958 resultados para Electric power factor measurement


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A new family of direct current (DC) to DC converters based on a zero current switching pulse width modulated (ZCS-PWM) soft commutation cell is presented. This ZCS-PWM cell is consists of two transistors, two diodes, two inductors and one capacitor; and provides zero voltage turn-on to the diodes, a zero-current turn-on and a zero-current zero-voltage turn-off to the transistors. In addition, a new commutation cell in a new ZCS-PWM boost rectifier is developed, obtaining a structure with power factor near the unity, high efficiency at wide load range and low total harmonic distortion in the input current.

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This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.

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In order to provide a low cost system of thermal comfort, a common model of home fan, 40 cm diameter size, had its manual four-button control system replaced by an automatic speed control. The new control system has a temperature sensor feeding a microcontroller that, by using an optic coupling, DIAC or TRIAC-based circuit, varies the RMS value of the fan motor input voltage and its speed, according to the room temperature. Over a wide range of velocity, the fan net power and the motor fan input power were measured working under both control system. The temperature of the motor stator and the voltage waveforms were observed too. Measured values analysis showed that the TRIAC-based control system makes the fan motor work at a very low power factor and efficiency values. The worst case is at low velocity range where the higher fan motor stator temperatures were registered. The poor power factor and efficiency and the harmonics signals inserted in the motor input voltage wave by the TRIAC commutation procedure are correlated.

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This paper discusses the utilization of Virtual Instrumentation to the implementation and evaluation of different power definitions, so that classical formulations and new definitions can be compared without the necessity of acquiring different power meters or analyzers. Accordingly, the definitions of IEEE Standard 1459-2000 for the measurement of power quantities under distorted and unbalanced situations, have been digitally implemented. Thus, several power and power factor components related to the decomposition of the measured voltage and current signals have been obtained. The proposed PC-based Virtual Instrument uses a high performance acquisition board and isolated sensors and transducers. All digital algorithms and routines have been implemented by means of a graphical development system. Regarding to the implementation of STD 1459, this paper also proposes several different algorithms to the required decompositions of voltage, current and power components. © 2005 IEEE.

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The present dissertation aims to explore, theoretically and experimentally, the problems and the potential advantages of different types of power converters for “Smart Grid” applications, with particular emphasis on multi-level architectures, which are attracting a rising interest even for industrial requests. The models of the main multilevel architectures (Diode-Clamped and Cascaded) are shown. The best suited modulation strategies to function as a network interface are identified. In particular, the close correlation between PWM (Pulse Width Modulation) approach and SVM (Space Vector Modulation) approach is highlighted. An innovative multilevel topology called MMC (Modular Multilevel Converter) is investigated, and the single-phase, three-phase and "back to back" configurations are analyzed. Specific control techniques that can manage, in an appropriate way, the charge level of the numerous capacitors and handle the power flow in a flexible way are defined and experimentally validated. Another converter that is attracting interest in “Power Conditioning Systems” field is the “Matrix Converter”. Even in this architecture, the output voltage is multilevel. It offers an high quality input current, a bidirectional power flow and has the possibility to control the input power factor (i.e. possibility to participate to active and reactive power regulations). The implemented control system, that allows fast data acquisition for diagnostic purposes, is described and experimentally verified.

