| With the widespread popularity of power electronics technology in modern power systems,a large number of nonlinear devices and impact loads are connected to the power grid,making power quality problems such as harmonics and unbalance become increasingly prominent.Power theory is the most basic theory involving power production and consumption,and plays an important role in power quality assessment,reactive power compensation design,etc.This paper studied the non-sinusoidal power theory based on Clifford algebra.The main research contents and results were as follows:(1)Starting from the power definitions of the traditional non-sinusoidal power theories,the definition method,physical mechanism and some defects of Budeanu power theory and currents’ physical components power theory in the frequency domain,Fryze power theory and instantaneous reactive power theory in the time domain were compared and analyzed.(2)Based on the Clifford algebra,the voltage and current were decomposed by Fourier,and the base vectors were established according to the frequency component and phase angle of the voltage,and then the voltage and current vectors were formed in the frequency domain.The geometric product of the two was defined as power multivector,and its components were divided into six categories:active power,scattered power,Budeanu reactive power,distortion reactive power,out-of-band reactive power and phase-to-phase unbalanced power.The power multivector theory was established in the frequency domain.Finally,the power multivector was simulated and calculated in single-phase circuits and three-phase circuits under non-sinusoidal conditions.The results showed that power components in the theory could describe power characteristics well,the physical meaning was clear,and it followed the basic theorem in the circuit,which could provide new ideas for power theoretical research in the frequency domain.(3)Based on the Clifford algebra,the voltage and current were subjected to Hilbert transform,and the base vectors were established according to each phase component,and then the voltage and current vectors were formed in the time domain.The geometric product of the two was defined as power multivector,and its components were divided into two categories:instantaneous parallel power and instantaneous quadrature power.The power multivector theory was established in the time domain.Finally,the power multivector was simulated and calculated in singlephase circuits and three-phase circuits under non-sinusoidal conditions.The results showed that the power and current components could be accurately measured,and it was still applicable in unbalanced conditions,which expanded the research scope of the power theory in the time domain. |
