Polar-Frame-Based Admittance Modeling And Small-Signal Stability Analysis For Grid-Connected Converter System

Due to the depletion of fossil energy and the aggravation of environmental pollution,the development of renewable energy resources has become a trend.Generally,renewable energy resources devices are connected to power grid by power electronic devices.The controllers of power electronic devices show the features of multiple timescale,and their dynamic characteristics are different from synchronous machines.With the ever-increasing penetration of power electronic devices,the ac grids become weaker and weaker,which poses great challenges to the stable operations of VSC-dominated power systems.To tackle such challenges,this paper proposes a polarframe admittance model for grid-connected voltage-source converters(VSCs)system.Based on polar-frame admittance models,the grid-connected VSC system can be modelled as a single-input single-output system.By this way,the small-signal stability of the grid-connected VSC system can be quantitatively analyzed.The main contributions are summarized as follows:1)The port characteristic equations of VSCs and power grids are derived in this paper.On this basis,the polar-frame admittance models for VSCs and grids are proposed.In particular,the admittance matrices have a special structure – namely,offdiagonal elements are the opposite of each other.Based on the special structure of admittance matrices,the primal-dual complex circuit of grid-connected VSC system is proposed.It is noteworthy that the system's resonance can be explained as the series resonance of the primal-dual complex circuit.Further,based on polar-frame admittance models,the equivalent single-input single-output model of the grid-connected VSC system is established,and the closed-loop characteristic equation of the system is derived.In particular,the output currents and power factors of VSCs can be explicitly expressed in the closed-loop characteristic equation.The influence of VSC's operating point on stability can be intuitively analyzed by closed-loop characteristic equations.2)The proposed SISO model enables to analyze the stability and assess the stability margin(i.e.,gain margin and phase margin)under varying power factors by simply using the well-known Nyquist Criterion.With the analytical expression of the gain margin,we demonstrate that the VSC's current output is in inverse proportion to the system's gain margin.This finding clearly explains the reason why increasing the VSC's current output will deteriorate the system's small-signal stability,especially in weak grids.And the analytical expression of the current output limit constrained by small-signal stability is derived to assess the admissible current output.Moreover,the influence of power factor on stability is analyzed.Through the equivalence of the closed-loop characteristic equation,it is shown that a change of the power factor can be equivalent to a change of the grid's impedance,when the dynamic of low-pass filter of voltage feedforward is ignored.In addition,we analytically evaluate the influences of the VSC control parameters on the stability of the grid-connected VSC by employing the stability margin.Simulations based on MATLAB/Simulink and RT-LAB hardwarein-the-loop platform verify the validity of the polar admittance model and analysis.