Synchronous Motor V-Curves

Transcription

1 Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel cage bars fr starting. In this experiment, synchrnus mtr starting is demnstrated. After starting, the mtr is lcked int synchrnism by applying a rtr field current. The field current is then varied t illustrate cntrl f the reactive pwer frm psitive t negative. When the reactive pwer is zer, the machine is perating with unity pwer factr and the armature current drawn frm the surce is a minimum. The armature current is pltted versus field current t btain the classical "V-curves". Synchrnus Mtr Starting Mst synchrnus mtrs can nt be line-started (suddenly applying rated vltage and frequency t the armature) when the rtr field is established. This is because the rtr starts with zer speed and if it has sufficient inertia will remain statinary while the statr ples rtate at synchrnus speed. This causes psitive and negative trque pulses, but the average trque is zer. Figure 1 illustrates this principle. Initially, the statr ples are in line with the rtr ples and n trque is prduced. At time ω t = 90, the statr ples are at quadrature t the rtr ples (assuming the rtr hasn't rtated in this shrt time) and a negative trque is prduced by the interactin f the statr and rtr fields (psitive trque being defined as shwn in Figure 1). At ω t =180 the statr ples are again aligned with the rtr ples prducing zer trque. At ω t = 270 the statr ples are aligned such that the trque is psitive. The trque versus time plt is shwn belw the machine crss-sectins in Figure 1. As can be seen, the trque scillates abut zer at the fundamental frequency and the average trque is zer. Fr this reasn, the machine will nt start and will nly emit a buzzing sund.

2 Synchrnus Mtr V-Curves 2 T facilitate starting, the synchrnus mtr has a set f shrt-circuited bars, knwn as damper windings (r smetimes called amrtisseur windings). Figure 2 illustrates the starting prcess where the rtr field current is remved s that the rtr ples will nly cme frm current induced in the damper windings. First, the damper winding is mdeled as ne shrt-circuited cil. Frm Figure 2, the flux linking this cil frm the statr can be seen t be a maximum at ω t = 90 then ging t zer at ω t =180 and becming a negative maximum at ω t = 270. This can be mdeled as λ = sin ω t (1) d Λ m where Λ m is the peak value f flux linkage. By Farady's law, the induced vltage in the damper cil is the derivative f the flux linkage r ( ) ( ω t) ed = Em cs (2) where E m is the peak induced vltage. If the damper cil inductance is neglected, the damper bar current can be apprximated by id = I m cs( ω t) (3) where I m is the peak vltage ver the damper winding resistance. Accrding t (3), at ω t = 0, the damper bar current is a psitive maximum prducing a set f rtr ples as shwn in Figure 2. It can be seen that these ples will result in a psitive trque. The current is a negative maximum at ω t =180 causing a set f ples in the ppsite directin. It can be seen frm Figure 2 that these ples als prduce a psitive trque. The trque versus time plt is shwn in the bttm part f Figure 2. As can be seen, the trque due t currents induced in the rtr damper bars has a psitive average value and scillates with a frequency f twice the fundamental. When this average trque is sustained n the rtr, it will accelerate the inertia and the machine will cme up t speed.

3 Synchrnus Mtr V-Curves 3 The abve analysis f starting with damper windings is nly apprximate. In the labratry, the damper winding will have inductance which will delay the rtr current wavefrm, but the interactin f the damper winding flux and statr flux will still result in a starting trque with pulsatins at twice the fundamental frequency and with a psitive average value (in the directin f the statr ples). After the machine starts, it will nt cmpletely reach synchrnus speed. This is because if the rtr is mving in synchrnism with the statr ples, the flux linking the rtr damper windings will be cnstant. Thus the induced vltage will be zer and the trque will g t zer. In practice, the rtr accelerates t near synchrnus speed since a small amunt f trque is required t vercme frictin lsses. At this pint, a DC current can be switched int the rtr field winding t establish rtr ples and the machine will lck int synchrnism with the rtr perating at a synchrnus speed f 2 ωs = 2π fe (4) ples where f e is the frequency f the statr currents. In RPM, the synchrnus speed may be calculated as 120 f n e s = (5) ples The mtr will nw remain at synchrnus speed unless it is verladed. Mtr V-curves After the mtr is started and is perating under nrmal cnditins, the machine perfrmance can be bserved. Fr this analysis, the traditinal per-phase mdel is shwn in Figure 3. One phase f the armature circuit is seen t cntain reactance and an induced vltage (back-emf) which is prprtinal t rtr field current. The rtr circuit is als depicted in Figure 3 as a field winding resistance. Typically the mtr is driven by a cnstant vltage surce and is supplying a mechanical lad. The mtr synchrnus mechanical speed is determined by the vltage surce frequency f e using (4)

