Switching Transients of Low Cost Two Speed Drive for Single-Phase Induction Machine L. Woods, A. Hoaifar, F. Fatehi M. Choat, T. Lipo CA&T State University University of Wisconsin-Madison Greensboro, C Madison WI Abstract- Heating, ventilating, air conditioning & refrigeration (HVAC&R) systes represent one of the largest potential applications for Adjustable Speed Drives (ASD s). The focus of this work is to sudy the switching perforance of a new alternative circuit topology. The drive is specifically aied at applications that do not require continuous speed control and enables the achine to efficiently operate at two different speeds. The drive consists of front-end diode bridge followed by an inverter with four MOSFET or IGBT switches. A coputer odel is developed for the proposed adjustable speed induction otor. The siulation results of the currents, voltages, speed and torque are illustrated to show the dynaic perforance and transient response of this adjustable speed induction otor during switching insants. I. ITRODUCTIO The purpose of this study is the switching behavior of a new low-cost drive setup utilizing a single-phase induction achine with speed control capability suitable for relatively broad range of HVAC applications [3]. The drive operates basically at two different fixed speeds full or half speed. The drive consists of a front-end rectifier followed by a one-phase inverter with four MOSFET or IGBT switches. The drive is designed to operate either at full speed with a supply frequency of 60 Hz or at half speed with a supply frequency of 30 Hz. In the forer case, the ain winding of the otor is supplied with the sinusoidal voltage directly fro the ains. In this case, the single phase PWM inverter generates a voltage wavefor with suitable agnitude and phase shift in relation to the ains for the auxiliary winding [3]. During reduced speed operation both windings are fed fro the 30Hz voltage source supplied by the inverter. The phase shift between the currents in the ain and auxiliary windings is then achieved by the connection of an AC capacitor in series with the auxiliary winding. The ain advantage of the proposed setup is that the power rating of the inverter can be lower in coparison to a classic adjustable-speed drive inverter for a single-phase induction achine. Matlab/Siulink software used to siulate the syste odel. In order to study switching behavior a suitable odel of unsyetrical single-phase induction otor (USPIM) driven by a single phase inverter has been developed. II. IDUCTIO MACHIE EQUATIOS A 2-Phase induction otor with identical rotor windings and nonsyetrical stator windings is coonly considered as unsyetrical 2-phase induction achine. The theory of operation of unsyetrical 2-phase induction achine is applicable to a wide variety of single-phase induction achines [4]. In the analysis of this type of achine, it is generally assued that: 1) Each stator winding is distributed to produce a sinusoidal f wave in space, 2) The rotor coils or bars are arranged so that, for any fixed tie, the rotor f waves can be considered as space sinusoids having the sae nuber of poles as the corresponding stator f wave, 3) The air gap is unifor, 4) The agnetic circuit is linear. The equations which describe the transient and steadystate perforance of an unsyetrical 2-phase achine can be established by considering the eleentary 2-pole achine shown in Figure 1. Figure 1. Unsyetrical 2-Phase Induction Motor In the case of a single-phase achine, the a-phase represents the ain winding and the b-phase the auxiliary winding. The echanical rotor position and speed are denoted r, and r, respectively. The positive direction for the shift angle r turns in the opposite direction of rotation of the rotor. In Figure 1 the sign ( ) represents an iaginary winding coing out of the topology, and (x) represents an iaginary winding going into the topology. The and ar -axes are displaced by r degrees. Since it is assued that each winding is distributed in such a way that it will produce a sinusoidal f wave, it is convenient to portray each winding as an equivalent single coil, Figure 2. The equivalent stator winding and rotor winding in Figure 2 are the auxiliary (a) and ain windings () respectively of a single-phase induction otor.
