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Practical Issues Concerned with Zero sequence component and Harmonic Compensation in Four-Wire systems

A minimization problem for the instantaneous active and reactive currents give the optimal solution for the three-wire three-phase systems. This basic solution is simple to implement, but posing practical issues when it is applied to a four-wire three-phase system. The generalized theory of instantaneous powers has been proposed as an alternative to the optimal solution for a general three-phase system. Various simulations performed using this method, showing similar issues like those of the optimal solution for the four- wire systems when the power system is unbalanced or distorted. This paper mathematically shows that the optimal solution can be presented like the generalized theory, concluding no difference between the two methods but their appearances. Further, complementary analytical discussions are suggested to overcome the stated problem. Finally, the improved solution is simulated for an unbalanced distorted four-wire system. Comparing the complementary solutions with those of previously emerged generalized definitions confirms that the proposed solution provides almost a complete cancellation of source zero sequence current under unbalanced three-phase load voltages.