Construction And Evaluation Of Small Signal Stability Region In Different Parameter Spaces

It is a growing trend of power grid in China that expanding the scale of synchronous power grid by regional interconnection and promoting the large-scale development and consumption of new energy sources,which takes the advantage of economy and environmental friendliness,while it brings about the issues of system stability.Low frequency oscillation(LFO)and sub/super-synchronous oscillation(SSO/Sup SO)are potential threats to power system,which will seriously affect the operating safety and stablility of power system.Both of them belong to the issues of small signal stability.Compared with the "point-wise" method,which relies on numerical simulation under one given real-time condition or eigenvalues distribution to estimate stability,the "region" method has the advantage of online application and many other advantages.For example,it is helpful for dispatchers in assistant decision-making,and can intuitively identify the stability margin of the current operating point of the system,and it is conducive to the overall evaluation of the system and so on.Therefore,it is of great theoretical significance and practical value to provide an evaluation method for the prevention and control of LFO and SSO/Sup SO from the perspective of small signal stability region.The paper studies three aspects in depth,including the research of the limit boundary of small signal stability region affected by damping controllers parameters,the small signal stability analysis based on the equivalent dual-machine electromagnetic torque analysis method(ETA)and the construction of time-delay stability region,and the construction of dominant control parameter stability region of sub/super-synchronous oscillation based on Gerschgorin disk theorem.Firstly,in the background of LFO,damping controller is usually adopted for suppressing the low frequency oscillation.And considering the influence of variable damping controller parameters on the boundary of the small signal stability region in injection power space and the premise that the change of the equilibrium point affects the matching of the optimal controller parameters,the paper proposes a limit boundary search strategy for the small signal stability region based on rolling optimization.The strategy is verified on the 4-machine-2-area benchmark with multiple power system stabilizers(PSS).The validation results show that the small signal stability region boundary obtained by the multi-round rolling optimization strategy which continuously updates the optimal set of parameters and further updates the expected boundary points has more feasible space than those obtained by the existing methods.The proposed method helps to reduce the conservativeness of the stability region and further generates a positive effect on the transmission capacity of important transmission sections such as tie lines.Then,still aimed at LFO,the equivalent two-machine electromagnetic torque method is deduced in detail,of which the validity is verified by compared with the result of eigenvalue analysis method.On this basis,it is explored that the influence of the damping controller parameters and operation mode change on the electromagnetic torque coefficients and damping ratio.Furthermore,considering that the wide-area damping control brings about time delay due to suppressing the inter-area oscillation mode,the time-delay effect is modified into the equivalent two-machine electromagnetic torque method,and the analytical expression of electromagnetic torque coefficient and damping ratio related to time delay and controller parameters are established.On this basis,on the one hand,a small signal time-delay stability region is established when the controller parameters are fixed,which can be used to evaluate the system operation status;on the other hand,when the measured time-delay set is outside the stability region,an optimization strategy of the controller parameters is proposed to improve the stability of the time-delay system.The validity of the proposed method is verified on the 4-machine-2-area benchmark.Finally,in the background of SSO/Sup SO,it is analysed in detailed that the limitations of the existing methods about constructing the parameter stability region by utilizing the Gerschgorin disk theorem.On this basis,the paper proposes a new method of eigenvalue estimation by using state transition matrix,that is,the eigenvector matrix of state matrix is calculated once based on one initial set of the analyzed control parameters to form the transition matrix,and then the transition matrix is used to construct parameter stability region by adopting Gerschgorin disk theorem and Lyapunov stability theory and further considering the analytic relationship between the original state matrix elements and the dominant control parameters to be studied.Then,the proposed method is proved mathematically by the theory of matrix analysis.Meanwhile,the relevant strategy is put forward to reduce the conservativeness of the stability region.Furthermore,it is proposed that the stability margin evaluation index of the control parameters for the prevention and control of SSO/Sup SO,which contributes to providing guidance for the reasonable selection of the control parameters and online refreshing of the control parameters according to the current operation mode,so as to ensure the safety and stability of the high-proportion new energy-injected grid.The validity and correctness of the proposed method are verified by the model of Direct-Drive Permanent Magnet Synchronous Generator(D-PMSG)connected the main ac grid by Voltage Source Converter-based High Voltage Direct Current(VSC-HVDC).The efficiency of the proposed method is highlighted by comparing the proposed method and the point-wise eigenvalue calculation of the state matrix from a time-consuming perspective.