Mechatronics 20 (2010) 464–473
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Optimal control of brushless PM motor in parallel hybrid propulsion system P. Bajec, B. Pevec, D. Miljavec * University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, 1000 Ljubljana, Slovenia
a r t i c l e
i n f o
Article history: Received 24 February 2009 Accepted 25 April 2010
Keywords: Brushless DC machines Converters Road vehicle control Road vehicle electric propulsion
a b s t r a c t The paper outlines a case study on optimal control of a brushless direct-current (BLDC) motor as a part of an Integrated Starter-Generator and torque Booster (ISGtB) application in a hybrid propulsion system. The main scope of the introduced research work is the optimization of the BLDC motor torque characteristics. The discussed hybrid propulsion system consists of an internal combustion (IC) engine and a BLDC machine and is in its origin intended to drive the motorcycle. Stringent starting torque demands, electrical machine geometry limitations and a wide rotational speed range of the BLDC motor are reasons for control algorithm analysis in the low-speed operation range. Two approaches for the optimization of the torque characteristics are discussed, the flux-weakening method and a modification of transistor conduction angle. A novel control principle which includes both of the above approaches is proposed. A comparison between a commonly used control method and the proposed control method is presented. Simulation and experimental results fully confirm improvements in the starting procedure of the hybrid propulsion system attained by the proposed control algorithm of the BLDC motor. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The idea of electrically driven vehicles dates far back to the 1830s. Through several years of development of internal combustion (IC) engines, electric machines, batteries, power electronics, microcontrollers and also increased environmental awareness, the approach with combined (hybrid) propulsion systems seems to be the most convenient solution. There are several combinations possible. One of them involves an IC engine and an electrical machine, supplied from a rechargeable power source, together forming a parallel or series hybrid propulsion system [1]. The subject of our research is the Integrated Starter-Generator and torque Booster (ISGtB) coupled to the IC engine, which is one of the derivatives of the above mentioned approach. Requirements for a high power density and an acceptable construction of the electrical machine have led to the permanent-magnet brushless DC (BLDC) machine with surface mounted rare-earth magnets on the external rotor [2,22]. The BLDC machine was chosen also due to its simplicity regarding the needed rotor position information accuracy, straightforward mechanical construction and therefore low manufacturing costs. During generator and motor operating mode the magnetic flux density is being kept at common adopted levels (1.5 T), during start-up of IC engine (short-circuit currents) the magnetic flux density is increased to 2 T for short periods of time. The thickness of magnets was calculated so to prevent demagnetization during IC engine start-up and flux-weakening * Corresponding author. Tel.: +386 1 4768 281; fax: +386 1 4264 630. E-mail address:
[email protected] (D. Miljavec). 0957-4158/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2010.04.004
operation mode. Finite element method calculations and Ampere’s law theory were used. The rotational speed range of modern IC engines (up to 15,000 rpm) dictates particular properties and capabilities of the switched-mode power converter (SPC) and of the ISGtB. The SPC has to support all operating modes of the ISGtB and enable a bidirectional energy flow (Fig. 1) [3,4]. High efficiency is of course an imperative. A part of the SPC is a three-phase inverter, composed of six MOSFET power switches, each comprising a MOSFET transistor and a parasitic body diode. The voltage levels of the supply battery and the DC link are interfaced with an additional bi-directional DC/ DC converter. The patent-pending DC/DC converter topology also enables the bypassing of the internal DC/DC converter circuit in both energy flow directions and therefore, a complete exclusion of the converter from the main current path. The exclusion of the DC/DC converter will be presumed in the following theoretical analysis and also during the evaluation of experimental results. During the design of the converter, our attention was also paid to efficient operation of the ISGtB at the operation range limits such as the optimization of the starting maneuver and extending the low-speed generator operation range [5,6]. Stringent IC starting demands (starting at 10 °C with battery SOC 50%), geometry limitations and a wide operating rotational speed range of the BLDC machine (high back EMF) are reasons for a particular focus on the motor torque characteristics [7]. The comprehensive research of BLDC machine torque characteristics was carried out in order to contribute to a faster and more efficient start-up of the IC engine. Two approaches are discussed in the
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Fig. 1. Topology of the switched-mode power converter.
