Distribution systems commonly operate with a radial topology, so all models of optimization problems in these distribution systems should consider radiality in their formulation. This work presents a literature review, a critical analysis, and a proposal for incorporating the radiality constraints in mathematical models of optimization problems for radial distribution systems. The objective is to show that the radiality constraints on such optimization problems can be considered in a simple and efficient way. The reconfiguration and expansion planning problems of distribution systems are used to test and verify the proposed radiality constraints. A generalization of radiality constraints is also examined.

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies—transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed—both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. the DC model) are used to represent the power flow equations—the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

This paper presents a hierarchical decomposition approach for optimal transmission network expansion planning. A major difficulty in obtaining global optimal solutions for complex, real-life networks is due to the nonconvexity of the problem. Hierarchical decomposition has proved to be an efficient heuristic for coping with nonconvexity, as illustrated in the test results section of the paper. Significant reductions in investment costs have been obtained in some practical cases for which results are available in the literature. The current implementation of the hierarchical decomposition approach utilizes three different levels of network modeling: transportation models, hybrid models, and linearized power flow models. An initial solution is obtained for the simplest model (transportation model) and as one moves towards the final solution the algorithm successively switches to more accurate models

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (nonpolynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

This paper presents a simulated annealing approach to the long term transmission expansion planning problem which is a hard, large scale combinatorial problem. The proposed approach has been compared with a more conventional optimization technique based on mathematical decomposition with a zero-one implicit enumeration procedure. Tests have been performed on three different systems. Two smaller systems for which optimal solutions are known have been used to tune the main parameters of the simulated annealing process. The simulated annealing method has then been applied to a larger example system for which no optimal solutions are known: as a result an entire family of interesting solutions have been obtained with costs about 7% less than the best solutions known for that particular example system.