Smart Hybrid AC/DC Microgrids

AInstantaneous Power Theory from Three‐phase and Single‐phase System Perspectives

A.1 Introduction

This appendix provides an instantaneous power analysis of the three‐phase power system from the three‐phase and single‐phase perspectives. Then, different reference currents to be tracked by the interfacing power converters to achieve specific performances for unbalanced voltage compensation are provided. The reference currents are used in the control strategies in Chapter 9. Finally, in this appendix, discussions and comparisons of the instantaneous power analysis from the three‐phase and single‐phase system perspectives are provided.

A.2 Principles of Instantaneous Power Theory

From Figure A.1 and according to instantaneous power theory [1, 2], the instantaneous active and reactive powers injected into the grid at the point of common coupling (PCC) can be described as in (A.1) and (A.2).

(A.1)

(A.2)

where v = [ v_a, v_b, v_c] and i = [i_a, i_b, i_c] are the three‐phase PCC voltage vector and the current vector, and v_⊥ lags v by 90^°. The operator “∙” denotes the dot product of vectors. Considering symmetric‐sequence component of the PCC voltage vector and the current vector, (A.1) and (A.2) can be described as:

(A.3)

(A.4)

where v⁺, v⁻, v⁰ and i⁺, i⁻, i⁰ are positive, negative, ...