maintenance scheduling in restructured …978-1-4615-4473-9/1.pdf · maintenance scheduling in ......
TRANSCRIPT
MAINTENANCE SCHEDULING
IN
RESTRUCTURED POWER SYSTEMS
THE KLUWER INTERNATIONAL SERIESIN ENGINEERING AND COMPUTER SCIENCE
Power Electronics and Power SystemsSeries Editor
M. A. Pai
Other books in the series:
POWER SYSTEM OSCILLATIONSGraham Rogers, ISBN: 0-7923-77 I2-5STATE ESTIMATION IN ELECTRIC POWER SYSTEMS: A Generalized Approach
A. Monticelli, ISBN: 0-7923-85 I9-5COMPUTATIONAL AUCTION MECHANISMS FOR RESTRUCTURED POWERINDUSTRY OPERATIONS
Gerald B. Sheble, ISBN: 0-7923-8475-XANALYSIS OF SUBSYNCHRONOUS RESONANCE IN POWER SYSTEMS
K.R. Padiyar, ISBN: 0-7923-8319-2POWER SYSTEMS RESTRUCTURING: Engineering and Economics
Marija Ilic, Francisco Galiana, and Lester Fink, ISBN: 0-7923-8 I63-7CRYOGENIC OPERATION OF SILICON POWER DEVICES
Ranbir Singh and B. Jayant Baliga, ISBN: 0-7923-8 I57-2VOLTAGE STABILITY OF ELECTRIC POWER SYSTEMS, Thierry
Van Cutsem and Costas Voumas, ISBN: 0-7923-8 I39-4AUTOMATIC LEARNING TECHNIQUES IN POWER SYSTEMS, Louis A.
Wehenkel, ISBN: 0-7923-8068-1ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY,
M. A. Pai, ISBN: 0-7923-9035-0ELECTROMAGNETIC MODELLING OF POWER ELECTRONIC
CONVERTERS, 1. A. Ferreira, ISBN: 0-7923-9034-2MODERN POWER SYSTEMS CONTROL AND OPERATION, A. S. Debs,
ISBN: 0-89838-265-3RELIABILITY ASSESSMENT OF LARGE ELECTRIC POWER SYSTEMS,
R. Billington, R. N. Allan, ISBN: 0-89838-266- ISPOT PRICING OF ELECTRICITY, F. C. Schweppe, M. C. Caramanis, R. D.
Tabors, R. E. Bohn, ISBN: 0-89838-260-2INDUSTRIAL ENERGY MANAGEMENT: Principles and Applications,
Giovanni Petrecca, ISBN: 0-7923-9305-8THE FIELD ORIENTATION PRINCIPLE IN CONTROL OF INDUCTION
MOTORS, Andrzej M. Trzynadlowski, ISBN: 0-7923-9420-8FINITE ELEMENT ANALYSIS OF ELECTRICAL MACHINES, S. 1. Salon,
ISBN: 0-7923-9594-8
MAINTENANCE SCHEDULING
IN
RESTRUCTURED POWER SYSTEMS
M. SHAHIDEHPOUR, PhD ILLINOIS INSTITUTE OF TECHNOLOGY
CHICAGO, ILLINOIS
M. MARWALI, PhD ABB ENERGY INFORMATION SYSTEMS
SANTA CLARA, CALIFORNIA
~.
" SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication
Shahidehpour, M., 1955-Maintenance scheduling in restructured power systcms / M. Shahidehpour, M. Marwali.
p. cm. -- (The Kluwer international series in engineering and computer science ; SECS 562. Power electronics and power systems)
IncIudes bibliographical references and index. ISBN 978-1-4613-7015-4 ISBN 978-1-4615-4473-9 (eBook) DOI 10.1007/978-1-4615-4473-9 1. Electric power systerns--Maintenance and repair. 2. Production scheduling. 1.
Marwali, M. II. Title. III. Kluwer international series in engineering and computer science ; SECS 562. IV. Kluwer international series in engineering and computer science. Power electronics & power systems.
TKlO05 .S445 2000 621.31 '2--dc21
Copyright ® 2000 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover Ist edition 2000
00-031338
AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC.
Printed an acid-free paper.
To the memory of my father who taught me the value of education.
