United States Office of Air Quality cPA-450/3-78-045
Environmental Protection Planning and Standards November 1977
A9ency Research Triangle Park NC 27711
Air
Linear Programming
Derived Optimization
Strategies for Control
of SOX from Coal-Fired
Power Plants
-------
Linear Programming Derived
Optimization Strategies for
Control of SOX from Coal-Fired
Power Plants
by
John Richards, A. Carl Nelson, and Albert Hardy
PEDCo Environmental, Inc.
11499 Chester Road
Cincinnati, Ohio 45246
Contract No. 68-02-1452
Task No. 12
EPA Project Officers: Constancio F. Miranda and Raymond M. Morrison
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air, Noise, and Radiation
Office of Air Quality Planning and Standards
Research Triangle Park, North Carolina 27711
November 1977 u.S. EiwifMtmenta! Protection Afwiey
Jegten 5, Library (PL-12J)
-------
ACKNOWLEDGEMENT
PEDCo Environmental, Inc. expresses appreciation to
Rayburn Morrison and Constancio Miranda of the Energy
Strategies Branch, Environmental Protection Agency, for
their active interest in the project, timely suggestions,
and review of the report. Appreciation is also expressed to
other reviewers from the EPA, industry and trade associ-
ations.
The PEDCo Project Director was Mr. Timothy Devitt and
the Project Manager was Mr. Carl Nelson. Report authors
were Mr. John Richards, Mr. Carl Nelson, and Mr. Albert
Hardy of System Sciences, Inc., under subcontract with
PEDCo. Consulting and technical support was provided by Mr.
Edward Zawadzki, Mr. Yatendra Shah and Dr. Gerald Isaacs.
Mr. Albert Hardy provided the computational support. This
study involved the development of a computational approach
consistent with an existing mathematical programming system,
preparation of data in proper format and the execution of
the program.
-------
CONTENTS
Page
LIST OF FIGURES iii
LIST OF TABLES iv
SUMMARY vi
1.0 INTRODUCTION !_!
1.1 Multi-Stream Coal Cleaning for SO 1-1
Control 2
1.2 Report Organization 1-1
1.3 Limitations of the Approach 1-2
2.0 PROBLEM DESCRIPTION 2-1
3.0 SINGLE PLANT SCENARIO 3-1
3.1 Explanation of Computer Output 3-4
3.2 Sensitivity Analysis 3-15
4.0 MULTIPLE PLANT SCENARIOS 4-1
4.1 Small Network Scenario 4-3
4.2 Large Network Example 4-12
5.0 APPLICATION OF LINEAR PROGRAMMING TECHNIQUES 5-1
5.1 Equipment Cost and Performance 5-2
Estimates
5.2 Power Generation Costs 5-17
5.3 Compilation of Input Data For Three 5-20
Plant Scenario
5.4 Compilation of Input Data For Seven 5-20
Plant Scenario
6.0 CONCLUSIONS AND RECOMMENDATIONS 6-1
7.0 REFERENCES 7_!
8.0 GLOSSARY Q.!
•APPENDIX A - SELECTED COMPUTER RESULTS A-l
APPENDIX B - STATEMENT OF THE PROBLEM IN B-l
MATHEMATICAL TERMS
11
-------
LIST OF FIGURES
No. Page
2-1 Linear Programming Problem 2-3
2-2 Transshipment Model for P Demand Points - 2-4
N Supply Points
3-1 Optimal Solution for Single Plant Scenario - 3-14
Case 1
4-1 Base Case; 63% Load (Non Optimized) 4-8
4-2 LP Results Using Combined Strategy 4-9
4-3 LP Results or LP Coal Distribution for 4-17
Network 1, 5 Plants
4-4 LP Results for Network 2, 2 Plants 4-19
4-5 LP Results for Combined Network 4-20
5-1 Simplified Coal Cleaning Plant Flowsheet 5-4
5-2 Costs for a Typical Coal Cleaning Plant 5-8
5-3 Estimated Cost for a Flue Gas Desulfurization 5-14
System, Limestone Scrubbing System
B-l Three Mine, Two Plant Network B-3
111
-------
LIST OF TABLES
No. Page
3-1 Coal Characteristics and Costs 3-2
3-2 Computation of Coefficients in the Objective 3-6
Function
3-3 Coal Characteristics for the Cleaned Coal 3-7
3-4 Computation of Coeffic. nts in SO- Regulation 3-9
Constraints
3-5 Computer Printout of Optimal LP Solution - 3-12
One Plant Scenario
3-6 Parameter Changes Made in Single Plant Scenario 3-16
4-1 Small Network Descriptive Data 4-3
4-2 Quality and Washability Characteristics of 4-4
Coal Supplies
4-3 Estimated Annualized Cost Data, $/MM Btu 4-6
4-4 Capital and Annualized Costs for the Base Case 4-10
(Non LP Optimized)
4-5 Comparison of LP Model Results and Base Case 4-11
Costs for Higher Coal Costs
4-6 Comparison of LP Model Results and Base Case 4-13
Costs With all SO? Regulations at 1.8 Ib SO-/
MM Btu
4-7 Large Network Descriptive Data 4-13
4-8 Quality and Costs of Coal Supplies 4-14
4-9 Capital and Annualized Costs for LP Combined 4-16
Strategy
5-1 General Cost Factors 5-3
5-2 Coal Cleaning Strategies 5-6
5-3 Effect of Retrofit Difficulty on FGD Capital 5-11
Cost
5-4 Specific Cost Factors and Design Assumptions 5-13
Used in FGD Cost Estimation Models
IV
-------
LIST OF TABLES (continued)
No. Page
5-5 Influence of Process Specific and Site Specific 5-15
Factors on FGD Costs
5-6 Capital Costs of Electrostatic Precipitators, 5-16
$106
5-7 Annualized Cost for Electrostatic Precipitators, 5-17
mills/kWh
5-8 Fuel Transportation Costs 5-18
5-9 Input Cost Data Matrix For 3-Plant Scenario 5-21
5-10 Computation of Coefficients in S0~ Regulation 5-23
Constraints for 3-Plant Scenario
5-11 Transportation Costs and Distances for 7-Plant 5-26
Scenario
5-12 Transportation Costs, $/MM Btu for 7-Plant 5-27
Scenario
5-13 Cost Data for 7-Plant Scenario 5-28
5-14 Coal Characteristics - 7-Plant Scenario 5-29
B-l Arcs and Cost Components Allocated to Flows B-6
v
-------
SUMMARY
A linear programming (LP) technique has been used to
determine a least cost S02 control strategy for a network of
coal-fired power plants. Tl general strategy consists of
multi-stream coal cleaning in conjunction with the use of
low sulfur coal supplies and flue gas desulfurization. The
use of linear programming is demonstrated to be a convenient
mechanism to rapidly identify the most economically attractive
fuel redistribution/SO2 control options. The structure of
the technique is a transshipment model. The simplex algorithm
is used to determine the minimum of an objective function
which includes the major cost components of interest. Non-
linear cost functions are handled with a heuristic approach.
The LP results for two hypothetical power plant networks
suggest that the use of flue gas desulfurization and coal
cleaning as a combined strategy yields a reduction in S09
compliance costs if moderate capital costs can be tolerated.
For a 3 plant system with a combined capacity of 1150 MW,
the LP solution resulted in an incremental capital cost of
36.5 million and an 11 percent reduction in total annualized
costs. Annualized costs for a large network of 7 plants
(combined capacity 12,970 MW) could potentially be reduced
4.5 percent. This saving results from a 30 percent reduction
in annualized S02 compliance costs.
Parametric studies were made to determine the impact of
changes in cost coefficients and in emission regulations on
the optimum solution. Generally the control strategy and
costs were not overly sensitive to changes within a reasonable
range.
VI
-------
General procedures for the preparation of input data
and for the adjustment of nonlinear cost functions are
provided to assist potential users of LP models on actual
networks. Recommendations have been presented to extend and
refine the application of linear programming techniques to
actual networks.
VII
------- OCR error (C:\Conversion\JobRoot\0000062N\tiff\2000ME1Z.tif): Unspecified error
-------
are determined for a 3 plant network and a 7 plant network
as described in Section 4. The sensitivity of the 3 plant
optimal solutions to various cost factors or technical
constraints is discussed. The impact of each optimum solu-
tion on capital requirements is also reviewed. Selected LP
computer runs are provided in Appendix A. A mathematical
description of the LP appro*-h is discussed in some detail
in Appendix B.
It is assumed throughout this report that a 2.0 Ib
S02/MM Btu coal will be in compliance with an emission
regulation of 2.0 Ib S02/MM Btu. For example, if a monthly
averaging time is being utilized and, if due to the varia-
tion of these monthly averages, a coal with an average of
1.7 Ib S02/MM Btu is required for compliance with the regu-
lation, then this complying coal will be designated as 2 Ib
S02/MM Btu coal. With this assumption, there is no need to
extend the discussion to consider the variability of sulfur
content and its implication on meeting emission regulations.
The inclusion of sulfur variability would add another dimen-
sion to the scope of this study.
The utilization of LP models is discussed in Section 5
The type and format of input data necessary for a run is
presented. The use of iteration procedures to arrive at a
technically feasible and economically optimal solution is
also discussed.
1.3 LIMITATIONS OF THE APPROACH
There are several practical limitations to the use of
linear programming models in this study for evaluating
multi-stream coal cleaning or other component processes
involved in power generation. Capital costs and total
annualized costs were not optimized simultaneously. The
total annualized cost may be minimized subject to a constraint
1-2
-------
on capital cost or multiple objective functions may be
optimized by a succession of linear programming problems.
The models used in this report are based on annualized costs
and are useful only in systems which can tolerate moderate
capital expenses in order to minimize the overall annualized
costs. In certain cases a utility may not have access to
the necessary capital for an "optimum" strategy.
The linear programming models herein are limited to the
extent that site specific factors are taken into account.
While the approach used in this report contains some flex-
ibility to incorporate these factors, the solutions are not
strictly applicable to a specific boiler or power plant
network. A slight modification in the network fuel supply/
pollution control strategy in a specific system may be
necessary to accomodate special conditions such as water
availability, power demand patterns, and control equipment
retrofit problems.
There are a large number of commercially available FGD
processes and coal cleaning processes which could be used in
a combined strategies approach. Selection of the specific
design and the specific operational conditions is a distinct
optimization problem. Optimization of component processes
within the overall problem is not considered in this study.
LP as used in this project is useful in indicating the
general region of the optimum solution but does not yield
specific information about any component processes. Optim-
ization of component processes may necessitate a rerun of
the LP as a result, for example, of either a change in the
coal characteristics or the cost of cleaning the coal in the
case of a proposed cleaning process.
1-3
-------
2.0 PROBLEM DESCRIPTION
Established techniques for S0? control at coal fired
industrial and utility boilers consist of either utilization
of naturally occurring low sulfur coal or utilization of one
of the FGD processes. With the increasing costs of low
sulfur coal supplies (particularly western coals) and the
high cost of desulfurization, S02 compliance costs are in-
creasingly important components of overall power generation
cost. It has been proposed that use of physical coal cleaning
in conjunction with flue gas desulfurization and/or natural
low sulfur fuels could yield a substantial reduction of SO-
12
compliance costs for a network of boilers. ' This combined
strategy would emphasize coal cleaning and fuel supply
redistribution with minimum reliance on desulfurization
systems and/or low sulfur coal supplies. Analysis of combined
strategy options are facilitated by using linear programming
methods.
The economics of a combined strategy partially depends
on the effective utilization of "waste coal" at a cleaning
plant. At the present time, coal is generally cleaned only
to the extent necessary to achieve acceptable ash content
without excessive loss of Btu's to the waste stream(s). The
output streams from conventional single-stream plants usually
consist of the following:
1. A "clean" stream containing 80 to 95 percent of
the total Btu's and 70 to 90 percent of the total
input weight. The ash content is generally 50-75
percent of that for raw coal, while the sulfur
content is 60 to 90 percent of that for raw coal.
