MEASURING INDUCTANCES ON A DC MACHINE

Transcription

1 ESURING INDUCTNCES ON DC CHINE Ning Chuang, Timthy Gale, Richard Langman Schl f Engineering, University f Tasmania GPO Bx , Hbart, Tasmania 700 ustralia T.Gale@utas.edu.au BSTRCT This paper describes a new methd f measuring selfinductance and mutual i nductance n a DC machine. The methd used a DC surce and vercame sme prblems assciated with traditinal methds usi ng an C surce. In pariticular, it enabled the field win ding t carry rated DC. The new methd demnstrated the feasibility f taking measurements f inductance values n a DC machine, and current which gave magnetic saturatin clse t the flux n the actual machine while running. ethds fr measurin g bth self and mutual inductance f DC machine armat ure cils were develped. KEY WORDS DC machine, magnetic saturatin, inductance.. Intrductin Due t the required data f t he inductance values fr the DC machine mdel, it was necessary fr us t take the measurement f self and mutual inductances n t he real machine. Traditinally, an C methd wuld be used fr measuring inductance which needs t measure the current and vltage, and calculate the impedance finding bth real and imaginary parts. Hwever, this C methd did nt w rk n the DC machine, because the measured values can be varying with different frequencies. 2 Principle f measuring inductance The initial idea fr measuring self -inductance is based n the methd f Jnes [ 5] which uses a Wheatstne Bridge circuit as shwn in Figure. I V + R /R 2 Vdt L = I 0 Derivatin f Equatin () The steady state f the bridge is reached after the switch has been clsed and R 2, R 3 and R 4 are adjusted until V = 0. Their steady state values are then given by R /R 2 = R 3 /R 4. Open the switch, then V = () di L + R /R dt (2) Taking integratin, di L I Vdt L 0 = + R /R 0 dt = + R /R (3) where I is the steady current (in amps) thrugh L befre the switch is pened. Hence, Equatin fllws directly. Likewise, a mutual inductance can als be measured using the Wheatstne Bridge circuit shwn in Figure 2. Figure 2. Wheatstne Bridge fr measuring mutual inductance Can shw that = + R /R V2 L2 I V 2 dt 0 R5 V I re simply, a mutual inductance can be measured by the circuit in Figure 3. (4) Figure. Wheatstne Bridge fr measuring self - inductance The bridge is in a balanced state when V = 0. Current in L is I, and V is remved at time t = 0. Can shw that SW V2 L2 t = 0 Figure 3. easuring mutual inductance circuit

