A synchronous generator supplies a network through two trans

A synchronous generator supplies a network through two transformers and a transmission line, as shown in Figure 8.71. The generator is rated at 750 MVA with a terminal voltage of 22.5 kV and a reactance of 107%. The identical transformers are rated at 800 MVA with primary and secondary voltages of 22.5 kV and 220 kV, respectively, and a 16% reactance. The transmission line is 120 mi long with line voltage of 220 kV and an impedance of 0.07+j0.5 /mi. The total transmission line capacitance is 3 µF. The network line voltage is 22 kV. A variable capacitor from 50 µF to 500 µF is connected in series with the transmission line.

(a) Determine the impedances of the system. Draw the single-phase equivalent circuit.

(b) Find the induced voltage of the generator at rated load and 0.83 lagging, assuming the terminal voltage of the generator is the same as the rated voltage. The absolute value of the obtained induced voltage is used for part (c).

(c) Plot the power transmitted to the network versus the capacitance in series with the line, at a power angle of 60° (angle between the network voltage and generator excitation voltage). Determine the capacitance value that is needed to transfer 950 MW.

The answers are as follows:

a) Xg = 0.722 ohm, Xfmr= 9.68 ohm, Zline = 8.4 + j60 ohm, Xc = 1.77 kohm

b) Eg = 24kV at 33.9deg,

c) C(950) = 206uF.

Please show all working to arrive at anwers.

The diagram is a single line diagram with the generator as the source connected to a step up transformer 22.5kV/220kV, in series with the capacitor which is in series with the transmission line followed by the step down transformer of 220kV/22.5kV and then the network\'s load.

Solution

The backfin of a power mosfet has dimensions 1.0 cm x 1.3cm and a thickness of 1.585mm. It is made out of copper. The purpose of the backfin here is to carry away the heat from the si-based chip attached to the backfin (and here burried in a black plastic case). Thus the backfin is (usually) electrically connected to the mosfet. To mount to a grounded case (Aluminum, quite thick, and at room temperature, 23 oC), an electrically insulating, plastic layer of thickness 0.2873mm and of thermal conductivity 90 W/oC/m is placed between the fin and the aluminum. Assume that the aluminum stays throughout at 23 oC degrees. The mosfet will fail catastrophically (thermal runaway) if its temperature gets above 180oC.
(a) If its RDS in the \"on\" state is 78.88 mOhms, what is the maximum current it can safely conduct in steady state in this mount?
(b) Supose the mosfet was operating just at the breaking point...what would then be the temperature at the shared surface between the copper and the plastic layer?