Converter-flux-based current control of voltage source PWM rectifiers - analysis and implementation

Pulsewidth-modulated (PWM) rectifier technology is increasingly used in industrial applications like variable-speed motor drives, since it offers several desired features such as sinusoidal input currents, controllable power factor, bidirectional power flow and high quality DC output voltage. To achieve these features,however, an effective control system with fast and accurate current and DC voltage responses is required. From various control strategies proposed to meet these control objectives, in most cases the commonly known principle of the synchronous-frame current vector control along with some space-vector PWM scheme have been applied. Recently, however, new control approaches analogous to the well-established direct torque control (DTC) method for electrical machines have also emerged to implement a high-performance PWM rectifier. In this thesis the concepts of classical synchronous-frame current control and DTC-based PWM rectifier control are combined and a new converter-flux-based current control (CFCC) scheme is introduced. To achieve sufficient dynamic performance and to ensure a stable operation, the proposed control system is thoroughly analysed and simple rules for the controller design are suggested. Special attention is paid to the estimationof the converter flux, which is the key element of converter-flux-based control. Discrete-time implementation is also discussed. Line-voltage-sensorless reactive reactive power control methods for the L- and LCL-type line filters are presented. For the L-filter an open-loop control law for the d-axis current referenceis proposed. In the case of the LCL-filter the combined open-loop control and feedback control is proposed. The influence of the erroneous filter parameter estimates on the accuracy of the developed control schemes is also discussed. A newzero vector selection rule for suppressing the zero-sequence current in parallel-connected PWM rectifiers is proposed. With this method a truly standalone and independent control of the converter units is allowed and traditional transformer isolation and synchronised-control-based solutions are avoided. The implementation requires only one additional current sensor. The proposed schemes are evaluated by the simulations and laboratory experiments. A satisfactory performance and good agreement between the theory and practice are demonstrated.

Identification of Some Additional Loss Components in High-Power Low-Voltage Permanent Magnet Generators

Permanent magnet generators (PMG) represent the cutting edge technology in modern wind mills. The efficiency remains high (over 90%) at partial loads. To improve the machine efficiency even further, every aspect of machine losses has to be analyzed. Additional losses are often given as a certain percentage without providing any detailed information about the actual calculation process; meanwhile, there are many design-dependent losses that have an effect on the total amount of additional losses and that have to be taken into consideration. Additional losses are most often eddy current losses in different parts of the machine. These losses are usually difficult to calculate in the design process. In this doctoral thesis, some additional losses are identified and modeled. Further, suggestions on how to minimize the losses are given. Iron losses can differ significantly between the measured no-load values and the loss values under load. In addition, with embedded magnet rotors, the quadrature-axis armature reaction adds losses to the stator iron by manipulating the harmonic content of the flux. It was, therefore, re-evaluated that in salient pole machines, to minimize the losses and the loss difference between the no-load and load operation, the flux density has to be kept below 1.5 T in the stator yoke, which is the traditional guideline for machine designers. Eddy current losses may occur in the end-winding area and in the support structure of the machine, that is, in the finger plate and the clamping ring. With construction steel, these losses account for 0.08% of the input power of the machine. These losses can be reduced almost to zero by using nonmagnetic stainless steel. In addition, the machine housing may be subjected to eddy current losses if the flux density exceeds 1.5 T in the stator yoke. Winding losses can rise rapidly when high frequencies and 10–15 mm high conductors are used. In general, minimizing the winding losses is simple. For example, it can be done by dividing the conductor into transposed subconductors. However, this comes with the expense of an increase in the DC resistance. In the doctoral thesis, a new method is presented to minimize the winding losses by applying a litz wire with noninsulated strands. The construction is the same as in a normal litz wire but the insulation between the subconductors has been left out. The idea is that the connection is kept weak to prevent harmful eddy currents from flowing. Moreover, the analytical solution for calculating the AC resistance factor of the litz-wire is supplemented by including an end-winding resistance in the analytical solution. A simple measurement device is developed to measure the AC resistance in the windings. In the case of a litz-wire with originally noninsulated strands, vacuum pressure impregnation (VPI) is used to insulate the subconductors. In one of the two cases studied, the VPI affected the AC resistance factor, but in the other case, it did not have any effect. However, more research is needed to determine the effect of the VPI on litz-wire with noninsulated strands. An empirical model is developed to calculate the AC resistance factor of a single-layer formwound winding. The model includes the end-winding length and the number of strands and turns. The end winding includes the circulating current (eddy currents that are traveling through the whole winding between parallel strands) and the main current. The end-winding length also affects the total AC resistance factor.

Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.

Fuzzy Principal Components Analysis

Due to the large number of characteristics, there is a need to extract the most relevant characteristicsfrom the input data, so that the amount of information lost in this way is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the principal components analysis (PCA) may be used. This thesis describes an extension of principal components analysis (PCA) allowing the extraction ofa finite number of relevant features from high-dimensional fuzzy data and noisy data. PCA finds linear combinations of the original measurement variables that describe the significant variation in the data. The comparisonof the two proposed methods was produced by using postoperative patient data. Experiment results demonstrate the ability of using the proposed two methods in complex data. Fuzzy PCA was used in the classificationproblem. The classification was applied by using the similarity classifier algorithm where total similarity measures weights are optimized with differential evolution algorithm. This thesis presents the comparison of the classification results based on the obtained data from the fuzzy PCA.

Protection of publicly distributed software components

The nature of client-server architecture implies that some modules are delivered to customers. These publicly distributed commercial software components are under risk, because users (and simultaneously potential malefactors) have physical access to some components of the distributed system. The problem becomes even worse if interpreted programming languages are used for creation of client side modules. The language Java, which was designed to be compiled into platform independent byte-code is not an exception and runs the additional risk. Along with advantages like verifying the code before execution (to ensure that program does not produce some illegal operations)Java has some disadvantages. On a stage of byte-code a java program still contains comments, line numbers and some other instructions, which can be used for reverse-engineering. This Master's thesis focuses on protection of Java code based client-server applications. I present a mixture of methods to protect software from tortious acts. Then I shall realize all the theoretical assumptions in a practice and examine their efficiency in examples of Java code. One of the criteria's to evaluate the system is that my product is used for specialized area of interactive television.

Jäänhoitokoneen voimansiirron kehittäminen

Diplomityön tavoitteena oli tutkia jäänhoitokoneen nykyisen voimanlähteen mahdollista korvaamista eri tekniikkaan perustuvilla voimanlähteillä. Teoriaosassa tutustutaan jäänhoidon historiaan eli mistä tarve jäänhoitokoneiden suunnitteluun ja valmistukseen on syntynyt. Samoin esitellään jäähoidon koko prosessi ja eri käyttövoimanlähteet mitä maailmalla jäänhoitokoneissa on käytössä. Käytännön osuus keskittyy aluksi esittelemään jäänhoitokoneen nykyisen toimintaperiaatteen, siinä käytetyt komponentit sekä kartoittaa koko järjestelmän heikkoudet ja vahvuudet. Osuudessa selvitetään myös kahden nykyisestä poikkeavien voimanlähteiden toimintaperiaatteet sekä niiden mahdollisuudesta korvata jäänhoitokoneen nykyinen järjestelmä. Näiden osalta selvitetään myös vaihtoehtoisten tekniikoiden heikkoudet ja vahvuudet. Työn tuloksena selvisi, että uudet korvaavat voimanlähteet ovat vielä kehitysvaiheessa eikä siis vielä tarpeeksi valmiita, suorituskykyisiä tai saasteettomia korvaamaan nykyistä 0-päästöistä sähkömoottorijärjestelmää. Sen sijaan kehitysehdotuksena syntyi idea nykyisen järjestelmän optimoimisesta paremman hyötysuhteen ja sitä mukaa akkujen eliniän parantamiseksi.

