This paper addresses the multistage expansion planning problem of a distribution system where investments in the distribution network and in distributed generation are jointly considered. Network expansion comprises several alternatives for feeders and transformers. Analogously, the installation of distributed generation takes into account several alternatives for conventional and wind generators. Unlike what is customarily done, a set of candidate nodes for generator installation is considered. Thus, the optimal expansion plan identifies the best alternative, location, and installation time for the candidate assets. 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. The costs of energy losses are modeled by a piecewise linear approximation. As another distinctive feature, radiality conditions are specifically tailored to accommodate the presence of distributed generation in order to avoid the isolation of distributed generators and the issues associated with transfer nodes. The resulting optimization problem is a mixed-integer linear program for which finite convergence to optimality is guaranteed and efficient off-the-shelf software is available. Numerical results illustrate the effective performance of the proposed approach.

Energy storage systems (ESS) have adopted a new role with the increasing penetration of electric vehicles (EVs) and renewable energy sources (RES). EVs introduce new charging demands that change the traditional demand profiles and RES are characterized by their high variability. This paper presents a new multistage distribution expansion planning model where investments in distribution network assets, RES, ESS and EV charging stations (EVCS) are jointly considered. The charging demand necessary for EVs transportation is performed using a vehicle model based on travel patterns. The variability associated with RES along with the demand requires the incorporation of uncertainty, which is characterized through a set of scenarios. These scenarios are generated by the k-means++ clustering technique that allows keeping the correlation in the information of the uncertainty sources. The resulting stochastic program is driven by the minimization of the present value of the total expected cost including investment, maintenance, production, losses and non-supplied energy. The associated scenario-based deterministic equivalent is formulated as a mixed-integer linear program, which can be solved by commercial software. Numerical results are presented for an illustrative 54-node test system.

The first part of this two-paper series describes the incorporation of demand response (DR) and energy storage systems (ESSs) in the joint distribution and generation expansion planning for isolated systems. The role of DR and ESS has recently attracted an increasing interest in power systems. However, previous models have not been completely adapted in order to treat DR and ESS on an equal footing. The model presented includes DR and ESS in the planning of insular distribution systems. Hence, this paper presents a novel model to decide the joint expansion planning of distributed generation and the distribution network considering the impact of ESS and price-dependent DR programs. The problem is formulated as a stochastic-programming-based model driven by the maximization of the net social benefit. The associated deterministic equivalent is formulated as a mixed-integer linear program suitable for commercially available software. The outcomes of the model are the location and size of new generation and storage units and the distribution assets to be installed, reinforced or replaced. In the second companion paper, an insular case study (La Graciosa, Canary Islands, Spain) is provided illustrating the effects of DR and ESS on social welfare.

This paper describes the incorporation of uncertainty and reliability in the dynamic expansion planning of distribution network assets and distributed generation. Several alternatives for the installation of feeders, transformers, and distributed generation are considered. Thus, the optimal expansion plan identifies the best alternative, location, and installation time for the candidate assets under the uncertainty related to demand and renewable energy sources. To that end, an iterative algorithm is devised to yield a pool of high-quality candidate solutions in terms of total investment and operational costs. Each candidate solution results from a stochastic-programming-based model driven by the minimization of the expected investment and operational costs. The associated scenario-based deterministic equivalent is formulated as a mixed-integer linear program for which finite convergence to optimality is guaranteed and efficient off-the-shelf software is available. Standard metrics are subsequently applied to each candidate solution to characterize its reliability so that valuable information is provided to the distribution system planner. Numerical results illustrate the effective performance of the proposed approach.

This paper presents a bi-level model for distribution network and renewable energy expansion planning under a demand response (DR) framework. The role of DR has recently attracted an increasing interest in power systems. However, previous models have not been completely adapted in order to treat DR on an equal footing. The target of the distribution network and generation planner, modeled through the upper-level problem, is to minimize generation and network investment cost while meeting the demand. This upper-level problem is constrained by the lower-level problem, stressing the importance of integrating DR to time-varying prices into those investment models. The objective function considered for the lower level is the minimization of overall payment faced by the consumers. Using the Karush-Kuhn-Tucker complementarity constraints, the proposed bi-level model is recast as a mixed-integer linear programming problem, which is solvable using efficient off-the-shelf branch-and-cut solvers. Detailed results from an insular case study (La Graciosa, Canary Islands, Spain) are presented.

This paper investigates the multistage expansion planning problem of a distribution network considering reliability. Thus, the best alternative, location, and installation time for the candidate assets are identified while jointly accounting for economic and reliability aspects. As a major salient feature, the conventional simulation-based reliability assessment is equivalently implemented through algebraic expressions whereby the effect of the network topology is explicitly represented by decision variables of the optimization process. For expository purposes, the focus is placed on the expected energy not supplied, which is a widely-used metric for reliability assessment. The resulting optimization problem is cast as an instance of mixedinteger linear programming. Hence, unlike existing heuristic and metaheuristic solution techniques for reliability-constrained distribution system planning, the proposed approach is finitely convergent to the optimal solution and can be readily implemented using commercially-available software. Simulation results show the effective performance of the proposed methodology.