Economic Dispatch of Combined-Cycle Generators
Design Report
May05-10
Client:
MidAmerican Energy Company
Alan Oneal
Matt Mitchell
Faculty Advisors:
Dr. John Lamont
Dr. James McCalley
Students:
Edward McDowell, EE
Richard Mott, EE/Econ
Adam Peterson, EE
Seth Thorp, EE
REPORT DISCLAIMER NOTICE
DISCLAIMER: This document was developed as a part of the requirements of an
electrical and computer engineering course at Iowa State University, Ames, Iowa.
This document does not constitute a professional engineering design or a
professional land surveying document. Although the information is intended to
be accurate, the associated students, faculty, and Iowa State University make no
claims, promises, or guarantees about the accuracy, completeness, quality, or
adequacy of the information. The user of this document shall ensure that any
such use does not violate any laws with regard to professional licensing and
certification requirements. This use includes any work resulting from this studentprepared document that is required to be under the responsible charge of a
licensed engineer or surveyor. This document is copyrighted by the students
who produced this document and the associated faculty advisors. No part may
be reproduced without the written permission of the senior design course
coordinator.
Submitted December 15, 2004
Table of Contents
1. Frontal Materials
1.1 List of Figures ........................................................................................... iii
1.2 List of Tables ............................................................................................ iv
1.3 List of Definitions ....................................................................................... v
2. Introductory Materials
2.1 Abstract ..................................................................................................... 1
2.2 Acknowledgement ..................................................................................... 2
2.3 Problem Statement .................................................................................... 2
2.4 Operating Environment .............................................................................. 3
2.5 Intended User(s) and Intended Use(s) ....................................................... 3
2.6 Assumptions and Limitations ..................................................................... 4
2.7 Expected End Product and Other Deliverables ......................................... 5
3. Approach and Product Design Results
3.1 Approach Used .......................................................................................... 6
3.1.1 Design Objectives ................................................................................ 6
3.1.2 Functional Requirements ..................................................................... 7
3.1.3 Design Constraints .............................................................................. 7
3.1.4 Technical Approach Considerations and Results ................................ 8
3.1.5 Testing Approach Considerations ........................................................ 8
3.1.6 Recommendations Regarding Project Continuation or Modification .... 9
3.2 Detailed Design ......................................................................................... 9
4. Resources and Schedules
4.1 Resource Requirements .......................................................................... 15
4.1.1 Estimated Personnel Effort Requirements ....................................... 15
4.1.2 Estimated Other Resource Requirements ........................................ 16
4.1.3 Estimated Total Financial Requirements .......................................... 17
4.2 Schedules
4.2.1 Revised Schedule ............................................................................ 18
4.2.2 Deliverables Schedule ..................................................................... 19
4.2.3 Gantt Chart....................................................................................... 20
4.2.4 Weekly Schedule – Spring 2005 ...................................................... 20
5. Closure Materials
5.1 Project Team Information ........................................................................ 22
5.1.1 Client Information ............................................................................. 22
5.1.2 Faculty Advisors ............................................................................... 22
5.1.3 Student Information .......................................................................... 22
5.2 Closing Summary .................................................................................... 23
i
6. Appendices
6.1 Appendix A – Input Data .......................................................................... 24
6.2 Appendix B – Calculated Coefficients ...................................................... 29
6.3 Appendix C – Hand Example ................................................................... 30
6.4 Appendix D – Unit Commitment Pattern .................................................. 36
ii
List of Figures
Figure 1. Monotonic Unit Power Curve ................................................................. v
Figure 2. Non-monotonic Unit Power Curve ......................................................... v
Figure 3. Combined Cycle Generator ................................................................... 1
Figure 4. Basic Flow of Programming Modules .................................................... 9
Figure 5. Detailed Flowchart of Program Flow .................................................... 13
Figure 6. Original and Revised Schedule............................................................ 19
Figure 7. Deliverables Schedule ......................................................................... 19
Figure 8. Revised Gantt Chart ............................................................................ 20
Appendix Figure 1. Initial I/O Fuel Rate Coefficients........................................... 24
Appendix Figure 2. Fuel Costs per Generation Unit............................................ 25
Appendix Figure 3. Combined Cycle Unit Relationship ....................................... 26
Appendix Figure 4. Generator Characteristics .................................................... 27
Appendix Figure 5. System Load Pattern For One Week ................................... 28
Appendix Figure 6. Calculated Fuel Rate Coefficients for AP2 + BP + C ............ 29
iii
List of Tables
Table 1. Project Assumptions and Justifications ................................................... 4
Table 2. Project Limitations and Justifications ...................................................... 4
Table 3. Coefficient Computation Example ......................................................... 10
Table 4. Nuke 1 Data .......................................................................................... 11
Table 5. Nuke 1 Computed Coefficients ............................................................. 11
Table 6. Display of Possible Output .................................................................... 14
Table 7. Original Personnel Effort Resource Requirement ................................. 15
Table 8. Revised Personnel Effort Resource Requirement................................. 16
Table 9. Original Other Resource Requirement .................................................. 16
Table 10. Revised Other Resource Requirement ............................................... 17
Table 11. Original Estimated Project Cost .......................................................... 17
Table 12. Revised Estimated Project Cost.......................................................... 18
Appendix Table 1: Generator Values .................................................................. 30
Appendix Table 2: Generator Fuel Costs ........................................................... 30
Appendix Table 3: Incomplete I/O Values .......................................................... 30
Appendix Table 4: Necessary CC Generator Data ............................................ 31
Appendix Table 5: Complete Fuel Rate Equation Table for BCoal2 .................. 31
Appendix Table 6: Complete Fuel Rate Equation Table for ICoal1 .................... 31
Appendix Table 7: Complete Fuel Rate Equation Table for the CC1 ................. 31
Appendix Table 8: Lambda Values for Power Generation Levels ...................... 32
Appendix Table 9: Total Cost for Power Dispatch Situations ............................. 33
Appendix Table 10: Non-Monotonic Power Dispatch Situations ........................ 34
Appendix Table 11: Non-Monotonic Total Cost for Dispatch Situations ............. 35
iv
List of Definitions
Combined cycle unit (Cc): a dual cycle generating unit that first produces
power through a combustion turbine, then uses the waste heat to vaporize
water and drive a steam turbine
Combustion turbine (Ct): a generating unit used to meet peak loading
conditions by the combustion of fuel, usually natural gas
Economic dispatch: the allocation of the total load demand among generating
units in order to achieve the most economical production of power
Heat recovery steam generator: the second process of the combined cycle that
recovers waste heat to drive a steam turbine
Incremental cost: the increase in cost in dollars per increase in mega-watt
hours