2-1
-------
2. A "waste" product containing the remainder of the
input Btu's and material. The sulfur content and
ash content can be exceptionally high (20 to 100
Ib S02/MM Btu and 40 to 80 percent ash).
By cleaning at lower specific gravities (1.3 to 1.6 instead
of 1.7 to 1.9) it is possible to substantially modify the
distribution of Btu's, material weight, sulfur, and ash in a
manner which makes multi-product physical coal cleaning more
amenable to a combined strategy approach. Between 10 and 60
percent of the carbonaceous matter and a similar fraction of
the total input material weight can be distributed into a
middling product stream. The "reject" stream still contains
very high levels of sulfur and ash. The reject stream
typically has too high of a sulfur and ash content and too
low of a Btu content to justify utilization. The avail-
ability of two coal streams (the clean and middling streams)
with moderate stilfur levels minimizes Btu loss in cleaning
and creates a large number of fuel supply options.
The generation of multiple coal streams of varying
qualities in addition to the complexity already involved in
selection of FGD or low sulfur coal supplies results in a
very large number of possible SO- control options for a
network of boilers. Linear programming techniques provide a
convenient mechanism to rapidly identify the most attractive
approaches. The structure of the problem is described by
Figure 2-1.
The boilers, P in number, are to be supplied with
sufficient coal to meet their hourly demands by their cus-
tomers. In order to comply with the emission regulations
they may use coal directly from a supplier, from a physical
coal cleaning plant (CCP) and/or utilize an FGD system. The
number of coal cleaning plants will be some number between 0
and N, the number of suppliers. The number of FGD systems
2-2
-------
PROJECT SCOPE-NETWORK
Boilers (P;
FGD facilities
(O to P)
Purchased power
PROJECT SCOPE-FUEL
Supply
Coal supplies (N)
Coal cleaning (O to N)
Coal streams (N to 4N)
TECHNICAL CONSIDERATIONS
Emission limits
Fuel requirements
Derating
Load constraints
ECONOMIC CONSIDERATIONS
Fuel costs
FGD annualized costs
CCP annualized costs
Coal transportation costs
ESP modification costs
Boiler maintenance costs
Boiler operating costs
Purchased power costs
Optimal
solution
(annualized
\cost basis)
Figure 2-1. Linear programming problem
2-3
-------
will be less than or equal to P, the number of boilers.
PEDCo Environmental, Inc. and its subcontractor,
Systems Sciences, Inc., have selected a transshipment model
and have used the IBM-MPS linear programming system in
obtaining an optimal solution.3 This technique utilizes the
SIMPLEX algorithm to derive the minimum and/or maximum of an
objective function within a regie defined by a set of con-
straints. The objective function basically defines a
problem of shipping a commodix./ (coal) from multiple supply
points through a network of intermediate points to one or
more demand points. Each arc between two points can be
associated with a cost and/or a constraint on the flow
between the points. An illustration of a relatively simple
case involving P boilers and IN coal suppliers (each with
physical coal cleaning plants) is shown in Figure 2-2.
(MINES)
SUPPLY
POINTS
COAL CLEANING
PLANTS
COAL
STREAMS
(BOILERS)
DEMAND
POINTS
Figure 2-2. Transshipment model for P demand points -
N supply points
There are other LP systems, e.g., the FMPS for use on the
UNIVAC-1110 computer system.
2-4
-------
The coal from any mine may be sent directly to any of the
P boilers or it may first be cleaned. If cleaned, it is sep-
arated into one of three coal streams, clean, middling and re-
ject, and from there is sent to any of the P boilers. The
reject stream is not used in any of the boilers.
The figure shows several of the possible paths of coal
from mine 1. The coal is sent from the mine to any boiler
or to the coal cleaning plant where the paths from coal
stream C are indicated. All other mines and coal cleaning
plants/streams have similar coal flows emanating from them.
Each boiler is divided into one with anu one without
an FGD system to permit the possibility that all, part, or
none of the flue gases may be cleaned.
Generalized equations for the objective function 2 and
constraint equations are presented in equations 1 and 2-1
through 2-M.
Z = c^ + C2x2 + . . . + CNXN Equation 1
allxl + a!2x2 + ' ' ' + aiNXNi bx Equation 2-1
+ a22x2 + . • • + a2NxNj>| b
321X1 + a22X2 •*••••+ ax '>_[ b Equation 2-2
aM!Xl + aM2X2 + • ' ' + aMNxNjl j *>M Equation 2-M
2-5
-------
The coefficients denoted by a's in equations 2-1 through 2-M
are determined by the physical characteristics of the net-
work. Constraint equations are used to define fuel require-
ments, SC>2 emission limits, mine capacities, and other
necessary restrictions. The symbols, x,, x , ... , x ,
represent coal-flow variables in iillion Btu, (MM Btu); for
example, x.^ might be the flow of coal from the first mine
(or source) to the first boil r. The objective function Z
is the total annualized cost for the examples in this report.
The coefficients denoted by c's in equation 1 are the input
cost coefficients. Each coefficient corresponds to a sum of
fuel, transportation, control system, and other pertinent
costs, and all are on a consistent basis ($ per million Btu).
The accuracy of these input cost coefficients determines the
overall accuracy of the linear programming results. Esti-
mation of input cost data for FGD systems, coal cleaning
plants, electrostatic precipitator modifications, and other
costs is described in Section 5. The major cost components
in the linear programming model are:
1. Coal costs (@ source).
2. Fuel transportation cost.
3. Flue gas desulfurization annualized cost.
4. Coal cleaning plant annualized cost.
5. Modified electrostatic precipitator annualized
cost.
6. Boiler operating and maintenance cost.
7. Purchased power cost.
Linear programming techniques require that the objec-
tive function and all of the constraint equations be linear
functions of the structural variables. This complicates the
computation procedure since some of the cost equations are
nonlinear functions of coal throughput. For example, general
annualized cost for FGD systems and physical coal cleaning
plants can be roughly approximated by an equation of the
2-6
-------
form,
c = ax°'4 Equation 2-3
where
c = Annualized cost, $.
a = Cost coefficient, $/MM Btu.
x = Coal throughput, MM Btu.
Furthermore, there are several other nonlinearities
inherent in coal combustion and pollution control. These
include derating requirements, the cost for ESP modification
as a function of average sulfur content, and the boiler
maintenance costs as a function of ash properties and
other factors. An iterative approach was used in this study
in order to consider these nonlinearities. This is dis-
cussed in detail in Section 5.
2-7
-------
3.0 SINGLE PLANT SCENARIO
A single plant example is provided to illustrate the
approach for obtaining an optimal solution. The following
plant characteristics were assumed, based on an actual
Plant- Boiler 1 Boiler 2
Maximum continuous capacity, MW 360 900
Capacity factor, % 37 65
Boiler remaining life, years 12 19
Fuel consumption/hour, tons/hour 192.2 480.6
Flue gas rate, cfm Q 1,152,000 2,790,000
Flue gas temperature, F 300 300
Estimated duct run, ft. - 800
Heating value of fuel, Btu/unit 10,300 10,300
Efficiency of FGD system, % - 85
Emission regulation, Ib S02/MM Btu 4 1.8
In many cases the emission regulations of 4 and 1.8 Ib
SO,,/ MM Btu would be the same for two boilers within the
same plant. However, in this example they are assumed to be
different in order to yield a solution which may utilize
more than one source of coal from the four assumed sources
described in Table 3-1. These data are assumed based on
common coal supplies and prevailing costs. The values 4 and
1.8 are changed in later examples in order to determine the
impact on the annualized cost of the fuel, transportation,
and SO_ control.
Using these plant/boiler characteristics a computer
model for flue gas desulfurization was run to estimate the
annualized costs (see Section 5.0). The coal washability
characteristics for the Eastern Midwest Coals, i.e., the
amount of coal in each stream (clean, middling, and residual
or reject), the heating content, Btu/lb, and Ib SO2/MM Btu
3-1
-------
Table 3-1. COAL CHARACTERISTICS AND COSTS'
MINE
SOURCE
1
2
3
4
Source: Region
and Coal Type
Eastern low sulfur
Western low Btu
low sulfur
Western high Btu
low sulfur
Eastern Midwest
high sulfur
GHVb
Btu/lb
12,500
8,150
12,300
12,190
Sulfur
%
0.80
0.50
0.80
3.90
Ib SO /MM
Btu
1.28
1.23
1.30
6.50
Ash
%
12.0
8.0
13.0
14.2
At mine
cost
$/MM Btu
1.60
0.42
0. 97
0. Siu
Transportation
costs
$/MM Btu
0. 35
1.08
0.72
0.15
U)
I
I\J
Coal quality based on Bureau of Mines data; cost data based on typical
costs reported for the respective coal producing regions.
Gross heating value.
-------
for each stream, and the coal cleaning plant design are
briefly described in Section 5. These data are used in a
computer model to estimate the annualized cost of the coal
cleaning plant.
The coal costs and transportation costs are assumed as
given in Table 3-1. These fuel costs are subject to con-
siderable variation and the resulting optimal solutions are
clearly dependent on these assumed costs. However, the
emphasis in this study is on the methodology of the approach
and not on a particular solution for assumed costs. The
costs will be varied to yield the sensitivity of the optimal
solution to these changes.
In the approach used, a coal cleaning plant may be
assumed for each coal source. The coal may be cleaned and
transported to the power plant, or it may be sent directly
from the mine to the power plant without any preparation.
In this particular example, only the Eastern Midwest coal
has the option to be cleaned; i.e., the optimal solution may
select this strategy. In addition the general approach
would select whether or not an FGD system is to be used with
each boiler/plant. To do this, two receptors are assumed
for each boiler, one with and one without an FGD. These two
receptors are then combined into a single boiler with the
appropriate proportion of the flue gases scrubbed in order
to comply with the emission regulations. An FGD system was
arbitrarily restricted to boiler 2 due to the lower emission
regulation of that boiler.
The approach is flexible in that it permits assigning
costs to each phase of the coal production, coal cleaning,
transportation, and flue gas cleaning. It permits the com-
bined use of coal cleaning with FGD or restricts the comb-
ined use by appropriate cost coefficients for a particular
coal stream.
3-3
-------
3.1 EXPLANATION OF COMPUTER OUTPUT
The objective function and constraint (including the
conservation) equations are given in this subsection. The
coal characteristics and costs for this problem are taken
from Table 3-1. The costs for coal cleaning and flue gas
desulfurization are obtained by use of computer models
described in Section 5. The estimated costs are $0.10/MM
Btu for coal cleaning and $0.60/MM Btu for flue gas desulfur-
ization. The washability characteristics are based on
results reported in reference 1 (see Section 5 for further
details on washability).
The statement of the problem is as follows. It is
desired to minimize the total annualized cost by determining
the optimum allocation of the four coals of Table 3-1, and
the use of coal cleaning and FGD systems in order to comply
with the regulations, 4 and 1.8 Ib S02/MM Btu for Boilers 1
and 2, subject to the constraints,
Coal available at each source (mine) <_ 70,000,000 MM
Btu, i.e., there is sufficient coal at each source
(mine) to provide for the operation of both boilers.
Boiler 1 demand <_ 34,690,000 MM Btu per year.
Boiler 2 demand <_ 86,724,000 MM Btu per year.
Plant demand j> 69,206,000 MM Btu per year.
The objective and constraint functions are given below
in the same form as they are used in the computer program
and followed by the derivation of the coefficients in the
equations.
aThe $0.60/MM Btu cost for an FGD system was estimated on
the basis of the size of the FGD system resulting from an
initial run at $0.50/MM Btu.