Workplace adjustment of an expatriate manager: identifying key components from a social capital perspective

Perustaen tutkimuksen kansainvälisen sopeutumisen teoreettiselle rungolle täydentäen sitä sosiaalisen pääoman teorialla, tämä tutkielma tutkii kuinka johtoasemassa oleva ulkosuomalainen luo hyvin toimivan sosiaalisen verkoston hong kongilaisella työpaikallansa. Tutkielma lähestyy aihetta Nahapietin ja Ghoshalin (1998) kehittämän sosiaalisen pääoman kolmen ulottuvuuden mallin avulla. Tutkielmassa kirjallisuudesta haettua teoriaa käytetään tutkimustavarten tehtyjen haastattelujen analysointiapuna. Tutkimalla sosiaalista pääomaa, kansainvälisen sopeutumisen kirjallisuutta, ekspatriootin perinteisiä menestystekijöitä ja guanxia (kiinalaisten henkilökohtaisia siteitä) tämän tutkimuksen teoriaosuus implikoi, että sosiaalisella pääomalla tulisi olla täydentävä rooli kansainvälisen sopeutumisen kirjallisuudessa. Sosiaalisen pääoman kolmen ulottuvuuden mallia käytetään pohjana empiirisen datan analysointiin. Tutkielman empiiriset tulokset osoittavat, että työpaikan sosiaaliseen verkostoon sopeutuminen liittyy exspatriootin kykyyn käsitellä estäviä ja mahdollistajia sosiaalisen pääoman luontiin vaikuttavia tekijöitä. Lisäksi sopeutuminen vaatii exspatriootin tunnistavan kohdemaalle tyypillisiä exspatriootin menestystekijöitä ja ekspatriootinomia tärkeitä henkilökohtaisia ominaisuuksia.

Effect of physico-chemical conditions and operating parameters on flux and retention of different components in ultrafiltration and nanofiltration fractionation of sweet whey

Tässä väitöstutkimuksessa tutkittiin fysikaaliskemiallisten olosuhteiden ja toimintaparametrien vaikutusta juustoheran fraktiointiin. Kirjallisuusosassa on käsitelty heran ympäristövaikutusta, heran hyödyntämistä ja heran käsittelyä kalvotekniikalla. Kokeellinen osa on jaettu kahteen osaan, joista ensimmäinen käsittelee ultrasuodatusta ja toinen nanosuodatusta juustoheran fraktioinnissa. Ultrasuodatuskalvon valinta tehtiin perustuen kalvon cut-off lukuun, joka oli määritetty polyetyleeniglykoliliuoksilla olosuhteissa, joissa konsentraatiopolariosaatioei häiritse mittausta. Kriittisen vuon konseptia käytettiin sopivan proteiinikonsentraation löytämiseksi ultrasuodatuskokeisiin, koska heraproteiinit ovat tunnetusti kalvoa likaavia aineita. Ultrasuodatuskokeissa tutkittiin heran eri komponenttien suodattumista kalvon läpi ja siihen vaikuttavia ominaisuuksia. Herapermeaattien peptidifraktiot analysoitiin kokoekskluusiokromatografialla ja MALDI-TOF massaspektrometrillä. Kokeissa käytettävien nanosuodatuskalvojen keskimääräinen huokoskoko analysoitiin neutraaleilla liukoisilla aineilla ja zeta-potentiaalit virtauspotentiaalimittauksilla. Aminohappoja käytettiin malliaineina tutkittaessa huokoskoon ja varauksen merkitystä erotuksessa. Aminohappojen retentioon vaikuttivat pH ja liuoksen ionivahvuus sekä molekyylien väliset vuorovaikutukset. Heran ultrasuodatuksessa tuotettu permeaatti, joka sisälsi pieniä peptidejä, laktoosia ja suoloja, nanosuodatettiin happamassa ja emäksisessä pH:ssa. Emäksisissä oloissa tehdyssä nanosuodatuksessa foulaantumista tapahtui vähemmän ja permeaattivuo oli parempi. Emäksisissä oloissa myös selektiivisyys laktoosin erotuksessa peptideistä oli parempi verrattuna selektiivisyyteen happamissa oloissa.