Input/output function: the ratio of fuel input in
MBtu per hour to power output in megawatts
Monotonic unit (MU): a generator that produces
more power output as fuel input is
increased
Figure 1. Monotonic Incremental
Cost Curve
Non-monotonic unit (NMU): a generator that
can have an increase in power output with
no increase in fuel input
Figure 2. Non-monotonic Incremental
Cost Curve
v
2. Introductory Materials
This section establishes project’s purpose, including a description of the problem,
plans for reaching a solution, and possible assumptions and limitations that the
project team will have to deal with along the way.
2.1 Abstract
Combined-cycle generating units are being added to current power systems in
order to meet increasing load requirements as efficiently as possible. These
units consist of two simple-cycle combustion turbines with a heat recovery steam
generator as shown in Figure 1. Combined-cycle units exhibit non-monotonically
increasing cost curves which cannot be solved using classical methods of
economic dispatch optimization such as Newton-Raphson, binary-search, and
lambda-iteration techniques. The project team will develop an algorithm to
calculate the optimal economic dispatch of the system including monotonically
and non-monotonically increasing generators.
Major milestones include
development of the optimization algorithm, implementation of the algorithm in
Microsoft Excel using Visual Basic macro programming, and delivery of the
software and documentation to the client. Optimal results will allow for power to
be produced at the lowest possible cost to the client.
Figure 3. Combined Cycle Generator
-1-
2.2 Acknowledgement
The senior design project team would like to acknowledge Alan Oneal and Matt
Mitchell from MidAmerican Energy Company as our client contacts for the
project. We would also like to thank Dr. Lamont and Dr. McCalley for advising
and overseeing the project.
2.3 Problem Statement
The problem statement is composed of two components: the general problem
statement and the general solution statement.
General Problem Statement
The project involves the development of an algorithm incorporated into Microsoft
Excel macros to give MidAmerican Energy the lowest cost solution to meet
power demand. The difficulty of the problem stems from the inclusion of both
monotonic and non-monotonic generating units. Standard solution techniques
used with monotonic units will not work in a system utilizing both types of
generators.
The algorithm to be developed shall be capable of performing dispatch
calculations on a large number of both monotonic and non-monotonic power
generators. These calculations will determine the most cost effective generation
dispatch combination of power generators. It shall accept piecewise-linear heatrate curves as input data from the generators. Results from this program,
including megawatt output and production cost, shall be written into a worksheet
within the same Excel workbook. These results will be for each specific unit, and
each hour of the supplied load schedule. Any iteration calculations shall also be
reviewable by the user. The program shall be constrained to a runtime of less
than five minutes. MidAmerican Energy shall validate the results of the program
to determine its success.
General Solution Approach
Data for the power generators shall be supplied by MidAmerican Energy. This
data shall include minimum and maximum load values, fuel costs, power
generation levels with their corresponding incremental heat rate values and I/O
values.
The algorithm to be developed shall take this data and create the
piecewise-linear cost functions for each power generator range. It shall also
determine whether a given unit is a monotonic or non-monotonic generator
based upon the piecewise-linear determinations.
After developing these equations the algorithm shall perform a standard lambda
search with the monotonic generators that the user specifies to be running. This
-2-
part of program shall populate a table for the lowest cost dispatch among the
MU’s at each possibly load value (a definable step, default = 1MW). The load
values extremes shall be determined using the combined generator minimum
and maximum values.
After the monotonic unit table is populated, the algorithm shall move on to the
non-monotonic power generators. A similar table to that of the monotonic units
shall be populated with minimum cost dispatches for each load value. These
minimum cost values shall be determined by running a series of loops that
compare all possible dispatch situations and then take the minimum value of
each specified load value.
At this point the algorithm shall determine the least cost dispatch available by the
generator to meet the load requirements. This will be accomplished by searching
through the monotonic and non-monotonic tables for the least cost combination
of units to meet the necessary power requirements.
Throughout the project, weekly e-mails to the client and faculty advisors will
detail the work that has been completed and future plans. After the initial
software is completed it will be turned over to MidAmerican Energy Company for
verification. The software will then be returned to the project team and any
necessary modifications will be made. At the completion of the project all
deliverables, including the completed software and final documentation, will be
handed over to MidAmerican Energy Company.
2.4 Operating Environment
The solution program will be written using Visual Basic macro programming
embedded in the form of a Microsoft Excel workbook. The software will run on a
windows based system with adequate processing capabilities. The operating
environment was required due to its wide use throughout MidAmerican Energy.
2.5 Intended User(s) and Intended Use(s)
This section shall outline the intended users and uses of the software we shall
develop. Any specific skills and/or environments shall be outlined.
Intended User(s)
The software will be designed for MidAmerican Energy employees who have a
basic understanding of how to use Microsoft Excel.
-3-
Intended Use(s)
The software will be used to optimize the economic dispatch of power between
monotonic and non-monotonic generators. Excel will be used to process input
data for generating units supplied by the user and produce output into a
workbook or an external file. The software is also intended to be used as a
validation tool for other algorithms.
2.6 Assumptions and Limitations
This section provides the assumptions and limitations concerning the problem.
Assumptions
Table 1 lists the project assumptions and their justifications.
Table 1. Project Assumptions and Justifications
The project team will have access to the current
methods for optimizing combined-cycle generators.
A unit commitment status will be placed on all
generation units.
Both combustion turbines that make up each Cc
assumed to operate identically.
Project ideas should not be shared outside the
project team.
A well designed solution method is more important
than the most efficient solution.
Testing Requirement
Client Requirement
Software Requirement
Confidentiality
Requirement
Client Requirement
Limitations
Table 2 lists the project limitations and their justifications.
Table 2. Project Limitations and Justifications
The software shall be written in Microsoft Excel with
Visual Basic macro programming.
The software code shall contain ample comments.
Software must permit generator status to be specified
hourly within a 7 day horizon.
Status Codes
- 1 Forced Off
1 On/dispatchable
0 Off/available
2 On/fixed output
-4-
Client Requirement
Client Requirement
Client Requirement
Software
Requirement
Software accepts input data for generating units that use
piece-wise linear incremental heat rate curves, with up to
10 segments each.
Software includes an elapsed time indicator for
performance measurements.
A switch must be provided to allow full output dumps (to
the workbook, or output file) of iterations tested, their
cost, total generation, and other relevant metrics as
agreed upon between the client and the team.
Results must be written into a single Excel workbook, by
unit and by hour (MW output, production cost), with
appropriate totals and other statistics as agreed upon by
the client.
Flexible for a non-specified number of monotonic and
non-monotonic units.
Client Requirement
Software
Requirement
Software
Requirement
Client Requirement
Client Requirement
2.7 Expected End Product and Other Deliverables
Below are some of the expected results from the project.
Microsoft Excel workbook file
The Excel workbook file will include user instructions along with the Visual Basic
code with embedded commenting. The software shall employ an economic
dispatch algorithm used for monotonic and non-monotonic generating systems.
The software shall meet the requirements listed in the limitations section.
Documentation
Test results from the software will be given to MidAmerican Energy Company. A
printed copy of the fully commented program code and any other documentation
will also accompany the software.
-5-
3. Approach and Product Design Results
The following section describes the project teams proposed approach toward
solving the problem, and tasks that will be successfully completed along the way.
3.1 Approach Used
A successful project will meet the following six requirements.
3.1.1 Design Objectives
These goals shall be attained upon the successful completion of the project.

