Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

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Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems

In this paper, the transmission planning state-of-the-art, which was obtained from the review of the most interesting models found in the international technical literature, is presented. The classification of publications was made, keeping in mind the solution methods, the treatment of the planning horizon, and the consideration of the new competitive schemes in the power sector. A discussion about the available tools for development of transmission planning models is also included.

Classification of publications and models on transmission expansion planning

This paper proposes analytical expressions for finding optimal size and power factor of four types of distributed generation (DG) units. DG units are sized to achieve the highest loss reduction in distribution networks. The proposed analytical expressions are based on an improvement to the method that was limited to DG type, which is capable of delivering real power only. Three other types, e.g., DG capable of delivering both real and reactive power, DG capable of delivering real power and absorbing reactive power, and DG capable of delivering reactive power only, can also be identified with their optimal size and location using the proposed method. The method has been tested in three test distribution systems with varying size and complexity and validated using exhaustive method. Results show that the proposed method requires less computation, but can lead optimal solution as verified by the exhaustive load flow method.

Analytical Expressions for DG Allocation in Primary Distribution Networks

This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver's 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique.

http://iot.ntnu.no/winterschool11/web/material/conejopapers/AJC2.pdf

Transmission expansion planning: a mixed-integer LP approach

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.

Transmission system expansion planning by simulated annealing

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 nonpolynomial time (NP) complete problem, 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.

Optimal Capacitor Placement in Radial Distribution Networks

In this paper, an efficient genetic algorithm (GA) is presented to solve the problem of multistage and coordinated transmission expansion planning. This is a mixed integer nonlinear programming problem, difficult for systems of medium and large size and high complexity. The GA presented has a set of specialized genetic operators and an efficient form of generation of the initial population that finds high quality suboptimal topologies for large size and high complexity systems. In these systems, multistage and coordinated planning present a lower investment than static planning. Tests results are shown in one medium complexity system and one large size high complexity system.

Multistage and coordinated planning of the expansion of transmission systems

Large scale combinatorial problems such as the network expansion problem present an amazingly high number of alternative configurations with practically the same investment, but with substantially different structures (configurations obtained with different sets of circuit/transformer additions). The proposed parallel tabu search algorithm has shown to be effective in exploring this type of optimization landscape. The algorithm is a third generation tabu search procedure with several advanced features. This is the most comprehensive combinatorial optimization technique available for treating difficult problems such as the transmission expansion planning. The method includes features of a variety of other approaches such as heuristic search, simulated annealing and genetic algorithms. In all test cases studied there are new generation, load sites which can be connected to an existing main network: such connections may require more than one line, transformer addition, which makes the problem harder in the sense that more combinations have to be considered.

Tabu search algorithm for network synthesis

The paper presents an extended genetic algorithm for solving the optimal transmission network expansion planning problem. Two main improvements have been introduced in the genetic algorithm: (a) initial population obtained by conventional optimisation based methods; (b) mutation approach inspired in the simulated annealing technique. The proposed method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Excellent performance is reported in the test results section of the paper for a difficult large-scale real-life problem: a substantial reduction in investment costs has been obtained with regard to previous solutions obtained via conventional optimisation methods and simulated annealing algorithms; statistical comparison procedures have been employed in benchmarking different versions of the genetic algorithm and simulated annealing methods.

R.A. Gallego

Papers

Transmission system expansion planning by simulated annealing

Optimal Capacitor Placement in Radial Distribution Networks

Multistage and coordinated planning of the expansion of transmission systems

Tabu search algorithm for network synthesis

Transmission system expansion planning by an extended genetic algorithm