Definition of position scalars of all voltage vectors in a delta‐connected IM.
Abstract
This chapter presents a position sensorless method for induction machines that only relies on the fundamental pulse width modulation (PWM) waveforms to excite saliency. Position signals can be synthesized through the measurement of the derivatives of the line currents induced by the PWM voltage vectors. This method is essentially saliency detection based, and therefore derivation of the rotor position is possible at low and zero speeds. In addition, it works also at higher speeds without the need of the knowledge of the machine’s fundamental model. Experimental results showing fully sensorless induction motor control at low and higher speeds validate the principle of this method.
Keywords
- sensorless control
- induction machine
- saliency
- PWM excitation
- current derivative
1. Introduction
Due to the incapacity of the fundamental model-based sensorless rotor position estimation at zero and low frequencies, alternative methods have been intensively studied. These methods exploit the anisotropy or saliency of the machine resulting from either saturation or geometric variation on the rotor. They can be classified into two categories according to the detection method for the anisotropy (or saliency) position. One category relies on the continuous injection of high-frequency voltage signals and then measuring the response of the high-frequency (
In this chapter, a method belonging to the second category is described. Instead of using extra test vectors or modifying the standard modulation scheme, this method integrates the test vectors with the standard PWM waveforms [16]. In the following paragraphs, the theory of the method will be presented first, then, its application on a 4-pole 30 kW Δ-connected cage machine having 56 open slots will be demonstrated. Other implementation issues related to the speed sensorless operation, such as the noise filter of the position signals, will also be introduced.
2. Position estimation with the fundamental wave PWM
When a three-phase, delta-connected induction machine has its stator leakage inductances modulated by the anisotropies introduced by either the main flux saturation or the rotor slotting, they can be assumed to vary according to:
where l0 is the average inductance and Δl is the amplitude of inductance variation caused by the anisotropy (nan = 2 for saturation-induced anisotropy or nan = nrs = Nr/p for rotor slotting, where Nr is rotor slot number and p the pole pairs).
The standard space vectors of Figure 1 are applied. Figure 2 shows the equivalent circuit when the machine is applied with vector u1 from which the following equations can be derived:
By the application of the null vector u0 or u7, one has:
If the instants of applying u1 and u0 are close enough, it is viable to assume that:
Additionally, the voltage drops across the stator resistance and can be ignored due to their small values compared with Ud.
Hence, the subtraction of the Eqs. (4)–(7), (5)–(8) and (6)–(9) yields:
From the relationship between phase currents and line currents, for example,
Considering Eqs. (1) to (3), one has:
from which three balanced position scalars
where
where
It should be noted that because the application of u1 and u2 results in the same position scalars, they are defined with the same terms,
By referring to (19), (20), (21) and (23), (24), (25), it is possible to define
Therefore,
whereby the position can be derived through the arctan operation as shown in (29).
Such a combination between two adjacent voltage vectors, and a null vector, also exists in other five sectors. Therefore, the position estimation is achievable using only the fundamental PWM sequence. Table 1 gives the position scalars corresponding to all the vectors.
3. Experimental implementation
3.1. Practical considerations
It can be seen that the correct position estimation relies on the precise measurement of the di/dt signals. For this aim, air-cored Rogowski [9], ferrite-cored Rogowski [18], or air-cored coaxial cable-typed [14] transducers can be used. Or direct digital calculation, di/dt = i(t2)−i(t1)/(t2−t1), can be employed instead. Figure 3 shows a typical di/dt signal along with ADC trigger signal when an air-cored coaxial cable-typed transducer is used.
Another important issue comes from the fact that due to the common/differential mode voltages produced by the inverter, high-frequency oscillation exists in the phase currents, which poses a challenge for accurate di/dt measurement. This is true when dwell times of the voltage vectors are too short or when the reference voltage vectors pass the boundaries of sectors. Therefore, a minimum dwell time, tmin, is imposed on voltage vectors for di/dt measurement. When the original dwell time of a voltage vector, t, is shorter than tmin, an opposite vector with a dwell time, tmin- t, is added to maintain the volt-second. This procedure can be realized simply by the edge-shifting technique, which is illustrated in Figure 4 when the reference voltage lies in Sector I.
3.2. System schematic
Figure 5 shows the system schematic of the sensorless speed control. Three di/dt sensors are connected in series with the lines of the induction motor, whose parameters are given in Table 2. The position vector formation block synthesizes the position vector
The Speed/Position Calculation block further refines the position signals. Because the ADI-compensated rotor slot position still consists of a speed dependent disturbance signal rotating at
The position signals obtained so far can be used for position acquisition in the way shown in (29). However, a mechanical observer similar to [19] is utilized to reduce the noise. The schematic is given in Figure 7.
Figure 8 shows an improved estimated rotor position signal before and after the observer. An offset angle can be observed between these two rotor positions. This is due to the fact that the mechanical observer’s estimation was aligned to the encoder’s angle initially, whereas the estimate from the SBF only yields the incremental position.
