Pse Problems Group Assignment

Note : Group 1 (up to 1st 130 Roll No. )2k17 problem 1 to 17 Group2 (from 130 to last Roll No.)2k17 + 2k16 problems 18 to 33

Problem: 1

(Book: Protective Relaying Principles and Applications by Black Burn)

A three phase generator feeds three large synchronous motors over a 16 km, 115 kV transmission line, through transformer bank, as shown in fig. Draw an equivalent single-line reactance diagram with all reactances indicated in per unit of a 100 MVA, 13.8 kV or 115 kV base.

Fig 3. One line diagram of Power System Problem: 2

(Book: Electrical Power Systems by Ashfaq Hussain)

Draw the reactance diagram for the system shown in Fig. 8.12. The specification of the components is given in the Table 8.2.

Fig. 8.12.

Table 8.2 Generator G

Transformer T1

Transformer T2

Motor 1

Motor 2

Line

13.8 kV

25 MVA

25 MVA

15 MVA

10 MVA

X=65Ω

25 MVA

13.2/69 kV

69/13.2 kV

13.0 kV

13.0 kV

𝒙.. = 𝟎. 𝟏𝟓 𝒑𝒖

xL=0.11 pu

xL=0.11 pu

𝑥 .. = 0.11 𝑝𝑢

0.15 pu

Determine the generator terminal voltage assuming both motors operating at 12 kV. 74% full load and unity power factor.

Problem: 3

(Book: Elements of Power System Analysis by William D Stevenson, Jr)

Draw the impedence diagram for the power system shown in the Fig. 8.15. Mark impedences in per unit. Neglect resistance, and use a base of 50,000 kVA, 138 kV in th 40-ohm line. The ratings of the generators, motors, and transformers are Generator 1: 20,000 kVA, 13.2 kV, 𝒙.. = 15% Generator 2: 20,000 kVA, 13.2 kV, 𝒙.. = 15% Synchronous Motor 3: 30,000 kVA, 6.9 kV, 𝒙.. = 20% Three phase Y-Y transformers: 20,000 kVA, 13.8Y-138Y kV, X=10%

Three phase Y-∆ transformers: 15,000 kVA, 6.9Y-138Y kV, X=10% All transformer are connected to step up the voltages of the generators to the transmission line voltages.

Fig. 8.15: One line diagram

Problem: 4

(Book: Elements of Power System Analysis by William D Stevenson)

The windings of a three winding transformer are rated as follows: Primary: Y- connected, 6.6 kV, 15,000 kVA Secondary: Y- connected, 33 kV, 10,000 kVA Tertiary: ∆- connected, 2.2 kV, 7,500 kVA With resistance neglected, the following leakage impedances are calculated from short circuit tests: Measured from the primary side:

Zps = j0.232 ohms Zpt = j0.290 ohms

Measured from the Secondary side:

Zst = j8.70 ohms

Find the impedances of the star connected equivalent circuit on a base of 15,000 kVA, 6.6 kV in the primary circuit. Problem: 5

( power system analysis by p.s.r murthy)

Three transformers each rated 30 MVA at 38.1/3.81 KV are connected in star-delta with a balanced load of three 0.5 ohm, star connected resistors. Selecting a base of 900 MVA 66 KV for the h.v. side of the transformer find the base values for the I. v. side.

Problem: 6

(power system analysis and design by j.duncan glover)

A balanced Y-connected voltage source with Eag = 277 volts is applied to a balanced-Y load in parallel with a balanced-delta load, where Zy = 20+ j10 and Zd = 30+ j15 ohms. The Y load is solidly grounded. Using base values of Sbase =10 kVA and VbaseLN =277 volts, calculate the source current Ia in per-unit and in amperes. Problem: 7

(electrical power system by d.das)

Three generators are rated as follows: G1 : 100 MVA,33kVA , Xg1= 0.10 p.u , G2 : 150 MVA,32kVA , Xg2= 0.08 p.u , G3 : 110 MVA,30kVA , Xg3= 0.12 p.u . Determine the reactance of generator corresponding to base values of 200 MVA and 35 kV. Problem: 8


