Low-Frequency Instability Induced by Hopf Bifurcation in a Single-Phase Converter Connected to Non-Ideal Power Grid

Abstract

With the high-density operation of China Railways High-speed (CRH) series vehicles in railways, a large number of power electronic converters are connected to the traction network. Due to the nonlinear characteristics of power electronic converter, it is easy to cause the low-frequency oscillation (LFO) in the single-phase vehicle-grid system of high-speed railways when the converter is connected to a non-ideal power grid. In order to solve this problem, the time domain nonlinear dynamic average model is proposed in this paper. Given Jacobian method to probe into the low-frequency stability of single-phase vehicle-grid system based on Hopf bifurcation, the characteristics and applicability of this method is summarized. The effects of electrical and control parameters can be analyzed with this model. In addition, with the emergence of LFO, the stability boundary leading to catastrophic bifurcation is discussed in detail. In the end, theoretical analysis results are verified by simulations and hardware-in-the-loop (HIL) platform. INDEX TERMS Single-phase vehicle-grid system, non-ideal power grid, low-frequency stability, time domain nonlinear dynamic average model, Hopf bifurcation, Jacobian method, HIL platform.

Stability-Margin-Oriented Key Parameter Design for Voltage-Source Rectifiers in Weak Power Grids With Inductive Impedance

“…the increase of the proportional gain of the dc-link voltage controller will reduce the stability of the system. This conclusion is consistent with the results given in [14], [15]. However, in the weak grid where multiple VSRs are connected, the system cannot obtain a stable operation by merely adjusting the proportional gain of the dc-link voltage controller, which has not been shown in [14]- [23].…”

“…According to the Routh Criterion, the condition under which GGM(s) is stable can be obtained as shown in (A5) in Appendix. According to (A5), the range of kpdc can be derived as shown in (14).…”

“…Fig. 9 shows the Nyquist plots of Zg(s)Yc(s) when choosing the proportional gain kpdc according to (14), where, the GM is 10dB (K=3). As shown, the system will have the designed GM, which verifies the effectiveness of the result in (14).…”

“…In a weak grid, the interaction between the VSR and the inductive grid impedance can jeopardize the stability of the dc-link voltage. As given in [14]- [16], the instability of the dc-link voltage in a weak grid has been revealed based on bifurcation theories. It has been found that the increase of the grid impedance or the proportional gain of the voltage controller is prone to destabilize the VSR, but the increase of the dc-link capacitor is beneficial for the stability of the VSR.…”

Modeling and analysis of nonlinear behavior for synchronous switching Z-source topology

“…The switching converter has a nonlinear variable structure control system. The on-off or off of the power switch tube makes the system switch periodically in different structures, which will lead to complex nonlinear behaviors of the switching converter, such as period doubling bifurcation [3] [4], Hopf bifurcation [5] [6], Flip bifurcation [7] [8], boundary collision bifurcation, and even chaos [9][10], subharmonic oscillation [11]. As a new type of converter, Z-source converter was first proposed by Professor Peng Fangzheng in 2002 [12].…”