M. Shahidehpour
TABLE OF CONTENTS
LIST OF FIGURES X111
LIST OF TABLES
LIST OF SYMBOLS
xv
XIX
PREFACE xxvii
ACKNOWLEDGMENTS xxix
CHAPTER
I. INTRODUCTION .
1.1 VERTICALLY INTEGRATED UTILITIES 2
1.2 RESTRUCTURED POWER INDUSTRY . . . . . . . . . 41.2.1 ISO.......................... 61.2.2 GENCOs . . . . . . . . . . . . . . . . . . . . . . . 81.2.3 TRANSCOs 91.2.4 DISCOs........................ 91.2.5 OASIS......................... 101.2.6 RETAILCOs . . . . . . . . . . . . . . . . . . . .. 101.2.7 Aggregator...................... 111.2.8 Marketer 111.2.9 Broker......................... II1.2.10 Customer . . . . . . . . . . . . . . . . . . . . . .. II
1.3 OPERATION AND MAINTENANCE INA RESTRUCTURED POWER SYSTEM
1.4 MAINTENANCE SCHEDULING INA RESTRUCTURED POWER SYSTEM
1.4.1 ISO's Function in Maintenance Scheduling .....
1.5 FORMULATION OF THE MAINTENANCESCHEDULING PROBLEM . . . . . . . . . . . . . . . .
lSI Optimization Objectives . . . . . . . . . . . . . . .1.5.2 Problem Constraints .1.5.3 Solution Methods .
II. MATHEMATICAL REVIEW .
2.1 DUALITY IN LINEAR PROGRAMMING
12
1213
14141515
17
17
2.2 INTEGER PROGRAMMING . . . . . . . . . . . . . .. 19
2.3 BENDERS DECOMPOSITION 212.3.1 Fonnulation of Benders Decomposition , 222.3.2 Steps of the Algorithm , 242.3.3 Example for Benders Decomposition 25
2.4 LAGRANGIAN RELAXATION 272.4.1 Introduction 272.4.2 Dual Optimization Technique 28
2.5 DANTZIG-WOLF DECOMPOSITION. . . . . . . 332.5.1 Fonnulation of Dantzig-Wolfe Decomposition 332.5.2 Steps for the Decomposition Algorithm . . . . 352.5.3 Example of the Dantzig-Wolfe Decomposition 36
2.6 APPLICATION OF THE DANTZIG-WOLFEDECOMPOSITION TO POWER LOSS MINIMIZATION 40
2.6.1 Introduction 402.6.2 Loss Minimization Problem 412.6.3 Application of Dantzig-Wolfe . . . . . . . . . . .. 47
m. LONG-TERM GENERATION MAINTENANCE SCHEDULING 53
3.1 INTRODUCTION...................... 53
3.2 MAINTENANCE PROBLEM FORMULATION . . . .. 543.2.1 Coupling Constraints 553.2.2 Decoupling Constraints 55
3.3 SOLUTION METHODOLOGY. . . . . . . . . . . . . .. 553.3.1 ISO Sub-Problem 593.3.2 Revised Maintenance Master Problem . . 60
3.4 EXAMPLE... 61
3.5 CASE STUDIES 64
3.6 PROBABILISTIC FORMULATION 67
3.7 EXAMPLE ... 70
3.8 CASE STUDIES 74
3.9 FUEL AND EMISSION CONSTRAINTS 753.9.1 Maintenance and ISO Constraints . . . . . . . . .. 763.9.2 System Emission Limit 763.9.3 Fuel Constraints 77
3.10 SOLUTION METHODOLOGY ., 77
3.11 DETAILED SOLUTION PROCESS3.11.1 Initial Master Problem (MP2) ..3.11.2 Fuel Dispatch Sub-Problem (SP2)
viii
797979
3.11.3 ISO (Network) Sub-Problem (SPI)3.11.4 Revised Master Problem (MP 1) . .
3.12 CASE STUDIES .
IV. SHORT-TERM GENERATION SCHEDULING .
4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . .
4.2 SECURITY-CONSTRAINED UNIT COMMITMENT . .4.2.1 SCUC Problem Formulation .4.2.2 Analysis of Constraints . . . . . . . . . . . . . . . .
4.3 APPLICATION OF DECOMPOSITION . . . . . . . . .
4.4 SCUC SOLUTION .4.4.1 Master Problem .4.4.2 Subproblems Formulation .4.4.3 Benders Cuts . . . . . . . . . . . . .4.4.4 Complications .