Accurate piecewise-linear cost curve segment generation and calculation.
o The algorithm will develop these mathematical functions from the
data input from an external file that Excel will read in. The external
file will include MW and MBTU/MWH data points for each unit.
Fuel cost, generator minimum and maximum power levels,
individual generation levels will be tunable parameters.

Accurate lambda search and table creation for the monotonic units.
o The lambda search method shall be used for the monotonic units to
calculate the most cost efficient method of unit dispatch. A table
will be created using the results of the lambda search that displays
lambda vs. MW for each generation level.

Accurate table creation for the non-monotonic units.
o Because lambda search cannot be used for non-monotonic
situations, these units shall be broken down to power generation
vs. cost tables by means of full iteration.

Produce the most cost efficient dispatch for the system.
o Using the generated monotonic unit table and the non-monotonic
unit tables, a combined table will be created that contains the best
(cheapest) dispatch among the units.

Create a user friendly graphical user interface.
o The interface needs to be easy to use for people with little or no
dispatch optimization experience. It needs to make the algorithm
solution easy to understand and the corresponding output easy to
navigate through.

Miscellaneous objectives to be met.
-6-
o The program must run in under five minutes. After completing the
project, we will spend any remaining time optimizing the speed with
which the program is able to come to a solution.
3.1.2 Functional Requirements
Required functions of the end product include the following:

The end product shall calculate economic dispatch results for both
monotonically and non-monotonically increasing generators using
Microsoft Excel with Visual Basic macros. It shall provide the least-cost
solution.

The output data will be able to be saved in an Excel workbook or external
file upon user request.
o The immediate visual output shall be broken up into four panes
displaying one weeks worth of data for each unit including unit
status, fixed power output, maximum power output, and minimum
power output.
o The output data should not be lost in the program or be difficult to
obtain. This data should also be easy to understand and be
incorporated into a readable table.
3.1.2 Design Constraints
The following design constraints must be considered:

The algorithm shall be implemented using
programming embedded in Microsoft Excel.

The design shall be flexible with regard to the number of monotonic and
non-monotonic units.
o This product should be able to be expanded upon by MidAmerican
Energy in the future. Limitations should not be placed on the
number or type of units that can be handled.

The final version of the algorithm shall have a run time of less than five
minutes.
o The algorithm will be used in a dynamic environment. Because of
this, it must be able to run and develop the appropriate output in a
period of time no greater than five minutes.

The upper and lower limits of all generators shall be observed.
o In an effort to streamline the computational process, the upper and
lower generating limits for each individual unit shall be observed.
-7-
Visual Basic macro
There is no need to run cost calculations for power dispatches that
are outside the feasible generating ranges.
3.1.3 Technical Approach Considerations and Results
The following are technological issues the project team must consider:

Becoming familiar with Visual Basic macro programming in Microsoft
Excel.
o Due to its wide use by MidAmerican Energy, Microsoft Excel will be
the program in which the algorithm will be used. Visual Basic
technology was also a requirement placed on the project by
MidAmerican, thus no other technologies will be considered.

A Windows platform will be used for this project.
o Windows is used entirely throughout MidAmerican Energy, thus
Windows will be the only choice used for the basis of this project.

Software may be first implemented using familiar languages such as C++.
o This consideration will be used only for the general format of the
code. By first developing modules using a programming language
the group is familiar with and then converting them to Visual Basic,
programming will be easier.
3.1.5 Testing Approach Considerations
Adequate testing will be done before and after client use. The project team
considers the following requirements essential to a successful end product:

Testing shall be performed using data supplied by the client.
o The client has provided one week of system load data which shall
be utilized for the purpose of testing.