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This thesis reports on the investigations, simulations and analyses of novel power electronics topologies and control strategies. The research is financed by an Australian Research Council (ARC) Linkage (07-09) grant. Therefore, in addition to developing original research and contributing to the available knowledge of power electronics, it also contributes to the design of a DC-DC converter for specific application to the auxiliary power supply in electric trains. Specifically, in this regard, it contributes to the design of a 7.5 kW DC-DC converter for the industrial partner (Schaffler and Associates Ltd) who supported this project. As the thesis is formatted as a ‘thesis by publication’, the contents are organized around published papers. The research has resulted in eleven papers, including seven peer reviewed and published conference papers, one published journal paper, two journal papers accepted for publication and one submitted journal paper (provisionally accepted subject to few changes). In this research, several novel DC-DC converter topologies are introduced, analysed, and tested. The similarity of all of the topologies devised lies in their ‘current circulating’ switching state, which allows them to store some energy in the inductor, as extra inductor current. The stored energy may be applied to enhance the performance of the converter in the occurrence of load current or input voltage disturbances. In addition, when there is an alternating load current, the ability to store energy allows the converter to perform satisfactorily despite frequently and highly varying load current. In this research, the capability of current storage has been utilised to design topologies for specific applications, and the enhancement of the performance of the considered applications has been illustrated. The simplest DC-DC converter topology, which has a ‘current circulating’ switching state, is the Positive Buck-Boost (PBB) converter (also known as the non-inverting Buck-Boost converter). Usually, the topology of the PBB converter is operating as a Buck or a Boost converter in applications with widely varying input voltage or output reference voltage. For example, in electric railways (the application of our industrial partner), the overhead line voltage alternates from 1000VDC to 500VDC and the required regulated voltage is 600VDC. In the course of this research, our industrial partner (Schaffler and Associates Ltd) industrialized a PBB converter–the ‘Mudo converter’–operating at 7.5 kW. Programming the onboard DSP and testing the PBB converter in experimental and nominal power and voltage was part of this research program. In the earlier stages of this research, the advantages and drawbacks of utilization of the ‘current circulating’ switching state in the positive Buck-Boost converter were investigated. In brief, the advantages were found to be robustness against input voltage and current load disturbances, and the drawback was extra conduction and switching loss. Although the robustness against disturbances is desirable for many applications, the price of energy loss must be minimized to attract attention to the utilization of the PBB converter. In further stages of this research, two novel control strategies for different applications were devised to minimise the extra energy loss while the advantages of the positive Buck-Boost converter were fully utilized. The first strategy is Smart Load Controller (SLC) for applications with pre-knowledge or predictability of input voltage and/or load current disturbances. A convenient example of these applications is electric/hybrid cars where a master controller commands all changes in loads and voltage sources. Therefore, the master controller has a pre-knowledge of the load and input voltage disturbances so it can apply the SLC strategy to utilize robustness of the PBB converter. Another strategy aiming to minimise energy loss and maximise the robustness in the face of disturbance is developed to cover applications with unexpected disturbances. This strategy is named Dynamic Hysteresis Band (DHB), and is used to manipulate the hysteresis band height after occurrence of disturbance to reduce dynamics of the output voltage. When no disturbance has occurred, the PBB converter works with minimum inductor current and minimum energy loss. New topologies based on the PBB converter have been introduced to address input voltage disturbances for different onboard applications. The research shows that the performance of applications of symmetrical/asymmetrical multi-level diode-clamped inverters, DC-networks, and linear-assisted RF amplifiers may be enhanced by the utilization of topologies based on the PBB converter. Multi-level diode-clamped inverters have the problem of DC-link voltage balancing when the power factor of their load closes to unity. This research has shown that this problem may be solved with a suitable multi-output DC-DC converter supplying DClink capacitors. Furthermore, the multi-level diode-clamped inverters supplied with asymmetrical DC-link voltages may improve the quality of load voltage and reduce the level of Electromagnetic Interference (EMI). Mathematical analyses and experiments on supplying symmetrical and asymmetrical multi-level inverters by specifically designed multi-output DC-DC converters have been reported in two journal papers. Another application in which the system performance can be improved by utilization of the ‘current circulating’ switching state is linear-assisted RF amplifiers in communicational receivers. The concept of ‘linear-assisted’ is to divide the signal into two frequency domains: low frequency, which should be amplified by a switching circuit; and the high frequency domain, which should be amplified by a linear amplifier. The objective is to minimize the overall power loss. This research suggests using the current storage capacity of a PBB based converter to increase its bandwidth, and to increase the domain of the switching converter. The PBB converter addresses the industrial demand for a DC-DC converter for the application of auxiliary power supply of a typical electric train. However, after testing the industrial prototype of the PBB converter, there were some voltage and current spikes because of switching. To attenuate this problem without significantly increasing the switching loss, the idea of Active Gate Signalling (AGS) is presented. AGS suggests a smart gate driver that selectively controls the switching process to reduce voltage/current spikes, without unacceptable reduction in the efficiency of switching.

