Current control is an important topic in modern power electronics system. For voltage source inverters, current control loop ensures the waveform quality at steady state and the fast response at transient state. To improve the current control performance, quite a few nonlinear control strategies have been presented and one well-known strategy is the hysteresis current control. It achieves fast response without stability issue and it has high control precision. However, for voltage source inverter applications, hysteresis current control has a wide switching frequency range, which introduces additional switching loss and impacts the design of harmonic filter. Other nonlinear current control strategies include one-cycle control, non-linear carrier control, peak current control, charge control, and so on. However, these control strategies are just suitable for specific topologies and it cannot be directly used by voltage source inverters. The recently proposed parabolic current control solves the frequency variation problem of hysteresis current control by employing a pair of parabolic carriers as the control band. By the use of parabolic current control, approximate-constant switching frequency can be achieved. Due to the cycle-by-cycle control structure, it inherently has fast response speed and high precision. These advantages make it suitable for voltage source inverters, including stand-alone inverters, grid connected inverters, active power filters, and power factor correction applications. However, parabolic current control has some limitations, such as dead-time effects, only working as bipolar PWM, complex hardware implementation, non-ideal converging speed. These problems are respectively solved in this dissertation and solutions include dead-time compensation, the implementation on dual-carrier unipolar PWM, sensorless parabolic current control, single-step current control. With the proposed dead-time compensation strategy, current control precision is improved and stable duty-cycle range are extended. Dual-carrier PWM implementation of parabolic current control has smaller harmonic filter size and lower power loss. Sensorless parabolic current control decreases the cost of system and enhances the noise immunity capability. Single-step current control pushes the convergence speed to one switching operation with simple implementation. High switching frequency is allowed and power density can be improved. Detailed analysis, motivation and experimental verification of all these innovations are covered in this dissertation. In addition, the duality phenomenon exists in electrical circuits, such as Thevenin's theorem and Norton's theorem, capacitance and inductance. These associated pairs are called duals. The dual of parabolic current control is derived and named parabolic voltage control. Parabolic voltage control solves the audible noise problem of burst mode power converters and maintains high efficiency in the designed boost converter. / Ph. D.

First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference approximations for deterministic linear second order partial differential equations of parabolic type and give sufficient conditions under which the approximations in space and time can be simultaneously accelerated to an arbitrarily high order.

This thesis presents and demonstrates procedures to model and optimize the collector field of a parabolic trough solar thermal power plant. The collector field of such a plant is universally organized into parallel loops of solar collectors. Heat transfer fluid returning from the energy conversion plant is heated to a moderately high temperature in the field. Typically fluid enters a collector loop around 270 °C and leaves at 380 °C. The fluid is then returned to the plant to generate steam. In the first part of this thesis, the collector field and the energy conversion system of a typical parabolic trough solar thermal power plant are modeled. The model is compared with actual performance data and is enhanced and verified as necessary. Originally, the collectors in the plants under consideration were provided with evacuated tube receivers of the highest feasible efficiency without much regard for cost effectiveness. In practice, these receivers have failed at an unexpected rate and need replacement. It is unlikely that a very expensive evacuated tube receiver is now the most cost effective for every location in a collector loop. In particular, a receiver optimized for 270 °C operation may not be optimal at 380 °C. For example, a relatively inexpensive receiver with a flat black absorber and no vacuum may be more cost effective in the lower temperature segments of a loop. In the second part of this thesis, a procedure for the optimum deployment of collectors is developed and demonstrated. The results of this research should be directly applicable to the refurbishment and upgrading of several of the largest solar energy plants in the world.

