Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Optimising the energy consumption on pultrusion process

This study is based on a previous experimental work in which embedded cylindrical heaters were applied to a pultrusion machine die, and resultant energetic performance compared with that achieved with the former heating system based on planar resistances. The previous work allowed to conclude that the use of embedded resistances enhances significantly the energetic performance of pultrusion process, leading to 57% decrease of energy consumption. However, the aforementioned study was developed with basis on an existing pultrusion die, which only allowed a single relative position for the heaters. In the present work, new relative positions for the heaters were investigated in order to optimise heat distribution process and energy consumption. Finite Elements Analysis was applied as an efficient tool to identify the best relative position of the heaters into the die, taking into account the usual parameters involved in the process and the control system already tested in the previous study. The analysis was firstly developed based on eight cylindrical heaters located in four different location plans. In a second phase, in order to refine the results, a new approach was adopted using sixteen heaters with the same total power. Final results allow to conclude that the correct positioning of the heaters can contribute to about 10% of energy consumption reduction, decreasing the production costs and leading to a better eco-efficiency of pultrusion process.

Estimating Effective Slowdown of Tasks in Energy-Aware Clouds

Consolidation consists in scheduling multiple virtual machines onto fewer servers in order to improve resource utilization and to reduce operational costs due to power consumption. However, virtualization technologies do not offer performance isolation, causing applications’ slowdown. In this work, we propose a performance enforcing mechanism, composed of a slowdown estimator, and a interference- and power-aware scheduling algorithm. The slowdown estimator determines, based on noisy slowdown data samples obtained from state-of-the-art slowdown meters, if tasks will complete within their deadlines, invoking the scheduling algorithm if needed. When invoked, the scheduling algorithm builds performance and power aware virtual clusters to successfully execute the tasks. We conduct simulations injecting synthetic jobs which characteristics follow the last version of the Google Cloud tracelogs. The results indicate that our strategy can be efficiently integrated with state-of-the-art slowdown meters to fulfil contracted SLAs in real-world environments, while reducing operational costs in about 12%.

Towards high-available and energy-efficient virtual computing environments in the cloud

Empowered by virtualisation technology, cloud infrastructures enable the construction of flexi- ble and elastic computing environments, providing an opportunity for energy and resource cost optimisation while enhancing system availability and achieving high performance. A crucial re- quirement for effective consolidation is the ability to efficiently utilise system resources for high- availability computing and energy-efficiency optimisation to reduce operational costs and carbon footprints in the environment. Additionally, failures in highly networked computing systems can negatively impact system performance substantially, prohibiting the system from achieving its initial objectives. In this paper, we propose algorithms to dynamically construct and readjust vir- tual clusters to enable the execution of users’ jobs. Allied with an energy optimising mechanism to detect and mitigate energy inefficiencies, our decision-making algorithms leverage virtuali- sation tools to provide proactive fault-tolerance and energy-efficiency to virtual clusters. We conducted simulations by injecting random synthetic jobs and jobs using the latest version of the Google cloud tracelogs. The results indicate that our strategy improves the work per Joule ratio by approximately 12.9% and the working efficiency by almost 15.9% compared with other state-of-the-art algorithms.

Saving energy in the GFRP pultrusion process

This study addresses to the optimization of pultrusion manufacturing process from the energy-consumption point of view. The die heating system of external platen heaters commonly used in the pultrusion machines is one of the components that contribute the most to the high consumption of energy of pultrusion process. Hence, instead of the conventional multi-planar heaters, a new internal die heating system that leads to minor heat losses is proposed. The effect of the number and relative position of the embedded heaters along the die is also analysed towards the setting up of the optimum arrangement that minimizes both the energy rate and consumption. Simulation and optimization processes were greatly supported by Finite Element Analysis (FEA) and calibrated with basis on the temperature profile computed through thermography imaging techniques. The main outputs of this study allow to conclude that the use of embedded cylindrical resistances instead of external planar heaters leads to drastic reductions of both the power consumption and the warm-up periods of the die heating system. For the analysed die tool and process, savings on energy consumption up to 60% and warm-up period stages less than an half hour were attained with the new internal heating system. The improvements achieved allow reducing the power requirements on pultrusion process, and thus minimize industrial costs and contribute to a more sustainable pultrusion manufacturing industry.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

How to reduce energy consumption on pultrusion

The global warming due to high CO2 emission in the last years has made energy saving a global problem nowadays. However, manufacturing processes such as pultrusion necessarily needs heat for curing the resin. Then, the only option available is to apply all efforts to make the process even more efficient. Different heating systems have been used on pultrusion, however, the most widely used are the planar resistances. The main objective of this study is to develop another heating system and compares it with the former one. Thermography was used in spite of define the temperature profile along the die. FEA (finite element analysis) allows to understand how many energy is spend with the initial heating system. After this first approach, changes were done on the die in order to test the new heating system and to check possible quality problems on the product. Thus, this work allows to conclude that with the new heating system a significant reduction in the setup time is now possible and an energy reduction of about 57% was achieved.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Support System for Rational Use of Electric Energy

This paper presents the system developed to promote the rational use of electric energy among consumers and, thus, increase the energy efficiency. The goal is to provide energy consumers with an application that displays the energy consumption/production profiles, sets up consuming ceilings, defines automatic alerts and alarms, compares anonymously consumers with identical energy usage profiles by region and predicts, in the case of non-residential installations, the expected consumption/production values. The resulting distributed system is organized in two main blocks: front-end and back-end. The front-end includes user interface applications for Android mobile devices and Web browsers. The back-end provides data storage and processing functionalities and is installed in a cloud computing platform - the Google App Engine - which provides a standard Web service interface. This option ensures interoperability, scalability and robustness to the system.