Accuracy of testing will be confirmed by comparing the results produced
by the software against hand calculated results.
o Hand calculations will be performed for a basic situation involving
only a few monotonic and non-monotonic units. This “base case”
will help guarantee that the algorithm is performing the correct
calculations before we use it with a detailed case. This step will
help make the team aware of problems, so that they can be
corrected.
-8-

After initial testing performed by the group is completed, MidAmerican
Energy Company will be given the software to validate the results
obtained.
o Any discrepancies between results obtained will be discussed and
any necessary modifications to the algorithm shall be completed.
3.1.6 Recommendations Regarding Project Continuation or Modification
This section includes the team recommendation
continuation at this point in the schedule.

regarding
project
The team will continue with the project as originally planned.
o The scope of the project is adequate considering the time
commitments the team has projected for the project.
The
deliverable schedules have been met up to this point in the project.
The team feels capable of completing the project.
3.2 Detailed Design
The design of the algorithm to supply the optimal dispatch can be broken down
into a number of different modules. These modules shall be individually coded
and tested in Microsoft Excel before being combined for the complete program.
By using this method the team hopes to speed the process of coding by
assigning modules to each individual rather than tackling them as a whole. The
team also hopes to cut down on the amount of end-product testing time
necessary since the individual modules will be tested before their
implementation. Figure 4 shows the basic break down of the programming
modules and the basic order in which they run.
MU
Dispatch
Combined Dispatch
NMU
Dispatch
Figure 4. Basic Flow of Programming Modules
-9-
Data for the power generators shall be supplied by MidAmerican Energy. This
data shall include minimum and maximum load values, fuel costs and power
generation levels. Heat rate data for each generation level will be supplied in the
form of an external file. The algorithm developed shall take the data from an
external file, load it into Excel, and create the piecewise-linear cost functions for
each power generator range. It shall also determine whether a given unit is a
monotonic or non-monotonic generator based upon the piecewise-linear
determinations. Given the following example data in Table 3, coefficients for a
quadratic equation which describes the fuel I/O curve of the unit can be
computed.
Table 3. Coefficient Computation Example
Generator Status
BCoal 1
MW
IHR
134
8.2836
214
8.7156
294
9.1476
374
9.5796
534
10.4436
BCoal 2
MW
IHR
134
8.2836
Hour 1
1
Hour 2
1
Hour 3
1
Hour 4
1
Hour 5
0
Hour 6
0
0
0
1
1
1
1
I/O
1,876
I/O
1,876
The calculations and determinations shall be made as follows:
For each two MW values, a linear approximation shall be calculated using the
incremental heat rate with regard to power production (type: 2Ax + B). The
integral of this line shall be set equal to the initial I/O value (type: Ax^2 + Bx + C).
From the equation produced by the integral, the “C” value, a constant, can be
calculated for this first piecewise function at the lower bound of the generation
range. With the calculated “C” value, a new I/O value can be calculated at the
upper bound of the generation range. At this point, the piecewise values shift to
the next pair of points.
- 10 -
An example using given data:
Table 4. Nuke 1 Data
Nuke 1
MW
IHR
100
125
150
175
195
200
At 100 MW level:
At 125 MW level:
I/O
8.0000
8.2000
8.4000
8.6000
8.7500
8.8000
1,250
.008(100) 2  7.2(100)  C  1250 C  450
.008(125) 2  7.2(125)  450  I / O  I / O  1475
It is now possible to continue down through the different MW values calculating
the C values and the next corresponding I/O values (calculate C at 125, I/O at
150 etc…).
With regard to the determination of the monotonic versus non-monotonic
characteristics of the line units the algorithm need only make a basic observation.
If any of the A values for the calculated piecewise-linear functions are negative,
the unit is non-monotonic. Otherwise, the unit can be assumed to be monotonic.
A complete listing of the A, B, C, with A, B and C being the coefficients to the
general Ax^2+Bx+c equation, and I/O values for the test generating units can be
found in Appendix A. The generated values for the units will likely look
something like what follows:
Table 5. Nuke 1 Computed Coefficients
Nuke 1
(MW) Range
100-125
125-150
150-175
175-195
195-200
A
0.008
0.008
0.008
0.0075
0.01
B
7.2
7.2
7.2
7.2875
6.8
C
450
450
450
450
450
I/O
1250
1475
1710
1955
2156.25
The user shall specify in the Excel file with the generator data whether the given
generator is on or off (unit commitment). This determination shall be made
through a specific status code in a specific column (see Table 2 on page 4). For
the purpose of testing the algorithm, the team shall develop a unit commitment
pattern that is realistic based on unit up and down times. This commitment shall
- 11 -
initially encompass only a single hour, but will be expandable based upon
algorithm performance.
After developing the piecewise-linear equations, the algorithm shall perform a
standard lambda search with the monotonic generators that the user has
specified to be running. This part of program shall populate a table for the lowest
cost dispatch among the monotonic units at each possible load value (a definable
step, default = 1MW). The load value extremes (minimum and maximum for the
system) shall be determined using the sum of the combined generator minimums
and maximums. Calculations outside these levels will be ignored.
After the monotonic unit table is populated, the algorithm shall move on to the
non-monotonic power generators. A similar table to that of the monotonic units
shall be populated with cost dispatches for each load value for each nonmonotonic unit.
At this point the program shall take the non-monotonic tables and the combined
monotonic unit table and determine the minimum cost situation for the given load.
This calculation will be run through the use of a number of loops. Each possible
combination of loads from the tables will be checked. If the load value for the
combination is not equal to the load specified by the user, no further calculations
shall be completed and the program will immediately move onto the next
combination. In the event that the load value is equal to that specified by the
user, the algorithm shall take the resulting cost value and compare it to the
lowest previously calculated value. If this new value is larger, it will not be
retained and the program will continue. If it is smaller than the previous value, it
will be retained for further comparisons and the program shall continue.
After all possible combinations have been tested, the smallest cost value (and its
resulting load dispatch) shall be output to the user. Additionally, a complete list
of all the minimum cost dispatches shall be retained for use by the user as an
output. Any load dispatches that were not cost optimizing shall not be included
due to the unreasonable length that such a document would have. Figure 5 on
the following page describes in more detail how the program is designed to flow.
- 12 -
Figure 5. Detailed Flowchart of Program Flow
- 13 -
Besides the output described in the above paragraph, an additional output shall
be included. A four pane window type of display will enable the user to look at
one of four additional data sets. These sets include the status codes for each
generator at each hour of each day, the load that the generator will be running at
for each hour of each day, the minimum value of the generator, and the
maximum value of the generator. Note that this output will only be feasible if the
program is able to run multiple load optimizations at one time.
The group expects the output to look similar to Table 6 below.
Table 6. Display of Possible Output
Status Codes ( 1 = on, 0 = off)
Hour 1
Hour 2
Day 1
1
1
Day 2
0
1
Day 3
1
1
…
Maximum Generator Value
150
…
Load Dispatch
Hour 1
Hour 2
Day 1
150
200
Day 2
0
200
Day 3
175
220
…
Minimum Generator Value
25
…
It is important to realize that the above module layout of this detailed design
needs to be run 168 times to complete a week-long calculation. Due to the
uncertainty of computational run-time for even a single load, there is no
guarantee that a series of 168 loads will be calculated within the time allotment.
For this reason, the design of the algorithm will allow for an unspecified number
of load dispatch situations to be solved. The algorithm will be allowed to run for a
single dispatch or a weeks worth of dispatches and all the values in between.
The complete solution for the given system load including power output of each
unit and total cost will be provided.
Throughout the project, weekly e-mails to the client and faculty advisors will
detail the work that has been completed and future plans. After the initial
software is completed it will be turned over to MidAmerican Energy Company for
validation. The software will then be returned to the project team and any
necessary modifications will be made. At the completion of the project all
deliverables, including the completed software and final documentation, will be
handed over to MidAmerican Energy Company.
- 14 -
4. Resources and Schedules
Knowledge of estimated resource requirements and the project schedule are
essential in order to properly evaluate the design report. This section will
describe the original and revised estimates for the project’s resources
requirements and schedules.
4.1
Resources Requirements
This section contains the original and revised estimates of personnel resource
requirements, other resource requirements, and total financial requirements for
the project.
4.1.1 Estimated Personnel Effort Requirements
To achieve the best personnel effort estimate, the project timeline has been
broken up by tasks which refer to the tasks listed in the project schedule.
These tasks include:








Task 1: Project Definition
Task 2: Technology Considerations and Selection
Task 3: End-Product Design
Task 4: End-Product Prototype Implementation
Task 5: End-Product Testing
Task 6: End-Product Documentation
Task 7: End-Product Demonstration
Task 8: Project Reporting
Table 7. Original Personnel Effort Resource Requirements
Edward McDowell
Richard Mott
Adam Peterson
Seth Thorp
Total
Task 1
10
10
10
10
40
Task 2
4
4
4
4
16
Task 3
43
42
44
44
173
Task 4
25
25
20
25
95
Task 5
15
15
15
15
60
Task 6
10
10
10
10
40
Task 7
8
8
8
8
32
Task 8
40
40
40
40
160
Total
155
154
151
156
616
To date, tasks 1-3 are complete and task 8 has been ongoing in the form of
weekly meetings and emails with the faculty advisors and project team.
- 15 -
Actual resource requirements for tasks 1-3 have been revised and are shown
in table 8. Resource estimates for tasks 4-7 have also been revised from
their original estimates. Tasks 1 and 2 required fewer resources than first
estimated due to all the team members understanding the problem rather
quickly. Weekly meeting with the faculty advisors and the two client meetings
also benefited the team in this aspect. The meetings also helped the team
select the best technology to solve the problem. Iteration and table lookup
methods were deemed the best solutions so that left few other algorithm
methods to be considered. Task 3 has required more resources simply
because the team underestimated the time commitment associated with the
design process. Task 5 is estimated to require more time due to the flexibility
that the client requires. The software must be able to operate using an
unspecified number of monotonic or non-monotonic units. An unspecified
number of unit commitment patterns should also be handled. The importance
of documentation was also underestimated therefore task 6 will require
additional resources. Task 8 was modified due to the importance of adequate
reporting on the project plan on future documents including the design
document. Adam Peterson’s resources in Task 8 were increased due to
communication chairperson responsibilities regarding weekly emails and
group communication throughout the period of the project.
Table 8. Revised Personnel Effort Resource Requirements
Edward McDowell
Richard Mott
Adam Peterson
Seth Thorp
Revised Total
Task 1
8
9
7
9
33
Task 2
2
2
2
2
8
Task 3
48
50
47
48
193
Task 4
25
25
20
25
95
Task 5
21
22
19
20
82
Task 6
15
15
15
16
61
Task 7
8
8
8
8
32
Task 8
45
45
55
45
190
Total
172
176
173
173
694
4.1.2 Estimated Other Resource Requirements
The original and revised other resource requirements are itemized below in
tables 9 and 10. This project requires only the use of Microsoft Excel, and
Microsoft Visual Basic, which are readily available to the team at no cost.
The only other costs were associated with the printing of materials.
Table 9. Original Other Resource Requirements
Item
Bound Project Plan
Printing of Project Poster
Bound Design Report
Total
Team Hours
Other Hours
Cost
0
12
0
12
0
0
0
0
$20.00
$62.00
$20.00
$102.00
- 16 -
Table 10 shows that material costs will likely result in a savings of $38.64
from previous estimates. It is assumed that the bound design report will
require approximately the same cost as the bound project plan.
Table 10. Revised Other Resource Requirements
Item
Bound Project Plan
Printing of Project Poster
Bound Design Report
Revised Total
Team Hours
Other Hours
Cost
0
14
0
14
0
0
0
0
$ 8.88
$ 55.60
$ 8.88
$ 73.36
4.1.3 Estimated Total Financial Requirements
Total financial requirements for the project are divided between material costs
and labor costs, as shown in Table 11. Material costs included the costs the
printing of deliverables. No labor costs from the team members were
included in material costs.
Table 11. Original Project Cost Estimates
Item
W/O Labor
With Labor
$ 20.00
$ 62.00
$ 20.00
$ 102.00
$ 20.00
$ 62.00
$ 20.00
$ 102.00
$ 0.00
$ 102.00
$ 1,550.00
$ 1,540.00
$ 1,510.00
$ 1,560.00
$ 6,160.00
$ 6,262.00
Materials:
a. Bound Project Plan
b. Poster
c. Bound Design Report
Subtotal
Labor at $10 per hour:
a. McDowell, Edward
b. Mott, Richard
c. Peterson, Adam
d. Thorp, Seth
Subtotal
Total
Table 12 displays the actual printing costs for materials along with revised
labor cost estimates. At $10 per hour labor costs, the total projected project
cost is $ 7,013.36.
- 17 -
Table 12. Revised Project Cost Estimates
Item
Materials:
a. Bound Project Plan
b. Poster
c. Bound Design Report
Subtotal
Labor at $10 per hour:
a. McDowell, Edward
b. Mott, Richard
c. Peterson, Adam
d. Thorp, Seth
Subtotal
Revised Total
4.2
W/O Labor
With Labor
$ 8.88
$ 55.60
$ 8.88
$ 73.36
$ 8.88
$ 55.60
$ 8.88
$ 73.36
$0.00
$73.36
$ 1,720.00
$ 1,760.00
$ 1,730.00
$ 1,730.00
$ 6,940.00
$ 7,013.36
Schedules
This section describes the project’s schedule. Figure 6 displays the original and
revised schedule for each task in the project. Figure 7 displays a schedule of
deliverables for the duration of the project. Figure 8 is a revised Gantt chart
showing each task and subtask for the duration of the project.
4.2.1 Revised Schedule
Figure 6 documents the revisions the team made to the schedule of the project.
The reasons for each change are listed below.




