A Geometric-based Power-Free Approach for Current Compensation

Traditional methods for current compensation in power systems and electrical circuits have heavily relied on ad hoc defined power concepts. This paper introduces a novel, power-free approach to both active and passive current compensation based on vector projection and rejection principles. The proposed method leverages vector geometric algebra as a robust mathematical framework, providing a clear and intuitive way to perform these operations in electrical systems. This approach simplifies the understanding and computation of circuit compensation, offering a unified method applicable to both single-phase and multiphase systems, in time and frequency domains. The main advantage is the complete avoidance of power definitions in the compensation process, focusing instead on the geometric relationships between voltage and current vectors. The paper develops the theoretical foundation and mathematical formulation of this power-free approach, demonstrating its versatility in handling various electrical scenarios, including non-sinusoidal and unbalanced conditions. By providing a geometric interpretation of current components, this novel approach offers a promising alternative to traditional power-based methods, laying the groundwork for more intuitive and efficient compensation system design in electrical circuits and power systems.