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Jesús Vicente Rodrigo

Ph.D. Thesis title:
Eliminación selectiva de armónicos en convertidores PWM continua-alterna mediante la transformada de Walsh

Jesús Vicente Rodrigo

Rafael Pindado Rico / Imma Martínez Teixidor

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The synthesis of alternating current (AC) voltage from direct current (DC) voltage by means of pulse width modulation (PWM) waveforms represents an economic and efficient method of making this conversion, since few semiconductor devices are required and they work in a more efficient way when doing it in commutation. However, the main drawback of these systems is the presence of harmonics to be cancelled.
It is well known that the generation of PWM signals using the technique of programmed harmonic elimination requires the solution of non-linear transcendental equations systems. Normally, because of its high processing time for needing an iterative solution, these equations must be solved off-line and the values corresponding to the optimal commutation angles have to be stored in look-up tables or interpolated by simple functions to allow the on-line operation. The flexibility of the system is very limited, especially for applications that require simultaneous control of amplitude and frequency.
This thesis studies the selective harmonic elimination by means of the Walsh transform as a more efficient alternative to the programmed harmonic elimination, since it permits the calculation of the switching angles by linear equations that depend on the fundamental amplitude, used as a reference.
In the first place, this thesis carries out an exhaustive study about the feasibility of the Walsh method presented in the consulted literature, where it is analysed a method of harmonic elimination with regulation of the fundamental amplitude. All this is achieved by means of linear equations that allow the calculation of the PWM signal switching angles from the desired fundamental amplitude. However, as demonstrated in this thesis, by this method the maximum fundamental amplitude range achieved doesn’t exceed 58% and it is also necessary to combine different equations sets to cover this range. This method, named conventional, has been significantly improved in this thesis with a new way of definition of the switching angles, by means of interval fractions that lead to a simplification of the mathematical calculation.
Secondly, this thesis presents a new method, named advanced, as a result of testing different alternatives to the conventional method, based on modifications of the waveform of the signal, restricted to the definition of the angle corresponding to the end of the notch, that is fixed in the conventional method, and variable in the new proposed method. With the new method the amplitude range is close to 100%. Therefore, it is possible to store in the signal generation system a single set of equations that allows solving any scalar modulation application, with a low processing cost.
Another studied aspect is the influence of different causes of non ideal behaviour on the harmonic distribution of a PWM waveform. The analyzed causes include: dead-time, transition times, uncertainty calculation and error due to truncation of switching angles digits. The obtained results allow the definition of the real limits of the converter performance and the requirements that has to satisfy its control system.
Finally, a test plant has been build for experimental verification of the methods studied in order to validate the simulation results. From the obtained results there are proposed the design rules to follow in order to implement the advanced method.
The simulation results shown and the experimental results obtained proof the generalized application of the proposed new methodology. For this reason, researchers should carefully consider the promising potentialities of techniques based on Walsh functions.