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Three different methods of inclusion of current measurements by phasor measurement units (PMUs) in a power sysetm state estimator is investigated. A comprehensive formulation of the hybrid state estimator incorporating conventional, as well as PMU measurements, is presented for each of the three methods. The behaviour of the elements because of the current measurements in the measurement Jacobian matrix is examined for any possible ill-conditioning of the state estimator gain matrix. The performance of the state estimators are compared in terms of the convergence properties and the varian in the estimated states. The IEEE 14-bus and IEEE 300-bus systems are used as test beds for the study.

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The operation of thyristor-controlled static VAR compensators (SVCs) at various conduction angles can be used advantageously to meet the unablanced reactive power demands in a system. However, such operation introduces harmonic currents into the AC system. This paper presents an algorithm to evaluate an optimum combination of the phase-wise reactive power generations from SVC and balanced reactive power supply from the AC system, based on the defined performance indices, namely, the telephone influence factor (TIF), the total harmonic current factor (IT) and the distortion factor (D). Results of the studies conducted on a typical distribution system are presented and discussed.

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State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

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The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

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In the engineering reinforcement of-rock and soil mass, engineers must consider how to obtain better reinforcing effect at the cost of less reinforcing expense, which, in fact, is the aim of reinforcement design. In order to accomplish the purpose, they require not only researching the material used to reinforce and its structure, but also taking into account of several important geological factors, such as the structure and property of rock and soil mass. How to improve the reinforcing effect according to engineering geomechanical principle at the respect of the reinforcement of engineering soil and rock mass is studied and discussed in this paper. The author studies the theory, technology and practice of geotechnical reinforcement based on engineering geomechanics, taking example for the soil treatment of Zhengzhou Airport, the effect analysis of reinforcement to the slope on the left bank of Wuqiangxi Hydropower Station and the reinforcing design of the No. 102 Landslide and unique sand-slide slope on the Sichuan-Tibet Highway. The paper is comprised of two parts for the convenience of discussion. In the first part, from the first chapter to the fifth chapter, trying to perform the relevant research and application at the viewpoint of soil mass engineering geomechanics, the author mainly discusses the study of reinforcing soft ground soil through dynamical consolidation and its application. Then, in the second part, from the sixth chapter to the eleventh chapter, the study of new technologies in the rock slope reinforcement and their application are discussed. The author finds that not only better reinforcing effect can be gained in the research where the principle and method of rock mass engineering geomechanics is adopted, but also new reinforcing technologies can be put forward. Zhengzhou Airport is an important one in central plains. It lies on Yellow River alluvial deposit and the structure of stratum is complex and heterogeneous. The area of airport is very large, which can result in differential settlement easily, damage of airport and aircraft accident, whereas, there are no similar experiences to dispose the foundation, so the foundation treatment become a principal problem. During the process of treatment, the method of dynamic compaction was adopted after compared with other methods using the theory of synthetic integration. Dynamic compaction is an important method to consolidate foundation, which was successfully used in the foundation of Zhengzhou Airport. For fill foundation, controlling the thickness of fill so as to make the foundation treatment can reach the design demand and optimum thickness of the fill is a difficult problem. Considering this problem, the author proposed a calculation method to evaluate the thickness of fill. The method can consider not only the self-settlement of fill but also the settlement of the ground surface under applied load so as to ensure the settlement occurred during the using period can satisfy the design demand. It is proved that the method is correct after using it to choose reasonable energy of dynamic compaction to treat foundation. At the same time, in order to examine the effect of dynamic compaction, many monitor methods were adopted in the test such as static loading test, modulus of resilience test, deep pore pressure -test, static cone penetration test and the variation