# Distribution System Expansion Planning

## Abstract

The widespread growth of distributed generation (DG), mainly due to its numerous operational and planning benefits and to the penetration of renewable energy, inevitably requires the inclusion of this kind of generation in distribution planning models. This chapter addresses the multistage expansion planning problem of a distribution system where investments in the distribution network and in DG are jointly considered. The optimal expansion plan identifies the best alternative, location, and installation time for the candidate assets. The incorporation of DG in distribution system expansion planning drastically increases the complexity of the optimization process. In order to shed light on the modeling difficulties associated with the co-optimized planning problem, a deterministic model is presented first. The model is driven by the minimization of the net present value of the total cost including the costs related to investment, maintenance, production, losses, and unserved energy. As a relevant feature, radiality conditions are specifically tailored to accommodate the presence of DG in order to avoid the islanding of distributed generators and the issues associated with transfer nodes. Since a large portion of DG relies on non-dispatchable renewable-based technologies, the uncertainty associated with the high variability of the corresponding energy sources needs to be properly characterized in the planning models. Based on the previous deterministic model, uncertainty is incorporated using a stochastic programming framework. Within such a context, the uncertainty featured by renewable-based generation and demand is characterized through a set of scenarios that explicitly capture the correlation between uncertainty sources. The resulting stochastic program is driven by the minimization of the total expected cost. Both deterministic and stochastic optimization problems are formulated as mixed-integer linear programs for which finite convergence to optimality is guaranteed and efficient off-the-shelf software is available. Numerical results illustrate the effective performance of the approaches presented in this chapter.

## Keywords

Distributed generation Distribution system planning Multistage Network expansion Stochastic programming Uncertainty## References

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