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Applied Optimization by Ross Baldick

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8

Solution of the non-linear simultaneous equations case studies

In this chapter we will apply the techniques described in the last chapter to the non-linear direct current circuit in Section 8.1 and to the power flow problem in Section 8.2.

8.1 Analysis of a non-linear direct current circuit

In Section 6.1 we developed equations for the non-linear DC circuit illustrated in Figure 6.3, which is repeated in Figure 8.1. The equations describing this circuit were expressed in the form g(x) = 0. In Section 8.1.1 we will discuss the Jacobian of g for this problem, while in Sections 8.1.2 and 8.1.3 we discuss the initial guess and the calculation of successive Newton–Raphson iterates. In Section 8.1.4 we investigate the application of the chord and ...

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