4 Synchrnus Mtr V-Curves 4 The input pwer can be defined frm the per-phase mdel as where θ = Vˆ a a P = V I cs( θ ) (6) 3 a a Iˆ. It can be shwn frm the machine equatins and pwer relatinships that Therefre, fr cnstant pwer peratin X I cs( θ ) = E sin( δ ) (7) s a a cs( ) af I θ = C (8) 1 where C 1 and C 2 are cnstants. E δ = C (9) af sin( ) 2 Frm a KVL equatin, the phase vltage is Eˆ af = Vˆ j X Iˆ (10) a s a Using the infrmatin frm (6-10), the circuit phasrs can be pltted fr cnstant pwer as the field current is varied. This is shwn fr three values f field current in Figure 4. Nte that the synchrnus mtr can perate with a lagging pwer factr, unity pwer factr, r leading pwer factr. Anther imprtant aspect f this is that the reactive pwer ges frm psitive t negative as field current is increased. This means that the synchrnus mtr can absrb r supply reactive pwer. Since the magnitude f Ê af is prprtinal t field current excitatin, the lagging pwer factr cnditin is smetimes referred t as under-excited peratin and leading pwer factr cnditin is referred t as ver-excited peratin fr the synchrnus mtr. These terms refer t the magnitude f the field current. Nte that the current Î a and the vltage Ê af fllw the lines f cnstant pwer given by (8-9).

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6 Synchrnus Mtr V-Curves 6 If the armature current is pltted versus field current fr several pwer levels, the regulating plts are the mtr V-curves shwn in Figure 5. The pints marked a, b, and c n the upper curve crrespnd t the perating cnditins in Figure 4. Nte that fr P=0, the lagging pwer factr peratin is electrically equivalent t an inductr and the leading pwer factr peratin is electrically equivalent t a capacitr. Leading pwer factr peratin with P=0 is smetimes referred t as synchrnus cndenser r synchrnus capacitr peratin. Typically, the synchrnus machine V-curves are prvided by the manufacturer s that the user can determine the resulting peratin under a given set f cnditins.

7 Synchrnus Mtr V-Curves 7 Labratry Sftware Figure 6 shws a screen-sht f the sftware fr this experiment. The synchrnus machine armature vltage, armature current, real pwer, and reactive pwer are displayed as well as graphs f the armature vltage and armature current. The field quantities are als displayed and a cntrl is built-in fr adjustment f the field current. After ging thrugh the start-up prcedure, the field current will be adjusted and the data is saved at each step fr pltting the machine V-curves. The standard "Add", "Clear", "Print", and "Save" buttns are included. Tw V-curves will be btained in this experiment and can be marked by selecting "n-lad" (shwn in Figure 6) r "lad". Technically, the n-lad curve has a bit f lad due t a dc machine which the synchrnus machine is cnnected t.

8 Synchrnus Mtr V-Curves 8 Labratry machines Figure 7 shws the a diagram f the mtr test stand used fr this experiment. The synchrnus machine is actually a wund-rtr inductin machine. It will perate as a synchrnus machine when a DC current is supplied t the rtr. Besides the rtr windings accessible frm the cnnectr bx, the machine als has shrt-circuited damper windings n the rtr. Bth sides f each statr winding (as, bs, cs, an, bn, and cn terminals) are brught ut n the cnnectr bx fr cnnectin in wye r delta. Hwever, in this experiment, the machine will be cnnected in wye. The rtr is wye-cnnected internally, and the three terminals are brught ut (ar, br, and cr). Synchrnizatin lamps are cnnected in-between the statr windings and the line cnnectin (terminals a, b, and c). A three-phase switch bypasses these lamps when switched n. This setup can be used fr synchrnizing the generatr t the line r fr synchrnus mtr starting. The synchrnus machine is rated at 208-V (line-t-line rms), 60-Hz, 250-W. It is a 4-ple machine and thus has a synchrnus speed f 1800-RPM. The dc machine armature and field terminals are available fr cnnectin (A1, A2, F1, and F2). The machine is designed t be shunt-cnnected (armature and field in parallel) and is used t drive the synchrnus machine as a generatr r absrb a mechanical lad when the synchrnus machine is perating as a mtr.

