POWER ELECTRONIC CONTROL OF INDUCTION MOTORS ppt

ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 74 6. POWER ELECTRONIC CONTROL OF INDUCTION MOTORS 6.1 Introduction Three-phase induction motors are the most frequently utilised electric machines in industry. They are characterised with low cost, high reliability, high efficiency, simple construction and, in the case of squirrel-cage induction motors, with virtually maintenance-free operation. If operated with stator three-phase voltage supply of fixed frequency and fixed rms value, induction motors will run at a speed that very slightly depends on loading. In contrast to DC machines, where choice of methods of speed control and associated power electronic converters that are nowadays in use is rather limited, there exists a variety of both speed control techniques and appropriate power electronic converters that are used in conjunction with three-phase induction motor drives. A three-phase induction machine requires three-phase AC supply at stator side. In a squirrel-cage type of induction machines this is simultaneously the only approachable winding. However, in slip-ring induction machines the three-phase rotor winding may be approached as well. Thus the speed of an induction machine may be controlled by controlling the stator AC supply for both types of induction machines; additionally, speed may be controlled in slip-ring machines from the rotor winding side as well. Squirrel-cage induction machines are by far the most frequently used machines. It is for this reason that the following discussion will be predominantly devoted to speed control methods associated with alteration of the stator supply, that are equally applicable for both types of induction machines. Only one method, specifically aimed at slip ring machines, will be looked at. If an induction machine is supplied with a voltage of frequency f then the so-called synchronous speed is determined with the frequency and the number of pole pairs P and is expressed in rpm as n s =60f/P (6.1) However, an induction motor will run at a speed n that differs from the synchronous. The difference between actual speed of rotation and the synchronous speed is characterised by the quantity called slip. Slip s is expressed in per unit as ratio of the speed difference normalised with respect to the synchronous speed, i.e., s=(n s − n) / n s (6.2) Thus zero speed of rotation indicates unity slip and synchronous speed of rotation corresponds to zero slip. Torque-speed characteristic of an induction machine can be derived for steady- state operation with sinusoidal supply from the per-phase equivalent circuit, given in Fig. 6.1. I s R s jX σs jX σr I r V n jX m I m R r /s Fig. 6.1: Steady-state per-phase equivalent circuit of an induction machine for purely sinuso- idal supply voltage. ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 75 All the parameters of the rotor winding in Fig. 6.1 are referred to the stator winding, by means of the transformation ratio. Symbols in bold denote phasors. Variable resistor in the rotor circuit represents both rotor copper loss and power converted into mechanical. Recall that stator winding of the machine can be connected in either star or delta; the equivalent circuit is valid for phase rather than line values, regardless of the winding connection. Thus V n stands for rated phase to neutral voltage of the stator. All the reactances are given at fixed, rated frequency. Torque-slip characteristic of a three-phase induction machine follows from power flow considerations in Fig. 6.1, in the form () () () Ts P f V Rs RRs X X P f V Rs RRs X en r sr s r n r sr ()= +++ = ++ 3 2 3 2 2 22 2 2 2 ππ σσ (6.3) while stator current phasor can be expressed directly from Fig. 6.1 as () IVZ ZRjX jX R s jX Rs jX X sne es s mr r rrm = =+ + + ++ σ σ σ () (6.4) Torque is a rather complicated function of motor parameters, supply voltage and slip and its typical appearance is given in Fig. 6.2 for rated supply conditions. The operating region is restricted to slips up to typically 10%, indicating that speed of rotation changes with load but remains within rather narrow boundaries from zero load up to rated load. Maximum (pull-out) torque, rated torque and starting torque, as well as corresponding slips, are indicated in Fig. 6.2 and can be calculated from the following expressions: T e maximum (pull-out) torque T en T est operating region slip 1s m s n 0s 0n s speed Fig. 6.2: Torque-speed characteristic of a three-phase induction machine for rated supply conditions. () () () s R RX TTss P