Proceeding of the th International Middle Eat Power Sytem Conference (MEPCON ), Cairo Univerity, Egypt, December 9-,, Paper ID 7. Digital Control of Boot PFC AC-DC Converter with Predictive Control H.Z.Azazi *, E. E. E-Kholy **, S.A.Mahmoud * and S.S.Shokralla * * Electrical Engineering Department, Faculty of Engineering, Menoufiya Univerity, Shebin El-Kom, Egypt ** King Abdulaziz Univerity, Faculty of Engineering, Electrical Engineering Department, Saudi Arabia Email: Dr_hn98@yahoo.com Abtract: For digital power-factor correction (PFC) control method, the duty cycle i calculated in every witching period. One main implementation barrier i the limited witching frequency, due to the limited proceor peed. In thi paper a predictive digital PFC control method i propoed to olve thi problem. The propoed control method generate all the duty cycle in advance, baed on the erence current and ened inductor current, input voltage and output voltage. It require only one multiplication and three addition operation for digital implementation, o that the propoed PFC control method can be implemented (by uing a low cot DSP or microproceor to achieve high witching frequency). A power factor correction rectifier, that require a current control with a rectified inuoidal erence, i controlled uing three method: i) Average current mode control ) Hyterei control i) Propoed predictive control. All thee controller are implemented on a digital platform. Simulation reult how that predictive control ha low THD, high PF, lower cot and better performance than the other control method (due to it lower calculation requirement). Alo, inuoidal input current can be achieved under a non-inuoidal input voltage condition for predictive control only. Keyword: Converter control, Power factor correction, Total harmonic ditortion (THD), Digital control. I. INTRODUCTION Power factor correction (PFC) converter are widely ued nowaday. Thee converter aim to increae the power factor (PF) and decreae the total harmonic ditortion (THD) of it input current. International tandard, a the IEC 6--, retrict the maximum allowed THD for the current drained from the electric ytem [-]. The boot converter with digital controller i one of the mot uitable for thi purpoe [-5]. The analog control ha been the conventional method of power factor correction (PFC) in witched mode power upplie (SMPS). The emergence of powerful, low cot microproceor, digital ignal proceor (DSP) and field programmable gate array (FPGA) have made it poible for the digital control to become a competitive option [6-8]. However, mot of the exiting digital PFC control method are baed on conventional analog control law. They baically implement the analog control law in a digital format [, 9-]. In conventional digital implementation, multiplication and divon operation are implemented by the oftware. Becaue all the calculation, are executed in every witching period, the implementation of conventional method require a high peed digital controller []. With the development of digital technique, many advanced control trategie can be implemented by digital proceor. Digital control i the trend in witching mode power upply application, however, it till face everal technique in the digital implementation of high witching frequency power upplie, including AC-DC and DC-DC converter. For AC-DC converter with power factor correction, there are everal diadvantage in the exiting digital control PFC implementation baed on conventional current mode control, uch a high computation requirement, limited witching frequency and high cot [9, ]. In order to take full advantage of digital technique, predictive control method are being explored and implemented in digital controlled PFC [-]. Reference [] and [5] preent a digital predictive deadbeat control, that doe not update the duty cycle in every witching cycle, becaue the DSP i not fat enough to complete all the calculation. In the predictive dead-beat (PDB) control, the duty cycle,, i calculated and updated once in every control period, which i everal, or everal ten of witching cycle. However, thi control method work only under the ideal input ituation, becaue the input voltage i determined by a look-up table. In addition, the harmonic in the line current i increaed in the Boot PFC implementation controlled by that method. Digital current program control, uing another predictive algorithm wa preented in Ref. []. In Ref. [], the duty cycle, ), wa calculated baed on the value of the preent duty cycle,, and ened inductor current, input voltage and output voltage. The problem i that, the duty