Open Loop V/f Control of Multiphase Induction Machine Under Open-Circuit Phase Faults Ahmed S.Morsy, A. S. Abdelkhalik, and Ahmed Abbas Electrical Engineering Department Alexandria University, Egypt {
[email protected],
[email protected],
[email protected]
Shehab Ahmed
Ahmed Massoud
Electrical and Computer Engineering Department Texas A&M University at Qatar
[email protected]
Electrical and Computer Engineering Department Qatar University
[email protected]
tolerant operation with the same pre-fault magneto-motive force. Obtaining the phase currents under fault conditions by solving non-linear equations is introduced in [12] and [13] where currents in healthy phases have the same magnitude but different phase angles. Field oriented control is usually employed to control multiphase induction machine. Several papers [14-17] introduce control schemes based on conventional field orientation to ensure the operation of the motor when one or more phases are open-circuited due to fault and to satisfy specific optimization criteria [10]. Generally, minimum torque ripples, equal phase currents, and minimum copper losses are the most common targeted functions [10]. Another widely used control technique for induction machines is the constant Volt/Hertz (V/f) method [18]. In the literature, there is no reported research to control a multiphase IM using V/f control under phase open.
Abstract —One of the main advantages of multiphase induction machines is their higher fault-tolerant capability. Under phase(s) loss, the machine currents can be optimally controlled to satisfy certain optimization criteria. In this paper, a simple open loop controller based on the conventional V/f control scheme of a five-phase induction machine is introduced which can ensure equal phase currents and minimum torque ripples under one phase open. The presented approach can be extended to any number of phases with any number of open phases. The fundamental dq components of the stator voltage are decided as in conventional V/f control. The measured currents are decomposed to their sequence components. The fundamental sequence is used to calculate the optimum reference third sequence current components that ensure equal stator currents under phase(s) open. The third sequence stator voltage components, that ensure equal remaining phase currents, are obtained using Proportional-Resonant (PR) controllers. The input errors of these controllers represent the difference between the actual third sequence current components and its optimum reference values. A prototype five-phase machine is used for experimental verification. I.
The multiple planes space vector representation is used to develop the fault-tolerant control technique and to analytically determine the stator currents in the healthy phases that ensure disturbance-free operation. To maximize the machine developed torque, the reference stator currents of the healthy phases are selected to nullify the negative fundamental sequence component [8-10]. With the reduction in the available degrees of freedom due to phase loss, the current components of the other sequences are no longer balanced. Consequently, the stator currents calculated by the control system may contain a remarkable inverse sequence component at angular frequency -ωs, which leads to a noticeable distortion in the waveforms. Additionally, due to the required unbalanced current components in the other sequence planes and the resulting negative sequence components of frequency -ωs in the reference signals, employing conventional PI regulators yield non-zero tracking errors. In [10], a control scheme to overcome this problem is proposed using multiple current regulators in synchronous reference frames. Two PI controllers for (d,q) of the first (+) sequence and four PI controllers for the third (+/-) sequences. This yields additional sophistication to the controller with a corresponding intricate tuning process.
INTRODUCTION
Recently, multiphase induction motors are promoted as a viable high power machine in both low and medium voltage applications [1]–[5]. Multiphase machines can be designed with a reduced per-phase voltage and correspondingly reduced semiconductor devices’ voltage rating, which is highly desirable in medium voltage applications. The additional degrees of freedom provided by multiphase machines offer many advantages over their three-phase counterparts especially during fault conditions [1], [6], and [7]. Theoretically, multiphase machines with n phases can continue running with (n-2) disconnected phases [8]. The multi-phase machine performance with open circuited phases has been studied in literature [8]-[13] providing control strategies to ensure fault This publication was made possible by NPRP grant NPRP 08 - 504 - 2 - 197 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.