f V Rs RRs X P f V RRX TTs P f V R RR X TTss P f V Rs RRs X m r s em e m n rm srm n ss est e n r sr en e n n rn srn = + === ++ = ++ === ++ === ++ 22 2 2 2 2 22 2 2 2 2 2 2 3 2 3 4 1 1 3 2 3 2 () () () ππ π π (6.5) ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 76 Equations (6.1)-(6.5) enable discussion of all the relevant methods of speed control, applicable to an induction machine. It follows from (6.1) that synchronous speed can be altered by changing the number of pole pairs. Assuming that load torque is constant, if pole pair number is doubled during operation of the machine, synchronous speed will be halved, leading to operation at essentially one half of the rated speed. This method of speed control is used in drives that typically require operation at two distinctly different operating speed (say, a washing machine; spinning is done at high speed, while normal washing cycle takes place at low speed). Speed control by pole pair changing requires special construction of the stator winding. It is usually realised for two different speeds of operation and pole pair changing is performed by mechanical reconnection of the stator winding from one pole pair number to another. Illustration of torque-speed characteristics is shown in Fig. 6.3 for change-over from one pole pair to two pole pairs. Power electronics converters are not involved in this speed control method, and its applicability is restricted to the cases when two speeds, rather than continuous speed variation, are needed. Therefore speed control by pole pair changing will not be considered further on. T e load torque AB 1500 3000 speed (rpm) Fig. 6.3: Speed control by change of pole pair number: drive operates either in point A or in B. The two methods of speed control, that are universally applicable to all the three-phase induction machines and that will be elaborated, are the speed control by stator voltage variation and speed control by simultaneous stator voltage and frequency variation. The former, although very simple, has restricted applicability for the reasons that will be explained; the latter is the most widely used method of speed control of induction machines. Finally, a method valid for slip-ring machines only, insertion of a resistance in the rotor circuit, will be considered as well. 6.2 Speed Control by Stator Voltage Variation Equation (6.3) shows that electromagnetic torque developed by an induction machine is proportional to the square of the applied rms stator phase voltage. Thus, given the load torque to be, say, a constant, reduction of voltage will lead to operation with increased slip, i.e., with decreased speed. As voltage is not allowed to exceed rated value, this method of speed control can be utilised only for reducing the speed below rated. Torque-speed (slip) characteristics for this speed control technique are shown in Fig. 6.4. Note that, according to (6.5), pull-out slip is not function of the applied voltage. Hence the motor develops maximum torque at constant slip (speed), determined with (6.5), regardless of the applied voltage. However, both maximum (pull-out) and starting torque are functions of voltage squared. Hence, when voltage is reduced, maximum torque and starting torque reduce as well, proportionally to the voltage reduction squared. This is one of the major drawbacks of this speed control method: reduction in starting torque means that the motor will be able to start only loads that are of small torque ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 77 at low speeds; reduction in maximum torque means that overloading capability of the motor reduces with reduction in voltage. T e rated voltage reducing voltage operating region slip 1s m 0s Fig. 6.4: Torque-slip characteristics of an induction machine with speed control by stator voltage variation. Additional drawback of this method is that, when voltage is reduced and speed therefore reduces as well, additional copper loss in rotor winding takes place. Regardless of these two serious shortcomings, this method of speed control is widely used in two distinct cases. When the load torque is proportional to the speed squared (pumps, ventilators, compressors, etc.) then even a small reduction in speed means significant reduction in the output power, which is proportional to the cube of the speed. For a number of applications with load torque of this type it is sufficient to vary the speed in this narrow region. The second application is in drives that run for prolonged periods of time with very light loads. In such a situation it is