Day-ahead Resource Scheduling Including Demand Response for Electric Vehicles

The energy resource scheduling is becoming increasingly important, as the use of distributed resources is intensified and massive gridable vehicle (V2G) use is envisaged. This paper presents a methodology for day-ahead energy resource scheduling for smart grids considering the intensive use of distributed generation and V2G. The main focus is the comparison of different EV management approaches in the day-ahead energy resources management, namely uncontrolled charging, smart charging, V2G and Demand Response (DR) programs i n the V2G approach. Three different DR programs are designed and tested (trip reduce, shifting reduce and reduce+shifting). Othe r important contribution of the paper is the comparison between deterministic and computational intelligence techniques to reduce the execution time. The proposed scheduling is solved with a modified particle swarm optimization. Mixed integer non-linear programming is also used for comparison purposes. Full ac power flow calculation is included to allow taking into account the network constraints. A case study with a 33-bus distribution network and 2000 V2G resources is used to illustrate the performance of the proposed method.

Modified Particle Swarm Optimization Applied to Integrated Demand Response and DG Resources Scheduling

The elastic behavior of the demand consumption jointly used with other available resources such as distributed generation (DG) can play a crucial role for the success of smart grids. The intensive use of Distributed Energy Resources (DER) and the technical and contractual constraints result in large-scale non linear optimization problems that require computational intelligence methods to be solved. This paper proposes a Particle Swarm Optimization (PSO) based methodology to support the minimization of the operation costs of a virtual power player that manages the resources in a distribution network and the network itself. Resources include the DER available in the considered time period and the energy that can be bought from external energy suppliers. Network constraints are considered. The proposed approach uses Gaussian mutation of the strategic parameters and contextual self-parameterization of the maximum and minimum particle velocities. The case study considers a real 937 bus distribution network, with 20310 consumers and 548 distributed generators. The obtained solutions are compared with a deterministic approach and with PSO without mutation and Evolutionary PSO, both using self-parameterization.

A Hybrid Simulated Annealing approach to handle Energy Resource Management considering an intensive use of Electric Vehicles

The massification of electric vehicles (EVs) can have a significant impact on the power system, requiring a new approach for the energy resource management. The energy resource management has the objective to obtain the optimal scheduling of the available resources considering distributed generators, storage units, demand response and EVs. The large number of resources causes more complexity in the energy resource management, taking several hours to reach the optimal solution which requires a quick solution for the next day. Therefore, it is necessary to use adequate optimization techniques to determine the best solution in a reasonable amount of time. This paper presents a hybrid artificial intelligence technique to solve a complex energy resource management problem with a large number of resources, including EVs, connected to the electric network. The hybrid approach combines simulated annealing (SA) and ant colony optimization (ACO) techniques. The case study concerns different EVs penetration levels. Comparisons with a previous SA approach and a deterministic technique are also presented. For 2000 EVs scenario, the proposed hybrid approach found a solution better than the previous SA version, resulting in a cost reduction of 1.94%. For this scenario, the proposed approach is approximately 94 times faster than the deterministic approach.

Distributed Generation and Demand Response Dispatch for a Virtual Power Player Energy and Reserve Provision

Recent changes in the operation and planning of power systems have been motivated by the introduction of Distributed Generation (DG) and Demand Response (DR) in the competitive electricity markets' environment, with deep concerns at the efficiency level. In this context, grid operators, market operators, utilities and consumers must adopt strategies and methods to take full advantage of demand response and distributed generation. This requires that all the involved players consider all the market opportunities, as the case of energy and reserve components of electricity markets. The present paper proposes a methodology which considers the joint dispatch of demand response and distributed generation in the context of a distribution network operated by a virtual power player. The resources' participation can be performed in both energy and reserve contexts. This methodology contemplates the probability of actually using the reserve and the distribution network constraints. Its application is illustrated in this paper using a 32-bus distribution network with 66 DG units and 218 consumers classified into 6 types of consumers.

Evaluation of the Electric Vehicle Impact in the Power Demand Curve in a Smart Grid Environment

Smart grids with an intensive penetration of distributed energy resources will play an important role in future power system scenarios. The intermittent nature of renewable energy sources brings new challenges, requiring an efficient management of those sources. Additional storage resources can be beneficially used to address this problem; the massive use of electric vehicles, particularly of vehicle-to-grid (usually referred as gridable vehicles or V2G), becomes a very relevant issue. This paper addresses the impact of Electric Vehicles (EVs) in system operation costs and in power demand curve for a distribution network with large penetration of Distributed Generation (DG) units. An efficient management methodology for EVs charging and discharging is proposed, considering a multi-objective optimization problem. The main goals of the proposed methodology are: to minimize the system operation costs and to minimize the difference between the minimum and maximum system demand (leveling the power demand curve). The proposed methodology perform the day-ahead scheduling of distributed energy resources in a distribution network with high penetration of DG and a large number of electric vehicles. It is used a 32-bus distribution network in the case study section considering different scenarios of EVs penetration to analyze their impact in the network and in the other energy resources management.

Impact of design options in zero energy building conception: the case of large buildings in Portugal

The new recast of Directive 2010/31/EU in order to implement the new concept NZEB in new buildings, is to be fully respected by all Member States, and is revealed as important measure to promote the reduction of energy consumption of buildings and encouraging the use of renewable energy. In this study, it was tested the applicability of the nearly zero energy building concept to a big size office building and its impact after a 50-years life cycle span.