Detailed presentation created on the topic of electrical power subject on the power system analysis. Shown about Ybus details, Ybus calculations, Power flow and design, Interconnected operation of power system etc.
Load flow solution is the solution of the network under steady state conditions subjected to certain inequality constraints under which the system operates.
Load flow solution is the solution of the network under steady state conditions subjected to certain inequality constraints under which the system operates.
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
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Unsymmetrical Faults
Unsymmetrical faults are the faults which leads unequal currents with unequal phase shifts in a three phase system.
The unsymmetrical fault occurs in a system due to presence of an open circuit or short circuit of transmission or distribution line. It can occur either by natural disturbances or by manual errors. The natural disturbances are heavy wind speed, ice loading on the lines, lightening strokes and other natural disasters.
The open circuit or short circuits of transmission or distribution lines will lead to unsymmetrical or symmetrical faults in the system. In case of tree branches falling on lines, a short circuit of transmission lines will occur.
These line faults are classified as,
1. Single line to ground faults (LG fault)
2. Double line fault (LL fault)
3. Double line to ground fault (LLG fault)
Single line to ground fault is the most frequently occurring fault (60 to 75% of occurrence). This fault will occur when any one line is in contact with the ground. Double line fault occurs when two lines are short circuited. This type of fault occurrence ranges from 5 to 15%. Double line to ground fault occurs when two lines are short circuited and is in contact with the ground. This type of fault occurrence ranges from 15 to 25% of occurrence.
Design of a generating substation with the description of designing a transformer. Here we show some basic components of a substation. and we also show the parameters and calculation to design a transformer of a specific ratings.
This presentation is about power system voltage stability.
What is voltage stability?
How voltage instability occurs?
How to improve voltage stability of the system?
Power System Analysis was a core subject for Electrical & Electronics Engineering, Based On Anna University Syllabus. The Whole Subject was there in this document.
Share with it ur friends & Follow me for more updates.!
Unsymmetrical Faults
Unsymmetrical faults are the faults which leads unequal currents with unequal phase shifts in a three phase system.
The unsymmetrical fault occurs in a system due to presence of an open circuit or short circuit of transmission or distribution line. It can occur either by natural disturbances or by manual errors. The natural disturbances are heavy wind speed, ice loading on the lines, lightening strokes and other natural disasters.
The open circuit or short circuits of transmission or distribution lines will lead to unsymmetrical or symmetrical faults in the system. In case of tree branches falling on lines, a short circuit of transmission lines will occur.
These line faults are classified as,
1. Single line to ground faults (LG fault)
2. Double line fault (LL fault)
3. Double line to ground fault (LLG fault)
Single line to ground fault is the most frequently occurring fault (60 to 75% of occurrence). This fault will occur when any one line is in contact with the ground. Double line fault occurs when two lines are short circuited. This type of fault occurrence ranges from 5 to 15%. Double line to ground fault occurs when two lines are short circuited and is in contact with the ground. This type of fault occurrence ranges from 15 to 25% of occurrence.
Design of a generating substation with the description of designing a transformer. Here we show some basic components of a substation. and we also show the parameters and calculation to design a transformer of a specific ratings.
This presentation is about power system voltage stability.
What is voltage stability?
How voltage instability occurs?
How to improve voltage stability of the system?
DSD-INT 2016 Urban water modelling - MeijerDeltares
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The use of waveform cross correlation for creation of an accurate catalogue o...Ivan Kitov
Page 3
In the current study of mining activity within the Russian platform, we use the advantages of location and historical bulletins/catalogues of mining explosions recorded by small-aperture seismic array Mikhnevo (MHVAR). The Institute of Geospheres Dynamics (IDG) of the Russian Academy of Sciences runs seismic array MHVAR (54.950N; 37.767E) since 2004.
Small-aperture seismic array “Mikhnevo” includes ten vertical stations (solid triangles), with one station in the geometrical centre of the array (C00) and other nine stations distributed over three circles with radii of 130 m, 320 m, and 600 m. The array aperture in approximately 1.1 km. Two 3C stations (solid triangles in circles) were added to the outer circle in order to improve the overall stations sensitivity (detection threshold) and resolution. All stations are equipped with short-period seismometers SM3-KV, which are characterized by flat response between 0.8 Hz and 30 Hz and gain of 180,000 [Vs/m]. Later, a 3C broad band station (BB) was installed in the centre of the array for surface wave measurements. The array response function (only for 12 vertical channels) is similar to that for many small-aperture arrays. Such arrays are designed to measure high-frequency signals from regional and near-regional sources with magnitudes above 1.5-2.0.
Page 4
MHVAR detects regional seismic phases (Pn, Sn, Lg, Rg) from various sources. Figure shows some selected waveforms with source-station distance decreasing up-down. Correspondingly the length of records decreases – for the closest mines it’s harder to distinguish between P and S phases.
