1. When travelers from the USA and Canada visit Europe, they encounter a different power distribution system. Wall voltages in North America are 120 V rms at 60 Hz, while typical wall voltages in Europe are 220-240 V at 50 Hz. Many travelers carry small step-up / step-down transformers so that they can use their appliances in the countries that they are visiting. A typical transformer might be rated at 1-kVA and 120/240 V. It has 5001 turns of wire on the 120-V side and 1000 turns of wire on the 240-V side. The magnetization curve for this transformer is shown in Figure P3-2, and can be found in file p32.mag at this book's Web site.
(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?
2. A 15-kVA 8000/230-V distribution transformer has an impedance referred to the primary of 80 + j300Ω.
The components of the excitation branch referred to the primary side are RC = 350 kW and X M= 70 kΩ .
(a) If the primary voltage is 7967 V and the load impedance is ZL = 3.2 + j1.5Ω, what is the secondary voltage of the transformer? What is the voltage regulation of the transformer?
(b) If the load is disconnected and a capacitor of -j3.5Ω is connected in its place, what is the secondary voltage of the transformer? What is its voltage regulation under these conditions?