14. starptautiskÄ konference 2012 - Latvijas JÅ«ras akadÄmija

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Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”whereUA UB UC[ U ( t)] (6)00 0 Fig.3. Equivalent physical model of induction motor[U(t)] - matrix. instant values of the voltages of stator and rotor phases;u 2 E sin( t),uuABC2 E2 Efffsin( tsin( tsss2323),),(7)E f - phase rms value of the supply voltage; s = p*f* - angular velocity of the stator field rotation, with the number of poles pairs - p , atthe network frequency f s ,[ R ] - square diagonal matrix of active resistances (R A ;R B ;R C ;R a ;R b ;R c );28
Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”iA(t) iB( i)iC( t)[ i (t) ] = - column matrix of the instant values of the phases currents; (8)ia( t)i( t)b ic( t)ΨA(t) ΨB( i)ΨC( t)[ (t) ]= - column matrix of the instant values of the phases flux linkages. (9)Ψa( t)Ψ( t)b Ψc( t)The phases flux linkages can be tentatively divided into the flux linkages produced by thecurrents being stationary according to the phase under consideration and by those rotating with therotor speed. A (t)= As (t) + Ar (t), B (t)= Bs (t) + Br (t), C (t)= Cs (t) + Cr (t),(10) a (t)= ar (t) + aS (t), b (t)= br (t) + bS (t), c (t)= cr (t) + cS (t),where:ΨΨΨΨΨΨΨAs(1Ψ222t) ( l1 3L1) iA(t)3L1cos( )iB(t)3L cos(2) iC( t);22(t) 2 3L1cos( )i ( t)( l13L1) i ( t)3L1cos( ) i ( tA B C);22(t 2 L cos( )i ( t) L cos( )i ( t) ( l L ) i ( t );BsΨCs)3 1A 3 1B 1 3 1 C2(t) 2 cos[ ( )] ( )23M p t i t3M cos[ p ( t)] i ( t)3M cos[ p ( t)] i ( tAr r a r b r c2(t) 2 cos[ ( ) ] ( )23M p t i t3M cos[ p ( t)]i ( t)3M cos[ p ( t)] i ( tBr r a r b r c2(t) 2 cos[ ( ) ] ( )23M p t i t3M cos[ p ( t)] i ( t)3M cos[ p ( t)]i ( tCr r a r b r c222Ψar( t) ( l2 3L2) ia( t)3L2cos( )ib( t)3L2cos(2) ic( t);22Ψ ( t)2 3L2cos( ) i ( t)( l23L2) i ( t)3L2cos( ) i ( tbr a b c);22Ψ ( t)2 3L2cos(2 ) i ( t)3L2cos( ) i ( t)( l23L2) i ( tcr a b c);2(t) 2 cos[ ( )] ( )23M p t i t3M cos[ p ( t)] i ( t)3M cos[ p ( t)] i ( tas r A r B r C2(t) 2 cos[ ( ) ] ( )23M p t i t3M cos[ p ( t)]i ( t)3M cos[ p ( t)] i ( tbs r A r B r C2(t) 2 cos[ ( ) ] ( )23M p t i t3M cos[ p ( t)] i ( t)3M cos[ p ( t)]i ( tcr r A r B r c);););););).(11)The sum of the components of equations (10, 11) results in the full flux linkages of thephases. The solution of the phases voltages equations (5) together with the equation of rotor movementallows define the character of the transient process, calculate the currents, flux linkages and theelectromagnetic torque of the motor [5, 6]:29
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