Page 5
More than 50 areas at regional and near regional distances with different levels of mining activity have been identified by MHVAR. Since 2004, thousands of events have been reported in the IDG seismic catalogue as mining explosions. The IDG publishes this mining event catalogue as a part of the annual issues of “Earthquakes in Russia”, which is available for the broader geophysical community. The map shows several selected mines at near-regional distances where MHVAR successfully detects events with magnitudes 1.0 and lower. We also show a few selected mines at regional distances with the largest events of magnitude (ML) 2.0 and above. Such events should be also detected by IMS arrays. Joint interpretation of signals detected by MHVAR and IMS arrays allows significant improvements in signal detection, location, characterization and identification of events in the IDG catalogue when the historical data are revisited. The work on joint analysis of the IDG and IMS data is possible under the “Contract for limited access to IMS data and IDC products” between the CTBTO and IDG, which allows obtaining data through 2011.
To begin with, we have chosen blasts with larger magnitudes from well-known ironstone mine Mikhailovskiy (red circle), which is situated at regional distances somewhere between MHVAR (~330 km) and IMS array AKASG
A Survey and Experimental Verification of Modular Multilevel ConvertersIAES-IJPEDS
This article primarily brings to limelight the Multi-level converters review and specifically the form and function of modular multilevel converter (MMC) with their modulation, design considerations, balancing issues, control schemes, and applications. This article intends to make a detailed analysis of MMC with their controller related issues in comprehensive manner. It is an approach for MMC design and modulation schemes in easy manner. Furthermore, a five level MMC have been designed with optimal controller and verified by its experimental results and explored. In addition to that, this approach draws strategic conclusions on MMC towards making the system more robust in operation, less complex in design and control.
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Thiết bị Điện Công Nghiệp - Điện Hạ Thế: http://dienhathe.org
Catalog LS, Catalog,
Catalog Thiết Bị Điện LS, Catalog Thiết Bị Điện,
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Steady Groundwater Flow Simulation towards Ains in a Heterogeneous SubsurfaceAmro Elfeki
Presented at the Forth International Conference on Ains, Water Resources Center at King Abdulaziz University, Jeddah, Saudi Arabia in Cooperation with UNESCO, April 2006, book of abstracts pp. 48.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
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Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
power system analysis PPT
1. EE 369
POWER SYSTEM ANALYSIS
Lecture 14
Power Flow
Tom Overbye and Ross Baldick
1
2. Announcements
Read Chapter 12, concentrating on sections
12.4 and 12.5.
Homework 12 is 6.43, 6.48, 6.59, 6.61,
12.19, 12.22, 12.20, 12.24, 12.26, 12.28,
12.29; due Tuesday Nov. 25.
2
3. 400 MVA
15 kV
400 MVA
15/345 kV
T1
T2
800 MVA
345/15 kV
800 MVA
15 kV
520 MVA
80 MW40 Mvar
280 MVAr 800 MW
Line 3
345 kV
Line2
Line1
345 kV
100 mi
345 kV
200 mi
50 mi
1 4 3
2
5
Single-line diagram
The N-R Power Flow: 5-bus Example
3
4. Bus Type
|V|
per
unit
θ
degrees
PG
per
unit
QG
per
unit
PL
per
unit
QL
per
unit
QGmax
per
unit
QGmin
per
unit
1 Slack 1.0 0 0 0
2 Load 0 0 8.0 2.8
3 Constant
voltage
1.05 5.2 0.8 0.4 4.0 -2.8
4 Load 0 0 0 0
5 Load 0 0 0 0
Table 1.
Bus input
data
Bus-to-
Bus
R
per unit
X
per unit
G
per unit
B
per unit
Maximum
MVA
per unit
2-4 0.0090 0.100 0 1.72 12.0
2-5 0.0045 0.050 0 0.88 12.0
4-5 0.00225 0.025 0 0.44 12.0
Table 2.
Line input data
The N-R Power Flow: 5-bus Example
4
5. Bus-to-
Bus
R
per
unit
X
per
unit
Gc
per
unit
Bm
per
unit
Maximum
MVA
per unit
Maximum
TAP
Setting
per unit
1-5 0.00150 0.02 0 0 6.0 —
3-4 0.00075 0.01 0 0 10.0 —
Table 3.
Transformer
input data
Bus Input Data Unknowns
1 |V1 |= 1.0, θ1 = 0 P1, Q1
2 P2 = PG2-PL2 = -8
Q2 = QG2-QL2 = -2.8
|V2|, θ2
3 |V3 |= 1.05
P3 = PG3-PL3 = 4.4
Q3, θ3
4 P4 = 0, Q4 = 0 |V4|, θ4
5 P5 = 0, Q5 = 0 |V5|, θ5
Table 4. Input data
and unknowns
The N-R Power Flow: 5-bus Example
5
10. Five Bus Power System Solved
slack
One
Tw o
ThreeFourFive
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1.000 pu 0.974 pu
0.834 pu
1.019 pu
1.050 pu
0.000 Deg - 4.548 Deg
-22.406 Deg
-2.834 Deg
- 0.597 Deg
395 M W
114 M var
520 M W
337 M var
800 M W
280 M var
80 M W
40 M var
10
11. 37 Bus Example Design Case
slack
Metropolis Light and Pow er Electric Design Case 2
SL A C K 3 4 5
SL A C K 1 3 8
R A Y 3 4 5
R A Y 1 3 8
R A Y 6 9
FER N A 6 9
A
MVA
D EM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN 6 9
SH I M K O 6 9
R O GER 6 9
U I U C 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N N A H 6 9
A M A N D A 6 9
H O M ER 6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER 6 9
B U C K Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 2 p u
1 .0 3 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 0 p u
1 .0 0 p u
1 .0 2 p u
0 .9 9 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
MVA
L Y N N 1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 10.70 MW
2 2 0 M W
5 2 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
0 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
1 4 M W
2 M v a r
3 8 M W
3 M v a r
4 5 M W
0 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
2 8 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
6 0 M W
1 9 M v a r
1 4 .2 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
7 .4 M v a r
0 .0 M v a r
5 5 M W
2 5 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
0 M v a r
1 7 M W
3 M v a r
1 6 M W
- 1 4 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
11
12. Good Power System Operation
• Good power system operation requires that
there be no “reliability” violations (needing to
shed load, have cascading outages, or other
unacceptable conditions) for either the current
condition or in the event of statistically likely
contingencies:
• Reliability requires as a minimum that there be no
transmission line/transformer limit violations and
that bus voltages be within acceptable limits
(perhaps 0.95 to 1.08)
• Example contingencies are the loss of any single
device. This is known as n-1 reliability. 12
13. Good Power System Operation
• North American Electric Reliability Corporation
now has legal authority to enforce reliability
standards (and there are now lots of them).
