\documentclass[13pts]{article}!\begin{document}!\begin{center}!\begin{large}!ECE509 Signal Processing for Power Systems!Homework Assignment 1!\end{large}!!\end{center}!1 .!! (a) Why switching operations in the power system will cause transients?!!Switching in power system causes transients because of the change in operating state of the system, as in case of circuit breaker when it opens, in transitory period the energy get accumulated in form of electromagnet fields is redistributed in the system causing transients. The oscillations or the frequencies of the generated transient current and voltages will depend on the system parameters such as inductance and capacitances.!\\!!!(b) Capacitor are used in power system to improve power factor and voltage regulation, capacitor supply reactive power needed by the system, when a capacitor is added to the system the system voltage drops momentarily and can rises to voltage twice of the peak voltage, this will cause severe transients in system. The resulting high in-rush current may affect the whole circuit and the appliances connected to it. The frequency and magnitude of the in-rush current are dependent on capacitor already in line and instantaneous voltage at the time of switching, the impedance between the capacitor is very low as compared to system so there is high in rush current and of very high frequencies.!\\! !(c) Why the 3rd harmonic component at the medium-voltage side is much less significant than that at the low-voltage side in power systems?\newline!The 3rd harmonic component at medium side voltage is less significant because of two reasons , firstly the measurement instruments and other appliances are connected to the low voltage side of the transformer, secondly in case of transformer being a delta-wye connection the 3rd harmonic component will be suppressed on delta side of the transformer, so there is no distortion due to third harmonic component on low voltage side. \newline \\!\\ 2. \\ !(a)! $$f_{c} = K * H * f_{1}$$ \\!$$A\ge 6.02 B + 1.76$$! we have the given harmonic as 35 so we have , !$$f_c = 1.2 * 35 * 50 $$!$$f_c = 2100hz $$!and : !$$A\ge 6.02*15 +1.76$$!$$A \ge 92.02 $$!$$f_s = 20Khz$$!

$$f_s \ge f^{'} + f_c $$!substituting the values we get : !$$f^{'} \leq 17.9Khz$$!$$f^{'} = \Omega * f_c$$!from this equation we get : !$$17.9Khz= \Omega * 2100Hz$$!$$\Omega = 8.5$$!!!we know that : !$$G = 20 * n *log\Omega$$!$$92.02 = 20 * n * log \Omega$$!where n is order of the system , which we have to find \newline by solving the above equation we get , !$$n = 4.95 \approx 5 $$ \newline!(b)!from the above solution we have calculated $$f_c = 2100 hz $$ !$$A \ge 92.02db$$!we know equation : !$$G = 20 * n *log\Omega$$!where , n is order of system , give as 5 !$$92.02 = 20 * 5 *log \Omega$$!$$\Omega = 8.32 {rad/s} $$!$$f^{'} = \Omega * f_c$$!$$f^{'} = 8.32 * f_c$$!we know $F_c = 2100 hz$!$$f^{'} = 17.475 hz$$!!$$f_s \ge f^{'}+ f_c $$!$$f_s \ge 19.575$$!This is the minimum sampling frequency. !!!!!!!!!!!!!!!!!!!

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