eeen 810 final assignment_21012012

8/3/2019 Eeen 810 Final Assignment_21012012

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DEPARTMENT OF ELECTRICAL ENGINEERING

AHMADU BELLO UNIVERSITY, ZARIA

EEEN 810: FINAL ASSIGNMENT

DATE DUE: ON THE DAY OF FINAL EXAMINATION

1. For the sample power system shown in Fig.Q1 with its network parameters given in

Table Q1:

a) Draw its directed graph and impedance diagrams.

b) Define and construct the referenced element -node incidence matrix, L for thenetwork, choosing the ground as the reference.

c) Using the direct method, build the Bus Admittance Matrix for the network.

d) Repeat c) using Singular Transformation Technique if there is mutual coupling of

j0.01 between elements 3 and 4.

FIG.Q1: Sample Power System

TableQ1: Network Data for the Sample Power System

2. For a 4 -bus sample power system, its upper triangle admittance bus matrix is givenbelow:

-

-

-

-

=

0.9

45.10

0.35.25.7

24210

jYBUS

Element

no.

Bus to Bus

R X

Total

BT1 1 2 0.02 0.05 0.2

2 1 3 0.0 0.08 0.2

3 3 4 0.05 0.2 0.4

4 2 4 0.04 0.15 0.3

431

2


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a) Draw the network for the 4 -bus system and construct its network parameter Table.

b) Apply step-by-step approach to construct its ZBUS, choosing bus1 as the reference.

3. For the system network shown in Fig. Q3:a) Develop its relevant power flow equations in polar form.b) Construct the matrices (B & B) required by the fast-decoupled power flow.

c) Using fast-decoupled power flow technique, obtain its power flow so lution at the

end of the second iteration. Assume initial flat start.

FIG.Q3: 3-Bus System

4. The network parameters for a four-bus network are shown in the Table below:

a) Formulate the DC power flow for the network, assuming bus 4 as the slack bus.

b) Given that load demands at buses 1 and 3 are 2.5pu and 3.0pu respectively whist thegeneration at bus 2 is 3.5pu, determine the DC power flow solution using triangular

factorization technique.

LINE DATA BUS DATA

Y12 = -j5.0pu

Y13 = -j7.5pu

Y23 = -j5.0pu

Ys3 = -j0.1pu

V1 = 1.050opu; V2 = 1.04pu

PG2 = 2.5pu

PD3 = 4.5pu

QD3 = 0.5pu

Bus to Bus X p.u.

1 2 0.2

1 3 0.12 4 0.05

3 4 0.1

12

3


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c) If line 3-4 is on outage, det ermine the line outage distribut ion factors for lines 1 -2,

1-3 and 2-4.

5. The DC power flow equations for some real power measurements in a sample power

system are given as follows:

+

-=

3

2

1

2

1

3

2

1

14

11

11

v

v

v

P

P

P

d

d

Where P 1, P 2 and P 3 are the measurements; d1 and d2 are the bus angles to be

estimated; v1, v2 andv3 are the measurement errors.

Given the measurement vector, P and covariance matrix, R as follows:

=

=

01.00.00

001.00

00001.0

&

5.3

5.2

0.4

RP

a) Using the weighted least squares (WLS) technique, obtain the best estimates of

the bus angles.

b) Compute the measurement errors.

6. a) For the 2 -bus sam ple power system shown in Fig.Q6 , develop the

relevant equations for the unconstrained optimal power flow (OPF). Define

very clearly all the state variables and control variables used.

Fig.Q6: 2-Bus Sample Power System

C2 = 1 + .75PG2 + 0.75PG22C1 = 1 +0.2 PG1 + 0.4PG1

2

y = 1 j7.5

PD1=2.0 pu PD2=3.0 pu

V1 = 1.0 pu

PG1 = ?

2 =?

V2 = 1.0 pu


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b) Compute the initial OPF solution starting from PG1 = 2.5pu and 2 =0.

7. Consider two interconnected areas 1 & 2, each having the following parameters on its

own base capacity;

R1 = 0.050pu Hz /pu MW; D1 = 3.5 pu MW/pu Hz on base capacity of 1000 MW

R2 = 0.025pu Hz /pu MW; D2 = 2.5 pu MW/pu Hz on base capacity of 1500 MW

Assume that the system is initiall y operating at 50 Hz when a decrease of 25 0 MW

occurs in area 2. Determine:

i) The steady state frequency of the interconnected areas ;

ii) The change in steady state tie-line flow in MW and

iii) Specify the Area Control Error (ACE) for each area.

8. For the sample 3 -bus system shown in Fig.Q8, the neutral of each generator is solidly

grounded. Assume all the generators are running at no -load at rated voltage and in phase

and that all the network data given on a 100 MVA base.

a) Draw the positive, negative and zero sequence diagrams for the sample network and

construct their respective ZBUS matrices.

b) Determine the fault current s for 3 - and1- through fault impedance of 4% at

bus 3.

Item V Raing X1(%) X2(%) X0(%)

G1 16 kV 15 15 15

G2 16 kV 15 15 15

T1 16/132 kV 10 10 10

T2 16/132 kV 10 10 10L1-2 132 kV 12.5 12.5 30

L1-3 132 kV 15 15 35

L2-3 132 kV 25 25 71.25

9. For a single machine feeding an infinite bus system, the P - curves that describe pre fault,

fault and post-fault conditions are as follows:

P = 3.5sin: Pre-fault P- curve;

L1-3 L2-3

21

T2T1

G2G1

3

L1-2


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P = 0.0: Fault P- curve;

P = 2.5sin: Post-fault curve.

The machine was initially delivering power of 1.2 pu to the infinite bus when a bolted 3 -

fault was applied for duration of 5 cycles. Assume that H= 2.5 seconds and f = 50Hz. For a

step size, T = 0.01 sec, apply step -by-step approach to determine the rotor angle after 0.1

sec using Euler method. (Hint: Use the Table given below)

Swing Curve Computation

k=(180f/H)(T)2

t(secs)

Pmax(p.u.)

Pmaxsin sin Pacc(p.u.)

kPacc (elect. deg.)

(elect. deg)

10. a) With the aid of an appropriate diagram, expla in very briefly the over-current protection

of a radial distribution feeder based on time grading scheme.b) Derive the torque equation for an electromagnetic induction type relay.

c) An induction disc type relay is designed to perform as an over -current relay. Assume

the spring torque is 0.0015Nm, the relay pickup current is 10 Amperes and the moment

of inertia of the disc is 1.2x10-4 Kg-m2.(i) Determine the relay parameter, k (i.e. its constant of proportionality).

If the Time multiplier setting of the relay is 1.0, corresponding to 90 o angle of

rotation between the back stopper and the relay fixed contacts, determine the

operating times of the relay for currents of 2.5, 5.5 and 15 times its pickupcurrent. Hence sketch the time versus current characteristics of the relay.

(ii) Starting from the generalized relay equation, derive the equation for a mho relay in

the R-X plane. Define very clearly all the parameters used.

eeen 810 final assignment_21012012

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