Project Success through Effective Decisions: Case Studies on Project Goal Setting, Success Evaluation and Managerial Decision Making

The objective of the thesis is to structure and model the factors that contribute to and can be used in evaluating project success. The purpose of this thesis is to enhance the understanding of three research topics. The goal setting process, success evaluation and decision-making process are studied in the context of a project, business unitand its business environment. To achieve the objective three research questionsare posed. These are 1) how to set measurable project goals, 2) how to evaluateproject success and 3) how to affect project success with managerial decisions.The main theoretical contribution comes from deriving a synthesis of these research topics which have mostly been discussed apart from each other in prior research. The research strategy of the study has features from at least the constructive, nomothetical, and decision-oriented research approaches. This strategy guides the theoretical and empirical part of the study. Relevant concepts and a framework are composed on the basis of the prior research contributions within the problem area. A literature review is used to derive constructs of factors withinthe framework. They are related to project goal setting, success evaluation, and decision making. On the basis of this, the case study method is applied to complement the framework. The empirical data includes one product development program, three construction projects, as well as one organization development, hardware/software, and marketing project in their contexts. In two of the case studiesthe analytic hierarchy process is used to formulate a hierarchical model that returns a numerical evaluation of the degree of project success. It has its origin in the solution idea which in turn has its foundation in the notion of projectsuccess. The achieved results are condensed in the form of a process model thatintegrates project goal setting, success evaluation and decision making. The process of project goal setting is analysed as a part of an open system that includes a project, the business unit and its competitive environment. Four main constructs of factors are suggested. First, the project characteristics and requirements are clarified. The second and the third construct comprise the components of client/market segment attractiveness and sources of competitive advantage. Together they determine the competitive position of a business unit. Fourth, the relevant goals and the situation of a business unit are clarified to stress their contribution to the project goals. Empirical evidence is gained on the exploitation of increased knowledge and on the reaction to changes in the business environment during a project to ensure project success. The relevance of a successful project to a company or a business unit tends to increase the higher the reference level of project goals is set. However, normal performance or sometimes performance below this normal level is intentionally accepted. Success measures make project success quantifiable. There are result-oriented, process-oriented and resource-oriented success measures. The study also links result measurements to enablers that portray the key processes. The success measures can be classified into success domains determining the areas on which success is assessed. Empiricalevidence is gained on six success domains: strategy, project implementation, product, stakeholder relationships, learning situation and company functions. However, some project goals, like safety, can be assessed using success measures that belong to two success domains. For example a safety index is used for assessing occupational safety during a project, which is related to project implementation. Product safety requirements, in turn, are connected to the product characteristics and thus to the product-related success domain. Strategic success measures can be used to weave the project phases together. Empirical evidence on their static nature is gained. In order-oriented projects the project phases are oftencontractually divided into different suppliers or contractors. A project from the supplier's perspective can represent only a part of the ¿whole project¿ viewed from the client's perspective. Therefore static success measures are mostly used within the contractually agreed project scope and duration. Proof is also acquired on the dynamic use of operational success measures. They help to focus on the key issues during each project phase. Furthermore, it is shown that the original success domains and success measures, their weights and target values can change dynamically. New success measures can replace the old ones to correspond better with the emphasis of the particular project phase. This adjustment concentrates on the key decision milestones. As a conclusion, the study suggests a combination of static and dynamic success measures. Their linkage to an incentive system can make the project management proactive, enable fast feedback and enhancethe motivation of the personnel. It is argued that the sequence of effective decisions is closely linked to the dynamic control of project success. According to the used definition, effective decisions aim at adequate decision quality and decision implementation. The findings support that project managers construct and use a chain of key decision milestones to evaluate and affect success during aproject. These milestones can be seen as a part of the business processes. Different managers prioritise the key decision milestones to a varying degree. Divergent managerial perspectives, power, responsibilities and involvement during a project offer some explanation for this. Finally, the study introduces the use ofHard Gate and Soft Gate decision milestones. The managers may use the former milestones to provide decision support on result measurements and ad hoc critical conditions. In the latter milestones they may make intermediate success evaluation also on the basis of other types of success measures, like process and resource measures.

