A Passivity-Based Solution for CCM-DCM Boost Converter Power

Revised Personal Version. Original Version Available at http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6700426.

A Passivity-Based Solution for CCM-DCM Boost Converter Power Factor Control Emanuele Alidori, Gionata Cimini, Gianluca Ippoliti, Giuseppe Orlando and Matteo Pirro Dipartimento d’Ingegneria dell’Informazione, Universit`a Politecnica delle Marche, Via Brecce Bianche 12, 60131, Ancona, Italy Email: {g.cimini,gianluca.ippoliti,giuseppe.orlando,m.pirro}@univpm.it

Abstract—In this paper a Power Factor Control (PFC) of an AC-DC boost converter operating in light load condition has been presented. A Passivity-Based current control able to operate in either Continuous Conduction Mode (CCM) and in Discontinuous Conduction Mode (DCM) has been presented. Cascaded control with outer PI voltage loop and intermediary input voltage feedforward has been implemented in order to increase Power Factor (PF). The proposed solution has been numerically tested using a powerful software simulation platform.

I.

I NTRODUCTION

The harmonic reduction requirements imposed by regulatory agencies (IEC 1000-3-2 and EN 61000-3-2) and the ever increasing penetration of single-phase power electronic-based appliances into the different segments of end-use have accelerated interest in active power factor corrected preregulators for switching power supplies. AC-DC converters are extensively used in various applications. These electronic equipments use a rectifier as input stage and a large capacitor as a filter on the DC side. Non-linear loads draw non-sinusoidal currents and this will result in large current harmonics: a poor power factor is a by-product of these injected harmonics. The most important effects of harmonics in current due to lagging power factor are the deformation of voltage waveform coming from the utility supply, the result of I 2 R losses on the “utility side” of the grid, the increase in current flow in the capacitors which results in additional heating of the capacitors and reduce its life, the increase, especially due to triplen harmonics, of neutral currents magnitude in three phase systems (the neutral line is usually not sized appropriately for large currents), the over-heating in transformers and induction motors. Harmonic contamination and low power factor in power systems caused by power converters have been a great concern in particular to increase the efficiency in motor drives [?], [?], [?], [1], industrial robots [?], [2] and LED lighting system [?], [?]. Regulations from international bodies prohibit from drawing too much non-sinusoidal current; the implementation of a PFC technique forces the equipment to draw a sinusoidal current and thus is a required feature for a good quality power converter system which needs to meet stringent specifications on efficiency, harmonic distortion and voltage regulation. Most of these key performance indexes are closely related with its output power and input voltage. Extensive research papers have been presented to reduce system cost and complexity, from either control techniques or topological implementations [3]– [7]. Typically, in AC-DC converter, a PFC stage is placed

between the diode bridge and the bulk capacitor in order to shape the current and to give a DC output voltage on the capacitor. However, the output voltage of this PFC stage is poorly regulated: an additional downstream converter after the bulk capacitor is needed, that provides stiff voltage regulation and also usually includes isolation as well as stepping the voltage down to an appropriate level. In general, a PFC converter is designed to be operated in continuous conduction mode (CCM) even if there are control techniques to improve the power factor applied to converters which work in DCM [8], [9]. When the converter is operating in light load condition, it will operate in DCM and the voltage conversion ratio becomes a nonlinear function of the inductor current and input voltage [10]. Thus it will result in a lower efficiency and higher harmonic distortion under light load operation conditions, more specifically for load smaller than 20% of the rated load. Up to now many new topologies have been proposed and discussed in literature with the aim to achieve the required power factor. However, the most used solution in industry consists in a boost preregulator controlled with a monolithic control using the average current mode control technique. Nevertheless conventional ICs PF controller using analog solutions are based on a fixed operating mode and can not satisfy modern requirements of power quality and efficiency over wider operation range. With the recent developments in the microprocessor and DSP technologies, there is the possibility to implement complex PFC algorithms using these fast processors [?], [11]–[13]. Several interesting proposals have been presented in order to improve efficiency of AC-DC power converters operating in light load condition [14]–[17]. If the CCM average current controller is used for control in DCM, it will result in input current distortion; it is caused by inaccurate average current values obtained in DCM. The inductor current goes to zero before the end of the switching period. Thus, the average is not given by sampling in the middle of the rising edge of the inductor current. In [9], [18] digital DCM control scheme for boost PFC have been proposed. For the electrical and electromechanical systems considered in this paper, an interesting feedback control methodology has been developed with the aim to modify the closed loop energy dissipation and potential energy properties of nonlinear passive systems [19] and references therein. Passive systems are a class of dynamical systems in which the energy exchanged with the environment plays a central role. In passive systems the rate at which the energy flows into the system is not less than the

(a) Il (t) trend in CCM. Fig. 1.

