Download Guru Tegh Bahadur Institute of Technology Fourth Semester

Guru Tegh Bahadur Institute of Technology
Fourth Semester - EEE
Power System – I (ETEE-206)
Assignment – 1
Power in AC circuits - Review
1. A supply voltage of v(t) = 100coswt is given to an impedance Z = 1.25 angle 60 0Ω. Determine
the expression for instantaneous current i(t) and the instantaneous power p(t). Use matlab to
plot i(t), v(t), p(t), PR(t), PX(t) over an interval 0 to 2π. Ans: p(t)=8000coswtcos(wt-600).
2. Calculate active and reactive power if V=100+j200V, I=10+j5A, Ans: 2000W, 1500VAr
3. A circuit has R=12Ω, L=0.15H, C=100µF in series, connected across 100V, 50Hz supply.
Calculate
a. Current in each branch Ans: IR=2A, IL=2.12A, IC=3.14A, I=2.24A
b. Supply current Ans: I=2.24A
c.
Phase angle between supply current and voltage
Ans: 0.893 radian
4. A circuit has three impedances in parallel. Z1=60+j0Ω, Z2=6+j12Ω, and Z3=30-j30Ω. These
are connected to supply voltage 1200V. Find power absorbed by each load and total complex
power. Draw phasors. Ans: S1=24000var, S2=48000+j96000var, S3=24000-j24000var.
5. Three loads are connected in parallel across a 1400Vrms, 60Hz single phase supply. They
are L1=Inductive load 125kVA at 0.28pf, L2=capacitive load, 10kW and 40kVar, resistive
load=15kW. Find total kW, kVAr, kVA, and supply pf.
Ans: S=60kW + j80kVAr, pf = 0.6lag
6. Two loads Z1=100+j0Ω and Z2=10+j20Ω are connected in parallel across a 200Vrms, 60Hz
source. Find total P and Q, pf at the source and total current.
Ans: S=1200+j1600VA=2000 angle 53.130., I=10 angle -53.130, pf =0.6lag.
7. In the above question, find capacitance of the capacitor connected across loads to improve
overall pf to 0.8lag. Also find new total power and supply current. Ans C=46.4microF.
Faculty: Harshpreet Kaur
Guru Tegh Bahadur Institute of Technology
Fourth Semester - EEE
Power System – I (ETEE-206)
Assignment – 2
Per Unit system and Single Line Diagram
1. A 90MVA, 11kV, three phase generator has a reactance of 25%. The generator supplies two
motors through transformers and transmission line as shown in Fig.1.The transformer T 1 is a
three phase transformer, 100MVA,10/132V, 6% reactance. The transformer T 2 is composed of
three single phase transformers each rated at 30MVA, 66/10kV, with 5% reactance. The
connections of T1 and T2 are shown. the motors are rated at 50MVA and 40MVA both 10kV and
20% reactance. Taking the generator rating as base, draw reactance diagram and indicate the
reactances in pu. The reactance of line is 100Ω.
2. A single phase system having three parts A, B, C is shown in Fig.2. The ratings of transformers
are A-B: 10MVA, 13.8/138kV, X=10%
B-C: 10MVA, 138/69kV, X=8%. If the base in circuit B is chosen as 10MVA, 138kV, find pu
impedance of 300Ω resistance load in circuit C referred to circuits C, B, and A. Find voltage on
side A if voltage at load is 66kV.
3. Redraw the circuit shown in Fig. 3 with pu impedance represented on 5000VA base and common
system base voltage of 250V for G1. Also draw impedance diagram. The data is as follows:
G1: 2000VA, 250V, Z=j0.2pu G2: 2000VA, 250V, Z=j0.3pu
T1: 4000VA, 250/800V, Z=j0.2pu Line: Z=40+j150Ω
T2: 8000VA, 1000/500V, Z=j0.06pu
4. For Fig. 4, draw impedance diagram with all values in pu on a base of 30MVA, 6.6kV in the circuit
of generator G1.
Faculty: Harshpreet Kaur
Guru Tegh Bahadur Institute of Technology
Fourth Semester - EEE
Power System – I (ETEE-206)
Assignment – 3
Line Parameters
1. Find the loop inductance and reactance per km of a single phase overhead line consisting of two
conductors, each 1.213cm diameter. The spacing between conductors is 1.25m and frequency is
50Hz. Ans: L=22.31*10-4H/km.
2. Fig. 5 shows a stranded conductor having seven identical strands each of radius r. Find GMR of
the conductor and the ratio of GMR to overall conductor radius. Ans:X=0.7Ω/km, Ds=2.177r, R=3r
3. A bundles conductor line has 4 conductors per bundle per bundle. The 4 sub-conductors are
placed at corners of square of side 25cm. The radius of each sub-conductor is 1.573cm. Find
GMR of this configuration. Ans: Ds=12.826cm
4. A three phase double circuit line has the configuration shown in Fig. 6. The radius of each
conductor is 0.9cm. Find the inductance per phase per km line length. Ans: L=6.136*104H/phase/km.