advantageous to reduce the voltage for light load operation as this improves the efficiency of the drive. In other words, considerable saving in electricity consumption may be achieved in this way. Example: A three-phase squirrel-cage induction motor drives a load of rated torque, with rated slip of 3%. Stator and rotor resistance (referred to stator) are both equal to 0.015 Ω. Sum of stator and rotor leakage reactance is X =0.09Ω. Calculate the necessary reduction in stator supply voltage if the induction motor is to drive the same load with slip equal to 15%. Solution: Pull-out slip of the motor is, from given parameters, equal to s R RX m r s = + =+== 22 22 0 015 0 015 0 09 0164 164% . The motor is required to operate at slip of 15%. As load torque is constant, this indicates that in new operating point motor torque will be very close to maximum torque, so that overloading capability will be almost non-existent. The necessary reduction of the voltage, that will yield operation with 15% slip, can be calculated as follows: ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 78 () () () () () () TT T P f V Rs RRs X TT P f V Rs RRs X ss T T P f V Rs RRs X P f V Rs RRs X V Rs RRs X V Rs RRs X V V Len en n rn srn een r sr n e en r sr n rn srn r sr n rn srn n = = ++ == ++ == == ++ ++ = ++ ++ at all speeds; hence 3 2 3 2 003 015 1 3 2 3 2 2 2 2 11 2 1 1 2 2 1 1 1 2 1 1 2 2 2 2 2 1 2 1 1 2 2 2 2 2 1 π π π π () () () () = ++ ++ = ++ ++ = = 2 1 1 2 2 2 2 2 2 2 2 1 015 003 0 015 0 015 015 009 0015 0015 003 009 039 0 624 s s RRs X RRs X VV n sr srn n . . /. . /. . . . Necessary voltage reduction is 37.6%. Situation is illustrated in accompanying Figure. T e rated voltage T L =T en 62.4% of rated voltage 0.16 0.03 slip 0.15 Let us examine, using this example, increase in rotor losses that takes place with this speed control method. Taking power transferred from stator to rotor to be P sr , for these two operating conditions one has () () () PsP PsP P P s PP P PT T s T s s P PsP P P s PPP PsP xP P n n srn curn n srn srn n n ncurn n en en s en n n n sr sr n n srn cur sr n n =− = = − == ==−= − − = =− = − ==≡ == = 1 1 103 0031 1 1 1 0876 1 1 0876 085 103 015 103 01545 11 1 1 111 1 1 1 111 . ./ . ωωω This consideration shows that power transferred from stator to rotor is the same for the two cases. Hence reduction in output power reflects itself directly as an increase in rotor copper loss, which goes up from 3% of the rated power to more than 15% of the rated power. As this loss takes place in the motor, it will essentially cause overheating. Needless to say, efficiency is sharply reduced. Starting problem with reduced voltage and this increase in loss are the two major reasons why this speed control method is not used with constant load torques. Situation is much improved in both respects when load torque is proportional to the square of the speed. Speed control by stator voltage variation is therefore applied in conjunction with this type of load in practice. Speed control by stator voltage variation is realised by using AC-AC voltage controller in each stator phase of the machine. Voltage controller is of the same structure as in Chapter 4 on reactive power compensation. Figure 6.5 illustrates the connection of the power electronic ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 79 converters for the case when only forward motoring is required. If the machine is required to run in both directions, two additional sets of back-to-back (anti-parallel) thyristors are required, in order to enable phase reversal of the stator supply. This part of the drive is shown in Fig. 6.5 as well, in dotted lines. It should be noted that although the principle of operation of an AC-AC controller is very simple, analysis of the system of Fig. 6.5 is extremely tedious even for steady-state operation. This is so because of the inductive nature of the machine, which makes the instant of cessation of the current flow through each of the thyristors essentially unknown. As the voltage exists as long as there is current flow, then it is actually very difficult to evaluate the actual voltage applied across the machine under given operating conditions. Note that the voltage value calculated in the previous example for reduced speed operation is the required rms value of the fundamental harmonic of the output phase to neutral voltage of the AC-AC voltage controller. Induction machine Fig. 6.5: Speed control of an induction machine by stator voltage variation. 