REGULAR PAPER. The Improvement Avalability of a Double Star Asynchronous Machine Supplied redondant voltage source inverters

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1 FAOUZI BEN AMMAR SAMI GUIZANI REGULAR PAPER The Improvement Avalability of a Double Star Asynchronous Machine Supplied redondant voltage source inverters This paper proposes the availability analysis of a double star stator windings asynchronous machine. Each star is supplied by its own static PWM inverter. The active redundancy of the inverters improves reliability, availability and safety of the system since the loss of a phase does not stopped the motor. Detailed Markov Models are developed to analyze the availability. A reintegration control strategy of the repaired faulty inverter increases system survivability by allowing faulty inverter to regain the drive motor operation. The reintegration control strategy is based on the special use of the field oriented control to resynchronise the output frequency of the repaired inverter with the motor speed. Simulation results are carried out to show the ability of a fault tolerant architecture. Keywords: Double star asynchronous machine Markov model- active redundancy - Reliability Availability field-oriented control. INTRODUCTION To improve reliability [] and availability of the speed drive applications (drive of the compressors in the methane tankers, electric propulsion of the ships, railway traction), the multiphase or multi-stars asynchronous machine, offer multiple redundancy degrees, since the loss of one star does not stop the machine [5]. The dual three-phase induction machine is composed by two sets of stator windings spatially shifted by 30 degrees angle with isolated neutral points [6]-[9]. In the fault tolerant topology, depicted in figure, each star is supplied by its own voltage source inverter, offer redundancy which can be utilized to enable the operation with faulty inverter. The faulty drive can be disconnected or isolated from the corresponding star stator winding to permit operation with the remaining healthy inverter. In case of failure in one inverter the motor will be driven with up to half of maximal torque. In the first part of the paper, the authors have been proposed to analyze availability using transition diagram based on Markov chain. The last part of the paper concerns the description of the fault management cycle software. The reconfiguration and reintegration control strategy of the repaired inverter is based on the special use of the field oriented control.. MARKOV MODELLING A drive-motor in a fault-tolerant configuration employs two identical inverters to supply the dual three phase asynchronous motor. The system detects faults in the inverters, and places a faulty unit offline while continuing to operate using the healthy inverter. The faulty inverter can be repaired or replaced and reintegrated into the system without over-voltage or over-current. A Markov chain is a series of states are described by a directed graph, where the edges are labelled by the probabilities of going from one state to the other states [], [3] [4]. The Markov model is state transition model for which the probability of a state ECE Department Pondicherry University Pondicherry Engineering College INDIA. ajayvimal@yahoo.com ECE Department Pondicherry University Pondicherry Engineering College INDIA. tgpvel@hotmail.com EEE Department Pondicherry University Pondicherry Engineering College INDIAm gnanadass@yahoo.com Copyright JES 007 on-line :

2 transition depends only on the current state; the past states carry no information about future states. Rectifier I Voltage source inverter I T T T 3 Vr T 4 T 5 T 6 Switch device Network 3 ~ Rectifier II Voltage source inverter II DSAM 3 ~ T T T 3 Vr T 4 T 5 T 6 Fig.: A double star asynchronous machine supplied with two voltage source inverter The four possible states of motor-drive Markov model is shown in figure. λ Inverter up Inverter down λ Inverter up Inverter up λ λ Inverter down Inverter down Inverter down Inverter up Fig. : Markov Model of active redundancy of the voltage source inverters. Each drive has the same failure rate λ and the same repair rate. An important assumption is that the failure time of each inverter is exponentially distributed, and failure rate is constant. When a failure occurs, the repair process will start immediately, the repair time of each inverter also follows exponential distribution. If the failure and repair rates are the same for both inverters its possible to combine the states Inverter up and inverter 9

