiconductor devices assume significance. This has motivated research into constant switching frequency methods [3]–[5], [9] applicable to boost-type converters. References [3] and [4] discuss a method called predicted current control with fixed switching frequency (PCFF) for three-phase converters. Here, the duty cycle of the legs of 0885–8993/98$10.00 1998 IEEE 48 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 converter bridge is controlled such that the input current reaches the value set by the reference current template at the end of the switching cycle. The method has the advantages of constant frequency besides having good dynamic characteristics. However, the method does not force the average of the input current to be sinusoidal. In [5], the HCC method is modified to achieve a constant-frequency control for a dc–ac three-phase inverter. A phase-locked loop (PLL) keeps the converter’s switching frequency constant by adjusting the hysteresis band. Here, too, fast dynamic response is possible as with HCC. However, the PLL with a large low-pass filter tends to create stability problems. Also, the PLL may lose synchronization during transients [6], which could cause large changes in the switching frequency. Reference [6] discusses an adaptive HCC method, where the hysteresis band is controlled adaptively to result in a nearly constant switching frequency together with fast dynamics. The method may be viewed as controlling the average value of input current indirectly in contrast to the method discussed in the present paper, which controls the average input current directly. Another constantfrequency control method is outlined in [9]. Here, the input current’s phase and magnitude are controlled by controlling the fundamental component of the rectifier input voltage using the sine pulse-width modulation method. A major drawback of this method is that the response of any current loop to step changes in load is slow. There is a dc component in the input current soon after the change, which dies down after a few line cycles. In this paper, a control method, which has been named as the predicted (on-time) equal-charge criterion (PECC) method, is proposed. This method seeks to combine the superior dynamics of the HCC method and the advantages offered by constantfrequency switching. Analysis-based simulation is adopted to verify the operation of the converter under this control method. A simple constant-frequency equal-charge criterion (ECC) method (Method A) is initially proposed, which is then found to be inherently unstable. The method is then modified by predicting the on time for the ECC (Method B). This method results in stable operation in only one half of a line-cycle waveform. A combination of two ways of implementing Method B after some fine tuning gives the PECC method, which is the main contribution of this paper. Simulated performance results like input-current ripple, variable power-factor operation, and comparison with the HCC method are presented. Details of microprocessor-based implementation and some experimental results are also given verifying the anticipated good performance of the scheme. Simulation results are compared with those of the HCC method also. II. ANALYSIS/SIMULATION OF CONVERTER UNDER A CONTROL METHOD In order to study the performance of the boost-type converter under different control methods, analysis-based simulation method was applied. The network equations which result when device set (1, 4) is on and (2, 3) is off or vice versa were first solved assuming the switches and diodes to be ideal. The Fig. 3. Current waveforms in simple ECC (Method A). solved equations were then used to simulate the performance of the converter under a specific control method. The input ac voltage and reference input current were assumed to be constant during a switching interval. This assumption simplifies the analysis and is justified since the switching frequency (20 kHz) is much greater than the line frequency (50 Hz). Besides, a stiff dc bus (250 V) at the output was assumed, again to simplify the analysis, and is justified in most applications. Other parameters of the converter include input voltage of 110 V (rms), input inductance of 2.5 mH, and a voltampere rating of 1 kVA. III. SIMPLE ECC: METHOD A The motivation of this method is to make the average current in the inductor equal to the average of the reference value on a switching-cycle-by-switching-cycle basis. In Fig. 3, device set (2, 3) of the converter is turned on (instants and ) once every period , causing the current to rise. At , the device set is switched off and (1, 4) switched on when the following condition is satisfied: or (1) shaded area. Thus, Method A is a simple control method, which can be implemented using opamps. It is to be noted here that the interval over which the average of is made equal to that of is not equal to the switching interval . It is the time between two successive turn ons of (2, 3), which is equal to . When the method was simulated using the SABER simulation tool, unstable waveforms (Fig. 4) were observed. As may be noticed, after a few switching cycles, the device set (2, 3) was switched on (as per the method) even before the integral could go to zero or negative. After this occurs, (1) is never satisfied. The current increases to large values (Fig. 4). Since the simulation clearly demonstrated the instability of this method, no further investigations regarding the same are included. To overcome this problem, modifications were made to the simple ECC method, which will be discussed in the subsequent sections. ORUGANTI et al.: CRITERION SCHEME FOR CONTROL OF BOOST-TYPE AC–DC CONVERTERS Fig. 4. Waveforms of iref (t) and iact (t) under Method A (SABER simulation). 