Digital Control of a Single-Phase Boost Rectifier with Power Factor Correction Using a dspic

Transcription

1 Digital Control of a Single-Phase Boost Rectifier with Power Factor Correction Using a dspic O. opez-santos, Member, IEEE, H.F. Murcia, Student Member, IEEE, J.M. Barrero Universidad de Ibague, Ibague, Colombia Abstract A digital implementation of a boost rectifier with power factor correction (PFC) is presented. The proposed control involves a current control loop and a voltage control loop. The current control loop is implemented with two different methods: (a) linear compensation; and (b) ON-OFF control. The voltage control loop is implemented with a proportional-integral (PI) controller. Several Simulink/MATAB simulations of the converter operating with both current control methods are presented. An assessment of the total harmonic distortion (THD) measurements shows the advantages of the simple ON-OFF controller. Finally, experimental results obtained from a 100W prototype using a low-cost 16-bit microcontroller are included and discussed. Index Terms AC-DC power converters, power factor correction, power factor correction, 16-bit microcontroller. I. I NTRODUCTION the last three decades, the switch mode power supplies (SMPS) have replaced the conventional power supplies based in low frequency rectification. This is mainly due to two necessities: a) higher efficiency, and b) less size, weight and cost. The application of power factor correction (PFC) techniques in the SMPS is an effective solution to avoid adding pollution to the power grid. Hence, academic and industrial efforts have allowing the development of the pulse-wih modulated (PWM) rectifiers [1]. These rectifiers have been studied in different converter topologies, such as, fly-back, Cu k, SEPIC and Boost. However, the boost PFC rectifier is the most commonly used topology in single-phase applications. This trend has prompted the industrial manufacture of integrated circuits that allow an easy implementation of the low-power boost PFC rectifiers [2][4]. Despite, the use of analogic electronics in control circuits is also common. Recently, the digital implementation has taken importance due to the availability of the digital technologies and the cost reduction [5]-[6]. Thus, the functionality of the boost PFC rectifiers can be enhanced [7]-[8]. In order to control the boost PFC rectifier, a cascaded control structure with two loops is commonly applied. The inner loop shapes the input current with a sinusoidal waveform at the same frequency and phase of the grid voltage. Thus, the source perceives the rectifier converter like a resistive load. With this aim, it has been applied different methods, such as, sliding-mode control, predictive control and nonlinear carrier control, among others [9]-[11]. The outer loop regulates the output voltage through a proportional-integral controller (PI) with a set-point always higher than the peak of the input voltage. Further, this control loop determines the amplitude of the current reference for the inner loop. I N /12/$ IEEE The implementation of the above mentioned control system using a digital device only requires three channels with analog-to-digital conversion capabilities. These inputs capture the signals of input current, input voltage and output voltage. Further, a digital output is needed for the switch control. This requirements are available in many low-cost digital devices and hence the truly challenge is to accomplish the control aims with an acceptable processing time. Thus, it is worth to point out that the information losses caused by quantization, output resolution, acquisition times and processing times can be accentuated by limitations in a low-cost digital implementation[6]. The paper is organized as follows: The second section presents both a linear and a non-linear model of the boost converter. After that, in third section we present the design of the control system with two different methods of the current control. The fourth section is dedicated to present the results of the Simulink/MATAB simulations. The fifth section shows the experimental results and explains micro-controller implementation. Finally, conclusions are discussed in the last section. II. C ONVERTER MODEING The basic configuration of the boost PFC rectifier uses a diode bridge followed of a conventional DC-DC boost converter. Thus, the converter operates always with a positive input voltage. The boost converter can operate in either continuous conduction mode (CCM) or discontinuous conduction mode (DCM) or both. The work here presented focuses in CCM operation in order to avoid high stresses in components and an additional filter stage. Figure 1 shows the ON and OFF states of the boost converter operating in CCM. Figure 1. Circuit configurations of a boost converter: a) ON-state, b) OFF-state.