5. A 220kV, 50Hz, 200km long three phase line has its conductors on the corners of a triangle with
sides 6m, 6m and 12m. The conductor radius is 1.81cm. Find the capacitance per phase per km,
capacitive reactance per phase, charging current and total charging MVAs.
Ans: C=1.8µF/phase Xc=1730Ω/phase I=73.42A/phase Charging MVAs=27.97MVar
6. A 400kV, three phase single circuit bundled conductor line with two sub conductors per phase has
a configuration shown in Fig. 7. The centre to centre distance between adjacent phases is 12m
and distance between two sub conductors of a phase is 45cm. The radius of each sub conductor
is 1.6cm. Find capacitance per phase per km. Ans: 0.0107µF/km.
Faculty: Harshpreet Kaur
Guru Tegh Bahadur Institute of Technology
Fourth Semester - EEE
Power System – I (ETEE-206)
Assignment – 4
Line Parameters
1. A 15km long 3-phase line has a resistance of 5.3Ω per phase and inductive reactance of 5.5Ω per
phase. The sending end voltage is 11kV. Recieving end load is 1200kW at a power factor of
0.8lg. Find receiving end current and line current. Ans: Ir=87.95A, Vr=5.685kV
2. A three phase load of 1MW at a power factor of 0.8lag is supplied by a 30kV line of resistance
25Ω and inductive reactance of 12Ω/phase. The voltage across the load is 10kV. A 30/10kV
transformer steps down the voltage at the receiving end. The equivalent resistance and reactance
of the transformer as referred to 10kV side are 0.8Ω and 2.5Ω respectively.Find sending end
voltage and regulation. Ans: Vs=18438.7V;Vs(line)=31.94kV, Regulation=0.0645%.
3. A three phase, 50Hz, 100km long overhead line has constant resistance of R=0.153Ω/phase/km,
inductance, L=1.21mH/phase/km, capacitance,C=0.00958µF/phase/km. Line load is 20MW at
0.9pf lag at a line voltage of 110kV at the receiving end. Using π representation, calculate
sending end voltage, current, power factor, regulation and efficiency.
Ans: Vs=66767.42 angle 2.880, (115.64kV - line)
Is=109.24 angle -16.670A
Sending end power factor =0.942 lag
Regulation = 5.74%, efficiency=97%
4. A three phase line is 500km long. The line constants are Z=0.105+j0.3768Ω/km, y=0+j2.822*10-6
siemens/km. The line delivers 40MVA at 0.9pf lag at 220kV. Find V s, Is, and power factor, MVA,
and power angle. Ans: Vs=124795.23 V angle8.930+ (Line voltage = 216.15kV)
Is=157.71A angle 58.80, sending end pf = 0.645lead, sending end MVA=59.042MVA
5. Find Vs, Is, and power factor if the line in Q4 is open circuit at receiving end. Recieving end
voltage, Vr=220kV. Ans: Vs=110571.8V angle 2.330 (Line voltage = 191.51kV)
Is=171.4A angle 90.7220, sending end pf = 0.0281 lead
6. A 300km, 132kV three phase overhead line has a total series impedance of 52=j200Ω per phase
and a total shunt admittance of
j105*10-3 siemens per phase to neutral. The line supplying
40MVA at 0.8pf lag at 132kV. Find Vs,Is, pf and power. Ans: Vs=96410V angle 15.340,
Is=122.73A angle 10.350.
7. Two three phase lines have the following constants
A1=D1=0.98 angle 20, B1=28 angle 690Ω, C1=0.0002 angle 800 siemens
A2=D2=0.95 angle 30, B2=40 angle 850 Ω, C2=0.0004 angle 900 siemens.
The two lines are connected in cascade. Find (a) ABCD constants for the composite system.
(b) Vs, Is, and pf (sending end) if the composite system delivers 200A at 110kV at 0.5pf lag.
Faculty: Harshpreet Kaur
Guru Tegh Bahadur Institute of Technology
Fourth Semester - EEE
Power System – I (ETEE-206)
Assignment – 5
Overhead Line Insulators
1. Determine the maximum voltage that the string of suspension insulators in Fig. 8 can withstand if
the maximum voltage per unit is 17.5kV.
2. Determine the voltage across each disc of suspension insulators a s a percentage of the voltage
to earth. The self and capacitance to ground of each disc is C and 0.2C respectively. The
capacitance between the link pin and the guard ring is 0.1C.
3. In Q2, if the capacitance to the line of the lower link pin were increased to 0.3C by means of
guard ring, determine the redistribution of voltage. Also determine the string efficiency in each
case.
4. A string of eight suspension insulators is to be filled with the guard ring. If the pin to earth
capacitances are all equal to C, find the values of line to pin capacitance that would give a
uniform voltage distribution over the string.
Faculty: Harshpreet Kaur
Faculty: Harshpreet Kaur