Generator calibration.

The procedure and results o f the tests fo r determ ining the g enerator pow er losses are p resented here.

a) E xperim ental procedure. Tests w ere carried out fo r a w ide range o f

rotational sp eed s (from 200 rpm to 1500 rpm ) an d currents (from 0.3 A to 2.2 A ). T he to ran g e w as d ete rm in e d by the tip speed ratio range required fo r th e system p rototype test. F or an u n d istu rb ed w ind speed o f 10 m /s, A.(CPjn>x) = 6.75 (see ch a p ter 3) and to(C pjniu) - 1 0 0 0 rpm . F o r to = 200 rpm , X = 1.35 and fo r 0) = 1500 rp m , X = 10.1. T he X range [1.35 - 10.1] is en ou g h fo r sam pling the turbine Cp(X) curve. The m inim um valu e o f I (= 0.3 A ) w a s determ in ed by the low er lim it o f the torque m eter m easurem ent. B elow I = 0 .3 A , the to rq u e readings were not repeatable. T he m axim um curren t (I = 2.2 A ) w as 1.1 tim es the g e n e rato r rated current and the generator heated-up excessively w hen operating fo r a co n siderab le tim e at higher currents, so it w as not co nsidered safe to continu e the tests fo r I v alues larg er than 2.2A. R eadings w ere taken for 10 values o f I, nam ely 0.3A , 0 .5 A .0 .8 A , 1.0A, 1.2A, 1.4A, 1.6A, 1.8A, 2.0A and 2.2A.

F or each I value, abou t 22 values o f w w ere sam pled. D u ring each run, to w as allo w e d to vary w hile I was kep t constant. T his w as d o ne in o rd e r to keep the g enerator tem p eratu re (and hence RA and the co pp er po w er losses) constant. In o rd e r to k eep the cu rren t constant for each value o f o>, the g en erato r load w as ch anged by adju stm en t o f the v ariable resistors. T he q uantities m easured w ere (see also figure 5.8): T h e ro tatio n al speed (0)), the input torque (Q ), the generator term inal voltage (V ) and curren t (I) an d the p ow er produced by the generator (Pout). Im m ediately after e a ch run, Ra w as m ea su red using a D C pow er source.

T h e g en erator w as allow ed to operate at a m edium rotational speed (about 7 0 0 rpm ) f o r a q u arter o f an hour, at the desirab le current value, before read ing s were taken. T his w as d o n e in o rder to allow the generato r and load and also the b earings to heat-up. It w a s found that the input torque was som ew hat larg er with co ld b earings, as th e lubrican t in them h ad a higher viscosity. O nce the bearings w ere w arm , no noticeable ch ang e in th e input torque was o bserved even i f they fu rth e r heated-up. D uring the

p ro to ty p e tests, the bearings can be heated-up by inverting the gen erator's o peration. The g en e rato r can operate as a m oto r w hen an A C cu rren t is pro v id ed to its arm ature.

W ith the inform ation obtained from th e test, it was p o ssible to estim ate Pmi^fl.O)) from eq u atio n 5.1.6:

Pmitc(I,a>) = Qco - Poul - I2Ra (5.1.7)

In th e abo ve equ atio n, Q w is the input pow er, Pout is the output po w e r re ad on the watt m eter an d I2RA is the co p p e r loss.

D uring th e early stag es o f the tests a problem w as encountered: The voltag e readings from the torque m eter am plifier o utp ut w ere fluctuating considerably w ith tim e. T h ese fluctuations co u ld be as high as ± 20 % o f th e m easured average. The flu ctu a tio n s d id not start im m ediately after the m oto r was turned on , but afte r about 5 m in u tes o f operation. V arious tests w ere carried o u t in o rder to isolate the source o f the p roblem . It is believ ed that they are real torque fluctuations associated w ith the g enerator and lo ad and not noise ca u sed by the torque m easuring eq u ip m en t. S ince only an e stim ate o f the average steady state torque was necessary, the problem w as solved by p assing the am p lifier o u tp ut signal through a low -pass filter before it w as read on the voltm eter. T h e filter arran gem ent is show n in figure 5.12. Its elem en ts are a re sisto r (R F = 10 M i l) and a ca p ac ito r (Cp = 1 n F ). The filter w as found to dam p en the voltage rip p les su fficiently. H ow ever, a significant voltage d ro p occu red o n the filter resistor. T h e filter o u tp u t voltage w as alm ost h alf o f the input voltage. T he filter w a s calibrated versu s the am p lifier ou tp ut and the calibration results are sh ow n in figure 5.13. Due to that voltag e dro p , the ov erall torque sensitivity w as halved and sin ce th e voltm eter sen sitiv ity was 0.0 05 V , (ie 0.01 V o f the am plifier ou tpu t voltage) the to rq ue sensitivity w as re d u ced to 0 .0 6 Nm w hich is equal to 1/32 o f the low est m easurab le torque. W ith that p ro blem solved, torque m easu rem ents w ere possible.