4.5 CASE STUDIES .4.5.1 Base Case .4.5.2 Transmission Constraints .4.5.3 Voltage Constraints .
4.6 PRICE-BASED UNIT COMMITMENT .
4.7 PBUC PROBLEM DESCRIPTION . . . . .4.7.1 Interaction between GENCOS and ISO
8082
85
89
89
909195
96
9797
100102102
103103104105
107
108108
4.8 GENCO'S BIDS . . . . . . . . . . . . . . . . . . . . .. 1084.8.1 Energy Bids to Supply Loads 1084.8.2 Spinning and Non-Spinning Reserve Bids 110
4.9 GENCO'S OBJECTIVE . . . . . . . . . . . . . . . . .. III
4.10 PBUC SOLUTION METHODOLOGY . . . . . . . . .. 114
V. COORDINATION BETWEEN LONG-TERM AND SHORT-TERMGENERATION SCHEDULING. . . . . . . . . . . . . . . . .. 119
5.1 INTRODUCTION . . . . . . . . . . . . . . . . . 119
5.2 LONG-TERM GENERATION MAINTENANCEFORMULATION 119
5.3 SHORT-TERM FORMULATION. . . . . . . . . . . . .. 121
5.4 DYNAMIC SCHEDULING OF LTS . . . . . . . . . . .. 123
5.5 ISO CONSTRAINTS. . . . . . . . . . . . . . . . . . .. 125
ix
5.6 CASE STUDIES 1265.6.1 Monte-Carlo Simulation . . . . . . . . . . . . . .. 1265.6.2 Results . . . . . . . . . . . . . . . . . . . . . . .. 127
VI. LONG-TERM TRANSMISSION MAINTENANCE SCHEDULING 133
6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . .. 133
6.2 PROBLEM FORMULATION . . . . . . . . . . . . . ., 133
6.3 SOLUTION METHODOLOGY 135
6.4 EXAMPLE . . . . . . . . 138
6.5 CASE STUDIES 139
6.6 PROBABILISTIC FORMULATION. . . . . . . . . . .. 141
6.7 EXAMPLE 143
6.8 CASE STUDIES 144
VII. COORDINATION BETWEEN LONG-TERM AND SHORT-TERMTRANSMISSION MAINTENANCE SCHEDULING. . . . . .. 147
7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . .. 147
7.2 PROBLEM FORMULATION. . . . . . . . . . . . . .. 1497.2.1 Long-term Maintenance Scheduling . . . . . . . .. 1497.2.2 Short-term Maintenance Scheduling. . . . . . . .. 150
7.3 SOLUTION METHODOLOGY . . . . . . . . . . . . .. 1547.3.1 Long-term Maintenance Scheduling (TRANSCO) . 1557.3.2 Short-term Maintenance Scheduling (ISO). . . . .. 155
7.4 CASE STUDIES 1587.4.1 Example 1 . . . . . . . . . . . . . . . . . . . . . .. 1587.4.2 Example 2. . . . . . . . . . . . . . . . . . . . . .. 163
VIII. COORDINATION BETWEEN GENERATION AND TRANSMISSIONMAINTENANCE SCHEDULING 167
8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . .. 167
8.2 PROBLEM FORMULATION . . . . . . . . . . . . . .. 167
8.3 SOLUTION METHODOLOGY. . . . . . . . . . . . .. 1698.3.1 Path 1: Schedule Driven by the GENCO . . . . . .. 1698.3.2 Path II: Schedules Driven by the TRANSCO. . . .. 1718.3.3 Final Maintenance Schedules 1728.3.4 Linearized Power Flow Model . . . . . . . . . . .. 175
8.4 EXAMPLE
x
177
8.5 CASE STUDIES 179
199199201203
204205205205
206
9.9 PV GENERATION PLANT MODEL .9.9.1 Radiation on Titled Surface .9.9.2 PV Cell Model .9.9.3 Battery Model .
9.10 CASE STUDIES
IX. APPLICATION OF SHORT-TERM SCHEDULING TOPHOTOVOLTAlC-UTILITY GRID . . . . . . . . . . . . . . .. 183
9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . .. 183
9.2 PROBABILISTIC PRODUCTION COST FORPHOTOVOLTAIC-UTILITY SYSTEMS. . . . . . . .. 184
9.3 RADIATION AND PV POWER 184
9.4 PRODUCTION COST ANALYSIS 187
9.5 NUMERICAL EXAMPLES AND TEST RESULTS. . .. 190
9.6 SHORT-TERM GENERATION SCHEDULING INPHOTOVOLTAlC-UTILITY GRID . . . . . . . . . . .. 196
9.7 SCHEDULING PROBLEM FORMULATION . . . . .. 196
9.8 PROPOSED METHOD FOR SCHEDULING .9.8.1 Initial Feasible Solution .9.8.2 Thennal Unit Commitment .9.8.3 Dynamic Economic Dispatch .
