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

The smart grid concept continues to evolve and various methods have been developed to enhance the energy efficiency of the electricity infrastructure. Demand Response (DR) is considered as the most cost-effective and reliable solution for the smoothing of the demand curve, when the system is under stress. DR refers to a procedure that is applied to motivate changes in the customers' power consumption habits, in response to incentives regarding the electricity prices. In this paper, we provide a comprehensive review of various DR schemes and programs, based on the motivations offered to the consumers to participate in the program. We classify the proposed DR schemes according to their control mechanism, to the motivations offered to reduce the power consumption and to the DR decision variable. We also present various optimization models for the optimal control of the DR strategies that have been proposed so far. These models are also categorized, based on the target of the optimization procedure. The key aspects that should be considered in the optimization problem are the system's constraints and the computational complexity of the applied optimization algorithm.

A Survey on Demand Response Programs in Smart Grids: Pricing Methods and Optimization Algorithms

The generic denomination of ‘Memetic Algorithms’ (MAs) is used to encompass a broad class of metaheuristics (i.e. general purpose methods aimed to guide an underlying heuristic). The method is based on a population of agents and proved to be of practical success in a variety of problem domains and in particular for the approximate solution of NP Optimization problems. Unlike traditional Evolutionary Computation (EC) methods, MAs are intrinsically concerned with exploiting all available knowledge about the problem under study. The incorporation of problem domain knowledge is not an optional mechanism, but a fundamental feature that characterizes MAs. This functioning philosophy is perfectly illustrated by the term “memetic”. Coined by R. Dawkins [52], the word ‘meme’ denotes an analogous to the gene in the context of cultural evolution [154]. In Dawkins’ words:

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A Gentle Introduction to Memetic Algorithms

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.

Imposing Radiality Constraints in Distribution System Optimization Problems

Microgrids can be operated either grid-connected to reduce system losses and for peak shaving or islanded to increase reliability and provide backup power during utility outage. Such dual configuration capability imposes challenges on the design of the protection system. Fault current magnitudes will vary depending on the microgrid operating mode. In this paper, a microgrid protection scheme that relies on optimally sizing fault current limiters and optimally setting directional overcurrent relays is proposed. The protection scheme is optimally designed taking into account both modes of operation (grid-connected and islanded). The problem has been formulated as a constrained nonlinear programming problem and is solved using the genetic algorithm with the static penalty constraint-handling technique. The proposed approach is tested on two medium-voltage networks: a typical radial distribution system and on the IEEE 30-bus looped power distribution system equipped with directly connected conventional synchronous generators.

Optimal Protection Coordination for Microgrids With Grid-Connected and Islanded Capability

The authors present a new methodology based upon the principles of optimization theory, to treat the problem of optimal coordination of directional overcurrent relays in interconnected power systems. With the application of the proposed technique, this coordination problem is stated as a parameter optimization problem, which in general, is of a large dimension, especially when many different system configurations and perturbations are to be considered. Several optimization procedures, including direct methods and decomposition techniques, for solving this large scale coordination problem are described, and results of optimally coordinating directional overcurrent relays in power systems with up to 30 buses are presented. >

Optimal coordination of directional overcurrent relays in interconnected power systems

The planning problem of electrical power distribution networks, stated as a mixed nonlinear integer optimization problem, is solved using the ant colony system algorithm (ACS). The behavior of real ants has inspired the development of the ACS algorithm, an improved version of the ant system (AS) algorithm, which reproduces the technique used by ants to construct their food recollection routes from their nest, and where a set of artificial ants cooperate to find the best solution through the interchange of the information contained in the pheromone deposits of the different trajectories. This metaheuristic approach has proven to be very robust when applied to global optimization problems of a combinatorial nature, such as the traveling salesman and the quadratic assignment problem, and is favorably compared to other solution approaches such as genetic algorithms (GAs) and simulated annealing techniques. In this work, the ACS methodology is coupled with a conventional distribution system load-flow algorithm and adapted to solve the primary distribution system planning problem. The application of the proposed methodology to two real cases is presented: a 34.5-kV system with 23 nodes from the oil industry and a more complex 10-kV electrical distribution system with 201 nodes that feeds an urban area. The performance of the proposed approach outstands positively when compared to GAs, obtaining improved results with significant reductions in the solution time. The technique is shown as a flexible and powerful tool for the distribution system planning engineers.

Ant colony system algorithm for the planning of primary distribution circuits

A successive linear programming methodology is presented to treat more effectively those applications where a local structure change is performed to a power system already in operation, and where the modification of the settings of already existent relays is not desirable. The dimension of the optimization problems to be solved is substantially reduced, and a sequence of small linear programming problems is stated and solved in terms of the time dial settings, until a feasible solution is reached. With the proposed technique, the number of relays of the original system to be reset is reduced substantially. It is found that there is a trade-off between the number of relays to be reset and the optimality of the settings of the relays.

Coordination of directional overcurrent relay timing using linear programming

This paper presents a method to consider the dynamic changes in the network's topology for the coordination of directional overcurrent relays using linear programming The proper coordination constraints are included by using linear approximations for the relay dynamics The application of the methodology as well as the importance of considering the transient configuration changes are illustrated with a practical example and a test case consisting of a real industrial power system

Optimal coordination of directional overcurrent relays considering dynamic changes in the network topology

Important research effort has been devoted to the topic of optimal planning of distribution systems. However, in general it has been mostly referred to the design of the primary network, with very modest considerations to the effect of the secondary network in the planning and future operation of the complete grid. Relatively little attention has been paid to the optimization of the secondary grid and to its effect on the optimality of the design of the complete electrical system, although the investment and operation costs of the secondary grid represent an important portion of the total costs. Appropriate design procedures have been proposed separately for both the primary and the secondary grid; however, in general, both planning problems have been presented and treated as different-almost isolated-problems, setting aside with this approximation some important factors that couple both problems, such as the fact that they may share the right of way, use the same poles, etc., among other factors that strongly affect the calculation of the investment costs. The main purpose of this work is the development and initial testing of a model for the optimal planning of a distribution system that includes both the primary and the secondary grids, so that a single optimization problem is stated for the design of the integral primary-secondary distribution system that overcomes these simplifications. The mathematical model incorporates the variables that define both the primary as well as the secondary planning problems and consists of a mixed integer-linear programming problem that may be solved by means of any suitable algorithm. Results are presented of the application of the proposed integral design procedure using conventional mixed integer-linear programming techniques to a real case of a residential primary-secondary distribution system consisting of 75 electrical nodes.

A.J. Urdaneta

Papers

Optimal coordination of directional overcurrent relays in interconnected power systems

Ant colony system algorithm for the planning of primary distribution circuits

Coordination of directional overcurrent relay timing using linear programming

Optimal coordination of directional overcurrent relays considering dynamic changes in the network topology

Integral planning of primary-secondary distribution systems using mixed integer linear programming