• See http://www.nerc.com for details (click on
Standards)
13
14. Looking at the Impact of Line Outages
slack
Metropolis Light and Pow er Electric Design Case 2
SL A C K 3 4 5
SL A C K 1 3 8
R A Y 3 4 5
R A Y 1 3 8
R A Y 6 9
FER N A 6 9
A
MVA
D EM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN 6 9
SH I M K O 6 9
RO GER6 9
U I U C 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N N A H 6 9
A M A N DA 6 9
H O M ER 6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER 6 9
B U C K Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 2 p u
1 .0 3 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
0 .9 0 p u
0 .9 0 p u
0 .9 4 p u
1 .0 1 p u
0 .9 9 p u
1 .0 0 p u
1 .0 0 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
MVA
L Y N N 1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 17.61 MW
2 2 7 M W
4 3 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
4 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
1 4 M W
2 M v a r
3 8 M W
9 M v a r
4 5 M W
0 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
4 0 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 6 .0 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
6 0 M W
1 9 M v a r
1 1 .6 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .9 M v a r
7 .2 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
7 .3 M v a r
0 .0 M v a r
5 5 M W
3 2 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
4 M v a r
1 7 M W
3 M v a r
1 6 M W
- 1 4 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
8 0 %
A
MVA
1 3 5 %
A
M VA
1 1 0 %
A
M VA
Opening
one line
(Tim69-
Hannah69)
causes
overloads.
This would
not be
Allowed.
14
16. Power Flow And Design
• One common usage of the power flow is to
determine how the system should be modified
to remove contingencies problems or serve new
load
• In an operational context this requires working with
the existing electric grid, typically involving re-
dispatch of generation.
• In a planning context additions to the grid can be
considered as well as re-dispatch.
• In the next example we look at how to remove
the existing contingency violations while serving
new load. 16
17. An Unreliable Solution:
some line outages result in overloads
slack
Metropolis Light and Pow er Electric Design Case 2
SL A C K 3 4 5
SL A C K 1 3 8
R A Y 3 4 5
R A Y 1 3 8
R A Y 6 9
FER N A 6 9
A
MVA
D EM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN6 9
SH I M K O 6 9
RO GER 6 9
U I U C 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N NA H 6 9
A M A N DA 6 9
H O M ER 6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER6 9
B U CK Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 2 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
0 .9 7 p u
0 .9 7 p u
0 .9 9 p u
1 .0 2 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
MVA
L Y N N1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
Syst em Losses: 14.49 MW
2 6 9 M W
6 7 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
1 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
1 4 M W
2 M v a r
3 8 M W
4 M v a r
4 5 M W
0 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
4 0 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
6 0 M W
1 9 M v a r
1 3 .6 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
7 .4 M v a r
0 .0 M v a r
5 5 M W
2 8 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
1 M v a r
1 7 M W
3 M v a r
1 6 M W
- 1 4 M v a r
1 4 M W
4 M v a r
K YLE6 9
A
MVA
9 6 %
A
MVA
Case now
has nine
separate
contingencies
having
reliability
violations
(overloads in
post-contingency
system).
