Multiple solutions of PMSG with different orientations and reference powers

The existing steady-state models for the permanent magnet synchronous generator (PMSG) are based on the constant voltage, or quantify electromagnetic transient. This paper proves that the equivalent voltage behind stator circuit is proportional to the rotor speed, and dependent on wind speeds, thus invalid. The steady-state constraints are proved to be indeterminate equations, whose unique solution requires additional constraint, i.e. stator current or stator voltage orientation which are not consistent with var constraint, yielding different stator voltages/currents, losses and efficiencies. Compared with current orientation, voltage orientation needs less var support, but with lower efficiency. With power dispatch by adjusting rotor speed or pitch angle, multiple solutions are quantified, and modified flat starts are proposed to improve convergence.