Predictive Torque Control for Five–Phase Induction Motor Drives J.A. Riveros1, J. Prieto1, F. Barrero1, S. Toral1, M. Jones2, E. Levi2 2 Dpto. de Ingeniería Electrónica School of Engineering Escuela Superior de Ingenieros, Universidad de Sevilla Liverpool John Moores University 41092 Sevilla, Spain Liverpool L3 3AF, United Kingdom
[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] 1
Abstract− −Multiphase electric drives have been recently proposed for applications where the highest overall system reliability, combined with a reduction in the total power per phase, are required. Strategies like Field Oriented Control (FOC) and Direct Torque Control (DTC) have been traditionally used in these high performance applications. In this paper, a Predictive Torque Control (PTC) method is introduced as an alternative to FOC and DTC methods. Simulation results are provided to illustrate the potential of the presented control technique, comparing the speed, torque and current performances with those obtained by applying FOC and DTC methods. Keywords− −Motion control, Multiphase drives, Predictive control.
I.
INTRODUCTION
Since the late 1990s multiphase drives have become a serious alternative to their three–phase counterpart in certain applications, due to some intrinsic advantages that they offer, such as fault tolerance and means for power splitting across more than three phases [1]. These advantages are especially interesting for safety–critical and propulsion applications (more–electric aircraft [1]–[2], electrical and hybrid vehicles [3]–[4], all–electric ship propulsion [5]), where if one of the phases is lost, it is no longer possible to maintain the rotating field in the three–phase machine. To the contrary, multiphase drives can continue to run with the rotating field when one or more phases are lost. This is so since, regardless of the actual number of stator phases, a multiphase machine always requires only two degrees of freedom to generate a rotating field. Thus post–fault operation with rotating field is possible, albeit with some derating. Further, the low inverter DC link voltage, provided by batteries in some of the aforementioned applications, imposes high phase current requirements, making multiphase drives especially suitable due to the reduction of the current per phase for the given power [6]. One of the most interesting multiphase machines for these applications is the five–phase machine [1]–[2]. Two different constructions of the five–phase electrical machine can be found in the literature. The first one is based on a sinusoidal MMF distribution. This multiphase drive requires only sinusoidal voltages, so that the low order harmonics are undesirable in the machine’s input voltage. The second one is designed with concentrated stator windings. In this case, torque production can be enhanced using stator current low– order harmonic injection. In particular, the third harmonic can be used for this purpose, although the evaluation of reference
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voltage vectors imposes a significant computational burden in the real−time processing system [7], [8]. In this work, a five– phase machine with sinusoidal MMF distribution is utilized as an example of a multiphase drive, but the conclusions can be extrapolated to a five–phase machine with concentrated windings. High performance applications in multiphase drives require specific control systems. The most common control structure is the well–known Field Oriented Control (FOC) technique, a cascaded scheme with an inner current control loop and an outer speed control loop [1], [2]. The inner control loop typically generates switching signals for control of a two– level multiphase voltage source inverter (MVSI). The MVSI is controlled using an appropriate carrier–based or space vector pulse width modulation technique (CPWM and SVPWM, respectively). While CPWM methods are simpler to implement, SVPWM technique offers a better insight into properties of multiphase drives and inverters. Direct Torque Control (DTC) and Predictive Torque Control (PTC) are viable alternatives to FOC when fast torque dynamic performance is required. The DTC, developed in the mid–1980s, is more widely used at present. Its basic principle is to select the appropriate stator voltage vectors from a table, according to the signs of the errors between the references of torque and stator flux and their estimated values, respectively. DTC has been recently applied in multiphase drives [9]–[11], and the good feature is low machine parameter dependence. PTC is a control theory developed at the end of the 1970s. It also provides fast torque response, but is a more flexible control scheme, compared to DTC. PTC determines and applies during a sampling time the optimal set of MVSI switching states, based on a model of the real system [12], [13]. It is therefore heavily dependent on the knowledge of the machine parameters. With regard to multiphase drives, PTC has so far been studied only as a mean for current control of dual three–phase (asymmetrical six–phase) induction motor drives, due to the difficulties in its real–time implementation [14]–[17]. Some initial considerations, related to the MPC applications for current control in five– phase inverter–fed systems, have been reported in [18] where however a static load was utilized in the evaluation. This work considers the use of PTC, along with the traditional schemes, for the speed control of five–phase machines with sinusoidal MMF distribution. The main
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will be evaluated. Stator flux is usually estimated from the stator currents and reconstructed stator voltages. The basic configuration of the PTC control scheme in electric drives is shown in Fig. 1, where ω*m is the reference mechanical speed, ωm is the measured mechanical speed, is is the measured stator current, T*e is the reference electromagnetic torque, Te[k+1] is the electromagnetic torque estimated using the predictive model of the drive, λ*s is the reference stator flux, λs[k+1] is the stator flux estimated using the predictive model of the drive, and Si[k+1] represents the VSI applied switching function. In each sampling period k, the control algorithm produces the gating signal combination to be applied during the next sampling period k+1, Si[k+1], using the algorithm that can be summarized as follows:
contribution of the paper is an evaluation of the performance and advantages of each control technique in high performance applications of multiphase electrical drives. The viability and effectiveness of the PTC–like speed control strategy are also proved. The paper is organized as follows. Section II introduces the PTC technique. Next, Section III derives the model of the five–phase propulsion drive. Section IV analyzes the PTC technique applied to the speed and torque control of the five–phase drive, and compares the obtained results with FOC and DTC methods. Finally, the conclusions are summarized in the last section. II. PTC GENERAL PRINCIPLES A system controlled by an energy modulator with a finite number of configurations has attracted much attention in recent years, where the output of a continuous controller is translated into a sequence of the converter states using a switching algorithm. This is the case of AC motor drives, where the voltage source inverter (VSI) is considered by the controller as a gain. When fast torque response is required, high performance current control is necessary. Among these control techniques, PTC techniques show faster torque and speed response compared to classical methods like FOC techniques, and are a more flexible control scheme than DTC. Among the identified advantages obtained using PTC some can be emphasized: constraints and nonlinearities are easily included, multivariable case can be considered, and the resulting controller is easy to implement and redefine. PTC uses a model of the set of the VSI and the machine to define the control action. This model, also called predictive model, is used at each sampling period to evaluate the system state vector for each possible VSI state. The control actions are then obtained solving an optimization problem aimed at minimizing a cost function named J. Different cost functions can be used to express different control criteria. For instance, the distance between the reference and the predicted flux and/or torque can be used if a propulsion drive is designed, obtaining the cost function of (1) where Tn and |λsn| are two gain factors corresponding to the rated torque and flux values during the operation in the base speed region. Thus torque and flux errors have the same weight in the cost function. If required, other terms can be included in the cost function to include secondary control criteria (for example, switching stress minimization, DC link voltage balancing, or the stator current harmonic minimization).
