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Letters to the Editor A Start-Up Method for a Speed Sensorless Stator-FluxOriented Vector-Controlled Induction Motor Drive Bimal K. Bose, Nitin R. Patel, and Kaushik Rajashekara
Abstract—This letter describes a zero-speed start-up method of a speed sensorless stator-flux-oriented direct vector-controlled induction motor drive with the help of a machine current model that does not use any speed signal. The machine starts smoothly with vector control at finite developed torque and then transitions to the standard direct vector-control mode with the voltage model signals as the speed begins to develop. The direct vector-control mode with voltage model uses programmable cascaded low-pass filters for flux-vector synthesis [2] and enables the drive to operate from zero speed to field-weakening mode. As the drive speed falls to zero, the drive again transitions to start-up mode, so that it can be smoothly started again. The performance of the start-up scheme has been verified on a 100-kW electric vehicle drive. Index Terms—Drive, induction motor, sensorless, vector control.
I. INTRODUCTION The speed and flux sensorless vector control of induction motor drive is currently receiving wide attention in the literature. In spite of extensive effort, precision synthesis of speed- and flux-vector signals yet remain a challenge today, particularly near zero-speed operation. Among different types of vector control, the direct vector control with stator-flux orientation [1] is very attractive, because the feedback signal estimation accuracy depends only on the stator resistance variation, which can be compensated for somewhat easily. Besides, the signal voltage behind the stator resistance that is to be integrated for flux-vector estimation is somewhat larger than that for rotor-flux estimation, which becomes particularly beneficial near zero speed. A new method of integration, called programmable cascaded low-pass filter, has been proposed in the literature [2], [3] and works well with voltage model feedback signals from zero speed, but with finite developed torque (i.e., slip frequency). However, the drive is not self-starting and, if an attempt is made to start directly with this control, severe torque pulsation will occur (see Fig. 3). A method of solving the problem is to start the drive with stator-flux-oriented indirect vector control that does not use a speed sensor [3] and then transition the drive to direct vector-control mode as speed begins to develop where it receives the flux-vector signals estimated from the machine terminal voltages and currents. This method is somewhat difficult to implement, and it introduces large torque jump during mode transitions. This letter describes zero-speed start-up of the drive with statorflux-oriented current model flux synthesis that does not use any speed signal. The current model (using the speed signal) flux vector synthesis was originally used by Blaschke for direct vector control servo-type drive (which can operate from zero speed) and will be defined as the Blaschke equation in this letter. With speed sensorless Manuscript received July 24, 1996; revised February 17, 1997. This work was supported by Delphi Systems—General Motors Corporation. B. K. Bose and N. R. Patel are with the Department of Electrical Engineering, The University of Tennessee, Knoxville, TN 37996-2100 USA. K. Rajashekara is with Delphi Energy Systems, Indianapolis, IN 46250 USA. Publisher Item Identifier S 0278-0046(97)05276-3.
Blaschke equation start-up, the drive always remains in direct vectorcontrol mode until it is shut down and restarted in Blaschke equation mode. It is somewhat easier to implement, and the performance is improved compared with indirect vector-control starting. II. SYSTEM OPERATION Fig. 1(a) shows the block diagram of the stator-flux-oriented direct vector-control system that incorporates the Blaschke equation start-up scheme. The control uses a programmable cascaded low-pass filter method of integration for feedback signal estimation, as discussed before. The drive is designed for electric-vehicle-type applications and, therefore, uses torque and flux control in the outer loops. The flux loop is added with decoupling compensation current idq , which is characteristic of stator-flux-oriented control [1]. The machine terminal voltages and currents are sensed and passed through hardware lowpass filters (not shown) before A/D conversion. The hardware filters also transform the input signals into ds 0 q s frame, as indicated. The voltage signals, after subtraction of stator resistance drops, are integrated within the cascaded low-pass filter estimation block. This block essentially consists of three identical programmable low-pass filters with the phase shift of 1=3(90 0 ) per stage at any frequency where is the phase-shift angle of the front-end hardware filter. The time constant ( ) of the filters and the gain are programmed as a function of frequency, so as to get ideal integration at any frequency. The signal computation block calculates the unit vectors, flux, and frequency signals, as indicated. At start-up condition, it accepts the flux signals from the Blaschke equation start-up block (B. E. mode) and then transitions to the standard direct vector-control mode (DVC) with a time delay td , as indicated. III. START-UP SCHEME As discussed before, the machine is started with the help of a current model, but no speed signal at zero speed, and then transitioned to the standard direct vector-control mode. The standard stationary frame current model equations (also known as Blaschke equations) can be given as [4] 3 d qr
dt
d
s dr
dt
Lm s iqs + !r TR Lm s ids !r = TR =
0
1 s dr 0 T R s 0 1 qr T R
s qr
(1)
s dr
(2)
where all are standard symbols. The equations accept stator currents
s
s
(iqs ; ids ) and speed (!r ) at the input and estimate the rotor-flux s ; s ) at the output. These equations are to be transformed vector ( qr dr
for stator-flux vector estimation so that stator-flux-oriented vector control can be used at start-up. Substituting Lr s s s qr = Lm qm 0 Llr iqs s s s as = am + Lls ias
and
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Lr s s s dr = Lm dm 0 Llr ids s s s ds = dr + Lls ids
(3) (4) (5) (6)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 4, AUGUST 1997
(a)
(b) Fig. 1. (a) Control block diagram of stator-flux-oriented vector control incorporating the Blaschke equation start-up scheme. (b) Block diagram of Blaschke equation start-up scheme.