9 Synchrnus Mtr V-Curves 9 Labratry Wrk Figure 8 shws the wiring diagram fr this experiment. Start by cnnecting the dc machine. It this case, the surce panel supplies the field vltage thrugh a meter channel. The mechanical pwer that will be absrbed by the DC machine is in the frm f generated armature vltage which is supplied t a resistive lad. The lad bx settings are shwn in Figure 9. Next, cnnect the Srensn DC utput t the synchrnus machine thrugh a meter channel as shwn in Figure 8. Nte the dashed cnnectin n the meter bx. This is a shrt-circuit cnnectin which must be cnnected, but will be remved later. Lastly, cnnect the synchrnus machine armature. Start by cnnecting the statr neutral pint n the synchrnus machine cnnectin bx. Then cnnect the armature (terminals a, b, and c) t the meter bx as shwn in Figure 8. Make sure the switch n the cnnectin bx is in the ff psitin. As a last step, cnnect the meter bx t the 208-V line vltage. This is the terminals A, B, and C directly belw the Srensn DC supply. Adapter plugs will be necessary t make this cnnectin. Keep in mind that yu are cnnecting int an energized surce. Fr this reasn, the switch n the synchrnus machine cnnectin bx must be ff. After cnnecting int this surce, the lamps n the cnnectin bx will light up. The next step is t establish a field current. Start the Synchrnus Mtr V-Curves experiment n the cmputer and switch n the Srensn pwer supply. Increase the cmmanded field current t 2.5-A using the sftware interface. Nte that this field current is ging thrugh the shrt circuit n the meter panel. T start the synchrnus mtr, flip the switch t the n psitin. This shrt-circuits the lamps and applies line vltage t the armature at rated vltage and rated frequency. The machine will start immediately due t the rtr damper bars as described abve. Measure the speed with the hand-held tachmeters. Nte that it will be slightly less than synchrnus speed. Next, remve the shrt-circuit wire in the field circuit (shwn as the dashed line in Figure 8). The best way t d this is t just discnnect the right side since it is nt cnnected t anything else. When this is discnnected, the 2.5-A dc current will flw int the synchrnus mtr field. Measure and recrd the speed under these cnditins. At this pint, the synchrnus mtr is running with a light lad. Reduce the field current t 1.5- A. Set the Lad Type t Light-lad in the sftware and btain a set f V-curves by increasing the field current frm 1.5-A t 3.5-A and lgging the data fr each pint (by clicking Add). Reduce the field back current t 1.5-A. Switch n the surce panel and increase the surce vltage until the synchrnus mtr is drawing 200-W as seen n the cmputer screen (nte this will be abut 30% f the surce panel vltage). This will take tw peple t d. Change the Lad Type t Rated-Lad in the sftware and btain anther set f V-curves with a field current frm 1.5-A t 3.5-A. Reduce the surce panel vltage t zer and switch ff the surce panel circuit breaker. Reduce the cmmanded field current t zer. Switch ff the synchrnus mtr (by the switch n its cnnectr bx) and the machine will cme t a stp. Switch ff the Srensn pwer supply.

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12 Synchrnus Mtr V-Curves 12 Calculatins and Questins 1. Calculate the value f rtr speed ω s using (5) and cmpare it t the measured value. Nte: the measured value is in RPM. 2. Create a plt f real pwer and reactive pwer versus field current fr bth levels f lading. Make a separate plt fr each lad level, but use the same axes scales fr bth plts. Nte that the real pwer remains cnstant and the reactive pwer transitins frm psitive t negative. 3. Create a plt f pwer factr versus field current. This shuld be ne plt with bth pwer levels. 4. Create the V-curve plts fr this mtr by pltting the armature current magnitude versus field current. This shuld be ne plt with bth pwer levels. 5. Sketch the phasr diagrams fr three perating pints lgged in the Rated-Lad test; ne fr leading pwer factr, ne fr unity pwer factr, and ne fr lagging pwer factr. Fr synchrnus reactance use a value f X = 152 Ω. s