paper to achieve the abovementioned goal: the flux-weakening method and the modification of the switch-on angle. Flux-weakening method is a principle to extend the motor operating mode of the BLDC motor, as already studied by many authors [1–3,11–13], which is achieved with a phase current leading technique. Weakening of the main magnetic flux decreases the back EMF in the stator winding which consequently increases the stator current. On the other hand, with this approach the main magnetic flux is decreased, which directly decreases the produced electromagnetic torque. Furthermore, two most common principles of BLDC control are a 120° angle switch-on mode and a 180° angle switch-on mode [8,9,11]. The first control principle has a higher efficiency, whereas with the second one the motor can produce higher peak electromagnetic torque. In the paper, the area between both control principles is additionally analyzed to determine the optimal conduction angle of switches of the three phase inverter. Consequently that means that the expected transistor conduction angle is between 120° and 180°.
2. Evaluation of proposed torque optimization approach 2.1. Flux-weakening method Electric motor operating rotational speed extension with fluxweakening method is a well known method described by many authors [8–11,14,15]. Electric motor physical laws dictate rotational speed dependence on the back EMF. Positive voltage difference between supply voltage and the back EMF induced in two phase windings (if stator windings are connected in star) is proportional to electric current of the BLDC motor and the developed torque. Voltage difference decreases with increasing rotational speed, which consequently decreases electric current and torque of the BLDC motor. Operating principle of the BLDC motor in flux-weakening operational mode is similar to a vector controlled induction machine or separately exited DC motor. With stator current d component of the vector controlled induction motor (direction of d-axis of motor model in the dq coordinate system), magnetic exciting is defined, whereas with additional stator current component at separately exited DC or BLDC motor, only the main magnetic flux is decreased.
Flux-weakening regime analysis requires transformation of the BLDC machine into the dq coordinate system so that d-axis points in direction of rotor magnetic flux vector ~ /rot . Brushless machine with sinusoidal back EMF have id and iq values in the dq coordinate system constant. Modeling and transformation of the brushless machine with trapezoidal back EMF (BLDC machine) is quite a difficult task. One of the possibilities is to write it down as a sum of the base and other high harmonic components of stator voltage. In the case of a symmetric stator voltage shape with zero mean value, the Fourier series includes only the odd higher harmonics. Finally, the model of the BLDC machine is defined in the mixed dq and ab coordinate system [16]. Operation of the BLDC motor in the flux-weakening mode can be described based on the model of the sinusoidal permanent magnet (SPM) motor in the dq coordinate system. As already mentioned, in the dq coordinate system a longitudinal component of the phase current id is influencing on the magnetic excitation of the motor and is pointing in direction of resultant magnetic flux ~ /rot , whereas a transversal component iq is proportional to the electromagnetic torque (Fig. 2) [17]. The longitudinal component of the phase current id is zero in the optimal operating mode of the BLDC motor (maximal torque). Operation of the motor is possible up to the rotational speed at which the control of the stator current is still realizable. Fig. 3 shows operation of the SPM motor in the flux-weakening area.
Fig. 2. Sinusoidal permanent magnet motor phaser diagram (Rs – stator winding resistance, Ls – stator winding inductance, x – electrical angular speed, E – induced stator voltage, us – stator voltage).
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Fig. 5. 120° angle switch-on mode.
Fig. 3. Phasor diagram of the SPM motor in the flux-weakening region (us1 - stator voltage in flux-weakening mode).
