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 authors present a method of finding a continuum of power flow solutions starting at some base load and leading to the steady-state voltage stability limit (critical point) of the system. A salient feature of the so-called continuation power flow is that it remains well-conditioned at and around the critical point. As a consequence, divergence due to ill-conditioning is not encountered at the critical point, even when single-precision computation is used. Intermediate results of the process are used to develop a voltage stability index and identify areas of the system most prone to voltage collapse. Examples are given where the voltage stability of a system is analyzed using several different scenarios of load increase. >

The continuation power flow: a tool for steady state voltage stability analysis

This paper presents a new mixed-integer linear formulation for the unit commitment problem of thermal units. The formulation proposed requires fewer binary variables and constraints than previously reported models, yielding a significant computational saving. Furthermore, the modeling framework provided by the new formulation allows including a precise description of time-dependent startup costs and intertemporal constraints such as ramping limits and minimum up and down times. A commercially available mixed-integer linear programming algorithm has been applied to efficiently solve the unit commitment problem for practical large-scale cases. Simulation results back these conclusions

A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem

The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this convex dual problem whenever the duality gap is zero. A necessary and sufficient condition is provided in this paper to guarantee the existence of no duality gap for the OPF problem. This condition is satisfied by the standard IEEE benchmark systems with 14, 30, 57, 118, and 300 buses as well as several randomly generated systems. Since this condition is hard to study, a sufficient zero-duality-gap condition is also derived. This sufficient condition holds for IEEE systems after small resistance (10-5 per unit) is added to every transformer that originally assumes zero resistance. We investigate this sufficient condition and justify that it holds widely in practice. The main underlying reason for the successful convexification of the OPF problem can be traced back to the modeling of transformers and transmission lines as well as the non-negativity of physical quantities such as resistance and inductance.

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Zero Duality Gap in Optimal Power Flow Problem

This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported.

A genetic algorithm solution to the unit commitment problem

This paper discusses the state of the art in short-term load forecasting (STLF), that is, the prediction of the system load over an interval ranging from one hour to one week. The paper reviews the important role of STLF in the on-line scheduling and security functions of an energy management system (EMS). It then discusses the nature of the load and the different factors influencing its behavior. A detailed classification of the types of load modeling and forecasting techniques is presented. Whenever appropriate, the classification is accompanied by recommendations and by references to the literature which support or expand the discussion. The paper also presents a lengthy discussion of practical aspects for the development and usage of STLF models and packages. The annotated bibliography offers a representative selection of the principal publications in the STLF area.

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Short-term load forecasting

In their attempt to cut down on greenhouse gas emissions from electricity generation, several countries are committed to install wind power generation up to and beyond the 10%-20% penetration mark. However, the large-scale integration of wind power represents a challenge for power system operations planning because wind power 1) cannot be dispatched in the classical sense; and 2) its output varies as weather conditions change. This warrants the investigation of alternative short-term power system operations planning methods capable of better coping with the nature of wind generation while maintaining or even improving the current reliability and economic performance of power systems. To this end, this paper formulates a short-term forward electricity market-clearing problem with stochastic security capable of accounting for nondispatchable and variable wind power generation sources. The principal benefit of this stochastic operation planning approach is that, when compared to a deterministic worst-case scenario planning philosophy, it allows greater wind power penetration without sacrificing security.

Stochastic Security for Operations Planning With Significant Wind Power Generation

A survey is presented of publications in the fields of optimal power flow and dispatching. It suggests a classification of methods based on the choice of optimization techniques. The survey is summarized in a single flow-chart-type figure, which indicates the relationship between methods, their chronology, and their popularity. This figure is based on a compilation of over three hundred publications. >

A survey of the optimal power flow literature

In their attempt to cut down on greenhouse gas emissions from electricity generation, several countries are committed to install wind power generation up to and beyond the 10-20% penetration mark. However, the large-scale integration of wind power represents a challenge for power system operations planning because wind power (i) cannot be dispatched in the classical sense; and, (ii) its output varies as weather conditions change. This warrants the investigation of alternative short-term power system operations planning methods capable of better coping with the nature of wind generation while maintaining or even improving the current reliability and economic performance of power systems. To this end, this paper formulates a short-term forward electricity market-clearing problem with stochastic security capable of accounting for non-dispatchable and variable wind power generation sources. The principal benefit of this stochastic operation planning approach is that, when compared to a deterministic worst-case scenario planning philosophy, it allows greater wind power penetration without sacrificing security.

Stochastic security for operations planning with significant wind power generation

A Lagrangian relaxation algorithm for power system generator unit commitment is proposed. The algorithm proceeds in three phases. In the first phase, the Lagrangian dual of the unit commitment is maximized by standard subgradient techniques. The second phase finds a reserve-feasible dual solution, followed by a third phase of economic dispatch. A mathematically based, systematic and generally applicable procedure to search for a reserve-feasible dual solution is presented. The algorithm has been tested on systems of up to 100 units to be scheduled over 168 hours, giving reliable performance and low execution times. Both spinning and time-limited reserve constraints are treated. >

Francisco D. Galiana

Papers

Short-term load forecasting

Stochastic Security for Operations Planning With Significant Wind Power Generation

A survey of the optimal power flow literature

Stochastic security for operations planning with significant wind power generation

Towards a more rigorous and practical unit commitment by Lagrangian relaxation