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2.3 CLASSICAL STATE ESTIMATION PROCEDURE

Оглавление

Traditionally, problem is simplified by ignoring inequality constraints (2.3) and then solving the system of nonlinear equations constituted by the first‐order optimality conditions of, i.e.

(2.8)

(2.9)

or

(2.10)

(2.11)

where W is a m × m diagonal matrix of the measurement weights wi, F = ∇xf (x) is the p × n equality constraint Jacobian, and λ is the p × 1 Lagrangian multiplier vector associated with equality constraints (2.2).

The nonlinear system of Eqs. can be solved by Newton through the iteration below:

(2.12)

where Δ z(ν) = zh (x(ν)).

The linear system of Eqs. (2.12) is iteratively solved until Δ x is sufficiently small. Further details can be found in [7].

It should be noted that the solution approach based on (2.12) was developed at the time that no efficient mathematical programming solvers (in terms of accuracy, required computing time, and sparsity treatment) were available. However, such solvers are nowadays available.

Advances in Electric Power and Energy

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