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IEEE 14-Bus Transmission System Analysis
Group Members
Jonathan Evangelista
Tyler Ross
Romair Wong
Francis Idehen
ENGI 4969Degree Project
Project Supervisor
Dr. Xiaoping Liu
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Presentation Subject Matter
Introduction
Topics of Analysis
1. Loadflow and State Estimation
2. Transient Stability Analysis
3. Fault Analysis
4. Economic Dispatch
Conclusion
Question Period
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IEEE 14 Bus Test System
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Load Flow and State Estimation
Load Flow: Results
Load Flow: Verification
Load Flow: Design Issues & Resolutions State Estimation: Justification
State Estimation: Results
State Estimation: Future Work
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Load Flow
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Load Flow Results & Verification
Our Load Flow Results
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.383 -16.9783
Bus 2 1.0192 -10.3343 -47.8 3.9
Bus 3 1.0205 -8.7835 -7.6 -1.6
Bus 4 1.07 -14.2012 -11.2 -31.6245
Bus 5 1.0691 -13.3736 0 0
Bus 6 1.09 -13.3736 0 12.9585
Bus 7 1.0584 -14.9473 -29.5 -16.6
Bus 8 1.053 -15.1015 -9 -5.8
Bus 9 1.058 -14.7844 -3.5 -1.8
Bus 10 1.0554 -15.056 -6.1 -1.6
Bus 11 1.0507 -15.1409 -13.5 -5.8
Bus 121.0371 -16.0293 -14.9 -5
Bus 13 1.045 -4.9808 18.3 29.4137
Bus 14 1.01 -12.7161 -94.2 5.1746
Total System Losses 13.383 -35.356
Verification Results: Capacitor Bank Susceptance =0.095
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.4232 -16.5455
Bus 2 1.0177 -10.313 -47.6246 4.0096
Bus 3 1.0195 -8.7774 -7.8563 -1.6539
Bus 4 1.07 -14.221 -11.291 -30.2953
Bus 5 1.0615 -13.36 -0.0061 -12.4472
Bus 6 1.09 -13.3596 0.0046 17.6355
Bus 7 1.0559 -14.939 -29.5205 -12.6304
Bus 8 1.051 -15.0973 -8.9783 -5.7809
Bus 9 1.0569 -14.791 -3.5074 -1.8015
Bus 10 1.0552 -15.0576 -5.9094 -1.7403
Bus 11 1.0504 -15.1563 -13.5668 -5.6964
Bus 121.0355 -16.034 -14.9027 -5.0034
Bus 13 1.045 -4.9826 18.3336 30.8398
Bus 14 1.01 -12.7251 -94.2055 6.0603
Total System Losses 13.3928 -35.0496
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Load Flow Results & Verification
Difference Between Results
|Voltage| Percentage Voltage Angle Percentage
Bus 1 0 0.00% 0 0.00%
Bus 2 0.0015 -0.15% -0.0213 -0.21%
Bus 3 0.001 -0.10% -0.0061 -0.07%
Bus 4 0 0.00% 0.0198 0.14%
Bus 5 0.0076 -0.72% -0.0136 -0.10%
Bus 6 0 0.00% -0.014 -0.10%
Bus 7 0.00247 -0.23% -0.0083 -0.06%
Bus 8 0.002 -0.19% -0.0042 -0.03%
Bus 9 0.00109 -0.10% 0.0066 0.04%
Bus 10 0.0002 -0.02% 0.0016 0.01%
Bus 11 0.0003 -0.03% 0.0154 0.10%
Bus 12 0.00157 -0.15% 0.0047 0.03%
Bus 13 0 0.00% 0.0018 0.04%
Bus 14 0 0.00% 0.009 0.07%
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Load Flow Design Issues & Resolutions
Our Load Flow Results: Capacitor Bank Susceptance=0.19
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.3815 -17.5155
Bus 2 1.0209 -10.367 -47.8 3.9
Bus 3 1.0216 -8.7916 -7.6 -1.6
Bus 4 1.07 -14.1069 -11.2 -36.202
Bus 5 1.0749 -13.4342 9.49E-14 -2.19E-13
Bus 6 1.09 -13.4342 -4.16E-14 9.3694
Bus 7 1.0699 -15.008 -29.5 -16.6
Bus 8 1.0625 -15.1374 -9 -5.8
Bus 9 1.0628 -14.7629 -3.5 -1.8
Bus 10 1.0562 -14.9641 -6.1 -1.6
Bus 11 1.0524 -15.0704 -13.5 -5.8
Bus 12 1.0444 -16.0215 -14.9 -5
Bus 13 1.045 -4.9801 18.3 27.6958
Bus 14 1.01 -12.71 -94.2 4.1137
Total System Losses 13.3815 -46.8386
Verification Results: Capacitor Bank Susceptance = 0.19