Use of innovative High Voltage components in GOST standard market

In Russian there are more than twenty thousand primary substations 35/110 kV and 10/110 kV. According to the Government Plan of Power Industry Development until 2020 year more than hundred new substations will e installed every year and even more renewed. The goal of this Thesis is to find out in this business environment what are the technology opportunities of prefabricated substation modules in new substation or in modernization of old substations in Russia.

Trigger and data link system for CMS Resistive Plate Chambers at the LHC accelerator

The purpose of the work was to realize a high-speed digital data transfer system for RPC muon chambers in the CMS experiment on CERN’s new LHC accelerator. This large scale system took many years and many stages of prototyping to develop, and required the participation of tens of people. The system interfaces to Frontend Boards (FEB) at the 200,000-channel detector and to the trigger and readout electronics in the control room of the experiment. The distance between these two is about 80 metres and the speed required for the optic links was pushing the limits of available technology when the project was started. Here, as in many other aspects of the design, it was assumed that the features of readily available commercial components would develop in the course of the design work, just as they did. By choosing a high speed it was possible to multiplex the data from some the chambers into the same fibres to reduce the number of links needed. Further reduction was achieved by employing zero suppression and data compression, and a total of only 660 optical links were needed. Another requirement, which conflicted somewhat with choosing the components a late as possible was that the design needed to be radiation tolerant to an ionizing dose of 100 Gy and to a have a moderate tolerance to Single Event Effects (SEEs). This required some radiation test campaigns, and eventually led to ASICs being chosen for some of the critical parts. The system was made to be as reconfigurable as possible. The reconfiguration needs to be done from a distance as the electronics is not accessible except for some short and rare service breaks once the accelerator starts running. Therefore reconfigurable logic is extensively used, and the firmware development for the FPGAs constituted a sizable part of the work. Some special techniques needed to be used there too, to achieve the required radiation tolerance. The system has been demonstrated to work in several laboratory and beam tests, and now we are waiting to see it in action when the LHC will start running in the autumn 2008.

The evaluation of hazardous gas components caused by the thermal degradation of plant oils and animal fats

Neste Oil has introduced plant oils and animal fats for the production of NExBTL renewable diesel, and these raw materials differ from the conventional mineral based oils. One subject of new raw materials study is thermal degradation, or in another name pyrolysis, of these organic oils and fats. The aim of this master’s thesis is to increase knowledge on thermal degradation of these new raw materials, and to identify possible gaseous harmful thermal degradation compounds. Another aim is to de-termine the health and environmental hazards of identified compounds. One objective is also to examine the formation possibilities of hazardous compounds in the produc-tion of NExBTL-diesel. Plant oils and animal fats consist mostly of triglycerides. Pyrolysis of triglycerides is a complex phenomenon, and many degradation products can be formed. Based on the literature studies, 13 hazardous degradation products were identified, one of which was acrolein. This compound is very toxic and dangerous to the environment. Own pyrolysis experiments were carried out with rapeseed and palm oils, and with a mix-ture of palm oil and animal fat. At least 12 hazardous compounds, including acrolein, were analysed from the gas phase. According to the experiments, the factors which influence on acrolein formation are the time of the experiment, the sphere (air/hydrogen) in which the experiment is carried out, and the characteristics of the used oil. The production of NExBTL-diesel is not based on pyrolysis. This is why thermal degradation is possible only when abnormal process conditions prevail.

On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.