Circuit-Base nuction Motor Drive Reliability uner Different Control Schemes an Safe-Moe Operation Ali M. Bazzi, Xiangyu Ding, Alejanro Dominguez-García, an Philip T. Krein Grainger Center for Electric Machinery an Electromechanics Department of Electrical an Computer Engineering University of llinois at Urbana-Champaign Urbana, L {abazzi2, ing3, alean, krein}@illinois.eu Abstract This paper proposes a reliability moeling metho for inuction motor rives base on an euivalent circuit moel. The machine input voltages or currents are moele as sources epenent on states an commans. This enables reliability analysis for ifferent control strategies. The metho utilizes failure moes an effects analysis, Monte Carlo simulations, an Markov moels. Different controllers, in aition to faults in the machine, power electronics, an sensors, are aresse. The control methos consiere in the analysis inclue constant volts per hertz (V/f), inirect fieloriente control (FOC), irect torue control (DTC), an feeback linearization control (FLC). Direct line operation (DLO) is also consiere. The propose circuit-base reliability moeling metho is versatile an easy to implement in commercial circuit simulators. The simulation moel, which is experimentally verifie, uses a reliability tool to evaluate the mean time to failure (MTTF) of the rive. Results show that, as expecte, V/f control has the highest MTTF, ue to its inepenence from sensor feeback, but poor ynamics. Among the close-loop controllers, FOC an DTC are better for fast ynamics, simplicity, an acceptable MTTF, but FLC is shown to have the longest MTTF. A safe-moe control scheme is propose uner which the rive is shown to have an even longer MTTF than V/f. Keywors Motor rive reliability, safe moe controller, backup controller inuction motor rives, faults in motor rives, reliability enhancement.. NTRODUCTON Avance inuction machine applications, e.g., vehicles, aircraft oil pumps, an riving conveyors, reuire careful esigns for safety an reliability. High reliability can be achieve through several approaches, e.g., multi-phase machines [1], sensorless control algorithms [2], fault tolerance [3], etc. While close-loop motor control provies better ynamic performance than open-loop, sensor feeback poses a reliability concern if no fault tolerance or back-up controls are implemente. Thus, it is important to ientify which close-loop controller will provie the best performance an highest reliability uner faults. Open-loop controllers, such as constant Volts-per-Hertz (V/f), reuire no sensors but have poor ynamic performance. Combining open- an close-loop controls in a safe-moe arrangement is expecte to prouce high reliability an goo ynamic performance. A versatile simulation tool is reuire to evaluate the reliability of ifferent motor control schemes. This prevents amage to an experimental setup; allow easy controller replacement an automation of the fault impact assessment. To simultaneously stuy physical effects an fault transients in the machine, power electronics an sensing reuires that the simulation tool runtime be reasonable. Some of the available literature aresses motor rives reliability moels in non-circuit-base methos [4], but the moel reuires significant moifications to simulate new control laws. Other methos an reliability moels have been elaborate upon in [4] an show a nee for a versatile reliability evaluation tool, especially when motor rive controllers are compare. This paper proposes a circuit-base reliability moeling an analysis approach of an inuction motor rive uner open- an close-loop control. This approach shows that a safe-moe topology enhances overall rive reliability. t is promising because moeling electrical faults is straightforwar in a circuit simulation environment, flexible in moeling ifferent controllers, an easy to implement in circuit-base simulators. The reliability tool evelope here performs fault simulations an evaluates the mean time to failure (MTTF) of the rive system. For every controller, the reliability moeling approach runs an automate fault moes an effects analysis (FMEA) that covers the effects of three consecutive faults on the rive. The machine moel use is shown in Fig. 1 [5] where the otte lines show the connection that can be moifie to reflect current-fe or voltage-fe control strategies. Depenent current or voltage sources are use to mimic the controller operation. Motor rive controllers usually set a esire input current or voltage that epens on commans an maybe feeback. The