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(c) Fig. 1. (Continued.) (c) Transition between B.E. start-up and DVC mode.
in (1) and (2) and simplifying, we can get
s d qs s + ! s 0 Ais = 0 T1R qss + A didtds + Biqs (7) r ds ds dt s d ds = 0 1 s + A dids + Bis 0 ! s 0 Ais (8) r qs ds qs dt TR ds dt where A = Lls + L LL and B = LLR . Equations (7) and (8) give
current model or Blaschke equations for stator-flux vector estimation. These equations will be used without the speed signal at zero speed to start the machine. Substituting !r = 0 in (7) and (8)
s d qs dt s d ds dt
= =
0 T1R 0 T1R
s diqs s qs + A dt s dids s ds + A dt
+
s Biqs
(9)
+
s : Bids
(10)
s ; s is shown in Fig. A block diagram to solve stator fluxes qs ds 1(b). The equations are actually implemented in discrete time. The s =dt (or dis =dt) in discrete time is basically an current derivative diqs ds increment or decrement of current in a sampling time of computation, irrrespective of magnitude of current at any speed. With a 32-b digital signal processor (DSP) (TMS320C30), this computation can be very precise. Note that this block diagram is valid to start the machine with stator-flux-oriented vector control strictly at zero speed. Fig. 1(c) shows the transition between the start-up (B.E.) mode and the regular vector control (DVC) mode. In the B.E. mode, the rated flux is established in the beginning before applying the torque command (see Fig. 2) which is proportional to i3qs . Then, as the command torque (i.e., ji3qs j) exceeds a threshold value (kiqsr , where iqsr corresponds to rated torque), the drive transitions to DVC mode with a time delay td . This delay is programmed to be 3 = k ) to the magnitude of i3 . This inversely proportional (td iqs qs can be explained as follows. As the command torque (positive or negative) is established at the stand-still condition of the drive, the actual torque and the corresponding speed develops with a time delay that is inversely proportional with the magnitude of the torque. Therefore, transition to DVC mode occurs before the drive develops speed, because the B.E. mode is invalid at any finite speed. Again, the DVC mode operates satisfactorily above a minimum threshold frequency (typically, 0.33 Hz). Therefore, transition to DVC mode can occur above a threshold accelerating torque (i.e., slip frequency). The satisfactory time delay (td ) can be determined by a test on the drive. As the drive speed slows down in DVC mode, the frequency also decreases proportionately. Below a threshold speed, the drive operation is disabled and transitions to B.E. mode before starting again. The frequency (!e ) can be computed with reasonable accuracy
Fig. 2. Start-up and transition performance between B.E. and DVC modes.
in the whole range by the following equation [1]:
!e =
s 0 is Rs s 0 vs 0 is Rs s vqs qs qs ds ds ds s2
:
(11)
In Fig. 1(c), the typical range of k is 0.2–1.0 and the corresponding range of td is 300 ms–30 ms. Note that, in B.E. mode, strongly parameter sensitive flux-vector estimation will tend to give some mismatch with that of DVC mode and may cause some jerk at transition. This has to be fine tuned by on-line parameter correction. IV. PERFORMANCE EVALUATION A complete drive system with the new start-up scheme, as shown in Fig. 1(a), was designed, and performance was verified by simulation study. Fig. 2 shows the smooth performance for several transitions between the B.E. and DVC modes. Note that the B.E. mode is activated for the second time when the drive is disabled at zero torque but finite speed. Fig. 3 shows the jerky start-up if an attempt is made to start the drive directly in the DVC mode. The control system including the start-up method is being implemented with a
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Linear Control of Inverter Output Voltage in Overmodulation Dong-Choon Lee and G-Myoung Lee Abstract—A novel overmodulation strategy for space-vector pulsewidth modulated (PWM) inverters is proposed. The method, which increases the range of linear control of the output voltage by 10%, is based on Fourier series representation of the reference voltage. Index Terms—Overmodulation, PWM.