17
18. A Reliable Solution:
no line outages result in overloads
slack
Metropolis Light and Pow er Electric Design Case 2
SL A C K 3 4 5
SL A C K 1 3 8
R A Y 3 4 5
R A Y 1 3 8
R A Y 6 9
FER N A 6 9
A
MVA
D EM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN 6 9
SH I M K O 6 9
RO GER6 9
U I U C 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N N A H 6 9
A M A N D A 6 9
H O M ER 6 9
L A U F6 9
M O R O 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER 6 9
B U C K Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 0 p u
0 .9 9 p u
1 .0 2 p u
0 .9 9 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
MVA
L Y N N 1 3 8
A
MVA
1 .0 2 p u
A
MVA
A
MVA
Syst em Losses: 11.66 MW
2 6 6 M W
5 9 M v a r
1 2 M W
3 M v a r
2 0 M W
1 2 M v a r
1 2 4 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
1 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
1 4 M W
2 M v a r
3 8 M W
4 M v a r
4 5 M W
0 M v a r
2 5 M W
3 6 M v a r
3 6 M W
1 0 M v a r
1 0 M W
5 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
3 8 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .8 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r
6 0 M W
1 9 M v a r
1 4 .1 M v a r
2 5 M W
1 0 M v a r
2 0 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .9 M v a r
7 .3 M v a r
1 2 .8 M v a r
2 8 .9 M v a r
7 .4 M v a r
0 .0 M v a r
5 5 M W
2 9 M v a r
3 9 M W
1 3 M v a r
1 5 0 M W
1 M v a r
1 7 M W
3 M v a r
1 6 M W
- 1 4 M v a r
1 4 M W
4 M v a r
KYLE6 9
A
MVA
Ky le1 3 8
A
M V A
Previous
case was
augmented
with the
addition of a
138 kV
Transmission
Line
18
19. Generation Changes and The Slack
Bus
• The power flow is a steady-state analysis tool,
so the assumption is total load plus losses is
always equal to total generation
• Generation mismatch is made up at the slack bus
• When doing generation change power flow
studies one always needs to be cognizant of
where the generation is being made up
• Common options include “distributed slack,” where
the mismatch is distributed across multiple
generators by participation factors or by economics.19
20. Generation Change Example 1
slack
SL A C K 3 4 5
SL A C K 1 3 8
R A Y 3 4 5
R A Y 1 3 8
R A Y 6 9
FER N A 6 9
A
MVA
D EM A R 6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN 6 9
SH I M K O 6 9
R O GER6 9
U I U C 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N N A H 6 9
A M A N D A 6 9
H O M ER 6 9
L A U F 6 9
M O R O 1 3 8
L A U F 1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER 6 9
B U C K Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 .0 0 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
-0 .0 0 2 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u 0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
A
MVA
- 0 .0 1 p u
A
MVA
A
MVA
L Y N N 1 3 8
A
MVA
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
1 6 2 M W
3 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 1 5 7 M W
- 4 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
2 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
3 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
4 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 0 .1 M v a r 0 M W
0 M v a r
0 M W
0 M v a r0 M W
0 M v a r
- 0 .1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r 0 M W
0 M v a r
- 0 .1 M v a r
0 .0 M v a r
- 0 .1 M v a r
- 0 .2 M v a r
0 .0 M v a r
0 .0 M v a r
0 M W
5 1 M v a r
0 M W
0 M v a r
0 M W
2 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
Display shows
“Difference
Flows”
between
original
37 bus case,
and case with
a BLT138
generation
outage;
note all the
power change
is picked
up at the slack
Slack bus
20
21. Generation Change Example 2
slack
SL A C K 3 4 5
SL A CK 1 3 8
RA Y 3 4 5
R A Y 1 3 8
RA Y 6 9
FER NA 6 9
A
MVA
D EM A R6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN6 9
SH I M K O 6 9
RO GER 6 9
UI U C6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A N NA H 6 9
A M A N DA 6 9
H O M ER 6 9
L A UF6 9
M O RO 1 3 8
L A UF1 3 8
H A L E6 9
P A T T EN6 9
W EB ER 6 9
B U CK Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
0 .0 0 p u
-0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
- 0 .0 3 p u
- 0 .0 1 p u
- 0 .0 1 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
-0 .0 0 3 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u 0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
A
MVA
L Y N N 1 3 8
A
MVA
0 .0 0 p u
A
MVA
0 .0 0 p u
A
MVA
0 M W
3 7 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 1 5 7 M W
- 4 5 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
4 2 M W
- 1 4 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
9 9 M W
- 2 0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
- 0 .1 M v a r 0 M W
0 M v a r
0 M W
0 M v a r0 M W
0 M v a r
- 0 .1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r 0 M W
0 M v a r
0 .0 M v a r
0 .0 M v a r
- 0 .1 M v a r
- 0 .2 M v a r
- 0 .1 M v a r
0 .0 M v a r
1 9 M W
5 1 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
0 M W
0 M v a r
Display repeats previous case except now the change in
generation is picked up by other generators using a
“participation factor” (change is shared amongst generators) approach.