flexibility of this moel lies in easy replacement of the euations controlling these epenent sources. Section escribes the open- an close-loop controllers in the stationary, synchronous, or rotor reference frames. Section elaborates on the reliability tool in regar to the faults, failure rates, an the reliability evaluation proceure. Section V shows the simulation moel valiation, an Section V presents the reliability evaluation of two open-loops an three close-loop controllers. Section V presents the propose safe-moe control scheme, an Section V conclues the paper. Fig. 1. Circuit-base inuction motor moel with control laws lumpe into epenent sources. MOTOR CONTROLLERS The moel shown in Fig. 1 is commonly use in inuction motor control esign. This moel was use for two reasons: 1) most close-loop controllers are esigne in the frame, an 2) the moel reference frame can be easily moifie by changing ω. All reuire feeback signals are assume to be available through sensors or estimators. Depenent sources were ae to the moel to mimic operation of ifferent controllers. Open-loop irectline operation (DLO) an constant volts per hertz control (V/f), in aition to three close-loop controllers, are stuie in the reliability analysis. The goals for analyzing both open- an close-loop controllers are to fin the best controllers an to stuy the safe-moe configuration where the open-loop runs as a backup for the close-loop. The DLO is expecte to have very low reliability as it runs at a single spee, but it has been wiely use when electronic rives are not employe. The V/f is expecte to have high reliability as it reuires no sensor feeback. However, the ynamic response to loa changes is generally worse than any close-loop controller. The close-loop controllers are inirect fiel-oriente control (FOC), irect torue control (DTC), an feeback linearization control (FLC), an they are all expecte to have acceptable reliability an goo ynamic performance ue to the corrective effects of feeback. V/f [6] an DTC [7] are moele in the stationary reference frame; FOC [5] is moele in the synchronous reference frame; an FLC [8] is moele in the rotor reference frame. Block iagrams of all controllers, except DLO, are shown in Figures 2 5 where ω e an ω m are the electrical an mechanical freuencies, respectively; ψ r is the rotor flux magnitue, * superscripts stan for commans, an Ks are fractions of the inverter c bus voltage. Fig. 2. FOC in the synchronous reference frame Fig. 3. DTC with torue an flux hysteresis Fig. 4. FLC in the rotor reference frame
7. Solve (3) to fin the state transitioning probabilities. 8. Solve (4) to fin R(t). 9. Solve (5) to fin the MTTF. Fig. 5. Open-loop V/f control The parameters λ r an λ r are rotor flux values; T e is electrical torue an v s, v s, i s, i s are stator voltages an currents. Euations f 1 an f 2 in Fig. 2 are shown in (1) an (2) an were erive in [6]. Machine parameters are assume to be well-known. Reaers can refer to [9] for more etails on parameter sensitivity of ifferent rive controllers. R n ω i + L i ( isλr isλr ) lr p r s m s 2 2 Llr λr + λr Lm s = σl + npωrλr λ λ r r Llr + u 2 2 spee + u 2 2 flux λr + λr λr + λ r v v R ( isλr isλr ) lr npωris Lmi s 2 2 Llr λr + λr L = σ n ω λ λr λ L r u 2 2 spee + u 2 2 flux λr λr λr λ + + r m s L p r r lr n (1) an (2), n p is the number of pole pairs; u flux an u spee are the flux an spee commans. The rest of the parameters are same as in Figures 2-5. Note that for all controllers shown in Figures 2 5, voltage control is utilize. Thus, epenent voltage sources controlle by euations that are moele by the block iagrams are use in the simulations.. RELABLTY MODELNG PROCEDURE A. Propose Proceure The reliability moeling proceure is use to stuy the fault impact on the rive performance an to calculate the reliability function R(t) an its corresponing MTTF. The propose proceure combines FMEA an Markov reliability moeling. t can be summarize as follows: 1. entify, moel, an assess the failure rates of possible faults. 2. Set esire system performance reuirements. 3. nject faults an assess system performance. 4. entify system states after every fault an buil Markov moel or state iagram. 5. Assign failure an recovery rates to all branches in the iagram. 6. Buil state-transition matrix Φ an eliminate rows an columns of absorbing states. (1) (2) Euations (3) (5) are funamental in etermining the transitioning probabilities an the rive reliability. n (3), the column vector P T (t) inclues the probability of occurrence of every fault seuence. Φ is usually sparse as not all states are connecte. Therefore, solving (3) is simple with computer tools. The initial probability vector, P T (), is a zero-vector except for the initial state before any fault occurs this term is one. T T Φ t T P () t = e P () (3) With Φ incluing transitions among K non-absorbing states only, i.e., states without permanent failure, these probabilities are summe to fin the overall rive reliability. The MTTF is then foun as the integral of R(t). Note that the expecte rive reliability at any time t can be foun by simply evaluating R(t). K R() t = P() t i= MTTF = R( τ) τ Reference [1] inclues the etaile mathematical founations of the reliability moeling an analysis proceure. B. Reliability Analysis Tool To implement the propose proceure, a MATLAB/Simulink tool was evelope. This tool performs Monte Carlo experiments, where faults are ranomly injecte. The system ynamic response after the fault occurrence is recore an evaluate accoring to preetermine criteria or performance reuirements. Faults in sensors are consiere as shown in [4], while electrical