2 We denote the variable u as the control variable. When u=1 then the converter is in ON-state, and when u=0, then the converter is in OFF-state. The ON-state differential equations system is: di = vi = v C The OFF-state differential equations system is: di = vi v C = i C v C On the other hand, the ON-state differential equation system (1) can be also represented in the form ẋ = A 1 x + B 1 u as follows: [ di ] [ ] [ ] [ ] i = vi (3) v C 0 and the OFF-state differential equation system (2) can be represented in the form ẋ = A 2 x + B 2 u as follows: [ di ] = [ C 1 ] [ i (1) (2) ] [ 1 ] + vi (4) v C 0 From expressions (1) and (2), or from expressions (3) and (4), we can derivate either a non-linear model or a linear average model in order to control the current waveform. A. Non-linear model Using the definition of the control signal u, the expressions (1) and (2), can be represented with the non-linear equation system (5). di B. inear average model = vi v C (1 u) = v C + i (1 u) C With a fixed frequency defined by a PWM modulator and considering δ 1 as the cycle-by-cycle average duty cycle, we obtain an average model from expressions (3) and (4). x = [A 1 δ 1 + A 2 (1 δ 1 )] x + [B 1 δ 1 + B 2 (1 δ 1 )] vi Finally, it is derived the small-signal transfer function of the inductor current with respect to duty cycle (6) using the method presented in [12]. 2V G id (s) = (1 D) 2 R 1 + s 1 + s 2 (1 D) 2 R + s2 C (1 D) 2 (5) (6) III. CONTROER DESIGN A cascaded control structure with two loops is used in order to obtain the control objectives. The inner loop achieves low distortion in the input current and unity power factor. For this, the current controller shapes the inductor current with a reference waveform which is a rectified version of the grid voltage. Thus, it is possible to keep the input current with the same frequency and phase that the input voltage. The outer loop regulates the output voltage with a set-point always higher than the peak of the input voltage and simultaneously it determines the amplitude of the current reference of the inner loop. It is worth to point out that in this cascaded scheme, the current controller must operate at least 10 times faster than the voltage loop in order to maintain stability. In this work, we compare two different controllers for the inner loop: an ON-OFF controller and a linear controller. A. ON-OFF current controller Since the boost converter is a variable structure system with only a control input, it is possible to achieve that the inductor current follows a defined reference. This is mainly due to the fact that in the ON-state the inductor current increases and in the OFF-state the inductor current decreases. Hence, if the control law leads the inductor current near to the current reference, a continuous tracking can be obtained. The accuracy of the ON-OFF controller depends of the physical limitations of the power and control stages. A simple ON- OFF control law can be defined as follows: u = { 0, If I ref I < 0 1, If I ref I 0 considering that the current reference I ref is a rectified sinusoidal waveform. Meanwhile, the amplitude of this current reference is defined by the outer loop. B. inear current controller The application of linear controllers in the current loop of the boost PFC rectifier bases on PWM. Hence, the controller manipulates the duty cycle in order to accomplish the tracking of the current reference. It is possible to use a classic method to design a linear controller since we have a current to duty cycle transfer function (6). Thus, the controller due forcing this second order minimum phase transfer function to track a reference signal with a frequency two times higher than the grid frequency. This requirement traduces in a wide band-wih and a generous phase margin. The band-wih is limited to 1/3 of the switching frequency in order to avoid interferences in the control loop caused by the power stage. Often, the phase margin is defined higher than 40 degrees. Thus, we propose the linear compensator of the expression (8) designed in the frequency domain. C c (s) = K c ( T1 s + 1 s ) ( ) α2 T 2 s + 1 T 2 s + 1 (7) (8)

