Il Bus A G1 Line 1 T2 G2 Bus B T3 Line 2 Bus C T4 A M3 M4 Figure 1. 1) The power system consists of generators, motors, transformers, and transmission lines. The ratings are as follows: G1: 3-phase generator 25 MVA, 11.8 KV, X" = 0.9747 G2:3-phase generator 20 MVA, 10.2 KV, X=0.7976 M3: 3-phase motor M4: 3-phase motor T1:3-phase transformer T2: 3-phase transformer T3:3 single phase transformer T4:3 single phase transformer Line 1 Line 2 30 MVA, 26 KV, X-3.025 Ω 15 MVA, 18 KV, X"-2.25 Ω 25 MVA, 11.8 Y - 115 KV Y X = 0.6962 on the low voltage 20 MVA, 10.2 Y- 115 KV Y X=0.5896 on the low voltage each rating 10 MVA, 27.5/66.4 KV X=41.8792 on the high voltage each rating 5 MVA, 10.4/115 KV X=41.8792 on the high voltage Χ = 100 Ω Χ = 100 Ω A) Find the reactance (X) in p.u. using the basic principle of 30 MVA, 26 KV. B) Draw a reactance diagram with all values of X in p.u.

Il Bus A G1 Line 1 T2 G2 Bus B T3 Line 2 Bus C T4 A M3 M4 Figure 1. 1) The power system consists of generators, motors, transformers, and transmission lines. The ratings are as follows: G1: 3-phase generator 25 MVA, 11.8 KV, X" = 0.9747 G2:3-phase generator 20 MVA, 10.2 KV, X=0.7976 M3: 3-phase motor M4: 3-phase motor T1:3-phase transformer T2: 3-phase transformer T3:3 single phase transformer T4:3 single phase transformer Line 1 Line 2 30 MVA, 26 KV, X-3.025 Ω 15 MVA, 18 KV, X"-2.25 Ω 25 MVA, 11.8 Y - 115 KV Y X = 0.6962 on the low voltage 20 MVA, 10.2 Y- 115 KV Y X=0.5896 on the low voltage each rating 10 MVA, 27.5/66.4 KV X=41.8792 on the high voltage each rating 5 MVA, 10.4/115 KV X=41.8792 on the high voltage Χ = 100 Ω Χ = 100 Ω A) Find the reactance (X) in p.u. using the basic principle of 30 MVA, 26 KV. B) Draw a reactance diagram with all values of X in p.u.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter3: Power Transformers

Section: Chapter Questions

Problem 3.25P: Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows:...

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Consider the three single-phase two-winding transformers shown in Figure 3.37. The high-voltage windings are connected in Y. (a) For the low-voltage side, connect the windings in , place the polarity marks, and label the terminals a, b, and c in accordance with the American standard. (b) Relabel the terminals a, b, and c such that VAN is 90 out of phase with Va for positive sequence.
1. A single-phase power system as shown in Figure 1 consists of a 240 V, 60 Hz generator supplying a load, Zod = 8 + j6 Q through a transmission line of impedance, Zne = 0.08 + j0.14 Q. Answer the following questions: (1) transformer, T; and T2. Determine the voltage at the load and transmission line losses without the (ii) Determine the voltage at the load and transmission line losses with the transformer, T, and T2. T1 T2 1:10 10:1 IG Zaine Zioad source Figure 1
b) Two synchronous generators, G2 and G2, are connected parallelly supplying a load. Generator G1 has a no-load frequency of 50.5 Hz and a slope of 300 MW/Hz. Generator G2 has a no-load frequency of 50.2 Hz and a slope of 500 MW/Hz. The load consumes 250 MW real power. (1) At what frequency does this system operate, and how much power is supplied by each of the two generators? (ii) An additional 100 MW load is added to this power system. What is the new system frequency, and how much power do G1 and G2 supply? (iii) The governor set point of G2 is changed to control system frequency back to 50 Hz. Determine the G2 governor set point.
Please, I do not want a theoretical solution or using artificial intelligence. I want a solution on paper using the mathematical laws of the topic
Consider the oneline diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by X1=0.24 (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio =N2/N1=10. The transformer bank is delivering 100 MW at 0.8 p.f. lagging to a substation bus whose voltage is 230 kV. (a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three-phase complex power supplied by the generator. Choose the line-to-neutral voltage at the bus, Va as the reference Account for the phase shift, and assume positive-sequence operation. (b) Find the phase shift between the primary and secondary voltages.
Consider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings are Generator 1: 1000MVA,18kV,X=0.2perunit Generator 2: 1000MVA,18kV,X=0.2p.u. Synchronous motor 3: 1500MVA,20kV,X=0.2p.u. Three-phase -Y transformers T1,T2,T3,T4,: 1000MVA,500kV,Y/20kV,X=0.1p.u. Three-phase YY transformer T5: 1500MVA,500kV,Y/20kVY,X=0.1p.u. Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 100 MA and 500 kV for the 50-ohm line. Determine the per-unit reactances.
Consider the single-Line diagram of a power system shown in Figure 3.42 with equipment ratings given: Generator G1: 50MVA,13.2kV,x=0.15p.u. Generator G2: 20MVA,13.8kV,x=0.15p.u. Three-phase -Y transformer T1: 80MVA,13.2/165YkV,X=0.1p.u. Three-phase Y- transformer T2: 40MVA,165Y/13.8kV,X=0.1p.u. Load: 40MVA,0.8PFlagging,operatingat150kV Choose a base of 100 MVA for the system and 132-kV base in the transmission-line circuit. Let the load be modeled as a parallel combination of resistance and inductance. Neglect transformer phase shifts. Draw a per-phase equivalent circuit of the system showing all impedances in per unit.
Determine the positive- and negative-sequence phase shifts for the three- phase transformers shown in Figure 3.36.
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.
Figure 3.39 shows a oneline diagram of a system in which the three-phase generator is rated 300 MVA, 20 kV with a subtransient reactance of 0.2 per unit and with its neutral grounded through a 0.4- reactor. The transmission line is 64km long with a cries reactance of 0.5-/km. The three-phase transformer T1 is rated 350MVA.230/20kV with a leakage reactance of 0.1 per unit. Transformer T2 is composed of three single-phase transformers, each rated 100 MVA, 127/13.2kV with a leakage reactance of 0.1 per unit. Two 13.2kV motors M1 and M2 with a subtransient reactance of 0.2 per unit for each motor represent the load. M1 has a rated input of 200 MVA with its neutral grounded through a 0.4- current-limiting reactor, M2 has a rated input of 100 MVA with its neutral not connected to ground. Neglect phase shifts associated with the transformers. Choose the generator rating as base in the generator circuit and draw the positive-sequence reactance diagram showing all reactances in per unit.
In developing per-unit circuits of systems such as the one shown in Figure 3.10. when moving across a transformer, the voltage base is changed in proportion to the transformer voltage ratings. (a) True (b) False
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.