2015-08-13
353
In an asynchronous machine there are next losses of energy: in windings of stator and rotor Рcp 1, Рcp 2; in steel of stator and rotor Рst 1, and Рst 2; mechanical Рmech; additional Рad; in the excitant and regulative devices Рex,c.
Total losses
∑ P = Pm 1 + PM 2 + Pst 1 + Pst 2 + Pmech + Pad + Рex,c. (61)
There are losses Рex,c in the generator mode. Losses are in windings of stator and rotor, conditioned by its currents:
Рcp 1= m 1 ∙I 12∙ r 1, Рcp 2= m 2 ∙I 22∙ r 2 = m 1 ∙I '22∙ r '2 (62)
Losses in stator steel are determined as a sum of losses in toothing Рz 1, in the back of armature Рj 1 and pulsation losses Рpl 1:
Рst = Pz 1 + Pj 1 + Pp l,
Pz 1 = kT ∙[ kh∙σh∙f 1 / 400 + ked∙σed (f 1 / 400)2]∙ B 2 z 1 av∙Mz 1, (63)
Pj 1 = kT ∙[ kh∙σh∙f 1 / 400 + ked∙σed (f 1 / 400)2]∙ B 2 j 1 ∙Mj 1, (64)
Ppl 1 = kT ∙ σed (fz 1 ∙Bpl 1 / 100)2 ∙Mz 1, (65)
where kT − technological coefficient, kT ≈ 2 for the toothing of armature and kT ≈ 1,4 for the yoke of armature; σ h and σ ed − coefficients, depending on the brand and the thicknesses of steel sheet; kh − coefficient, taking into account the unevenness of distribution of magnetic induction on the thickness of sheet; at frequency 400 Hz magnetic induction practically does not change on the thickness of sheet and it is possible to accept kh = 1; Bz1av and Bj 1 − magnetic inductions accordingly in a tooth and in a back of stator armature; Вpl 1 − amplitude of pulsations of magnetic induction in the stator toothing,
Вpl 1 = γ z 2∙δ∙ Bzav / (2 tz 1 min),
where γ z 2 = [(bsl 1 / δ)2]/(5 + bsl 2/δ); Mz 1and Мj 1 is a mass of toothing and back of stator armature.
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The pulsation losses Рpl arise up because of toothed structure of rotor.
For the count of losses in rotor steel it is possible to apply the same formulas, what for stator; in these formulas, however, instead of f 1 it is necessary to put frequency of rotor current f 2. Because frequency f 2 is small, then losses in a rotor at normal frequency of rotation are ussualy small, what these losses are usually ignored because of.
Losses of a friction in bearing and convection losses behave to mechanical. The relative value of mechanical losses depends on frequency of rotation and power of machine. At a speed-down and increasing power of asynchronous machine the relative value of its mechanical losses diminishes. In asynchronous motors at frequency 400 Hz and power from 0,5 to 5 kW relative values of mechanical losses
Рmech/Рnom = 0,1 ÷ 0,03.
Losses from a friction in rolling bearing of asynchronous machines, losses of air friction and losses on a ventilator it is possible to count up by formulas (2.303) ÷ (2.306), [1]. The value of mechanical losses for asynchronous generators it is possible to accept from 0,03÷0,02 up to 0,015÷ 0,01 of a nominal active-power. The first values of losses are typical for generators by power of units kVA, and second − for generators by power in ten kVA and f = 400 Hz.
Additional losses are conditioned by the ultraharmonics of MMF, pulsations of main magnetic flux, by the presence of massive details in the construction and other. Additional losses are usually accepted by equal 0,01 of the active-power of generator.
Losses Рex , c consist of losses in the capacitors Pex and losses in the control circuit Рc.
Losses in capacitors are determined by the angle of losses tg δ:
Рc = Рex ∙ tg δ = 2π∙10-6∙ m 1∙ f 1/ Сc∙U 2 c ∙ tg δ. (66)
If capacitors are connected in a star, then Uc = Uph 1, and if in a triangle, then Uc = √3∙ Uph 1. But because at the set reactive-power of capacitors Рex their capacity diminishes in three times, then losses in capacitors turn out identical.
The value of losses angle tg δ increases with the increase of frequency. In the range of frequencies 400÷1000 Hz it is growth small. For the capacitors К75-10 a value of tg δ at a temperature 100° C not exceed 0,008; for the capacitors К71-4 at a temperature 85° C a tg δ ≤ 0,002; for the capacitors МБГ4 at a temperature 70° C a tg δ ≤ 0,015.
Losses in the control circuit depend on the system of adjusting. At the choice of the control system with bias of armature back
Pc = m 1 ∙Uph 1 ∙kI∙Ib,max / η rc,
where a kI − coefficient of current convertion in the rectification circuit; Ib, max − maximal value of current in bias winding; η rc – efficiency of rectifier, accepted η rc ≈ 0,85.
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Efficiency of asynchronous machine:
а) for the tractive mode
η M = [(P 1 − ∑ P)/ P 1]∙100; (68)
b) for the generator mode
η G = 1 − ∑ Р /(Р∙соs φ + ∑ P), (69)
where Р − full output power of generator.