A generator (which may be represented by an emf in series with an inductive reactance) is rated 500 MVA, 22 KV.Its Y-connected windings have a reactance of 1.1 per-unit. Find the ohmic values of the reactance of the winding. Problems: 9


The generator of the problem 8 is in a circuit for which the bases are specified as 100 MVA, 20KV.starting with the per-unit values given in prob 2.21,find the per-unit values of reactance of the windings on the specified base. Problem: 10


Draw the single phase equivalent circuit for the motor(an emf in series with inductive reactance).Motor specification are 440 V line by a three phase 15 hp having 0.3+j0.1 impedance of each the phase. Show on the diagram the per-unit value of the impedance and the voltage at

the motor terminals on the base of 20 KVA,440 V then using per-unit values find the supply voltage in per-unit and convert the per-unit value of the supply voltage to volts. Problem: 11


A 120 MVA, 19.5 KV generator has Xs=1.5 p.u is connected to a transmission line by a transformer rated 150 MVA, 230/18 KV (Y-∆) with X=0.1 p.u if the base to be used in the calculations is 100 MVA, 230 KV for the transmission line find the per unit values to be used for the transformer and generators reactances. Problem: 12

Electrical Power Systeme by C.l Wadhwa

Two generators rated at 10 MVA, 13.2 kV and 15 MVA, 13.2 kV are connected in parallel to a bus bar. They feed supply to two motors of inputs 8 MVA and 12 MVA respectively. The operating voltage of motors is 12.5 kV. Assuming base quantities as 50 MVA and 13.8 kV draw the reactance diagram. The percent reactance for generators is 15% and that for motors is 20%. Problem: 13

Electrical Power Systems by C.l Wadhwa

Three generators are rated as follows: Generator 1–100 MVA, 33 kV, reactance 10%; Generator 2–150 MVA, 32 kV, reactance 8%; Generator 3–110 MVA, 30 kV and reactance 12%. Determine the reactance of the generator corresponding to base values of 200 MVA, 35 kV. Problem: 14

Electrical Power Systems by C.l Wadhwa

A 3-bus system is given in Fig. P1.3. The ratings of the various components are listed below: Generator 1 = 50 MVA, 13.8 kV, X″ = 0.15 p.u. Generator 2 = 40 MVA, 13.2 kV, X″ = 0.20 Generator 3 = 30 MVA, 11 kV, X″ = 0.25 Transformer 1 = 45 MVA, 11 kV, Δ/110 kV Y, X = 0.1 p.u. Transformer 2 = 25 MVA, 12.5 kV, Δ/115 kV Y, X = 0.15 p.u. Transformer 3 = 40 MVA, 12.5 kV, Δ/115 kV Y, X = 0.1 p.u. The line impedances are shown in Fig. P1.3. Determine the reactance diagram based on 50 MVA and 13.8 kV as base quantities in Generator 1.

Problem: 15

Protective Relaying, Principles and Applications J. Lewis Black Burn

A three phase generator feeds three large synchronous motors over a 16km, 115 kV transmission line, through transformer bank, as shown in fig. All reactances indicated in per unit of a 100 MVA, 13.8 kV or 115 kV base. In this system it is desired to maintain the voltage at the motor bus of 1 00 per unit. The three motors are operating at full rating and 90% power factor. 

Determine the voltage required at the generator terminals assuming that there is not voltage regulating taps or similar equipment in this system.



What is the voltage required behind the sub transient reactance.

Problem: 16

Electric Machinery Fundamentals by Chapman

A 5000 kVA, 230/13.8 kV single phase power transformer has a per-unit resistance of 1% and a per-unit reactance of 5% (data taken from transformer’s nameplate). The open circuit test performed on the low voltage side of the transformer yielded the following data: Voc = 13.8 kV Ioc = 15.1 A Poc = 44.9 kW a) Find the equivalent circuit referred to the low voltage side of this transformer. b) If the voltage on the secondary side is 13.8 kV and the power supplied is 4000 kW at 0.8 PF lagging, find the voltage regulation of the transformer. Find its efficiency. Problem: 17

