Judgment and application of Hessian matrix positive definiteness for multi-machine system Hamiltonian realization

The positive definiteness judgment of Hessian matrix of Hamilton function is a sufficient condition to guarantee the system stability in the Lyapunov sense for the generalized Hamiltonian realization of the traditional power system。However,the Hessian matrices of complex power system are usually high-dimension blocked matrices and the judgments of positive definiteness are very difficult。The general method to judge the positive definiteness of high-order blocked matrix is derived based on the idea of quadratic form and block diagonal dominance,and it can be realized by using the characteristics of the blocked rows or columns of matrix and blocked matrix theory。The calculating process will be simpler,and it greatly reduces the amount of calculations。At the same time,it will be conducive to the research and design of the control by means of the transient energy function method of power system,and the positive definiteness of Hessian matrix at the equilibrium point is judged by the above methods。The simulation example is given for four-machine system to prove the accuracy of the criterion and the effectiveness of the control strategy,which simplifies the judgment process of the positive definiteness of Hessian matrix of generalized Hamiltonian realization。