of the pore volume measurement. Through the tests, the author summarized the discipline of the accumulation and dissipation of pore pressure in Yellow River alluvial deposit under the action of dynamic compaction, gave a correct division of the property change of silt and clay under dynamic compaction, determined the bearing capacity of foundation after treatment and weighted the reinforcing effect of dynamic consolidation from the variation of the soil particle in microcosmic and the parameter of soil mass' density. It can be considered that the compactness of soil is in proportion to the energy of dynamic compaction. This conclusion provided a reference to the research of the "Problem of Soil Structure-the Central Problem of Soil Mechanics in 21 Century ". It is also important to strengthen rock mass for water conservancy and electric power engineering. Slip-resistance pile and anchoring adit full of reinforced concrete are usually adopted in engineering experience to strengthen rock mass and very important for engineering. But there also some deficiency such as the weakest section can't be highlighted, the monitor is inconvenient and the diameter of pile and adit is very large etc. The author and his supervisor professor Yangzhifa invented prestressed slip-resistance pile and prestressed anchoring adit full of reinforced concrete, utilizing the advantage that the prestressed structure has better anti-tensile characteristic (this invention is to be published). These inventions overcome the disadvantages of general slip-resistance pile and anchoring adit full of reinforced concrete and have the functions of engineering prospecting, strengthening, drainage and monitor simultaneous, so they have better strengthened effect and be more convenient for monitor and more economical than traditional methods. Drainage is an important factor in treatments of rock mass and slop. In view of the traditional drainage method that drainage pore often be clogged so as to resulted in incident, professor Yangzhifa invented the method and setting of guide penetration by fiber bundle. It would take good effect to use it in prestressed slip-resistance pile and anchoring adit full of reinforced concrete. In this paper, the author took example for anchoring adit full of reinforced concrete used to strengthen Wuqiangxi left bank to simulate the strengthened effect after consolidated by prestressed slip-resistance pile, took example for 102 landslide occurred along Sichuan-Tibet highway to simulate the application of slip-resistance pile and the new technology of drainage. At the same time the author proposed the treatment method of flowing sand in Sichuan-Tibet highway, which will benefit the study on strengthening similar engineering. There are five novelties in the paper with the author's theoretical study and engineering practice: 1. Summarizing the role of pore water pressure accumulation and dissipation of the Yellow River alluvial and diluvial soil under the action of dynamical consolidation, which has instructive significance in the engineering construction under the analogical engineering geological conditions in the future. It has not been researched by the predecessors. 2. Putting forward the concept of density D in microcosmic based on the microcosmical structure study of the soil sample. Adopting D to weight the reinforcing effect of dynamic consolidation is considered to be appropriate by the means of comparing the D values of Zhengzhou Airport's ground soil before with after dynamically consolidating reinforcement, so a more convenient balancing method can be provided for engineering practice. 3. According to the deep research into the soil mass engineering geology, engineering rock and soil science, soil mechanics, as well as considerable field experiments, improving the consolidating method in airport construction, from the conventional method, which is dynamically compactmg original ground surface firstly, then filling soil and dynamically layer-consolidating or layer-compacting at last to the upgraded method, which is performing dynamical consolidation after filling soil to place totally at the extent of the certain earth-filling depth. The result of the dynamical consolidation not only complies with the specifications, but also reduces the soil treatment investment by 10 million RMB. 4. Proposing the method for calculating the height of the filled soil by the means of estimating the potential displacement produced in the original ground surface and the filled earth soil under the possible load, selecting the appropriate dynamically-compacting power and determining the virtual height of the filled earth soil. The method is proved to be effective and scientific. 5. According to the thought of Engineering Geomechanics Metal-Synthetic Methodology (EGMS), patenting two inventions (to the stage of roclamation, with Professor Yang Zhi-fa, the cooperative tutor, and etc.) in which multi-functions, engineering geological investigation, reinforcement, drainage and strength remedy, are integrated all over in one body at the viewpoint of the breakage mechanism of the rock slope.

