用虚功平衡原理求解无损耗系统的主谐波

Solving the Main Harmonic of Lossless System Using the Reactive Power Balance Principle

摘要: 含耗能元件的非自治电路，自振分量的存在性取决于实功率能否保持平衡。具有激励源不含耗能元件的非自治电路是一个无损耗系统。自振与受迫两振荡分量无条件同时共存。激励源只输出虚功率，谐振回路不消耗任何实功率，谐振回路的储能每一瞬时都在变化，但经历一周期后其储能保持原值。根据虚功平衡条件可以求出自振频率与两个电压振幅值的关系，主谐波解不但与外激源有关，还与初始条件有关，本文以含有压控非线性电感的谐振电路为例，论证自激与受迫两振荡分量的非线性耦合能产生混沌。

Abstract:

In the nonautonomous circuit which contains the dissipative element, the existence of self excited oscillation depends upon whether or not active power can maintain balance. The nonautonomous circuit with excited source has no dissipative element. It is a lossless system. The forced and self-excited oscillation components can simultaneously coexist unconditionally. The excited source export only reactive power. The resonant circuit does not consume any active power. The energy stored in this resonant circuit varies at all time; but after a cycle, the energy stored maintains original quantity. The relation between self-oscillation frequency and two voltage amplitude of oscillation can be found from the condition for reactive power balance. The main harmonic solutions are relative to both excited source and the initial condition. Taking the resonant circuit which contains the voltage-controlled nonlinear inductor as example, this paper demonstrates that the chaos can be produced by nonlinear coupling of forced and self-excited oscillation components.