T ¼ k~ /rot ~ Imot ; Additional current components id and iq are influencing on the main magnetic flux and on the electromagnetic torque respectively. Simplified phasor diagram of the BLDC motor, which includes conditions on the Figs. 2 and 3 is shown in the Fig. 4. In the normal operating mode (no flux-weakening) of the BLDC motor an angle between stator and rotor magnetic flux is 90°, whereas in the flux-weakening mode that angle is larger and is assigned with e. /w , which Phasor ~ /stat1 can be disassembled on the component ~ is weakening magnetic flux of rotor and on component ~ /st w , which generates electromagnetic torque. The later is smaller than ~ /stat , which results in lower electromagnetic torque at low speeds. On the other hand, as a result of lower back EMF stator current and electromagnetic torque could increase. 2.2. Modification of the switch-on angle Two basic control principles for BLDC motor are 120° angle switch-on mode and a 180° angle switch-on mode. At first control principle at any instant two switches are on, one in the upper group and another in the lower group of the AC–DC converter, which consecutively means that always two phase windings appear in series across the inverter input (Fig. 1). Fig. 5 shows an example where electric current flows into the phase A winding and exits out of winding B. The conduction pattern changes every 60° angle, indicating six switching modes in a full cycle. BLDC motor produces maximal torque when the rotor is blocked (no back EMF). Source current can then be written as:
Is ¼
U ; RF 2
ð3Þ
where /rot is rotor magnetic flux and k encompasses all motor construction constants. All components of the stator current have to be included in calculation of electromagnetic torque calculation (Fig. 5):
T ¼ k /rot ðIA sin c þ IB sin d þ IC sin kÞ;
ð4Þ
where c is the angle between rotor magnetic flux vector and phase A magnetic flux vector, d is the angle between rotor magnetic flux vector and phase B magnetic flux vector and k is the angle between rotor magnetic flux vector and phase C magnetic flux vector. According to the Eq. (4) and Fig. 5 maximum electromagnetic torque for 120° switch-on angle mode is:
T max ¼ k /rot
I I sin 120 þ sin 60 2 2
¼ k /rot I
pffiffiffi 3 : 2
If we turn the rotor for 30° backwards, minimum electromagnetic torque can be calculated as:
ð1Þ
where U is the source voltage, and RF is the resistance of the phase winding. If the quotient U/RF = I, upper equation can be written as: Fig. 6. 180° angle switch-on mode.
Is ¼
I : 2
ð2Þ
Hence it follows that electromagnetic torque is:
Fig. 4. Phasor diagram of the BLDC motor in the flux-weakening region.
ð5Þ
Fig. 7. The proposed transistor switching algorithm.
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T min ¼ k /rot
I I sin 90 þ sin 30 2 2
3 ¼ k /rot I : 4
ð6Þ
The ratio between developed electromagnetic torque and source current is an efficiency indicator of the BLDC motor; higher value of the ratio means higher efficiency. At blocked rotor and at 120° angle switch-on mode the given ratio is:
pffiffiffi T max ¼ 3; k /rot Is
T min 3 ¼ : k /rot Is 2
ð7Þ
The operating principle of the 180° angle switch-on mode is, that at any instant three switches are on, which means that electric current flows through all three-phase windings of the BLDC motor. Fig. 6 shows an example where electric current flows into phase A winding and out of windings B and C. Magnetic flux phasor diagram is shown on the right hand side of Fig. 6 at the time when the motor is producing maximal electromagnetic torque. Similar as at 120° angle switch-on mode all three components of the electric current have to be considered to calculate electromagnetic torque. Source electric current is:
Is ¼
U 2 ¼ I: RF 32 3
467
ð8Þ
Considering conditions in Fig. 6 we could write down maximum electromagnetic torque for 180° angle switch-on mode:
2 1 1 T max ¼ k /rot I sin 90 þ I sin 30 þ I sin 150 3 3 3 T max ¼ k /rot I
ð9Þ
Turning the rotor for 30° backwards will give us minimum electromagnetic torque when the rotor is blocked:
2 1 1 T min ¼ k /rot I sin 60 þ I sin 0 þ I sin 120 3 3 3 : pffiffiffi 3 T min ¼ k /rot I 2
ð10Þ
Maximum and minimum ratios between the electromagnetic torque and source current at blocked rotor and 180° angle switch-on mode are:
Fig. 8. The simulation model of a hybrid propulsion system.