3 Failed and Inverter Failed and inverter up into a single state called inverter Failed. Figure 3, shows the condensed Markov model, the failure rate is λ when inverters are operating and there is single repair maintenance crew with repair rate that either repairs one inverter at a time. λ One Inverter up λ Inverter up Inverter up Inverter down Inverter down Fig.3: Condensed Markov model of active redundancy of the voltage source inverters with single crew repairing inverter at a time Figure 4 describe a single crew repairing both inverter. λ One Inverter up λ Inverter up Inverter up ' Inverter down Inverter down Fig.4: Condensed Markov model of active redundancy of the voltage source inverters with single crew repairing both inverters The failure of one inverter may cause an increase load on the healthy inverter. If that increased load causes a higher inverter failure rate, the transition rate from the inverter failed state to the inverter down and inverter down state could be adjusted to be higher than λ. The rated value λ must be multiplied by the π factors that take into account the overload. This configuration is shown in figure 5, where the failure rate of the inverter with a heavier load has been increased from λ to λ by the following equation: λ ' λ.( π + π + π + π +...) () = A E T Q With: π T : temperature factor, π P : power factor,π S : power stress factor, π E : environment factor and π Q : Quality factor. 0

4 λ One Inverter up λ' Inverter up Inverter up Inverter down Inverter down Fig.5: Condensed Markov model of active redundancy of the voltage source inverters with single crew repairing inverter at a time It has been assumed in all the previous Markov models that a switching device can disconnect or isolate instantaneously the faulty inverter from the corresponding star stator winding. In the Markov chain shown in figure 6, the switch device probability per request γ is incorporated. The switch probability per request may represent software-related issues or the probability of detecting the failure of an active inverter. λ.γ one Inverter up λ' Inverter up Inverter up.λ(-γ) Inverter down Inverter down Fig.6: Condensed Markov model of active redundancy of the voltage source inverters with single crew repairing both inverters including switch device probability per request. 3. AVAILABILITY CALCULATIONS The availability of the speed drive system can be defined us the probability that the system will function satisfactory at a given time t. The transition diagram represents a set of differential equations that can be solved to determine the availability that the system is in each state. dp( t) dt P( t) t [ T ]. P( t) [ P( t) P( t) P3( t) Pn( )] = () = T A probability vector with n components is a column vector whose entries are non negative and sum to. The process starts in one of these states and moves successively from one state to another. [T], [T], [T3], [T4] and [T5] are respectively the transition matrices of the Markov chains M, M, M3, M4 and M5 of the several configurations presented above by the figures,3,4,5 and 6. ' 9

5 [ ] ( λ + λ ) 0 ( ) λ λ+ 0 T = λ 0 ( λ + ) 0 λ λ ( + ) (3). λ 0 T =. λ ( λ ) + 0 λ (4). λ ' T 3 = ( ). λ λ λ ' (5). λ 0 T 4 =. λ ( λ' ) + 0 λ ' (6). λ ' T 5 =. λ. γ ( λ ' +) 0. λ. γ λ' ' (7) ( ) Table I represents the steady state availably calculation of the 5 Markov chains configurations M, M, M3, M4 and M5. A : is the probability that the system will be available at any random point of time. A lim t A( t) = (8) Markov configuration M chain TABLE I: STEADY-STATE AVAILABILITY CALCULATIONS Steady-state Availability calculations A λ + λ + λ λ + λ + λ + λ. + M. λ + λ. + M3 M4 M5 λ. +. λλ' + λ. + 3λ. +. λ + 3λ. + λ' ' +. ' + λγ '. λλ' + λ ( γ ) + λ' ' +. ' + λγ ' Assuming the failure rate is constant (exponential distribution) 0