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This thesis is concerned with inductive charging of electric vehicle batteries. Rectified power form the 50/60 Hz utility feeds a dc-ac converter which delivers high-frequency ac power to the electric vehicle inductive coupling inlet. The inlet configuration has been defined by the Society of Automotive Engineers in Recommended Practice J-1773. This thesis studies converter topologies related to the series resonant converter. When coupled to the vehicle inlet, the frequency-controlled series-resonant converter results in a capacitively-filtered series-parallel LCLC (SP-LCLC) resonant converter topology with zero voltage switching and many other desirable features. A novel time-domain transformation analysis, termed Modal Analysis, is developed, using a state variable transformation, to analyze and characterize this multi-resonant fourth-orderconverter. Next, Fundamental Mode Approximation (FMA) Analysis, based on a voltage-source model of the load, and its novel extension, Rectifier-Compensated FMA (RCFMA) Analysis, are developed and applied to the SP-LCLC converter. The RCFMA Analysis is a simpler and more intuitive analysis than the Modal Analysis, and provides a relatively accurate closed-form solution for the converter behavior. Phase control of the SP-LCLC converter is investigated as a control option. FMA and RCFMA Analyses are used for detailed characterization. The analyses identify areas of operation, which are also validated experimentally, where it is advantageous to phase control the converter. A novel hybrid control scheme is proposed which integrates frequency and phase control and achieves reduced operating frequency range and improved partial-load efficiency. The phase-controlled SP-LCLC converter can also be configured with a parallel load and is an excellent option for the application. The resulting topology implements soft-switching over the entire load range and has high full-load and partial-load efficiencies. RCFMA Analysis is used to analyze and characterize the new converter topology, and good correlation is shown with experimental results. Finally, a novel single-stage power-factor-corrected ac-dc converter is introduced, which uses the current-source characteristic of the SP-LCLC topology to provide power factor correction over a wide output power range from zero to full load. This converter exhibits all the advantageous characteristics of its dc-dc counterpart, with a reduced parts count and cost. Simulation and experimental results verify the operation of the new converter.

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Trabalho Final de Mestrado para a obtenção de grau de Mestre em Engenharia Electrotécnica Ramo de Automação e Electrónica Industrial

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Uusiutuvan sähköntuotannon osuuden kasvaessa kasvaa tarve tasata sähköntuotannon ja kulutuksen vaihteluita varastoimalla sähköä. Power to Gas (PtG) - sähköenergiasta luonnonkaasua tarjoaa yhden mahdollisuuden varastoida sähköä. Sähköä käytetään veden elektrolyysiin, jossa syntynyt vety käytetään metanoinissa yhdessä hiilidioksidin kanssa muodostamaan korvaavaa luonnonkaasua. Näin syntynyttä korvaava luonnonkaasua sähköstä kutsutaan e-SNG-kaasuksi. Tässä työssä tutkitaan PtG-laitoksen investointi, käyttö- ja kunnossapitokuluja. Työssä luodaan laskentamalli, jolla lasketaan PtG-laitoksen neljälle käyttötapaukselle kannattavuuslaskelma. Käyttötapauksille lasketaan myös herkkyystarkasteluja. Kannattavuuslaskelmien perusteella päätellään PtG-laitoksen liiketoimintamahdollisuudet Suomessa. Työssä laskettujen kannattavuuslaskelmien perusteella PtG-laitoksen perustapausten liiketoimintamahdollisuudet ovat huonot. Laskettujen herkkyystarkastelujen perusteella havaittiin, että investointikulut, laitoksen ajoaika ja lisätulot hapesta ja lämmöstä ovat kannattavuuden kannalta kriittisimmät menestystekijät.

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Three multivariate statistical tools (principal component analysis, factor analysis, analysis discriminant) have been tested to characterize and model the sags registered in distribution substations. Those models use several features to represent the magnitude, duration and unbalanced grade of sags. They have been obtained from voltage and current waveforms. The techniques are tested and compared using 69 registers of sags. The advantages and drawbacks of each technique are listed