Time-Domain CPC Decomposition: Answers to Comments on “Physical Interpretation of the Reactive Power in Terms of CPC Power Theory Revisited”

This note addresses critical issues raised in previous works concerning the time-domain Currents’ Physical Components (CPC) decomposition, providing refined assertions and clarifications. The main objective is to enhance the understanding of the reactive power's physical implications through the CPC power theory. The methodology involves recalling and analyzing a single-input single-output (SISO) linear and time-invariant (LTI) system framework, alongside a detailed investigation of the system's impulse response. Key observations are made regarding the decomposition of the impulse response into even and odd parts, which are crucial for analyzing the corresponding current and voltage relationships. By establishing a comprehensive framework for decomposing signals, the study reveals that active, scattered, and reactive currents can be effectively categorized and defined. This refined approach not only solidifies the theoretical foundations of CPC decomposition but also rectifies earlier misconceptions, offering a clearer interpretation of reactive power in electrical systems. The results indicate a more nuanced understanding of reactive power and enhance its practical applications in system and control theory. This work contributes valuable insights into the ongoing discourse within power systems analysis and optimization.