(b) Il (t) trend in DCM.

Il (t) trends in CCM and DCM for a DC-DC boost converter.

increase in storage. The purpose of this approach, known as Passivity Based Control (PBC) design [19] is to render the closed-loop system passive with respect to a desired storage function. Passivity-based method has clear advantages in terms of considering the system physical structure in the control design procedure [20]–[22]. The main objective of the paper is to exploit PBC methodology of [19] in AC/DC boost converter and to extend the methodology to a light load scenario, deriving the control law from a mathematical model suitable for both DCM e CCM operation. The paper is organized as follows. Section II presents the two operation modes (CCM and DCM) of an AC-DC boost converter; in Section III boost model solution for DCM operation has been discussed and PFC cascaded scheme has been illustrated, focusing on DCM passivity current loop control design. Finally, in Section IV, PFC and voltage regulation performances have been compared in three different light load scenarios using a powerful software simulation platform. II.

DCM AND CCM OVERVIEW

In this section a description of CCM and DCM in a common DC-DC boost converter, together with a simple example, is provided. In a boost converter operating in continuous conduction mode, the current through the inductor ig (t) never falls to zero. During the first subinterval MOSFET is on and ig (t) increases; during the second subinterval, the MOSFET is off and the inductor current (identical to the diode current) decreases. The inductor current ig (t) waveform is sketched in Figure 1(a) for the CCM. The DCM arises when the switching ripple in the inductor current is large enough to cause the polarity of the applied switch current to reverse, such that the current-unidirectional assumptions usually made in realizing the switch with semiconductor devices are violated; briefly inductor current ripple is larger than average current value; thus DCM typically occurs with large inductor current ripple in a converter operating at light load and containing current-unidirectional switches. Since it is usually required that converters operate with their loads removed, DCM is frequently encountered. Indeed, some converters are purposely designed to operate in DCM for all loads. The properties of converters change radically in the DCM: the conversion ratio M becomes load-dependent, and the output impedance is increased. The converter operating in DCM is shown in Figure 1(b). Inductor current waveform contains a DC component I, plus switching ripple of peak amplitude ∆Ig . During the first subinterval MOSFET is on and ig (t) increases; during the second subinterval, the MOSFET is off and the inductor current (identical to the diode current) decreases. The inductor current DC component I is equal to the load current: I = V /R since no DC current flows through capacitor C. It can be

seen that I depends on the load resistance R. If the load resistance R is increased, during the first subinterval of length D1 Ts the transistor conducts, and the diode conducts during the second subinterval of length D2 Ts . At the end of the second subinterval the diode current reaches zero, and for the remainder of the switching period neither the transistor nor the diode conduct. Considering an AC-DC boost converter, the AC line current and voltage will then have the same waveshape and will be in phase. Ideally, unity power factor rectification is the result. Thus, the rectifier input current ig (t) should be proportional to the applied input voltage vg (t) according to the relationship ig (t) = vg (t)/Re where emulated resistance Re is the constant of proportionality. An AC-DC boost operates in CCM when: vg (t) vg (t)d(t)Ts = hig (t)iTs > ∆ig (t) = Re 2L

(1)

that is equivalent to Re
0

(16)

Error dynamics associated to storage function (14) is DB z˜˙ (t) − d1 (t)Θ(t)JB z˜(t) + RB z˜(t) = Ψ(d1 (t))

(17)

where Ψ(d1 ) = εB (d1 ) − (z˙d − (1 − d1 )JB zd + RB zd − R1B z˜) (18)

is a perturbation term. Unperturbed error dynamics, obtained setting Ψ(d1 (t)) = 0 in (17), with the injection designed term (16) is exponentially convergent; in fact the time derivative of Hd along solutions of unperturbed dynamics is H˙ d = −˜ z T RBd z˜ < 0