Project Definition – The project definition took longer than the team
originally anticipated because the team had to meet with the clients in
order to properly define the project.
Technology Considerations and Selection – The technology
considerations and selection took less time than originally estimated
due to the requirements of the project dictating what technologies the
team is to use. The technologies that the project will use were given to
the team by the client.
End-Product Design – The team was able to spend more time on the
end-product design due to the technology consideration aspect
requiring less time than originally anticipated. This additional time
allowed the team to develop a more thorough design approach.
End-Product Implementation – Through the development of the design
process, the team realized the intricacies of the project. This caused
the end-product implementation to require additional time.
- 18 -




End-Product Testing – The end-product testing time was pushed back
due to the extension of the end-product implementation process. The
testing period was also extended to allow the clients additional time to
verify the program developed by the team was sufficient.
End-Product Documentation – The end-product documentation time
was extended to overlap with the testing phase. This was to allow the
team time to document changes and features that may be
implemented in the testing phase.
End-Product Demonstration – The end-product demonstration period
was shortened to a week at the end of the semester because the time
allotted for demonstration is mandated by the course instructors.
Project Reporting – The project reporting phase did not change.
Figure 6. Original and Revised Schedule
4.2.2 Deliverables Schedule
Figure 7 is a schedule showing the date of all deliverables for the duration of the
project. All deliverables to date have been delivered at the time designated in
the schedule. No revisions have been made to the deliverables schedule.
Figure 7. Deliverables Schedule
- 19 -
4.2.3 Gantt Chart
Figure 8 displays a revised Gantt chart with the tasks and subtasks for the
duration of the project. The revisions to the schedule correspond to the reasons
given at the beginning of this section.
Figure 8. Revised Gantt Chart
4.2.4 Weekly Schedule – Spring 2005
A tentative weekly schedule was developed for the spring semester of 2005. The
schedule is listed below.
Jan 10-16
 Creation of database structure for user input values that will be used to
determine heat rate, generation maximum and minimum levels, and
incremental costs.
Jan 17-23
 Coding of monotonically increasing generation lambda search.
Jan 24-Feb 6
 Coding of non-monotonically increasing table(s).
- 20 -
Feb 7-13
 Coding of combination of MU and NMU tables to find least-cost dispatch
Feb 14-28
 Development of Graphical User Interface (GUI) in MS Excel using VB
macros
Mar 1-6
 Project team testing to determine accuracy of dispatch
 Project team testing to determine effectiveness of GUI
Mar 7-11
 Project team testing to remove any additional bugs
 Deliver program to client for testing
Mar 12-20
 Spring Break
Mar 21-Apr 15
 Further necessary modifications to program as determined by client
testing
 User manual detailing operation of program
Apr 25-29
 Industrial review - week before final report.
Apr 15-May 4
 Final report describing success of project
- 21 -
5 Closure Materials
This section provides contact information and a closing summary.
5.1
Project Team Information
This section provides contact information for the client contacts, faculty advisors
and team members.
5.1.1 Client Information:
MidAmerican Energy Company
Client Contacts:
Alan Oneal
[email protected]
(515) 252-6449
Matt Mitchell
[email protected]
(515) 252-6458
5.1.2 Faculty Advisors:
Dr. John Lamont
324 Town Engineering
Ames, IA 50011-3060
Office Phone:
(515) 294-3600
Fax:
(515) 294-6760
Email:
[email protected]
Dr. James McCalley
1113 Coover Hall
Ames, IA 50011-3060
Office Phone:
(515) 294-4844
Fax:
(515) 294-4263
Email:
[email protected]
5.1.3 Student Information:
Edward McDowell
Electrical Engineering
1300 Coconino Rd. Apt. 210
Ames, IA 50014
(515) 292-4562
[email protected]
Adam Peterson
Electrical Engineering
1134 Frederiksen Ct.
Ames, IA 50010
(515) 572-7704
[email protected]
Seth Thorp
Electrical Engineering
3336 Frederiksen Ct.
Ames, IA 50010
(515) 572-8077
[email protected]
Richard Mott
Electrical Engineering and
Economics
2408 Knapp Street
Ames, IA 50014
(319) 573-1084