b) P resentation o f results. F o r all values o f I, the m easured torque w as fo u n d to be nearly constant for values o f co larger than 5 00 rpm . B elow 500 rpm , the torque increased slightly with to increasing. B etween 700 rpm and 800 rpm , an o th e r phenom enon was observed: The test rig was resonating and the noise produced by it as w ell as the shaft vibrations (w hich w ere kept at low levels at all oth er rotational sp eed s) w ere increased. A lso, within the resonance regim e, the input torque levels were slightly low er. The resonance intensity depended on the generator current and with it increasing th e noise and vibrations increased. During the open circuit test how ever, (w hen I = 0 ), n o reso n an ce was observed. It is therefore safe to conclude that it w as the g enerator that w a s resonating. It m ust therefore be noted that before the prototype test is carried out, the turbine blades' resonant frequencies m ust be evaluated. If they are found to be nea r th e g en erato r resonance band, certain operating conditions m ust be avoided du rin g the proto ty p e test o therw ise serious dam age o f the turbine m ay result.

F luctuations o f the torque readings were observed even after the filter w as installed . T hey w ere found to be within the torque transducer accuracy levels (ie ± 0 .5 % o f fsd). H ow ever, for low values o f I, the torque was also low and the relative erro rs w e re considerable. The m axim um relative errors in torque together with the averag e to rq u e level for each value o f I are show n in table 2. It is evident that the torque v alu es m easured are qu ite low com pared to the torque m eter ratings. F o r I = O J A , the averag e to rque level w as less than the low est m easurable torque o f the transducer. Even fo r I = 2 .2 A , fo r w hich the m axim um torque was m easured, the torque level w as still 5.5 tim es less than the transducer m axim um m easurable torque. For better results, a m ore sensitiv e torq u e transducer is necessary, w hich how ever was not available.

TA B LE 2

I (A) _{error in torque readings}Maximum relative Average torque _{level (N m)}

0.3 9.0% 1.57 0.5 6.6% 2.00 0.8 5.0% 2.84 1.0 4.0% 3.58 1.2 3.0% 4.28 1.4 2.8% 5.01 1.6 2.6% 5.43 1.8 2.3% 6.08 2.0 2.1% 6.65 2.2 2.0% 6.94

W ith use o f equation 5.1.7, a ch a n o f Pmisc(I,to) w as m ade, show n in figure 5.14. T h e scatter w hich is m ore pronounced for the lo w er v alues o f I (0.3A to 1.4A) is d ue to the torque fluctuations. F o r larger currents, (above 1.4A) the sca tte r is red u ced . T h e b ehaviour o f Pmisc(I,to) is as expected. F o r the sam e co and w ith I increasing, it increases d ue to increasing co re losses. F o r the sam e 1 and with co increasing, it also increases due to increasing m echanical losses. F o r all values o f I ab o v e 0.5A , the slope o f the Pmisc curves is reduced w ithin the co ran g e [700 rpm -8 50 rpm ] d u e to the low er torque values caused by the g enerator resonance. T h e value o f Pmilc is alm ost do ub led (for all co) betw een the low est and largest values o f I, w hile the o u tp u t po w e r in creases m ore than 7 tim es. The curv es shown in figure 5.14 w ere interpo lated through the experim ental data fo r elim inatin g scatter. T h o se cu rv es ra th e r than th e experim ental d ata w ere u sed in all the calculatio ns that follow . T h e repeatability o f th e m easurem ents w as tested by checking the torque levels after each run w as com pleted a n d no significant differences w ere observed. It w as felt that there w asn't an y need to test the repetability o f the electrical quantities m easurem ents, because they seem ed to be q u ite consistent. A fu ll set o f readings for I = 1.0A was repeated and the results o f both ru n s are show n in figure 5.15. T h e experim ental points seem to lie in the sam e band.

In fig u re 5.16, Poul(I,to) m ea su red on the w a ttm ete r is s h o w n . It can be seen that the g en e rato r po w er output fo r the sam e I increases lin earily w ith to increasing. F or the sam e co, w ith I increasing Poul increases except fo r the regim e w ith I > 1.0A and to < 6 0 0 rpm w here th e trend is reversed. T he accuracy o f the w attm eter re a d in g s is m uch better than that o f the torque m eter, and the sca tte r is in significant. T h e g ra p h s o f figures 5.1 4 an d 5 .1 6 w ere u sed fo r calculating the g en erato r efficiency (fig) w h ich is show n in figure 5.17 plotted v ersu s I for constant co values. The efficien cy w as c h o s e n to be plotted that w ay, so th at only one param eter w ould be ch an gin g (ie the g e n e ra to r load). If fig w as plotted v ersu s to for constant valu es o f I, both th e g en erato r lo ad and the rotational speed w o u ld be changing. The g e n e rato r efficiency increases w ith to increasing fo r the sam e I, but at a reducing rate. T h e value o f I at which the m axim um o f efficiency is achieved fo r each o> in creases with co increasing.

