15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia
Modeling of a Five-Phase Induction Motor Drive with a Faulty Phase H. Guzmán1, J.A. Riveros1, M.J. Durán2, F. Barrero1 1
Universidad de Sevilla, Sevilla, Spain,
[email protected] Universidad de Málaga, Málaga, Spain,
[email protected]
2
Abstract — Fault-tolerance capability is one of the most attractive characteristics of multiphase machines for industrial applications. Resent research has proven that post-fault ripple-free operation is possible as long as the reference currents generate a smoothly rotating magnetomotive force (MMF). However, the power converter and multiphase machine behaviour and interaction during different types of faults has been hardly studied, modelled and verified. This work analyses the behaviour of a real five-phase induction machine when a fault appear in one phase of the power converter. Two cases are considered, an open-phase fault condition where a power leg of the converter is disconnected, and an openphase fault condition where the free-wheel diodes continue working. Two models are also presented based on PSIM and SIMULINK for the analytical study of the system under the fault conditions, and verified comparing the obtained results with the real case. Keywords — Multiphase machines, Fault operation, Drive Modeling.
I. INTRODUCTION Multiphase drives have gained special attention during the last years due to the benefits they present for industrial applications such as traction, ship propulsion or wind energy conversion systems [1-2]. The high fault tolerance capability that these types of machines possess makes them attractive in systems where high reliability is required ensuring non-stop operation (electrical vehicles and offshore wind farms), due to the high economical and safety repercussions caused by fault occurrence. Multiphase machines fault-tolerance is possible due to the additional degrees of freedom it possesses over conventional three phase machines that allow the generation of a smoothly rotating MMF. Extensive research has been done in this topic for different number of phases and type of machines [3-7], concluding that post-fault ripple-free operation can be achieved if there exists more than three healthy phases, ensuring the generation of a symmetrical rotating airgap field. Different control strategies have been proposed in order to ensure minimum copper losses [4,7], equal peak currents [5,7], minimum torque oscillations [6,7] and minimum derating [3,7] of the faulty drive in post-fault operation. Although an enormous amount of work has been focused on multiphase machines fault tolerance, contributions are focused on post-fault control and current reference calculation for multiphase drives under open-phase faults. The analysis of the machine under fault condition and the description of the models in the
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post-fault asymmetrical situation have been much scarcer. Moreover analytical study of the complete system under faulty conditions (i.e. power converter and multiphase machine), have exclusively focused on openphase faults and there exists the need to develop and verify different machine fault scenarios. In this paper, a comprehensive analysis of one phase fault condition in a real five-phase induction drive is done. Two fault conditions are reproduced in the multiphase drive. The first case reproduces the typically considered post-fault operation, where the open-phase is modeled as the disconnection of a power leg. This case does not consider anti-parallel free-wheel diodes operation. Notice however that industrial Voltage Source Inverters (VSI) are normally based on standard power stacks which do not allow the disconnection of any individual phase. These industrial VSIs do not normally manage one phase fault condition. When the fault appears all the switches are disconnected and the drive no longer rotates or the switches of the faulty phase are stalled but the free-wheel diodes continue