Electric Machinery Fundamentals by Chapman

A 200 MVA, 15/200 kV single phase power transformer has a per-unit resistance of 1.2% and a per-unit reactance of 5% (data taken from the transformer’s nameplate). The magnetizing impedance of j80 per-unit. a) Find the equivalent circuit referred to the low voltage side of this transformer. b) Calculate the voltage regulation of this transformer for a full load current at power factor of 0.8 lagging. c) Assume the primary voltage of this transformer is a constant 15 kV, and plot the secondary voltage as a function of load currents from no load to full load. Repeat this process for power factor of 0.8 lagging, 1.0 and 0.8 leading. Problem: 18

Power System Analysis by William D. Stevenson

Three 25 kVA, 24000/277 V distribution transformers are connected in delta-why. The open circuit test was performed on the low voltage side of the transformer bank, and the following data are recorded: Vline,oc = 13.8 kV Iline,oc = 15.1 A P3-phae,oc = 44.9 kW The short circuit test was performed on the high voltage side of this transformer bank, and the following data were recorded: Vline,sc = 1600 V Iline,sc = 2.00 A P3-phae,sc = 1150 kW a) Find the per-unit equivalent circuit of this transformer bank. b) Find the voltage regulation of his transformer bank at the rated load and 0.90 PF lagging. c) What is the transformer banks efficiency under these conditions?

Problem: 19

Power System Analysis by William D. Stevenson

A 20 kVA, 20000/480 V, 60 Hz distribution transformer is tested with the following results: Open Circuit Test Short Circuit Test (measured from secondary side) (measured from primary side) Voc = 480 V Vsc = 1130 V Ioc = 1.6 A

Isc = 1.00 A

Poc = 305 W

Psc = 260 W

a) Find the per-unit equivalent circuit for this transformer at 60 Hz. b) What would be the ratting of this transformer be if it were operated on 50 Hz power system. c) Sketch the per-unit equivalent circuit of this transformer referred to the primary side if it is operating at 50 Hz. Problem: 20

POWER SYSTEM ANALYSIS BY ARTHUR R.BERGEN & VIJAY VITTAL

Prepare a per phase schematics of the system shown in figure below and show all impedances in per unit on a 100 MVA, 132 KV base in the transmission-line circuit. The necessary data for this problem are as follows: i. ii. iii. iv. v.

G1 : 50 MVA, 12.2 KV, X = 0.15 p.u. G2 : 20 MVA, 13.8 KV, X = 0.15 p.u. T1 : 80 MVA, 12.2 / 161 KV, X = 0.10 p.u. T2 : 40 MVA, 13.8 / 161 KV, X = 0.10 p.u. Load : 50 MVA, 0.80 PF lagging, operating at 154 KV.

Determine the p.u impedances of the load for the following cases: a. Load modeled as a series combination of resistance and inductance b. Load modeled as a parallel combination of resistance and inductance

Problem: 21


Draw an Impedance diagram for the system whose One line diagram is shown in figure below. The 3Ø and line-line ratings are as follows: Generator: 30 MVA, 13.8 KV, XS = 0.10 p.u Motor

: 20 MVA, 13.8 KV, XS = 0.08 p.u

T1

: 20 MVA, 13.2 – 132 KV, XL = 0.10 p.u

T2

: 15 MVA, 13.8 – 138 KV, XL = 0.12 p.u

Line

: 20 + j 100Ω (actual)

Pick the generator ratings for the bases in the generator section.

Problem: 22


Draw an Impedance diagram for the system whose One line diagram is shown in figure below. The 3Ø and line-line ratings are as follows: Generator G

: 15 MVA, 13.8 KV, XS = 0.15 p.u

Motor M1

: 5 MVA, 13.8 KV, XM = 0.15 p.u

Motor M2

: 5 MVA, 14.4 KV, XM = 0.15 p.u

Transformer T1

: 25 MVA, 13.2 – 161 KV, XL = 0.1 p.u

Line

: j 100Ω (actual)

Select a base of 100 MVA and 161 KV in the transmission line.