cycle calculation require the duty cycle value in the previou witching cycle. Theore, if there i an error in the calculation value of, thi error will affect the calculation value of ). Although o many digital PFC control method were preented in the erence paper, there are till everal problem that needed to be olved for digital implementation. In digital control PFC, the problem are mainly related to the following apect: high calculation required in one witching cycle, high cot of the digital controller and limited witching frequency compared with analog control. In thi paper, in order to achieve higher witching frequency with low cot, low calculation requirement and better performance than the conventional PFC control method a predictive digital PFC control i propoed. One of the ignificant characteritic of the propoed digital PFC 7
control method i that the witching frequency i not directly dependent on the peed of the DSP. Theore, a low-cot DSP/microproceor could be ued to control the witch operating at a high witching frequency. In order to evaluate predictive control a an alternative to control a PFC rectifier, two claical input current control method are conidered: average current mode control and hyterei control. II. DIGITA PFC CONTRO BASED ON AVERAGE CURRENT MODE CONTRO DSP control of a boot PFC baed on average current mode control i illutrated in Fig. In the outer voltage loop, the output voltage i ened and compared with the voltage erence. The error become the input of the voltage proportional-integral (PI) controller. The output of thi PI controller i the caling factor for the rectified voltage that i ued a one of the input to the multiplier. The product of the caling factor and the rectified voltage divided by the quare of the root mean quare (RMS) of input voltage i the current erence, i. The inner current loop implement average current mode control to force the average inductor current to follow the erence current. In digital implementation for average current mode control, multiplication and divon operation are implemented by the oftware. Becaue all the calculation, including multiplication and divon, are executed in every witching period, the implementation require a high peed digital controller. The procee in a digital control PFC baed on average current mode control include: output voltage ample, voltage error calculation, voltage PI controller, erence current controller (including two multiplication and one divo, current error calculation, current PI controller and duty cycle calculation. Becaue thi proce i iteratively running in every witching cycle, a high performance DSP i needed. The average current mode control work well in analog controlled PFC ytem, however, it i not uitable for digital control PFC implementation, becaue it high calculation requirement. III. HYSTERESIS CURRENT CONTRO Thi i a continuou current, variable witching frequency current control cheme. The boot inductor current i continuouly compared with the erence current waveform (which i obtained from the voltage control loop) and the error ignal (after amplificatio i fed into a hyterei comparator. When the actual inductor current goe above the erence current by the comparator hyterei band, the comparator change it tate to witch off the boot witch and the current ramp goe down. When the actual current goe below the erence current by the comparator hyterei band, it change tate again and turn the boot witch on. Thu, the inductor current i alway maintained within ±H, where H i the total hyterei band. A imple diagram of a typical hyterei current controller i hown in Fig.. (a) Functional diagram. (b) Current and PWM waveform. Fig. General hyterei current control cheme. IV. PREDICTIVE AGORITHM FOR BOOST CONVERTER The topology of Boot converter i hown in Figure. The propoed predictive PFC algorithm i developed baed on the following aumption: () Boot converter operate at continuou conduction mode; () The witching frequency i much higher than the line frequency. Theore, the input voltage, V in,, and output voltage, V, can be aumed a contant during one witching cycle, T. Thu, when the witch S i on or off, the boot converter i decribed by two mode of operation, a hown in Fig.. Fig. Boot converter topology. Fig. Digital control PFC implementation baed on average current mode control. 7