can then be expressed as the new reference frae voltage equations: 1qsqsqs vpri = (5) 1dsdsads vpri = Figure 2. Equivalent Stator and Rotor Windings The stator windings are unsyetrical; the windings have an unequal resistance and an unequal nuber of turns. The resistance and the effective nuber of turns of the () winding are denoted as r 1 and, respectively. In the case of the (a) winding, r 1 a and a denote that the windings are in quadrature and are identical; that is, the windings have an identical nuber of effective turns 2, and identical resistance r 22 [1]. Stator Voltages v = p ir1 (1) va = p a iar1 a (2) Rotor Voltages var = p ar iar r 22 (3) 22 brbrbr vpir = (4) where is the total flux linkages of a particular winding and d p is the operator. dt In the case of a syetrical achine, tie-varying coefficients appear in the voltage equations. Because of the variation of the utual inductances with respect to displaceent r, these coefficients can be eliinated by transforing the voltages and currents of both the stator and the rotor to a coon reference frae. In the case of an unsyetrical 2-phase induction achine, it is convenient to select a reference frae fixed in the stator. The derivation of the transfored equations to this new reference frae, the d- q transforation, can be found in [1]. Developent of Induction Machine Equivalent Circuits In the developent of the induction achine equivalent circuits, it is custoary to refer all quantities to the stator windings. If the achine is syetrical, the quantities can be referred to either stator winding by the sae turns ratio. In the case of the unsyetrical 2-phase achine, however, the stator windings do not have the sae nuber of effective turns. Although in soe instances it ay be desirable to refer all quantities to one of the stator windings, in this developent, the q quantities will be considered as the winding and the d quantities will be considered as the a winding. All the q quantities are then referred to the winding ( effective turns) and all d quantities referred to the a winding ( effective turns). The voltage-equations a v = dr 0 = p dr p r r2 i a v = (6) where qs ds dr a 0 = p dr p r r2 aidr ( iqs i ) ( ids i ) ( i ) qs i ( ids idr ) = (7) L 1iqs LM = L 1aids LMa dr (8) = L i L (9) 2 M L 2aidr LMa = (10) in which L M = M 2 (11) Ma 2 a M a2 2 L = (12) where L 1 is the leakage inductance of the winding and L 1 a is the leakage inductance of the a winding. The quantities M 2 and M a2 are the ain winding/rotor winding and auxiliary winding/rotor winding utual inductances respectively. The equivalent circuit of the unsyetrical induction otor in the new transfored frae is given in Figure 3. Figure 3. d-q Equivalent Circuit of Unsyetrical 2-Phase Induction Machine Coputer Representation of an Unsyetrical 2-Phase Induction Machine The coputer equations that can be used to siulate ()1qsqsMq il= the unsyetrical achine are given by: ()1dsdsMd ail= (13) (14) 2
()21 Mq il= ()21dr Md ail= (15) (16) The following equation is used to obtain the capacitor 121dsdsdsds VVRiidt C= run voltage, (32) () MqMqs Lii = where: Lii = ()dr MdMads (17) (18). where e is the base electrical angular velocity corresponding to rated frequency.,,, dr qsdsand If (5) through (10) are solved for the flux then, are obtained rvdt L= as: ()1qsqsMqqs ()1adsdsMdds arvdt L= () 2ara dr Mq ea r dt L = () 2ara drdr Md ea r dt L = 12 qs Mqq LL = where: LL = 12 qs Mqq in which: 1/1/1/ q M LLL = ()()()12 1/1/1/ Maaa LLL = ()()()12 da (19) (20) (21) (22) (24) (25) (26) (27) In these equations, r is the rotor speed in electrical radians per second Although the currents can also be eliinated fro the torque expression, it is generally desirable to observe the four currents. Therefore, it is convenient to obtain the instantaneous torque by using 2a dr dr a P Ti i = (28) III. ADJUSTABLE SPEED DRIVE Figure 4 shows the proposed reduced cost adjustable speed drive with the unsyetrical single-phase induction otor. The figure consists of a full bridge inverter fed PWM with four MOSFET or IGBT switches. A large capacitor is used to filter out voltage ripple. The PWM has a control signal v control (constant or slowly varying in tie) that is copared with triangular wavefor, to generate the switching signals [2]. This adjustable speed otor is designed to operate either at full speed with a supply frequency of 60 Hz or at half speed with a supply frequency of 30 Hz. In the forer case, the ain winding of the otor is supplied with the sinusoidal voltage directly fro the AC source. In this case, the single-phase PWM inverter generates a voltage wavefor with suitable agnitude and phase shift in relation to the ains for the auxiliary winding. During reduced speed operation both windings are fed fro the inverter. The phase shift between the currents in the ain and auxiliary windings is then achieved by the connection of an AC capacitor in series with the auxiliary winding. The ain advantage of the proposed setup is that the power rating of the inverter can be lower in coparison to a classic adjustable-speed drive inverter for a singlephase induction achine. The inverter supplies only the auxiliary winding during full-speed operation and both windings in half-speed operation. This can result in saller size of the drive and, therefore, in lower anufacturing costs of the drive as well. Another iportant feature of this drive is the fact that it could continue to operate in the event of a failure of the seiconductor portion of the inverter. The otor would be, in such a case, supplied directly fro the ains with the AC capacitor connected in series with the auxiliary where P is the nuber of poles. 3