3-4
-------
Objective Function: (Cost)
Total annualized cost = 2.015 S1B1 + 2.015 S1B2
+ 2.615 S1B2F + 1.630 S2B1 + 1.630 S2B2
+ 2.230 S2B2F 4- 1.755 S3B1 + 1.755 S3B2
+ 2.355 S3B2F + 1.010 S4C + 1.050 S4B1
+ 0.140 S4AB1 + 0.160 S4MB1 + 0.590 S4RB1
+ 1.050 S4B2 + 0.140 S4AB2 + 0.160 S4MB2
+ 0.590 S4RB2 + 1.650 S4B2F -I- 0.740 S4AB2F
+ 0.760 S4MB2F + 1.190 S4RB2F
Equation 3-1
The notation is
S1B1: denotes coal from source 1, SI, to boiler 1, Bl,
S1B2F: denotes coal from source 1 to boiler 2 with
an FGD.
S4C: denotes coal from source 4 to coal cleaning
plant.
S4CA: coal from source 4 to coal cleaning plant (CCP)
and coal clean stream (A)a from the CCP.
S4CM: coal from source 4 to coal cleaning plant (CCP)
and middling stream (M) from the CCP.
S4CR: coal from source 4 to coal cleaning plant (CCP)
and reject stream (R) from the CCP.
S4AB2F: coal from source 4, coal cleaning plant A or
clean stream, to boiler 2 with FGD.
The derivation of the coefficients in the objective
function is shown in Table 3-2. The transportation cost of
the three streams leaving the CCP is determined by the
Btu/lb, and thus increases as the Btu/lb decreases from that
of the clean stream. The coal characteristics for these
three streams are given in Table 3-3. These were calculated
based on float sink data for an Eastern Midwest region mine.
a
In later sections the clean coal is denoted by C and not A.
3-5
-------
Table 3-2. COMPUTATION OF COEFFICIENTS IN THE
OBJECTIVE FUNCTION
Variable
S1B1
S1B2
S1B2F
S2B1
S2B2
S2B2F
S3B1
S3B2
S3B2F
S4C
S4B1
S4AB1
S4MB1
S4RB1
S4B2
S4AB2
S4MB2
S4RB2
S4B2F '
S4AB2F
S4MB2F
S4RB2F
Coal
1.60
1.60
1.60
.42
.42
.42
.97
.97
.97
.90
.90
0
0
0
.90
0
0
0
.90
0
0
0
Clean
0
0
0
0
0
0
0
0
0
.10
0
0
0
0
0
0
0
0
0
0
0
0
Transp
.35
.35
5
1.08
1.08
1.08
.72
.72
.72
.01
.15
.14
.16
.59
.15
.14
.16
.59
.15
.14
.16
.59
FGD
0
0
.60
0
0
.60
0
0
.60
0
0
0
0
0
0
0
0
0
.60
.60
.60
.60
ESP*
.065
.065
.065
.13
.13
.13
.065
.065
.065
0
0
0
0
0
0
0
0
0
0
0
0
0
TOTAL
2.015
2.015
2.615
1.630
1.630
2.230
1.755
1.755
2.355
1.010
1.050
0.140
0.160
0.590
1.050
0.140
0.160
0.590
1.650
0.740
0.760
1.190
Assumed ESP modification costs
3-6
-------
Table 3-3. COAL CHARACTERISTICS FOR THE CLEANED COAL
Clean stream, A
Middling stream, M
Reject stream, R
Raw coal
Ib S02/MM Btu
3.8
8.54
109.00
6.50
Btu/lb
13,358
11,186
3,097
12,190
Ib/coal
100 Ib feed
64.60
30.47
4.93
100.00
% ash
5.9
20.76
78.97
14.2
Thus the transport costs of the three streams are $0.14,
$0.16, and $0.59/MM Btu for the clean, middling, and reject
streams, respectively. The transportation cost for the
clean stream is determined by the product of $0.15 (the
average cost) by 12,190/13,358 = $0.14, for the middling
stream by $0.15 x 12,190/11,186 = $0.16, and for the reject
stream by $0.15 x 12,190/3,097 = $0.59.
Constraint Equations
Mine: (Ml, M2, M3f M4)
The following four constraints state that the coal
supply from each source is less than or equal to 70,000,000
MM Btu, i.e., sufficient coal to meet the plant demand on
the following page.
1. S1B1 + S1B2 + S1B2F <_ 70,000,000 MM Btu
2. S2B1 + S2B2 + S2B2F <_ 70,000,000 MM Btu
3. S3B1 + S3B2 + S3B2F <_ 70,000,000 MM Btu
4. S4C + S4B1 + S4B2 + S4B2F <_ 70,000,000 MM Btu
Equation 3-2
3-7
-------
Boiler: (Bl, B2)
The following two constraints state that the coal con-
sumed by each boiler is not to exceed a specified amount in
MM Btu.
1. S1B1 + S2B1 + S3B1 + S4B1 + S4AB1 + S4MB1
+ S4RB1 £ 34,690,000 MM Btu
2 S1B2 + S1B2F + S2B2 + L2B2F + S3B2 + S3B2F + S4B2
+ S4AB2 + S4MB2 + S4RB2 + S4B2F + S4AB2F
+ S4MB2F + S4RB2F *_ 86,724,000 MM Btu
Equation 3-3
Plant; (PL)
This constraint ensures that the plant meets the total power
demand.
S1B1 + SIB IF + ... + S4RB2F >_ 69,206,000 MM Btu
Equation 3-4
S0_ Emissions Regulation: (EC1, EC2)
These two regulations ensure that each boiler complies
with the sulfur dioxide emission regulations. For each
boiler,
actual Ib SO2/MM Btu - Ib S02/MM Btu allowed by regulation
1 0.
For a boiler with an FGD system with an assumed 85 percent
efficiency, this inequality is
(actual Ib SO2/MM Btu)(0.15) - Ib SO2/MM Btu allowed by
regulation 5 0-
For the actual calculations involved in computing the co-
efficients for these constraints see Table 3-4.
3-8
-------
Table 3-4. COMPUTATION OF COEFFICIENTS IN SO,
4
REGULATION CONSTRAINTS
Variable
S1B1
S2B1
S3B1
S4B1
S4AB1
S4MB1
S4RB1
S1B2
S1B2F
S2B2
S2B2F
S3B2
S3B2F
S4B2
S4AB2F
S4MB2
S4RB2
S4B2F
S4AB2F
S4MB2F
S4RB2F
Actual Lba
S02/MM Btu
1.28
1.23
1.30
6.5
3.8
8.54
109.0
1.28
0.192
1.23
0.185
1.3
0.195
6.5
3.8
8.54
109.00
0.975
0.57
1.28
16.35
Lb SO2/MM Btu
Emission Regulations
4.0
4.0
4.0
4.0
4.0
4.0
4.0
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
Difference
-2.72
-2.77
-2.70
2.5
-0.2
4.54
105.0
-0.52
-1.608
-0.57
-1.615
-0.50
-1.605
4.70
2.0
6.74
107.20
-0.825
-1.23
-0.519
14.55
Multiplied by 0.15 when the variable corresponds to a
boiler utilizing an FGD system to reflect an 85 percent
removal efficiency.
3-9
-------
Boiler 1: - 2.72 S1B1 - 2.77 S2B1 - 2.7 S3B1 + 2.5 S4B1
- 0.2 S4AB1 + 4.54 S4MB1 + 105.0 S4RB1 <_ 0.
Boiler 2: - 0.52 S1B2 - 1.608 S1B2F - 0.57 S2B2
- 1.615 S2B2F - 0.50 S3B2 - 1.605 S3B2F
+ 4.7 S4B2 + 2.0 S4AB2 + 6.74 S4MB2
+ 107.2 S4RB2 - 0.825 S4B2F - 1.23 S4B2
- 0.519 S4MB2F + 14.55 S4RB2F £ 0
Equation 3-5
Washability; (CCA, CCM, CCF
These equalities ensure that the three coal streams
leaving the CCP are in the proper proportions as given in
Table 3-3.a 70.8 percent of the Btus entering the CCP (S4C)
leaves in the clean stream, S4CA; 28.0 percent leaves in the
middling stream, S4CM; and 1.2 percent leaves in the reject
stream, S4CR. These coal cleaning results are based on the
results stated in reference 1.
Clean Stream: S4CA - 0.708 S4C = 0
Middling Stream: S4CM - 0.280 S4C = 0
Reject Stream: S4CR - 0.012 S4C = 0
Equation 3-6
Conservation of coal from CCP: (BTUA, BTUM, BTUR)
These inequalities ensure that the amount of coal leaving
the CCP is no more than the amount that enters the CCP. The
coal in each of the three streams (A, M, and R) can be sent
to any of the three receptors , Boiler 1, 2 or 2F.
Clean: S4AB1 + S4AB2 + S4AB2F - S4CA <_ 0
Middling: S4MB1 + S4MB2 + S4MB2F - S4CM <_ 0
Reject: S4RB1 + S4RB2 + S4RB2F - S4CR <• 0
Equation 3-7
aNote that the distribution values in Table 3.3 provided in
(Ibs coal/100 Ibs feed) have been converted to (Btus/Btus) for
consistency with the LP equations. (i.e. (13,358 Btu/lb x .646
lb coal/lb feed) - (12,190 x.l Ib coal/lb feed = .708)
3-10
-------
The above data, coefficients and variable names, become
inputs to the Mathematical Programming System (MPS) which
solves for the most economical allocation of the coals, CCP,
and FGD systems while complying with the stated constraints.
Two runs were made in order to converge to a solution
for which the estimated costs of coal cleaning and the FGD
systems (both of which depend on throughput) are consistent
with the costs for the sizes of the two systems implied by
the optimal solution. Only the second run is given here.
The computer printout from MPS is in the form of Table
3-5. Section 1 - Rows in the upper portion of the table
give the following information:
!• Constraint name in column 2.
2. Status of the constraint at optimality:
BS: in the basis
EQ: nonbasis fixed
LL: nonbasis, rhs at lower limit
UL: nonbasis, rhs at upper limit
3. Right hand side of constraint at optimality in
column 4
4. In column 5 difference between optimal RHS and
upper/lower bound on RHS as stated in the con-
straints
5. Upper and lower bound on the constraints in
columns 6 and 7
6. Column 8, DUAL ACTIVITY, can be interpreted as
follows:
The values in this column are the increases
(decreases) in the objective function, total
annualized cost, for a unit increase in the
corresponding right-hand side of constraint
If the value is zero as in lines 2 through 5,
an increase in the constraint from say
3-11
-------
Table 3-5. COMPUTER PRINTOUT OF OPTIMAL LP SOLUTION - ONE PLANT SCENARIO
1 -
IOHBEI ...IOH.
AT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
COST
HINE1
HINE2
MINE3
HINE4
BOILEB1
BOILEB2
PLANT
S02A1
S02A2
AH
HH
BH
S4AC
SUHC
S4BC
BS
BS
BS
BS
BS
UL
BS
LL
UL
DL
EQ
EQ.
EG
UL
UL
as
..ACTIVITY...
95220. 40157
69891.62385
3U689.S9961
34516. 15234
69205.75195
SLACK ACTIVITY
.LOWER LIMIT.
.DPPEB LIMIT.
95220.40157-
70000.00000
70000.00000 .
7COOO.OOOCO
108.37615
*
52207.84766
•
•
•
NODE
NONE
NONE
NONE
NONE
NONE
NONE
69205.75195
NONE
NONE
NONE
70000.00000
70000.00000
70000. 00000
70000.00000
34689.59961
86724.00000
NONE
•
•
685.87190-
685.87190
NONE
NONE
NONE
,DUAL ACTIVITY
1.00000
•
•
.30356
1.52806-
.06980
. 14780
1.09246
.84477
1.09246
.84477
U)
SECTION 2 - COLUMNS
NOMBEB .COLUMN. AT
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
S1B1
S1B2
S1B2P
S2B1
S2B2
S2B2F
S3B1
S3B2
S3B2F
S4C
S4CA
S4CM
S4CB
S4B1
S4AB1
S4HB1
S4BB1
S4B2
S4AB2
S4HB2
S4BB2
S4B2F
S4AB2P
S4HB2F
S4BB2P
LL
LL
LL
LL
LL
LL
LL
LL
LL
BS
BS
BS
BS
BS
BS
LL
LL
LL
BS
LL
LL
BS
LL
BS
LL
*
•
«
•
•
•
•
57155.99184
40466.44222
16003.67772
685.87190
2569.59997
32119.99964
8346.44258
10166.03204
•
16003.67772
•
.ACTIVITY ..... INPUT COST..