2 Thus, V dt = 2 I 0 In practice, errrs due t resi dual flux are avided by reversing I during the integrating perid, and then V dt = 2 2 I 0 (6) The actual measurement n the DC machine used a D irect Current Inductance Bridge (DCIB) in the Pwer Labratry f the Schl f Engineering. This DCIB unit cnsists f three main parts: a Kelvin Duble Bridge (instead f a Wheatstne Bridge), an electrnic in tegratr (INT), and a digital vltmeter (DV), as in Figure 4. SW (5) 3.2 Effect f magnetic saturatin n measured inductances The 0.2 field current was set fr the saturated field flux, which prduces apprximately the same amunt f flux as 5 in the cmplete armature. Rated field current I f is 0.2, and reated armarture current I a is 3.2. In rder t select values f I a fr the sub-cil inductance measurements, we examined whether the inductance depended n armature current. This was dne by using the DCIB and a 20 -turn cil that was temprarily wund arund ne ple f the machine. The inductance was measured with 0.2 in the field cil. We fund that the different armature currents frm t 3 did nt vary the inductance significantly (ie. nly a few percent difference), which was clse t the inherent errr in this methd. sub-cil inductance was then measured under a similar flux cnditin t what wuld exist when the mtr is running. R C INT R DV It was als fund by mutual inductance measurement that the 0.2 field current prduced the sam e amunt f flux as 5 armature current, when the rtr was turned, s that the armarture flux. 5C 6C 7C Figure 4. Direct Current Inductance Bridge ( Kelvin Duble Bridge is a develpment f the Wheastne Bridge t eliminate the errrs due t the cntact and lead resistance, and is suitable fr t he measurement f lw resistances.) 3 rmature inductance measurements 3. Cnnectin f the armature int the DCIB T establish the equivalent circuits n the DC machine [6], the DCIB circuit needed t be mdified fr each measurement. T measure the self -inductance f the six sub-cils in series fr the 7-cil circuit, the cnnectin t the DCIB was as in Figure 5. Rati Figure 5. easuring self-inductance fr the 7-cil circuit It can be seen that the segments frm t and frm t are shrted ut and ideally carry zer current. The series cnnected cils - and - have amp flwing thrugh them frm the supply V. The DCIB measures the self-inductance f tw sets f the six sub -cils in parallel. In this di agram, the field circuit is nt shwn, but it carries 0.2 DC during the measurement. Under the unsaturated cnditin (ie. a zer field current) the self-inductance f the ttal armature winding varies with angular psitin. Referring t Figure 6, the self-inductance measured between the segments 2 and 0 was f und t vary almst sinusidally between 0.5H and 0.3H as the rtr was turned. By cntrast, when there was 0.2 field current, the armature self-inductance was 0.07 ± 0.0H, almst independent f the rtr psitin. Thus, the self and mutual inductances f the armature sub -cils can be assumed t be cnstant and independent f the armature current used and their lcatin n the rtr. 3.3 easuring ther self -inductance n the machine We als needed t measure ther cils f less than six armature cils in series f the machine fr the faulty machine mdel. The cncept f measuring self -inductance remains the same. The nly mdificatin is t add a piece f wire int the armature, which will shrt sme cils depending n hw many cils f self-inductance are needed t be measured. Fr example, Figure 6, is the cnnectin t measure a tw cil self-inductance in the 7-cil circuit f the DC machine s armature (cil numbers frm 7C t and frm t in Figure 6). 5C 6C 7C Rati Figure 6. easuring self -inductance n different cils fr the 7-cil circuit 2

3 Hence, ne t five cil self -inductance fr the 7-cil circuit can be measured in the same way. T measure selfinductance in the 5-cil equivalent circuit, the changes made in this cnnecti n were t shrt ne cil at bth ends (- and - in Figure 7), as required by the cmmutating cnditin. 3 f -6C with -5C and - can be given as 3ax cs 45 and 3ax cs67.5 etc. Refering t Figure 9, the measured results f the mutual inductance n the DC achine with I = 2 can be summarised in Table. 5C 6C 7C Rati Cnnected Cils easured V 0 (Vlt) + Rati = 2 I Rate (mh) V 0 Ntatin f I C C C Figure 7. easuring self -inductance n different cils fr the 5-cil circuit 3.4 easuring mutual inductance n the machine The new methd used fr measuring mutu al inductance fr the 7-cil equivalent circuit is in Figure 8. T integratr 5C 6C 7C Figure 8. easuring mutual inductance n different cils fr the 7-cil circuit - 6C C - 6C Table. Three cil mutual inductance in the 7 -cil circuit In the abve table, each mutual inductance is dented with a last number subscript fr a number f cils affected by the flux linkage f the current thr ugh frm t 6C. It will be nticed that the measured mutual inductances f 3 r 32 in the different cil psitins are bviusly different. The single cil, fr example, between and, and 5C r 5C and 6C is m agnetically cupled by a different flux linkage depending n the angle θ. Therefre, the flux linkage assciated mutual inductance t each single cil is given t csθ, as presented in Figure 9. In Figure 9, the integrate d vltage V 0 n three cils frm t 6C is attributed t the current flwing thrugh frm t 6C. Thus, it is cnsidered that the mutual inductance is prduced between these tw circuits. N ω S d-axis It is nted that there is a.6 Ω rhestat cnnected between 6C and as shwn in Figure 9. This was because f the small vltage (ie. nly a few millivlts) between 6C and. This adversly affected the ttal vltage f the integratr. This prbl em was slved by adjusting the slide psitin until there was less than mv crss -6C befre the current was reversed. Similarly, each different mutual inductance n the machi ne was measured based n this methd. 4 Prductin f mutual i nductance and verificatin with the measurements It is necessary t verify the measurements we btained. Each segment was 22.5 apart n the armature fr this 2 ple/6 slt machine. Hence the mutual inductance 3 defined between -6C and 5C-6C can be written as 3ax cs 22.5 with the current directi n frm t 6C. ls Figure 9. Rtating psitin q dfinitin Theretically, these mutual inductances shuld be expected including the term f cs θ as: 3ax 3ax 3ax 3ax cs 22.5 cs 45 cs 45 cs = = =.3 =.85 The measured value f 3 fr 5C - 6C at 22.5 was 7.0 mh, and 3 fr - 5C at 45 was 5.0 mh. Thus we have 7.0/5.0 =.4. This answer is clse t the value f.3 frm the calculatin. Thus, an errr btai ned fr this is (.4-.3)/.3 = 0.069, r 6.9 %. 3

