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Cuk Converter-Based PF Correction for PMBLDCM Drive with Hysteresis Controller Elizabeth Alphonsa Jose Mr.Thomas K.P. M.Tech. Scholar Rajagiri School of Engineering and Technology, Kakkanad Kochi, India [email protected] Dept. of Electrical and Electronics Engg. Rajagiri School of Engineering and Technology, Kakkanad Kochi, India [email protected] Abstract—Permanent magnet brushless DC motor (PMBLDCM) drives are being employed in many variable speed applications due to their high efficiency, silent operation, compact size, high reliability, ease of control, and low maintenance requirements. These drives have power quality problems and poor power factor at input AC mains. Solid-state switch-mode rectification converters have reached a matured level for improving power quality in terms of power-factor correction (PFC), reduced total harmonic distortion at input ac mains etc. This paper deals with a hysteresis controller for a permanent magnet brushless DC motor (PMBLDCM) with Cuk dc–dc converter based power-factor-correction. A three-phase voltage-source inverter is used as an electronic commutator to operate the PMBLDCM. Hysteresis current control method is used for gating of VSI so as to reduce the power consumption. Test results of the controller is also presented to validate the design and the advantage using the same. Index Terms—Cuk converter, power factor correction (PFC), permanent-magnet brushless dc motor (PMBLDCM), Hysteresis Control, voltage-source inverter (VSI). I. INTRODUCTION Household appliances are the one of fastest-growing endproduct market for electronic motor drivers. The major appliances include washing machine, room air conditioners, refrigerators, vacuum cleaners, freezers, etc. For household appliance, usually we prefer historical classic electric motor technologies such as single phase AC induction motor, including split phase, capacitor-start, capacitor–run types, and universal motor. These classic motors typically are operated directly from main AC power without regarding the efficiency, at constant-speed. Consumers now demand for lower energy costs, better performance, reduced noise, and more convenience features. Those traditional technologies cannot provide the solutions. In low-power appliances the use of a permanent-magnet brushless dc motor (PMBLDCM) is increasing because of its features of high efficiency, wide speed range, and low maintenance[1]. Due to the use of PMs on the rotor, it is a rugged three-phase synchronous motor. The commutation in a PMBLDCM is accomplished by solid state switches of a three-phase voltage-source inverter (VSI). A typical motor drive consists of an ac/dc converter, LC dc link, and an inverter as shown in Fig.1. The motor is fed from a single-phase sc supply through a diode bridge rectifier (DBR) followed by a dc capacitor and a voltage source inverter. A large electrolytic capacitor is usually installed in dc link to stabilize the dc voltage.[2] Fig. 1. Typical Motor Drive System This PMBLDC motor drive draws a pulsed current from ac mains due to uncontrolled charging of dc link capacitor, having peaks higher than the amplitude of the fundamental input current. This is because, the diodes are reverse biased during the period when the ac voltage is less than the dc link voltage, and they does not draw any current from the ac mains; however, it draws a large current when the ac voltage is higher than the dc link voltage. Therefore, many power quality (PQ) problems arise at input ac mains including poor power factor, increased total harmonic distortion (THD), etc. These PQ disturbances are undesirable. There are many means explored and proposed to solve this severe problem. Power factor correction method is a good candidate for ac to dc power conversion in order to reduce the line current harmonics as well as increase the efficiency and capacity of motor drives. The use of power factor correction topologies is, therefore, mostly recommended for such drives[3]. The dc-dc converters, which act as PFC converters, forces the drive to draw sinusoidal ac mains current in phase with its voltage. A DC-DC converter topologies such as buck, boost, buck-boost, Cuk, SEPIC, zeta converters with variations of capacitive/inductive energy transfer are mostly preferred[4]. The net result is improved performance, such as reduction of ac mains current harmonics, reduction