Notes on the Dimension of the Solution Space in Typical Electrical Engineering Optimization Problems

Nowadays, optimization methodologies based on combinatorial strategies (i.e., metaheuristic methods) and exact methods can be easily found through-out the scientific literature in all areas of engineering, including electrical, mechanical, chemical, computational, and food engineering, among others. The common denominator in these areas of research corresponds to the complexity of the optimization models, as well as to the large dimensions of the solution space where these models are defined [1]. In addition, most of these models combine binary (also integer) decision variables with continuous ones into nonlinear non-convex formulations, which complicates the application of exact solution methods

Solución de un problema de optimización clásico usando el paquete optimizador GAMS: implementación del problema de despacho económico

This paper presents an effectiveness strategy to model and solve nonlinear mathematical optimization problems in electrical engineering using General Algebraic Modeling System (GAMS) for undergraduate students. A classical problem known as economic dispatch has been selected to show the need of using mathematical tools to solve a large scale optimization problem related with engineering. The economic dispatch is a classical optimization problem in operation of thermal electric systems, being the main idea to find an economical operation for thermal generators. This operation is based on a quadratic cost curve with some operating constraints, i.e., power balance and generation capacities. A numerical simulation is implemented using GAMS optimization package in demo version. This research has been developed with the support of 36 students of the course of Regulation and Operation of Electrical Systems (ROES) in the program of Electrical Engineering at Universidad Tecnológica de Pereira (UTP).En este artículo se presenta una estrategia para modelar y resolver problemas no lineales de optimización con estudiantes de pregrado en ingeniería eléctrica empleando el Sistema de Modelado Algebraico General (GAMS). El problema clásico conocido como despacho económico ha sido seleccionado para mostrar la necesidad de usar herramientas matemáticas para resolver problemas de gran tamaño relacionados con ingeniería. El despacho económico es un problema clásico de optimización en operación de sistemas termoeléctricos, cuya idea principal es encontrar la operación más económica para los generadores térmicos. Esta operación está basada en una curva cuadrática de costos con algunas restricciones operativas, como por ejemplo, balance de potencia y capacidades de generación. La simulación numérica es implementada en GAMS usando una versión de prueba. Esta investigación ha sido desarrollada con la ayuda de 36 estudiantes del curso de Regulación y Operación de Sistemas Eléctricos (ROES) del programa de Ingeniería Eléctrica de la Universidad Tecnológica de Pereira (UTP)

Passivity-based analysis and control of AC microgrids: Integration, operation and control of energy storage systems

Microgrids are essential subsystems of modern electric power systems. They allow providing electrical energy service for millions of people around the world by integrating multiple distributed energy resources and energy storage technologies at a small scale. This thesis studies these systems from the dynamical analysis and control point of view, to ful ll three main objectives: rst, to model pulse-width-modulated voltage and current source converters for integrating distributed energy resources in ac microgrids (Grids) with single-phase and three-phase topologies; second, to develop Hamiltonian models for representing the whole dynamics of ac Grids via classical circuit theory, since this model exhibits interconnection and dissipation structures typical in Lagrangian and Hamiltonian modeling; third, to design passivity-based controllers for guaranteeing stable operation of the entire Grids when these are operated under grid-connected or isolated modes. Hamiltonian modeling of power electronic converters based on voltage and current source technologies as well as Hamiltonian models of electrical Grids facilitate the dynamical analysis under the passivity paradigm with stability and scalability criteria. The main contributions of this thesis are: integrating supercapacitors and superconducting coils in ac power grids through a uni ed control model; uni ed ac grid modeling via circuit theory and active and reactive power decoupling in power converters under grid-connected mode as well as voltage and frequency control for isolated Grid con gurations. Finally, simulation results corroborate the theoretical developments presented in this thesis

Planeación optima de sistemas de distribución considerando reconectadores automáticos para aislamiento de fallas y transferencia de carga

En este trabajo se presenta una metodología para resolver el problema de planeamiento de sistemas de distribución primarios en conjunto con la ubicación optima de reconectadores automáticos para aislamiento de fallas y transferencia de carga. Para solucionar el problema del planeamiento se formula un modelo mono-objetivo de tipo no lineal entero mixto, el cual tiene como objetivo la minimización de los costos de inversión y operación sujeto a un conjunto de restricciones técnicas y operativas; para solucionarlo se emplea el algoritmo Búsqueda Tabú (BT). Para el problema de la ubicación de reconectadores se plantea un modelo multi-objetivo de tipo no lineal entero mixto, el cual tiene como objetivos la minimizaci on de los costos de inversi on y la minimizaci on del nivel de energía no servida; para solucionarlo se emplea el Algoritmo Genético de Ordenamiento no dominado(NSGA II, por sus siglas en inglés). Para darle solución al problema de la planeación de sistemas de distribución considerando reconectadores, en este trabajo se proponen dos enfoques: el primero emplea una metodología en cascada y el segundo una metodolog ía integrada. En el primer enfoque inicialmente se soluciona el problema de la planeación optima de la red y luego son ubicados los reconectadores normalmente cerrados y normalmente abiertos para aislamiento de fallas y transferencia de carga, respectivamente. El segundo enfoque considera la planeación de la red de distribución en conjunto con la ubicación de reconectadores en forma integrada, lo que quiere decir que cada propuesta de solución para el problema de planeamiento lleva consigo la propuesta de ubicación optima de los elementos de protección. Para validar ambas metodologías propuestas son empleados dos sistemas de prueba de la literatura especializada de diferentes tamaños. Debido a que en la solución de este tipo de problemas los sistemas son modelados por su equivalente monofásico, en este trabajo se modificaron estos dos sistemas para introducir el efecto del desbalance de cargas, con el fin de ajustarlos a la realidad de los sistemas eléctricos en Colombia. Finalmente los resultados de las metodologías son comparados para verificar su eficiencia