6.3 Speed Control of Slip Ring Machines by Addition of Resistance in the Rotor As rotor winding of a slip ring machine can be approached from the outside world, it is possible to add a resistance in each of the three rotor phases. Let R add denote per-phase value of the added resistance in the rotor circuit, referred to the stator winding. From (6.3) and (6.5) it follows that () () () () () () s RR RX fR R TTss P f V RR s RRR s X T P f V RRX fR R TTs P f V RR RRR X m radd s r add em e m n raddm s r add m em n ss r add est e n radd s r add = + + =+ === + ++ + = ++ ≠+ === + ++ + 22 2 2 2 2 22 2 2 2 3 2 3 4 1 1 3 2 () () π π π (6.6) ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 80 Equation (6.6) shows that pull-out slip is proportional to the added resistance. Hence the speed at which maximum torque occurs varies with the amount of added resistance. On the other hand, maximum torque is not affected by addition of resistance, indicating that overloading capability of the machine is not affected. Compared with stator voltage variation method, addition of resistance in rotor is to be preferred, for the following reasons: a) any speed of operation between zero and rated can be obtained (with stator voltage variation speed control region is confined to speeds higher than pull-out speed); maximum torque is not affected (with stator voltage variation it reduces proportionally to the stator voltage reduction squared); additional copper loss is now developed in added resistance, which is external to the machine and therefore the problem of overheating does not take place. Note however, that problem of low efficiency remains to be present: as speed is reduced, larger and larger portion of the total input power is dissipated in the additional resistors. Principle of this speed control method and resulting torque speed curves are shown in Fig. 6.6. Stator T e R add =0 IM Load torque Rotor Increasing R add R add 1s 1 s 2 s n 0 slip Fig. 6.6: Speed control by addition of resistance in rotor winding - principle and torque - slip curves. Three possible operating points are shown in Fig. 6.6 for assumed constant load torque. As added resistance increases slip increases as well (i.e., speed decreases). Of special interest is the curve with operating slip given as s 1 . Note that for this curve the amount of added resistance is assumed to be exactly such as to yield development of maximum torque at zero speed (i.e., slip of one). By doing so, it is possible to start the motor with starting torque equal to maximum torque: this indeed is one of frequent applications of addition of resistance in the rotor circuit, even when speed control is not required. If the motor parameters are known the value of added resistance that gives starting with maximum torque can easily be determined from (6.6), where it is only necessary to equate slip s m to unity. Example: A slip ring induction machine is loaded with constant load torque equal to 5 Nm (rated value). Machine is star connected, its stator is supplied with rated 380 V, 50 Hz voltage, and the machine has two pairs of poles. Stator and rotor resistance are 10 Ω and 6.3 Ω, respectively, while leakage reactances of stator and rotor are 12 Ω each. Magnetising reactance can be neglected. Rotor parameters are referred to stator. a) Determine slip for rated operating conditions; b) Calculate added resistance that is needed to reduce the speed to 1000 rpm; ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 81 c) Calculate added resistance that will enable starting of the motor with starting torque equal to maximum torque. Solution: a) Calculation of rated slip: () () () () () TT T P f V Rs RRs X X V ss s nfP n sn s R RXX T P f V R RR X Len en n rn srn s r n nn n snnn m r ssr est n r sr == = +++ = == −+= == == =− = = ++ == = ++ 5 3 2 5 380 3 220 676 1039 5 39 7 0 0039 39% 60 1500 1 14415 0 242 24 2% 3 2 1 1 2 22 2 2 2 2 2 Nm = constant Nm Note that due to star connection V Substituting all the known values in rated torque expression, one gets rpm rpm Further, π π σσ σσ /. () () () σσ σσ π sr em n rm srm s r X T P f V Rs RRs X X + = = +++ = 2 2 2 2 692 3 2 12 84 . . Nm Nm b) For operation at 1000 rpm with the same load torque the following resistance is needed: () s nn n TT P f V RR s R RR s X RR R RR R R s s een n radd s radd radd add 1 1 1 2 1 1 2 2 2 1500 1000 1500 0 3333 5 3 2 0 016 0 9 12168 0 54 7 54 7 6 3 48 4 = − =− = === + + + + =+ −+ = = =−= ()/. . . π Let . Substituting all the known values in torque equation Ω Ω c) If machine is to start with starting torque equal to maximum torque, then TT s RR RX RRXR em est m radd s add s r = = = + + =+−= 1 1197 22 22 . Ω All the three torque-slip curves are shown in Figure. Note that for operation with 1000 rpm (part b) slip at which maximum torque occurs is 2.1. For 19.7 Ω machine would operate at 0.16 slip. T e 48.4 Ω 19.7 Ω R add =0 5Nm 2.1 1 0.33 0.16 0.039 s ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 82 Example: A three-phase 220 kW, 60 Hz slip ring induction machine has 16 poles and rated slip of 2.5%. It drives a pump and operates at rated speed with rated torque. Pump’s torque is proportional to the speed squared. Rotor resistance is 0.0175 Ω. Determine the value of the added resistance that needs to be inserted in rotor phases if the required speed of rotation is 300 rpm. Solution: Only rotor resistance is given out of motor’s parameters. It is therefore not possible to use full expression for torque in calculations. However, torque of the motor in the operating region (i.e., for slips between rated and zero) can be approximated with a straight line. Thus T e =ksand calculations in this example will be based on this expression. () () nfPx nsn TP x TK T K K TK x snnn TksTks s nns en n n LLnn L ss een == = =− =− = == = = == = == = =− = − = == == 60 60 60 8 450 1 1 0 025 450 439 220000 30 439 4785 4785 2 26 300 30 22305 450 300 450 0 333 22305 4785 22 11 22 11 22 // (.) /( ) () / .( /) . /( )/ . . rpm rpm Nm Nm = 2.26 Nms rad In new steady - state at 300 rpm Nm At natural characteristic operation with torque of 2230.5 Nm would result in slip 2 ωπ ωωωω ωπ nn e en en r s r en radd s radd r r add add r r ss T T x n T P f V Rs R R s X T P f V RR s R RR s X R s RR s R s s RR rpm However, required speed with this torque is 300 rpm. Hence natural characteristic at curve with added resistance Thus == = = == + + == + + + + = + =−= 2 2 2 2 2 2 2 2 1 2 1 1 2 2 21 1 2 0 025 22305 4785 0 01165 444 75 22305 3 2 22305 3 2 0 0175 0333 /. . . . () .(./ π π 0 01165 1 048.).−= Ω Torque-slip curves are illustrated in Figure. T e T L 0.48 Ω 4785 Nm 2230.5 Nm 0 300 444.75 n(rpm) 439 ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 83 If slip ring induction motor speed is to be continuously varied, it is necessary to provide a method of continuous additional resistance variation. Such a continuous resistance variation is possible if power electronic converters are used. Figure 6.7 illustrates electronic additional resistance variation. A three-phase bridge diode rectifier is connected to the rotor winding, via slip rings. The output of the rectifier is connected to a chopper, whose circuit contains a resistor R. When chopper switch S is closed, resistor R is short circuited; when switch is open, resistor R is connected to the output of the rectifier. Inductor between rectifier and chopper is large and its purpose is to provide almost level DC current at the rectifier output, regardless of the state of the chopper switch S. Three-phase diode bridge rectifier L DC stator rotor IM S R Fig. 6.7: Speed control of a slip ring induction machine by addition of an electronically con- trolled variable resistance in the rotor circuit. What now has to be considered is the correlation between resistance R of Fig. 6.7 and per phase added resistance R add , used previously in all the calculations. If switch S is open all the time (duty cycle equal to zero), resistance seen by the rectifier will be R.Ifswitchisclosed all the time (duty cycle equal to one), resistance seen by the rectifier is zero. Hence resistance presented to the rectifier by the chopper equals () RR tT eon =− =1 δδ (6.7) The input rectifier current (i.e., phase rotor current) is, due to large inductance at the DC side, of quasi-square waveform, discussed in Chapter 4, with 120 degrees of non-zero value in each half-period. For level DC current, of value I DC , total rms of the rotor current (i.e., rectifier input current) is IIdI rDCDC == 1 2 2 2 3 2 0 23 π θ π / (6.8) Required equivalent per-phase value of the added resistance, R add , is determined from the power balance at the input and at the output of the rectifier. Assuming that there are not any power losses in the rectifier, chopper and the DC side inductor, real power at the input of the rectifier must equal real power delivered to the resistance of (6.7). Hence, using (6.7) and (6.8), () () () () () PRI RI P per phase RI II P per phase R I RI P per phase R I RR DC e DC DC rDC DC r rrr raddr add ==− −=− = −=− =− −= =− 22 2 2 2 2 1 1 3 1 3 2 1 3 1 3 2 051 051 δ δ δδ δ () () . () . (6.9) [...]