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(a) Suppose that this transformer is connected to a 120-V, 60 Hz power source with no load connected to the 240-V side Sketch the magnetization current that would flow in the transformer (Use MATLAB to plot the current accurately, if it is available) What is the rms amplitude of the magnetization current What percentage of full-load current is the magnetization current (b) Now suppose that this transformer is connected to a 240-V, 50 Hz power source with no load connected to the 120-V side Sketch the magnetization current that would flow in the transformer (Use MATLAB to plot the current accurately, if it is available) What is the rms amplitude of the magnetization current What percentage of full-load current is the magnetization current (c) In which case is the magnetization current a higher percentage of full-load current Why SOLUTION (a) When this transformer is connected to a 120-V 60 Hz source, the flux in the core will be given by the equation

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The magnetization current required for any given flux level can be found from Figure P3-2, or alternately from the equivalent table in file p32mag The MATLAB program shown below calculates the flux level at each time, the corresponding magnetization current, and the rms value of the magnetization current

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% M-file: prob3_5am % M-file to calculate and plot the magnetization % current of a 120/240 transformer operating at

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% 120 volts and 60 Hz This program also % calculates the rms value of the mag current % Load the magnetization curve It is in two % columns, with the first column being mmf and % the second column being flux load p32mag; mmf_data = p32(:,1); flux_data = p32(:,2); % Initialize values S = 1000; Vrms = 120; VM = Vrms * sqrt(2); NP = 500;

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% Calculate angular velocity for 60 Hz freq = 60; % Freq (Hz) w = 2 * pi * freq; % Calculate flux versus time time = 0:1/3000:1/30; % 0 to 1/30 sec flux = -VM/(w*NP) * cos(w * time); % Calculate the mmf corresponding to a given flux % using the MATLAB interpolation function mmf = interp1(flux_data,mmf_data,flux); % Calculate the magnetization current im = mmf / NP; % Calculate the rms value of the current irms = sqrt(sum(im^2)/length(im)); disp(['The rms current at 120 V and 60 Hz is ', num2str(irms)]); % Calculate the full-load current i_fl = S / Vrms; % Calculate the percentage of full-load current percnt = irms / i_fl * 100; disp(['The magnetization current is ' num2str(percnt) '% of full-load current']); % Plot the magnetization current figure(1) plot(time,im); title ('\bfMagnetization Current at 120 V and 60 Hz'); xlabel ('\bfTime (s)'); ylabel ('\bf\itI_{m} \rm(A)'); axis([0 004 -05 05]); grid on;

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