Impedance Analysis of Voltage Source Converter Based on Voltage Modulated Matrix

The phase-locked loop (PLL) is essential for accurate power control of grid following voltage source converter (VSC). However, the adoption of PLL will introduce a negative resistance in the VSC, which might jeopardize the stability when it is connected to a weak grid. Thus, the voltage modulated matrix is proposed to avoid using PLL. Nevertheless, the effect of voltage modulated matrix on the impedance of VSC is ignored. In this paper, the mathematical derivation of voltage modulated matrix is presented and it is first revealed that the essence of voltage modulated matrix is equal to an open-loop arctan-PLL. Then, the small-signal model of the arctan-PLL is established, which can be considered as a conventional PLL with infinite bandwidth. Hence, the frequency coupling phenomenon is more serious by using a voltage modulated matrix, which is verified by the frequency scan in Matlab/Simulink. Furthermore, the stability of VSC under a weak grid has even deteriorated by using the voltage modulation matrix since it has no filtering ability, which has also been validated by the Generalized Nyquist Criterion and simulation results.

I. Introduction

In recent decades, the voltage source converter (VSC) is widely used in renewable energy generation systems [1]. The synchronization block is essential for the power control of VSC. Conventionally, the phase-locked loop is applied for acquiring the orientation angle of VSC. However, a lot of research has proved that the PLL will introduce a negative resistance to the VSC which will deteriorate the stability when the VSC is connected to a weak grid [2] –[4]. Thus, some works are aimed to control the VSC without PLL. In [5] –[7], the voltage modulated matrix is proposed to replace the PLL and avoid the instability issue caused by the PLL. In [8] –[11], a virtual synchronous frame is employed for substituting the PLL and a voltage matrix in the synchronous dq frame is necessary for the voltage modulation. Generally speaking, these two methods are essentially the same, which are both based on the grid voltage modulated matrix. However, it should be noted that just the conventional PLL is not used in these methods, the grid voltage is still necessary for the power or current control. Furthermore, the stability performance and the impedance characteristic of VSC based on voltage modulated matrix are not depicted in these papers. It is difficult to say whether the stability under a weak grid is improved or not. Thus, in this paper, the relationship between the voltage modulation matrix and the conventional PLL is revealed. It is proved that the voltage modulation matrix is essentially an open-loop PLL with infinite bandwidth by using impedance analysis.