The pqr-coordinate in the mapping matrices model of Kim-Akagi on power transformation based on Euler angle rotation method

The pqr-coordinate in the mapping matrices model of Kim-Akagi developed in order to find a solution to the problems of harmonic caused by non-sinusoidal power system and non-linear loads. This model is designed for the active/reactive power filter under energy balance and compensation condition. The pqr-coordinate is developed as well as space-vector transformation of the active/reactive power by using Euler angle rotation. The mapping matrices model of Kim-Agaki revisited by the Euler angle rotation method. By using the Euler angles methods of twice rotation the available mapping matrices model of Kim-Akagi is resulted. Furthermore, the Euler angles methods of three times rotation will result in a correction factor. Also conducted to orthogonal test and invariant transformation properties and the results obtained show that space-vector transformation is part of Clarke transformation.