(19)

Controller dynamics are derived from (23) and unperturbed version of (17), obtaining DB z˙d (t)−d1 (t)Θ(t)JB zd (t) + RB zd (t) − R1B z˜d (t) = εB (d1 (t)) (20)

The implicit definition of Passivity-Based Control is given as Lz˙1d + r¯(d1 )z1d + d1 Θz2d − R1 (z1 − z1d ) = vg − (1 − d1 )Vd (21) z2d C z˙2d − d1 Θz1d + − R2 (z2 − z2d ) = 0 (22) R

Regulating z1 (t) = ig (t) towards a desired value z1d (t), provided by input voltage feedforward stage, in [19] has been shown that zero-dynamics associated with controller (21) and (22) is locally stable around the only physically meaningful equilibrium point. With the same procedure used previously, a CCM passivity based control for boost inner control loop has been derived; it is useful to show performances increasing given by the DCM passivity base approach of controller (21) and (22) used under light load condition. The CCM averaged model (8) can be used to derive an Euler-Lagrange (EL) matrix equivalent formulation as ¯ B z(t) ¯ B z(t) = ε¯B (d(t)) D ˙ − (1 − d(t))J¯B z(t) + R

(23)

where ig (t) ¯ L 0 0 −1 ¯ z(t) = ; DB = ; JB = ; v(t) 0 C 1 0 r(d(t)) 0 vg (t) − (1 − d(t))Vd ¯ RB = ; ε¯B (d(t)) = ; 0 1/R 0 and implicit control formulation is derived L z˙1d + r(d)z1d + d0 z2d − R1 (z1 − z1d ) = vg − d0 Vd (24) 2 z2d C z˙2d − d0 z1d + − R2 (z2 − z2d ) = 0 (25) R IV.

N UMERICAL R ESULTS

A. Scenario Overview Numerical tests have been performed in order to verify control performances using current DCM PBC and comparing results to those obtained with a current CCM PBC. Figure 3 shows the complete simulated scenario implemented in PSIM by Powersim Inc., a powerful simulation software useful for power electronic design and control. Control purpose of test scenarios is to supply a resistive load with a rectified DCbus at 24V without degrading AC power quality: in particular Power Factor and Total Harmonic Distortion indexes are calculated using PSIM tools. Experimental results are collected in different scenarios using three light loads: 130Ω, 150Ω and 170Ω. The system setup consists of a 13V (rms) AC voltage source rectified by a diode bridge with 0.8V diode threshold voltage and 0.4Ω diode resistance. A 56µH inductor with 0.5Ω parasitic resistance, a 3mF output capacitor and a 0.8V threshold voltage diode with 0.58Ω parasitic resistance are used in boost converter stage. A non-ideal MOSFET with 1.3V diode threshold voltage and 26.5mΩ on-resistance is also considered. Referring to the equation (11), the rectified voltage vg (t) RMS value is calculated using a moving average filter with a 1000 samples window. The simulation time step is 1µs. PWM Mosfet control signal frequency is 100KHz.

Line current and voltage comparison − DCM−CCM PBC VPFC

VP F C (V),IP F C (A)

30

I

20

PFC

(10x)

10 0 −10 −20 −30 0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms)


Line current and voltage comparison − CCM PBC 30

VPFC

20

IPFC (10x)

10 0 −10 −20 −30 0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms)

Fig. 4. Trend of VP F C (t) and IP F C (t) using DCM PBC and CCM PBC, with 130Ω load. AC-DC Boost PFC Simulation Scenario in PSIM.

Line current and voltage comparison − DCM−CCM PBC


Fig. 3.

SCENARIO I - 130Ω LOAD PF THD DCM-CCM PBC 87.16% 55.81% CCM PBC 86.19% 58.79% SCENARIO II - 150Ω LOAD PF THD DCM-CCM PBC 84.57% 62.72% CCM PBC 82.83% 68.00% SCENARIO III - 170Ω LOAD PF THD DCM-CCM PBC 81.95% 69.75% CCM PBC 79.81% 76.49%

V

20

IPFC (10x)

PFC

10 0 −10 −20 −30 0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms) Line current and voltage comparison − CCM PBC


TABLE I.