Fig. 9. Meshed 2D FEM BLDC machine model coupled with switched-mode power converter.
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T max 3 ¼ ; k /rot Is 2
pffiffiffi T min 3 3 ¼ ¼ 1; 3: 4 k /rot Is
ð11Þ
3. Evaluation of the proposed torque optimization approach From the theoretical background given in the previous chapter it could be seen that amount of flux-weakening is dependent on
motor rotational speed and that optimal switch conducting angle is between two common BLDC motor control modes (120° and 180°). Magnetic flux-weakening is lowering back EMF and consequently increasing maximal possible phase winding current. On the other hand, this method is directly decreasing electromagnetic torque. That is why suitable flux-weakening level has to be defined at certain rotational speed in the speed range directed by staring maneuver of the IC engine. In practice magnetic flux-weakening is achieved with phase current leading technique (Fig. 4). In other words, three phase inverter switches are fired earlier than the change of the Hall sensor logic state appears. From Eqs. (5) and (9) the difference in maximum torque produced by the BLDC motor can be seen between two discussed control principles. Similarly from Eqs. (7) and (11) the difference in efficiency between both control principles is presented. From the given comparisons we could conclude that the optimal BLDC motor control is achieved if the switch-on angle is between 120° and 180°. That is why optimal switching angles have to be determined where the torque/efficiency ratio is at its maximum. Optimal performance of the BLDC motor is achieved with the implementation of both above discussed approaches. That means that current commutation no longer appears when Hall sensors change their logical state, but is conditioned with the switch-on lead angle b (flux-weakening) and the switch-on prolongation angle a at defined rotational speed, with regard to 120° switch-on control mode (Fig. 7). Conduction period is then between 120° and 180°. Nonsinusoidal shape of the back EMF and nonlinearity of the BLDC motor make torque dependence on switch-on lead angle b, on prolongation angle a and on rotational speed, which is analytically very difficult to describe. Defining the optimal torque characteristics in the entire rotational speed range of IC engine starting maneuver encompassed a computer-based simulation of the hybrid propulsion system and additional laboratory torque characteristics measurements on the prototype BLDC machine.
3.1. Computer-based simulation of the hybrid propulsion system
Fig. 10. Mechanical layout of the piston and the cranking handle.
The complex simulation model of BLDC machine coupled to the IC engine was build up to simulate the start-up of the IC engine with a BLDC machine in the starter operation mode (Fig. 8).
Fig. 11. IC engine cranking torque at 100 rpm.
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Simulation model is consisting of an AC–DC converter model, IC engine model and BLDC machine model. The control part of the system and IC engine model is realized in Matlab/Simulink and the second part including BLDC machine model with inverter is built up in Flux2D finite element software. The connection between these models is provided by Flux to Simulink application. This method has the great advantage so that a complex drive model can be used in combination with accurate flux-linkage calculation. With regard to the input data the software performs the 2D time stepping finite-element computation of BLDC machine and returns the results back to Simulink. The Flux to Simulink coupling block function is to pass all the necessary data as IC engine load torque and inverter switch control pulses to the BLDC machine finite element model (FEM) (Fig. 9) [18,19,21] . The IC engine model characteristic was derived with regard to the analytical evaluation of the mechanical construction of the piston and its handle (Fig. 10) and taking into consideration all other construction parameters of the used prototype IC engine [20]. The torque on the crankshaft of the IC engine can be derived as:
Fig. 14. Torque dependence on b and rotational speed at a = 22.5°.
Fig. 12. Simulated IC engine start-up maneuvers.
