The predictor is used to produce an estimate for the next solution. The better the
prediction, the faster is the convergence to the solution point.

| (5.8) |

The matrix on the left-hand side is simply the standard power ﬂow Jacobian with an additional column and row added. The extra column is simply the negative of the power transfer vector and the extra row, required to make the system non-singular and deﬁne the magnitude of , is the derivative of the the parameterization function at the previous solution point .

The resulting tangent vector is then normalized

| (5.9) |

and used to compute the predicted approximation to the next solution using

| (5.10) |

where is the continuation step size.