Analytical equations of the current excited synchronous machine

The analytical equations for the salient pole synchronous machine with a current excited rotor are derived. The equations concern the d- and q-components of the stator current space vector and the excitation or field current. The speed is considered as constant within a given short time. It is shown, that the common differential equations can be solved and the results coincide with the numerical approach. The analytical equations can be used in on-line control schemes and monitoring with voltage source inverter operation, such as wind turbine generators.