In a given system of base power of 250 MW, and bus 3 is taken as reference. The per-unit reactances are X12 = 0.2 p.u., X13 = X23 = 0. 1 p.u. The power flow in the system is given as: PF12 = 50 MW, PF13 = 150 MW, PF23 = 50 MW. Based on readings from 2 meters (not including M12 meter), M13 = 145 MW (not calibrated), and M23 = 50 MW (well calibrated), deduce the flow on line 1-2.
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- Consider two interconnected voltage sources connected by a line of impedance Z=jX, as shown in Figure 2.27. (a) Obtain expressions for P12 and Q12. (b) Determine the maximum power transfer and the condition for it toConsider a three-phase generator rated 300MVA,23kV, supplying a system load of 240 MA and 0.9 power factor lagging at 230 kV through a 330MVA,23/230Y-kV step-up transformer with a leakage reactance of 0.11 per unit. (a) Neglecting the exciting current and choosing base values at the load of 100 MVL and 230 kV. Find the phasor currents IA,IB, and IC supplied to the load in per unit. (b) By choosing the load terminal voltage IA as reference, specify the proper base for the generator circuit and determine the generator voltage V as well as the phasor currents IA,IB, and IC, from the generator. (Note: Take into account the phase shift of the transformer.) (C) Find the generator terminal voltage in kV and the real power supplied by the generator in MW. (d) By omitting the transformer phase shift altogether, check to see whether you get the same magnitude of generator terminal voltage and real power delivered by the generator.Consider three ideal single-phase transformers (with a voltage gain of ) put together as three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for Va,Vb, and Vc find Va,Vb, and VC. in terms of Va,Vb, and Vc, respectively. (a) Would such relationships hold for the line voltages as well? (b) Looking into the current relationships, express IaIb and Ic in terms of IaIb and Ic respectively. (C) Let S and S be the per-phase complex power output and input. respectively. Find S in terms of S.
- Consider Figure 3.25 of the text for a transformer with off-nominal turns ratio. (i) The per-unit equivalent circuit shown in part (c) contains an ideal transformer which cannot be accommodated by some computer programs. (a) True (b) False (ii) In the - circuit representation for real c in part (d), the admittance parameters Y11 and Y12 would be unequal. (a) True (b) False (iii) For complex c, can the admittance parameters be synthesized with a passive RLC circuit? (a) Yes (b) NoConsider Figure 3.4. For an ideal phase-shifting transformer, the imda nce is unchanged when it is referred from one side to the other. (a) True (b) FalseThree single-phase, two-winding transformers, each rated 450MVA,20kV/288.7kV, with leakage reactance Xeq=0.10perunit, are connected to form a three-phase bank. The high-voltage windings are connected in Y with a solidly grounded neutral. Draw the per-unit equivalent circuit if the low-voltage windings are connected (a) in with American standard phase shift or (b) in Y with an open neutral. Use the transformer ratings as base quantities. Winding resistances and exciting current are neglected.
- What is a microgrid?While the instantaneous electric power delivered by a single-phase generator under balanced steady-state conditions is a function of time havi ng two components of a constant and a double-frequency sinusoid, the total instantaneous electric power delivered by a three-phase generator under balanced steady-state conditions is a constant. (a) True (b) FalsePowerWorid Simulator case Problem 3_60 duplicates Example 3.13 except that a resistance term of 0.06 per unit has been added to the transformer and 0.05 per unit to the transmission line. Since the system is no longer lossless, a field showing the real power losses has also been added to the oneline. With the LTC tap fixed at 1.05, plot the real power losses as the phase shift angle is varied from 10 to +10 degrees. What value of phase shift minimizes the system losses?
- What are the benefits of microgrids?A single-phase 100-kVA,2400/240-volt,60-Hz distribution transformer is used as a step-down transformer. The load, which is connected to the 240-volt secondary winding, absorbs 60 kVA at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: (a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power supplied to the primary winding.The per-unit equivalent circuit of two transformers Ta and Tb connected in parallel, with the same nominal voltage ratio and the same reactan of 0.1 per unit on the same base, is shown in Figure 3.43. Transformer Tb has a voltage-magnitude step-up toward the load of 1.05 times that of Ta (that is, the tap on the secondary winding of Tb is set to 1.05). The load is represented by 0.8+j0.6 per unit at a voltage V2=1.0/0 per unit. Determine the complex power in per unit transmitted to the load through each transformer, comment on how the transformers share the real and reactive powers.