i ( n + ) = i ( + d ( )) + ( Vin ( ) ( ) ( d ( ) (6) (a) Mode (b) Mode Fig. Boot converter equivalent circuit. When the witch i on, the inductor current, i (t), can be expreed a: di = Vin(t) For t < + () dt When the witch i off, the inductor current, i (t), can be expreed a: di = Vin( t) ( t) For + t < ) () dt Where V in (t) i the input voltage, (t) i the output voltage, and ) are the beginning intant of n th and () th witching cycle, i the duty cycle in the n th witching cycle, and T i the witching period. Becaue the witching frequency i much higher than the line frequency, the differential equation () and () can be expreed a: i ( + ) i( ) = Vin( ) () i( )) i( + ) = Vin( ) V o( ) Where i [], i [)] are the inductor current at the beginning of nth and () th witching cycle. The inductor current in one witching cycle i hown in Fig. 5. () Subtituting equation (5) and (6), the inductor current at the beginning intant of () th witching cycle in term of the inductor current at the beginning intant of nth witching cycle can be derived a: i( n + ) = i( ) + Vin( ) (7) ( ) ( ) The dicrete form of equation (7) can be expreed a: Vin( t) ( ( ) i( ) = i( ) + (8) The above equation indicate that the inductor current at the beginning of the next witching cycle i determined by the inductor current at the beginning of the preent witching cycle, the input voltage, the output voltage and the duty cycle for the preent witching cycle. Equation (8) can be rewritten a i( n + ) i( Vin( = + (9) TS It i oberved that the required duty cycle for the preent witching cycle,, can be determined baed on the boot circuit parameter, the output voltage, the input voltage and the required inductor current. In a properly deigned AC-to-DC converter with PFC, i (), i forced to follow the erence current, i (), which i a rectified inuoidal waveform. V o, i controlled to follow the erence voltage, V.. Subtituting i (), V for i () and V o in equation (9), the duty cycle can be derived a: i ( ) i( V Vin( = + () T V V S The erence current, i i determined a: i ()=K PI. in(ω line.) () K PI i the peak value of erence current, which i the output of the voltage loop controller, (i the rectified inuoidal waveform), it can be determined by a look-up table in digital implementation or a reitor divider from the rectified input voltage. The block diagram of the digital controlled boot PFC baed on the Predictive control algorithm i hown in Fig. 7. Fig. 5 Inductor current in one witching cycle. The inductor current at the witching off intant, +T, can be derived from equation () a: i( + ) = i( ) + Vin( ) (5) The inductor current at the beginning intant of () th witching cycle,), can be derived from equation () a: V. SIMUATION RESUTS The control algorithm of the current control method have been developed and implemented on the MATAB/SIMUNK programming environment. The purpoe of thi imulation i to how the effectivene of the different control trategie for PFC circuit and in reducing the upply current harmonic ditortion. 7
5 Supply Current in Amp. - - i( ) i( V Vin( = + T V V S - - -5.9.95.9.95.9.95.9.95.9 (b) Hyterei current control. 5 Fig. 7 Digital implementation of propoed Predictive control. The PFC boot converter i deigned with the following pecification: ac input voltage, V; dc output voltage, V; load reitance, 7 Ω ; line frequency (f),5 Hz ; inductor (), mh and dc link capacitor (C), 5 uf. The teady tate imulation reult of input current and it pectrum for all current control method are hown in Fig.8 and Fig.9 repectively. It i hown that, the predictive current control imulation how maller harmonic content of the three control method, and an input current i nearly inuoidal. The power factor for average current mode control, hyterei current control and predictive current control are.9889,.996 and.9998 repectively. Figure how the teady tate input voltage (V i ) and current (i i ) for ideal input voltage for the three control method. It i hown that, the input current in phae with the input voltage for three control method. The rectified voltage (V R ), rectified current (i R ) and erence current (i ) under the teady tate are hown in Fig. for three current method. The input current waveform under a ditorted input voltage condition are hown in Fig.. Reult how that inuoidal input current waveform can be achieved under a non-inuoidal input voltage condition for predictive current control only. The dynamic performance under the tranient tate for a tep change in load i hown in Fig.. It i hown that, dynamic repone for the predictive current control i fater than other two method. Supply Current in Amp. 5 - - - - -5.9.95.9.95.9.95.9.95.9 7 Magnitude in Amp Magnitude in Amp Supply Current in Amp. - - - - -5.9.95.9.95.9.95.9.95.9.5.5.5.5.5 Fig. 8 Input current waveform. 5 Harmonic Number.5.5.5.5.5 (b) THD=% THD=9% 5 Harmonic Number Hyterei current control.