operating. This second case will be the normal situation in a real application of the multiphase drive, but it is not considered in previous post-fault studies. This work presents an experimental analysis of the aforementioned one-phase fault situations. A simulation environment is also derived for the analytical study of the post-fault operation. The model is verified comparing simulation and experimental results. The paper is organized as follows. Section II discusses the five-phase induction drive model in normal operation. The one-phase fault conditions are detailed in section III, where a real test rig is used to force the faulty conditions and the obtained results are depicted and analyzed. A simulation environment based on PSIM and Simulink/Matlab is presented in section IV. This simulation tool is also validated comparing with the real system behavior. Finally, the conclusions are presented in the last section. II. SYMMETRICAL FIVE-PHASE INDUCTION DRIVE One of the most frequently considered multiphase machines is the symmetrical five-phase induction machine [1-2]. Two different types of five-phase induction machines are normally referred in the literature. The first one uses distributed windings that create a nearsinusoidal airgap MMF. This multiphase drive requires only sinusoidal voltages, so low order harmonics are undesirable in the machine’s input voltage. The second one is designed with concentrated stator windings that generate low order airgap MMF harmonics. In this case, torque production can be enhanced using stator current low-order harmonic injection. In particular, the third
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harmonic can be used in five-phase induction motors. In this work, a five-phase machine with sinusoidal MMF distribution is utilized. However, the obtained conclusions can be extrapolated to other multiphase machines (n-phase induction machine, with n>5, n = an odd number). The electrical drive scheme is shown in Fig. 1. The power converter is a five-phase voltage source inverter with 25=32 possible switching states (30 active and two zero). The vector [Sa Sb Sc Sd Se]T, where Si∈{0,1}, characterizes each switching state, where Si =0 indicates that the lower power switch is ON and the upper power switch is OFF, while the opposite holds true when Si =1. Each stator phase voltage vsi can be then obtained from the switching state and the DC link voltage Vdc as follows: ⎡ v sa ⎤ ⎢v ⎥ ⎢ sb ⎥ V ⎢ v sc ⎥ = dc 5 ⎢ ⎥ ⎢v sd ⎥ ⎢ vse ⎥ ⎣ ⎦
⎡4 ⎢− 1 ⎢ ⎢− 1 ⎢ ⎢− 1 ⎢⎣− 1
− 1 − 1 − 1 − 1⎤ ⎡ S a ⎤ 4 − 1 − 1 − 1⎥⎥ ⎢⎢ S b ⎥⎥ − 1 4 − 1 − 1⎥ ⋅ ⎢ S c ⎥ ⎥ ⎢ ⎥ − 1 − 1 4 − 1⎥ ⎢ S d ⎥ − 1 − 1 − 1 4 ⎥⎦ ⎢⎣ S e ⎥⎦
(1)
Although the phase variable and space phasor models for distributed-winding symmetrical five-phase induction machines with sinusoidal MMF distribution are wellknown, they are briefly reviewed in this section. All the standard assumptions of the general theory of electrical machines (sinusoidal spatial MMF distribution is expected, uniform air gap is considered, and the magnetic saturation and the core losses are neglected) apply as for a three-phase machine. Taking this into account, it is possible to model the five-phase machine by a set of stator and rotor phase voltage equilibrium equations referred to a fixed reference frame linked to the stator as follows: d [λ s ] dt d d = [ Rs ] ⋅ [is ] + [ Lss ] [is ] + [ Lsr (θ )] ⋅ [ir ] dt dt
[ v s ] = [ R s ] ⋅ [i s ] +
d [λ r ] dt d d = [ Rr ] ⋅ [i r ] + [ Lrr ] [i r ] + [ Lrs (θ )] ⋅ [i s ] dt dt
[v r ] = [ Rr ] ⋅ [ir ] +
(2)
(3)
Rotor voltages are zero in the squirrel-cage induction machine, and the impedance matrices can be written as follows: (4) [Rs ] = Rs ⋅ [I 5 ] (5) [ Rr ] = Rr ⋅[ I 5 ] (6) [ Lss ] = Lls ⋅ [ I 5 ] + M ⋅ [Λ (ϑ ) ] (7) [ Lrr ] = Llr ⋅ [ I 5 ] + M ⋅ [ Λ (ϑ )] cos(ϑ ) cos( 2ϑ ) cos( 3ϑ ) cos( 4ϑ ) ⎤ ⎡ 1 ⎢cos( 4ϑ ) 1 cos(ϑ ) cos( 2ϑ ) cos( 3ϑ ) ⎥⎥ ⎢ (8) [ Λ (ϑ )] = ⎢ cos( 3ϑ ) cos( 4ϑ ) 1 cos(ϑ ) cos( 2ϑ ) ⎥ ⎥ ⎢ 1 cos(ϑ ) ⎥ ⎢cos( 2ϑ ) cos( 3ϑ ) cos( 4ϑ ) ⎢⎣ cos(ϑ ) cos( 2ϑ ) cos( 3ϑ ) cos( 4ϑ ) 1 ⎥⎦