2.01500
2.01500
2.61500
1.63000
1.630CO
2.23000
1.75500
1.75500
2.35500
1.01000
1.05000
.14600
.16600
.59000
1.05000
. 14000
.16000
.59000
1.65000
.74000
.76000
1.19000
. LOWEB LIMIT.
.UPPER LIMIT.
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
.BEDHCEC -OST.
.60064
.41008
.84927
.21215
.01769
.46309
.34203
.15304
.58972
.10317
6.69460
.21660
•
.47289
14.90618
.12260
1.81244
-------
70 x 10 to 70,000,001 MM Btu results in no
change in cost because there is already slack
activity in each case. However, a unit
increase in the boiler 1 capacity will result
in a decrease of 0.30912 units in the object-
ive function, provided the current optimal
basis remains feasible (see reference 8 for a
discussion of the dual problem).
Section 2 - Columns in the bottom section of the table
give similar information as that in Section 1, but refer
to the variables rather than constraint equations.
1. Variable name in column 2.
2. In column 3 is the status of the variable, i.e.,
BS: variable is in the basis
FR: nonbasis free
LL: variable is nonbasic and at lower bound
UL: variable is nonbasic and at upper bound
3. In the ACTIVITY column is the value of the corres-
ponding variable in the optimal solution. This
variable is the number of Btu in billions (10
millions) per year that are in each stream. Refer
to Figure 3-1 for a schematic representation of
the optimal solution. The flowrate is given above
the arc and the corresponding costs of transship-
ment, $/MM Btu, are given below the arc. The coal
cleaning and FGD costs are shown below the corres-
ponding circles (nodes) of the network.
4. In the last column, column 8, the reduced cost is
given. The usefulness of this value can be appre-
ciated when seen in the following manner.
This is the quantity by which the optimal
solution would increase per unit increase of
the associated variable if that variable were
allowed to enter the basis. (NOTE: Reduced
costs for variables in the basis are zero.)
3-13
-------
CO
I
6.5 Ib Sty
m Btu
$0.90/MM Btu
Optimal annual1zed cost
is $95,027,937
4 Ib S02/MM Btu
Ib S02/MM Btu
$0.60
Figure 3-1. Optimal solution for single plant scenario-case 1.
-------
Since this is a minimization problem, it is
not desired to have an increase, but rather a
decrease, in the optimal solution, and there-
fore, at optimality all reduced costs should
be zero or positive.
If the input costs for any variable are reduced by less
than the corresponding amount in the reduced costs column,
then the current solution will remain optimal. If, however,
any one of the input costs is reduced by more than the
reduced costs, then the current solution will no longer
remain optimal. For example, one solution was obtained with
the input cost for S1B2 reduced by $0.60, which is more than
the associated reduced cost of $0.41008 and the solution was
altered, causing mine 1 (source 1) coal to be used. It is
clear that a very small reduction in the cost of the coal
from source 2 to boiler 2 will alter the solution because
the reduced cost is $0.01769 per million Btu.
This section also gives the allocation of coal from the
source to the coal cleaning plant and ultimately to each
boiler. The only coal allowed to be cleaned is that from
source 4 (Midwest coal). The other coal sources produce low
sulfur coals and do not require cleaning to meet SO,, regula-
tions.
3.2 SENSITIVITY ANALYSIS
From previous discussion it is possible to make several
remarks concerning the sensitivity of the optimal solution
to changes in the costs. However, if the change in any one
of the costs exceeds the corresponding reduced cost in Table
3-2, then the solution is altered. Several runs were made
in which the solution was changed by selected changes in several
parameters. These changes are indicated in Table 3-6. Case
1 represents the baseline case or the solution of the prob-
lem as originally stated in this section. Cases 2 through 7
3-15
-------
Table 3-6. PARAMETER CHANGES MADE IN SINGLE PLANT SCENARIO
Case
no.
Parameter
Change in parameter
Optimum
annualized
cost
1
2
3
4
6
7
Baseline case
Cost of mine 1 coal
Emission regulation on Boiler 1
Emission regulation on Boiler 2
Boiler 2, all flue gases
cleaned, no coal cleaning
FGD
Fuel and transportation costs
No changes
Reduced from $1.60 to $1.00/MM Btu
Reduced from 4 to 3 Ib S02/MM Btu
Reduced from 1.8 to 1.2 Ib S02/MM Btu
also FGD increased to 0.70
FGD used on all flue gases
FGD cost increased to $0.70/MM Btu
No emission regulations, source 4
$ 95,027,937
90,073,457
99,932,620
100,480,811
102,920,308
96,985,723
72,666,040
-------
represent various changes from this case, such as cost of
coal (Case 2), change in emission regulations (Cases 3 and
4), FGD used 100% on Boiler No. 2 (Case 5), change in FGD
annualized cost (Case 6). Case 7 is one with no emission
regulations, i.e., using the least expensive coal and trans-
portation costs. The difference between Case 1 and Case 7
is the annual compliance cost, i.e., $22,361,897. These
parameter changes are useful for relating the cost of com-
pliance with changes in regulations, cost of fuels, and/or
strategies with respect to cleaning coals or flue gases.
3-17
-------
4.0 MULTIPLE PLANT SCENARIOS
The economic potential of combined strategies derived
from linear programing has been evaluated using two hypo-
thetical power plant networks. Both cases closely simulate
actual systems (or parts of systems) so that the LP results
can be compared with real costs. The potential impact of
the combined strategy has been determined by comparison of
the LP least cost solution with the costs for the present
"non-optimized" base case.
The first scenario involves a rather simple network of
3 plants (5 boilers total) with a combined generating capac-
ity of only 1150 megawatts. The primary purpose in studying
this example is to determine if the LP results could be
economically applied to a small system which could not bear
substantial capital expense. The network which serves as
the model for this scenario is subjected to stringent S02
emission regulations which supposedly require either high
quality coal or flue gas desulfurization.
Power plant operators do not have the luxury of chang-
ing the basic SO control strategies on a frequent basis.
JC
Therefore, several studies were done using the three plant
example to determine how LP results compared with non-
optimized base case costs when the relative costs of coal
supplies change or when the SO- regulations are modified.
These analyses address the justified concern of plant
operators that "optimal" approaches adopted in 1977 could
become obsolete in the time necessary to complete system
adjustment.
4-1
-------
The second scenario involves a very large network of 7
plants with a combined generating capacity of 12,970 mega-
watts. Obviously the economics of scale with respect to
FGDs and CCPs have a considerably smaller impact in the
large network example than in the smaller network which is
less than 10% its size. The obj .ctive of this example is to
determine if LP models can be conveniently applied to a
network composed of two sepaxate utility companies. The
equitable distribution of annualized cost savings and cap-
ital cost expenses is a major issue in the large network
analyses. A further objective of this example is to deter-
mine if the complexity of a large network creates problems
in preparing and applying LP models and in the interpreta-
tion of the results.
In both the small and large network scenarios, the cost
data have been inflated to a 1980 basis using a factor of
1.4 applied to 1977 costs. The rationale is that it would
take 2 to 3 years to complete installation of component
systems (FGDs, CCPs, modified ESPs) used in a combined
strategy.
The power demand in both examples has arbitrarily been
assumed to be 63% of rated capacity. This value is based on
a weighted average of 60% during 22 hours and 100% during
the 2 hour peak demand period. Due to the diurnal variation
in power demand, it was necessary to run 2 LP computer runs
for each weighted average LP result. This somewhat cumber-
some procedure is necessary to insure that an optimal solu-
tion based primarily on 60% load still provides compliance
with SO_ regulation at 100% load.
While the scenarios are based on actual systems, it
should be noted that the LP results are not strictly applic-
able.
4-2
-------
No attempt has been made to consider some site specific
factors which conceivably influence cost.
4 1 SMALL NETWORK SCENARIO
The three plant network used in this example represents
the minimum size power plant system expected to benefit from
a linear program derived combined strategy S02 control
approach. With a total generating capacity of 1150 MW, this
network is smaller than many existing single power plants.
The hypothetical network consists of five boilers at
three plants, all located in a hundred mile radius of a
midwestern city. Data concerning this network are provided
in Table 4-1.
Table 4-1. SMALL NETWORK DESCRIPTIVE DATA
Plant
no.
1
2
3
Generating
capacity
(MW)
400
150
600
Coal firing
rate
(MM Btu/hour)
3730
1440
Boiler 1-1190
Boiler 2-2490
Boiler 3-3280^
6960
===== _
Applicable S02
regulations
(Ib S02/MM Btu)
1.2
1.8
1.8
1.8
1.8
Plant
age
(years)
1 -
1
10
10
10
10
All five boilers are designed to burn the locally
available coal with the quality and washability character-
istics indicated in Table 4-2.
Three additional coal supplies were incorporated in the
model to provide maximum flexibility in the control options.
These added supplies represent the three general types of
low sulfur coals. These three additional sources are the
same as those used for the one plant scenario (see Table 3-1)
4.3
-------
Table 4-2. QUALITY AND WASHABILITY CHARACTERISTICS OF COAL SUPPLIES
MINE
SOURCE
A
B
C
** D
I
Type of coal
Eastern low sulfur
Western low sulfur,
low Btu
Western low sulfur,
high Btu
Midwestern coal (raw)
0 OPTION A CLEANING
Float 1.30
Sink 1.30-float 1.9
Sink 1.90
0 OPTION B CLEANING
Float 1.40
Sink 1.40-float 1.9
Sink 1.90
0 OPTION C CLEANING
Float 1.60
Sink 1.60-float 1.9
Sink 1.90
Btu recovery
at cleaning
plant, %
NA
NA
NA
NA
51
48
1
78
21
1
86
13
1
Gross
heating
value
Btu/lb
12,500
8,150
12,300
12,074
13,777
11,359
2,390
13,268
10,250
2,390
12,924
10,224
2,390
Sulfur
content ,
Ib SO2/MM Btu
1.23
1.23
1. 30
6.96
3.68
8.06
121.0
4.43
10.92
121.0
5.47
7.99
121.0
Ash
content
12.0
8.0
13.0
IS.?"-
4.70
17.93
79.1
7.20
24.18
79.1
9.29
26.0
79.1
At mine
cost,b
$/MM Btu
1.60
0.42
0.97
0.70
NA
NA
NA
NA
NA
NA
NA
NA
NA
Transportation
cost
$/MM Btu
0.28
0.92
0.41
0.09
0.08
0.09
0.43
0.08
0.09
0.43
0.08
0.09
0.43
-------
The transporation costs are different due to the differences
in the two networks. The fourth coal supply for each scen-
ario is coal local to that particular network and thus the
two have different characteristics.
Due to the small network fuel demand, it is assumed
that there are no mine production constraints on any of
these supplies. Purchased power was provided whenever
necessary at a rate of $3.00/MM Btu which is roughly equiv-
alent to 30 mill/kWh for a typical boiler with a heat rate
of 10,000 Btu per KWh.
Due to the small plant sizes, the physical coal clean-
ing plant generally was smaller than 200 tons per hour which
is the minimum size limit of the cost estimation models.
Since it is unlikely that a plant smaller than 200 tons per
hour would be built, the capital and annualized costs have
been calculated based on this 200 tons per hour minimum
size. It is assumed that excess production is sold to other
utilities at cost.
4.1.1 Base Case Definition
To measure the potential benefit of combined strategy
control, it is necessary to estimate costs of the present
non-optimized network. For this three plant scenario the
base case simulates an actual existing power plant system.