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.4232 -16.5455
Bus 2 1.0177 -10.313 -47.6246 4.0096
Bus 3 1.0195 -8.7774 -7.8563 -1.6539
Bus 4 1.07 -14.221 -11.291 -30.2953
Bus 5 1.0615 -13.36 -0.0061 -12.4472
Bus 6 1.09 -13.3596 0.0046 17.6355
Bus 7 1.0559 -14.939 -29.5205 -23.2228
Bus 8 1.051 -15.0973 -8.9783 -5.7809
Bus 9 1.0569 -14.791 -3.5074 -1.8015
Bus 10 1.0552 -15.0576 -5.9094 -1.7403
Bus 11 1.0504 -15.1563 -13.5668 -5.6964
Bus 12 1.0355 -16.034 -14.9027 -5.0034
Bus 13 1.045 -4.9826 18.3336 30.8398
Bus 14 1.01 -12.7251 -94.2055 6.0603
Total System Losses 13.3928 -45.642
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Load Flow Design Issues & Resolutions
Our Load Flow Results: Inductor Bank = 0.25
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.383 -16.9783
Bus 2 1.0192 -10.3343 -47.8 3.9
Bus 3 1.0205 -8.7835 -7.6 -1.6
Bus 4 1.07 -14.2012 -11.2 -3.002
Bus 5 1.0691 -13.3736 -5.30E-14 5.98E-13
Bus 6 1.09 -13.3736 -2.19E-14 12.9585
Bus 7 1.0584 -14.9473 -29.5 -16.6
Bus 8 1.053 -15.1015 -9 -5.8
Bus 9 1.058 -14.7844 -3.5 -1.8
Bus 10 1.0554 -15.056 -6.1 -1.6
Bus 11 1.0507 -15.1409 -13.5 -5.8
Bus 12 1.0371 -16.0293 -14.9 -5
Bus 13 1.045 -4.9808 18.3 29.4137
Bus 14 1.01 -12.7161 -94.2 5.1746
Total System Losses 13.383 -6.7335
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State Estimation
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State Estimation Justification
State Estimation Results with only Ammeters
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.4307 -17.0215
Bus 2 1.0191 -10.3413 -47.2628 3.5936
Bus 3 1.0205 -8.7859 -5.2704 -1.0163
Bus 4 1.07 -14.4591 -14.0875 -30.8252
Bus 5 1.0692 -13.4532 -0.5992 0.419
Bus 6 1.09 -13.4532 2.06E-13 12.8902
Bus 7 1.0583 -15.0312 -29.3543 -17.4161
Bus 8 1.0532 -15.1995 -8.4753 -5.5637
Bus 9 1.0578 -14.9584 -3.5714 -2.0719
Bus 10 1.0553 -15.3063 -6.0599 -1.5662
Bus 11 1.0506 -15.3832 -13.8465 -5.9414
Bus 12 1.0372 -16.1718 -14.7264 -4.902
Bus 13 1.045 -4.9819 18.3457 29.4057
Bus 14 1.01 -12.7178 -94.144 5.191
Total System Losses 13.3787 -34.8248
Our Load Flow Results
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 232.383 -16.9783
Bus 2 1.0192 -10.3343 -47.8 3.9
Bus 3 1.0205 -8.7835 -7.6 -1.6
Bus 4 1.07 -14.2012 -11.2 -31.6245
Bus 5 1.0691 -13.3736 0 0
Bus 6 1.09 -13.3736 0 12.9585
Bus 7 1.0584 -14.9473 -29.5 -16.6
Bus 8 1.053 -15.1015 -9 -5.8
Bus 9 1.058 -14.7844 -3.5 -1.8
Bus 10 1.0554 -15.056 -6.1 -1.6
Bus 11 1.0507 -15.1409 -13.5 -5.8
Bus 12 1.0371 -16.0293 -14.9 -5
Bus 13 1.045 -4.9808 18.3 29.4137
Bus 14 1.01 -12.7161 -94.2 5.1746
Total System Losses 13.383 -35.356
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State Estimation Results
State Estimation Results
|Voltage| Voltage Angle Total MW Total MVAR
Bus 1 1.06 0 231.5597 -16.9621
Bus 2 1.0188 -10.1864 -45.7472 1.0942
Bus 3 1.0205 -8.6489 -5.4136 -1.4732
Bus 4 1.07 -14.0739 -12.4318 -30.8687
Bus 5 1.0697 -13.2223 -0.1336 2.0601
Bus 6 1.09 -13.2223 -2.08E-15 12.5355
Bus 7 1.0579 -14.7869 -29.921 -18.9127
Bus 8 1.0535 -14.932 -9.2096 -4.11
Bus 9 1.0576 -14.5067 -1.5761 -3.2759
Bus 10 1.0554 -14.9276 -6.0775 -1.5762Bus 11 1.0507 -15.0114 -13.6507 -5.9201
Bus 12 1.0374 -15.8773 -14.6957 -4.7037
Bus 13 1.045 -4.9902 14.2583 30.5225
Bus 14 1.01 -12.6292 -93.8491 5.2924
Total System Losses 13.1121 -36.2979
Measurement Tag Error(%)
21 23.4392
51 10.7101
18 10.5085
80 19.4064
40 14.7082
42 4.2677