Transitioning the industrial sector’s energy system to renewable sources is crucial to reduce climate change. There is no exception for China, currently having the highest absolute levels of greenhouse gas (GHG) emissions in the world. The industrial sector accounts for about two thirds of the national energy consumption and coal is the country’s most important energy source. The integration of alternative energy sources such as solar can help transitioning the country’s energy system. By presenting a techno-economic analysis, this thesis gives an indication for profitability and in what extent there is a potential to cover the steam demand with a decentralized solar heat technology for two industries, fish and textile, in the Zhejiang province in eastern China. The used solar technology is a system with parabolic trough collectors (PTCs) with an integrated gas fired boiler. The PTC-system is compared with a coal-fired centralized supplier. The analyzed factors were roof area, solar irradiation, solar fraction, cost for steam from the centralized suppliers and cost of coal and natural gas. The maximum CO2 reduction is found to be dependent on the potential installation area. The greater area installed, the larger is the capacity and thus also the CO2 savings. The share of total steam demand covered by solar is directly proportional to the demand in relation to the installed solar capacity. The fish industry, having the lowest steam demand in relation to the roof area, is found to be able to save the largest relative proportion of CO2 emissions. Different scenarios are presented, modifying the fuel cost and fuel type for the PTC-system’s boiler, adjusting the steam cost from the centralized suppliers and using two different solar fractions of 35% and 50%. The CO2 savings depends on what fuel is being used and the solar fraction. Larger CO2 reductions are possible with a gas fired boiler compared to a coal fired one. But using a coal fired boiler makes it more economically profitable, matching the low coal price used for the centralized supplier. The scenario with most CO2 reductions is attained when using a high solar fraction of 50% and a natural gas fired boiler. The annual CO2 savings is then ranging from 15 tons per year for the company having the lowest steam capacity, up to 2090 tons/year for the company with one of the highest. Another significant factor is the companies’ seasonal activity. For the company having the least amount of active days per year (84 out of 365 days), the PTC-system is unprofitable whichever scenario. However, fuel costs for the boiler is found to be one of the most significant factors for the outcome determining if the investigated PTC-system is profitable or not. For all of the companies, there was only one that could provide all its steam demand with the PTC-system. This indicates that other energy sources need to be integrated to provide the steam demand of the enterprises with a renewable energy system. / Att omvandla industrins energisystem med förnyelsebara energikällor är väsentligt för att bromsa klimatförändringarna. Det är inget undantag för Kina, som nuvarande har de största absoluta nivåerna av utsläpp av växthusgaser i världen. Industrin står för ca två tredjedelar av den nationella energiförbrukningen och kol är landets största energikälla. Integrerandet av andra alternativ såsom solenergi kan dock hjälpa till i landets energiomvandling. Denna rapport syftar till att presentera en tekno-ekonomisk analys av en decentraliserad solfångare och ge indikation på lönsamhet samt i vilken grad tekniken kan förse behovet av ånga för två industrier, textil och fiske, i Zhejiang provinsen i östra Kina. Den solfångarteknik som används är ett system med Parabolic trough collectors (PTCs) med integrerad gaseldad ångpanna. Systemet jämförs med kraftvärmeverk som drivs med kol. De analyserade faktorerna är takytan, solar fraction, solinstrålning, kostnad för ånga samt ångpannans bränslekostnader. Besparingarna för CO2-utsläpp beror på den potentiella installationsytan. Ju större installationsyta, desto högre kapacitet och därmed högre CO2-besparingar. Andelen av behovet ånga som kan förses med solfångare är i direkt proportion till takytan och det totala behovet. Fiskeindustrin, som har lägre