A Graphical Method For Reactive Power Analysis Of Single-Phase Rectifier Circuits

In the fields of modern industry,agriculture and transportation,electric power plays a vital role in promoting the development of science and technology.However,with the widespread application of power electronic devices in recent decades,a large number of harmonics are injected into the power grid.The voltage and current waveforms on the grid side are seriously distorted,and the power system is becoming more and more unstable.But the traditional sinusoidal power theory is not applicable to reactive power compensation and harmonic suppression of power equipment.Although numerous scholars at home and abroad have carried out in-depth research on the measurement of reactive power under non-sinusoidal conditions,and put forward their different views,these views have been pointed out that there are some defects and deficiencies.There is no unified conclusion on non-sinusoidal reactive power so far.In this paper,the single-phase rectifier circuit is taken as the research object,and a reactive power graphical method based on three-dimensional Lissajous curve is proposed.The reactive power calculation is discussed by establishing the model of phase-controlled rectifier circuit with back EMF load,uncontrolled or phase controlled rectifier circuit with LC filter load.Firstly,the development history of reactive power theory is introduced,the current mainstream schools of reactive power theory are summarized,the advantages and disadvantages of each theory are pointed out,and the importance and urgency of research and improvement of reactive power theory are indicated.Secondly,the transmission mechanism of energy in the circuit is analyzed from the point of view of Poynting vector.A new concept of pseudo-reactive power is proposed.In addition,a new method of drawing three-dimensional Lissajous curve by grid side voltage,current and flux is presented.This method can be used to calculate active and reactive power.Then,the active power and reactive power of single-phase rectifier circuit with back EMF load are analyzed in detail by three-dimensional graphic method.The fundamental reactive power can be obtained indirectly by calculating the area of the two-dimensional u-i curve from the projection of the three-dimensional diagram.The active power can be obtained indirectly by calculating the area around two-dimensional ?-i projection curve.For single-phase rectifier circuits with simple load topology,the two-dimensional projection curves drawn by graphical method are usually regular graphics.Reactive power can be obtained by simply calculating its area.Then,the graphic method is applied to the single-phase uncontrolled or phase-controlled rectifier circuit with LC filter.This load model contains inductance and capacitance,which increases the complexity of the grid side current expression.Therefore,this paper uses the MATLAB/Simulink toolbox to simulate the circuit,directly sample the current signal,and then draw the three-dimensional Lissajous curve to calculate the active and reactive power.However,the two-dimensional projection curves drawn from this model are mostly irregular,so the area of the projection curves can be measured by using the coordinate method in cadastral surveying.In practical engineering,the load parameters of the circuit are often complex and changeable.This graphic method can effectively reduce the difficulty of reactive power measurement.Finally,the results obtained by the graphical method are compared with those obtained by the current power theory to verify the correctness and feasibility of the power graphical method.The analysis results show that the three-dimensional graphical method of reactive power proposed in this paper is simple,intuitive,easy to measure and calculate,and has good real-time performance,which can provide reference for reactive power compensation work.