30

N UMERICAL S CENARIOS C OMPARISON TABLE

30

VPFC

20

IPFC (10x)

10 0 −10 −20 −30

B. Numerical Tests

0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms)

PFC and DC-bus numerical performances are presented in the following. Figures 4, 5 and 6 show line variables comparison for both DCM-CCM and CCM based PBC. PF and THD indexes are calculated, exploiting PSIM tools, over this trends and all summarized in Table I. From results analysis it is clear that the increase of the resistance value degrades significantly the performances of the control scheme as expected, since average inductor value is inversely proportional to load value. Furthermore the central achievement is the increase of both PF and THD indexes using DCM-CCM PBC compared to results obtained with CCM PBC. Numerical increase is evident in figures 4, 5 and 6; DCM-CCM PBC line current has approximately a sinusoidal waveshape whereas in CCM PBC plots a non-sinusoidal current waveshape is shown. Figure (7) shows DC-bus voltage comparison in the three different scenarios; 24V reference value is correctly reached in every scenarios and for both passivity controllers. CCM PBC bus transient response has been compared to DCM-CCM PBC one showing better performances novel passivity control technique. Furthermore DCM-CCM PBC scheme seems to be less susceptible to resistance value increase.

Fig. 5. Trend of VP F C (t) and IP F C (t) using DCM PBC and CCM PBC, with 150Ω load.

presented. Two operation modes (CCM and DCM) of an ACDC boost converter have been illustrated, a model solution for DCM operation has been discussed and finally a PassivityBased Current Control able to operate in either Continuous Conduction Mode (CCM) and in Discontinuous Conduction Mode (DCM) has been designed and tested. The proposed solution has been numerically tested using a powerful software simulation platform in three different light load scenarios and compared with the CCM Passivity-Based control. The DCM-CCM approach seems to have a better behavior in simulated tests respect to the CCM approach in terms of PF and THD. Also DC bus transient response is more performing R EFERENCES

V.

C ONCLUSION

In this paper a Power Factor Control (PFC) of an ACDC boost converter operating in light load condition has been

[1]

G. Cimini, G. Ippoliti, G. Orlando, and M. Pirro, “PMSM control with power factor correction: Rapid prototyping scenario,” in 4th IEEE International Conference on Power Engineering, Energy and Electrical Drives, 13-17 May 2013.

Line current and voltage comparison − DCM−CCM PBC VPFC


30

I

20

PFC

(10x)

[10]

10 0 −10 −20

[11]

−30 0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms)


Line current and voltage comparison − CCM PBC

[12]

30

VPFC

20

IPFC (10x)

10 0

[13]

−10 −20 −30 0

0.005

0.01

0.015

0.02

0.025

0.03

Time (ms)

[14]

Fig. 6. Trend of VP F C (t) and IP F C (t) using DCM PBC and CCM PBC, with 170Ω load.

[15]

DC−bus Comparison − 130 Ohm Load

v(t) (V)

30

[16]

20

v(t) DCM−CCM PBC v(t) CCM PBC

10 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time (ms)

[17]

DC−bus Comparison − 150 Ohm Load

v(t) (V)

30 20


10 0 0

[18] 0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time (ms) DC−bus Comparison − 170 Ohm Load

v(t) (V)

30

[19]

20


10 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time (ms)

Fig. 7. Trend of output v(t) voltage using CCM or DCM-CCM current observer, with 130Ω load.

[20]

[21]

[22] [2]

[3] [4]

[5]

[6]

[7]

[8]

[9]