3 This transfer function corresponds to a two-stage phase compensator. The first stage introduces a pole in zero in order to eliminate the steady-state error and a zero what maintains the proper transfer function condition. The second stage is a simple phase compensator. In our design the first stage of the controller is add directly to the converter transfer function and after that, we design the phase compensator using the frequency domain technique [14]. After design, the linear controller is leaded to the discrete time form (9). C c (z) = K d (z b 1 ) (z b 2 ) (z 1) (z a 1 ) (9) C. Voltage regulator Normally, the voltage control loop regulates and stabilizes the output voltage in a value a few times higher than the peak amplitude of the grid voltage. A PI controller is a good choice due to the fact that this controller provides minimum error and its low band-wih does not affect considerably the transient response. In order to design the PI controller it is necessary obtaining a transfer function of the system controlled by an ideal inner loop. Hence, we consider the energy balance presented in (10). vi I ref = vo i C + vo io (10) By replacing of i C, the expression (9) becomes in the differential equation (11). C dvo = 1 ) (vi I ref vo2 (11) vo R However, this expression leads to a non-linear dynamic. By applying linearization, it obtains: C dṽo = 2 vi ṽo + (12) R voĩref Thus, the dynamics in the output voltage can be represented by the transfer function (13). G v (s) = ṽo (s) Ĩ ref (s) = K T v s + 1 (13) where K = R/2 y T v = /2. With this result, the PI controller can be designed. We use the pole placement technique in order to minimize the Integral of Time Absolute Error (ITAE) performance index [13]. The characteristic polynomial in continuous time is selected as s s + 1. After design, the PI controller is leaded to the discrete time PI form (13). Gc P I = Kp + Ki 1 z 1 (14) The sample time of the voltage loop is selected 10 times higher than the sample time of the current loop. However, this consideration can be constrained by the minimum sample time obtained with a digital device. Figure 2 depicts the complete control scheme of the boost PFC rectifier. Figure 2. Control scheme of the boost PFC rectifier with cascade control IV. SIMUATIONS In order to verify the proposed design, we have been built a Simulink/MATAB model. In this model has been assessed the cascade control system with both current control methods and the PI voltage controller. A. ON-OFF current controller The non-linear controller law presented in (7) was digitally implemented in simulations. The expected dynamic of an ideal comparator changes due to the processing time in the digital device. The simulations work with the minimum sample time obtained with a dspic when the control system operates with both loops. Thus, the inductor current remains around of the desired instantaneous value with a non-periodic deviation introduced by the processing time. Figure 3a depicts the current waveform and figure 3c shows that this control method reduces the THD about 6.71%. All harmonic components have individual percentages below 2% and hence this result is in good agreement with the IEEE and IEC normativities [15]-[16] considering a maximum power level of 600W. B. inear current controller Using the aforementioned design method we obtain firstly the transfer function of a continuous time linear controller. (s ) (s ) C c (s) = (s) (s ) (15) After that, we obtain the discrete time transfer function using a sample time T s = 50µs. (z 0.895) (z ) C c (z) = (z 1) (z ) (16) Figure 3b depicts thecurrent waveform and figure 3d shows that this control method reduces the THD about 7.92%. This result is also consistent, however does not exceed the better performance of the ON-OFF controller.

4 Figure 3. Simulation results: a) steady-state inductor current waveform with ON-OFF controller; b) steady state current waveform with linear controller; c) THD on input current with ON-OFF controller; d) THD on input current with linear controller; e) steady-state output voltage; and, f) load disturbance rejection. C. Voltage regulation As stated earlier, the voltage regulation was obtained using a PI controller. The continuous time transfer function has been discretized with a sample time T s = 500µs resulting in the discrete time transfer function (17). (z 0.959) C v (z) = (z 1) (17) As show in figure 3e, the PI voltage loop regulates the mean value of the output voltage with zero error using either a ON-OFF current controller or a linear controller. Also, it is possible to observe the ripple in the output voltage. In figure 3f, the dynamic performance of the voltage controller has been tested imposing two step load perturbations. Initially, in 0.6 seconds the load resistance changes from 50Ω to 25Ω. After that, in 1.2 seconds the load resistance changes from 25Ω to 50Ω. It is possible to observe that the voltage deviation caused by the load disturbance has acceptable values of amplitude and settling time. To summarize, with a 50% load disturbance, the output voltage shows a maximum deviation less than 8% which is controlled in about 300ms. Based on the simulation results, the experimental work will be focused on the digital implementation of the control system with an ON-OFF current controller.