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State Estimation ResultsIdentifying Good Data over Ten Iterations
Branch Information Error Percentage on Fixed Specified Measurement
Branch Tag # Branch Power Load Flow Powers 20%:P1-13 20%:P2-3 20%:Q13-2
1 P1-3 75.5528 60% 60% 80% 100% 100% 90%
2 Q1-3 3.4136 90% 90% 100% 100% 100% 100%
3 P1-13 156.8302 0% 0% 70% 100% 80% 100%
4 Q1-13 -20.392 90% 80% 90% 100% 100% 100%
5 P2-3 -61.3705 70% 90% 0% 0% 100% 90%
6 Q2-3 17.2562 80% 100% 40% 80% 100% 100%
7 P2-5 28.246 90% 100% 100% 100% 100% 100%
8 Q2-5 -24.1087 90% 100% 100% 100% 100% 100%
9 P2-7 16.0969 100% 100% 100% 100% 100% 100%
10 Q2-7 -6.7685 100% 100% 100% 100% 100% 100%
11 P2-13 -54.4895 80% 90% 100% 100% 100% 100%
12 Q2-13 3.8999 100% 100% 100% 100% 100% 100%
13 P2-14 23.7171 100% 100% 90% 90% 90% 90%
14 Q2-14 -3.9695 100% 100% 100% 100% 100% 100%
15 P3-1 -72.7896 60% 70% 100% 100% 100% 90%
16 Q3-1 2.6675 100% 90% 100% 100% 100% 100%
17 P3-2 61.8928 70% 90% 20% 40% 100% 90%
18 Q3-2 -15.6085 80% 100% 30% 50% 100% 80%
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State Estimation Future Work
Creating a Database
Adjust for redundancy lower than one
Incorporate Phasor Measurement Units intothe algorithm
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Transient Stability Analysis
What is Transient Stability?
Multimachine System
Classical Stability Model 5 Assumptions associated with a Classical
Stability Study
Test Bench (9-Bus System) IEEE 14-Bus Test System
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What is Transient Stability?
Transient disturbances
Mechanical analogy
This image is from Transient Stability of Large Scale Power Systems
by Vijay Vittal of Iowa State University.
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Multimachine System
Equal area Criterion vs. Swing Equation
Single Machine System
Multi Machine System(9-Bus Test Bench Model)
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Classical Stability Model
Classical Representation of a
Multimachine System
Assumptions associated with this model:
1. Constant mechanical power input
during swing
2. Negligible damping power
3. Constant transient reactance in series
with constant transient internal
voltage
4. Internal generator voltage angle
coincides with mechanical rotorangle
5. Constant load admittances
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Calculations
2 + cos +
=1
The Swing Equation:
Internal Generator Voltages:
+
+
Constant Load Admittances:
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9 Bus System - Test Bench
The 9 Bus transmission system which was used as a test bench was taken from Power
System Control and Stability 2ndEdition by Anderson and Fouad:
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9 Bus System - Test Bench
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9 Bus System - Test Bench
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9 Bus System - Test Bench
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Fault Analysis
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FAULT ANALYSIS
Background
Objective
Methodology
Sample Calculations
GUI Flow Chart
Graphical User Interface
Extension of the project
Future Expansion
Problems Encounter
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Fault Analysis (cont.)
Background
Causes of Faults
1. Insulation failure
2. Flashover
3. Physical Damage
4. Human error
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Fault Analysis (cont.)
