#### The Value of Reactive Power for Voltage Control in Lossy Networks

##### Matthew Deakin, Thomas Morstyn, Dimitra Apostolopoulou, Malcolm McCulloch

Reactive power has been proposed as a method of voltage control for distribution networks, providing a means of increasing the amount of energy transferred from distributed generators to the bulk transmission network. The value of reactive power can therefore be measured according to an increase in transferred energy, where the transferred energy is defined as the total generated energy, less the total network losses. If network losses are ignored, an error in the valuation of a given amount of reactive power will be observed (leading to reactive power provision being under- or over-valued). The non-linear analytic solution of a two-bus network is studied, and non-trivial upper and lower bounds are determined for this `valuation error'. The properties predicted by this two-bus network are demonstrated to hold on a three-phase unbalanced distribution test feeder with good accuracy. This allows for an analytic assessment of the importance of losses in the valuation of reactive power in arbitrary networks.

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