Problem: 23


Draw an Impedance diagram for the system whose One line diagram is shown in figure below. The 3Ø and line-line ratings are as follows: Generator G1

: 50 MVA, 13.8 KV, XS = 0.15 p.u

Generator G2

: 20 MVA, 14.4 KV, XS = 0.15 p.u

Motor M

: 20 MVA, 14.4 KV, XM = 0.15 p.u

Transformer T1

: 60 MVA, 13.2 – 161 KV, XL = 0.10 p.u

Transformer T2

: 25 MVA, 13.8 – 161 KV, XL = 0.10 p.u

Line 1

: 20 + j 80Ω (actual)

Line 2

: 10 + j 40Ω (actual)

Line 3

: 10 + j 40Ω (actual)

Load

: 20 + j 15 MVA at 12.63 KV

Problem: 24

Power System Analysis by P.S.R Murthy

A 100 MVA, 13.8 KV, 3-phase generator has a reactance of 20%. The generator is connected to a 3-phase transformer T I rated 100 MVA 12.5 KV 1110 KV with 10% reactance. The h.v. side of the transformer is connected to a transmission line of reactance 100 ohm. The far end of the line is connected to a step down transformer T 2' made of three single-phase transformers each rated 30 MVA, 60 KV / 10 KV with 10% reactance the generator supplies two motors connected on the l.v. side T2. The motors are rated at 25 MVA and 50 MVA both at 10 KV with 15% reactance. Draw the reactance diagram showing all the values in per unit. Take generator rating as base. Problem: 25


Obtain the per unit representation for the three-phase power system shown in Fig. 6.3.

Fig. 6.3 Generator 1 : 50 MVA 10.5 KV; X = 1.8 ohm, Generator 2 : 25 MVA, 6.6 KV; X = 1.2 ohm, Generator 3 : 35 MVA, 6.6 KV; X = 0.6 ohm, Transformer T 1: 30 MVA 11/66 KV, X = 15 ohm/phase, Transformer T2 : 25 MVA, 66/6.2 KV, as h.v. side X = 12 ohms, Transmission line : XL = 20 ohm/phase

Problem: 26


A single phase two winding transformer is rated 20 KVA, 480/120 V at 50 HZ. The equivalent leakage impedance of the transformer referred to I.v. side is 0.0525 78.13° ohm using transformer ratings as base values, determine the per unit leakage impedance referred to the h.v. side and t.v. side.

Problem: 27


Consider the system shown in Fig. 6.4. Selecting 10,000 KVA and 110 KVas base values, find the p.u. impedance ofthe 200 ohm load referred to 110 KV side and 11 KV side.

Problem: 28


A Wye connected generator has a nameplate rating of 200 MVA, 20 kV and its sub transient reactance (Xd’’) is 1.2 per unit. Determine its reactance in ohms. Problem: 29


The generator of problem 1 is connected in a power system where the base is specified as 100 MVA, 13.8 kV. What is the generator reactance (Xd’’) in per unit on this system base? Problem: 30


Convert the per unit answer calculated in problem 2 to ohms. Does this check the value determined in problem 1?

Problem: 31


Three 5 MVA single phase transformers, each rated 8:1.39 kV , have a leakage impedance of 6%. These can be connected in a number of different ways to supply three identical 5 ohm resistive loads. Various transformer and load connections are outlined in the table. Complete the table columns. Use a three phase base of 15 MVA.

Three transformers each rated 30 MVA at 38.1/3.81 KV are connected in star-delta with a balanced load of three 0.5 ohm, star connected resistors. Selecting a base of 900 MVA 66 KV for the h.v. side of the transformer find the base values for the I. v. side.

Problem: 32

power system analysis and design by Duncan Glover

A balanced Y-connected voltage source with Eag = 277 volts is applied to a balanced-Y load in parallel with a balanced-delta load, where Zy = 20+ j10 and Zd = 30+ j15 ohms. The Y load is solidly grounded. Using base values of Sbase =10 kVA and VbaseLN =277 volts, calculate the source current Ia in per-unit and in amperes.

Problem: 33

power system analysis and design by Duncan Glover

Three generators are rated as follows: G1 : 100 MVA,33kVA , Xg1= 0.10 p.u , G2 : 150 MVA,32kVA , Xg2= 0.08 p.u , G3 : 110 MVA,30kVA , Xg3= 0.12 p.u . Determine the reactance of generator corresponding to base values of 200 MVA and 35 kV.

Pse Problems Group Assignment

Recommend Documents