winding. i where C is the link filter capacitance and current created by the PWM. is the inverter IV. SIMULATIO RESULTS The following figures are siulation results for the proposed adjustable speed drive as the input source changes fro an AC voltage input to a PWM voltage input. The siulation paraeters based on the _ hp otor are described by the following easured paraeters [3]. Figure 4. Induction Motor Drive Topology The controller shown in Figure 5 controls the level of the full-bridge output voltage. The function of the controller is to iniize the drop in speed of the USPIM when switching fro a AC source input to a PWM schee. The equations for this controller are derived as follows: sin(2) ac VVft =???? The sinusoidal input voltage is defined as: (29) where: 2230325.3 VV =?=. The source inductance is defined as L where: 1 L = L s where L s is the stator inductance: 5 Hence,s the rectifier dc current i 1 will be: i = 1 1 ( Vac Vdc )dt L, when V ac > V dc or i 1 > 0. (30) Table 1 _ hp Machine Paraeters Main Winding Auxiliary AC Capacitor (-winding) winding (awinding) r 1 = 8.69 Ω r 1a = 7.14 Ω R 1 = 0.67 Ω L M =366 µh L M = 137.982 C 1 = 4.833µf L 1 =32.8 h L 1a = 31.0174 Link Capacitor a / = 1.36 r 2a = 5.74 Ω C=500µf Three transient condition have been investigated in this study: 1) the changeover fro the 60 Hz supply to 30 Hz after accelerating fro zero speed on the 60 Hz supply, 2) the changeover which occurs when the drive switches fro the 30 Hz PWM supply to 60 Hz in order to accelerated to full speed., 3) the transient which occurs when a coand is given to reduce the speed fro full speed (60 Hz source) to half speed. The transient conditions which occur when the otor is suddenly switched fro the 60 Hz supply to a 30 Hz PWM frequency is illustrated in Figs. 6 to 9. It can be noted that the transients under this condition are inial indicating that this condition is not a serious proble V ac V dc - V ac Coparator abs Value V ac - OR 1 i 1 s? L R s Output i 1 Input Sine Wave Switch V dc Coparator 0 0.000 1 - Figure 5. Controller Siulating Rectified Voltage V dc When the rectifier bridge is operational the voltage across the ()1dci Viidt C= capacitor V dc, is calculated as follows: (31) Figure 6. Currents i and i a for _ hp Machine for Switchover fro 60 Hz Supply to 30 Hz PWM Inverter Supply. 4
switchover is fro a 30 Hz PWM inverter to a 60 Hz sine wave. In this a ore serious transient is noted and the current peak suddenly triples. However, since this current flows in the ac supply rather than the PWM inverter it is again not of concern. Figure 7. Main and Auxiliary Winding Voltages for _ hp Machine with Switchover fro Line to Inverter Supply Figure 10. Currents i and i a for _ hp Machine for Switchover fro 30 Hz PWM Supply to 60 Hz AC Supply Figure 8. Total Motor Current and DC Link Voltage Transient with Switchover fro Line to Inverter Supply at Half Speed Figure 11. Main and Auxiliary Winding Voltages for _ hp Machine with Switchover fro inverter to AC Supply at Half Speed Figure 9. Torque and Speed Transients for Changeover fro Line to Inverter Supply at Half Speed Figures 10 to 14 illustrate the transients which occur when a request is ade for full speed operation when the drive is operating with a 30 Hz inverter supply. In this case the 5
Figure 12. Total Motor Current and DC Link Voltage Transient with Switchover fro Inverter to Utility Supply at Half Speed Figure 13. Torque and Speed Transients for Changeover fro PWM Inverter to Line Supply at Half Speed Figure 16. Total Motor Current and DC Link Voltage Transient with Switchover fro Line to 30 Hz Inverter Supply at Full Speed In Figures 14 to 17 the case in which the drive operates at 60 Hz and a coand to reduce the speed to 30 Hz is issued. In this case the initial speed is full rather than half speed. Figure 17. Torque and Speed Transients for Changeover fro Line to Inverter Supply at Full Speed Figure 14. Currents i and i a for _ hp Machine for Switchover fro 60 Hz Supply to 30 Hz PWM Inverter Supply at Full Speed It can be noted that the current transient is considerably ore severe for this case than for the switchover at 30 Hz (Figs. 7-10). A peak inverter current of roughly 150% of the peak steady state load current is encountered. It is interesting to note that this peak transient did not vary appreciably with closing under various phase angle relationships of the AC source and PWM voltages. Hence, it was established that only a odest current argin (200%) is needed to ensure safe operation of the drive under all scheduled switching events. Also it can be noted that since the drive begins to regenerate under this considion, the dc link voltage rises above the value set by the line side diode bridge. However, it is apparent that this transient is very odest and should not ipact the voltage rating of the inverter switches. Figure 15. Main and Auxiliary Winding Voltages for _ hp Machine with Switchover fro Line to Inverter Supply at Full Speed 6 V. COCLUSIOS The purpose of this study is to evaluate the transient perforance of a new low cost dive setup unitizing a single-phase induction otor with speed control
capability suitable for relatively broad range of HVAC applications in which discrete speeds are utilized. In particular, the proposed ethod is designed to operate either at full speed with a supply frequency of 60Hz or at half speed with a supply frequency of 30Hz. A coputer odel has been developed to study the proposed adjustable speed induction otor drive. Siulation traces of the currents, voltages, speed, and torque illustrate that the switching transients of this new discrete speed drive are not severe and will not significantly ipact the voltage and current rating of the inverter switches. REFERECES 1. Krause P.C., Siulation of Unsyetrical 2-Phase Induction Machines, IEEE Transactions on Power Apparatus and Systes, 1965, pp. 1025-1037. 2. ovotny, D.W., Lipo, T.A., Vector Control and Dynaics of AC Drives, ew York: Oxford Press 1996. 3. F.C. Lee, Center For Power Electronic Systes, Annual Report to the ational Science Foundation, 1999. 7