49 The assumption of constant input ac voltage during the switching cycle (Section II) results in linear variations of as shown. With Mode Sequence I, in the positive line-current half cycle, the inductance charges up (stores energy) first and then discharges into the dc bus. However, in the negative half cycle, with the same sequence, the inductor first discharges as it drives current against the dc bus and then charges. In Mode Sequence II, the sequence of inductor charging and discharging during the positive and negative line-current half cycles is reversed. By setting the shaded area equal to zero (see Appendix A), a quadratic equation in is obtained for each mode sequence. They are (3) where and (4) for Mode Sequence I and (a) (b) Fig. 5. Reference and actual input-current waveforms in Method B. (a) Mode Sequence I. (b) Mode Sequence II. IV. DEVELOPMENT OF PECC METHOD In this section, the basic concept of the PECC method and the problems faced in realizing good performance will be discussed. The final control scheme will be discussed in Section V. A. Initial Proposed PECC Method In Method A (Fig. 3), the on time – is determined such that the ECC will be satisfied over the interval – (which is not the cycle period ). In the modification proposed (Method – is determined such that ECC will B), the on time be satisfied over the cycle period , – . Two ways of implementation (Mode Sequences I and II) of this control method are possible [see Fig. 5(a) and (b)]. The following explanation is made with reference to Mode Sequence I [Fig. 5(a)]. A similar explanation can be made for Mode Sequence II by interchanging the roles of device sets (1, 4) and (2, 3) (Fig. 1). In Fig. 5(a), device set (2, 3) is switched on at the start of the switching cycle of period , followed by (1, 4) at time . As stated earlier, the control method predicts the value of such that the ECC is satisfied at the end of the cycle. Thus or (2) and (5) for Mode Sequence II, where and are the input ac voltage and reference input current for the switching interval and is the current at the start of the interval . The control system must solve (3) in each switching cycle to obtain , which determines the switching instant within the period . 1) Instability in Method B and Modification: Upon simulation, it was found that if a single mode sequence (I or II) is used throughout the line cycle, the system is unstable for half a line cycle. For example, as in Fig. 6, instability is noted in the negative half cycle if Mode Sequence I is used throughout. Similarly, the system is unstable in the positive half cycle when Mode Sequence II is used throughout. In the unstable condition, the input current strays away from the reference. At one point, the current goes so far away from the reference that ECC cannot be satisfied for that switching cycle, and the appropriate devices have to be kept on or off throughout the period. The current no longer keeps in step with the reference, resulting in very high values of peak-to-peak values ripple current (Fig. 6). In Section IV-A2 and Appendix B, an analysis of the observed instability is presented. 2) Stability Analysis for Method B: Ignoring the slow-line waveform variation, when there is a small perturbation in from the steady-state value, it results in a disturbance in , which, in turn, causes the current at the end of the . The perturbations in sample to be perturbed by a factor Mode Sequence I are shown in Fig 7. The initial perturbation may be due to noise. In simulation, the rounding-off errors 50 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 Fig. 6. Input-current waveform with Mode Sequence I used in both the line-voltage half cycles. Fig. 8. Input-current waveform when Mode Sequences I and II are combined. Fig. 9. Spectrum of waveform in Fig. 8 (fundamental not shown). Fig. 7. Perturbations in ix and resultant perturbations in Mode Sequence I. TON and iz in appear as perturbations. The system will be unstable if the magnitude of the ratio to , which shall be denoted , is greater than or equal to one. That is, a disturbance in results in a larger disturbance in , which is the for the subsequent sample. Upon analyzing the system equations with these perturbations (Appendix B), the ratio is given by (6) is greater than one if is greater The magnitude of than or, in other words, the duty ratio is greater than 50%. Since and are nearly constant over a switching cycle, the current rise and fall in each switching cycle may be equated. The following equation is then obtained for Mode Sequence I: Duty ratio (7) Thus, with Mode Sequence I, it can be seen that duty ratio 50 in the negative line-voltage half cycle and 50 in the positive half cycle. This is the reason for the system tending to be unstable in the negative half cycle if Mode Sequence I is used. The above instability is somewhat similar to that seen in peak-current control in dc–dc converters. The operation in these