of noise and electromagnetic pollution, minimum number of components, enhanced efficiency, utilization of the full input voltage range etc. In this paper a Cuk dc–dc converter is used as a PFC converter because of its continuous input and output currents, small output filter, and wide output voltage range as compared to other single switch converters. A three-phase voltagesource inverter is used as an electronic commutator to operate the PMBLDCM. Hysteresis current control method is used for gating of VSI so as to reduce the power consumption. The detailed modeling, design, and performance evaluation of the proposed drive are presented. maintain the speed of the motor close to its desired reference value. The output of the PI controller is given to a limiter to produce the reference torque (T*). The reference current generator outputs the three phase reference currents (ia *, ib *, ic *) from the reference torque and position signal. The winding currents (ia, ib, ic), are compared with the reference currents (ia *, ib *, ic *) and the switching signals for VSI is generated by using a hysteresis current controller. In response to switching signals the VSI provides voltage across the motor terminals to produce desired currents in the winding of the motor. These winding currents produce an electromagnetic torque to maintain the desired speed[5]. II. CUK CONVERTER FED PMBLDCM III. DESIGN OF CUK PFC CONVERTER FOR PMBLDCM The Cuk PFC converter is designed for a PMBLDCM drive having DBR at front end, on the basis of PQ constraints at ac mains and allowable ripple in dc-link voltage. The output voltage (Vdc) of the Cuk PFC converter is given as, Vdc = Vin D/(1-D) (1) Where, Vin is the average value of the output DC voltage from a DBR, derived from an ac input voltage (Vs) as, Vin = Vs 2√2 / π (2) The values of boost inductor and capacitor used in cuk converter for energy transfer is given by, L1 = DVin / (fS ΔIL1) C1=D Idc / (fS ΔVC1) Fig.2. Hysteresis Controlled BLDCM Drive with PF Correction Fig.2 shows the Hysteresis Controlled PMBLDC motor drive with PF Correction. The Cuk dc–dc converter controls the dc link voltage using capacitive energy transfer which results in non-pulsating input and output currents. Here, the use of current multiplier approach with average current control scheme in continuous conduction mode (CCM) of the PFC converter is used. In this topology, a conventional DBR is fed from single-phase ac mains. Its output is given to a DC-DC converter, and a VSI is used to feed the PMBLDC motor. The DC-DC converter provides a controlled dc voltage from uncontrolled dc output of DBR, while controlling the power factor through high frequency switching of the PFC switch. The control loop used for PFC action involves outer voltage loop and inner current loop. This converter draws unity power factor current from the ac mains; eliminates harmonic currents and regulates the dc link voltage even under fluctuating voltage conditions of ac mains. A VSI is used to feed the PMBLDC motor. For the speed control of the PMBLDCM, an outer speed & an inner current loop with hysteresis controller is used to drive a constant torque load. By using hall effect sensors, the rotor position of PMBLDCM is sensed and converted to speed signal. A proportional-integral (PI) controller is used to (3) (4) where ΔIL1 is the inductor current ripple, ΔVC1 is the voltage ripple in the intermediate capacitor (C1), and Idc is the current drawn by the PMBLDCM from the dc link. For ripple-free voltage at the dc link of the Cuk converter a ripple filter is designed. For a given switching frequency (fs), the inductance (L2) of the ripple filter restricts the inductor peak-to-peak ripple current (ΔI L2) within a specified value. The capacitance (C2) is calculated for the allowed ripple in the dc link voltage (ΔVC2)[6],[7]. The values of the ripple filter inductor and capacitor are given as, L2 = Vdc (1-D) / (fS ΔIL2) C2 = Idc / (2ω ΔVC2) (5) (6) IV. MODELING OF PFC CONVERTER-BASED PMBLDC MOTOR DRIVE The modeling of PMBLDCM drive involves modeling of the PFC converter and PMBLDCM drive. These components are modeled in the form of mathematical equations and the complete drive is represented as a combination of these models. A. PFC CONVERTER The PFC converter consists of a DBR at front end and a Cuk converter with an output ripple filter. The PFC converter modeling consists of the modeling of a speed controller, a reference current generator, and a PWM controller as given below. 