5 Figure 4. Detail of the circuit implementation of the digitally controlled boost PFC rectifier. V. EXPERIMENTATION In order to verify the theoretical analysis and the simulation results, a 100W prototype has been built. Figure 3 depicts the complete schematic circuit diagram of the prototype. Components and power electronic devices are listed in Table I. This section describes the control circuit and the control algorithm. After that, it present and discusses the measured results. Table I COMPONENTS AND DEVICES USED IN THE EXPERIMENTA PROTOTYPE PARAMETER REFERENCE VAUE Inductor 600µH Capacitor C 10µF oad Resistance R 2 50Ω Schottky Diode APT30S20BG-ND 10A MOSFET IRFP V/45A Diode bridge KBPC A Current sensor ACS A Voltage sensor VP V/6V A. Prototype Figure 5 shows the two circuit printed circuit boards (PCB) used in the prototype: the power PCB and the control PCB. The power PCB contains the power converter and the regulated sources of the control circuit. The control PCB contains the conditioning circuits and the microprocessor. The power stage is a well-known circuit and hence, we mention only characteristics of our control circuit: A 16-bit microcontroller dspic16f4011 from Microchip was utilized for the control system. This microprocessor operates with a clock frequency of 119.6MHz synchronized by an internal phase looked loop (P). We use three independent channels of the analog-to-digital converter module operating with simultaneous sampling. The input-current sensor was conditioned using a secondorder low-pass filter and an instrumentation amplifier with high common mode rejection ratio (CMRR) to reduce the effect of the interferences induced by the power stage.

6 C. Measurements Figure 6 shows the current waveform measured with a oscilloscope S4622D from Agilent. It is possible to observe the inductor current in comparison with the reference current. The experimental results are in good agreement with the simulation results. However, a zero-crossing distortion can be observed. This effect is mainly due to the fact that the converter topology is limited to increase the inductor current near to the zero-crossing of the grid voltage. Figure 5. stage. Modules of the experimental prototype: a) power stage, b) control The output-voltage sensor was conditioned with a secondorder low-pass filter with a cut-frequency of 80Hz in order to reduce the ripple component without to affect considerably the transient response of the outer control loop. The input voltage reference is obtained through a lowpower, low-frequency transformer that reduces the grid voltage from 120V to 2V. This signal is rectified with a precision rectifier implemented with operational amplifiers and low drop-voltage diodes. A ±15V dual voltage source is necessary to feed the control circuit. The positive source is obtained with a linear regulator and the negative source with a switched capacitor inverter circuit. A auxiliary source of 5V is used to feed the microprocessor. The driver circuit of the power MOSFET has been implemented with a IR2110 from International Rectifier. Figure 6. Oscilloscope capture of the steady-state inductor current waveform The dynamic performance of the voltage controller has been tested with a pulsating load perturbation. The load changes between 50Ω and 25Ω with a period of 5.5s. The output voltage shows a maximum deviation less than 10% which is controlled in about 300ms. The differences in the dynamics of the real implementation can be attributed to both the rounding of the coefficients in the difference equation of the controller and the effect of the filtering stage in the output votage measurement. B. Algorithm The algorithm operates with an internal timer interruption that defines a global sample time in 50µs. Data acquisition, analog-to-digital conversion and inner control loop need 27µs. The difference equation of the voltage controller is segmented in order to distribute the computational charge cycle-by-cycle. Thus, the global sample does not increase considerably and the sample time of the outer loop can be defined easily. We work with a sample time of 500µs in the voltage loop. Figure 7. Oscilloscope capture of the output voltage with a pulsanting load disturbance

