Calculation of stator winding leakage reactance of 3 and 12-phase machines with AC and DC output

3/12-phase synchronous machines with AC and DC output are being widely used in self-contained electrical power systems for their obvious virtues. On their stator, two separate windings are distributed, one three-phase winding delivers AC power and the other twelve-phase winding, termed DC windings, are connected to the bridge rectifier to supply DC power. Unlike ordinary three-phase machines, there are four layers winding in each stator slot of the 3/12-phase machine and the total air gap magnetometive force produced by the 12-phase winding is more complex than 3-phase machines. By analyzing the leakage magnetic flux and the magnetometive force, relevant formulas are derived to calculate the leakage reactances of the machines. All the stator leakage reactances of a realistic 3 and 12-phase machine were calculated through the methods presented and the simulation of a sudden short-circuit test of the machine was carried out with the parameters calculated. The simulation and test results agree quite well, and show that the formulas presented are correct.