Fig. 13. Static torque vs. speed characteristic of prototype BLDC machine at 120° switch-on mode.
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T ¼ r P1 ;
ð12Þ
where r is the length of the cranking handle and P1 a tangential force. Taking into consideration all construction parameters the tangential force is defined as:
0 1 s0 0 s 0 P1 ¼ K sin u þ n sin 2u þ 1 G sin u G þ G00 2 l l 2 rx k 1 sin 2u ðsin u 3 sin 3uÞ sin u þ n sin 2u 2 2 2g ð13Þ where K is the pressure force inside the combustion compartment of the cylinder, G, G0 and G00 are the weights of the designated mechanical parts, n is the ratio l/r, and x the rotational speed of the cranking shaft. The pressure force is derived with regard to the requested pressure inside the combustion compartment of the prototype IC engine for reliable ignition of the gasoline mixture.
Fig. 15. Torque dependence on a and b at rotational speed 500 rpm.
The final torque (load) characteristic of the IC engine during cranking is accomplished when considering the prototype configuration of a two-cylinder IC engine with a phase shift of 180° (mech.) between each piston. The IC engine torque characteristic during cranking (at 100 rpm) is shown in Fig. 11. Based on the above given definition of the IC engine torque several simulations of the hybrid propulsion system were carried out. Different inverter control strategies were applied in order to investigate and also evaluate the influence of the suggested three phase inverter control strategy on the start-up procedure of the IC engine. The comparison of start-up of the IC engine at using the conventional 120° angle switch-on mode and in the paper introduced control strategy is given in Fig. 12. 3.2. Laboratory measurements on the prototype BLDC motor The introduced three phase inverter control strategy was further evaluated also through comprehensive BLDC machine characteristics measurements on a dedicated laboratory test bed allowing
Fig. 16. Efficiency dependence on a and b at rotational speed 500 rpm.
Fig. 17. ‘‘Optimal torque” IC engine starting maneuver.
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for more precise BLDC motor characteristics measurements. Static torque vs. speed characteristic of prototype BLDC machine at 120° switch-on mode is shown in Fig. 13. An example of one of many measured characteristics which shows electromagnetic torque dependence on switch-on lead angle and on rotational speed of the BLDC at prolongation angle a = 22.5° is shown in Fig. 14. The measured results also confirm the expected torque dependence on rotational speed and different angles a and b. An example of the discussed dependence at rotational speed 500 rpm is shown in Fig. 15. BLDC motor optimal performance demands maximum produced electromagnetic torque and of course high efficiency of the motor is always an imperative. Fig. 16 shows decreasing of efficiency with the increase of prolongation angle a.
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Starting maneuver of the IC engine is strongly connected also to the instantaneous operation conditions of the engine, such as IC engine crankcase temperature, state of the charge of the battery. . . To achieve optimal performance of the BLDC machine as well as the entire hybrid propulsion system, maximum electromagnetic torque and efficiency at certain rotational speed have to be considered. That is why two starting procedures which meet above mentioned demands are proposed. At a cold start it is reasonable to choose the conduction angles (a and b) where BLDC motor produces maximum torque (Fig. 17) in order to assure the reliable start of the IC engine. On the contrary, when the IC engine is already at nominal working temperature the BLDC motor is controlled in the way to achieve the highest efficiency and to preserve the on-vehicle battery charge (Fig. 18). The values of angles alpha and beta were incorporated in the control software as a
Fig. 18. ‘‘Optimal efficiency” IC engine starting maneuver.
Fig. 19. Comparison of torque and efficiency at a, b = 0° and at optimal a and b.