Prior to 1975 the company operated two plants with a
combined generating capacity of 759 MW. The total power
generating costs using local coal were estimated at 14.7
mills per kWh based on the cost factors shown in Table 4-3.
The promulgation of an SO2 regulation of 1.8 Ib SO?/MM Btu
resulted in fuel switching to a high rank, western low
sulfur coal. At the lower fuel sulfur levels, modification
of the electrostatic precipitator was necessary to maintain
particulate control efficiency. Average network cost increased
4-5
-------
Table 4-3. ESTIMATED ANNUALIZED COST DATA,
. $/MM Btu
1.
2.
3.
4.
Coal Costs
A. Eastern low sulfur coal
B. Western low sulfur, Ic rank coal
C. Western low sulfur, hic,n rank coal
D. Midwestern coala
Transportation Costs
Eastern low sulfur coal
Western low sulfur, low rank coal
Western low sulfur, high rank coal
Midwestern coal (Raw)"
Flue Gas Desulf urization Costs
Plant 1
Plant 2
Plant 3
Electrostatic Precipitation Costs
Plant 1
Plant 2
Plant 3 Boiler 1
Boiler 2
Boiler 3
1975
1.15
0.30
0.70
0.70
0.20
0.66
0.30
0.07
0.43
NA
NA
NA
0.046
0.090
0.046
0.090
1980
1.60
0.42
0.97
0.70
0.28
0.92
0.41
0.09
0.60
0.82
0.53
NA
0.065
0.130
0.065
0.130
aFixed price, long term contract assumed.
"'For cleaned coals.
^Depending on fuel quantity,
4-6
-------
to 18.2 mills per kWh due to the use of low sulfur coal and
to the ESP modification. In 1975 a new power plant went on-
line. This plant was subject to Federal Standards of Per-
formance and a flue gas desulfurization system was neces-
sary. None of the assumed coal supplies had sulfur contents
lower than the 1.2 Ib S02/MM Btu. The FGD system increased
average network power production costs to 18.5 mills/kWh.
This annualized cost represents the base case for 1975
conditions. The base case is illustrated in Figure 4-1.
4.1.2 Combined Strategy Derived by Linear Programming
Approach
The "optimum" strategy determined by the LP model is
illustrated in Figure 4-2. This strategy is limited only to
the extent that each plant must have a load factor between
40 and 80 percent. The strategy uses flue gas scrubbers on
all three boilers of plant 3 and a 100 ton per hour coal
cleaning plant. Incremental capital costs are 36.5 million,
and the network average annualized cost is 19.6 mills/kWh
(1980 cost factors). The annualized costs are 11 percent
lower than the equivalent base case cost of 21.9 mills/kWh
as listed in Table 4-4. Without the load factor constraints
it is probable that the annualized costs could have been
reduced further. The LP solution suggests that with some
moderate capital expense a significant reduction in annua-
lized costs can be achieved.
The sensitivity of the LP results to rising fuel costs
and changing S0? regulations have been evaluated. The
purpose is to determine if annualized costs continue to be
lower than the base case and if any unnecessary capital
costs would have been spent. In certain cases the LP re-
sults have been modified slightly to minimize capital costs.
4-7
-------
B
Western
low sulfur
low rank
oal
2350 MM Btu/hr
Plant 1 with FGD
system; S02 limit
of 1.2 Ib S02/MM Btu
890 MM Btu/hr
Plant 2 with modified
ESP's to utilize low
sulfur coals; SC>2
limit of 1.8 Ib SO2/
MM Btu
4385 MM Btu/hr
Plant 3 with modified
ESP's to utilize low
sulfur coals; SO2
limit of 1.8 Ib S02/
MM Btu
Figure 4-1.
Base case; 63% LOAD
(Non optimized)
4-8
-------
ESTERN LOW
SULFUR, HIGH
BTU COAL
PLANT 1;
400 MW, 1.2 LB
S02/MM BTU S02
REGULATION
PLANT 2;
150 MW, 1.8 LB
S02/MM BTU S02
REGULATION;
MODIFIED ESP FOR
LOW SULFUR COAL
PLANT 3;
600 MW, 1.8 LB
S02/MM BTU S02
REGULATION;
MODIFIED ESP FOR
LOW SULFUR COAL
NOTE: coal flows shown as MM Btu/hour with network at
63 percent load.
Figure 4-2. LP results using combined strategy
4-9
-------
Table 4-4. CAPITAL AND ANNUALIZED COSTS FOR THE
BASE CASE (NON LP OPTIMIZED)
Incremental
capital cost
Annualized cost
Base case 1975
1980 - no change
1980 -
All regs to 1.8 Ib S02/MM Btu
1980 - higher coal cost
(MM)
36.5'
(mills/kWh)
18.5
21.9
21.9
26.0
4.1.2.1 Higher Coal Costs - It is logical that costs of all
coal supplies will continue to increase. For this analysis
it is assumed that 1980 coal costs for the low sulfur coals
increase 50 percent and that the cost of local coal in-
creases 25 percent. Western low sulfur coals in particular
have experienced more rapid price increases than the low
quality coal supplies. This uneven rate of fuel cost esca-
lation should favor use of the combined strategy alternative
identified earlier. Three coal cleaning plant operations
have been included in order to expand the scope of the
analysis.
The results of the LP solution are presented in Table
4-5. The unmodified strategy utilizes new FGD systems at
plants 2 and 3 and a coal cleaning plant between 60 and 125
tons per hour depending on the cleaning option. The an-
nualized costs for all three coal cleaning options are
approximately 30 percent lower than the base case (see Table
4-5.
Due to application of S02 regulation and the use of low
sulfur western coal.
4-lo
-------
Table 4-5. COMPARISON OF LP MODEL RESULTS AND
BASE CASE COSTS FOR HIGHER COAL COSTS
Base case
LP Models
Coal cleaning
to float 1.9
Coal cleaning
to float 1.4
Coal cleaning
to float 1.3
Standard Calculations
Incremental
capital cost
(MM)
50.20
49.86
51.04
Annualized
cost
(mills/kWh)
26.00
20.96
20.84
21.00
Capital Cost Adjustment
Incremental
capital cost
(MM)
38.62
38.68
40.45
Annualized
cost
(mills/kWh)
26.00
20.99
20.86
21.14
A slight adjustment of the LP solution can substan-
tially improve the capital cost requirements. Low sulfur,
high rank western coal has been substituted for the local
high sulfur coal at plant 2, thereby eliminating the small
FGD system at that plant. The annualized cos-t difference
between the optimum and the capital cost adjusted strategies
is insignificant.
The results indicate the optimal combined strategy
would be more economical than the base case if the coal
costs increased as assumed. A different result would occur
in the improbable event that the high sulfur coal prices
increased faster than that of the low sulfur coals.
4.1.2.2 Relaxation of SO^ Standards - The relaxation of SO-
regulations in one or more of the plants is improbable;
4-11
-------
nevertheless, this could make a previously attractive com-
bined strategy approach uneconomical. To test the impact of
a regulatory change on LP solution costs, the LP solution
and base case costs have been recalculated assuming the
regulatory requirement on plant 1 changes from 1.2 Ib SO^/MM
Btu to 1.8 Ib 50,,/MM Btu. While this appears to be only a
modest relaxation of the str ^dard, it allows use of low
sulfur coals at plant 1 without any coal cleaning or flue
gas scrubbing.
The results are presented in Table 4-6. It is apparent
that the LP solution appears relatively stable to slight
relaxation of the S02 standards. If the regulation limits
were increased to 3 or 4 Ib SO2/MM Btu, the FGD system at
plant 3 would not be economical.
4.2 LARGE NETWORK EXAMPLE
A seven plant network with a combined generating capac-
ity of 12,970 MW was used to represent a large power plant
system. The plants and coal supplies used in this scenario
are provided in Table 4-7. It is assumed that all boilers
are designed to burn Eastern Midwest Region coals. Six
typical coal sources with various cleanability properties
were selected along with the three low sulfur coal supplies
used in the small network scenario. Coal quality and cost
data are presented in Table 4-8.
Due to the large network fuel demand, it has been
assumed that each coal source can supply no more than 20
percent of the total fuel demand. Coal cleaning plants have
been allowed for Eastern Midwest coal sources numbered 1
through 5, but not for mine no. 6, due to the low sulfur
content. Cleanability data are based on tests of TVA sup-
plied coal samples. Purchased power was provided whenever
necessary at a rate of $3.00/MM Btu, which is roughly
4-12
-------
Table 4-6. COMPARISON OF LP MODEL RESULTS AND BASE CASE
COSTS WITH ALL S02 REGULATIONS AT 1.8 Ib S02/MM Btu
Base Case
LP Models
Minimum cleaning
Moderate cleaning
Intense cleaning
Incremental
capital cost
(MM)
39.3
41.0
40.5
Annualized
Cost
(mills/kWh)
21.9
19.5
19.4
19.5
Table 4-7. LARGE NETWORK DESCRIPTIVE DATA
Plant
number
1
2
3
4
5
6
7
Utility3
company
1
1
1
1
1
2
2
Generating
capacity
(MW)
1750
2560
2600
990
1700
1400
1980
Coal firing
rate
(MM Btu/hr)
1.75 x ioj
2.56 x ioj
2.60 x 10*
9.90 x 10^
1.70 x ioj
1.40 x ioj
1.98 x 10*
Applicable S02
regulation
(Ib S02/MM Btu)
1.2
5.2
5.0
4.0
1.2
4.0
1.2
Plant
age
(years)
10
10
10
10
10
10
10
aThe plants are arbitrarily assigned to two different utility
companies in order to consider the problem of suboptimization
of the individual networks and to compare these results with
those obtained by optimization of the total system of both
networks.
4-13
-------
Table 4-8. QUALITY AND COSTS OF COAL SUPPLIES
Type of coal
Eastern low sulfur
Western low sulfur,
low Btu
Western low sulfur,
high Btu
Eastern Midwest No. 1
Eastern Midwest No. 2
Eastern Midwest No. 3
Eastern Midwest No. 4
Eastern Midwest No. 5
Eastern Midwest No. 6
Gross
heating
value
(Btu/lb)
12,500
8,150
12,300
12,074
10,955
10,502
11,502
10,971
11,169
Sulfur content
(Ib S02/MM Btu)
1.28
1.23
1.30
6.96
5.64
8.10
6.21
7.72
1.71
Ash
content
(%)
12.0
8.0
13.0
18.
20.9
18.1
17.3
21.9
15.0
At mine
cost
($/MM Btu)
1.60
0.42
0.97
0.70
0.70
0.70
0.70
0.70
1.30
aThe costs used in this report are not based on actual coal contracts.
-------
equivalent to 30 mills/kWh for a typical boiler with a heat
rate of 10,000 Btu per kWh.
4.2.1 Base Case Definition
The estimated costs from the LP solution are compared
with those for a non-optimized system. It has been assumed
that all plants presently utilize one or more of the Eastern
Midwest Region coals. Fuel distribution is allowed, how-
ever, the assumption of equal costs for all high sulfur
midwestern coals reduces the importance of redistribution.
The base case involves the addition of FGD systems, wherever
necessary, in order to comply with S02 emission regulations.
Coal cleaning is not utilized in the base case calculations.
The capital and annualized costs for the base case
control approach are summarized in Table 4-9. All costs are
escalated by a factor of 1.4 to approximate 1980 costs.
4.2.2 Linear Program Derived Combined Strategy
The "optimum" strategy has been identified for each
power plant network separately and for the total seven plant
network. As indicated in Table 4-9, there is a 4.5 percent
reduction in the complete network annualized costs and a 20
percent reduction in capital costs. This results from a
decrease in the number of FGD units and from the use of coal
cleaning on all major coal supplies. While the 4.5 percent
decrease in annualized cost does not appear to be large, it
represents a 30 percent reduction in the annualized SO2
control cost (FGDs, CCPs and ESPs). These results for
the seven plant system suggest that the LP model is useful
in identifying optional S02 control strategies for a large,
complex power plant-fuel supply system.