978-1-4673-4355-8/13/$31.00 ©2013 IEEE
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Alternatively, adaptive resonant controllers proposed in [19] can replace the multiple synchronous frame controllers. One of the main challenges of multiphase machine control, during fault conditions, is the simplicity and the robustness of the proposed controller. I.
control [21, 22] is susceptible to noise. Predictive current control [23] increases the computational burden of the Digital Signal Controller. Synchronous reference frame (dq) control [10, 24] requires back and forth transformations with several trigonometric calculations, and the need for angle estimation. On the other hand, proportional resonant control can achieve zero tracking error like the (dq) with reduced calculations and without the need of the angle. Moreover, it has the ability to track unbalanced reference currents without sophisticated transformations. However to be able to achieve zero tracking error at a variable fundamental frequency its resonant poles must be adaptively tuned to the fundamental frequency of the tracked signal which is naturally available in V/f control. Figure 2 shows adaptive PR controller (in continuous form) implemented to track the third sequence stationary current (iαβ3) reference computed as previously discussed. kp and ki are the proportional and resonant controller constants. Based on and , the two PR controllers the two current errors of are used to develop the required third plane voltage and . components
OPTIMUM CURRENTS FOR ONE PHASE OPEN
For five phase machine with one phase open, the third sequence current components which ensure equal remaining phase currents and minimum torque ripples correspond to the following relations [8-10]
i sα 3 = −i sα 1 , isβ 3 = 0.236isβ 1
(1)
Controlling the αβ current components of the third sequence plane to comply with (1) yields equal stator phase currents in the remaining healthy phases and minimum machine torque ripples. Moreover, the fundamental negative sequence will equal zero, which maximize torque production. II.
SYSTEM BLOCK DIAGRAM
The complete system block diagram for the proposed V/f controller is shown in Figure 1. In this controller, the fundamental stator voltage is decided as in conventional V/f control. The measured currents are decomposed to their sequence components. The fundamental sequence is used to calculate the optimum reference third sequence current components, using (1), that ensure equal stator currents under phase(s) open. The third sequence stator voltage components, that ensure equal remaining phase currents, are obtained using only two Proportional-Resonant (PR) controllers.
For digital implementation on DSP, the PR controllers given in Figure 2 are discretized at 5 kHz. Although several discretization techniques are known in literature [25, 26], not all of them are applicable for finding acceptable discrete form of resonant controllers. Forward Euler (2) and Backward Euler (3) methods are not the proper techniques; forward Euler causes instability (since its poles are outside the unit circle), while backward Euler causes damping (since its poles are inside the unit circle). On the other hand, the Tustin method (4) provides a stable discrete resonant controller; however, it causes a shift in the resonant frequency of interest. The discretization method that best suits the resonant controller is the Zero order hold (ZOH) (5) it provides the closest discrete equivalent of the continuous resonant controller.
Several current control techniques for multiphase machines are available in literature. Nevertheless they encounter some drawbacks and they are usually employed with field oriented vector control. For instance, hysteresis current
|Vs1| Sinusoidal Generator Fundmanetal
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Figure 1. Proposed V/f Block Diagram.
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Sequence Trans.
Figure 2. Proportional resonant for the third sequence current.
Forward Euler
H z
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Backward Euler
H z
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Tustin
H z
Zero order hold
.
(4)
H z
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Figure 4. Experimental Setup.
Figure 3 presents the impulse response of the four discretization methods presented at (50Hz resonant frequency and 5 kHz sampling frequency), in order to simply demonstrate the aforementioned features from a time domain perspective. The output from forward Euler increases exponentially, while that of backward Euler damps to zero. Both Tustin and ZOH produce a sustained oscillation; ZOH resonates at its defined frequency (50Hz) while Tustin resonant frequency is shifted to (43.3Hz).
It is worthy to note that with full fundamental voltage applied to the controller, the required third sequence voltage components will cause the instantaneous value of some of the phase voltages to exceed the maximum allowed peak voltage, ⁄2. Hence, certain DC voltage reserve should be retained to avoid over modulation operation which yield undesired injected harmonics. If the DC-link voltage is limited to the peak value of the fundamental voltage, more sophisticated and challenging controller, which ensure stable operation, is required. This is postponed to future consideration.
Impulse Response
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EXPERIMENTAL RESULTS
In order to evaluate the proposed controller, the machine is operated under open phase faulty condition to test different transient cases as well as the characteristic curves under the proposed control.
Tus tin -1
EXPERIMENTAL SETUP
Based on the proposed controller, an experimental setup, shown in Figure 4, is used to investigate the proposed controller. A prototype of 1.5Hp five-phase induction machine is used for the experimental verification. The machine is built using an existing squirrel cage rotor. The stator comprises 4pole five-phase winding occupying 40 slots with conventional distributed winding. The machine is fed from a five-phase inverter operating at 5 kHz switching frequency and fed from a DC programmable supply. Conventional SPWM is used to control the five-phase inverter. The machine is coupled to a PM DC generator which acts as a mechanical load.