faults are moele by moifying the circuit moel shown in Fig. 1. For example, rotor over-temperature changes the rotor resistance, which changes the value of R r. The reliability tool also computes fault coverage the probability of the rive surviving a fault over a reuire spee range for a preset number of input steps. The input use here for the fault coverage stuy is the spee comman. The truncation level efine as the number of fault levels that can occur seuentially prior to total failure is chosen to be three. n a fault seuence, only one fault per component occurs, an failure moes for each component are assume to be inepenent. For example, a short circuit on the stator sie will not cause a rotor bar to break, an vice versa. Different fault seuences are generate as permutations. For every seuence, the tool i (4) (5)
checks whether the system meets the performance reuirements. Performance reuirements are preset to etermine whether the system functions or fails. Finally, the state transition matrix is compute, the survivor function R(t) is plotte, an the overall system mean time to failure (MTTF) is calculate. The pseuo-coe of the tool is shown in Fig. 6. n Table, power electronics an machine faults have been surveye from common literature. Sensor faults shown are similar to those in [4, 11] Gain: incorrect gain ue to a sensor or interface circuit malfunction; Constant: Sensor or interface circuit saturation; Bias: incorrect shifting cause by the sensor interface circuit; Omission: zero output where sensor signal is shorte to groun or igital encoer malfunctions. Two types of fault injection blocks were implemente circuit faults an signal faults. Both have a similar structure where the pre-fault ynamics an the postfault ynamics are fe into two separate inputs of a multiplexer. The Boolean fault moe etermines whether or not a fault is injecte in each component. Fault injection blocks in the inuction motor an power electronics are built using two ieal switches as shown in Fig. 7. The signal fault injection blocks are implemente using switch blocks as shown in Fig. 8. Fig. 7. Circuit fault injection block Fig. 6. Pseuo-coe of the reliability analysis tool C. Faults, Failure Rates, an Performance Reuirements Faults similar to those shown in [4] are utilize here an inclue most major faults that coul occur in the machine, power electronics, an sensors (current sensors an spee encoer). n the simulation moel, fault injection blocks have two variables: fault moes an failure rates. The fault moe is a Boolean parameter that is either (No Fault) or 1 (Fault). Components with several fault moes, e.g., sensors, have multiple fault injection blocks. For this rive, 11 fault moes were implemente an are summarize in Table. TABLE. FAULT MODES AND FALURE RATES Power electronics an machine faults (λ in Failures/hour) Rotor over-temperature λ ROT = 5 1-7 Broken rotor bar λ BRB = 5 1-7 b-c Phase-to-phase short circuit λ PP = 3.2 1-6 Phase a short circuit to groun λ SCG = 5 1-7 Phase a open circuit λ OC = 5 1-7 A-Phase current sensor faults Bias = + 1 A λ CSB = 1 1-7 Constant = 1 A λ CSC = 1 1-7 Gain = 1.5 λ CSG = 1 1-7 Omission λ CSO = 1 1-7 Spee encoer fault Constant = 143 RPM λ SEC = 1.9 1-7 Gain = 1.5 λ SEG = 1.9 1-7 Omission λ SEO = 7.4 1-7 Fig. 8. Sensor fault injection Faults that occur in the abc frame are transforme to the frame to be consistent with the machine moel. n general, the transformation between abc to can be formulate for a variable f as shown in [5] where K s matrix is given by K s f = K f, (6) s abc 2π 2π cosθ cos( θ ) cos( θ + ) 3 3, 2 2π 2π = sinθ sin( θ ) sin( θ + ) 3 3 3 1 1 1 2 2 2 an the arbitrary reference spee is ω = θ / t. n the stationary reference frame, θ = an K s can be simplifie to
2 1 1 1. K s = 3 3 3 1 1 1 CSO in the stationary frame is erive here as an example. n the case of CSO, the currents are given by a. (7) 1 3 b = 2 2 c 1 3 + 2 2 For omission in the a-phase current sensor, the current feeback for a is set zero. The faulte euation is transforme to the frame using (7) an the fault in this frame can be moele as o 2 o 1, (8) = 3 + o 1 where o, o, an o are the stator currents in the stationary frame. Examples of fault transformations are shown in Table. n Table, x, x, x are post-fault current values an,, are the pre-fault values, where x is g for gain, b for bias, o for omission, c for constant an O for open circuit. Similar notation is use for the voltages. TABLE FRAME FAULT MODELS Phase a OC: V a = Phase a CSG: a =k a O g V 1 V 2 ( k 1) O g 2 V = V + V = 3 + O 3 g V 1 V 1 ( ) k 1 2 2 Phase a CSB: a = a +B Phase a CSC: a = C b c B ( C ) 2 b c 2 = + = + 3 b 3 c 1 B 1 ( C ) 2 2 Failure rates (failure/hour) shown in Table are obtaine from open-access literature such as [1, 12]. Note that the same fault moes an failure rates are use in all rives except for current sensor an spee encoer faults which are ignore in open-loop controllers. There is no claim of failure rate accuracy, but failure rates are common among all five controllers for comparison purposes. Knowing the orers of the