Alternative solutions to network reinforcement are now being investigated in distribution network planning studies to reduce the costs and periods for integrating renewable energy sources. However, a thorough techno-economic analysis of these solutions requires a large number of multi-period load-flow calculations, which makes it hard to implement in planning tools. A non-intrusive approximation method is therefore proposed to obtain fast and accurate multi-period load-flows. This method builds a surrogate model of the load-flow solver using polynomial regression and kriging, combined with Latin hypercube sampling. Case studies based on real distribution networks show that the proposed method is more efficient for distribution network planning in presence of renewable energy sources than time subsampling and, in some cases, voltage linearization. In particular, accurate 10-minute profiles of voltages, currents, and network power losses are obtained in a satisfactory computation time.