... structures of autonomous inverters The first one, voltage source inverter (VSI), has already been introduced in Chapter 4 in its single-phase form and is the most frequently applied power supply source for V/f control of induction motors The second one, current source inverter (CSI), is beyond the scope of interest here Principle of operation of a threephase VSI is explained next Three-phase version of a... fed induction machine Phase voltages, given in Fig 6.12, can be looked at as being composed of two waveforms: the first one is a square-wave of amplitude VDC /3, while the second one is a quasisquare wave of amplitude VDC /3 and 60 degrees duration of non-zero value Hence harmonic content of phase to neutral voltages can be determined as sum of Fourier series of a squarewave and Fourier series of a... carrier wave of constant amplitude and frequency The instants for turn-on and turnoff of semiconductors in Fig 3.9 are then determined with intersections of the reference signal and the carrier wave Switches are turned on and off in pairs: S1 and S2 are always together either on or off and similarly, S3 and S4 are always together either on or off The advantage of this approach is two-fold First of all,... composed of a series of rectangular pulses, fundamental component of the output voltage is of the same frequency and magnitude as the reference sinusoidal signal is Analysis of the PWM inverter output voltages is always conducted using the notion of the modulation index Modulation index m is defined as the ratio of the sinusoidal signal E Levi, Liverpool John Moores University, 2002 96 ENGNG3070 Power Electronics... that operation of a VSI in PWM mode yields two substantial benefits, when compared to operation in 180 degrees conduction mode A diode rectifier can be used instead of a controllable rectifier, since the inverter is now capable of controlling both the frequency and the rms value of the fundamental component of the output voltage Additionally, higher harmonics of the voltage are now of substantially... VDC ( ) Locus of the maximum achievable voltage in VSI with space vector PWM is shown in Fig 6.23 vsmax* 4 Fig 6.23: Non-zero voltage vectors of the inverter and the achievable maximum output voltage locus 6.6 Suggested Further Reading [1] [2] [3] W.Leonhard; Control of electric drives, 2nd Edition, Berlin: Springer-Verlag, 1996 J.M.D.Murphy, F.G.Turnbull; Power electronic control of AC motors, Oxford:... true sine waveform One special type of PWM, that is nowadays extremely frequently applied, is the socalled voltage space vector modulation For reasons that are beyond the scope here, this PWM method is the prevailing one in closed-loop control of induction motors fed from PWM inverters Explanation of this method however requires at first the introduction of the notion of the space vector Let us at first... difference between synchronous speed and speed of rotation remains constant and equal to 20 rpm The operating speed is then 500 - 20 =480 rpm This compares well with the exact value of 481.3 rpm 6.5 Inverters and Inverter Control of Induction Machines 6.5.1 Six-step (Quasi Square-wave) Voltage Source Inverter Variable voltage, variable frequency operation of induction machines is realised utilising autonomous... provide control of the output voltage magnitude (output voltage magnitude is proportional to the input DC voltage) Each switch in the inverter circuit is again composed of two back-to-back connected semiconductor devices One of these two is a controllable switch (say, BJT), while the other one is a diode Diode is essential for correct operation of the VSI as output voltage and current are out of phase... the six-step mode of operation, two additional vectors (no 7 and 8) are added at the bottom of the Table These two vectors can be obtained only in PWM operation of the VSI and they describe the condition when the induction motor terminals are short circuited either through the positive rail of the dc supply (vector 7) or through the negative rail of the dc supply (vector 8) Calculation of the leg voltage . ENGNG3070 Power Electronics Devices, Circuits and Applications  E Levi, Liverpool John Moores University, 2002 74 6. POWER ELECTRONIC CONTROL OF INDUCTION MOTORS 6.1 Introduction Three-phase induction. choice of methods of speed control and associated power electronic converters that are nowadays in use is rather limited, there exists a variety of both speed control techniques and appropriate power. the required rms value of the fundamental harmonic of the output phase to neutral voltage of the AC-AC voltage controller. Induction machine Fig. 6.5: Speed control of an induction machine by stator