1. Speed Controller: The Speed Controller is a PI controller which closely monitors the speed error as an equivalent voltage error and generates control signal (Ic) to minimize the error. If at kth instant of time, V*dc(k) is reference DC link voltage, Vdc(k) is sensed dc link voltage then the voltage error Ve(k) is calculated as, Ve(k) = V*dc(k) - Vdc(k) (7) The output of the controller Ic(k) at kth instant is given as, Ic(k) = Ic(k- 1) +KpvVe(k) -Ve(k - 1) +KivVe(k) (8) Where, Kpv and Kiv are the proportional and integral gains of the voltage PI controller. 2. Reference Current Generator: The reference current at the input of the Cuk converter is, i*d = Ic(k)ud (9) where ud is the unit template of the ac mains voltage, calculated as, ud = vd/Vsm; vd = |Vs|; Vs = Vsm sinωt (10) 3. PWM Controller: The reference input current of the Cuk converter (i*d) is compared with its current (id) sensed after DBR to generate the current error Δi. This current error is amplified by gain kd and compared with fixed frequency (fs) sawtooth carrier waveform md(t) to get the switching signal for the MOSFET of the Cuk converter as, if kdΔid > md(t) then S = 1 if kdΔid < md(t) then S = 0 (11) where S denotes the switching of the MOSFET of the Cuk converter representing ‘on’ position with S=1 and its ‘off’ position with S=0. reference speed, ωr(k) is the rotor speed then the speed error ωe (k) can be calculated as, ωe(k) = ωr*(k) - ωr(k) (12) This speed error is processed through the speed controller to get desired control signal. 1. Speed controller: The speed of the motor is compared with its reference value and the speed error is processed in PI speed controller. The speed controller’s output at kth instant T(k) is given as, T(k) = T(k - 1) + Kpω [ωe(k) - ωe(k - 1)] + kiω(k) (13) where Kpω and kiω are the proportional and integral gains of the PI speed controller. The output of this controller is considered as the reference torque. 2. Reference Current Generator: The magnitude of the three phase current iref is determined by using reference torque Tref. iref = Tref / Kt (14) where Kt is the torque constant. Depending on the rotor position, the reference current generator block generates three phase reference currents ( i*a, i*b, i*c ) by taking the value of reference current magnitude as iref . These reference currents are compared with sensed phase currents (ia, ib, ic) to generate the current errors Δia, Δib, & Δic for three phases of the motor. 3. Hystresis current controller: The Hysteresis current controller contributes to the generation of the switching signals for the inverter. Hysteresis-band PWM is basically an instantaneous feedback current control method of PWM where the actual current continually tracks the command current within hysteresisband. Each comparator determines the switching state of the corresponding inverter leg (Sa, Sb &Sc) such that the load currents are forced to remain within the hysteresis band. Fig. 3. PWM controller signals of PFC converter B. PMBLDC MOTOR DRIVE The PMBLDCM drive has a speed controller, a reference winding current generator, a hysteresis current controller, a voltage source inverter and a PMBLDC motor as the main components. The speed controller is a PI controller which closely tracks the reference speed. If at kth instant of time, ωr*(k) is the Fig. 4. Fixed band Hysteresis Current Controller As the current exceed upper band limit, the upper switch is off; and lower switch is on as the current exceed lower band limit. ie; If ia < (ia* − hb ) Sa1 is ON and Sa2 is OFF If ia < (ia* + hb ) Sa1 is OFF and Sa2 is ON (15) Similarly for other switches also. where, hb is the hysteresis band around the three phase’s references currents, according to above switching condition. 