ångbehov i relation till takyta, visar sig kunna spara den största relativa mängden CO2-utsläpp. Olika scenarier presenteras, där bränslekostnaden och typ av bränsle för PTC-systemets ångpanna modifieras, kostnaden för ånga från de centraliserade leverantörerna justeras och solar fraction ändras mellan 35% och 50%. Besparingarna i CO2-utsläpp beror på vilket bränsle som används samt solar fraction. Större CO2-reduktion är möjlig med en gaseldad panna jämfört med en koleldad. Dock är en koleldad panna lönsammare när den matchar det låga priset på kol som används för de centraliserade leverantörerna. Scenariot med de största CO2-besparingarna uppnås med en hög solar fraction på 50% och en naturgaseldad panna. De årliga CO2-besparingarna varierar från 15 ton per år för det företag som har den lägsta ångkapacitet, upp till 2090 ton per år för ett företag med en av den högsta kapaciteten ånga. En annan viktig faktor är företagens aktivitet per år. Företaget som har minst aktiva dagar per år (84 av 365 dagar), är ej lönsamt i något av de testade scenarierna. Bränslekostnaderna för pannan har emellertid visat sig vara en av de viktigaste faktorerna för resultatet som avgör om det undersökta PTC-systemet är lönsamt eller inte. Bland alla företagen fanns det bara ett som kunde förse hela sitt ångbehov, med PTC-systemet. Detta indikerar att andra energikällor måste införas för att förse företagens ångbehov med ett förnybart energisystem.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2005. / Parabolic trough solar collectors (PTSCs) constitute a proven source of thermal energy for industrial process heat and power generation, although their implementation has been strongly influenced by economics. In recent years, environmental concerns and other geopolitical factors have focused attention on renewable energy resources, improving the prospects for PTSC deployment. Further work is needed to improve system efficiencies and active areas of research include development of advanced heat collecting elements and working fluids, optimisation of collector structures, thermal storage and direct steam generation (DSG). A parabolic trough collector, similar in size to smaller-scale commercial modules, has been developed locally for use in an ongoing PTSC research programme. The aim of this study was to test and fully characterise the performance of the collector. Specialised logging software was developed to record test data and monitor PTSC performance in real-time. Two heat collecting elements were tested with the collector, one unshielded and the other with an evacuated glass cover. Testing was carried out according to the ASHRAE 93-1986 (RA 91) standard, yielding results for the thermal efficiency, collector acceptance angle, incidence angle modifier and collector time constant. Peak thermal efficiency was 55.2 % with the unshielded receiver and 53.8 % with the glass-shielded unit. The evacuated glass shield offered superior performance overall, reducing the receiver heat loss coefficient by 50.2 % at maximum test temperature. The collector time constant was less than 30 s for both receivers, indicating low thermal inertia. Thermal loss tests were conducted and performance of the trough’s tracking system was evaluated. The measured acceptance angles of 0.43° (unshielded) and 0.52° (shielded) both exceeded the tracking accuracy of the PTSC, ensuring that the collector operated within 2 % of its optimal efficiency at all times. Additionally, experimental results were compared with a finite-volume thermal model, which showed potential for predicting trough performance under forced convection conditions.

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Most rural African villages enjoy high levels of sunlight, but rolling out solar power generation technology to tap into this renewable energy resource at remote rural sites in Africa pose a number of design challenges. To meet these challenges, a project has been initiated to design, build and test/evaluate a knock down 3 kW peak electrical stand-alone self-tracking dual-axis concentrating solar power system. This study focusses on the mechatronic engineering aspects in the design and development of a dynamic mechatronic platform and digital electronic control system for the stand-alone