converters can be stabilized by slope compensation [13], where a slope is incorporated into the reference. It is possible that such an approach may be effective here also. But, it was not pursued here for the following reasons. The input voltage varies over a wide range, so the slope required for stable operation would also vary widely. Such slope compensation would add to the complication in processing, which is undesirable. Furthermore, since there is always a mode sequence that is stable in any half cycle, it is not necessary to go in for any external stabilization technique. B. Combination of Mode Sequences I and II for Stable Operation By using Mode Sequence I for the positive line-voltage half cycle and Mode Sequence II for the negative half cycle, stable operation over a complete cycle may be expected. The input current for this combination is shown in Fig. 8. The figure shows that there is a considerable amount of transients, seen as a 10-kHz component in spectrum (Fig. 9), just after the zero crossings. This phenomenon is explained as follows. As the reference current crosses zero, operation changes from one mode sequence to the other, introducing an abrupt change in the sequence of the devices being switched. The current is far different from the steady-state value of at this point required under the second mode sequence for a smooth operation. By making the current vary in the same direction as it had before the switching cycle, the current is made to go even farther from the reference. This part of the waveform is shown in detail in Fig. 10. The transient dies down eventually due to the inherent stability of the mode sequence, but being appreciable, it is observable on the spectrum. The transient could be minimized by making the transition from one mode sequence to the other after the current is close to a value of , which will result in smooth operation. This is discussed in the next section. ORUGANTI et al.: CRITERION SCHEME FOR CONTROL OF BOOST-TYPE AC–DC CONVERTERS 51 Fig. 12. Input-current waveform under the PECC method (1-kVA output). Fig. 10. Input-current waveform during the zero crossing. Fig. 13. Spectrum of waveform in Fig. 12 (fundamental not shown). Fig. 11. Input-current waveform during transition from Mode Sequence I to II under the PECC method. V. PROPOSED PREDICTED ON-TIME ECC METHOD The on-time value is used as the criterion for deciding to changeover. When it goes beyond a threshold value (say, 55% of ), mode sequence is changed as follows. Fig. 11 shows a transition from Mode Sequence I to Mode Sequence II. Mode Sequence I is used until , with Mode Sequence II after . At , device set (2, 3) is turned on. It is kept on for time interval – , which is equal to calculated for Mode Sequence I , the - . At also changes to a value that is close to input current a value, which gives smooth operation in Mode Sequence II. Then, at - is calculated based on Mode Sequence II. Device set (1, 4) is turned on for a duration of - . A similar changeover is carried out when operation is to change over from Mode Sequence II to Mode Sequence I. The resultant waveform is shown in Fig. 12 and the spectrum in Fig. 13. Essentially, during the transition, the switching period is constant until and after . There is a transition interval – , which is not equal to the switching interval. Note, however, that - will be nearly equal to a period . Thus, the operation is not constant frequency for a very small part of the line cycle. The current waveform is smooth, and the spectrum shows only the sidebands due to the switching frequency, as is the case with constant switching frequency. Stable operation is achieved, minus the zero-crossing transients. This final method has been named the PECC method. Fig. 14. Waveform of the ripple in current in Fig. 12. VI. SIMULATION RESULTS A. Input-Current Ripple The ripple in the input current using the PECC method is shown in Fig. 14. The ripple was calculated by simply subtracting from . The magnitude of ripple depends upon the switching frequency and boost inductance alone and is independent of the input-current amplitude. A small jump in ripple may be observed at the points where the mode sequence transitions occur near 0.01 s. This may be attributed to the fact that the current at the start of the transitional period is not exactly the same as the steady-state value for the later sequence. Fig. 12 shows the input-current waveform at a power rating of 1 kVA and Fig. 15 shows the input current at a light load of about 100 VA. It shows that at light loads, the ripple swamps the fundamental component as would be expected. B. Variable Power Factor and Regenerative Operation In the derivation of (3)–(5), no assumption was made regarding the ac voltage or current waveforms. In other words, the phase difference between the current and voltage waveforms need not be fixed. Thus, using a boost-type converter with 52 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 TABLE I COMPARISON OF HCC AND PECC SCHEMES AT 110 V, 9.09-A INPUT, 250 Vdc, AND 1-kW OUTPUT Fig. 15. Input-current waveform at 100-VA output. TABLE II COMPARISON OF HCC AND PECC SCHEMES AT 70 V, 9.09-A INPUT, 200 Vdc, AND 0.636-kW OUTPUT Fig. 16. Input-current and voltage waveforms at zero power factor (capacitive load and = 90 ). Fig. 18. I). Fig. 17. iact (t) and Iref for successive