Modeling Methodology Suitable for Converters Integrating Renewables: The QMQI Method

This paper presents a new approach for time-domain analyses using model quadratization quadratized model and subsequent quadratic integration of the quadratized dynamic-models quadratized model-quadratic integration (QMQI) method. The modeling methodology is suitable for analysis of power systems with nonlinear components and switching subsystems. The quadratic integration (QI) method has been demonstrated to be more numerically stable, robust, and accurate than trapezoidal integration (TI), one of the most popularly used methods for power transient analyses. The model quadratization enables nonlinearities to be modeled with equations of nonlinearities no higher than second order without approximations or simplifications. Upon QI, the resulting companion form is a model with nonlinearities no higher than second order (quadratic companion form). Newton´s method is employed for the solution of the quadratic companion form equations. The numerical convergence of the overall method is robust and fast. The performance of the QMQI method is quantified with a couple of systems of nonlinear components and power electronics. The method can be expanded to cubic integration (CI) as well as higher-order integration methods. This paper compares the QMQI method with the TI and the CI, for the purpose of determining the pros and cons as higher (or lower)-order integration methods are used.