The previous chapters have considered how to achieve efficient short-run use of a set of generation and consumption resources in the absence of network constraints. As we will see, the issues become more complex and more interesting when we seek efficient use of generation and consumption resources in the presence of network constraints.

The first step in the process of introducing network constraints into our analysis is to show how the physical limits of the network can be represented as a set of equations known as constraint equations. These constraint equations, which define the technical capability of the network, depend on the net power injection at each node on the network. The first step in the process, therefore, is an understanding of how the physical limits of the electricity network can be expressed as a set of constraints on the net power injection at each node of the network.

In Part II of this book we discussed all of the elements of the power system – the transformers, the transmission lines, the switches and so on. It turns out that for the purposes of modelling the power flows on an AC network we can abstract away from much of that detail. In fact, it turns out that we can model an AC network as simply a collection of *nodes* (also called ‘buses’) and *links* between the nodes.

Figure 6.1 illustrates a number of different network configurations. The power flow on each network can be adequately ...

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