Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> A model to obtain the optimal allocation and timing of renewable distributed generation under uncertainty is proposed as part of distribution expansion planning. The problem is formulated using a stochastic two-stage multiperiod mixed-integer linear programming (MILP) model, where investment decisions are done in the first stage and scenario-dependent operation variables are solved in the second stage. The model aims to minimize renewable distributed generation (photovoltaic and wind) investment costs, substation expansion investment cost, operation and maintenance costs, energy losses cost, and the cost of the power purchased from the transmission system. Active and reactive power flow equations are linearized and constraints include voltage limits, substation and feeders capacities, renewable generation limits, and investment constraints. The model is tested on a 34-bus system and conclusions are duly drawn. <s> BIB001 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> 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. <s> BIB002 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> Energy storage systems (ESS) have adopted a new role with the increasing penetration of electric vehicles (EV) and renewable energy sources (RES). EV 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 are jointly considered. The charging demand necessary for EV 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. <s> BIB003 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> The second part of this two-paper series analyzes the incorporation of demand response (DR) and energy storage systems (ESSs) in the joint distribution and generation expansion planning for the isolated system of La Graciosa, Canary Islands, Spain. Based on the stochastic programming model developed in its companion paper, the impact of DR and ESS on the location and size of new generation and storage units and the distribution assets to be installed, reinforced, or replaced are defined. Numerical results illustrate the effective performance of the proposed approach. Additionally, a set of metrics showing the welfare achieved by the different stakeholders has been implemented. <s> BIB004 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> Planning the distribution network of the future involves forecasting the most likely scenario to make appropriate investment decisions. Many uncertainties concerning, e.g. the evolution of conventional loads, renewable production and electric vehicles (EVs) make it difficult to predict the location of the distribution network's weaknesses (overvoltages, undervoltages and overcurrents) and their occurrence. In some cases, alternative solutions such as demand response (DR) and reconfiguration can remove the constraints and prevent expensive network investment. This study proposes a two-stage algorithm that is able to give the probability that no technical constraints will appear as a function of the reinforcement cost with and without using DR and/or reconfiguration. The first stage of the algorithm consists in running Monte Carlo simulations based on realistic scenarios for loads, EVs and renewable production development provided by French governmental roadmaps. The cost of reinforcement per line and per hour of constraints enables selection of the feeders, where DR (solved with linear programming) and/or reconfiguration (exhaustive research) will be implemented in the second stage of the algorithm to remove these constraints. The methodology is applied to a real part of a French distribution network. <s> BIB005 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> Second order conic programming (SOCP) has been used to model various applications in power systems, such as operation and expansion planning. In this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model for the distribution system expansion planning problem that considers uncertainty and also captures the nonlinear AC power flow. To avoid costly investment plans due to some extreme scenarios, we further present a chance-constrained variant that could lead to cost-effective solutions. To address the computational challenge, we extend the basic Benders decomposition method and develop a bilinear variant to compute stochastic and chance-constrained MISOCP formulations. A set of numerical experiments is performed to illustrate the performance of our models and computational methods. In particular, results show that our Benders decomposition algorithms drastically outperform a professional MISOCP solver in handling stochastic scenarios by orders of magnitude. <s> BIB006 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> One of the distribution network operators’ (DNOs’) responsibilities is to design distribution networks in order to reliably and efficiently meet a portfolio of demands with different attributes. The advent of plug-in electric vehicles introduces a number of new network players, such as gridable parking lot owners (GPLOs), which might have conflicting objectives with DNO’s ones. This paper presents a dynamic bi-level model for distribution network planning considering different objectives of DNO and GPLO. The power injection capability of gridable parking lots (GPLs) is employed as an alternative supply source to enhance the network flexibility in supplying loads under faulty conditions. Moreover, the proposed planning approach is developed in a way that the economic risk of the plan associated with the stochastic nature of the GPL behavior is controlled. Different test networks are used to validate the effectiveness of the proposed model. <s> BIB007 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> The incorporation of the reconfiguration into the expansion planning of smart distribution networks is addressed in this paper, in which the potential of distributed energy resources and demand response (DR) are modeled. The system of systems (SoS) architecture is employed to model the strategy of a distribution company (DISCO), a private investor (PI), and a DR provider (DRP). The SoS is an efficient modeling architecture to model the behavior of independent and autonomous systems with distinct objective functions who are able to share some data and work together. The aim of the DISCO is to upgrade the system with the optimal cost and reliability, whereas the PI and DRP want to maximize their profit. The DISCO should try to persuade the PI to install DGs (Distributed generations) by offering the guaranteed purchasing prices. Furthermore, the DRP is a market player who can negotiate with the DISCO to sign a contract to sell the purchased DR capacities from the customers. The uncertainties of the DISCO problem is handled by using the chance-constraint method, but the PI and DRP use the conditional value at risk method to model their uncertainties. Finally, to solve the proposed model, the multiobjective optimization algorithm is employed. <s> BIB008 </s> Overview of Electric Energy Distribution Networks Expansion Planning <s> I. STOCHASTIC PROGRAMMING <s> This study describes a methodology to solve the multi-period distribution expansion planning problem considering reliability, distributed generation (DG), capacitor and switch placement in the context of smart grids. The developed computational model is formulated as a mixed integer nonlinear optimisation problem and solved through the combination of meta-heuristics, stochastic simulation methods (Monte-Carlo simulation), and application of optimal power flow. The main objectives of this optimisation problem are defining the best choice to install power system components and determining the installation period and size of components to minimise investment cost while maximising system reliability. The proposed method was implemented in a modified version of the IEEE-RBTS bus 2 and in a 90-bus test system. The obtained results show a reduction of >20% of the operating cost and >70% of the average interruption time. In addition, it was performed scenarios not including DG, self-healing, and reliability analysis, individually. The analyses show the impact in the results by including a new variable in the expansion planning, increasing up to 40% in the fitness function value. Furthermore, it is presented with a discussion of the impact of the method to estimate the reliability indexes on the optimisation process. <s> BIB009
Stochastic Programming (SP) allocates a specific probability to a set of scenarios representing the uncertain parameter. Although scenario generation drastically considers the inherent nature of uncertain parameters, computational efficiency is reduced by the increasing number of scenarios. Researchers proposed scenario-reduction techniques to enhance tractability; to name a few, backward and forward scenario reduction, clustering methods, interval programming, Taguchi's orthogonal testing array, and in the context of DEP we can mention the works in BIB008 , BIB003 , BIB002 , BIB004 BIB005 BIB006  BIB001 BIB007 BIB009 . In BIB008 , a framework is proposed to solve a stochastic DEP problem, and in BIB004 , a coordinated stochastic DEP and renewable expansion planning are presented considering demand response and storage systems. The authors consider power transfer capacity as an uncertainty resource in a stochastic DEP problem in  . In BIB002 , multi-stage stochastic optimization is proposed to consider both generation and network expansion planning in a DEP problem.