M. Corradini, V. Fossi, A. Giantomassi, G. Ippoliti, S. Longhi, and G. Orlando, “Minimal resource allocating networks for discrete time sliding mode control of robotic manipulators,” IEEE Transactions on Industrial Informatics, vol. 8, no. 4, pp. 733 –745, nov. 2012. R. Erickson and D. Maksimovic, Fundamentals of Power Electronics. Springer, 2001. J. Sun and R. Bass, “Modeling and practical design issues for average current control,” in Appl. Power Electr. Conf. and Exp., vol. 2, 1999, pp. 980 –986. R. Redl and B. Erisman, “Reducing distortion in peak-current-controlled boost power-factor correctors,” in Appl. Power Electr. Conf. and Exp., 1994, pp. 576 –583. J. Spangler and A. Behera, “A comparison between hysteretic and fixed frequency boost converters used for power factor correction,” in Applied Power Electr. Conf. and Exposition, 1993, pp. 281 –286. R. Zane and D. Maksimovic, “Nonlinear-carrier control for high-powerfactor rectifiers based on up-down switching converters,” IEEE Trans. on Power Electr., vol. 13, no. 2, pp. 213 –221, 1998. R. Ghosh and G. Narayanan, “Input voltage sensorless average current control technique for high-power-factor boost rectifiers operated in discontinuous conduction mode,” in Applied Power Electronics Conference and Exposition, vol. 2, march 2005, pp. 1145 –1150 Vol. 2. K. Yao, X. Ruan, X. Mao, and Z. Ye, “Variable-duty-cycle control to

[23]

achieve high input power factor for DCM boost PFC converter,” IEEE Trans. on Ind. Electr., vol. 58, no. 5, pp. 1856 –1865, 2011. K. De Gusseme, D. Van de Sype, A. Van den Bossche, and J. Melkebeek, “Input current distortion of CCM boost PFC converters operated in DCM,” in Power Electronics Specialist Conference, 2003. PESC ’03. 2003 IEEE 34th Annual, vol. 4, june 2003, pp. 1685 – 1690 vol.4. W. Zhang, G. Feng, Y.-F. Liu, and B. Wu, “A digital power factor correction (PFC) control strategy optimized for DSP,” IEEE Trans. on Power Electr., vol. 19, no. 6, pp. 1474 – 1485, 2004. G. Cimini, M. L. Corradini, G. Ippoliti, G. Orlando, and M. Pirro, “Passivity-based PFC for interleaved boost converter of PMSM drives,” in 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, July 3-5 2013, pp. 128–133. G. Cimini, G. Ippoliti, G. Orlando, and M. Pirro, “Current sensorless solutions for PFC of boost converters with passivity-based and sliding mode control,” in 4th IEEE International Conference on Power Engineering, Energy and Electrical Drives, 2013. W.-S. Wang and Y.-Y. Tzou, “Light load efficiency improvement for AC/DC boost PFC converters by digital multi-mode control method,” in Power Electronics and Drive Systems (PEDS), 2011 IEEE Ninth International Conference on, 2011, pp. 1025 –1030. J. Su and C. , “A novel phase-shedding control scheme for improved light load efficiency of multiphase interleaved DC-DC converters,” Power Electronics, IEEE Transactions on, vol. PP, no. 99, p. 1, 2012. H. Kon and H. Kira, “Novel switching control method for soft-switching DC-DC converter at light loads,” in Power Conversion Conference, 2002. PCC-Osaka 2002. Proceedings of the, vol. 2, 2002, pp. 621 –626 vol.2. G. Cimini, G. Ippoliti, G. Orlando, and M. Pirro, “Current sensorless solution for PFC boost converter operating both in DCM and CCM,” in 21st Mediterranean Conference on Control and Automation, June 25-28 2013, pp. 137–142. S. F. Lim and A. Khambadkone, “A simple digital DCM control scheme for boost PFC operating in both CCM and DCM,” Industry Applications, IEEE Transactions on, vol. 47, no. 4, pp. 1802 –1812, july-aug. 2011. R. Ortega, J. Perez, P. Nicklasson, and H. Sira-Ramirez, Passivitybased Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications, ser. Communications and Control Engineering. Springer, 1998. A. Rosa, S. Junior, L. Morais, P. Cortizo, and M. Mendes, “Passivitybased control of PFC boost converter with high-level programming,” in Power Electr. Conf., 2011, pp. 801 –806. B. Wang and Y. Ma, “Research on the passivity-based control strategy of buck-boost converters with a wide input power supply range,” in Int. Symp. on Power Electr. for Distrib. Generat. Syst., 2010, pp. 304 –308. H. Sira-Ramirez and R. Ortega, “Passivity-based controllers for the stabilization of DC-DC power converters,” in Conf. on Decision and Control, vol. 4, 1995, pp. 3471 –3476. R. Ridley, “Average small-signal analysis of the boost power factor correction circuit,” in Proceedings of the Virginia Power Electronics Center Seminar, 1989, pp. 108–120.