(9)
[ Lsr (θ )] = [ Lrs (θ )]T = M ⋅ [ Ψ (θ )]
⎡ cos(Δ1 ) ⎢ cos(Δ ) 5 ⎢ [Ψ (θ )] = ⎢cos( Δ 4 ) ⎢ cos(Δ ) 3 ⎢ cos( Δ ) 2 ⎣⎢
cos( Δ ) 2 cos( Δ ) 1 cos( Δ ) 5 cos( Δ ) 4 cos( Δ ) 3
cos( Δ ) 3 cos( Δ ) 2 cos( Δ ) 1 cos( Δ ) 5 cos( Δ ) 4
cos( Δ ) 4 cos( Δ ) 3 cos( Δ ) 2 cos( Δ ) 1 cos( Δ ) 5
cos( Δ ) ⎤ 5 cos( Δ ) ⎥ 4 ⎥ cos( Δ ) ⎥ 3 cos( Δ ) ⎥ 2 ⎥ cos( Δ ) ⎥ 1 ⎦
(10)
where ϑ=2π/5 is the spatial shifting between adjacent phases. Notice that [I5] is the identity matrix of order 5, and the Δi angles are defined as: Δi=θ+(i−1)ϑ, being i={1,2,3,4,5}. III. ONE-PHASE FAULT CONDITION IN THE FIVE-PHASE DRIVE In order to analyze the system behavior during faulty conditions, an experimental evaluation has been conducted. The test rig is based on a 30 slots, 2 pairs of poles three-phase induction machine, whose stator has been rewound to give a five-phase induction machine with 3 pairs of poles. Parameters of the machine have been determined using stand-still tests with inverter supply [8-10], and the obtained values are shown in Table I. A schematic of the rig and photos of the complete system are given in Fig. 2. Two industrial threephase VSIs from Semikron (SKS21F) were used to drive the machine. These conventional three-phase drives manage independently the fault condition of each phase which means that the IGBTs of the faulty phase are no longer turned on in post-fault operation but the rest of the power switches continue operating. These power modules simplify the emulation of one of the considered fault conditions, where the free-wheel diodes continue working. The open-phase faulty condition has been emulated using a power relay connected in series with the machine’s phase. The DC link voltage was set to 200V using a DC power supply system. The control system is based on the MSK28335 board and the TMS320F28335 DSP, and the induction machine was operated in the V/f operation mode with a modulation index and fundamental frequency of M = 0.5 at f = 25 Hz. TABLE I ELECTRICAL PARAMETERS OF THE FIVE-PHASE INDUCTION MACHINE Parameter Value Parameter Value M (mH) Rs (Ω) 12.85 688.92 τr (ms) σLs (mH) 151.65 179.49 Ls (mH) P (kW) 768.80 1.4 Lr (mH) p 768.80 3
Fig. 1. Schematic diagram of the symmetrical five-phase drive.
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Fig. 2. Test rig scheme. The power and control systems are shown at the left side, while the five-phase machine appears in the right side.
Fig. 3. Stator current (a, b, c and d phases) evolution when a fault is generated in phase a. The free-wheeling diodes are biased using a power relay in series with the faulty phase (lower plot) or remain conducting (upper plot).
Figures 3 and 4 summarize experimental results. The fault is impressed in the phase ‘a’ of the real system. Symmetrical phase stator currents are initially obtained, but the symmetry disappears when the fault condition is introduced. Notice that stator current in the faulty phase is zero when the free-wheeling diodes are biased (Figs. 3 and 4 lower scope plots), but a residual current remain while the power relay is being switched off. Notice also that to bias the free-wheeling diodes, additional hardware must be included in the power converter design. In our case, a power relay has been introduced in the faulty phase in series with the power leg, and it is commanded to open the phase when the fault is emulated and the IGBTs of the leg stop switching. This is not the case when free-wheeling diodes are not biased (Figs. 3 and 4 upper scope plots), and the generated MMF in the faulty phase forces non-controlled conduction of the freewheeling diodes. Figure 4 depicts the generated MMF in the faulty phase which justifies the free-wheeling diodes non-controlled operation. Stator currents were measured in Fig. 3 using HAMEG HZ56-2 probes, and a TEKTRONIX TCP202 scope in Fig. 4 to obtain better resolution. Phase voltages were measured using TEKTRONIX P5205 high voltage differential probes with 2X attenuation.