APPENDIX
A. IEEE-RTS SYSTEM DATA 211
B. PRODUCTION COST MODEL . . . . . . .. . . . . . . . " 217
C. PHOTOVOLTAlC SYSTEM MODEL 223
D. MONTE-CARLO SAMPLING ALGORITHM WITHGENERALIZED REGRESSION 229
E. IEEE 118-BUS TEST SYSTEM DATA 231
BIBLIOGRAPHY 241
INDEX 259
XI
LIST OF FIGURES
Figure
1.1 Power System Structure under Vertically Integrated Utilities 3
1.2 Power System Structure under the PURPA of 1978 . . . . . 4
1.3 Power System Structure under the EPAct and theFERC Mega-NOPR. . . . . . . . . . . . . . 6
1.4 Relationships between Participants . . . . . . . . 7
2.1 Benders Decomposition Flowchart 25
2.2 Transmission Line k Connecting Bus i and Bus} 41
2.3 Model of Tap-Changing Transformer 42
2.4 Flowchart for Reactive OPF Solution Algorithm 46
2.5 Iterative Procedure of Dantzig-Wolfe Method . . . . . 46
2.6 Schematic Diagram of the Decomposed 30-Bus System 48
3.1 Interactions between the ISO and GENCO. . . . . . . . . . . . .. 53
3.2 Maintenance Scheduling Decomposition . . . . . . 56
3.3 Three-Bus System Example 62
3.4 Long-term Decomposition with Fuel and Emission . . . . . . . .. 78
3.5 Equivalent Load Curve . . . . . . . . . . . . . . . . . . 82
3.6 Double Decomposition Algorithm . . . . . . . . . . 84
3.7 Effect of Maintenance Window on System Reliability. . 87
3.8 Scheduling Method Effects on System Reliability . . . . 88
4.1 SCUC Problem with Transmission and Voltage Constraints 94
4.2 Duality Gaps vs. Number of Iterations in Unit Commitment 100
4.3 Flowchart of SCUC . . . . . . . . . . . . . . . . . . . 103
4.4 Interaction between GENCOs and ISO . . . . . . . . . . . . . . .. 109
4.5 Bids for Energy to Supply Load . . . . . . . . . . . . . . . . . .. 109
4.6 Spinning Reserve Bid . . . . . . . . . . . . . . . . . 110
4.7 Non-Spinning Reserve Bid . . . . . . . . . . . . . . 111
5.1 Dynamic Scheduling of the Generation Maintenance 120
5.2 Proposed Dynamic Scheduling 124
5.3 Dynamic Scheduling Algorithm 125
5.4 Generation Reserve without Dynamic Scheduling. . . . . . . . . .. 128
5.5 Generation Reserve with Dynamic Scheduling 129
5.6 Effect of Reserve Limit on Maintenance Cost. " 131
Figure
7.17.2
7.38.18.2
8.3a
8.3b
8.3c
8.4
9.19.2
9.3
9.4
9.59.69.79.8
9.9
9.10
9.119.12
Transmission Maintenance Scheduling .
Decomposition Method for Line Maintenance Scheduling
Hourly Peak Transaction in Percent of Weekly Peak
Interactions between Entities
Two Scenarios Problem
Path 1 .
Path 2 .
Proposed Coordination among GENCO, TRANSCO and ISO.
Three-Bus System Example . . . . . . . . . .
Power ys. Voltage Characteristic for a PV Generator
PV Efficiency ys. Radiation .
Sharing Process of an Impulse
Pdf of Photoyoltaics . . . . . . . . .
Load Curve .
Nusa Penida's System Configuration .
Tilted Angle Effect on EENS of PV .
Battery Capacity Effect on EENS of PV . . . . . . . . . . .
PV-Utility Grid with Battery Storage ....
Generation Scheduling Flowchart . . . . .
Thermal Unit Generation . . . . . . . . ..
Penetration to the Utility from PV Plant ..
XlY
148154159168169173174175177
186187189190191193
195195196199207
208
LIST OF TABLES
Table Page
2.1 Primal-Dual Correspondence . . . . . . . . . . . . . . . . .. 18
2.2 Results of Different Methods Applied to the IEEE 30-Bus System. 50
2.3 Line Data for the IEEE 30-Bus System . . . . .. . . . . . . . . . 51
2.4 Bus Data for the IEEE 30-Bus System . 52
3.1 Generator Data for 3-bus System 62
3.2 Line Data for 3-bus System 62
3.3 Generating Units Considered For Maintenance . . . . . . . . . .. 65
3.4 Generating Unit Operating Cost Data. . . . . . . . . . . . . . . .. 65
3.5 Unit Maintenance Cost Penalty Factors . . . . . . . . . . . . . . .. 65
3.6 Overflow in Transmission Lines (l2-week horizon,E=I% of load) .. 66
3.7 Total Cost for Generating Unit (12-week horizon, E=1% of load) 66
3.8 Effect of Network Constraints on Generating Units Maintenance(12-week horizon, c:= I% of load) . . . . . . . . . . . . . . . . . 66
3.9 Generating Unit Maintenance in Case I(52-week horizon, c:=I% of load) . . . . . . . . . . . . . . . . . 67
3.10 Total Cost for Generating Unit (52-week horizon,E=I% ofload) . 67
