This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of t...This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of the Jacobian matrix and the structure of the boundary of the DA, it is found the DA of the state-reduction model and that of the full model of a power system are topological isomorphism. There are one-to-one correspondence relationships between the number of equilibrium points, the type of equilibrium points, and solutions of the two system models. Based on these findings, an expanding interior algorithm is proposed with SOS programming to estimate the DA of the state-reduction model. State trajectories of the full model can be transformed to those of the state-reduction model by orthogonal or equiradius projection. In this way, CCT of a grid fault is estimated with the DA of the state-reduction model. The calculational burden of SOS programming in the DA estimation using the state-reduction model is rather small compared with using the full model. Simulation results show the proposed expanding interior algorithm is able to provide a tight estimation of DA of power systems with higher accuracy and lower time costs.展开更多
基金supported in part by Science and Technology Projects in Guangzhou under Grant No.202102020221Young Elite Scientists Sponsorship Program by CSEE under Grant No.CSEE-YESS-2018007State Key Program of National Natural Science Foundation of China under Grant No.U1866210.
文摘This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of the Jacobian matrix and the structure of the boundary of the DA, it is found the DA of the state-reduction model and that of the full model of a power system are topological isomorphism. There are one-to-one correspondence relationships between the number of equilibrium points, the type of equilibrium points, and solutions of the two system models. Based on these findings, an expanding interior algorithm is proposed with SOS programming to estimate the DA of the state-reduction model. State trajectories of the full model can be transformed to those of the state-reduction model by orthogonal or equiradius projection. In this way, CCT of a grid fault is estimated with the DA of the state-reduction model. The calculational burden of SOS programming in the DA estimation using the state-reduction model is rather small compared with using the full model. Simulation results show the proposed expanding interior algorithm is able to provide a tight estimation of DA of power systems with higher accuracy and lower time costs.