4. Voltage Source Inverter: Where x can be phase a, b, or c and fx(θ) represents a function of rotor position with a maximum value ±1, identical to trapezoidal induced EMF, given as, ea = (6E/π)θ for (0< θ < π/6) =E for (π/6 < θ < 5π/6) = - (6E/π)θ + 6E for (5π/6 < θ < 7π/6) = -E for (7π/6 < θ < 11π/6) = (6E/π)θ - 12E for (5π/6 < θ < 7π/6) (23) The functions eb and ec are similar to ea with phase differences of 1200 and 2400, respectively. The mechanical torque equation of motion is given by, Te – Tl = P/2 (J pωr + B ωr) where ωr is the derivative of rotor position θ, P is the number of poles, Tl is the load torque in newton meters, J is the moment of inertia in kilogram square meters, and B is the friction coefficient in newton meter seconds per radian. The derivative of rotor position is given as, Fig.5. Brushless dc motor drive system Fig.5. shows an equivalent circuit of a VSI fed PMBLDCM. The output of VSI to be fed to phase ‘A’ of the PMBLDC motor is given as, Vao = (Vdc/2) for Sa1 = 1 Vao = (-Vdc/2) for Sa2 = 1 Vao = 0 for Sa1 = Sa2 = 0 Van = Vao – Vno (16) where Vao, and Vno are voltages of phase A and neutral terminal with respect to virtual mid-point of the dc link. Using similar logic Vbo, Vco, Vbn, Vcn are generated for other two phases of the VSI feeding PMBLDC motor. The voltages Van, Vbn, and Vcn are voltages of three-phases with respect to the motor neutral terminal (n). 5. (24) PMBLDC Motor: The PMBLDCM is represented in the form of a set of differential equations given as, Va = iaRa + L (d/dt) ia + ea (17) Vb = ibRb + L (d/dt) ib + eb (18) Vc = ibRb + L (d/dt) ic + ec (19) In these equations, ia, ib, and ic are currents, and ea, eb, and ec are the back EMFs of PMBLDCM, in respective phases; R is the resistance of motor windings/phase and L is the inductance. The developed torque Te in the PMBLDCM is given as, Te = (ea ia + ebib + ecic)/ωr (20) where ω is the motor speed in radians per second. Since PMBLDCM has no neutral connection, ia + ib + ic = 0 (21) The back EMF is a function of rotor position (θ) as, ex = Kb fx(θ)ωr (22) pθ = ωr (25) These equations represent the dynamic model of the PMBLDC motor. V. RESULTS AND DISCUSSION A. Performance During Starting: Fig. 6 shows the variation of single-phase ac supply voltage (Vs), current (Is), dc link voltage (Vdc), motor speed, and motor winding currents ia, ib, and ic with time. It can be seen from this figure that the input current remains sinusoidal and is found to be in time phase with the input voltage. The supply current during starting is distortion free and therefore the operating power factor is close to unity. During starting of the motor the supply current is found to increase with the speed because the power demand of the system is proportional to the speed (the load torque being constant). Once the motor attains the steady speed, the supply current also decreases due to absence of accelerating torque. B. Comparison between open loop & closed loop: Fig.6 shows the simulated performance of power factor corrected PMBLDC motor drive under open loop, and Fig.7 shows that of hysteresis current controlled method. It can be seen that in case of open loop method, the speed is settled at 2000rpm at 0.45secs. Once the machine reaches its steady value, the supply current also decreases. In case of hysteresis current controlled method, the drive reaches its reference value ie. 1500rpm. Once the machine reaches its steady value, the supply current decreases. In this method, the active power consumed from the source is less compared to open loop method, and therefore there is an energy saving. The tables I & II shows a comparison between the two. REFERENCES [1] T. Kenjo and S. Nagamori, Permanent Magnet Brushless DC Motors. Oxford, U.K.: Clarendon, 1985. [2] Tze-Yee Ho, Mu-Song Chen, Lung-Hsian Yang, Wei-Lun, Lin, “The Design of a High Power Factor Brushless DC Motor Drive”, International Symposium on Computer, Consumer and Control,2012 [3] Sanjeev Singh, Member, IEEE, and Bhim Singh, “A VoltageControlled PFC Cuk Converter-Based PMBLDCM Drive for AirConditioners”, IEEE Trans.on Ind. Appl., vol. 48, no. 2, March/April 2012 [4] B. Singh, B. N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, and D. P. Kothari, “A review of single-phase improved power quality ac– dc converters,” IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 962– 981, Oct. 2003. Fig 6. Performance of Hysteresis controlled PMBLDC motor Drive [5] Alamelu Nachiappan, Sundararajan K, and Malarselvam V “Current Controlled Voltage Source Inverter Using Hysteresis Controller And PI Controller” IEEE Trans 2012 [6] N. Mohan, M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications and Design. Hoboken, NJ: Wiley, 1995. [7] Daniel W Hart, Power Electronics Fig.7. Performance of open loop PMBLDC motor Drive Table I. Variation of Active power, power factor and speed with load for open loop BLDC motor Drive Table II. Variation of Active power, power factor and speed with load for Hysteresis controlled BLDC motor Drive