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Recently, several authors have reported specific criteria to support the widely accepted use of a convex operational model for bulk energy storage in the formulation of power system operation and planning problems involving binary variables. Using two counterexamples, we show that this modeling simplification may give rise to impractical solutions featuring simultaneous charging and discharging, even though the recently published criteria are satisfied. Thus, both counterexamples invalidate those criteria and demonstrate that the customarily used convex model may be unsuitable for the precise incorporation of bulk storage in such instances of mixed-integer programming. [ABSTRACT FROM AUTHOR]

This paper addresses the multistage or dynamic investment decision-making problem arising in a distribution system within a transactive energy environment. Under such a framework, three agents are involved, namely the distribution company (DISCO), the owner of distributed generation (DG) units (DGENCO), and the independent distribution system operator (IDSO). Here, we propose characterizing this planning problem as an instance of trilevel programming. In the upper level, the DISCO identifies the optimal investment plan in network assets and the best potential locations for DG in order to supply the customer demand at maximum profit. In the middle level, the DGENCO determines the best location, sizing, and timing for DG installation so that the corresponding profit is maximized. Finally, in the lower level, the IDSO is responsible for the optimal operation of the expanded distribution system. The resulting mixed-integer trilevel program is solved by a novel approach relying on Benders decomposition. The performance of the proposed approach has been illustrated with a case study based on a 37-node test system. [ABSTRACT FROM AUTHOR]

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 mixed-integer 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. [ABSTRACT FROM PUBLISHER]

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, the solution of practical large-scale instances remains a challenge. In order to address this issue, this paper presents an alternative column-and-constraint generation algorithm wherein the max–min problem associated with the second stage is solved by a block coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked case-dependent, nontrivial, and time-consuming tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for the transmission network expansion planning under generalized joint generation and transmission n-K security criteria. The proposed methodology identifies the optimal expansion plan while modeling the power system operation under both normal and contingency states. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing the investment, operation, and system power imbalance costs. The middle-level problem identifies, for a given expansion plan, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency and investment plan by minimizing the system power imbalance. The resulting trilevel program is solved by a primal-dual algorithm based on Benders decomposition combined with a column-and-constraint generation procedure. The proposed approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models. [ABSTRACT FROM PUBLISHER]

Reliability is an essential factor in distribution networkt expansion planning. However, standard distribution reliability assessment techniques rely on quantifying the impact of a pre-specified set of events on service continuity through the simulation of component outages, one at a time. Due to such a simulation-based nature, the incorporation of reliability into distribution network expansion planning has customarily required the application of heuristic and metaheuristic approaches. Recently, alternative mixed-integer linear programming (MILP) models have been proposed for distribution network expansion planning considering reliability. Nonetheless, such models suffer from either low computational efficiency or over-simplification. To overcome these shortcomings, this paper proposes an enhanced MILP model for multistage reliability-constrained distribution network expansion planning. Leveraging an efficient, yet accurate reliability evaluation model, proposing a customized technique for effectively imposing radial operation, as well as utilizing pragmatic measures to model reliability-related costs are the salient features of this work. In this respect, practical reliability-related costs are considered based on reliability incentive schemes and the revenue lost due to undelivered energy during customer outages. The proposed planning approach is tested on four networks with 24, 54, 86, and 138 nodes to illustrate its efficiency and applicability. [ABSTRACT FROM AUTHOR]

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This paper differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results from structural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach. [ABSTRACT FROM AUTHOR]