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A three-phase shunt active filter is used for current and/or voltage unbalance compensation. Two control schemes with two different theory, instantaneous power theory and Generalized Fryze are considered to compensate the unbalance of current, voltage, or both that are due to the unbalanced load. The compensation results of the different control schemes in unbalance case are simulated and results are shown here. Different compensation objectives can be achieved, i.e., balanced and unity power factor source current, balanced and regulated voltage, or both, by choosing appropriate control schemes by using Instantaneous Power theory. In the case of Generalized Fryze it is seen that the current compensated by means of the generalized Fryze currents method makes the compensated line current proportional to the corresponding phase voltage, that is, they have the same waveform and behave like a " pure resistive " load.

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... So, based on this control strategy, the SAPF should compensate all harmonics in the current, but because the supply voltage primarily contains positive sequence harmonics, it may also contain negative sequence and zero sequence harmonics, a positive-sequence detector is required in the filter to extract the amplitude, phase angle, and frequency of the fundamental positive-sequence voltage and provide it in the form of instantaneous voltage. By adding the positive-sequence detector to the PQ-theory, the controller becomes able to avoid source voltage distortions and the controller is called the sinusoidal source current control strategy (Sinusoidal PQ-theory).The positive-sequence voltage detector which is necessary and based on dual active-reactive power (PQ) control theory depending on an important part of the Phase Locked Loop (PLL) circuit, the complete functional control block diagrams for overall control technique, positive-sequence voltage detector, and PLL circuit are shown in Fig. 2, Fig. 3, and Fig. 4 respectively [16][17][18][19]. ...

A different interpretation of the power decomposition proposed by
H. Akagi et al. (1984) for distorted three-phase situations is given.
This makes it possible to generalize the technique to single-phase
systems and polyphase systems and also to include rigorously zero
sequence currents and voltages

Power Definitions Under Sinusoidal Conditions Voltage and Current Phasors and the Complex Impedance Complex Power and Power Factor Concepts of Power Under Non-Sinusoidal Conditions—Conventional Approaches Electric Power in Three-Phase Systems Summary References

This book presents a deep review of various power theories and shows how the instantaneous active and reactive power theory provides an important basic knowledge for understanding and designing active filters for power conditioning. The only book of its kind, it also demonstrates how the instantaneous active and reactive power theory can be used for combined shunt-series filters and in Flexible AC Transmission Systems (FACTS). © 2007 the Institute of Electrical and Electronics Engineers, Inc.

The main features of the instantaneous reactive power (IRP) p-q theory, considered as a power theory of three-phase systems, are analyzed in this paper using the theory of the currents' physical components (CPC). This analysis shows that the p and q powers are not associated with separate power phenomena, but with multiple phenomena. Moreover, the results of the IRP p-q theory contradict some common interpretations of power phenomena in three-phase circuits. Namely, according to the IRP p-q Theory the instantaneous reactive current can occur even if a load has zero reactive power, Q. Similarly, the instantaneous active current can occur even if a load has zero active power, P. Moreover, these two currents in circuits with a sinusoidal supply voltage can be nonsinusoidal even if there is no source of current distortion in the load. The analysis shows that a pair of values of instantaneous active and reactive p and q powers does not enable us to draw any conclusion with respect to the power properties of three-phase unbalanced loads even in a sinusoidal situation. Thus, the instantaneous reactive power p-q theory does not identify power properties of such loads instantaneously. This conclusion may have an importance for control algorithms of active power filters. The paper reveals the relationship between the p and q powers and the active, reactive and unbalanced powers, P, Q, and D and specifies the required energy storage capability of active power filters operated under sinusoidal unbalanced conditions.

Reactive Power and Unbalanced Circuits

- W V Lyon

W.V. Lyon, "Reactive Power and Unbalanced Circuits",
Electrical World, vol. 75, no. 25, 1920, pp. 1417-1420.

Generalized Theory of the lnrtrntansour Reactive Power in Three-PhsscCircuirs

- H Y Akagi
- A Kanazawa
- Nabae

H. Akagi. Y. Kanazawa and A. Nabae. "Generalized Theory of
the lnrtrntansour Reactive Power in Three-PhsscCircuirs," in
Pror IPEC-Tokyo'93 Int. CO"[ Power Electronics, pp.
1375-1186. Tokyo, 1983.