The LP models for the individual five- and two-plant
networks indicate large differences in the capital and
annualized costs. As shown in Figure 4-3, the strategy for
4-15
-------
Table 4-9. CAPITAL AND ANNUALIZED COSTS FOR
LP COMBINED STRATEGY
Capital Costs (106$)
Network 1
Network 2
Total system
Annualized Costs (mills/kWh)
Network 1
Network 2
Total system
Base
case
N.D.
N.D.
184.0
N.D.
N.D.
16.48
Combined
strategy
83.90
91.30
141.40
15.47
17.50
15.77
Combined strategy
with less
restrictive SO2
limits at plants
1, 5, and 7a
N.D.
N.D.
122.8
N.D.
N.D.
15.52
Combined strategy
with more
restrictive SO2
limits at plants
2 and 3
N.D.
N.D.
191.5
N.D.
N.D.
16.21
!
H
CT\
N.D. = Not determined.
^0 regulations changed from 1.2 to 1.8 Ib S02/MM Btu.
3S02 regulations changed from 5.2 at plant 2 and 5.0 at
plant 3 to 4.0 Ib S02/MM Btu at each plant.
-------
MINE
PLANT
13122 TO PIT B
6865 TO PIT 5
DC) 16492 TO PLT 3
2515 TO PLT 2
T5563 TO PLT 3
EC H 9139 TO PLT 1
(1137 TO PLT 5
[2976 TO PLT 1 FGD
[ 172 TO PLT 4
(6182 TO PLT 2
fa?) TO PLT 3
(8127 TO PLT 5 FGD
J871 TO PLT 5 FGD
|588 TO PLT 4
[15540 TO PLT 2
[ 723 TO PLT 3
[2625 TO PLT 2
) 140 TO PLT 1 FGD
13122 FROM B[ 1
2976 FROM EM
140 FROM GM
2515 FROM Of.
6182 FRCM FC
15540 FROM GC
2625 FROM GM
16492 FROM DC
5563 FROM E
3221 FROM FO
723 FROM GC
9139 FROM EC
172 FROM EM
588 FROM FM
1137 FROM
6865 FROM
8127
871
FROM FC
FROM FM
Figure 4-3.
LP results or LP coal distribution for network 1, 5 plants.
Flows are in MM Btu/hour.
4-17
-------
network 1 involves cleaning four of the Eastern Midwest
coals. Extensive fuel redistribution is done to reduce loads
on the plants subject to the most stringent S02 regulations.
While the LP program indicated that FGD would still be the
most economical control technique for the "peaking units",
use of FGD for such service was not considered realistic.
Therefore, low sulfur western (high Btu) was substituted for
FGD's at a slight cost penally. This substantially reduced
the capital cost impact of the LP strategy. The strategy
for network 1 involves FGD systems at two plants and exten-
sive cleaning of three Eastern Midwest coals.
Despite the much smaller size of network 2 compared
with network 1 (3380 MW versus 9590 MW) the capital costs
for SO2 compliance systems at network 2 exceed those for
network 1. Consequently, the annualized cost for network 2
is 13 percent higher than for network 1. The high cost for
S02 control at network 2 is primarily due to the lower
average sulfur limits. The weighted average sulfur dioxide
regulation for network 2 is only 2.35 Ib/MM Btu compared
with 3.60 Ib/MM Btu for network 1. See Figure 4-4 for
details.
The LP solution for the complete seven plant network
(see Figure 4-5) yields substantially lower capital costs
than those for either the base case or the LP solutions for
the individual networks. This economy results from more
efficient fuel redistribution which allows deletion of an
FGD system on plant 6. Savings also result from the sharing
of coal cleaning plants. With the LP approach, both utility
companies in this hypothetical problem should realize a
reduction in capital costs for S02 control. Unfortunately,
the changes in annualized cost are not equitable. As shown
in Table 4-9, the total cost for network 2 decreases sub-
4-18
-------
MINE
PLANT
[1561 TO PLT 6
(5238 TO PLT 7
5841 TO PLT 7 FGD
DM) 891 TO PLT 7 FGD
[3989 TO PLT 6
0621 TO PLT 7
1115 TO PLT 7 FGD
("2689 TO PLT 6
[3519 TO PLT 7
517 TO PLT 7 FGD
5760 TO PLT 6
GM) 979 TO PLT 7 FGD
1561 FROM C
3989 FROM EC
2689 FROM FC
5760 FROM GC
5238 FROM C
1621 FROM EC
3519 FROM FC
5841 FROM DC
891 FROM DM
1115 FROM EM
517 FROM FM
979 FROM GM
Figure 4-4. LP results for network 2, 2 plants
Flows are in MM Btu/hour.
4-19
-------
MINE
7907 TO PIT 1
18958 TO PIT 7
PLANT
7907 FROM B
2015 FROM
2766 FROP EM
1067 FROM FM
3744 FROM GM
DC i)l3578 TO PLT 2
" 8755 TO PLT 3
[2015 TO PLT 1 FED
11391 TO PLT 2
f 3315 TO PLT 3
\ 8102 TO PLT 4
\2332 TO PLT 5
<6860 TO PLT 6
( 841 TO PLT 7
[2766 TO PLT 1 FGD
(1498 TO PLT 4
f9678 TO PLT 3
(14059 TO PLT 5 FGD
fl067 TO PLT 1 FGD
< 301 TO PLT 4
(_608 TO PLT 5 FGD
\10640 TO PLT 2
< 4251 TO PLT 3
(_7140 TO PLT 6
3744 TO PLT 1 FGD
13578 FROM DC
1391 FROM DM
10630 FROM CC
8755 FROM DC
3315 FROM EC I
9678 FROM FC(
4251 FROM GC
8102 FROM ECl
1498 FROM EM
301 FROM FM
2332 FROM EC
14059 FROM FCi
608 FROM FMl
6860 FROM
7140 FROM
EC]
GCJ
18958 FROM C ( 7
841 FROM EC
Figure 4-5.
LP results for combined network.
Flows are in MM Btu/hour.
4-20
-------
stantially (10%), while costs for network 1 increase slightly
(2%) .
The LP results for the complete seven plant network are
relatively insensitive to minor changes in S0? regulatory
requirements. A relaxation of the 1.2 Ib SO /MM Btu limits
at plants 1, 5, and 7 would not change the basic control
approach discussed above. An FGD would continue to be
necessary at plant 7. The only change would be decreased
dependence on the coal cleaning plants, one of which could
be eliminated entirely. Due to the deletion of the CCP at
mine 1 (Eastern Midwest Region) and a slight size reduction
at the other CCPs, there is a $18.6 million capital cost
decrease. A 2 percent reduction in annualized cost is
possible with the less stringent regulations. A tighter
constraint (4.0 Ib S02/MM Btu) on plants 2 and 3, which
presently are subject to 5.2 and 5.0 Ib S02/MM Btu, re-
spectively, has a contrary result. With this change, new
FGD systems are required at plants 2 and 6. The capital
costs for the entire system increase $50.1 million, due
primarily to this regulation change. It is uncertain
whether network 2 could justify its share of this increase,
which was necessitated by regulatory changes applying only
to network 1. Despite this potential legal problem, the
average annualized cost remains below that for the non-
optimized base case.
While the application of LP derived strategies appears
to have considerable potential in reducing SO_ compliance
costs for large networks or combinations of moderately sized
networks, certain possible legal problems may complicate
acceptance by regulatory commissions. As discussed above,
there can be situations in which the average power pro-
duction cost increase slightly for one member while it
4-21
-------
decreases for another. Furthermore, capital cost may not be
equitably distributed among the member utilities. Both
problems would complicate rate determination for each sepa-
rate utility.
4-22
-------
5.0 APPLICATION OF LINEAR PROGRAMMING TECHNIQUES
The general procedures necessary to prepare the LP
program input data and to adjust nonlinear cost factors are
presented in this section. The purpose is to assist poten-
tial users in the development of LP models specific to
actual power plant networks. It is assumed that source
operators have accurate estimates of fuel costs, boiler
ooeration and maintenance costs, and purchased oower costs.
Therefore, these three cost components are not discussed in
detail. Emphasis is placed on estimating the performance
and costs of flue gas desulfurization systems, coal cleaning
plants, and electrostatic precipitators. A set of typical
cost estimates is provided for_ all three systems9. Use of
such generalized values is a defensible shortcut since
experience with the multiple plant scenarios indicates that
the LP solution is much more sensitive to fuel cost and
quality than to FGD, CCP, Or ESP costs. Relative to fuel
prices, the equipment associated costs vary over a limited
range.
The FGD, CCP and ESP cost coefficients are inherently
nonlinear functions of the plant size. A heuristic approach
is provided to insure that the input cost coefficients for
these three components and the cost implied by the plant
size of the LP solution are compatible.
This section stops short of a complete user's manual.
Guidance is provided with respect to compiling input data
matrices and to managing nonlinear functions. The user
should consult the programming manual of the type of LP
It should be noted that the generalized results were devel-
oped using the same computerized cost models used in the
multiple plant scenarios; nevertheless, cost values may
differ slightly due to NETWORK specific assumptions employed
5-1
-------
program selected (e.g. MPS, FMPS) for details concerning the
program set-up and operation.
5.1 EQUIPMENT COST AND PERFORMANCE ESTIMATES
The engineering and cost data generally needed to
estimate the LP input data of FGD, ESP and CCP systems are
discussed in the following three subsections. The user has
the option of utilizing his r-'n cost estimating procedures
for this data or the generalized results provided which are
based on PEDCo computerized procedures. Standard cost
factors used in all three programs are identified in Table
5-1.
5.1.1 Coal Washability and Cleaning Plant Costs
5.1.1.1 Washability - Coal washability characteristics are
major variables in the cost optimization study. Accurate
prediction of clean stream and middling stream coal quality
is necessary in the derivation of representative LP models.
The data requirements for evaluating coal washability
potential are identified by reviewing typical coal cleaning
plant design.
Raw coal received at the CCP is first subjected to one
or two stage crushing with subsequent size segregation into
coarse, intermediate, and fine size fractions. Typical coal
sizes in these three groups are respectively 1 1/2" by 3/8",
minus 3/8" x 35 mesh, and minus 35 mesh. These three size
fractions are treated separately in order to achieve re-
ductions in ash and pyrites. All of the techniques used in
the coarse and intermediate size processing circuits utilize
differences in specific gravity of the carbonaceous coal
(0.9 to 1.3) and the ash (2.0 to 2.3) and pyrites sulfur
(2.0 to 2.3). A simplified flowsheet is provided in Figure
5.1. The coarse fraction is processed in heavy medium
vessels or cyclones while the intermediate fraction is
5-2
-------
Table 5-1. GENERAL COST FACTORS
Cost Component
Percentage of total direct cost
Capital Costs
Interest during construction
Contractor fees
Engineering
Free agent
Off Site
Taxes
Spares
Shakedown
Contingency
Annualized Costs
Electricity
Water
Operating labor
Direct labor
Supervision
Maintenance
Labor and materials
Supplies
Overhead
Plant
Payroll
Fixed Costs
Depreciation
Interim replacement
Insurance
Taxes
Capital costs
8
10
6
1.25
3
1.50
1
3
20% (direct & indirect)
30 mills/kWh
3 C/M gal
$8.50/manhour
15% direct labor
4% of fixed investment
15% of labor and materials
50% of operation and maintenance
20% of operating labor
5% fixed investment
0.35% fixed investment
0.30% fixed investment
4.0% fixed investment
9.0% fixed investment
5-3
-------
R.O.M. Coal
Crushing
Coarse
Fraction
Intermediate
,. Fraction
Low S.G.
Cut
High S.G.
Cut
Low S.G.