I. INTRODUCTION
Fig. 3. Start-up performance of the system directly from DVC mode.
TMS30C30-type DSP, and the experimental results of the total drive system will be reported in the future.
V. CONCLUSION A zero-speed start-up method has been developed and investigated for a speed sensorless induction motor drive that uses stator-fluxoriented direct vector control. The stationary frame current model of the machine (Blaschke equations) without a speed signal has been modified for stator-flux vector estimation and used to start the machine and, then, switched to standard direct-vector-control mode at zero speed. The start-up scheme has been verified by simulation study and its performance was found to be excellent. It is being implemented on a 100-kW electric vehicle drive with a TMS320C30type DSP, and the experimental performance of the total system will be reported later.
REFERENCES [1] X. Xu, R. W. De Donker, and D. W. Novotny, “A stator flux oriented induction motor drive,” in Conf. Rec. IEEE-PESC, 1988, pp. 870–876. [2] B. K. Bose and N. R. Patel, “A programmable cascaded low-pass filter synthesis for a stator flux oriented vector controlled induction motor drive,” IEEE Trans. Ind. Electron., vol. 44, pp. 140–143, Feb. 1997. [3] B. K. Bose, M. G. Simoes, D. R. Crecelius, K. Rajashekara, and R. Martin, “Speed sensorless hybrid vector controlled induction motor drive,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1995, pp. 137–143. [4] B. K. Bose, Power Electronics and AC Drives. Englewood Cliffs, NJ: Prentice Hall, 1986. [5] B. K. Bose, Ed., Power Electronics and Variable Frequency Drives. Piscataway, NJ: IEEE Press, 1997.
For better utilization of the dc-bus voltage in pulsewidth modulated (PWM) inverters, novel methods of overmodulation have been proposed. In sinusoidal PWM (SPWM), the control range can be extended by 15% by adding the third harmonic [1]. Recently, a new scheme using the describing function of the saturated output voltage has been developed, where a compensated reference voltage is generated with amplified inverter gain, which fully provides a linear control range [2]. On the other hand, the space-vector PWM has been popularly applied to voltage modulation of the inverter, since its linear control range is wider than that in the SPWM [3]. In overmodulation, the voltage reference that deviates from the hexagon envolope is usually scaled down to the point on each side, with the phase angle unchanged [4]. Therefore, the correct fundamental component cannot be obtained, and the maximum output voltage of the inverter is not available. An overmodulation scheme proposed by Holtz involves two modes of overmodulation depending on the modulation index (MI). In mode I, however, the fundamental voltage cannot be generated as exactly equal to the reference voltage, since the contribution of the voltage increment around each corner of the hexagon to the fundamental component differs from that of the voltage decrement around the center of each side of the hexagon. In this letter, a novel overmodulation strategy for the space-vector PWM to produce the exact fundamental voltage is proposed, where reference angles based on Fourier series expansion of the desired output voltage are derived. It is confirmed by numerical data that linear control of the inverter output voltage is feasible over the whole overmodulation range. II. A NOVEL OVERMODULATION STRATEGY The modulation index for PWM inverters is defined here as
V3
(1) MI = 2 Vdc where V 3 is the phase voltage reference and Vdc is the inverter input voltage. The limit of linear output range for the space vector PWM is at MI = 0.906. If MI is higher than this value, overmodulation occurs. The basic concept of the proposed strategy is similar to [5], where the insufficient output voltage around the center of the sides of the hexagon is compensated near vertices. According to MI, the overmodulation range is divided into two modes. Manuscript received October 22, 1996; revised March 4, 1997. This work was supported by the EESAI Project, No. 95-67. The authors are with the School of Electrical and Electronic Engineering, Yeungnam University, Kyungbuk, 712-747 Korea (e-mail:
[email protected]). Publisher Item Identifier S 0278-0046(97)05277-5.
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