7 Figure 8 shows the measurements obtained with a Fluke 43B Power Quality Analyzer. It is possible to observe in figure 8a a THD of 7.7% and in figure 8b a unity power factor. Also, the waveform of both grid current and grid voltage are presented in figura 8c and 8b in order to recognize the difference with and without control. REFERENCES [1] R.W. Erickson, and D. Maksimovic. Fundamentals of Power Electronics. Kluwer Academic Publishers, th. Edition. pp [2] P.C. Todd. UC3854 Controlled Power Factor Correction Circuit Design. UNITRODE. Application Note U pp [3] ON Semiconductor. MC33368 High Voltage Greenine Power Factor Controller [online]. Available: [4] Fairchild Semiconductor. Theory and Application of the M4821 Average Current Mode PFC Controller. Application Note [5] P. Mattavelli, and S. Buso. Digital Control in Power Electronics. Morgan & Clypool Publishers [6] A. Emadi, A. Khaligh, Z. Nie, and Y. ee. Integrated Power Electronic Converters and Digital Control. C Press [7] P. Athalye, D. Maksimovic, and R.W. Erickson. DSP implementation of a single-cycle predictive current controller in a boost PFC rectifier. 20th Annual IEEE Applied Power Electronics Conference and Exposition - APEC Vol. 2. pp [8] F. De Belie, D. Van de Sype, K. De Gussemé, W. Ryckaert, and J. Melkebeek. Digitally controlled boost PFC converter with improved output voltage controller. Electrical Engineering. Springer Vol. 89. No. 5. pp [9] G. Chu, S-C. Tan; C.K. Tse, and S-C.Wong. General control for boost PFC converter from a sliding mode viewpoint. IEEE Power Electronics Specialists Conference - PESC pp [10] D. Maksimovic, Y. Jang, and R.W. Erickson. Nonlinear-carrier control for high-power-factor boost rectifiers. IEEE Transactions on Power Electronics Vol. 11. No. 4. pp [11] M. Perez, J. Rodriguez, and A. Coccia. Predictive current control in a single phase PFC boost rectifier. IEEE International Conference on Industrial Technology - ICIT pp [12] M. Rashid. Power Electronics Handbook. Academic Press pp [13] C-T. Chen. Control system design: Transfer-Function, State-Space, and Algebraic Methods. Saunders College Publishing pp [14] K. Ogata, Sistemas de control en tiempo discreto. Ed. Prentice Hall [15] Standard IEEE 519. [online]. Available: [16] Standard IEC [online]. Available: AUTHORS Figure 8. Experimental results: a) harmonic spectrum of the input current, b) power measurements, c) steady-state variables without control, and d) steadystate variables with control CONCUSIONS This work presents a favorable result in the digital implementation of a single-phase boost PFC rectifier using a low-cost digital processor. Also, simulation results indicate that the ON- OFF controller has a better performance than a linear controller tracking the current reference. Further, the real implementation of the ON-OFF controller requires less processing time. The implemented cascade control using an ON-OFF controller in the current loop accomplishes sufficiently the control aims. Finally, the THD measured on an experimental prototype is in good agreement with the simulation results and is conform to IEEE and IEC normativities. The results allows to continue in future works focuses in analytical argumentation of the ON-OFF controller using a sliding-mode approach and also to apply other techniques to reduce the processing time. ACKNOWEDGEMENT This work has been sponsored by the Universidad de Ibagué with the research project ID Oswaldo ópez Santos, received the Electronic Engineering degree from the Universidad Distrital F.J.C., Bogotá, Colombia, in 2002, and the M.S. degree in Industrial Automation from the Universidad Nacional, Bogotá, Colombia, in He is currently working toward the Ph.D. degree in the abortoire d Analysis et d Architecture des Systemes, Universite de Toulouse, Toulouse, France. From 2004 to 2009 he works as design engineer in the industry of uninterruptible power supplies. Actually he is a full time professor in the Program of Electronic Engineering of the Universidad de Ibague. There, he is member of the D+TEC Research Group, and his research is focused in linear and non-linear control of power converters applied in power factor correction, photovoltaic generation and uninterruptible power supplies. Harold Fabian Murcia Moreno, received the Electronic Engineering degree (with distinction mention) from the Universidad de Ibague, Ibague, Colombia, in He is currently working toward the Industrial Control M.S. degree in the same University. His research interests are in digital control, digital signal processing, power electronics and industrial applications. John Mauricio Barrero Junco, studies Electronic Engineering in the Universidad de Ibague, Ibague, Colombia. At the moment, he develops his final work in the industrial electronics area focused to power converters. His research interests are in digital control of power converters, digital signal processing and real-time computing.