Power System Small Signal Stability Analysis and Control

5.3 Computation of initial conditions of the state variables

The initial conditions of the state variables for the model are computed systematically by solving the standard load-flow equations of the network, first, and then computing the other algebraic and state variables. The load-flow equations are part of the network equations, as shown in the succeeding text.

• Load-flow formulation:

The standard load flow is computed on the basis of constant PQ loads and has been the traditional mechanism for computing a proposed steady-state operating point.

The net power injected at a bus is defined as

$\begin{array}{c}{P}_i\left({\delta }_i,I_{d_i},I_{q_i},V_i,{\theta }_i\right)+j{Q}_i({\delta }_i,I_{d_i},I_{q_i},V_i,{\theta }_i=\\ \left(P_{{\mathrm{G}}_i}+P_{{\mathrm{L}}_i}\left(V_i\right)\right)+j\left(Q_{{\mathrm{G}}_i}+Q_{{\mathrm{L}}_i}\left(V_i\right)\right),\mathrm{for}i=1,2,\dots ,m.\end{array}$

  (5.88)

Thus, the real and reactive power-balance equations at the buses 1, ...