The m axim um value o f fig is ob tain ed at co = 1500 rpm , w ith I = 1.4A and is about 70% . T his value o f efficiency is ra th e r low for a typical generator, b u t this was expected as the g en e rato r arm ature resistan ce is considerable. A lso, the s ta to r windings do not have iron cores fo r enhancing the m agn etic flux through them . O f th e p o w e r loss fo r that case, about 1/3 is due to electrical losses (I2RA) and the o th er 2/3 are due to m echanical, co re and o th e r losses (Pmisc).

# U sing the charts o f figures 5 .1 4 an d 5.16, the ra tios Pmisc/Poui a n d I*Ra/

P0ut w crc calculated fo r v arious values o f I an d to. T hey are show n in tab les 3 an d 4. It can be seen from those tables that for low v alues o f I (ie I = 0 .3 A ), PmifC is b y fa r the m ost im portant p o w e r loss com ponent throu gho u t the to range e x a m in e d . For interm ediate values o f I (ie I = 1.0A), Pmisc an d the electrical lo sses are o f th e sam e ord er o f m agnitude fo r low to, but with to increasing, Pmjsc dom inates. F o r large v a lu e s o f I (ie I = 2.0A ), I2RA is larg e r fo r low to. W ith to increasing, Pmisc and the ele ctrica l losses are

TABLE 3 Pou. (A) 0) ( r p m ) \ . 0.3 1.0 2.0 500 0.658 0.356 0.456 1000 0.901 0.375 0.361 1500 0.917 0.424 0.357

com parable. In figure 5.18, plots o f V(to)

TA B L E 4 I2 r a Pou. \ I (A) to ( r p m ) \ . 0.3 1.0 2.0 500 0.185 0.256 0.833 1000 0.031 0.117 0.303 1500 0.021 0.077 0.185

shown fo r three v alu e s o f I. (0.5A , 1.0A and 2.0A ). It can be seen that the term inal voltage increases linearly with 0) increasing. A lso, fo r the sam e to, V drops with I increasing. The slope o f all th re e lines shown in figure 5.1 8 is sim ilar. Using the graphs o f figures 5 .1 6 an d 5.18, the an g le <)> betw een the term inal v oltage (V ) and the cu rrent (I) phasors can be estim ated as follow s: The g enerator's apparent pow er is VI w hile the real pow er is Poul = V Ico s$ . H ence:

0 = co s ' (Poul/VI)

In figure 5.19, 0(o>) is shown for three values o f I (0.5A , 1.0A an d 2.0A ). It is evident that th e resistors used are not purely ohm ic loads and <J> gets c o n sid erab le values. The b ehaviour o f <}> changes with I:

•F or I = 0.5A , <(> d rop s with increasing o>. •F o r I = 1.0A, <J> is nearly constant. •F or I = 2.0A , <|> increases with increasing to.

This can be explained as follow s: A ngle $ depends on the re lativ e m agnitude o f the resistive and reactive com ponents o f the load im pedance. D uring th e tests, w hen co increased, the load was changed fo r keeping I constant. B oth lo a d resistance and reactance increase with co increasing, the form er due to the increase o f the resistor active length, the latter due to the sam e effect that increases the coil self-ind uctan ce, and also due to the o> increase. Hence, fo r I = 0.5A , the load resistance in cre ase s m ore rapidly than its reactance with to increasing. For I = 1.0A, both load re sistan c e and reactance

increase by the sam e ra te and thus <)> is kep t nearly co n s ta n t. F o r I = 2.0A , the load reactance increases m o re rapidly than the resistance, c a u s in g 0 to increase with 0) increasing.

The load angle 5 (see figure S.2) was also c a lcu lated using equation 5.1.3. F o r do in g so, the resu lts o f the open circuit test (ie the K e v alue), the sh ort circuit test (ie the L s value) and the g en e rato r calibration (ie figures 5 .1 1 , 5.18 and 5.19) w ere used. 5 w as ca lculated for I ■ 2 .0A and for various values o f to. T he results are shown in the follow ing table:

TA B LE 5 to (rpm) 6 (°) 0)eLs ( C l ) 500 1.89 14.8 600 4.66 17.8 700 6.05 20.8 1000 8.01 29.7 1500 9.26 44.5 Ra(I = 2.0A) = 31.64 Q

It is ev id e n t that w ith increasing to the angle 5 also in cre ase s. T his is due to the increase o f the synchronous re actan ce (Q)eLs ). T he v alues o f 8 are relativ ely low , because o f the large RA. In a typical syn ch ronous m achine, the sy n ch rono u s reactance is about 10 tim es as large as the arm ature resistan ce as ex p la in e d in [61] a n d the load angle is about 15° to 20®. F o r th e g enerator tested how ever, (as w ell as for o th e r s im ilar m achines described in [60]), Ra an d coeLs are o f the sam e order o f m agnitude, a n d hence 8 gets low values (see

also figure 5.2). F or lo w er currents, 8 is ev e n lower. F o r I = 0 .5 A fo r exam ple, the