  In this paper, the power flow solution of the two bus network is used to
analytically characterise maximum power transfer limits of distribution
networks, when subject to both thermal and voltage constraints. Traditional
analytic methods are shown to reach contradictory conclusions on the
suitability of reactive power for increasing power transfer. Therefore, a more
rigorous analysis is undertaken, yielding two solutions, both fully
characterised by losses. The first is the well-known thermal limit. The second
we define as the `marginal loss-induced maximum power transfer limit'. This is
a point at which the marginal increases in losses are greater than increases in
generated power. The solution is parametrised in terms of the ratio of
resistive to reactive impedance, and yields the reactive power required. The
accuracy and existence of these solutions are investigated using the IEEE 34
bus distribution test feeder, and show good agreement with the two bus
approximation. The work has implications for the analysis of reactive power
interventions in distribution networks, and for the optimal sizing of
distributed generation.