3.11 Generation Unit Data 71
3.12 Feasibility Check State Spaces 71
3.13 Feasibility Check State Spaces 72
3.14 Feasibility Check State Spaces 72
3.15 Feasibility Check State Spaces 72
3.16 Feasible Sub-problem State Spaces 73
3.17 Feasible Sub-problem State Spaces 73
3.18 Feasible Sub-problem State Spaces 73
3.19 Total Cost for Generation Maintenance(l2-week horizon, c:=I% ofload) 74
3.20 Effect of Forced Outages on Generation Maintenance Scheduling(l2-week horizon, c:=I% of load) 75
3.21 Generating Unit Maintenance in Case 2(52-week horizon, c:=I% of load) 75
3.22 Total Cost for Generation Maintenance . . . . . . . . . . . . 75
3.23 Fuel Price 85
Table
3.24 Maintenance and Production Cost of Generating Units(l2-week horizon) 85
3.25 Generating Unit Schedule (12-week horizon) 86
3.26 Generating Unit Maintenance in Case 4 (52-week horizon) 86
3.27 Total Cost of Generating Unit 87
4.1 Unit Commitment without Network Constraints 104
4.2 Cost and Transmission Violations . . . . . . . 105
4.3 Cost and Cuts for Transmission Contingencies 105
4.4 Voltage Violations and Benders Cuts ..... 106
4.5 Costs and Benders Cuts for Contingency Cases 106
4.6 SCUC in Case V . . . . . . . . . . . . . . . . 107
5.1 Generating Unit Maintenance Schedule for Case 1 127
5.2 Unit Rescheduling during Simulations 128
5.3 Generating Unit Maintenance Schedule for Case 2 129
5.4 Overflow in Transmission Lines (I2-week horizon, E= 1% of load) 130
5.5 Total Cost for Generating Unit (12-week horizon, E= I% of load) 130
5.6 Generating Unit Maintenance Schedule for Case 3 130
6.1 Line Maintenance Data 138
6.2 Transmission Line Data 139
6.3 Overflow on Transmission Lines (I2-week horizon) 140
6.4 Effect of Transmission Capacity on Transmission MaintenanceSchedule (l2-week horizon) . . . . . . . . . . . . . . . . . . 140
6.5 Total Cost for Maintenance (I2-week horizon) . . . . . 140
6.6 Line Forced Outage Rate 143
6.7 Feasibility Check State Spaces 144
6.8 Total Cost for Maintenance (12-week horizon, E= I % of load) 145
6.9 Overflow on Transmission Lines (12-week horizon, E=l% of load) 145
6.10 Effect of Transmission Capacity on Transmission MaintenanceSchedule (12-week horizon, E= I% of load) 145
7.1 Transmission Maintenance Windows (l2-week horizon) 158
7.2 Transaction Weekly Peak 159
7.3 Recallable Contract in week 18-29 160
7.4 Ancillary Services for Reactive Power in week 18-29 160
7.5 Line Maintenance Cost in weeks 18-29 . . . . . 161
7.6 Overflow on Transmission Lines (Case I) . . . . . . . . . . . . .. 161
xvi
Table
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9.1
9.2
9.3
9.4
9.5
9.6
Violated Bus Voltages (Case 1) .
Transmission Maintenance Windows (Case 2)
Violated Bus Voltages (Case 2) ...
Transmission Maintenance Windows
Line Maintenance Cost .
Line Maintenance Cost .
Line Maintenance Schedule without Network Constraints (Case 1).
Overflow on Transmission Lines (Case 1) . . . . . . . . . . . . . .
Bus Voltages without Constraints in Local Area (Case I) .
Line Maintenance Schedule with Transmission Constraints (Case 2) .
Bus Voltages without Voltage Constraints in Local Area (Case 2) ..
Line Maintenance Schedule with Transmission and VoltageConstraints (Case 3) .
Bus Voltages with Voltage Constraints in Local Area (Case 3) .
Paths for 2 GENCOs and a TRANSCO
Generator Data . . . . . . . . . . . . . . . . . .
Line Data .
Generating Unit Maintenance Schedule Case I(l2-week horizon, f;= 1% of load) .
Transmission Maintenance Schedule Case 2(l2-week horizon, f;=I% of load) .
Transmission Maintenance Schedule Driven by GENCO(l2-week horizon, f;= I % of load) .
Generating Unit Maintenance Schedule Driven by TRANSCO(l2-week horizon, f;= I% of load) .
Final Generating Unit Maintenance Schedule(l2-week horizon, f;= 1% ofload) . . . . . . .
Final Transmission Maintenance Schedule Case 3(l2-week horizon, f;= 1% of load) .
Radiation and PV Output . . . . . .
The Probabilistic Modeling for PV .....
Monthly Climate Data in Nusa Penida Island
PV Expected Energy Output .
Diesel Generator Expected Energy Output
Average Hourly Radiation .