4 If we substitute the measured value t 3 n - at 67.5, then 5.0/2.6 =.92 is bt ained. It can be cnsidered that the measurement is als clse t the 3ax cs 45 calculated 3ax cs 67.5 which is.85, and the abslute errr invlved here is = The errr is given as (.92.85)/.85 = 0.04, r 4 %. Φ This is anther way t explain these angles. S the given angles in the calculatins abut the mutual inductances n the armature winding can be verified, and are fund t exist in intervals f 22.5, such as 22.5, 45, 67.5 and 90 etc. Figure 4.4 is just a particular case if the mutual inductance between a 3-cil inductance (-6C) and -cil inductance, shwn as an example f the 90 angular between them. Figure 0 illustrates the flux directins f -6C and which frms a 90 angle. Φ6C- 5C Figure 0. mutual inductance angle with the flux directins 5 Impact f the measured inductance values in the mdel In ur measurement f the armature current I a [6], the peakt-peak ripple is abut 0.5 %. Hwever, the ripple f the simulated I a is abut 8.5 %. The ripple percentage in the mdel shuld be affected by the inductances f the armature winding. We checked whether the mdel s utput I a ripple current can be changed by varing its inductance values. We first dubled every self-inductance and mutual inductance. Figure shws the ripple f the simulated I a. 90 6C 7C The I a ripple becmes smaller, reducing t abut 4 % peak - t-peak ripple. We then halved all self and mutual inductance's, and the ripple increased as in Figure 2. Figure 2. Simulated I a with halved inductances Thus, there is an inverse relatinship between the inductance values and the ripple amplitude in the current I a. In ther wrds, dubli ng inductances led t a 50% reductin in I a, and halving the inductances l ed t a 00% increased in I a. The evidence indicates that the inductances btained frm the measurements might be t high. 6 Cnclusin This new methd f measuring self and mutual induct ance using a DC surce has been demnstrated. Hwever, the existence f this methd was nt perfect. Fr accurate mdelling results, the inductances must be measured under cnditins apprximating as clsely as pssible t thse f nrmal peratins. 7 cknwledgements The authrs wuld like t acknwledge the assistance f r Steve very and r Glenn ayhew in prviding technical assistance relating t the experimental wrk. 8 References: [] S.Y.S. H, Cnditin mnitring f electric mtrs. PhD thesis, University f Tasmania, ustralia, 999. [2] S.Y.S. H and R. Langman, The mathematical mdel f a DC mtr, Prc. UPEC 98, University f Tasmania, ustralia, Sept 998, 2, [3].G. Innes, Cnditin mnitring f inductin mtrs: the detectin f brken rtr bars in variable speed inductin mtr drivers, PhD thesis, University f Tasmania, ustralia, 996. Figure. Simulated I a with dubled inductances [4] S.Y.S. H, and R. Langman, Statr current frequency analysis fr the cnditin mnitring f inductin mtrs, J. Electrical and Electrnics Eng., ustralia, 7 (), 43-70, arch

5 [5] C.V. Jnes, The unified thery f electrical machines, Butterwrths, Lndn, 967. [6] N.Chuang, T.Gale and R.Langman, del based simulatin n a DC machine, UPEC, Hbart ustralia,