Steady state modelling of non-linear power plant components

TK Electrical engineering. Electronics Nuclear engineering

Rico Melgoza, J. Jesús. ; Acha, Enrique

University:University of Glasgow

Department:School of Engineering

关键词: TK Electrical engineering. Electronics Nuclear engineering;   

Others  :  http://theses.gla.ac.uk/5319/1/1997RicoMelgozaPhD.pdf

来源: University of Glasgow

【 摘 要 】

This thesis studies the problem of periodic. waveform distortion in electric power systems. Ageneral framework is formulated in the Hilbert domain to account for any given orthogonalbasis such as complex Fourier. real Fourier. Hartley and Walsh.· Particular applications ofthis generalised framework result in unified frames of reference. These domains are unifiedframeworks in the sense that they accommodate all the nodes. phases and the full spectrumof coefficients of the orthogonal basis. Linear and linearised, non-linear elements can becombined in the same frame of reference for a unified solution.In rigorous waveform distortion analysis. accurate representation of non-linear characteristicsfor all power plant components is essential. In this thesis several analytical formsare studied which provide accurate representations of non-linearities and which are suitablefor efficient. repetitive waveform distortion studies.Several harmonic domain approaches are also presented. To date most frequency domaintechniques in power systems have used the Complex Fourier expansion but more efficientsolutions can be obtained when using formulations which do not require complex algebra.With this in mind. two real harmonic domain frames of references are presented: the realFourier harmonic domain and the Hartley domain. The solutions exhibit quadratic rate ofconvergence. Also, discrete convolutions are proposed as a means for free-aliasing harmonicdomain evaluations; a fact which aids convergence greatly.Two new models in the harmonic domain are presented: the Three Phase ThyristorControlled Reactor model and the Multi-limb Three Phase Transformer model. The formeruses switching functions and discrete convolutions. It yields efficient solutions with strongcharacteristics of convergence. The latter is based on the principle of duality and takesaccount of the non-linear electromagnetic effects involving iron core, transformer tank andreturn air paths. The algorithm exhibits quadratic convergence. Real data is used tovalidate both models.Harmonic distortion can be evaluated by using true Newton-Raphson techniques whichexhibit quadratic convergence. However, these methods can be made to produce faster solutionsby using relaxation techniques. Several alternative relaxation techniques are presented.An algorithm which uses diagonal relaxation has shown good characteristics of convergenceplus the possibility of parallelisation.The Walsh series are a set of orthogonal functions with rectangular waveforms. Theyare used in this thesis to study switching circuits which are quite common in modern powersystems. They have switching functions which resemble Walsh functions substantially.Accordingly, switching functions may be represented exactly by a finite number of Walshfunctions, whilst a large number of Fourier coefficients may be required to achieve the same result. Evaluation of waveform distortion of power networks is a non-linear problemwhich is solved by linearisation about an operation point. In this thesis the Walsh domainis used to study this phenomenon. It has deep theoretical strengths which helps greatly inunderstanding waveform distortion and which allows its qualitative assessment.Traditionally, the problem of finding waveform distortion levels in power networks hasbeen solved by the use of repetitive linearisation of the problem about an operation point.In this thesis a step towards a true non-linear solution is made. A new approach, which usesbi-linearisations as opposed to linearisations, is presented. Bi-linear systems are a class ofsimple, non-linear systems which are amenable to analytical solutions. Also, a new method,based on Taylor series expansions, is used to approximate generic, non-linear systems usinga bi-linear system. It is shown that when using repetitive bi-linearisations, as opposed tolinearisations, solutions show super-quadratic rate of convergence.Finally, several power system applications using the Walsh approach are presented. Amodel of a single phase TCR, a model of three phase bank of transformers and a model offrequency dependent transmission lines are developed.