Power System Small Signal Parametric Stability Analysis Based On Value Set Approach

The development of interconnected power systems is making the network structure increasingly complex,producing small-signal stability problems,such as low-frequency oscillations and subsynchronous oscillations,that threaten the stability of large-scale power systems.Changes in operating conditions and network configuration adds more complications to the oscillation.By analyzing the impact of uncertainty,measures can be taken accordingly to improve the damping,while insights are gained into power system operations and planning.The current parametric stability analysis literature falls short in unravelling the impact of each parameter on system stability in large-scale power systems.In this dissertation,we probe into the impact of uncertainty on large-scale power system stability based on the value set approach.The proposed method translates the robust stability of the uncertain system into two-dimensional sets in the complex plane,which makes the parameters' impacts transparent.The method applies to robust D-stability analysis,and can analyze robust stability of the modes that are not close to the imaginary axis.In addition,the value set approach enjoys advantages of fast computational speed,low conservativeness,and simplicity,and can check robust stability over a wide frequency range for a large number of parameters.The main contributions of this dissertation are as follows.1.Before the value set approach can be applied to large-scale power systems,we use a combination of methods that include uncertainty separation,dimension reduction,modal truncation,and diagonal expansion formula for matrix determinants to obtain the parametric characteristic polynomial.Based on the uncertainty structure of the characteristic polynomial,the edge theorem and the mapping theorem are used to generate the value set plot,and the parametric stability is analyzed according to the zero exclusion theorem.During the value set construction,the logarithmic scale and the denominator polynomial are used to reduce the magnitude of the value set.Parallel computation and semi-symbolic computation are also used to speed up the value set construction and reduce memory usage.2.The finite frequency test is used so that the value set plot can be generated automatically.It dispenses with the need for a trial-and-error frequency sweep,and avoids the possibility of missing instability frequencies.By taking advantage of the value set geometry,the combinatorial explosion of value set construction is overcome so that a large number of parameters can be analyzed.The parametric stability margins are calculated over the frequency range of interest,where the parametric distances from the nominal condition to instability are quantified.The advantages of the above methods derive from the affine uncertainty of the characteristic polynomial.For large-scale power systems like North China system,we explain that the characteristic polynomial can usually be approximated with affine uncertainty when the dominant modes are not highly sensitive to the parameters we study..3.The value set approach is used for robust stability analysis of the low-frequency oscillation in North China system and the ultra-low-frequency oscillation in Yunnan power grid.Eigenvalue analysis and simulations are performed to verify the results of the value set approach.The errors arising from model reduction and characteristic polynomial approximation are analyzed.The uniform-frequency model for ultra-low-frequency oscillation is derived from the Phillips-Heffron model,based on which the ultra-low-frequency oscillation of Yunnan power grid is analyzed.Effects of hydraulic turbine parameter coefficients on the stability are analyzed,and parameters of hydropower governors are optimized.4.The value set approach is compared with related works in terms of theory,parametric stability analysis,computational complexity,conservativeness,so that insights are gained into the problem of parametric uncertainty.The methods in comparison include:the Kharitonov theorem that has been applied in the robust design of power system controller parameters,the recently proposed sign decomposition approach that shows promise in robust stability analysis of the polynomial family whose coefficients are polynomial functions of the parameters of interest,and the well-known structured singular value techniques.The comparison shows the advantages and disadvantages of each method,and serves as a guide for researchers.