21
22. Voltage Regulation Example: 37 Buses
Display shows voltage contour of the power system
slack
SL A C K 3 4 5
SL A C K 1 3 8
RA Y 3 4 5
R A Y 1 3 8
RA Y 6 9
FERN A 6 9
A
MVA
D EM A R6 9
B L T 6 9
B L T 1 3 8
B O B 1 3 8
B O B 6 9
W O L EN6 9
SH I M K O 6 9
R O GER 6 9
UI UC 6 9
P ET E6 9
H I SK Y 6 9
T I M 6 9
T I M 1 3 8
T I M 3 4 5
P A I 6 9
GR O SS6 9
H A NN A H 6 9
A M A N D A 6 9
H O M ER 6 9
L A U F6 9
M O RO 1 3 8
L A U F1 3 8
H A L E6 9
P A T T EN 6 9
W EB ER 6 9
B U C K Y 1 3 8
SA V O Y 6 9
SA V O Y 1 3 8
JO 1 3 8 JO 3 4 5
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
A
MVA
1 .0 3 p u
1 .0 1 p u
1 .0 2 p u
1 .0 3 p u
1 .0 1 p u
1 .0 0 p u
1 .0 0 p u
0 .9 9 p u
1 .0 2 p u
1 .0 1 p u
1 .0 0 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 1 p u
1 .0 2 p u
1 .0 0 p u
1 .0 0 p u
1 .0 2 p u
0 .9 9 7 p u
0 .9 9 p u
1 .0 0 p u
1 .0 2 p u
1 .0 0 p u
1 .0 1 p u
1 .0 0 p u
1 .0 0 p u 1 .0 0 p u
1 .0 1 p u
1 .0 2 p u
1 .0 2 p u
1 .0 2 p u
1 .0 3 p u
A
MVA
1 .0 2 p u
A
MVA
A
MVA
L Y N N1 3 8
A
MVA
1 .0 2 p u
A
MVA
1 .0 0 p u
A
MVA
2 1 9 M W
5 2 M v a r
2 1 M W
7 M v a r
4 5 M W
1 2 M v a r
1 5 7 M W
4 5 M v a r
3 7 M W
1 3 M v a r
1 2 M W
5 M v a r
1 5 0 M W
0 M v a r
5 6 M W
1 3 M v a r
1 5 M W
5 M v a r
1 4 M W
2 M v a r
3 8 M W
3 M v a r
4 5 M W
0 M v a r
5 8 M W
3 6 M v a r
3 6 M W
1 0 M v a r
0 M W
0 M v a r
2 2 M W
1 5 M v a r
6 0 M W
1 2 M v a r
2 0 M W
9 M v a r
2 3 M W
7 M v a r
3 3 M W
1 3 M v a r
1 5 .9 M v a r 1 8 M W
5 M v a r
5 8 M W
4 0 M v a r5 1 M W
1 5 M v a r
1 4 .3 M v a r
3 3 M W
1 0 M v a r
1 5 M W
3 M v a r
2 3 M W
6 M v a r 1 4 M W
3 M v a r
4 .8 M v a r
7 .2 M v a r
1 2 .8 M v a r
2 9 .0 M v a r
7 .4 M v a r
2 0 .8 M v a r
9 2 M W
1 0 M v a r
2 0 M W
8 M v a r
1 5 0 M W
0 M v a r
1 7 M W
3 M v a r
0 M W
0 M v a r
1 4 M W
4 M v a r
1 .0 1 0 p u
0.0 M va r
Syst em Losses: 11.51 MW
22
Automatic voltage regulation system controls voltages.
23. Real-sized Power Flow Cases
• Real power flow studies are usually done with
cases with many thousands of buses
• Outside of ERCOT, buses are usually grouped into
various balancing authority areas, with each area
doing its own interchange control.
• Cases also model a variety of different
automatic control devices, such as generator
reactive power limits, load tap changing
transformers, phase shifting transformers,
switched capacitors, HVDC transmission lines,
and (potentially) FACTS devices. 23
24. Sparse Matrices and Large Systems
• Since for realistic power systems the model
sizes are quite large, this means the Ybus and
Jacobian matrices are also large.
• However, most elements in these matrices are
zero, therefore special techniques, sparse
matrix/vector methods, are used to store the
values and solve the power flow:
• Without these techniques large systems would be
essentially unsolvable.
24
25. Eastern Interconnect Example
Pe o r ia
R o ck f o r d
Nor th Chi cago
Abbott Labs Park
U. S. N Tr ai ni ng
O l d El m
Deerfi el d
Nor thbr ook
Lakehur st
W a u k e g a n
Zi on
G ur nee
Anti och
P l e a s a n t
Round Lake
Z i o n ( 1 3 8 k V )
Lake Zur i ch
Lesthon
Aptaki si c
Buf fal o G roove
Wheel i ng
Pr ospect Hei ghts
Pal ati ne
Arl i ngt on
M ount Prospect
Pr ospect
G ol f Mi l l
Des Pl ai nes
El mhur st
I tasca
G a r f i e l d
Tol l w ay
W407 (Fermi )
Wi l son
Bar ri ngt on
D u n d e e
S i l v e r L a k e
C h e r r y V a l l e y
W e m p l e t o n
N e l s o n
H - 4 7 1 ( N W S t e e l )
Pa d d o c k
P o n t i a c M i d p o i n t
Br ai dw ood
S t a t e L i n e
S h e f i e l d
C h i a v e
M u n s t e r
S t . J o h n
El ectr i c Juncti on
Pl a n o
L a S a l l e
Lombar d
L i s l e
Co l l i n s
D r e s d e n
L o c k p o r t
Ea s t F r a n k f o r t
Go o d i n g s G r o v e
Li bert yvi l l e
345 kV
Li bertyvi l l e
138 kV
L a k e G e o r g e
D u n a c r
G r e e n Ac r e s
S c h a h f e r
T o w e r R d
B a b c o c k
Hei ght s
P r a i r i e
R a c i n e
M i c h i g a n C i t y
E l w o o d
D e q u i n e
L o u i s a
E a s t M o l i n e
S u b 9 1
W a l c o t t
D a v e n p o r t
Su b 9 2
R o c k C r k .
