The integration of Distributed Energy Resources (DERs) in distribution networks comes with challenges, like power quality concerns, but also opens up new opportunities, e.g., DERs can offer competitive energy prices for final users by leveraging time arbitrage. A suitable method to fully exploit such opportunities is to compute the optimal DER schedule, either with a full three-phase network model or a more computationally efficient single-line equivalent. This paper presents under which conditions a single-line equivalent can and cannot be used to properly represent a modern and unbalanced power distribution network able to dispatch high levels of DER integration optimally. Results show that single-line equivalents might be helpful when the problem objective function limits counterflows, for example, when minimizing active power losses. Moreover, single-line equivalents might be helpful for low levels of DER integration. However, enabling single-line equivalents results in a lower hosting capacity for high levels of DER integration.

The increase of solar photovoltaic penetration poses several challenges for distribution network operation, mainly because such high penetration might cause reliability problems like protection malfunctioning, accelerated decay of voltage regulators and voltage violations. Existing solutions based on mathematical programming solve a 3-phase ACOPF to optimally exploit the available energy, however, this might increase all reliability problems above if done carelessly. As a solution to optimally exploit DERs (like local photovoltaic and storage systems) without compromising the network reliability, this paper presents a novel algorithm to solve the 3-phase ACOPF as a sequence of convex Quadratically Constrained Quadratic Programs. Results show that this solution has a lower voltage unbalance and computation time than its non-linear counterpart, furthermore, it converges to a primal feasible point for the non-linear formulation without major sacrifices on optimal DER active power injections.