Simplified Analytic Procedure to Calculate the Electric Variables at Steady State of Type-III and Type-IV Wind Generators

This paper presents a set of analytic expressions to obtain the electric variables in the steady state operational point of type-III and type-IV wind generators, based on the simplification of their time domain models. This approach is an attractive alternative over traditional electromagnetic transients (EMT) simulation and numerical iterative methods as it requires no computational resources and little modeling detail. This work was motivated from the necessity of such operational point to calculate detailed impedance vs. frequency profiles of the generators for wind park resonance assessment, when including the effects of their phase-locked loops, DC bus couplings, and outer control loops for power and voltage regulation. From this work, it was possible to derive didactic circuit equivalents of the wind generators which can be used to: observe the behavior of inner variables of the generator such as magnetic fluxes and currents for several setpoints and wind conditions; study the power losses of the generators; calculate the capacity of power electronics converters of type-III generators; and even set protections and saturation limits of generator controllers. Detailed EMT simulations were used to validate the expressions.