failure rates, e.g., 1-7 failures/hour, is sufficient to fin a reasonable reliability estimate. Performance reuirements are essential in etermining whether the system survives or fails after a fault occurs. The reuirements use in this stuy are shown in Table. Note that the choice of these reuirements efinitely affects the reliability evaluation, e.g., setting the settling time to be very long gives the rive longer time to recover from a fault an thus some failures might not occur. TABLE PERFORMANCE REQUREMENTS Performance reuirement Value Torue & spee settling time < 25 ms steay-state spee error < 72 RPM steay-state torue error < 1N m Current peak < 5 A V. MODEL VALDATON Simulations provie a fast an safe environment to evaluate the rive reliability, but they nee to be experimentally verifie to valiate their accuracy. The moel in Fig. 1 was experimentally verifie for both V/f an FOC uner several faults that o not cause catastrophic failures. Simulation an experiments utilize a prototype 1.5hp inuction machine. Examples are shown in Figures 9 12. i a (A) spee (RPM) 1-1 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 1 5-5 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 time (s) Fig. 9. Simulation results of FOC uner SEO Fig. 1. Experimental result of FOC uner SEO: i a (Top, 1 A/iv), spee (bottom, 1 rpm/iv), time (2 ms/iv)
spee (RPM) i a (A) 5-5 15 1 5 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 time (s) Fig. 11. Simulation result of V/f uner OC in phase a certain controller. The resulting R(t)s an MTTF s of the rive uner the ifferent controllers are shown in Fig. 13 where the top plot shows close-loop rives, an the bottom plot shows the open-loop rive. As expecte, V/f has the best reliability an highest MTTF as it is inepenent of sensors. While FOC is slightly more reliable than DTC, FLC is the most reliable close-loop controller, which can be attribute to its three PD loops that compensate for errors an maintain system operation. DLO is not reliable as it can only operate at the line freuency, so for a fault coverage stuy that consiers 1 spee steps, the DLO automatically fails with a probability of 9%. R(t) 1.8.6.4 FLC MTTF = 59 Years DTC MTTF = 54 Years FOC MTTF = 58 Years Fig. 12. Experimental result of V/f uner OC in phase a: i a (Top, 5 A/iv), spee (bottom, 2 rpm/iv), time (2 ms/iv) Results show that the simulation response agrees with that of the experiments. n Figures 9 an 1, the rive fails uner SEO as the spee rops below the esire comman even though the current peaks remain within bouns. This is consiere a failure because violating any of the performance reuirements is consiere as a system failure. Figures 11 an 12 show that once an OC occurs in phase a, the current rops to zero, but the spee is maintaine as esire. Thus, the rive survive by operating only two phases, b an c, as none of the performance reuirements are violate. Note that the general pre- an post-fault behaviors match well for these two examples. The simulation moel behaves as expecte from experiments. Thus, the simulation moel is use hereafter to perform the reliability analysis. Note that in the simulation results shown, currents from were transforme to the abc frame for comparison with measurements. V. RELABLTY RESULTS AND ANALYSS The reliability analysis proceure escribe in Section -A was applie to the five controllers. Fault coverage over a wie spee range was stuie. The reliability analysis tool along with the time-omain simulations of any rive evaluate the rive reliability in less than three hours. The runtime for V/f an DLO are especially fast since they o not consier sensor faults. This runtime is fast when consiering three levels of faults an all possible fault permutations iscusse in Section -B. The overall runtime for all of the controllers i not excee 12 hours. Thus, the propose proceure an reliability tool are versatile for evaluating ifferent controller an have a short runtime. The two main outputs of the proceure escribe in Section -A are R(t) an the MTTF of the rive uner a R(t).2.5 1 1.5 2 2.5 3 time (million hours) x 1 6 1.8.6.4.2 V/f MTTF = 65 Years No Control MTTF = 1 Years.5 1 1.5 2 2.5 3 time (million hours) x1 6 Fig. 13. R(t) an MTTF of the rive uner ifferent controllers The MTTFs are also tabulate from highest to lowest in Table V for convenience. TABLE V PERFORMANCE REQUREMENTS Controller Drive MTTF (years) V/f 65 FLC 59 FOC 58 DTC 54 DLO 1 The comparison of rive controllers woul be incomplete if only the MTTF is use as the juging criterion. This is clear especially since the MTTFs of V/f, FLC, FOC, an DTC are very close. Two other comparison criteria are aresse: the control complexity, an the ynamic response. From Figures 2 5, one can infer that V/f is the simplest, an DTC is the simplest among close-loop controllers. The ynamic response of the rives uner a spee step was compare for these four controllers, i.e., excluing DLO, an the results are shown in Fig. 14. t is evient in Fig. 14 that V/f has the worst ynamic response, while FOC an DTC both have excellent performance.