Cut
»-\ Fine Fraction
\
\
Blended with
Clean or
Middling Streams
High S.G.
Cut
.1.
Clean
Stream
Middling
Stream
Reject
Stream
Figure 5-1. Simplified coal cleaning plant flowsheet
5-4
-------
treated on concentration tables. In both circuits the new
raw coal undergoes low specific gravity treatment which
splits into clean and middling-refuse streams. A second
treatment at higher specific gravity completes separation of
the middling and refuse streams. The plant operator has
considerable discretion in selecting the specific gravity
cut ranges in both stages. In this way it is possible
to partially control the coal quantity and quality in each
of the three output streams. It should be noted that the
fine fraction is not amenable to conventional cleaning
techniques based on specific gravity. While such material
can be cleaned using froth flotation which takes advantage
of differing surface properties, generally this material is
dried and reblended with the clean or middling streams. A
considerably more extensive discussion of CCP design and
operation is available in reference 1.
Based on typical operating practice it is apparent that
the following engineering data is necessary to estimate
multistream coal quality:
1. Coal grindability (weight distribution of raw
coal into three size categories).
2. Float-sink data applicable to coarse and inter-
mediate size ranges, including the following
variables:
a. weight distribution
b. Btu distribution
c. total sulfur distribution
d. ash distribution.
3. Specific gravity cut values for each stage of
coarse and intermediate circuits.
4. Deposition of fine fractions.
The first two variables are a function of the coal
supply. Due to the substantial variability of these wash-
5-5
-------
ability characteristics, actual test data for this antici-
pated coal supply must be available. Even with actual mine
samples some error is inevitable since the separation effi-
ciencies of commercial cleaning plant equipment cannot be
readily taken into account. Also it is difficult to obtain
a fully representative sample of the unmined coal supply.
Nevertheless, with the data i -ntified above and with simple
material balance calculations, it is possible to approximate
the characteristics of output coal streams.
In the multiplant scenarios, actual data from some Mid-
west Region mines were used in conjunction with three sets of
assumed specific gravity cuts. The make-up of the clean,
middling, and reject streams for these three cleaning
strategies is identified in Table 5-2.
Table 5-2. COAL CLEANING STRATEGIES
Coal
cleaning
strategy
A
B
C
.Coal Streams
Clean
float 1.30
float 1.40
float 1.60
Middling
(sink 1.30-float 1.90)
+ Fines (dried)
(sink 1.40-float 1.90)
+ Fines (dried)
(sink 1.60-float 1.90
+ Fines (dried)
Reject
sink 1.90
sink 1.90
sink 1.90
The three strategies listed above are considered represent-
ative of over 150 logical operating conditions. Strategy C
would primarily accomplish some ash reduction while strategy
A represents maximum cleaning for ash and pyrite removal.
Economical separation at a specific gravity of 1.3 has not
been commercially proven.
5-6
-------
The three cleaning strategies of Table 5-2 are recommended
as a starting point for the evaluation of LP derived strate-
gies. Ultimately the user will want to optimize the CCP
plant design and rerun the corrected models.
5.1.1.2 Cleaning Plant Costs - The estimation of coal
cleaning plants costs is a complex problem involving the
selection and size of all major plant components. It is
recognized that some potential users will not desire to
perform independent cost analyses based on the engineering
variables identified in Section 5.1.1.1. Accordingly, some
generalized results obtained using the PEDCo computerized
physical coal cleaning plants model are provided. This
section also serves to document the assumptions employed in
the scenarios discussed in Section 4. A more detailed
discussion of the CCP cost model is available in reference
1.
The size ranges considered vary from 200 tons/hour
(assumed economical minimum) .to 3000 tons/hour. The capa-
city factor is assumed to average 60% for 6000 hours of
operation per year. An escalation factor of 1.4 has been
used to adjust cost to a 1980 basis. It is assumed that the
cleaning plant is located in the general vicinity of the
mine.
The resulting annualized and capital costs for a typi-
cal coal cleaning plant are shown in Figure 5-2. These
costs correspond to a plant between 200 and 1400 tons per
hour with product streams equivalent to strategy C (see
Table 5-2). Costs did not vary substantially for the 3
cleaning options.
The cost model has been developed based on extensive
analysis of cost data provided by major vendors of coal
cleaning plant equipment. While the results generally
5-7
-------
40 4x10 -
20 2x10
-P
CD
to-
o
-H f-H
< U
10 IxlQ'-
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Capacity, tons/hour
Figure 5-2. Costs for a typical coal cleaning plant
5-1
-------
correspond to within ± 40% of reported costs for coal
cleaning plants, a detailed evaluation of the accuracy of
the model is not included in this study.
The user has the option of allocating the costs to
three output coal streams as appropriate. In this project
such costs have been assigned to the clean and middling
streams strictly on a Btu basis. The reject stream was
assigned no cost other than a transportation cost from CCP
to the utility plant.
5.1.2 Flue Gas Desulfurization Costs
The role of FGD systems is to provide for compliance
with SO- emission regulations at plants having excessive
quantities of sulfur in the fuel. This fuel may be un-
cleaned coal or a blend of coals that include streams from
one or more physical coal cleaning plants. Since the SO2
removal efficiency of FGD systems is typically in the range
of 75 to 90 percent efficiency (85 percent was used for this
project), the average sulfur content of the input fuel can be
4 to 10 times higher than the applicable S02 limit. Depend-
ing on the quality and cleanability of the fuel supplies
available, this capability to use higher sulfur coals repre-
sents a possible fuel cost savings. These savings are
offset by FGD annualized costs ranging from 4 to 8 mills/kWh.
5.1.2.1. Variables Affecting FGD Costs - A variety of
process and site specific factors can have a large influence
on the capital and annualized costs of FGD systems. Capital
costs can vary from $34 to $116/kW (installed basis - 1975
dollars) while the annualized cost can vary from 4 to 8
mills/kWh. The factors responsible for this variability
partially determine whether FGD is economically competitve
with the relatively expensive low sulfur coals. Factors of
5-9
-------
importance include plant size, plant remaining life, average
fuel sulfur content, maximum allowable SO- emission rate,
waste disposal costs, retrofit complexity, energy consump-
tion, and replacement power requirements. Costs for par-
ticulate control are not considered in the FGD models used
in this project.
System Capacity - Redundancy requirements impose a strong
scale factor on the capital cjsts of an FGD system. A
system composed of two 150 MW capacity units could require
one additional redundant train, whereas a system composed of
six 150 MW capacity units would probably require two redun-
dant trains. Obviously the relative cost in the smaller
network is larger than for the 900 MW system.
In addition to these redundancy requirements, there are
also normal economies of scale involved where a scrubber
module less than 150 MW is necessary. A 50 MW FGD system
has been used as the minimum since the capital costs on a
$/kW basis increase exponentially below this size.
Plant Remaining Life - Flue gas desulfurization systems are
not generally installed on boilers with a limited remaining
life since the costs cannot be amortized at an acceptable
rate. Boilers with less than 10 years serviceable life
remaining can have annualized FGD costs substantially
greater than new boilers with expected life of 35 to 40
years. Furthermore, old boilers tend to be swing loaded
or restricted to peaking service due to the high cost
per kWh. A plant remaining life of 20 years has been
used in all model calculations for the present project.
Installation Status - Capital costs for a new system can be
substantially lower than for retrofit FGD systems due to
construction costs. Retrofit applications can involve ex-
tensive modifications of the existing site, non-optimal
An FGD system is considered as one or more trains each of
which contains ducting, absorber, holding tank, agitators,
recirculation pump(s), demistor, reheater, soot blowers,
ducting shut-off valves, piping and controls.
5-10
-------
system layout, increased construction labor, and longer con-
struction periods. The potential impact of these problems
is illustrated in Table 5-3.
Table 5-3. EFFECT OF RETROFIT DIFFICULTY
ON FGD CAPITAL COST
Capital cost
increase, %
Large duct runs
Tight space
Delayed construction
New stack
Possible range
4-7
1-18
5-15
6-20
(one or more retrofit problems)
It has been assumed in the example of this study that retro-
fit costs for FGD systems in the hypothetical power plants
are insignificant. LP model results for actual networks
could be altered substantially in cases where retrofit of
FGD systems is difficult.
Sludge Disposal - Waste disposal for nonregenerable FGD
processes can have a major impact on both capital costs and
operating costs. The costs depend on the sulfur and ash
content of the coal, the rate of limestone use, moisture
content of the sludge, and treatment processes.
The capital costs for sludge disposal vary from $3.5/kW
to $10/kW depending on the location of the disposal area
relative to the plant and on the need to stabilize the
sludge for landfill. Operating costs can range from 0.2 to
1.5 mills per kWh depending primarily on the same two factors,
SO Removal Requirements - The quantities of S02 which must
be removed affect both the capital and operating costs. The
5-11
-------
capital costs for limestone storage and feeding and for
sludge treatment and disposal are a function of the removal
requirements. The costs for most raw materials and utili-
ties are also proportional to removal requirements. The
impact on total annualized costs ^an be 1 to 2 mills per
4
kWh. Relatively inexpensive pond disposal has been used in
the models for the present pr ject.
5.1.2.2 Capital and Annualized Cost Estimates - Specific
cost factors and design assumptions incorporated into the
FGD cost estimation models are presented in Table 5-4. An
escalation factor of 1.4 was used to adjust the cost to a
1980 basis. A limestone scrubbing system was used through-
out this project.
The resulting annualized and capital costs for one of
the plants are illustrated in Figure 5-3. These correspond
to an FGD ranging in size from 50 to 500 MW equivalent
capacity, with an inlet sulfur content of 7 Ib SO^/MM Btu
and an outlet concentration of less than 1.8 Ib SO_/MM Btu.
It was assumed that the power plant had a remaining life of
20 years and did not require extensive retrofit modifications,
Ponding was assumed for sludge disposal. Costs for install-
ations with somewhat different conditions vary as indicated
in Table 5-5.
The cost estimates determined using the computer model
have been compared with a survey of actual costs reported in
an Edison Electric Institute study. The range in reported
costs is in close agreement with the range predicted by the
4
model. The costs also agree within ± 20 percent (depending
on retrofit assumptions) with the estimates of two vendors.
Based on these comparisons, the FGD model used in this
project is considered to be accurate to ± 20 percent for
both annualized and capital costs.
5-12
-------
Table 5-4. SPECIFIC COST FACTORS AND DESIGN
ASSUMPTIONS USED IN FGD COST ESTIMATION MODELS
Design Assumptions
1. Absorber
2. Fan
3. Reheater
4. Limestone storage
5. Waste disposal
Cost Factors
Limestone costs
Fixation chemicals
Utilities
Electricity
Water
Reheat steam
Operating labor
Direct labor
Supervisor
Maintenance
Labor and materials
Supplies
Overhead
Plant
Payroll
Fixed costs
Depreciation
Interim replacement
Taxes
Insurance
Capital costs
Two stage turbulent content
absorber with Ap = 10 ^0 and
L/G =65 GPM/MACFM. Gas velo-
city of 10 FPS, Chevron entrain-
ment separator of 2" Ap, 85%
S02 removal efficiency.
Double inlet centrifugal fan
with static pressure of 16" Ap.
Indirect tubular reheater using
low oressure steam to achieve
AT of 50°F.
Dead storage pile sized for 30
days capacity; live storage
sized for 3 day capacity.
Clarifiers used to concentrate
effluent slurry from 15 to 30%
solids. Following vacuum
filtration to 60% solids
fixation additives are added
and the slurry is discarded in
the sludge pond.
$12/tons
$2/ton
30 mills/kWh
3.0 C/M gal
$0.76/MM Btu
$8.50/manhour
15% of direct labor
4% of fixed investment
15% of labor and materials
50% of operation and maintenance
20% of operating labor
5.0%
0. 35%
4.0%
0. 3%
9.0%
5-13
-------
4 -
3 ~
1
•P
tn
[O
0)
N
200
p |- 100
70
50
40
30
20
10
Capital cost
($/kW)
(0
4J
0)
c
Annualized cost
(mills/kWh)
NOTE: Sulfur content of fuel
3%; SC>2 regulation
1.8 Ib S02/MM Btu;
60% boiler capacity
factor.
