Power SystemOperation and Control (EET 415)
Laboratory Module
EXPERIMENT 1
ECONOMIC POWER SYSTEM OPERATION
1. OBJECTIVE:
To analyze the economic power flow on the power system by means of MiPower
software
2. EQUIPMENT:
MiPower software
3. INTRODUCTION:
Focus of economic operation study is to schedule or arrange power go out from each
existing central in system to load on the system so that the amount of cost generating as
minimum as possible or maximum efficiency. Maximum efficiency is minimizes the cost
of kilowatthour to consumer and the cost to the company of delivering that kilowatthour
in the face of constantly rising prices for fuel, labor, supplies and maintenance.
When we study about economic dispatch in a power system, assumed the system in a
“power balance’ state. In the system consists of n thermal-generating units connected to
a single busbar serving a received electrical load PR as Fig.3.3 below
1
T
G
P1
C1
2
T
G
P2
C2
PR
n
T
G
Pn
Cn
Fig.3.3 n thermal unit commited to serve a load
of PR
So, total system generated equal to the total system load plus losses in the transmission
line including tie line flows out of the system
n
PG   Pi  PR  PL
1
i 1
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Power SystemOperation and Control (EET 415)
Laboratory Module
where:
PG
= total output generated electrical power
Pi
= output-generated electrical power for the ith generating unit [per- unit] on
a common power base
PR
= total system load, including tie line flows,[per-unit]
PL
= total system transmission losses [per-unit]
n
= number of generators in service in the system
A basic constraint is that for each generator:
Pmin i  PGi  Pmax
2
To determine economic dispatch in the power plants, we can divided to two categories:
a) System without transmission losses
n
PG   Pi  PR
3
i 1
The operating cost of a unit includes fuel cost, labor, supplies and maintenance in
expressed as
C i  Fi Pini
4
where:
Ci
= operating cost of unit i [$/H]
Fi
= cost of fuel for unit i [$/ M Btu]
Pini = input unit i power [M Btu/H] (NOTE: this is NOT Pi)
The curve Ci can be represented by a second-order expression
Ci   i   i Pi   i Pi 2
5
where:
i = generator i, one of n units
Ci = operating cost of generator i [$/H]
Pi = electrical power output of generator i [per-unit] on a common power
base
 ,  and  are coefficients in units of $/H
The condition for optimal economic dispatch is given by Langrange’s method;
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Power SystemOperation and Control (EET 415)
Laboratory Module
dC i

dPi
for Pi ,min  Pi  Pi ,max
dC i

dPi
for Pi  Pi ,max
dC i

dPi
for
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Pi  Pi ,min
This is the requisite to minimize cost of the system.
A general solution is called the method of Lagrangian multipliers.
a) If without losses and no generator limits, the most economic operation can be
found iteratively using gradient method where an initial value for λ has to be assumed,
then a better value is obtained by extrapolation. The process is continued until ΔPi = 0 or
within a specified accuracy. The proof is given in lecture notes. At the kth iteration,
Pi k 
k    i
2 i
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is called Coordination Equation
and an analytical solution can be found for this trivial case by using the summation of
equation (7):
P  
i
λ  βi
 PR
2γi
Or:
βi
i 1 2γi
n
1

i 1 2γi
ng
λ
PR  
g
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Power SystemOperation and Control (EET 415)
Laboratory Module
b) System with transmission losses :
If transmission losses is represented by its simplified expression:
n
n
n
PL   Pi Bij Pj or PL   Bii Pi
i 1 j 1
2
9
i 1
Where Bii is called loss coefficient or loss coefficient..
Analytical solution for the system with losses is tedious and only the iterative solution
is normally carried out, Then the solution for economic dispatch reduces to:
λ (k)  βi
Pi 
2(γi  λ (k) Bii )
(k)
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4. PROCEDURE
Figure 1 shows a 9-bus power system network of an Electric Utility Company. The load
data, voltage magnitude, generation schedule and reactive power limits for regulated
bus are tabulated in Table below. Bus 1, whose voltage is specified as V1 = 1.03 0 is
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Power SystemOperation and Control (EET 415)
Laboratory Module
taken as slack bus. Obtain the optimal dispatch of generation for the power system
within accuracy of 0.001MW
GENERATION DATA
Bus
Voltage
No
MW
Magnitude Generation
1
1.03
2
1.04
7
1.01
Mvar
Min
Max
Max
50
200
80
50
200
0
250
120
50
100
0
100
LOAD DATA
Bus
Min
LINE DATA
Load
From Bus i to
Bus j
R
X
B/2
1-2
0.018
0.054
0.0045
1-8
0.014
0.036
0.003
2-9
0.006
0.03
0.0028
2-3
0.013
0.036
0.0030
3-4
0.010
0.050
0.0000
4-5
0.018
0.056
0.0000
5-6
0.020
0.060
0.0000
No
MW
Mvar
1
0
0
2
20
10
3
25
15
4
10
5
5
40
20
6
60
40
7
10
5
6-7
0.015
0.045
0.0038
8
80
60
6-9
0.002
0.066
0.0000
9
100
80
7-8
0.032
0.076
0.0000
7-9
0.022
0.065
0.0000
The generator’s operating costs $/h are as follows:
C1 = 240 + 6.7P1 + 0.009P12
C2 = 220 + 6.1P2 + 0.005P22
C7 = 240 + 6.1P7 + 0.008P72
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Power SystemOperation and Control (EET 415)
Laboratory Module
1. Open Power System Network Editor.
2. Refer to the user manual provided to You for the procedure to draw all relevant
and necessary elements and database configuration for the system.
3. After finish editing, conduct load flow analysis.
4. Set P and Q tolerance at 0.0001. Select Slack Bus as Bus 1. Also select B
Coefficient & Economic Dispatch method to solve the load flow analysis.
5. Execute the load flow program and print out the single line diagram with relevant
Information.
6. Click on the Report button. The detail report for the analysis will be display. Print
the report.
7. What is the total generation for cost for all the generators and optimal dispatch of
generation for all generators?
8. What is the incremental cost of delivered power (system lambda)?
9. What is the system total loss?
10. Write the B matrices of the loss formula for the system.
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Power SystemOperation and Control (EET 415)
Laboratory Module
PART B: QUESTIONS
1. A power system is supplied by three plants, all are operating on economic
dispatch. At the bus of plant 1 the incremental cost is $ 10.0 per MWh. Plant 2 at
$9.0 per MWh and at plant 3 is $11.0 per MWh. Which plant has the highest
penalty factor and which one is the lowest.
2. What are the purpose of Optimal Power flow study?
3. Describe in your own words the meaning of Unit Commitment
DISCUSSION
CONCLUSION
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Power SystemOperation and Control (EET 415)
Laboratory Module
NAME:__________________________________ MATRIX NO __________________
EXPERIMENT NO:________________________ DATE________________________
ANSWER:
7.
8.
9.
10.
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