Fig. 4. Stator current evolution (upper plots, dark blue ink) and stator voltage (lower plots, light blue ink) in phase a (faulty phase). Faulty case considering free-wheeling diodes (upper scope figure) and open phase (lower scope figure).
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IV. SIMULATION ENVIRONMENTS Two simulation environments have been designed to analyze the post-fault operation of the VSI–fed fivephase induction machine. The first one studies the fault condition taking into account the free-wheeling diodes. The model of the multiphase induction machine is the same as in healthy state, due to the fact that the freewheeling diodes avoid zero stator current in the faulty phase. The power converter can be then modeled using the PSIM environment, and the stator voltages in the healthy phases are impressed using the power converter while it is imposed by the free-wheeling diodes in the faulty phase. Consequently, the electrical characteristics of the power switches (IGBTs in our case) and the freewheeling diodes can be taken into account. The multiphase machine and the modulation strategy are modeled using Matlab/Simulink tools. A complete scheme of this model is shown in Fig. 5. This simulation environment is configured as in the experimental tests. The DC link voltage is set to 200 V, and the induction machine is operated in the V/f operation mode with a modulation index and a fundamental frequency of M = 0.5 at f = 25 Hz. Figure 6 shows the stator phase currents before and after the fault condition, considering the freewheeling diode conduction (upper and middle plots). Stator current evolution is very similar to the one obtained in the experimental tests. Stator voltage is also shown (Fig. 6, lower plot) and a good agreement is achieved with the experimental test (Fig. 4, upper plot). On the contrary, the open-phase fault condition must be emulated using a multiphase induction machine model completely different from the one used in healthy state. This is so since there is no stator current in the faulty phase, and the stator voltage is not a state variable in the model. Then, the opening of phase a implies the loss of one degree of freedom and the machine is further on considered as a four-phase machine where the remaining four healthy phases are no longer symmetrical in space. Assuming isolated star neutral connection, the new state variables’ system has only three degrees of freedom and
it was also implemented using the Matlab/Simulink tool. The induction machine is now modeled in pre and post fault operation using a five and four phase system, respectively. A transition between both models occurs as soon as the fault is generated using all the variables evaluated in the pre-fault model as initial conditions in the post-fault simulation system. Figure 7 shows the scheme of this second model which takes into account that the stator current in one phase is cancelled. Some tests have been done to compare simulation and experimental results in order to validate this second simulation environment. Figure 8 summarizes the obtained results. Stator phase currents in the pre and post fault operations are shown in the upper and middle plots, while the stator voltage of the faulty phase is also shown in the lower plot. A good agreement is achieved with the experimental test (Fig. 4, lower plot). VI. CONCLUSION A five-phase induction motor drive with one faulty phase has been analyzed. Two cases have been considered, namely open-phase fault (which would be the normal considered post-fault operation) and freewheeling diode conduction (which would be the normal situation when industrial power converters are used) resulting in a non-controlled current. Experimental results have been provided to make a comprehensive analysis of the fault conditions. Two simulation tools based on PSIM and Simulink/Matlab environments have been presented to study the post-fault operation. These simulation environments have been validated comparing with its equivalent experimental systems. Obtained results guarantee the feasibility of the simulation systems for the analysis of the post-fault operation. ACKNOWLEDGEMENT The authors gratefully acknowledge the Spanish Government (National Research, Development and Innovation Plan, under project references DPI2011–25396 and DPI2009–07955 and the Junta de Andalucía 2010 research program, under reference TEP–5791) for the financial support provided.
Fig. 5. Modeling of the five-phase induction drive in post fault operation considering the free-wheeling diodes.
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Fig. 6. Obtained simulation results using the model that considers freewheeling diodes conduction during the fault. Stator current evolution in the healthy phases (upper plot) and the faulty phase (middle plot). Evolution of the stator voltage in the faulty phase (lower plot).
Fig. 8. Obtained simulation results using the model that considers an open-phase during the fault. Stator current evolution in the healthy phases (upper plot) and the faulty phase (middle plot). Evolution of the stator voltage in the faulty phase (lower plot).
Fig. 7. Modeling of the five-phase induction drive in post fault.
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[6]
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