switching intervals (Mode Sequence Input-current and voltage waveforms at regenerative operation ( = 180 ). C. Comparison with HCC Method the proposed control, operation at arbitrary power factors as well as regeneration is possible. For this general case, the input-current reference is given by (8) where is the peak value of input-current reference, is the fundamental angular frequency, and is the current phase shift with respect to input voltage. A value between 90 and 270 indicates regenerative operation. For the PECC method, operation under different values of power factor were simulated and waveforms studied. The waveforms for 90 (leading) phase shift (capacitive load) and regenerative operation are shown in Figs. 16 and 17, respectively. It can be observed that the operation is stable and transient-free for these cases also. Also, the behavior of the switching ripple is different for different power factors. At unity power factor, the peakto-peak value of ripple is maximum at the zero crossings of the current waveform and is minimum at the peaks. At zero power factor, the ripple value is maximum at the peaks. A brief comparison is made between the PECC and HCC methods. Both were simulated for the same converter under identical input and output conditions (see Section II). The comparative results under full-load conditions are given in Table I. In the HCC method, for a certain hysteresis band, the switching frequency varies over a wide range, by a factor of nearly two. The PECC operates at constant frequency, making input filtering relatively easier, which is its significant advantage. It should also be noted that with HCC, the range of switching frequencies varies widely at different operating conditions for a given hysteresis band. Furthermore, it has been noted from simulation studies that when the input and output voltages are lower, then, for a given input current, PECC results in less ripple. This is another advantage of the PECC method over the HCC method (see Table II). On the negative side, the PECC method is more complex. Also, the ripple current is higher at certain parts of the waveform, as in all constant-frequency schemes. This could result in slightly higher device stresses. More importantly, this could also result in higher conducted EMI (electromagnetic interference). However, since the switching frequency is constant, the filtering of this ripple would be simple. ORUGANTI et al.: CRITERION SCHEME FOR CONTROL OF BOOST-TYPE AC–DC CONVERTERS Fig. 19. 53 Block diagram of the 80 386 system used for implementing the PECC method. D. Comparison with Average Current Control The PECC method involves the control of the average of input current in each switching interval. In the average current control typically used in the single-phase power-factorcorrection systems [13], the average of the input current, after filtering out the switching frequency components, is made to follow the reference. The filtering results in poor currentloop dynamics. However, in the PECC method, the average current is controlled in each switching cycle. Hence, the PECC method is expected to exhibit good dynamic performance at the expense of increased complexity. It has also been verified experimentally that the dynamic performance of the PECC method is very good, with the system responding very fast to step changes in input-current reference. VII. PRACTICAL IMPLEMENTATION The implementation of the PECC method requires the solution of a quadratic (3) based on the parameters such as and . In the present work, it is carried out using the Intel 80 386 microprocessor. This processor was chosen for the 32-b data bus and the reasonably fast execution of instructions. The parameters and are acquired from the actual quantities. Their acquisition and further computation cannot be performed instantaneously. Hence, in each switching period, the value of for the subsequent cycle is calculated. The following explanation is for Mode Sequence I (refer to Fig. 18). is calculated in the switching period prior to Period A. In Period A, is sensed using an analog–digital converter (ADC) as well as and . With these quantities, the value of is estimated from (A-7). and are is calculated during also estimated. Using these values, Period A itself. The value of is fed to a logic circuit, which converts this quantity to the gate-drive signals to appropriate devices of the converter. Fig. 19 shows the block diagram of the hardware. Slight changes in the line frequency are accounted for by sensing the zero crossings of the line voltage [zero-crossing detector]. The line frequency is worked out from the squarewave output of the zero-crossing detector. The accurate value of line frequency is used in generation of the reference current value . Fig. 20. Flowchart for computation of interval. TON for the subsequent switching The flowchart in Fig. 20 shows how is computed in interval A. The method is the same throughout the line cycle irrespective of the mode sequence. Only the equations used for estimating and are different for different mode sequences. In the case of a transition interval between mode sequences, is computed as per (A-3) using the existing 54 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 (a) (b) Fig. 21. Input-voltage and current waveforms (scale: voltage—60 V/div; current—14 A/div). (a) Input current (rms) = 10:03 A. (b) Input current (rms) = 5:38 A. mode sequence and the computation of for the subsequent interval using the next mode sequence. is shown to be In the flowchart, processing for interleaved with the analog–digital conversions. This is done to save time while waiting for a certain quantity to be digitized. However, it is not always possible, since it will be necessary to wait for the digitized value of in order to proceed further in the computations. Thus, there is an overhead in the processing in the form of ADC time. The ADC that was used for the present work was slow (digitization time 15 s), hence, working with a switching interval of 50 s (for 20-kHz switching) as originally anticipated was not possible. Therefore, a switching interval of 100 s (10-kHz switching) was decided upon. It should be noted that this is not due to a limitation of the method or the implementation. Having decided upon 10-kHz switching, the boost inductance was changed to 5 mH instead of 2.5 mH, which was used for simulation studies. All other specifications of the converter remain the same as in Section II. The switching frequency can be raised by using faster ADC’s and processors with faster clocks and processing speed. Due to limitations of space, further details of implementation are not provided. Fig. 22. Input-voltage and current waveforms [Vdc = 91:7 V and input current (rms) = 7 A] (scale: voltage—30 V/div; current—14 A/div). VIII. EXPERIMENTAL RESULTS The PECC method was implemented on an insulated gate bipolar transistor (IGBT) converter (using IRGTI050U06) based on the 80 386 system explained in Section VII. The converter was run at different power levels, input and output voltages, and power factors. All claims made from the simulation studies were verified experimentally. This section will describe the results. A. Zero Phase Shift Fig. 21 shows the input-voltage and current waveforms for zero-phase-shift (unity power factor) operation, with V(rms), V, and two different input-current levels. Current waveforms were obtained from the output of the circuit sensing , which is a voltage signal proportional . to The system was run at different input and output voltages apart from the ones specified in Section II. It was seen to Fig. 23. Spectrum of input-current waveform in Fig. 22 (without fundamental). be satisfactory for different conditions. Just one condition is shown here. Fig. 22 shows the waveforms for V(rms). The spectrum of the ripple component of input current was examined. The fundamental component of the input current was removed using a high-pass filter, giving a voltage signal proportional to the ripple current. The spectrum of the inputcurrent waveform in Fig. 22 is given in Fig. 23. The spectrum in Fig. 23 indicates components centered around integral multiples of the switching frequency of 10 kHz. (The amplitude of the 10-kHz component is about 4% of the fundamental.) This clearly indicates constant-frequency switching. It may be noted from Fig. 23 that there is a very small component around 5 kHz. This is due to slight instability in the current waveform just after the zero crossings ORUGANTI et al.: CRITERION SCHEME FOR CONTROL OF BOOST-TYPE AC–DC CONVERTERS (a) 55 (b) Fig. 24. Input-current waveform with 60 phase shift. (a) Current leading. (b) Current lagging. Fig. 25. Response to a step change in input-current reference between 2–6.6 A (rms). (a) Step rise. (b) Step fall. (a) before switching over to the stable mode of operation. The changeover between mode sequences is done once the value of goes beyond a threshold value, which is ideally 50% of . This threshold value was decided based on the software execution time. This value has to be at least equal to the maximum execution time (including the ADC time). Due to this consideration, the threshold was made 65 s. As a result of this, the instability after zero crossings is allowed to persist. This instability shows up as the component around 5 kHz. This can be minimized by limiting this threshold to close to 50% of . This is possible by using faster ADC’s and optimizing the program for faster operation. B. Nonzero Phase Shift The system was run for nonunity power-factor operation also. The software needed little change to accommodate the nonzero phase shifts. Fig. 24 shows the input-current and voltage waveforms with a 60 phase shift at input voltage of 110 V(rms) and current of 7.7 A(rms). Regenerative operation was not tried out due to nonavailability of active load that can sustain at the dc link. Still, nonunity power-factor operation demonstrates the feasibility of bidirectional power flow using the PECC method. C. Transient Response Fig. 25 shows the response of the converter with the PECC method for a step change in input current. Current is made to (b) rise and fall between 2–6.6 A(rms). The response is seen to be extremely fast. It can be clearly seen from the plots that the current is made to change to the new value of reference in the fastest possible way. IX. CONCLUSION A control method for a single-phase boost-type ac–dc converter was developed and evaluated through simulation. Experimental results proved the workability of the method. The method was shown to have the advantages of constant switching frequency with fast dynamic response. The main idea behind the method is to determine the duty cycle