S a l e m
G I L M A N
W A T SE K A 1 7 G O D L N D
E L PA S O T
M I N O N K T
O G L ES BY
1 5 5 6 A T P
O T T A W A T
O G L SB Y M
O G L E S; T
H E N N E P I N
E S K T A P
L T V T P N
L T V T P E
H E N N E ; T
L T V S T L
P RI N C T P
P R I N C T N
RI C H L A N D
KE W A N I P
S S T T AP
G AL E S BR G
N O RM A ; BN O R M A ; R
R F A L ; R
M O N M O U T H
GA L ES BR 5
KE W A N ;
H A L L O C K
C A T M O S S
F AR GO
S P N G B AY
E P EO RI A
R SW E AS T
P I O N E ER C
RA D N O R
C AT T A P
C A T S U B 1
SB 1 8 5
E M O L I N E
S B 4 3 5
S B 1 1 2 5
K PE C KT P5
S O . SU B 5
S B 8 5 5
S B 3 1 T 5
S B 2 8 5
S B 1 7 5
SB 4 9 5
SB 5 3 5
S B 4 7 5
SB 4 8 5
SB A 5
S B 7 0 5
S B 7 9 5
S B 8 8 5
SB 7 1 5
B VR C H 6 5 B V R C H 5
A L B A N Y 5
YO R K 5
S AV A N N A 5
G A L EN A 5
8 T H ST . 5
L O RE 5
S O . GV W . 5
SA L EM N 5
A L B A N Y 6
G A RD E ;
H 7 1 ; B T
H 7 1 ; B
H 7 1 ; R
R F A L ; B
N E L S O ; R
N EL SO ; R T
S T E RL ; B
D I X O N ; B T
M E CC O R D 3
C O R D O ;
Q u a d Ci t i e s
L E E C O ; B P
B y r o n
M AR YL ; B
M E N D O ; T
S T I L L ; R T
B4 2 7 ; 1 T
L A N C A; R
PE C A T ; B
F RE EP ;
E L E R O ; BT EL E R O ; R T
L E N A ; R
L EN A ; B
H 4 4 0 ; R T
H 4 4 0 ; R
S T E W A ; B
H 4 4 5 ; 3 B
R o s c o e
P i e r p o n t
S PE C; R
F O RD A ; R
H a r l e m
S a n d Pa r k
N W T 1 3 8
B L K 1 3 8
R O R 1 3 8
J A N 1 3 8
A L B 1 3 8
N O M 1 3 8
D A R 1 3 8
H L M 1 3 8
P O T 1 3 8
M RE 1 3 8
CO R 1 3 8 D I K 1 3 8
B C H 1 3 8
Sa b r o o k e
B l a w k h a w k
A l p i n e
E . R o c k f o r d
C h a r l e s
B e l v i d e r e
B4 6 5
M a r e n g o
W I B 1 3 8
W B T 1 3 8
EL K 1 3 8
N L G 1 3 8
N L K G V T
S G R C K5
B RL GT N 1
B RL GT N 2
S G R CK 4
U N I V R S T Y
U N I V N E U
W H T W T R 5
W H T W T R 4
W H T W T R 3
S U N 1 3 8
V I K 1 3 8
L B T 1 3 8
T I C H I GN
PA R I S W E
A L B E R S - 2
C434
El m wood
Ni l es
Evanston
Devon
Rose Hi l l
Skoki e
Nort hw est
Dr i ver
F o r d C i t y
H a y f o r d
S a w y e r
Nor thri dge
Hi ggi nsDes Pl ai nes
Fr ankl i n Park
Oak Par k
Ri dgel and
D799
G al ew ood
Y450
Congr ess
Rockw el l
Cl ybour n
Q u a r r y
L a s a l l e
St a t e
Crosby
Ki ngsbury
J e f f e r s o n
O h i o
T a y l o r
C l i n t
D e k o v
F i s k
Cr a w f o r d
U n i v e r s i t y
R i v e r
Z - 4 9 4
W a s h i n g t o n P a r k
H a r b o r
Ca l u m e t
H e g e w i s c h
Z - 7 1 5
S o u t h H o l l a n d
E v e r g r e e n
D a m e n
W a l l a c e
B e v e r l y
G 3 8 5 1
Z - 5 2 4
G3 8 5 2
W i l d w o o d
H a r v e y
Gr e e n L a k e
S a n d Ri d g e
C h i c a g o H e i g h t s
B u r n h a m
L a n s i n g
F - 5 7 5
F - 5 0 3
G l e n w o o d
B l o o m
P a r k F o r e s tM a t t e s o n
C o u n t r y Cl u b H i l l s
Al t G E
Natoma
W o o d h i l l
U . P a r k
M o k e n
M cHenry
Cr ystal Lake
Al gonqui n
Huntl ey
P V a l
W o o d s t o c k
Bl u e I s l a n d
G 3 9 4
A l s i p
C r e s t w o o d
K- 3 1 9 # 1
K - 3 1 9 # 2
B r a d l e y
K a n k a k e e
D a v i s Cr e e k
W i l m i n g t o n
W i l t o n Ce n t e r
F r a n k f o r t
N L e n
B r i g g
O akbrook
D o w n e r s G r o o v e
W o o d r i d g e
W 6 0 4
W 6 0 3
Bo l i n g b r o o k
S u g a r Gr o v e
W. De Kal b G l i dden
N Au r o r a
El gi n
Hanover
Spaul di ng
Bart l et t
Hof fman Est at es
S. Schaumber g
Tonne
Landm
Busse
Schaum berg
How ar d
Ber kel ey
Bel l w ood
La G range
Chur ch
Addi son
Nor di
G l endal e
Gl en El l yn
But te
York Cent er
D775
Be d f o r d P a r k
C l e a r n i n g
Sa y r e
B r i d g e v i e w
T i n l e y Pa r k
Ro b e r t s
P a l o s
R o m e o
W i l l ow
Bur r Ri dge
J o 4 5 6
J 3 2 2
South El gi n Wayne
West Chicago
Auror a
Warr envi l l e
W 5 0 7
M o n t g o m e r y
O s w e g o
