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Fourier Series in Electrical Engineering: Understanding Sinusoidal Waveforms<br>

Learn how Fourier series represent periodic waveforms, power electronics, non-sinusoidal sources, reactive power computation, and distortion analysis in electrical engineering lectures at the Islamic University of Gaza.<br>

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Fourier Series in Electrical Engineering: Understanding Sinusoidal Waveforms<br>

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  1. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Fourier Series Anonsinusoidal periodic waveform that meets certain conditions can be described by a Fourier series of sinusoids. The Fourier series for a periodic function f(t) can be expressed in trigonometric form as The term a0 is a constant that is the average value of f(t) and represents a dc voltage or current in electrical applications. The coefficient C1 is the amplitude of the term at the fundamental frequency 0. Coefficients C2, C3, . . . are the amplitudes of the harmonics that have frequencies 20, 30, . . . . Lecture 8 Introduction to Power Electronics

  2. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Average Power Total average power is the sum of the powers at the frequencies in the Fourier series. Lecture 8 Introduction to Power Electronics

  3. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Nonsinusoidal Source and Linear Load If a nonsinusoidal periodic voltage is applied to a load that is a combination of linear elements, the power absorbed by the load can be determined by using superposition. A nonsinusoidal periodic voltage is equivalent to the series combination of the Fourier series voltages Lecture 8 Introduction to Power Electronics

  4. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Lecture 8 Introduction to Power Electronics

  5. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Lecture 8 Introduction to Power Electronics

  6. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Sinusoidal Source and Nonlinear Load If a sinusoidal voltage source is applied to a nonlinear load, the current waveform will not be sinusoidal but can be represented as a Fourier series Lecture 8 Introduction to Power Electronics

  7. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Note that the only nonzero power term is at the frequency of the applied voltage. Lecture 8 Introduction to Power Electronics

  8. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department The power factor of the load is computed from Lecture 8 Introduction to Power Electronics

  9. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department The ratio of the rms value of the fundamental frequency to the total rmsvalue is the distortion factor (DF). The distortion factor represents the reduction in power factor due to the nonsinusoidal property of the current Lecture 8 Introduction to Power Electronics

  10. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Total harmonic distortion (THD) is another term used to quantify the nonsinusoidal property of a waveform. THD is the ratio of the rms value of all the nonfundamentalfrequency terms to the rms value of the fundamental frequency term Lecture 8 Introduction to Power Electronics

  11. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Lecture 8 Introduction to Power Electronics

  12. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Reactive power for a sinusoidal voltage and a nonsinusoidal current can be expressed following. The only nonzero term for reactive power is at the voltage frequency The term distortion volt-amps D is traditionally used in the computation of S Lecture 8 Introduction to Power Electronics

  13. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Lecture 8 Introduction to Power Electronics

  14. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department Lecture 8 Introduction to Power Electronics

  15. Islamic University of Gaza • Faculty of Engineering • Electrical Engineering Department End of chapter 2 . Next week : Quiz#1 Lecture 8 Introduction to Power Electronics

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