(T * − Tepred [k + 1])2 + λs J= e Tn2
*
− λspred [k + 1] 2 λsn
For each sampling period k Read future speed reference: ωm* Read current and speed measurements for sample k Initiate J to INF (Jo) For each possible voltage vector Produce an estimation of next torque and stator flux Evaluate J If J iαβ − MAX + K xy isxy [k + 1] > i xy − MAX
(17)
)
Here Kαβ and Kxy are weighting factors that penalize excessive stator current in the α–β and x–y planes, respectively. It is interesting to note that these terms do not affect the cost function if the stator currents in the α–β and x–y planes are within the established limits. Figures 4 and 5 summarize the obtained results. A speed reference variation from 0 to ωm is considered, using different load torque values. The following performance parameters are obtained for the comparative analysis: overshoot and rise time. These performance parameters are evaluated and the results are graphically summarized in Fig. 4. Figure 5 details the obtained results when load torque is zero. PTC offers better performance, when compared to both DTC and IRFOC methods. The overall performance of all the control techniques is qualitatively similar (Fig. 4), although PTC quantitatively improves the performance parameters (Fig. 5). Acceleration and braking responses are also tested, and the speed, the torque and the stator current behavior are analyzed. A reference step from 0 to the 750 rpm reference speed is applied at 0.1 ms, and a load torque is then impressed. Further, a reference step from 750 to the nominal speed is applied at 0.5 ms, when the steady state is reached. Finally, the reference speed is reduced from nominal to 750 rpm at 0.8 ms. Figure 6 shows the obtained results. Figures 7 and 8 depict the obtained results using a DTC scheme similar to the one proposed in [11] and using the IRFOC presented in [21], respectively. The same stator current limitation is applied for all the methods, and a sampling frequency of 15 kHz is used for the DTC scheme, while 7.5 kHz is utilized in IRFOC. Consequently, similar switching frequency is expected using all the methods (7.5 kHz), as one switching can be produced per VSI leg in each sampling interval in the DTC and PTC methods while two are generated in the IRFOC. Faster speed and torque responses are obtained using the proposed PTC technique. However, lower ripple in the stator current is obtained using the IRFOC, especially when compared to the DTC technique. Notice that stator current evolution using PTC offers better response using the aforementioned cost function, which penalizes stator over–current in the α–β and x–y planes, than the other control techniques.
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(a)
(b)
Fig. 6. Control performance using the PTC method and the speed reference stepping from 0 to the nominal speed: speed, torque and stator phase current responses (upper, middle and lower traces, respectively).
(c) Fig. 4. Performance parameters obtained using (a) PTC, (b) DTC, and (c) IRFOC techniques, impressing different reference speed and load torque values.
(a)
(b) Fig. 5. Control performance parameters obtained for TL=0. (a) Overshoot, and (b) Rise Time.
Fig. 7. Control performance using the DTC method: speed, torque and stator phase current responses (upper, middle and lower traces, respectively). Conditions are the same as in Fig. 6.
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[3]
[4] [5] [6]
[7] [8] [9] [10] [11]
Fig. 8. Control performance using the IRFOC method: speed, torque and stator phase current responses (upper, middle and lower traces, respectively). Conditions are the same as in Fig. 6.
[12]
[13]
V. CONCLUSIONS In this paper, a Predictive Torque Control technique for the speed and torque regulation of a five–phase drive is introduced. The method avoids the use of complex modulation techniques, providing a flexible design through the re–definition of a cost function. The introduced control technique is analyzed using a Matlab/Simulink environment, and compared with the DTC and RFOC techniques. Its viability has been assessed for the case when the cost function includes a term to limit the α–β and x–y stator current components to physically meaningful values.
[14]
[15] [16]
[17]
ACKNOWLEDGMENT
[18]
The authors gratefully acknowledge PTI–Itaipú Binacional and the Spanish Government (National Research, Development and Innovation Plan, under reference DPI2009– 07955) for the financial support provided.
[19] [20]
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