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5.2 Predictor

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. Matpower uses a tangent predictor for estimating the curve to the next solution. The tangent vector j [ ] T z = dx d λ j at the current solution j j (x ,λ ) is found by solving the linear system

[ ] [ ] fx fλ j 0 pj−1 pj−1 z = 1 . x λ
(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 fλ is simply the negative of the power transfer vector b and the extra row, required to make the system non-singular and define the magnitude of j z , is the derivative of the the parameterization function at the previous solution point pj− 1 .

The resulting tangent vector is then normalized

j -zj--- z¯ = ||zj||2
(5.9)

and used to compute the predicted approximation (ˆxj+1,ˆλj+1) to the next solution (xj+1,λj+1) using

[ ˆxj+1 ] [ j ] j+1 = xj + σj¯zj, ˆλ λ
(5.10)

where j σ is the continuation step size.

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