Multimachine Systems. Integrating Individual Dynamic Models into a Global Model.
This post follows the method proposed in “Power System Stability and Control” by Prabha S. Kundur and Om P. Malik.
- The linearized model of each dynamic device is expressed in the following form :
- Where:
- \(\Delta x_i\) : perturbed values of the individual device state variables.
- \(\Delta i_i\) : perturbed value of the current injection into the network from the device.
- \(\Delta v_i\) : perturbed value of the network bus voltages.
- Such state equations for all the dynamic devices in the system may be combined into the form :
- Where :
- \(\Delta x\) : state vector of the complete system.
- \(A_D\) , \(B_D\) , \(C_D\) and \(D_D\) : block diagonal matrices composed of \(A_i\) , \(B_i\) , \(C_i\) and \(D_i\) matrices respectively, associated with the individual devices.
- The interconnecting transmission network is represented by the node equation : \(\Delta i = Y_N \Delta v\)
- The elements of \(Y_N\) include the effects of nonlinear static loads.
- Hence : \(C_D \Delta x + D_D \Delta v = Y_N \Delta v \rightarrow \Delta v = (Y_N - D_D)^{-1} C_D x \rightarrow \Delta \dot{x} = A_D x + B_D (Y_N - D_D)^{-1} C_D x = Ax\)