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Applied Optimization by Ross Baldick

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6

Case studies of non-linear simultaneous equations

In this chapter, we will develop two case studies of problems that involve the solution of non-linear simultaneous equations. Both case studies will involve circuits, but the non-linearities will arise in different ways. The case studies are:

(i)   the solution of Kirchhoff’s laws in a non-linear direct current (DC) circuit (Section 6.1), and

(ii)   the solution of Kirchhoff’s laws in a linear alternating current (AC) circuit where the variables of interest are not currents and voltages but instead are power (and “reactive power”) injections (Section 6.2).

The first case study will draw on the development from the linear circuit study described in Section 4.1 and we will not repeat in detail ...

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