Spee (RPM) 2 15 1 5 FLC DTC FOC V/f -5.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (s) Fig. 14. Dynamic rive response for a loa step V. SAFE-MODE OPERATON Close-loop controllers have better ynamic performance when compare to open-loop controllers, an open-loop V/f has high reliability compare to its close-loop counterparts. Thus, Combining both close-loop an openloop controls in a switche control system is expecte to prouce even higher reliability with excellent ynamic performance. The propose configuration is to have the sensor-inepenent V/f run as a safe moe in parallel with the close-loop controller. The safe moe is utilize once a sensor fault is etecte. This system is shown in Fig. 15 where the close-loop or regular controller is FOC an the open-loop safe-moe is V/f. The choice of FOC comes from the results in Section V where it was shown to be more reliable than DTC, less complex than FLC, an goo ynamic performance. Fig. 15. Propose safe-moe operation The system shown in Fig. 15 is expecte to have higher MTTF than both FOC an V/f V/f will mitigate sensor faults while the feeback control of FOC will offer better reliability uring other faults. n Fig. 15, the sensor fault etection circuitry is the ecision maker in the switche control system. n this stuy, the fault etection circuitry is assume to be ieal, i.e., it can etect a sensor fault instantaneously upon occurrence. One limit of a real fault etection circuit is the processing time or response elay time. This time, t f, is expecte to be within a few linefreuency perios. t is only uring t f, that the system is affecte by the sensor fault there is no problem before the sensor fault occurs, an once V/f is engage after t f, the sensor fault no longer affects the system. The rive reliability was evaluate for ifferent values of t f an the reliability functions are plotte in Fig. 16. t is clear that as t f increases, the MTTF ecreases because the rive will be operating for a longer time uner the sensor fault. As expecte, the MTTF of the propose system is higher than that of V/f or FOC, an the rive reliability increases to over 71 years compare to 58 an 65 years of FOC an V/f, respectively. Fig. 16. Effect of elay switching time on the propose safe-moe scheme t is important to mention that aing the safe-moe controller oes not significantly increase the system cost, especially when igital control is utilize. This is true as the two controllers can be programme into the same rive controller chip. The only incurre cost is that of the fault etection circuitry which is expecte to be insignificant whether being analog or igital. Thus, this safe-moe configuration offers significant increase in the rive reliability while maintaining FOC ynamic performance except uner sensor faults. V. CONCLUSON This paper presente a versatile circuit-base reliability moeling proceure an reliability evaluation tool. The propose proceure is straightforwar an can be extene or reuce to stuy more or less faults in the system. The circuit-base moeling provies the flexibility of changing the rive controller an re-evaluating the rive reliability without significant changes to the simulation moel. The simulation moel utilize was verifie experimentally, an results show that open-loop V/f has the highest reliability at the cost of poor ynamic performance. Close-loop controllers were shown to have acceptable reliabilities which can be improve by reucing the sensor fault impact. Thus, a safe-moe scheme was propose an results show that it is significantly more reliable. The effect of the sensor fault etection elay was also stuie where as the the elay increases, the rive MTTF ecreases. Further research on the sensor fault etection circuit or subsystem is part of the intene future work.
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