Increasing deployment of renewable energy resources for power generation has been playing a pivotal role in reducing carbon emissions associated with electrical power systems. Distributed Energy Systems (DES) enable the integration of small-scale renewable energy resources and storage technologies within low-voltage (LV) distribution networks, which supply power to residential and commercial consumers. Care must be taken when designing these systems, as they could potentially impair the operation and infrastructure of existing power networks. While nonlinear balanced optimal power flow formulations have historically been incorporated into oversimplified Mixed-Integer Linear Programming (MILP) DES design models, these do not accurately model the distribution networks to which most DES are connected. Low-voltage radial distribution networks are most closely represented by nonconvex multi-phase formulations, which are computationally complex and difficult to solve. The exclusion of these constraints within DES design models could, however, lead to infeasible designs, i.e., designs which are incompatible with the existing network and its operations. This study proposes a novel optimisation algorithm, capable of solving the large-scale and combined problem of designing DES with multiphase optimal power flow. A large-scale Nonlinear Programming (NLP) model with full power flow constraints and reformulated complementarity constraints for DES operation is used to find a feasible upper bound, if the lower bound proposed by the MILP for DES design is infeasible. The algorithm is tested using a residential case study based on a section of the IEEE EU LV network. Results for this case study show that the proposed algorithm finds a feasible DES design and operational schedule by installing three times the battery capacity initially recommended by the MILP. The MILP design remains infeasible with respect to the multiphase power flow constraints. This framework could be used to support the increase of local renewable energy generation and consumption, and the subsequent reduction of carbon intensity in existing power networks.