Types of fault
1. Symmetrical (Balanced)
2. Unsymmetrical (Unbalanced)
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Module Objective
Build a dynamic software package to assist users
to perform fault analysis
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Extension to the Project
Modification of an existing Z bus Case 1: Adding Zb from a new bus P to reference node
Case 2: Adding Zb from a new bus P to an existing bus k
Case 3: Adding Zb from Existing bus k to the reference node
Case 4: adding Zb between two existing buses (j) and (k)
Kron Reductions
M h d l Fl Ch
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Methodology Flow Chart
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Method of Calculation and Procedure
To illustrate, impedance matrix was used
Consider a bus Power system shown below
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Method of Calculation(cont.)
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Method of Calculation(cont.)
Y11Y21y31y41
y12y22y32y42
y13y23y33y43
y14y24y34y44
V1VFV3V4 = 0I F0
0
If
V1VFV3V4
Z11Z1y31Z41
Z1ZZ3Z4
Z13Z3Z33Z43
Z14Z4Z34Z44
0If
00
V Y1
buI ZbuI
1 1If 1 3 3If
3
4 4I
f
4
V1V2V3
V4
= VfVfVf
Vf
+ V1V2V3V4 = Vf
Vf
Vf
Vf
+ 12
22 VfVf3222 Vf
42
22
Vf
=
1 12
22 VfVf1 3222 Vf1
42
22
Vf
Impedance MatrixAdmittance Matrix
Current
Post Fault VoltagesDuring Fault Voltage
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Method of Calculation(cont.)
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GUI Flow Chart
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MATLAB GUI Menu
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MATLAB GUI Menu
Figure 1: shows the Impedance matrix
Figure 3: shows the post
fault voltages
Figure 2: shows the current matrix after the fault
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Some Problems Encounter
Making the program dynamic
Expansion of the 4 cases
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Summary
Future Expansion
And also implementation of a unsymmetrical fault, which could be the
continuation of this project to enhance the fault states of the network. This
causes a single line, line to line and double line fault to occur. A pop menu is
also created within the Graphical User Interface for this application Addition of different zones around the network grid to aid in simulation of the
location of the faulted in order to gather information in the selection of
switchgears and relays.
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Optimal Economic
Dispatch
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Points to be covered
What is Optimal Economic dispatch?
Design Phases
Calculations Findings
Summary
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The Goal of Optimal
Economic dispatch
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Design Phases
Phase 1: Devise Algorithm suitable for
calculation of the Loss or B-Coefficients
of the system.
Phase 2: Obtain Optimal Economic
Dispatch.
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Transmission Loss
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Obtaining an
Expression for Transmission loss
for the System
Overall
transmission lossexpression for the
system
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Flowchart for
Obtaining LossCoefficients
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Optimal Economic Dispatch
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Classic Economic Dispatch
The goal of economic dispatch is to determine
the generation dispatch that minimizes the
instantaneous operating cost.
Such ThatMinimize
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CalculationsIncremental Transmission LossIncremental Production Cost
Overall Expression
Taking into Account all Generators
Condition for
Optimum Dispatch
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Economic
Dispatch
Flowchart
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Graphical User Interface
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B-Coefficients and Power Loss
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Optimal Economic Dispatch
T t b h d i i /
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Test bench used in comparisons/
verification
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Discuss Results/Problems
These results Verified with Test-bench. Graphs show after each iteration, the system starts from a max
value then gradually begins to decrease closer to an optimaloperating point.
The values and cost functions used in 14-bus economic dispatch
were from another 14-bus system (Port Land State University). 15.21MW total system loss - compared to the 13.386MW on
original 14-bus data sheet.
14 bus incremental losses, cost and overall economic dispatch leftquestionable.
At 15
th
iteration during the calculations of incremental loss, cost andoverall economic dispatch, error message stating matrix singularor badly scaled occurred.
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Future Improvements
dynamic retrieval of voltage and powers from
the Load Flow module of the program.
Include generator limits
Include transmission limits were omitted from
the analysis system. Simply, we considered the
system without these restrictions.
contingency in place should stability and fault
issues severely impede its ability to function.
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Conclusion
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Demonstration
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IEEE 14 Bus Test System
Pre-Post
Bus No. V Voltage Angle Real Power Reactive Power1 0 0 -0.1299 -0.05772 0.0009 0.032 0 03 0.0002 -0.0203 0 04 0 -0.3685 0 2.05025 0.0022 0.2409 8.9359E-14 3.68549E-136 0 0.2409 1.2837E-14 -1.3547 0.0041 0.354 0 08 0.0035 0.2269 0 09 0.002 -0.068 0 0
10 -0.0017 -0.5135 0 011 -0.0045 -0.619 0 012 0.015 1.0763 0 013 0 0.0095 0 -0.722814 0 0.032 0 -0.5035