XVll
161
161
162
162
162
163
164
164
164
165
165
166
166
172
177
178
180
181
181
182
182
182
190
192
193
194
194
206
Table
9.7 Battery Constraints. . . . . . . . . . . . . . . . . . . . . . . . . .. 206
9.8 Production Cost 207
9.9 Thermal Unit Commitment Schedule without PY 209
9.10 Thermal Unit Commitment Schedule with PY 210
xviii
LIST OF SYMBOLS
Symbol
A
B
C(r)
CPi
d;
d'k
d
DR;
ei
ek
Definition
Fit parameter for PV (between I and 5)
Sensitivity coefficient of unit i to flow of line k
Susceptance matrix
Lost of revenue per-MW at bus i in week t due to real power
interruption; in hour is Cit
Lost of revenue per-MVAR at bus i in hour r due to reactive
power interruption or purchasing reactive power
Fuel cost per MBtu of fuel m in week t
State of charge of battery at hour 't
Coefficient of saturation current density [V-I]
Coefficient [Am-zK-3]
Coefficient [Am-zK-s1z]
State of charge of battery at the end of study horizon
Generation maintenance cost for unit i in week t
Transmission maintenance cost per-line in right-away k in week t ;
in hour is CktMaximum state of charge of battery
Capacity of thermal unit i
Battery state of charge at beginning of study horizon
Minimum state of charge of battery
Duration of maintenance for generator unit i
Load demand at bus i at hour 't
Duration of maintenance for line k
A vector of the weekly peak load at every bus in week t
Ramp down rate of unit i (MW/hr)
Earliest period to begin maintenance of generator unit i
Earliest period to begin maintenance of line k
E
£J)(1)
E~,Jj)
EMA
EMA,
EMS
f
f
f
FL
FU
g
g
Expected value
Energy in segment J after unit i committed
Sensitivity coefficient matrix of unit i to flow of line k due to
outage of line j
Unserved energy after the first i units committed
Expected generation for unit i (i= I is PV)
Emission cap for area emission in the study period
Emission cap for area emission in week t
Emission cap for system emission in the study period
Emission cap for system emission in week t
Power flow at peak load in vector form
Upper limit of line flow in vector form
Lower limit of line flow in vector form
Flow of line k at hour t
Upper limit flow of line k
Lower limit flow of line k
Fuel cost of unit i
Power density function for the PV
Flow limit vector for line outage j
Steady state flow limit in vector form
Fuel cost of unit i when generating power is g it
Penalty vector for contingency flow constraints in case of
line outage j
Penalty vector for steady state flow constraints
Lower limit offuel constraint for a group of units
Upper limit of fuel constraint for a group
Vector of power generation by each unit at peak load in week t
Maximum generation capacity in vector form
xx
Hi
J
J;
k
Ki
Upper real power limit of unit i; in BUC: maximum limit for
power to supply load and bilateral contracts
Lower real power limit of unit i; in PBUe: minimum limit for
power to supply load and bilateral contracts
Real power output of unit i at hour T, PBUC: power to supply
bilateral contracts and to be sold to supply load from unit i at hourr
Bilateral contracts for energy to supply load from generator i at
hour r
Reactive limit vector for line outage j
Steady state reactive limit vector
Global radiation on a horizontal plane (W/m2)
Global radiation outside the atmosphere (W/m2)
Instantaneous radiation on a tilted surface (W/m2)
Penalty vector for voltage constraints in line outage j
Penalty vector for steady state voltage constraints
Average heat rate (MBtu/MWh) of unit i burning fuel m
Duration hour of maintenance for lines in right-away k
Emission function of unit i
Emission function of unit i
Cell current (A)
Commitment state (I or 0) of unit i at hour r
Light generated current (A)
Diode saturation current (A)
Segmentation number
Segmentation number can be served by i units
Boltzmann Constant (1.3854xlO-23 JK 1)
Temperature difference between PV cell and ambient at windspeed zero (OK)
The temperature gradient ofPV cell (OK sec/m)
Maximum fuel allocation for unit i
XXI
MSRi
NB
NE
NR ir
Latest period to begin maintenance of generator unit i
Latest period to begin maintenance of line k
Energy to supply load bid slope of generator i at hour r
Number of lines that need maintenance in right-of- way k
Maximum sustain ramp rate of unit i. (MW/min)
Number of contingencies
Number of hours in a week
Number of candidate lines to be operated in right-of-way k in week
t; in the vector form is N; in hour is Nkr
Maximum number of lines allowed in right-of-way k
Number of PV cells in parallel
Number of power states for PV
Number of PV cells in series
Number of buses in the power system
Number of segmentation in EEF
Non-Spinning reserve from generator i at hour r
Total GENCO self-supplied non-spinning reserve at hour r
Maximum limit for non-spinning reserve at hour r
Availability of unit i
PV daily average power in day i with sd=k
Maximum power at radiation G1
Charge/discharge power to the battery at hour r
Total real power demand of the system at hour r
Load demand at bus j at hour r
Fix charged for battery equalization
Instantaneous PV power output at hour r
PV spillage power at hour r
Total intermittent power injected to the network at hour r
Maximum charge/discharge power of battery
xxii
Pu
PC
P~t
q
Qbi
flJi
R(r)
s
s
sd
s
Maximum intennittent power injected to the network
STS production cost
Power injection equivalent of phase shifter at hour T
Charge of an electron (1.6021xlO- 19As)
Forced outage rate of unit i, SCUe: quick start capability of unit i
Maximum reactive power of unit i
Minimum reactive power of unit i
Total reactive power demand at hour T
Upper limit reactive power injection at bus i
Lower limit of reactive power injection at bus i
Upper limit equivalent reactive power injection of tap changer