W o l f C r e e k
F r o n t e n a c
W 600 ( Napervi l l e)
W 6 0 2
W 6 0 1
J 3 0 7
S a n d w i c h
Water man
J 3 2 3
M a s o n
J - 3 7 1
J - 3 7 5
J - 3 3 9
St r e a t o r
M a r s e i l l e s
L a s a l l e
N L A SA L
M e n d o t a
J 3 7 0
S h o r e
G o o s e L a k e
J - 3 0 5
J - 3 9 0
J - 3 2 6
P l a i n f i e l d
J - 3 3 2
A r c h e r
B e l l R o a d
Wi l l Co.
H i l l c r e s t R o c k d a l e
Jol i et
K e n d r a
C r e t e
U p n o r
L A K EV I E W
B A I N 4
Kenosha
S O M E R S
S T R I T A
BI G B EN D
M U K W O N G O
N ED 1 3 8
N E D 1 6 1
L A N 1 3 8
E E N 1 3 8
CA S VI L L 5
T RK R I V5
L I B E R T Y 5
A S B U R Y 5
C N T RG RV 5
J U L I A N 5
M Q O KE T A5
E C A L M S 5
G R M N D 5
D E W I T T 5
SB H Y C5
S U B 7 7 5
S B 7 4 5
S B 9 0 5
S B 7 8 5
D A V N P R T 5
S B 7 6 5
SB 5 8 5
S B 5 2 5
S B 8 9 5
I PS C O 5
I PS CO 3
N EW P O R T 5
H W Y 6 1 5
W E S T 5
9 S U B 5
T R I P P
Z - 1 0 0
O r l a n
Ke n d a
M P W S P L I T
W YO M I N G5
M T V ER N 5
B E R T R A M 5
P CI 5
S B J I C 5
S B UI C 5
- 0 . 4 0 d e g
2 . 3 5 d e g
- 1 3 . 3 d e g
- 1 3 . 4 d e g
M c C o o k
- 1 . 1 d e g
1 . 9 d e g
0 . 6 d e g
9 3 %
B
MVA
1 0 5 %
B
MVA
Example, which models the Eastern Interconnect
contains about 43,000 buses. 25
26. Solution Log for 1200 MW Outage
In this example the
losss of a 1200 MW
generator in Northern
Illinois was simulated.
This caused
a generation imbalance
in the associated
balancing authority
area, which was
corrected by a
redispatch of local
generation.
26
27. Interconnected Operation
Power systems are interconnected across
large distances.
For example most of North America east of
the Rockies is one system, most of North
America west of the Rockies is another.
Most of Texas and Quebec are each
interconnected systems.
27
28. Balancing Authority Areas
A “balancing authority area” (previously called a
“control area”) has traditionally represented the
portion of the interconnected electric grid
operated by a single utility or transmission
entity.
Transmission lines that join two areas are
known as tie-lines.
The net power out of an area is the sum of the
flow on its tie-lines.
The flow out of an area is equal to
total gen - total load - total losses = tie-line flow28
29. Area Control Error (ACE)
The area control error is a combination of:
the deviation of frequency from nominal, and
the difference between the actual flow out of an
area and the scheduled (agreed) flow.
That is, the area control error (ACE) is the
difference between the actual flow out of an
area minus the scheduled flow, plus a
frequency deviation component:
ACE provides a measure of whether an area
is producing more or less than it should to
satisfy schedules and to contribute to
controlling frequency. 29
actual tie-line flow schedACE 10P P fβ= − + ∆
30. Area Control Error (ACE)
The ideal is for ACE to be zero.
Because the load is constantly changing,
each area must constantly change its
generation to drive the ACE towards zero.
For ERCOT, the historical ten control areas
were amalgamated into one in 2001, so the
actual and scheduled interchange are
essentially the same (both small compared
to total demand in ERCOT).
In ERCOT, ACE is predominantly due to
frequency deviations from nominal since
there is very little scheduled flow to or from
other areas. 30
31. Automatic Generation Control
Most systems use automatic generation
control (AGC) to automatically change
generation to keep their ACE close to zero.
Usually the control center (either ISO or
utility) calculates ACE based upon tie-line
flows and frequency; then the AGC module
sends control signals out to the generators
every four seconds or so.
