Research On Stability Analysis And Parameter Design Of Grid-Connected Converter Using Stationary Reference Frame Model Under Weak Grid Conditions

Grid-connected converter is the interface between the power grid and renewable energy generation system,such as solar power,wind power,hydropower,and the power grid.It is used to transmit stable and efficient power produced by the renewable energy into the grid.The power grid is weak,since the renewable energy sources are usually located far away from the consuming centers.The weak grid would affect the dynamic responses of the grid-connected converter.Under weak grid conditions,the current loop,the phase-locked loop(PLL)will be coupled together through the grid impedance.Hence,the grid-connected converter with sufficient stability margin in strong grid might suffer from performance decline,or even be unstable in weak grid.The ??-domain current control is widely used for the grid-connected converters,thus the small-signal model of the grid system is derived in the stationary reference frame in this paper.Furthermore,the stability analysis method based on the impedance model,the influence of the implement methods of the controller on the stability of the converter,and the optimization design method for the controllers are discussed in this paper.With and without considering the sideband components,the small-siganl model of the converter would be different.In this paper,the sideband components are considered.Considering the complex modeling process and the different control strategies of the converter,the grid system is divided into three parts,i.e.the current loops,the PLL and the grid impedance.With harmonic linerazaiton method,the small-signal models of the grid current loops with ??-and dq-domain current control are derived first.Then,the small-signal model of SRF-PLL(Synchronous Reference Frame Phase-Locked Loop)and DSOGI-FLL(Dual Second Order Generalized Integrator Frequency-Locked Loop)are given.Finally,the small signal model of the grid system in the stationary reference frame are obtained based on the relationships between the terminals of the three parts.The accuracy of the model is verified by numericall simulations.Based on the small signal model of the grid system,it can be observed that the sideband components can affect system dynamic performance through the PLL and the grid impedance.The influence of the sideband conponents on the dynamic performance of the converter and the stability criterion are discussed.First,for different bandwidths of the PLL and grid strengths,the influence of the sideband components on the dynamic performance of the converter are discussed.With the faster PLL and the weaker grid,the influence of the sideband components is more serious.Then,the stability criterion based on the sequence impedances without considering the influence of the sideband conponents is introduced,and the accuracy of the criterion for different bandwidths of the PLL and grid strengths is dissucessed.It can be obtained that the criterion is not conservative,and with the faster bandwidth of the PLL,the probability of misjudgment would be arised if using the criterion for stability analysis.Simulations and experiment results the correctness of theoretical analysis.As the grid frequency would change within a certain range,the PR controllers with fixed resonant frequency cannot meet the design requirements,hence the frequency adaptive PR(Proportional-Resonant)controllers are widely used nowadays.The resonant frequency of the adaptive PR controller is provided by the PLL,and it can track the grid frequency.First,the small signal model of the controller with different implement methods are derived using harmonic linearzation method.Then,for the converters with SRF-PLL or DSOGI-FLL,the influence of the implementation methods on the stability of the converter under weak grid conditions are discussed.It is shown that: if SRF-PLL is used,the stabilities of the converter with different implementation methods would be different;if DSOGI-FLL is used,the stabilities of the converter with different implementation methods would be almost the same;DSOGI-FLL is better for supplying the resonance frequency of the adaptive PR controller.The concutions are verified by experiment results.As the use of the SiC,GaN components,the switching frequencies of the grid converters are deigned higher and higher,and the current loops are designed faster and faster.In this paper,the relationship between the bandwidths of the PLL and the current loop is discussed.It is pointed out that the current loop and the PLL are coupled in weak grids,and the bandwidth of the PLL can not be increased linearly with the increasing of the bandwidth of the current loop.This paper proposes an optimization design method for the controllers of the converter with dqdomain current control under weak grid conditions,i.e.the current controller is designed separately and the PLL controller is designed considering the coupling between the current loop and the PLL.Using the proposed method,the PLL can be designed fast and the converter would have adequate stability margin under weak grid conditions.The method is extended to the design of the grid-connected converter with ??-domain current control.Simulations and experimental results verify the correctness of the theoretical analysis and the validity of the proposed method.