[email protected]
- 22 -
5.2
Closing Summary
This project will create a software application that will seek to produce the most
economical power distribution between monotonically and non-monotonically
increasing generators. An algorithm will be created to incorporate the two
types of generators and will be combined with a user interface to produce a
usable program. This program will be written in Microsoft Excel using Visual
Basic macros and will meet the many outlined requirements. MidAmerican
Energy can expect to benefit from this project through a reduction in fuel costs
due to improved generator distribution.
- 23 -
6 Appendices
The following appendices are supplements to the content found in the design
report.
6.1
Appendix A – Input Data provided by MidAmerican
Energy Co.
The following data was provided by MidAmerican Energy Company for use in
this project.
Appendix Figure 1. Initial I/O Fuel Rate Coefficients
- 24 -
Appendix Figure 2. Fuel Costs per Generation Unit
- 25 -
Appendix Figure 3. Combined Cycle Unit Relationship
- 26 -
Appendix Figure 4. Generator Characteristics
- 27 -
Appendix Figure 5. System Load Pattern for One Week
- 28 -
6.2
Appendix B – Calculated Coefficients
A complete listing of computed coefficients is shown below in Appendix Figure 6.
Appendix Figure 6. Calculated Fuel Rate Coefficients for AP2 + BP + C
- 29 -
6.3
Appendix C – Hand Example
The following hand calculation will show some of the basic calculations and
steps involved in finding the optimum generation dispatch between a few
different units. For this example two monotonic and one non-monotonic unit
will be considered. These units are BCoal2, ICoal1, and CC1. The data input
for these units will include the following information:
Appendix Table 1: Generator Values
BCoal 2
ICoal 1
CCCT 1A
CCCT 1B
HRSG 1
PMax
500
300
200
200
190
Min
Up
48
12
PMin
300
150
80
80
50
Min
Dn
36
12
Cold
>24 h
9000
4000
4740
4740
Warm
6-24h
7500
3000
4500
4500
Hot
<6h
7000
2500
4200
4200
Time to
Start (Hr)
10
8
0.33
0.33
2
Ramp
MW/min
5
4
6
6
4
Status
Econ
Econ
Econ
Econ
Econ
Appendix Table 2: Generator Fuel Costs
BCoal 2
ICoal 1
CCCT 1A
CCCT 1B
HRSG 1
$
$
$
$
--
1.11
1.22
5.29
5.29
Appendix Table 3: Incomplete I/O Values
BCoal 2
MW IHR
134
214
294
374
454
534
8.2836
8.7156
9.1476
9.5796
10.0116
10.4436
I/O
1,876
ICoal 1
MW IHR
50
70
90
140
180
220
275
300
7.6009
7.9833
8.1706
8.4756
8.9184
9.7412
10.9675
11.2809
- 30 -
I/O
675
CC 1A&B
MW IHR
190
290
335
378
420
490
530
590
6.4000
6.8000
6.2000
5.8000
5.1000
4.7000
4.5000
4.9000
I/O
2,178
Initial
Cond
ON
OFF
OFF
OFF
OFF
Appendix Table 4: Necessary CC Generator Data
1
2
3
4
5
6
7
8
9
MW
MW
MW
MW
MW
MW
MW
MW
MW
CCT1A
0
60
90
110
130
150
170
180
200
CCCT2A
0
60
90
110
130
150
170
180
200
HRSG
0
70
110
115
118
120
150
170
190
Total
0
190
290
335
378
420
490
530
590
Before any real calculations can be performed, the data input by the user must
be converted into equations to be utilized by the algorithm. From Appendix
Table 3, the following tables can be generated using basic mathematical
operations.
Appendix Table 5: Complete Fuel Rate Equation Table for BCoal2
BCoal 2
(MW) Range
134-214
214-294
294-374
374-454
454-534
A
0.0027
0.0027
0.0027
0.0027
0.0027
B
7.56
7.56
7.56
7.56
7.56
C
814.4788
814.4788
814.4788
814.4788
814.4788
I/O
1876
2556
3270
4020
4803
Appendix Table 6: Complete Fuel Rate Equation Table for ICoal1
ICoal 1
(MW) Range
50-70
70-90
90-140
140-180
180-220
220-275
275-300
A
0.00956
0.0046825
0.00305
0.005535
0.010285
0.011148182
0.006268
B
6.6449
7.32775
7.6216
6.9258
5.2158
4.836
7.5201
C
318.855
294.95525
281.732
330.438
484.338
526.116
157.05225
I/O
675
830.842
992.381
1408.536
1756.416
2129.608
2699.0973
Appendix Table 7: Complete Fuel Rate Equation Table for the CC1
CC 1A&B
(MW) Range
190-290
290-335
335-378
378-420
420-490
490-530
530-590
A
0.002
-0.00666666
-0.00465116
-0.00833333
-0.00285714
-0.0025
0.003333333
B
5.64
10.66666667
9.31627907
12.1
7.5
7.15
0.966666667
- 31 -
C
1034.2
305.3333333
531.5232558
5.4
971.4
1057.15
2695.733333
I/O
2178
2838
3130.5
3388.5
3617.4
3960.4
4144.4
This calculated data is important because it defines the fuel rate equations for
the generators between different power generation ranges. Using these tables
and the fuel prices listed in Appendix Table 2 it is possible to calculate the cost
of generation for any load value.
For the monotonic generators (BCoal2 and ICoal1) the lambda values can be
calculated for each specific generation level through the following equation:
(