0.1
Time (seconds)
Figure 3. Impulse response of different discrete controllers
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A. Proposed control feasibility during transient In all transient cases, the proposed controller preserves equal current magnitude of the remaining four healthy phases, hence torque ripples are minimized during transient and steady state. Speed control is based on traditional V/f control and optimum current control is additionally applied for equalizing the current in the healthy phases to achieve minimum torque ripples. Figure 5(a) depicts three transient cases; starting from stationary to half rated speed Figure 5(b), then step reference to rated speed Figure 5(c) and finally step loading Figure 5(d). Generally, the machine currents experience notable third harmonic component caused mainly due to saturation effect. The saturation effect on the current prototype machine is relatively high especially during no-load and light load conditions. With the machine mechanically loaded, the current waveform tends to be more sinusoidal.
a)
Starting + step speed reference + step load
B. Effect of proposed control on torque ripples In order to highlight the effect of the proposed control on torque ripples, experimental current waveforms are recorded at rated voltage (110V phase-voltage) and frequency (60Hz) for three cases; healthy case Figure 6(a), fault case (open phase) without optimal current control Figure 6(b), fault case (open phase) with the proposed optimal current control Figure 6(c). Based on these current waveforms, the machine torque is estimated using the machine mathematical model [27], and shown in Figure 7. In the healthy case: negligible torque ripples are noticed. In fault case (open phase) without optimal current control the torque ripples are significant and causes higher audible noise, however, by applying the proposed control the torque ripples are minimized. It has to be noted that this was attained without complex vector control and without sophisticated transformations.
b)
Starting
C. Machine characteristic curves under the proposed control In this subsection, three cases are compared, namely, healthy case, open loop control with one phase open, and optimal current control with one phase open. Under open loop control with one phase open, the current magnitudes of healthy phases under open loop control are given in Figure 8(a). It is clear that the magnitudes of the phase currents are higher than healthy case with a high diversion in magnitude between different phases, yielding higher machine losses, lower efficiency, and lower maximum torque.
c)
Step speed reference
With one phase open and optimal current control applied, the line currents are approximately equal. For same load torque, the line current increases by a factor of 1.382 with respect to healthy case as shown in Figure 8(b). The torque speed characteristics for both healthy and optimal current control cases are approximately equal, as depicted from Figure 8(c), but with higher copper loss and lower efficiency especially for lower loads, as given by Figure 8(d, e).
d)
Step load
Figure 5. Transient under open phase with optimal current control
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Figure 6. Experimental results for current waveforms for three different cases
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Figure 7. Torque waveform for the three cases
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[3]
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e) Output power/Efficiency characteristic Figure 8. Experimental results for different conditions (a) torque/current char (Healthy and open loop control cases), (b) torque/current char. (Healthy and optimal control cases) (c) torque/speed characteristics, (d) output power/input power char, (e) output power/efficiency char
V.
[8] [9]
CONCLUSIONS
In this paper, a simple fault tolerant control scheme based on conventional V/f control to five-phase induction machine is presented. In the literature, field oriented control is usually employed with relatively sophisticated controllers that use high number of PI controllers to maintain same optimization objectives. On the contrary, the proposed control scheme allows for a disturbance-free operation in cases of open-circuit faults using only two PR controllers to control the third sequence current component in accordance with the fundamental sequence current. The paper gives experimental results for transient operation that ensures minimum divergence in the current of remaining healthy phases. Accordingly, torque ripples are minimized compared to the uncontrolled fault case. Also, machine characteristic curves show that the proposed control during fault gives similar behavior to the healthy case at the expense of increased phase currents and lower overall efficiency.
[10]
[11] [12]
[13] [14] [15]
APPENDIX
[16]
The prototype 1.5Hp five-phase machine ratings are listed in Table I. [17]
Table I. Prototype five-phase induction machine Ratings Rated phase Voltage (V) 110 Rated Power (Hp) 1.5 Rated phase current (A) 3.5 Rated frequency (Hz) 60 No. of poles 4 Rated Speed (rpm) 1700
[18]
[19]
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