concentrating solar power system. Design specifications require an accurate automatic positioner and control system for a motorized parabolic solar reflector with an optical solar harnessing capacity of 12 kWt at solar noon. It must be suitable for stand-alone rural power generation. This study presents a conceptual design and engineering prototype of a balanced cantilever tilt-and-swing dual-axis slew drive actuation means as mechatronic solar tracking mobility platform for a ∼12 m2 lightweight parabolic solar concentrator. Digital automation of the concentrated solar platform is implemented using an industrial Siemens S7-1200 programmable logic controller (PLC) with digital remote control interfacing, pulse width modulated direct current driving, and electronic open loop/closed loop solar tracking control. The design and prototype incorporates off-the-shelf components to support local manufacturing at reduced cost and generally meets the goal of delivering a dynamic mechatronic platform for a concentrating solar power system that is easy to transport, assemble and install at remote rural sites in Africa. Real-time experiments, conducted in the summer of South Africa, validated and established the accuracy of the engineering prototype positioning system. It shows that the as-designed and -built continuous solar tracking performs to an optical accuracy of better than 1.0◦ on both the azimuth and elevation tracking axes; and which is also in compliance with the pre-defined design specifications. Structural aspects of the prototype parabolic dish are evaluated and optimized by other researchers while the Stirling and power handling units are under development in parallel projects. Ultimately, these joint research projects aim to produce a locally manufactured knock down do-it-yourself concentrated solar power generation kit, suitable for deployment into Africa. / AFRIKAANSE OPSOMMING: Landelike gebiede in Afrika geniet hoë vlakke van sonskyn, maar die ontwerp van betroubare sonkrag tegnologie vir die benutting van hierdie hernubare energie hulpbron by afgeleë gebiede in Afrika bied verskeie uitdagings. Om hierdie uitdagings te oorkom, is ’n projek van stapel gestuur om ’n afbreekbare 3 kW piek elektriese alleenstaande selfaangedrewe dubbel-as son-konsentreeder te ontwerp, bou en te toets. Hierdie studies fokus op die megatroniese ingenieurs-aspekte in die ontwerp en ontwikkeling van ’n dinamiese megatroniese platform en ’n digitale elektroniese beheerstelsel vir die alleenstaande gekonsentreerde sonkrag stelsel. Ontwerp spesifikasies vereis ’n akkurate outomatiese posisionering en beheer stelsel vir ’n motor aangedrewe paraboliese son reflekteerder met ’n optiesekollekteer- kapasiteit van 12 kWt by maksimum sonhoogte, en veral geskik wees vir afgeleë sonkrag opwekking. Hierdie studie lewer ’n konsepsuele ontwerp en ingenieurs-prototipe van ’n gebalanseerde dubbelas swaai-en-kantel swenkrat aandrywingsmeganisme as megatroniese sonvolg platform vir ’n ∼12 m2 liggewig paraboliese son konsentreerder. Digitale outomatisering van die son konsentreerder platform is geimplementeer op ’n industriële Siemens S7-1200 programmeerbare logiese beheerder (PLB) met ’n digitale afstandbeheer koppelvlak, puls-wydte-gemoduleerde gelykstroom aandrywing en elektroniese ooplus en geslote-lus sonvolg beheer. Die ontwerp en prototipe maak gebruik van beskikbare komponente om lae-koste plaaslike vervaardiging te ondersteun en slaag in die algemeen in die doel om ’n dinamiese megatroniese platform vir ’n gekonsentreerde sonkrag stelsel te lewer wat maklik vervoer, gebou en opgerig kan word op afgeleë persele in Afrika. Intydse eksperimente is gedurende die somer uitgevoer om die akkuraatheid van die prototipe posisionering sisteem te evalueer. Dit toon dat die sisteem die son deurlopend volg met ’n akkuraatheid beter as 1.0◦ op beide die azimut en elevasie sonvolg asse, wat voldoen aan die ontwerp spesifikasies. Strukturele aspekte van die prototipe paraboliese skottel word deur ander navorsers geëvalueer en verbeter terwyl die Stirling-eenheid en elektriese sisteme in parallelle projekte ontwikkel word. Die uiteindelike doel met hierdie groepnavorsing is om ’n plaaslik vervaardigde doen-dit-self sonkrag eenheid te ontwikkel wat in Afrika ontplooi kan word.