6 4. THE REDUNDANT FIELD ORIENTED CONTROL As shown in Figure 7, the control strategy and fault manager software of the double stator supplied by redundant voltage source inverters are realised in an orthogonal reference the field rotating (d,q) axes reference frame running at ω dq. d V sd q V sd Vrd V sq V sq Vrq θ dq ψ Sα Sα Fig. 7: The double star asynchronous machine (d,q) System. The model obtained by using Park s transformation in undoubtedly the best adapted for the description of the dual-stator induction motor behavior at the transient, as well as steady state operation. The decoupling between the torque and the flux are be accomplished by properly aligning the rotor flux vector along the d-axis.. In the field rotating (d,q) axes reference frame the electric equivalent scheme is represented by Figure 8. Vsd Rs (Ls Mss)ω s Isd (Lr )ω s (Mss )ω s Rs (Ls - Mss) ω s A Isd Rr/g ω s Vsd B Vsq Rs (Ls Mss)ω s (Mss )ω (Lr )ω s Isq s Rs (Ls - Mss) ω s A Isq Rr/g ω s Vsq B Fig. 8: Equivalent electric scheme of double star induction machine in Park reference frame d,q. 9

7 Rr: Rotor resistance Rs: Stator resistance Mss: Mutual Inductance between two stars of the stator = Mutual cyclic inductance between star and rotor = Mutual cyclic inductance between star and rotor == Ls: stator cyclic Inductance Lr = rotor cyclic Inductance Te: The electromagnetic torque, T L : load torque ψ: Angle between two stars of the stator Φ rd,φ rq : Direct and orthogonal components of rotor flux. I sd, I sq, I sd, I sq : Direct and orthogonal components of star and star current. V sd, V sq, V sd, V sq : Direct and orthogonal components of star and star voltages. 5. THE CONTROL REINTEGRATION OF A REPAIRED INVERTER The availability of the motor drive is assured under 3 states Inverter up inverter up, Inverter up Inverter down and Inverter down inverter up. The block diagram of double star asynchronous machine with field-oriented control strategy is given on figure 9. The control system is divided in two redundant three phase subsystems; this allows a fault tolerant capability. The feedback regulators are working in coordinates which rotates synchronously with the rotor flux. In all operating modes, the direction of axis d is always coincident with the rotor flux representative vector. The measurements stators current are transformed to field oriented quantities Isd, Isq and Isd, Isq. In a large speed range, rotor flux Φrd is kept at constant nominal values controlling direct axis currents isd and/or isd. Tabel II shows the electromagnetic torque, the speed of rotor flux vector and the magnitude of rotor flux in all operating configurations. During operation of feedback loop in limitation the integral component of PI controller is corrected with anti-reset-windup technique. The sampling period, is chosen to be equal to the inverters pulse period (fc=5 khz). 6. SIMULATION RESULTS OF FAULTY OPERATION A fault management software cycle has been defined in phases: detection, location, isolation, reporting repair and reintegration. Once a faulty inverter has been identified, a control system can triggers a system reconfiguration to stop sending switching PWM signals to the faulty inverter and to isolate it from the corresponding star stator windings. The motor drive continues operation with a degraded capability. Figure 0, shows the simulation results of 45 kw dual star windings induction machine under the following cycle of operation: 0 t < 0.s: fluxing of the machine at zero speed. Note that for this operating mode, the fluxing of the machine is ensured by the two currents Isd and Isd, the references flux Φrdref=Φrdref = the half of rated flux Φrnom/. 0. t < 0.8s: acceleration from 0 to 460 rpm. 0.8 t <.49s: steady state of the speed. At t =.49s, failure of inverter occurs..49 t <.59s: the current Isd of the healthy star winding is controlled to impose the rated rotor flux. The motor will be driven with up to half of the speed. 0

8 .6 t <.s: deceleration from 460 rpm to 730 rpm.48 t < 3.s: Once the faulty inverter is replaced or repaired, it will attempt to regain correct state. The necessary precondition for the repaired inverter to regain the healthy state is to resynchronize the output frequency with the motor speed. t 3.s: operation in Steady state at nominal speed. Simulation parameters P = 45 kw; Rs = 0.5Ω; Rr = 0.046Ω; Inertia J = 0.8 kgm, pn= pair poles Ls=7.9 mh Lr=8.6 mh Mss = = =7. mh. ω Blocking Isq r + + Vsq r f θ dq Vs Vs Φ rdref ω Isd r + + Isq Vsd r R(θ dq Vs T 3 Vs Vs Inverter ω Φ rdref Isd Blockin Isq r + + ω Isd r Isq + + Vsq r Vsd R(θ dq - Vs Vs Vs Ψ) - T 3 Inverter Vs Vs MASD Isd θ dq - Ψ Φrd Φrd Tr /x Tr /x Isq x x + + Ψ - + Isq Fig. 9: The block diagram of double star asynchronous machine with field-oriented control strategy 9

