Question about A matrix in eigenvalue analysis #438
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@shebuxin Hello Buxin, In the control theory, it is common to describe a system in the below formulation (1): In And A matrix is calculated in equation (3): How to understand these two formats? Are they the same thing? Regards, |
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To my understanding, a system in the steady state is an autonomous system that can be described as below (1): We can compute the Jacobian matrices of the system below (2): $$ Here, Please correct me if I misunderstood anything. @shebuxin Regards, |
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Hello, Jinning, Based on my understanding, equation (1) describes an ODE system with For system (1), Jocobian matrix is If we build up EMT model of power system, the newtwork side phasor power flow will be replaced by DE, then it is possible to represent power system by ODE. |
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Hello, Jinning,
Based on my understanding, equation (1) describes an ODE system with$\dot{x}$ and $y$ being explictly expressed by state variables, while for power flow equations (phasor model) in power system, they are implicty related to state variables $x$ . Hence, we may have DAE system described in equation (2).
For system (1), Jocobian matrix is$A$ ; and for system (2), Jicobian matrix is expressed in (3).
If we build up EMT model of power system, the newtwork side phasor power flow will be replaced by DE, then it is possible to represent power system by ODE.