.5 5.5 THD=.9% V R Magnitude in Amp.5.5 ltage in V 5 5 I I R.5 5 5 Harmonic Number Fig. 9 Total harmonic ditortion..9.95.9.95.9.95.9.95.9 5 5 V R - - ltage in V 5 5 I R I -.9.95.9.95.9.95.9.95.9.9.95.9.95.9.95.9.95.9 (b) Hyterei current control. 5 V R - - -.9.95.9.95.9.95.9.95.9 (b) Hyterei current control. ltage in V 5 5 5 I R I.9.95.9.95.9.95.9.95.9 Fig. Rectified voltage, rectified current and erence current. - - i i - - - i i -.9.95.9.95.9.95.9.95.9 Fig. Input voltage and current for ideal upply voltage..9.95.9.95.9.95.9.95.9 75
.8.6 - - Error in V.. -. -. -.6 (b) Hyterei current control. Fig. Input voltage and current for ditorted input voltage. Error in V.8.6.. -. -. -.6 -.8 Error in V - - - - -.8.6.. -. -. -.6 -.8.9.95.9.95.9.95.9.95.9.6.7.8.9.. - (a).9.95.9.95.9.95.9.95.9 Average current mode control..6.7.8.9.. (b) Hyterei current control. -.8 -.6.7.8.9.. Fig. Tranient repone for tep change in load. VI. CONCUSIONS One diadvantage of the exiting digital PFC control method i that the witching frequency i limited due to the proceing time of the DSP. Predictive digital PFC control method wa propoed in thi paper to olve thi problem. The propoed control method generate all the duty cycle in advance baed on the erence current and ened inductor current, input voltage and output voltage. It require only one multiplication and three addition operation for digital implementation, o that the propoed PFC control method can be implemented by a low cot DSP or microproceor to achieve high witching frequency. Other two control method have been ued in order to evaluate predictive control a an alternative to control a PFC converter. The predictive control method i impler than other commonly ued method. Simulation reult howed that predictive PFC control ha low THD, high PF, lower cot and better performance than the other control method due to it lower calculation requirement. Alo, inuoidal input current can be achieved under a non-inuoidal input voltage condition for predictive control only. The predictive digital PFC control method can achieve good dynamic performance for load change. REFERENCES [] Compliance Teting to the IEC -- (EN 6--) and IEC - - (EN 6- -) Standard, Application Note 7, Hewlett Packard Co., December 995. [] Wanfeng Zhang, Guang Feng, Yan-Fei iu and Bin Wu," New Digital Control Method for Power Factor Correction", IEEE Tranaction on INDUSTRIA EECTRONICS, l. 5, no:, pp. 987-99, 6. [] Supratim Bau and Math.H.J.Bollen, "A Novel Common Power Factor Correction Scheme for Home and Office," IEEE Tranaction on Power Delivery, l., No., July 5. [].Roggia, F.Beltrame, J.E.Baggio and J.R.Pinheiro,"digital control ytem applied to a PFC boot converter operating in mixed conduction mode", in Proc. IEEE Appl. Power Electron. Conf., pp. 698 7, 9. [5] Yu-Tzung in and Ying-Yu Tzou, "Digital Control of Boot PFC AC/DC Converter with ow THD and Fat Dynamic Repone," IEEE IPEMC Conf. Rec., pp. 67 677, 9. [6] F.J.Azcondo, A.de Catro, V.M.opez and O.Garcia, "Power Factor Correction without Current Senor baed on Digital Current Rebuilding," IEEE Tranaction on Power Electronic, l. 5, pp. 57 56, 9 [7] V.M.Rao, K.A.Jain, K.K.Reddy and A.Behal,"Experimental Comparion of Digital Implementation of Single-Phae PFC Controller," IEEE Tranaction on Power Electronic, l. 55, No., pp.67-78, 8. 76
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