of operation of the switches in a given switching period such that the input average current tracks the input-current waveform template on a cycle-by-cycle basis. The paper discussed how the problems encountered in achieving stable and smooth operation are overcome by incorporating changes in the control method. The final method arrived at is named the PECC method. Both the PECC and conventional HCC methods have been compared. The PECC method was also simulated and experimentally verified for arbitrary power factors and found to give stable and smooth operation. The control implementation is somewhat complex, necessitating the use of microprocessors as it involves calculations for on time in each switching interval. Nevertheless, the scheme offers several advantages 56 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 1, JANUARY 1998 like simplified input filter design, fast dynamic response, and stable operation under different power factors and inputcurrent levels. The switching frequency of 10 kHz can be increased appreciably by using faster ADC’s and higher end processors that are currently available. APPENDIX B DERIVATION OF (6) and is obtained. First, the relation between The variables and are substituted by the perturbed values and in (3) and (4) to give APPENDIX A DERIVATION OF (3)–(5) are derived. Then, from these First, the equations for equations, the areas under and are found and equated to get the condition to satisfy ECC. Refer to Fig. 5(a). During the time – , device set (2, 3) is on. Then, the equation for voltage across the inductor is (B-1) The higher order perturbation terms can be neglected. Expanding the terms in (B-1) and substituting (A-14) in (B-1) (B-2) (A-1) Perturbing the variables in (A-7) Simplifying and integrating (A-2) In (A-2), at is the current (denoted as at . The value of ) from (A-2) is (A-3) , device set (1, 4) is switched on. The voltage across At the inductor when (1, 4) is on is (A-4) Simplifying and integrating (A-5) at The value of (denoted as ) from (A-5) is (A-6) Substituting for from (A-3) in (A-6) and simplifying (A-7) For ECC to be satisfied [see Fig. 5(a)] Area ADEB Area BEFC Area AGHC (A-8) ADEB (A-9) BEFC (A-10) AGHC (A-11) Substituting (A-3), (A-7), and (A-9)–(A-11) in (A-8), (3) and (4) are obtained. Following the same approach for Mode Sequence II in Fig. 5(b), the other condition for ECC can be worked out. (B-3) Substituting (A-7) in (B-3) and simplifying (B-4) Equation (6) is obtained by substituting (B-2) in (B-4) and simplifying. REFERENCES [1] B. T. Ooi, J. C. Salmon, J. W. Dixon, and A. B. 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[13] Unitrode Power Supply Design Seminar Manual, Unitrode Corp., Lexington, MA, 1991. [14] R. Oruganti, K. Nagaswamy, and K. S. Lock, “A constant frequency variable power factor PWM scheme for single phase boost type ac–dc converter,” in IEEE Int. Conf. Energy Management and Power Delivery, 1995. ORUGANTI et al.: CRITERION SCHEME FOR CONTROL OF BOOST-TYPE AC–DC CONVERTERS Ramesh Oruganti (S’83–M’85) received the B.Tech. and M.Tech. degrees from the Indian Institute of Technology, Madras, India. In 1987, he received the Ph.D. degree from Virginia Polytechnic Institute and State University, Blacksburg. He worked for two years at the Corporate R&D Division of the General Electric Company on advanced power converter systems. Since 1989, he has been a Senior Lecturer in the Electrical Engineering Department, National University of Singapore. His research interests in power electronics include soft-switched converters, active power-factor improvement, and converter modeling and control. He is currently the Director of the Center for Power Electronics in the Faculty of Engineering, National University of Singapore. Dr. Oruganti is a Member of the honor societies of Phi Kappa Phi and Eta Kappa Nu. Kannan Nagaswamy received the Master of Engineering degree in electrical engineering from the Indian Institute of Science, Bangalore, India, in 1991. He worked as a Senior Engineer (R&D) at the Industrial Systems Group, National Radio and Electronics Co. Ltd., from August 1991 to August 1994, where he was involved in the design, development, and testing of microprocessor-based induction motor drives. From September 1994 to September 1996, he was a Research Scholar in the Department of Electrical Engineering, National University of Singapore, Singapore, pursuing research in single-phase boost-type ac–dc converters. He is now with HewlettPackard, Singapore, where he provides electrical engineering and systems support for the assembly lines making inkjet cartridges. 57 Lock Kai Sang received the B.Sc. and Ph.D. degrees from the University of Strathclyde, U.K., in 1975 and 1979, respectively. He was the Head of the Power and Machines Division in the Department of Electrical Engineering, National University of Singapore, Singapore. He is currently with the Center for Power Electronics, Department of Electrical Engineering, National University of Singapore. His areas of specialization are design and analysis of small electric machines, control of electric drives, and power system harmonics. He has undertaken a number of industrial consultancy projects related to these areas. Dr. Sang is a Member of the Institution of Electrical Engineers, U.K., and a registered Professional Engineer in Singapore.