9 TABLE II: Electromagnetic torque and rotor flux in (d,q) plane aligned with the rotor flux in four operating inverters states State of motor drive 3. Te = Lr Electromagnetic Torque Inverter p Φ ( I + I ) n rd sq sq up Inverter up ω = ω + ( I + I ) dq Tr.Φ rd sq 3 Te = p Φ ( Lr n rd sq I ) sq Inverter up Inverter down ω = ω + ( I ) dq 3 p Φ Lr n rd Tr.Φ rd sq Inverter Te = ( down Inverter up ω = ω + ( I ) Inverter down Inverter down dq I ) sq Φ rd Rotor flux (p) = + Trp Φ rd ( I sd (p) = + Trp Φ (p) = rd + Trp Tr.Φ sq rd I ) sdq I (p) sd I sd (p) 7. CONCLUSION The active redundancy of the inverters improves reliability, availability and safety of the system since the loss of a phase does not stopped the motor. Five configurations are presented by several Markov Models to analyze the steady state availably. A reintegration control strategy of the repaired faulty inverter increases system survivability by allowing faulty inverter to regain the drive motor operation. The reintegration control strategy is based on the special use of the field oriented control to resynchronise the output frequency of the repaired inverter with the motor speed. Simulation results of 45 kw double star induction machine are carried out to show the ability of a fault tolerant architecture. 0

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11 Speed (rpm) Tem (Nm) Isa (A) Isa (A) Time Fig. 0: Simulation results of a fault tolerant motor drive. (s) REFERENCES [] M. Molaei, H.Oraee, M. Fotuhi-Firuzabad Markov model of Drive Motor Systems for reliability Calculation IEEE ISIE 006, July 9-, 006, Quebec, Canada pp86-9 [] Alain Wood, Availability Modeling /94/S IEEE Circuits and Devices pp -7 [3] Marc Bouissou, Jean Louis Bon A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes, Reliability Engineering and System Safety 8 (003) [4] Shi Jian, Wang Shaoping Integrated availability model based on performance of computer networks Reliability Engineering and System Safety 9 (007) pp [5] Moubayed N., Meibody-Tabar F., Davat B., Rasoanarivo I., Conditions of safely supplying of DSIM by two PWM-VSI, EPE 99, Lausanne. [6] Mogens Blanke, Jesper Sandberg Thomsen Electrical Steering of vehicles fault-tolerant analysis and design Elsevier Microelectronics Reliability 46 (006)pp

12 [7] G.K Singh, V.Pant, Y.P Singh Voltage source inverter driven multi-phase induction machine Journal of computer and Electrical Engineering Elsevier 9 (003) pp [8] S.N Vukosavic, M. Jones, E. Levi and J. Varga, Rotor flux control of symmetrical six phase induction machine Journal of Electric Power Systems Research Elsevier 75 (005) pp4-5.j. [9] Hadiouche D., Razik H., Rezzoug A., Modelling of a double-star induction motor with an arbitrary shift angle between its three phase winding. 9 th international conference on EPE, PEMC 000 Kosice, Slovak Republic. [0] Mantero S., De paola E., Marina G. An optimised control strategy for double star motors configuration in redundancy operation mode, EPE 99, Lausanne. [] Lyra R.O.C., member, IEEE, and T.A.Lipo,Fellow, Six-phase induction machine with third harmonic current injection, ELECTRIMACS 8- August 00 9