Induction MotorswithConstant Speed

induction motorrunning atconstant speed issuddenly taken offthelines and putbackafter anextremely brief interval.Although thetransient torques and currents thatoccurina single-phase motordonotinpractice, produce any adverse effects ofaserious character, it wasfelt thatitwouldbeinteresting and instructive toanalyze this problem andto examine thecharacter ofthetransients produced atthetimeofreclosing, short circuiting ofstator terminals, andplugging.Thispaperdeals withtheanalysis ofthepreceding problem withthe helpofsymmetrical components ofinstantaneous potentials andcurrents and theLaplace transform technique forthe solution ofintegro-differential equations. Ithasbecomethestandard practice for design engineers tousetheaverage steadystate value oftorque asasoundbasis for thedesign ofcouplings, shafts, andbearings.Thisistheresult ofinadequate appreciation ofthefact that, atthetime ofstarting, reclosing, andplugging the actual instantaneous peak. valueofthe developed electromagnetic torque isconsiderably higher thantheaverage value. Thefollowing analysis shows clearly that, inthecaseofa capacitor-run singlephaseinduction motorthere isafundamental frequency decaying torque which persists forseveral cycles ifthereclosing isdonewhentheapplied potential passes through itszerovalue. Shouldthe switching bedonewhenthepotential passes through itspeakvalue, thedeveloped electric torqueattains itsfinal steady-state value inless thanthree cycles without anyovershoot. By andlarge, these results aresimilar tothose reported bytheauthor inhispaperreferred to earlier. I Assumptions