4. Experimental results
The following experiments show the operation of the drive under sensorless speed control at low and higher speeds. The induction motor drive is under speed sensorless control. The load machine is under torque control. The rating of the dynamometer converter is such that only a loading of 80% rate can be applied to the induction motor. It is emphasized that all the experimental waveforms were recorded on an experiment rig.
Figure 9 shows that under no load condition the IM is reversed at 6 rpm, corresponding to the excitation frequency
In Figure 11, the drive was taken between ±210 rpm under no load. This test confirms the capability of the drive to perform larger speed transients.
5. Conclusion
A sensorless position scheme for AC machines is presented relying on the line-current derivative measurements in response to a fundamental PWM switching sequence. The rotor position angle is derived due to the tracking of rotor slotting and the signal is used for sensorless control. If the anisotropy caused by the main flux saturation is tracked, for example, in a permanent magnet machine, this method is applicable throughout a very wide speed range. If rotor slotting is tracked, then the maximum speed is limited by the Nyquist frequency associated with the rotor slot passing frequency. In principle, however, the method can work over the entire torque-speed envelope.
References
- 1.
Jansen PL, Lorenz RD. Transducerless field orientation concepts employing saturation induced saliencies in induction machines. In: Proceedings of the IEEE IAS Annual Meeting; Nov/Dec 1995. p. 174‐181 - 2.
Holtz J. Sensorless position control of induction motors – An emerging technology. IEEE Transactions on Industrial Electronics. 1998; 45 (6):840-852. DOI: 10.1109/41.735327 - 3.
Teske N, Asher GM, Sumner M, Bradley KJ. Encoderless position estimation for symmetric cage induction machines under loaded conditions. IEEE Transactions on Industrial Applications. 2001; 37 (6):1793-1800. DOI: 10.1109/28.968193 - 4.
Silva CA, Asher GM, Sumner M, Bradley KJ. Sensorless rotor position control in a surface mounted PM machine using HF voltage injection. In: Proceedings of the EPE –PEMC on CD-ROM; 2002 - 5.
Linke M, Kennel R, Holtz J Sensorless position control of permanent magnet synchronous machines without limitation at zero speed. In: Proceedings of the IEEE IECON 2002 on CD-ROM; 2002 - 6.
Corley MJ, Lorenz RD. Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds. IEEE Transactions on Industry Applications. 1998; 34 (4):784-789. DOI: 10.1109/28.703973 - 7.
Ha JI, Sul SK. Sensorless field orientation of an induction machine by high frequency signal injection. In: Proceedings of the IEEE IAS Annual Meeting; 1997. p. 426‐432 - 8.
Schroedl M. Sensorless control of AC machines at low speed and standstill based on the INFORM method. In: Proceedings of the IEEE IAS Annual Meeting; 1996. p. 270‐277 - 9.
Caruana C, Asher GM, Clare J. Sensorless flux position estimation at low and zero frequency by measuring zero-sequence current in delta connected cage induction machines. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 2003 - 10.
Staines CS, Asher GM, Sumner M. Sensorless control of induction machines at zero and low frequency using zero sequence currents. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 2004 - 11.
Holtz J, Pan H. Elimination of saturation effects in sensorless position controlled induction motors. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 13–18 October 2002; Pittsburgh - 12.
Robeischl E, Schroedl M. Optimized INFORM measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion. IEEE Transactions on Industrial Applications. 2004; 40 (2):591-598. DOI: 10.1109/TIA.2004.824510 - 13.
Wolbank T, Machl J. A modified PWM scheme in order to obtain spatial information of ac machines without mechanical sensor. In: Proceedings of the IEEE APEC; 2002. p. 310‐315 - 14.
Juliet J, Holtz J. Sensorless Acquisition of the rotor position angle for induction motors with arbitrary stator windings. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 2004 - 15.
Erdman JM, Kerkman RJ, Schlegel DW, Skibinski GL. Effect of PWM inverters on AC motor bearing currents and shaft voltages. IEEE Transactions on Industrial Applications. 1996; 32 (2):250-259. DOI: 10.1109/28.491472 - 16.
Gao Q, Asher GM, Sumner M, Makyš P. Position estimation of AC machines at all frequencies using only space vector PWM based excitation. In: Proceedings of the IEE 3rd International Conference on Power Electronics, Machines and Drives (PEMD); 2006. p. 61‐70 - 17.
Gao Q, Asher GM, Sumner M. Sensorless position and speed control of induction motors using high frequency injection and without off-line pre-commissioning. In: Proceedings of the 31st Annual Meeting of IEEE, IES 2005 on CD-ROM; 2005 - 18.
Wolbank TM, Machl JL, Hauser H. Closed-loop compensating sensors versus new current derivative sensors for shaft-sensorless control of inverter fed induction machines. IEEE Transactions on Instrumentation and Measurement. 2004; 53 (4):1311-1315. DOI: 10.1109/TIM.2004.830561 - 19.
Jansen PL, Lorenz RD. Transducerless position and velocity estimation in induction and salient AC machines. IEEE Transactions on Industry Applications. 1995; 31 (2):240-247. DOI: 10.1109/28.370269