## 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, ...

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