  Power systems face increasing challenges on reliable operations due to the
widespread distributed generators (DGs), e.g., rooftop PV system in the low
voltage (LV) distribution grids. Characterizing the hosting capacity (HC) is
vital for assessing the total amount of distributed generations that a grid can
hold before upgrading. For analyzing HC, some methods conduct extensive
simulations, lacking theoretical guarantees and can time-consuming. Therefore,
there are also methods employing optimization over all necessary operation
constraints. But, the complexity and inherent non-convexity lead to non-optimal
solutions. To solve these problems, this paper provides a constructive model
for HC determination. Based on geometrically obtained globally optimal HC, we
construct HC solutions sequentially according to realistic constraints, so that
we can obtain optimal solution even with non-convex model. For practical
adaption, we also consider three-phase unbalance condition and parallel
computation to speed-up. We validated our method by extensive numerical results
on IEEE standard systems, such as 8-bus and 123-bus radial distribution grids,
where the global optimums are obtained and performance illustrations are
demonstrated.
