[Paper Review] A Novel Time-Domain Perspective of the CPC Power Theory: Single-Phase Systems

Dimitri Jeltsema, J.W. van der Woude+1 more|arXiv (Cornell University)|Mar 31, 2014

Microgrid Control and Optimization14 references3 citations

TL;DR

This paper introduces a novel time-domain interpretation of the Currents' Physical Components (CPC) power theory for single-phase systems under nonsinusoidal conditions. By decomposing the reactive current into average and scattered components using Iliovici’s reactive power integral—defined as the area of the Lissajous loop between voltage and current—it enables precise, physically measurable power compensation. The key contribution is a method to fully optimize power factor using shunt compensators that replicate the Lissajous loop with opposite orientation, outperforming traditional Budeanu-based approaches.

ABSTRACT

This paper presents a novel time-domain perspective of the Currents' Physical Components (CPC) power theory for single-phase systems operating under nonsinusoidal conditions. The proposed CPC decomposition reveals some appealing physical characteristics of the load current components in terms of measurable powers that are distributed over the branches in the load network. Instrumental in the time-domain equivalent of the reactive current is the concept of Iliovici's reactive power, which is a measure of the area of the loop formed by the Lissajous figure when plotting the current against the voltage. For sinusoidal systems, Iliovici's reactive power integral is included in the IEEE Standards on power definitions. Furthermore, the reactive current is decomposed into two new currents that represent the reactive counterparts of the active and scattered current.

Motivation & Objective

• To address the limitations of Budeanu’s power model in nonsinusoidal systems, where reactive and distortion power do not fully capture physical power phenomena.
• To develop a time-domain interpretation of the CPC power theory that links measurable power components to physical current decomposition in load networks.
• To propose a physically meaningful decomposition of reactive current into average and scattered components using Iliovici’s integral as a foundation.
• To enable optimal power factor improvement through compensators that replicate the Lissajous loop of the load with opposite orientation.
• To demonstrate that traditional shunt capacitors only compensate average reactive power, not scattered reactive power, in nonsinusoidal systems.

Proposed method

• The method introduces a time-domain decomposition of the load current into active, scattered active, reactive, and scattered reactive components based on physical power distribution in resistive and reactive branches.
• It uses Iliovici’s reactive power integral, defined as the area of the Lissajous figure formed by plotting current against voltage, to quantify the average reactive power.
• The active and scattered active currents are derived from power integrals proportional to voltage and current products, measurable via standard power measurement setups.
• The reactive and scattered reactive currents are derived from integrals involving the time-derivative of voltage and current, measurable using a modified power measurement circuit.
• The theory is grounded in Tellegen’s theorem, ensuring conservation of power across individual components, and aligns with Conservative Power Theory (CPT).
• Compensation is achieved by designing shunt elements that generate a Lissajous loop identical in shape but opposite in orientation to the load’s loop, fully canceling reactive power.

Experimental results

Research questions

• RQ1 Can a time-domain interpretation of the CPC power theory provide a physically meaningful decomposition of current components in single-phase systems under nonsinusoidal conditions?
• RQ2 Does Iliovici’s reactive power integral, defined as the area of the Lissajous loop, offer a more accurate and measurable representation of reactive power than Budeanu’s model in nonsinusoidal systems?
• RQ3 Can shunt compensators be designed to fully compensate both average and scattered reactive power by replicating the Lissajous loop with opposite orientation?
• RQ4 How does the proposed decomposition improve power factor optimization compared to traditional Budeanu-based compensation, especially in the presence of harmonic distortion?
• RQ5 What is the relationship between the time-domain CPC decomposition and Conservative Power Theory (CPT), and can it be extended to nonlinear and time-varying loads?

Key findings

• The proposed method decomposes the reactive current into two physically meaningful components: average reactive current and scattered reactive current, both measurable via power integrals.
• Iliovici’s reactive power integral, representing the area of the Lissajous loop, is equivalent to the standard reactive power in sinusoidal systems but generalizes to nonsinusoidal systems as the average of harmonic reactive powers.
• For the test RL circuit with nonsinusoidal voltage, the power factor improved from 0.403 (uncompensated) to 0.905 (fully compensated), demonstrating significant enhancement over Budeanu’s method.
• A shunt capacitor alone only compensates the average reactive power (Q_i), leaving the scattered reactive power (Q_s) uncompensated, which is why Budeanu’s method fails to optimize power factor.
• Full compensation requires a more complex shunt architecture, such as an LC filter (L_x = 0.922 H, C_x = 0.252 F), which fully cancels both Q_i and Q_s, reducing apparent power from 50.309 VA to 22.368 VA.
• The method enables physical measurement of active and reactive power components through standard power measurement setups, with P_n and Q_n directly measurable via the integrals ∫u_n i_n dt and ∫(du_n/dt) i_n dt, respectively.