31
32. Power Transactions
Power transactions are contracts between
generators and (representatives of) loads.
Contracts can be for any amount of time at
any price for any amount of power.
Scheduled power transactions between
balancing areas are called “interchange” and
implemented by setting the value of Psched
used in the ACE calculation:
ACE = Pactual tie-lineflow – Psched + 10β Δf
…and then controlling the generation to bring
ACE towards zero.
32
33. “Physical” power Transactions
• For ERCOT, interchange is only relevant over
asynchronous connections between ERCOT
and Eastern Interconnection or Mexico.
• In Eastern and Western Interconnection,
interchange occurs between areas connected
by AC lines.
33
34. Three Bus Case on AGC:
no interchange.
Bus 2 Bus 1
Bus 3Home Area
266 MW
133 MVR
150 MW
250 MW
34 MVR
166 MVR
133 MW
67 MVR
1.00 PU
-40 MW
8 MVR
40 MW
-8 MVR
-77 MW
25 MVR
78 MW
-21 MVR
39 MW
-11 MVR
-39 MW
12 MVR
1.00 PU
1.00 PU
101 MW
5 MVR
100 MW
AGC ON
AVR ON
AGC ON
AVR ON
Net tie-line flow is
close to zero
Generation
is automatically
changed to match
change in load
34
35. 100 MW Transaction between
areas in Eastern or Western
Bus 2 Bus 1
Bus 3Home Area
Scheduled Transactions
225 MW
113 MVR
150 MW
291 MW
8 MVR
138 MVR
113 MW
56 MVR
1.00 PU
8 MW
-2 MVR
-8 MW
2 MVR
-84 MW
27 MVR
85 MW
-23 MVR
93 MW
-25 MVR
-92 MW
30 MVR
1.00 PU
1.00 PU
0 MW
32 MVR
100 MW
AGC ON
AVR ON
AGC ON
AVR ON
100.0 MW
Scheduled
100 MW
Transaction from Left to Right
Net tie-line
flow is now
100 MW
35
36. PTDFs
Power transfer distribution factors (PTDFs)
show the linearized impact of a transfer of
power.
PTDFs calculated using the fast decoupled
power flow B matrix:
1
Once we know we can derive the change in
the transmission line flows to evaluate PTDFs.
Note that we can modify several elements in ,
in proportion to how the specified generators would
par
−
∆ = ∆
∆
∆
θ B P
θ
P
ticipate in the power transfer. 36
37. Nine Bus PTDF Example
10%
60%
55%
64%
57%
11%
74%
24%
32%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
44%
71%
0.00 deg
71.1 MW
92%
Figure shows initial flows for a nine bus power system
37
38. Nine Bus PTDF Example, cont'd
43%
57%
13%
35%
20%
10%
2%
34%
34%
32%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
34%
30%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows for a change in transaction from A to I
38
39. Nine Bus PTDF Example, cont'd
6%
6%
12%
61%
12%
6%
19%
21%
21%
A
G
B
C
D
E
I
F
H
300.0 MW
400.0 MW 300.0 MW
250.0 MW
250.0 MW
200.0 MW
250.0 MW
150.0 MW
150.0 MW
20%
18%
0.00 deg
71.1 MW
Figure now shows percentage PTDF flows for a change in transaction from G to F
39
41. Line Outage Distribution Factors
(LODFs)
• LODFs are used to approximate the change in
the flow on one line caused by the outage of a
second line
– typically they are only used to determine the
change in the MW flow compared to the pre-
contingency flow if a contingency were to occur,
– LODFs are used extensively in real-time
operations,
– LODFs are approximately independent of flows but
do depend on the assumed network topology.
41
42. Line Outage Distribution Factors
(LODFs)
42
,
change in flow on line ,
due to outage of line .
pre-contingency flow on line
,
Estimates change in flow on line
if outage on line were to occur.
l
k
l l k k
P l
k
P k
P LODF P
l
k
∆ =
=
∆ ≈
43. Line Outage Distribution Factors
(LODFs)
43
,
If line initially had 100 MW of flow on it,
and line initially had 50 MW flow on it,
and then there was an outage of line ,
if =0.1 then the increase in flow
on line after a continge
k
l
l k
k P
l P
k
LODF
l
=
=
,
ncy of line would be:
0.1 100 10 MW
from 50 MW to 60 MW.
l l k k
k
P LODF P∆ ≈ = × =
44. Flowgates
• The real-time loading of the power grid can be
assessed via “flowgates.”
• A flowgate “flow” is the real power flow on
one or more transmission elements for either
base case conditions or a single contingency
– Flows in the event of a contingency are
approximated in terms of pre-contingency flows
using LODFs.
• Elements are chosen so that total flow has a
relation to an underlying physical limit. 44
45. Flowgates
• Limits due to voltage or stability limits are
often represented by effective flowgate limits,
which are acting as “proxies” for these other
types of limits.
• Flowgate limits are also often used to
represent thermal constraints on corridors of
multiple lines between zones or areas.
• The inter-zonal constraints that were used in
ERCOT until December 2010 are flowgates
that represent inter-zonal corridors of lines. 45