Study Of Active And Reactive Power Under Time-varying Amplitude-Frequency Signals In Dynamic Process Of AC Power System

In the actual dynamic process of power system,the amplitude and frequency of the internal voltage in each generator are time-varying due to the changes of excitation and the speed of rotor.The relationship between the output power of each generator and the states of each internal voltage in power system is the key factor to determine the dynamic process.The active/reactive power are also important electrical quantities concerned by the system operators.Thus,it is of great significance to study the active and reactive power in the dynamic process.To begin with,this paper reviews the research status of the power.Then it finds that the current researches were almost aimed at the steady-state AC power system.Firstly,in terms of the cognition and description of the physical concept of active/reactive power,the existing circuit power theories almost focused on the cases of periodic systems,including the current instantaneous reactive power theory still uses Fourier series to represent the instantaneous values of the voltage/current in each phase when analyzing the power characteristics and the power physical phenomena.The dynamic process of AC power system in which the amplitude/frequency of voltage/current can change arbitrarily with time has not been discussed yet.Secondly,in the aspect of power system analysis,most of the existing studies established the relationship with the terminal power of AC transmission line via describing the internal voltage based on the phasor.However,the phasor is strictly the method for the sinusoidal steady-state circuit analysis.Therefore,this paper focused on the dynamic process of power system and used the instantaneous amplitude/instantaneous frequency to describe the three-phase AC electrical quantities,and then explained the physical concepts and the mathematical descriptions of the active/reactive power in the dynamic process of three-phase symmetrical AC power system under concepts of the time-varying amplitude-frequency signals.Besides,the relationship between the active/reactive power of the terminals of the AC transmission line and the amplitude/frequency states of the internal voltages was studied by this paper.The specific contents include the following aspects:(1)Basic characteristics of three-phase AC electrical quantity which is corresponding to the time-varying amplitude-frequency signals in the dynamic process of power system was expounded and revealed.It also gave the analytical expressions of each AC value and the corresponding geometric description on the complex plane.Firstly,the formation principles of the internal voltages in the synchronous generator and the direct drive fan were introduced.Secondly,based on the time-varying amplitude-frequency internal voltage,this paper expounds the basic characteristics of the three-phase AC voltages and currents corresponding to the time-varying amplitude-frequency signals in the dynamic process.And thirdly,this paper focuses on the dynamic process of three-phase symmetrical AC power system and gives the basic expressions of the three-phase AC voltage/current under the time-varying amplitude-frequency signals which are based on the instantaneous amplitude/frequency.(2)The decomposition method of the three-phase AC current was discussed under the time-varying amplitude-frequency signals according to the basic physical meaning of the active/reactive power in the three-phase AC power system.Then,the mathematical expressions of the active/reactive current and the active/reactive components of the instantaneous power in each phase were obtained.And the physical concepts of active/reactive power during the dynamic process was proposed.Besides,the calculation formulas of the three-phase active/reactive power were deduced based on the space rotation vectors,the three-phase rotating phasors and the three-phase AC instantaneous values.The formulas have very clear physical significances,which is suitable for the analysis of the dynamic process when the amplitude/frequency of the voltage/current can vary with time arbitrarily.The formulas and explanation can also be consistent with the physical concepts of active/reactive power described in the traditional sinusoidal steady-state three-phase AC system.(3)Based on the explanation and mathematical descriptions of the active/reactive power,the original mathematical relationship between the terminal power and the internal voltage of AC transmission line in the dynamic process was characterized when exciting with the time-varying amplitude-frequency internal voltage.Owing to the original relationship could completely reflect the influence of the amplitude and the frequency of each internal voltage on the power change of each terminal in power system,and thus,the establishment of the original relationship will provide a theoretical basis for understanding the dynamic behaviors of the complex power system.Besides,based on the original mathematical relationship,it is found that the original dynamic response of the current and the active/reactive power of each terminal of the inductive line in the dynamic process,is actually corresponding to the series which are composed of infinite terms.(4)Based on the original mathematical relationship,the research perspective of the time-varying amplitude-frequency "phasor" sequence was proposed.Thus the formation mechanism and the influencing factors of the original dynamic response of the inductive line in the dynamic process were analyzed and discussed.This perspective draws on and expands the phasor method of sinusoidal steady-state circuit analysis in the past.It establishes the corresponding relationship between the integral relationship of the instantaneous values of voltage/current of each phase with the "phasor complex operation" of the time-varying amplitude/frequency.And then,it also explains the integral relationship between the instantaneous values of the voltage/current in the form of "phasor diagram" geometrically.Besides,the proposed research perspective could provide some theoretical references for the further simplifying and the using of the original mathematical relationship.(5)Based on the understanding of the original relationship from the perspective of time-varying amplitude-frequency "phasor" sequence,by simplifying the original current responses of the inductive line,then a simplified relationship was established in the two-node system for the study of electromechanical time scale dynamic process.The simplified relationship can reflect the influence of the changes of the amplitude and the frequency of each internal voltage on the terminal power changes of the line.Thus,the simplified relationship will not be bound by the "quasi steady state" assumption.At the same time,the mathematical form is quite simple,which will be convenient for the engineers to grasp the power transmission characteristics of the AC transmission line in the dynamic process.Finally,by comparing the time-domain simulation results with the original power dynamics and the power angle relationship under the traditional "quasi steady state" assumption which is based on the phasor,the effectiveness of the simplified relationship proposed in this chapter were verified.