fuel price
Power Generation 
2* A
 B)
The calculated lambda values for the monotonic units BCoal2 and ICoal1 will
be put into a table for further use by the algorithm. These values determine the
order in which the units will pick up additional load as it is added to the system.
Appendix Table 8: Lambda Values for Power Generation Levels
Bcoal2
Power
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
…
Icoal1
Lambda
10.19
10.20
10.20
10.21
10.21
10.22
10.23
10.23
10.24
10.24
10.25
10.26
10.26
10.27
10.27
10.28
10.29
10.29
10.30
10.30
10.31
10.32
10.32
10.33
10.33
10.34
10.35
…
- 32 -
Power
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
...
Lambda
10.48
10.49
10.50
10.52
10.53
10.54
10.56
10.57
10.58
10.60
10.61
10.62
10.64
10.65
10.66
10.68
10.69
10.70
10.72
10.73
10.75
10.76
10.77
10.79
10.80
10.81
10.83
…
Any additional power above 450 MW (for what is shown above) will be provided
by BCoal2. This is apparent due to the lower lambda values corresponding to
the power generation of the unit.
It is now possible to combine the monotonic units into one single table based
upon their lambda values and the resulting power dispatch. This is done by
considering every possible lambda between the lambda min and lambda max
of the two units. The resulting dispatch looks like this:
Appendix Table 9: Total Cost for Power Dispatch Situations
Lambda
10.19
10.20
10.21
10.22
10.23
10.24
10.25
10.26
10.27
10.28
10.29
10.30
10.31
10.32
10.33
10.34
10.35
10.36
10.37
10.38
10.39
10.40
10.41
10.42
10.43
10.44
10.45
10.46
…
Monotonic Unit Table
BCoal2 ICoal1 Total P
300.03
150.00 450.03
301.70
150.00 451.70
303.37
150.00 453.37
305.04
150.00 455.04
306.71
150.00 456.71
308.38
150.00 458.38
310.04
150.00 460.04
311.71
150.00 461.71
313.38
150.00 463.38
315.05
150.00 465.05
316.72
150.00 466.72
318.39
150.00 468.39
320.05
150.00 470.05
321.72
150.00 471.72
323.39
150.00 473.39
325.06
150.00 475.06
326.73
150.00 476.73
328.40
150.00 478.40
330.06
150.00 480.06
331.73
150.00 481.73
333.40
150.00 483.40
335.07
150.00 485.07
336.74
150.00 486.74
338.41
150.00 488.41
340.07
150.00 490.07
341.74
150.00 491.74
343.41
150.00 493.41
345.08
150.00 495.08
…
…
…
Total Cost
$4,819.60
$4,834.92
$4,850.26
$4,865.62
$4,880.98
$4,896.37
$4,911.77
$4,927.18
$4,942.61
$4,958.05
$4,973.51
$4,988.98
$5,004.47
$5,019.97
$5,035.49
$5,051.03
$5,066.58
$5,082.14
$5,097.72
$5,113.31
$5,128.92
$5,144.54
$5,160.18
$5,175.84
$5,191.51
$5,207.19
$5,222.89
$5,238.60
…
This integration supports the conclusion outlined above that any additional
power to be provided above 450 MW (for the small piece visible) will be
supplied by BCoal2. Once the lambda value of the power provided by BCoal2
increases above 10.48 (from Appendix Table 8) ICoal2 will begin to supply the
increasing load.
- 33 -
It is now time to shift attention to the non-monotonic unit. First, it is necessary
to know the relationship between the output of the combustion turbines (CTs)
and the power output of the heat recovery steam generator (HRSG). A linear
regression must be performed on the data in Appendix Table 4 to determine
this relationship. To get the best fit for the data, a 6 th or 7th order exponential
regression is best. For time and simplicity in this example a 2 nd order
regression was used. The values for the CTs and HRSG can be found for any
point within the minimum and maximum values of the generator using the
developed equation. This results in the following table:
Appendix Table 10: Non-Monotonic Power Dispatch Situations
CCCT 1A
80.00
80.50
81.00
81.50
82.00
82.50
83.00
83.50
84.00
84.50
85.00
85.50
86.00
86.50
87.00
87.50
88.00
88.50
89.00
89.50
90.00
90.50
91.00
91.50
92.00
…
Non-Monotonic Unit Table
CCCT1A+1B
HRSG
Total Power
160.00
97.42
257.42
161.00
97.67
258.67
162.00
97.93
259.93
163.00
98.18
261.18
164.00
98.44
262.44
165.00
98.69
263.69
166.00
98.95
264.95
167.00
99.21
266.21
168.00
99.47
267.47
169.00
99.72
268.72
170.00
99.98
269.98
171.00
100.24
271.24
172.00
100.51
272.51
173.00
100.77
273.77
174.00
101.03
275.03
175.00
101.29
276.29
176.00
101.56
277.56
177.00
101.82
278.82
178.00
102.09
280.09
179.00
102.35
281.35
180.00
102.62
282.62
181.00
102.89
283.89
182.00
103.15
285.15
183.00
103.42
286.42
184.00
103.69
287.69
…
…
…
- 34 -
After the generation of this table, the cost of generation at each power level for
the non-monotonic generator can be calculated using the fuel rate equations
calculated in Appendix Table 7 and the fuel cost outlined in Appendix Table 2.
The heat recovery steam generator does not have a fuel cost because it runs
on the waste heat of the two combustion turbines. Because of this, only the
total of the turbines (CCCT1A+CCCT1B) needs to be considered when using
Appendix Table 7.
Appendix Table 11: Non-Monotonic Total Cost for Dispatch Situations
CCCT 1A
80.00
80.50
81.00
81.50
82.00
82.50
83.00
83.50
84.00
84.50
85.00
85.50
86.00
86.50
87.00
87.50
88.00
88.50
89.00
89.50
90.00
90.50
91.00
91.50
92.00
…
Non-Monotonic Unit Table
CCCT1A+1B HRSG Total Power
160.00
97.42
257.42
161.00
97.67
258.67
162.00
97.93
259.93
163.00
98.18
261.18
164.00
98.44
262.44
165.00
98.69
263.69
166.00
98.95
264.95
167.00
99.21
266.21
168.00
99.47
267.47
169.00
99.72
268.72
170.00
99.98
269.98
171.00
100.24
271.24
172.00
100.51
272.51
173.00
100.77
273.77
174.00
101.03
275.03
175.00
101.29
276.29
176.00
101.56
277.56
177.00
101.82
278.82
178.00
102.09
280.09
179.00
102.35
281.35
180.00
102.62
282.62
181.00
102.89
283.89
182.00
103.15
285.15
183.00
103.42
286.42
184.00
103.69
287.69
…
…
…
Total Cost
$10,404.37
$10,441.00
$10,477.67
$10,514.38
$10,551.14
$10,587.94
$10,624.77
$10,661.66
$10,698.58
$10,735.55
$10,772.56
$10,809.61
$10,846.70
$10,883.84
$10,921.01
$10,958.24
$10,995.50
$11,032.80
$11,070.15
$11,107.54
$11,144.97
$11,182.45
$11,219.96
$11,257.52
$11,295.12
…
At this point it is possible to search through the tables for the cheapest
combination of loads from the monotonic and non-monotonic unit tables. This
search can be easily conducted using a Visual Basic Macro inside Excel. A
general evaluation of cost can be achieved using the predetermined values in
Appendix Table 9 and Appendix Table 11. A more accurate evaluation of cost
can be calculated from the exact values of the dispatch using Appendix Table 2
and Appendix Table 7. This method may prove too time-consuming to be used
effectively.
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6.4
Appendix D – Unit Commitment Pattern Developed
by Dr. John W. Lamont
A listing of all the possible commitment patterns is shown in below.
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