Lower limit equivalent reactive power injection of tap changer
Real power interruption at bus i in week t; in vector fonn is r ;
in hour is ril;
Contribution of unit i to spinning reserve at hour T
Maximum limit for spinning reserve at hour T
Spinning reserve from generator i at hour T
System operating reserve requirement at hour 't PBUC: Total
GENCO's self-supplied spinning reserve at hour T
Series resistance (0)
System spinning reserve requirement at hour T
Shunt resistance (0)
State index
(maximum state) - (state index)
Reactive power interruption or ancillary services at bus i in hour r,in vector fonn is s
Number of storage days
Node-branch incidence matrix
Start up cost of unit i at hour T
xxiii
T
T
I
Tamb
r;on/off (1:)
Tp
offYk { I-I)
zon/oJ!i{t)
I1P
Time
Contribution of unit i to operating reserve at hour r
PY cell temperature eK) or tap changer position
Upper limit of tap changer position
Lower limit of tap changer position
Ambient temperature (OK)
Minimum up/down time of unit i
Power period
Ramp up rate of unit i. (MW/hr)
System voltage in vector form
Battery voltage at hour 1:
PY cell voltage (volt)
Maximum fuel In allocation in week I
Maximum fuel In allocation in month)
Maximum fuel In allocation in year v
Unit maintenance status, 0 ifunit is off-line for maintenance;in vector form is x
Number of weeks that unit i has been on maintenance at week [-I
Line maintenance status in week I, 0 if Mk line in right-of-way k
is off-line for maintenance; in hour is Y let
Number of weeks that lines k have been on maintenance at week I-
I h. off
at our IS Yk ( t-I)
Time in which unit i has been on/off at hour r
Integrates labor starting up cost and equipment maintenance cost
of unit i
Starting up cost of unit i from cold conditions
Cost per MWh of energy purchased from outside sources at week [
Power to be purchased to supply the GENCO bilateral contracts atgeneration bus i and at hour r
Phase shifter angle at hour 1:
Power increment
xxiv
e
pg(i, r)
pori, r)
Ps(i, r)
Pnli, r)
pji, r)
Acceptable level of expected energy not served
MBtu of fuel from the m-th contract (fuel m) allocated tounit i during week t
Susceptance of branch k; in vector form is y
Instantaneous efficiency of PV
Efficiency of battery at hour,
Probabilistic vector that defines the state of the system
Win speed (m/sec)
Voltage angle associated to node i; in vector form is eTime constant that characterizes unit i cooling speed
Bid for energy to supply load by generator i at hour ,
Marginal price of generator i at hour ,
Bid for spinning reserve by generator i at hour,
Bid for non-spinning reserve by generator i at hour,
Bid for power to be purchased at generation bus i and at hour ,
xxv
PREFACE
The overall goal of this book is to introduce algorithms for improving theeconomic posture of a utility company in a restructured power system by promotingcost-effective maintenance schedules.
Today, cutting operations and maintenance (O&M) costs and preserving servicereliability) are among the top priorities for managers of utility companies. Preventivemaintenance is perhaps the single largest controllable cost of a utility2 operation. It isperceived that a careful planning and a good coordination among self-interestedentities in a restructured power system are essential to achieving an optimal trade-offbetween the cost of maintenance and the service reliability. Traditional maintenanceprograms in verticall/ integrated utilities relied heavily on time-directedmaintenance and manufacturer recommendations. This book offers a logicalalternative to traditional electric utility maintenance practices and a basis formaintenance decisions.
The book is organized as follows. Chapter I reviews various issues related to thepower system operation and presents the role of restructuring in maintenancescheduling. In Chapter II, fundamental topics related to linear and nonlinear systemsare reviewed. The duality in linear programming is discussed and integerprogramming is reviewed. Benders decomposition, Lagrangian relaxation, andDantzig-Wolfe decomposition are presented. Several examples are given todemonstrate the applications ofdifferent methods. The formulation of reactive poweroptimization is discussed which will be used again in Chapter VII.
In Chapter III, the formulation of long-term generating unit maintenancescheduling is given which includes a GENCO's maintenance cost as the objectivefunction, and numerous network and maintenance constraints such as flowconstraints, availability of crews and other resources, as well as maintenancewindows. Here, since we deal with independent entities (such as GENCOs and theISO), Benders decomposition is used to solve the generating unit maintenanceformulation. The proposed technique decomposes the original problem into a masterproblem, which is a relaxation of the original problem, and several independent subproblems. The results for a simple system are analyzed and the application of theproposed method to IEEE-RTS is discussed. The complex fuel dispatch andemission constraints are included later and the network is modeled as a probabilisticproblem to include the effect of generation and transmission outages. Further resultsillustrate the proposed comprehensive generation maintenance scheduling.
Chapter IV describes the details of short-term generation scheduling. First, asecurity constrained unit commitment (SCUC) package with real and reactive power
) Reliability of a system is interpreted as satisfying two major functions: adequacy andsecurity, where an adequate amount of capacity resources should be available to meet thepeak demand (adequacy) and the system should be able to withstand changes orcontingencies on a daily and hourly basis (security).