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look-up table. Final values of alpha and beta were calculated using linear interpolation. 4. Experimental results Theoretical statements and simulation results were finally verified through several experimental measurements carried out on the laboratory hybrid propulsion system. It consisted of a twocylinder, four stroke, 1200 ccm gasoline IC engine with opposed piston layout and the proposed BLDC machine on a common crankshaft, serving as ISGtB (10-pole, three-phase, outer rotor machine layout, stator diameter: 128 mm, rotor outer diameter: 160 mm, magnet thickness: 5 mm, air-gap length: 0.5 mm, overall axial machine length: 70 mm, RA,B,C = 8 mX, LA,B,C = 50 lH). Key parameters of the hybrid propulsion system and start-up processes were monitored by a digital signal processor (DSP), used also for proper driving of MOSFET power switches (6 MOSFETs IRFS4227, paralleled per one power switch (Fig. 1)). The ISGtB e-machine drive is supplied from on-vehicle battery (12 V, 19 Ah). Fig. 19 shows the improvement of the torque characteristics and also rotational speed range extension with the proposed control of the BLDC motor. Efficiency comparison between
common-known 120° angle switch-on mode control and introduced BLDC motor control is presented in Fig. 16, too. As it can be concluded, the BLDC machine has 15% higher maximal electromagnetic torque and 30% wider rotational speed range using the proposed control strategy compared to common 120° angle switch-on mode control, which confirms theoretical statements from chapter two. The proposed control strategy was also verified through IC engine starting maneuver comparison between conventional 120° angle switch-on mode control and introduced control of the BLDC motor (Fig. 20). Rotational speed ripple (Fig. 20a) is a consequence of IC engine compression and expansion cycles (four-stroke engine). Fig. 20b shows averaged starting characteristic where acceleration improvements and a difference in terminal rotational speed of the hybrid propulsion system is clearly seen. Instantaneous battery currents during start-up of an IC engine reached up to 300 A. Meanwhile, during generator operation mode the battery current was up to 104 A (Pgen = 1.5 kW at Ubat = 14.4 V). During the starting maneuver the definition of angles a and b is based on the measured rotational speed. Due to the simple and cost-effective rotor position detection (three Hall sensors) and high
Fig. 20. IC engine starting maneuver comparison.
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rotational speed dynamic introduced by IC engine the bottom limit of applying of the discussed BLDC motor control strategy is set to 40 rpm. 5. Conclusion In the paper the motor operation mode in the case of the ISGtB in hybrid propulsion system was studied in detail. As a result a novel control strategy which includes two control principles is suggested. The first one is a well known flux-weakening method and the second one is modification of switch-on angle. Experimental results have proven the control strategy of the BLDC motor to be very effective. Maximal electromagnetic torque has on average risen for 15%, BLDC motor rotational speed range has also been extended from 600 rpm to 800 rpm. Consequently, the expected starting maneuver of the IC engine has significantly improved, which was verified with measurements on the prototype hybrid propulsion system. The drawback of the proposed BLDC motor control is slightly lower efficiency, which is a consequence of a longer conduction of power converter switches. The proposed control strategy can be used in applications where maximal electromagnetic torque or efficiency is required in wide rotational speed range. References [1] Kim T, Lee HW, Parsa L, Ehsani M. Optimal power and torque control of brushless DC (BLDC) motor/generator drive in electric and hybrid electric vehicles. In: Conference record of the 2006 IEEE industry applications conference, Forty-first IAS annual meeting, vol. 3; 2006. p. 1276–81. [2] Chan CC, Chau KT, Jiang JZ, Xia W, Zhu M, Zhang R. Novel permanent magnet motor drives for electric vehicles. IEEE Trans Ind Appl 1996;43:331–9. [3] Bose BK. Power electronics – a technology review. Proc IEEE 1992;80:1303–34. [4] Bose BK. Energy, environment, and advances in power electronics. IEEE Trans Power Electr 2000;15:688–701. [5] Bajec P, Pevec B, Voncina D, Miljavec D, Nastran J. Extending the low-speed operation range of pm generator in automotive applications using novel AC– DC converter control. IEEE Trans Ind Electr 2005;52:436–43.
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