Control híbrido del péndulo de furuta

Este proyecto muestra el modelado matemático del péndulo de furuta mediante funciones de energía, teniendo en cuenta las dinámicas no lineales propias de los sistemas físicos y considerando los acoples existentes entre los dispositivos eléctricos y mecánicos. Se desarrolla un proceso de control basado en realimentación de variables de estado para el punto de equilibrio y se abordan dos temáticas para la zona no lineal de la planta. En primera instancia se implementan las funciones que representan los estados energéticos de la planta en forma global y se establecen las regiones de operación (zona de "Swing UP") y finalmente se emplean redes neuronales (RNA) para emular el comportamiento de las funciones de energía. Se presenta la combinación de las técnicas de control considerando las restricciones propias del actuador y sensores utilizados, además se presenta un estudio de fenómenos físicos que pueden alterar el comportamiento del sistema

On the Use of the p-q Theory for Harmonic Current Cancellation with Shunt Active Filters

Discussion and mathematical proof on necessary and sufficient conditions for the application of the {p-q} theory for compensating the harmonic currents consumed by non-linear load using a shunt active filter are presented. These conditions over instantaneous active and reactive powers were not addressed before and must be considered on the design of new control strategies based on {p-q} theory. Theoretical demonstration is proposed and an application example with simulations results is used to validate the theoretical results

Optimal selection and location of bess systems in medium-voltage rural distribution networks for minimizing greenhouse gas emissions

This paper explores a methodology to locate battery energy storage systems (BESS) in rural alternating current (AC) distribution networks fed by diesel generators to minimize total greenhouse gas emissions. A mixed-integer nonlinear programming (MINLP) model is formulated to represent the problem of greenhouse gas emissions minimization, considering power balance and devices capabilities as constraints. To model the BESS systems, a linear relationship is considered between the state of charge and the power injection/consumption using a charging/discharging coefficient. The solution of the MINLP model is reached through the general algebraic modeling system by employing the BONMIN solver. Numerical results in a medium-voltage AC distribution network composed of 33 nodes and 32 branches operated with 12.66 kV demonstrate the effectiveness of including BESS systems to minimize greenhouse gas emissions in diesel generators that feeds rural distribution networks

On the mathematical modeling for optimal selecting of calibers of conductors in DC radial distribution networks: An MINLP approach

This paper addresses the problem of optimal conductor selection in direct current (DC) distribution networks with radial topology. A nonlinear mixed-integer programming model (MINLP) is developed through a branch-to-node incidence matrix. An important contribution is that the proposed MINLP model integrates a set of constraints related to the telescopic structure of the network, which allows reducing installation costs. The proposed model also includes a time-domain dependency that helps analyze the DC network under different load conditions, including renewable generation and battery energy storage systems, and different voltage regulation operative consigns. The objective function of the proposed model is made up of the total investment in conductors and the total cost of energy losses in one year of operation. These components of the objective function show multi-objective behavior. For this reason, different simulation scenarios are performed to identify their effects on the final grid configuration. An illustrative 10-nodes medium-voltage DC grid with 9 lines is used to carry out all the simulations through the General Algebraic Modeling System known as GAMS

Method for estimating solar energy potential based on photogrammetry from unmanned aerial vehicles

This study presents a method to estimate the solar energy potential based on 3D data taken from unmanned aerial devices. The solar energy potential on the roof of a building was estimated before the placement of solar panels using photogrammetric data analyzed in a geographic information system, and the predictions were compared with the data recorded after installation. The areas of the roofs were chosen using digital surface models and the hemispherical viewshed algorithm, considering how the solar radiation on the roof surface would be affected by the orientation of the surface with respect to the sun, the shade of trees, surrounding objects, topography, and the atmospheric conditions. The results show that the efficiency percentages of the panels and the data modeled by the proposed method from surface models are very similar to the theoretical efficiency of the panels. Radiation potential can be estimated from photogrammetric data and a 3D model in great detail and at low cost. This method allows the estimation of solar potential as well as the optimization of the location and orientation of solar panels

Mixed-integer programming model for transmission network expansion planning with Battery Energy Storage Systems (BESS)

This article assesses the costs and benefits of incorporating battery energy storage systems (BESS) in transmission network expansion planning (TEP) over multiple time periods. We propose a mixed-integer programming model (MIP) for joint planning of the installation of battery energy storage systems (BESS) and construction of new transmission lines in multiple periods of time. The mathematical formulation of the presented model is based on the strategies of the agents of a transmission network to maximize their benefit, and on the operational restrictions of the power flows in transmission networks. This analysis is performed for the Garver 6 node test system takes into account the power losses in the lines and the restrictions for the energy stored in BESS. The power flows obtained with the MIP model are compared with AC power flows generated with specialized software for flows in power systems. This allows us to demonstrate the potential of models based on DC power flows to achieve approximate results applicable to the behavior and characteristics of real transmission networks. The results show that the BESS increase the net profit in the transmission networks and reduce their power losses