2 Utility industry in the United States is a $200 billion per year business.3 Vertical integration is an arrangement where the same company owns all the different
aspects of making, selling and delivering a product or a service.
constraints IS presented. Two different systems are used to demonstrate theefficiency of the SCUC package. Next, the fonnulation of price-based unitcommitment (PBUC) is proposed for trading energy and ancillary services in therestructured market. The objective in PBUC is to maximize the GENCO's revenues.The short-tenn generation scheduling fonnulation is used in Chapter V.
Chapter V discusses the coordination between short-tenn and long-tenngeneration scheduling problems in a GENCO. This chapter links Chapters III andIV. rhe results show that some of the solutions presented in Chapter III willencounter short-tenn scheduling violations if we do not consider the short-tennconstraints in the long-tenn maintenance scheduling of generating units.
Chapter VI discusses the problem of long-term transmission maintenancescheduling in a restructured system. The chapter presents the fonnulation of longtenn transmission maintenance scheduling with probabilistic constraints. Thecoordination of TRANSCOs and the ISO for satisfying network flow and reliabilityconstraints is discussed. A large set of constraints is included in the fonnulation anda step by step calculation is discussed for a simple power system. The application ofthe proposed method to IEEE-RTS is also presented.
Chapter VII presents the coordination between short-tenn and long-tenntransmission maintenance scheduling problems. The fonnulation includes costrevenue tradeoffs and constraints that impact transmission line maintenancescheduling. The long-tenn maintenance of transmission lines is scheduled and theresulting maintenance windows and other variables are passed on to the short-tennscheduling problem, which will detennine the appropriate times within the givenwindows to perfonn maintenance. The method provides a dynamic schedule forcalculating short-tenn maintenance periods. The IEEE 118-bus system network with186 lines is tested and results are presented
Chapter VIII discusses the coordination of GENCOs' and TRANSCOs'maintenance schedules through the ISO. The solution will satisfy the objectives ofthese self-interested entities, as well as reliability and network flow constraints. Theresults point out that without the ISO's coordination, some of the objectives and/orconstraints will not be satisfied in maintenance scheduling.
Chapter IX discusses the impact of unconventional sources of energy (i.e.,photovoltaic with battery storage) on short-tenn generation scheduling. The chapterpresents a method to simulate the production cost of GENCOs using a probabilisticapproach, and a pilot project in the Eastern Islands of Indonesia is evaluated. Severalconstraints including the battery capacity, minimum up/down time and ramp ratesfor thennal units as well as photovoltaic (PV) capacity are considered in theproposed model. A new approach is also considered for incorporating PV-battery inthennal unit commitment. By incorporating battery storage, we can reduce loadfollowing requirements in the PV-utility grid. Furthennore, we can keep out peakinggenerators during peak hours by utilizing PV-battery. The fonnulation developed inthis study is very flexible and can be applied to other renewable energy sources withintennittent natures. A case study composed of 26 thennal units and a PV-batteryplant is presented. The short-tenn generating unit scheduling results presented inChapter IX would enhance those of Chapter IV.
xxviii
ACKNOWLEDGMENTS
We would like to take this opportunity to acknowledge the efforts of several peoplewho guided us in writing this book.
We were inspired by Professor M.A. Pai (University of lIlinois, Urbana) to write thisbook. His support of our ideas and his encouragement throughout this process aregreatly appreciated. Many of the earlier thoughts for writing this book were based onthe authors' conversations with Siemens engineers in Minneapolis. We alsoacknowledge the review of our book proposal and very constructive commentsprovided by Dr. Jay Giri (ALSTOM-ESCA Corporation), James Waight (SiemensCorporation), Professor Muwaffaq Alomoush (Yarmouk University of Jordan) andtwo of our senior research associates at lIlinois Institute of Technology (Dr. HatimYamin and Dr. Yaoyu Wang). The last three individuals were very instrumental inediting several of the chapters in this book, and their unconditional support isgenuinely appreciated. In addition, we acknowledge the editorial support of Mr.Alex Greene of Kluwer.
The first author has been fortunate to work with many engineers and educatorsthroughout his twenty year career in power engineering. However, the two mostsignificant individuals who have inspired him greatly to learn and research moreabout electric power systems are Dr. John Endrenyi (Ontario Hydro) and Dr. BruceWollenberg (University of Minnesota). These two individuals continue to inspirehim with technical ideas as time progresses.
The second author would like to thank his colleagues at ABB, Drs. Arthur Cohen,Show Chang and Vladimir Brandwajn, for invaluable discussions on electric powerrestructuring paradigm.
This book could not have been completed without the moral support of ourrespective families. Their understanding and sacrifice are gratefully recognized.
M. Shahidehpour, Chicago, IllinoisM. Marwali, Santa Clara, California