基于时变幅频“相量”序列的交流电力系统电感元件端口电流及功率分析

Analysis of Inductor Current and Power in AC Power System Based on Time-varying Amplitude-frequency Phasors Sequence

在实际交流系统中,伴随励磁及转子转速的变化,各台发电机内电势节点的幅值/频率为时变量。相量法作为分析正弦稳态电路的经典方法,已在电力系统分析中得到广泛的应用。该文针对交流输电线中的电感元件,根据其各相电压/电流瞬时值之间的时域积分关系,首先得到输电线端口的有功/无功功率与内电势幅值/频率状态之间的无穷项级数原始数学关系,进而基于该原始关系,提出时变幅频“相量”序列的新概念,对端口电流及功率的形成机制与影响因素进行分析和探讨。所提出的新概念可以把传统正弦稳态电路分析的相量法拓展至交流电力系统的动态过程,同时,利用“相量图”的几何化描述手段。该方法也为工程上简化与利用交流输电线端口功率与内电势的原始数学关系提供了一定参考。最后时域仿真验证了方法及结论的有效性。

With the changes of excitation and rotor speed,the amplitude/frequency of internal voltage in each generator is time-varying in the AC power system.The phasor method has been a classical method to analyze the sinusoidal steady-state circuits and has been widely used in power system analysis.First,with the integral relationship for the inductor between the instantaneous values in each phase,this paper describes the original series relationship composed of infinite terms between the power and the amplitude/frequency states of internal voltage for the transmission line.Then,the time-varying amplitude-frequency phasors sequence concept is proposed to analyze the formation mechanism and the influencing factors of the current and active/reactive power on inductor.The proposed new concept extends the phasor method of traditional sinusoidal steady-state circuit analysis to the dynamic process of AC power systems,and also uses the geometric description means of"phasor diagram".This method could also provide a reference in engineering for simplifying and using the original relationship between the terminal power and the states of internal voltage for the AC transmission line.Finally,the rationality of the method and conclusion can be verified by simulation.