<p>Low-frequency, long-range sound propagation over a seasurface has been calculated using a wide-angel Cranck-NicholsonParabolic Equation method. The model is developed toinvestigate noise from off-shore wind turbines. Thecalculations are made using normal meteorological conditions ofthe Baltic Sea. Special consideration has been made to a windphenomenon called low level jet with strong winds on rather lowaltitude.</p><p>The effects of water waves on sound propagation have beenincorporated in the ground boundary condition using a bossmodel. This way of including roughness in sound propagationmodels is valid for water wave heights that are small comparedto the wave length of the sound. Nevertheless, since only lowfrequency sound is considered, waves up to the mean wave heightof the Baltic Sea can be included in this manner.</p><p>The calculation model has been tested against benchmarkcases and agrees well with measurements. The calculations showthat channelling of sound occurs at downwind conditions andthat the sound propagation tends towards cylindrical spreading.The effects of the water waves are found to be fairlysmall.</p><p><b>Keywords:</b>wind turbine noise, off-shore wind power,long-range sound propagation, parabolic equation, scattering,water waves</p>

Darbe nagrinėjamas parabolinių lygčių su nelokaliąja daugiataške sąlyga ir tikrinių reikšmių uždaviniai antrosios eilės paprastajam diferencialiniam operatoriui. Uždavinio specifika yra ta, kad vietoje vienos arba abiejų klasikinių kraštinių sąlygų duota nelokalioji sąlyga. Tokio tipo kraštiniai uždaviniai diferiancialinėms lygtims paskutiniaisiais metais gana intensyviai nagrinėjami matematinėje literatūroje. Darbe naudojamas M. Sapagovo ir A. Štikono 2005 straipsnio metodika tikrinių reikšmių savybėms tirti. / The parabolic equation with nonlocal multi-point condition and the eigenvalue problem for differential operation with nonlocal multi-point condition is investigated in the work. Nonlocal condition is given instead one or both classical boundary conditions. These problems are investigated in the mathematical literature in recent years. The method of analysis to eigenvalue of the article [5] by M. Sapagovas and A. Štikonas on 2005 are used in the work.

The industry sector accounts for a high share of the final energy consumption, with industries in EU-28accounting for a quarter of the final energy demand. Studies also show that 45 % of the industrial heatdemand in EU-27 is in a temperature range that can be supplied with present day solar collectors. Despitethis large potential, solar heat faces obstacles hindering its growth in the industrial sector. The mostsignificant obstacle is the low insight of the industrial system designs and energy demands. Those arecrucial factors for the feasibility and dimensioning of solar heating systems. Three case studies aretherefore conducted in dairy and pharmaceutical plants in order to review the most promising integrationpoints for parabolic trough solar collectors in terms of annual heat demand, temperature level andintegration effort. Two case studies are performed in dairy plants and one in a pharmaceutical plant, alllocated in Sweden. The analyses comprised reviewing energy mappings, process and instrumentationdiagrams of processes and boiler systems, and hourly energy demand data. Simulations have beencarried out with Polysun for the processes with hourly energy data available.Four integration points have been determined to be high priority solar heat integration points in dairyplants, when considering annual thermal energy demand, temperature levels and integration effort.Those are the low pressure steam line, heating of feedwater, clean in place systems and pasteurizers.Solar heat integration concepts have been presented for all the aforementioned heat sinks andsimulations have been conducted for the low pressure steam line and heating of feedwater. A significantamount of excess heat is produced as a result of fluctuating heat demands and peak solar heat productionhours. Further investigation should be carried out, in order to review the potential of supplying excessheat to other heat sinks. Despite the reviewed potential of the clean in place systems and pasteurizers,lack of the hourly energy demand has hindered further analyses of those systems. It is thereforerecommended to conduct energy measurements before taking further measures.Two integration points have been identified in the pharmaceutical plant, namely autoclaves andmultiple-effect distillers. Solar steam generation concepts have been presented for both processes. Theautoclaves are provided with 4,5 bar steam intermittently, as they work with batches and can have ondutyand off-duty intervals ranging from 3-30 minutes. The multiple-effect distillers are providedwith 7 bar steam, which is of rather high pressure for the solar collectors model on which thesimulations are based. The heat demand of the distillers is more or less constant.It was generally easier to acquire data for the integration points at the supply level. For instance, all heatsinks at the supply level had energy demand data available, contrary to the process level. This inclinesadditional focus on integration to the supply level, if the extent of the feasibility study is to be kept to aminimum.

A two-dimensional numerical model has been developed to simulate wave-current induced nearshore circulation patterns in beaches and surf zones. The wave model is based on the parabolic wave equation for mild slope beaches. The parabolic equation method has been chosen because it is a viable means of predicting the characteristics of surface waves in slowly varying domains and in its present form dissipation and wave breaking are also included. The two dimensional parabolic mild slope equation was discretised and solved in a fully implicit manner, so stability did not create a major problem. This wave model was then embedded into the existing numerical model DIVAST. The sediment transport formulae from Van Rijn was used to calculate the nearshore sediment transport rate.