Research On The Power Margin Of Small Disturbance Stability In Power Systems

The small disturbance stability of power systems is affected due to the random variations of grid loads.The power margins of small disturbance stability under different load power increasing directions are also different.What is more concerned about are the most dangerous power increasing direction and the minimum power margin.Among the algorithms for the power margin of small disturbance stability in multi-machine systems,the existing direct solution methods are only suitable for calculating the power margin under a given increasing direction.There is no direct solution algorithm for the most dangerous power increasing direction and the minimum power margin.In static voltage stability analysis,the shortest path method has been successfully applied to solve the minimum power margin conveniently.This thesis attempts to apply the shortest path method to solve the minimum power margin of small disturbance stability directly.The main tasks are as follows.(1)According to the given damping ratio threshold,the dynamic performance boundary of small disturbance stability is formed.The boundary conditions under nonzero eigenvalues are analyzed.And the system feature equations including steady state equation,characteristic equation and damping ratio requirement are established.Onedimensional search is used to solve the critical point of small disturbance stability under a given power increasing direction.This point satisfies the feature equations.And the power margin from the initial operating point to the critical point is calculated.(2)It is very important to determine the specific expression of the normal vector on the dynamic performance boundary.This is the key to using the shortest path method to solve the most dangerous power increasing direction of small disturbance stability.The existence of the damping ratio threshold makes the state matrix non-singular.In addition,on the dynamic performance boundary,the real and imaginary parts of the eigenvalue corresponding to the minimum damping ratio are not zero.Since there are many complex numbers in the eigenvectors corresponding to the electromechanical oscillation modes,all calculations must be done in the complex number domain.The difficulty of solving normal vectors is increased due to these features.The relationship between the normal vector on the boundary and the minimum power margin is analyzed.The composition method of the boundary normal vector is determined.By adding a virtual observation vector and according to the vertical relationship in the real vector space,the analytical expression of the power increasing direction suitable for calculating the minimum power margin of the small disturbance stability is derived.(3)Based on the analytical expression of the power increasing direction and the boundary characteristic equation,a general calculation model of the minimum power margin for small disturbance stability is constructed.By analyzing the advantages of the model,the alternate iteration method is selected to achieve a fast solution.Callculations are carried out on 8-machine 24-bus system and 16-machine 68-bus system respectively.The convergence process of the proposed algorithm is analyzed.Multiple sets of different power increasing directions are randomly generated for the two cases.The corresponding power margins are calculated and compared with the results obtained by the shortest path method to verify the effectiveness of the algorithm.