Abstract
This paper provides complex circuit equations of cylindrical synchronous machine taking damper winding currents into consideration and its analytical solutions. I expressed cross section of synchronous machine as complex plane and named it space complex plane. I named voltages, currents and magnetic fluxes in this complex plane, space voltages, space currents, and space magnetic fluxes respectively.To distinguish ordinary complex quantities, such as complex currents of single-phase circuit, from space complex quantities, such as space complex currents, I named it time complex quantity temporarily in this paper.Using these space complex quantities and time complex quantities, I analyzed cylindrical synchronous machise.For instance, calculated results of transient phenomena of 3-phase sudden short circuits and step change of field voltages of cylindrical synchronous machine are showed in this paper.
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