I
T3 40 50
0)
70 100 200
Equivalent Capacity, MW
300 400 500
b
700
Figure 5-3. Estimated cost for a flue gas
^ desulfurization system, limestone scrubbing system
^ aAn annualized cost of 5 mills/kWh corresponds to
.J a cost of about $0.50 per MM Btu.
u Size of scrubber necessary to treat the flue gas from
,_, a boiler of the size indicated.
to
u
5-14
-------
Table 5-5. INFLUENCE OF PROCESS SPECIFIC AND SITE
SPECIFIC FACTORS OF FGD COSTS
Factor
1.
2.
3.
4.
5.
SO- removal requirement
Installation status
System size
Waste Disposal
Plant remaining life
Typical
capital cost
impact, %
s 15-20
10-40
10-40
10-30
-
Typical
annualized cost
impact, %
10-15
10-20
10-20
10-20
10-200
5.1.3 Electrostatic Precipitator Costs
The use of low sulfur coals in boilers originally
designed for 2-4% sulfur coals can alter the collection
efficiency of existing electrostatic precipitators. In the
300°F to 400°F range the low sulfur coal ash typically
exhibits a low surface conductivity which adversely affects
the precipitation rate parameter. The source operator has
the choice of modifying the ESP to account for the resist-
ivity problem or of using surface conditioning agents such
as sulfuric acid vapor. The latter option is not considered
to be commercially proven under all circumstances; there-
fore, ESP modification costs are provided. It should be
noted that in those cases where conditioning is feasible,
costs would be considerably lower than ESP modification
costs.
5.1.3.1 Variables Affecting ESP Costs - The average sulfur
content of the boiler coal stream is the principal variable
5-15
-------
affecting costs. This value in conjunction with the flue
gas temperature in the ESP determines the resistivity of the
particulate to be collected. Other variables of importance
include the gas flow rate, efficiency required, and retrofit
difficulty.
5.1.3.2 Capital and Annualir- 1 Costs - Cost estimates are
provided in Tables 5-6 and 5-7. The incremental cost for a
specific size of system can be calculated by subtracting
costs for the new sulfur content from that of the design
sulfur content. These costs include an escalation factor of
1.4 to adjust to a 1980 basis.
5.2 POWER GENERATION COSTS
There are a variety of power generation costs which
must be considered in the LP model in order to derive real-
istic costs. These cost components include coal costs, coal
transportation costs, boiler operation and maintenance
costs, and purchased power costs. Due to the hypothetical
nature of the scenarios, only general estimates were used
for such costs. It is assumed that potential users of LP
models will have comprehensive, accurate data available for
the specific network studied. Nevertheless, there is some
advantage in discussing the procedures used in the pre-
viously described scenarios.
5.2.1 Coal Transportation Costs
The variables affecting fuel transportation cost (on a
MM Btu basis) include the distance of transport, mode of
travel, and the heating value. The values in Table 5-8 were
used to approximate coal transport cost.
5-16
-------
Table 5-6. CAPITAL COSTS OF ELECTROSTATIC
PRECIPITATORS, $10
MW capacity of
boiler controlled
by ESP
10
20
30
50
70
100
200
500
Percent Sulfur in Fuel
3%
1.10
1.98
2.75
3.96
4.87
5.97
8.91
19.64
2.5%
1.27
2.28
3.12
4.41
5.38
6.53
10.05
23.18
2%
1.50
2.67
3.60
4.98
6.00
7.30
11.81
28.42
1.5%
1.87
3.23
4.26
5.74
6.88
8.50
14.79
36.49
1.0%
2.46
4.07
5.21
6.89
8.39
10.84
20.48
51.16
Table 5-7. ANNUALIZED COST FOR ELECTROSTATIC
PRECIPITATORS, mills/kWh
MW capacity of
boiler controlled
by ESP
10 .
20
30
50
70
100
200
500
Percent Sulfur in Fuel
3%
2.67
2.20
1.97
1.66
1.46
1.23
0.91
0.80
2.5%
3.00
2.49
2.21
1.84
1.59
1.35
1.03
0.94
2%
3.45
2.88
2.52
2.07
1.77
1.50
1.21
1.15
1.5%
4.18
3.42
2.96
2.37
2.02
1.75
1.51
1.47
1.0%
5.34
4.26
3.60
2.84
2.46
2.22
2.08
2.06
5-17
-------
Table 5-8. Fuel Transportation Costs
Mode of Travel
Rail
Rail-Barge Combined
Barge
Truck
Cost; C /TON-MILE
7
6
5
15
The values in Table 5-8 should be multiplied by the
appropriate conversion factor;, to convert to the $/MM Btu
basis used for all cost components in the LP model. A
factor of 1.4 can be used to adjust costs to a 1980 basis.
In lieu of actual cost data, the resulting estimates should
adequately account for shipping costs.
5.2.2 Boiler Operation and Maintenance Costs
Highly simplified procedures have been applied to
account for the operation and maintenance costs for the
boiler, turbine, and associated equipment. Obviously the
change in fuel quality resulting from ash and pyrite re-
duction can affect pulverizer wear, conveyor requirements,
and burner maintenance. To account for this cost, a vari-
able B has been calculated according to the equation below:
B = 0.5 + M(0.2), $/MM Btu.
The variable M is allowed to vary from 0 to 2 depending on
the ash content of the feed coal. Values greater than 1.0
represent increases in ash content above the design level,
whereas reductions in ash content are accounted for with M
values less than 1. The 0.5 $/MM Btu constant represents
amortization cost and a general operating cost not affected
by changes in fuel properties.
5.2.3 Fuel Costs
Typical fuel costs on a $/MM Btu basis have been pre-
sented in Table 3-1. These are based on internal PEDCo data
5-18
-------
and are not intended to represent cost for any one coal
source.
Fuel costs were one of the most powerful variables
affecting the LP solution. The user is strongly encouraged
to use actual costs based on coal contracts or other reli-
able bases.
5.2.4 Purchased Power Costs
The load demand on a typical utility boiler network
varies seasonally and diurnally. Total system load can vary
from as low as 35 to 40 percent at night to 100 percent at
peak periods during the day. Linear programming must derive
the optimum solution while allowing for SO2 emission com-
pliance at all individual boilers during peak periods. This
generally requires somewhat greater reliance on low sulfur
fuel and on desulfurization systems than in the solution at
the average load level. During "average" conditions it is
sometimes possible to minimize the power generation at
plants subject to stringent S02 regulations.
Peaking requirements also affect the amount of pur-
chased power that may be necessary. The FGD system demands
4
between 2 to 6 percent of station power. When the load
factor on a network exceeds 94 to 98 percent it is necessary
to obtain supplemental power in order to satisfy the needs
of the FGD system. This can be obtained from peaking units
within the network or from external sources within the same
energy pool. In either case, a cost of 30 mills/kWh has
been assumed. With an actual network it would be possible
to refine these estimates by taking into account capital
costs for peaking boilers (e.g., gas turbines) and for
transmission equipment.
5-19
-------
5.3 COMPILATION OF INPUT DATA FOR THREE PLANT SCENARIO
Regardless of the specific LP program selected (IBM-
MPS, UNIVAC-FMPS, etc.), the user is encouraged to compile
data described in Sections 5.1 and 5.2 into a set of mat-
rices. Experience indicates that the matrices facilitate
input of all data into the LP program. This network con-
sists of three power plants '-i fourth power plant variable
was added to represent purchased power) and four mines (a
fifth mine was added to represent a source of purchasable
power). The following notation is used:
DCC1 = coal from mine D that is cleaned, placed in the
clean stream (C) and sent to Plant 1.
DCM1 = coal from mine D that is cleaned, placed in the
middling stream (M) and sent to Plant 1.
The other symbols used are consistent with this notation.
One matrix for the cost coefficients for the small network
scenario (see Section 4) is provided in Table 5-9. Table
5-10 illustrates the calculations necessary to compute the
coefficients in the SO- regulation constraints. The con-
straints for the three plant scenario are very similar to
those for the one plant (see Section 3.1).
In addition, a constraint was necessary to tie the
three plants together. The network constraint assures that
at least a minimum amount of power is supplied by the three
plant system.
5.4 COMPILATION OF INPUT DATA FOR SEVEN PLANT SCENARIO
This scenario consists of seven power plants (plus one
to represent purchased power) and nine coal sources (plus a
tenth to represent purchasable power). Although the input
procedure is similar to that shown previously for the one
and three plant cases, there are a few differences due to
the increased complexity of the system.
5-20
-------
Table 5.9. INPUT COST DATA MATRIX FOR 3-PLANT SCENARIO
Variable
Al
A1F
A2
A2F
A3
A3F
Bl
B1F
B2
B2F
B3
B3F
Cl
C1F
C2
C2F
C3
C3F
Dl
D1F
D2
D2F
D3
D3F
E4
DCC1
DCC1F
DCC2
DCC2F
DCC3
DCC3F
DCM1
DCM1F
DCM2
DCM2F
DCM3
DCM3F
DCR1
DCR1F
DCR2
DCR2F
Coal
1.60
1.60
1.60
1.60
1.60
1.60
0.42
0.42
0.42
0.42
0.42
0.42
0.97
0.97
0.97
0.97
0.97
0.97
0.70
0.70
0.70
0.70
0.70
0.70
3.00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Clean
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Transp
0.28
0.28
0.28
0.28
0.28
0.28
0.92
0.92
0.92
0.92
0.92
0.92
0.41
0.41
0.41
0.41
0.41
0.41
0.09
0.09
0.09
0.09
0.09
0.09
0 b
0.08
0.08
0.08
0.08
0.08
0.08
0.09
0.09
0.09
0.09
0.09
0.09
0.43
0.43
0.43
0.43
FGD
0
0.60
0
0.82
0
0.53
0
0.60
0
0.82
0
0.53
0
0.60
0
0.82
0
0.53
0
0.60
0
0.82
0
0.53
0
0
0.60
0
0.82
0
0.53
0
0.60
0
0.82
0
0.53
0
0.60
0
0.82
ESP
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.065
0.065
0.065
0.065
0.065
0.065
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Boiler
Operation
and
Maintenance
0.70
0.70
0.70
0.70
0.70
0.70
0.90
0.90
0.90
0.90
0.90
0.90
0.80
0.80
0.80
0.80
0.80
0.80
0.70
0.70
0.70
0.70
0.70
0.70
0
0.50
0.50
0.50
0.50
0.50
0.50
0.70
0.70
0.70
0.70
0.70
0.70
1.00
1.00
1.00
1.00
Total
2.71
3.31
2.71
3.53
2.71
3.24
2.37
2.97
2.37
3.19
2.37
2.90
2.245
2.845
2.245
3.065
2.245
2.775
1.49
2.09
1.49
2.31
1.49
2.02
3.00
0.58
1.18
0.58
1.40
0.58
1.11
0.79
1.39
0.79
1.61
0.79
1.32
1.43
2.03
1.43
2.25
r>-21
-------
Table 5.9 (continued)
Variable
DCR3
DCR3F
DC
DCC
DCM
OCR
Coal
0
0
0.70
0
0
0
Clean
0
0
0
0.197
0.193
0
Transp
0.43
0.43
0
0
0
0
FGD
0
0.53
0
0
0
0
ESP
0
0
0
0
0
0
Boiler
Operation
and
Maintenance
1.00
1.00
0
0
0
0
Total
1.43
1.96
0.70
0.197
0.193
0
See Table 4-3.
See Table 4-2, OPTION C for the transportation costs of the
cleaned coal streams.
CBoiler costs vary with the type of coal being used; thus,
the cost differs depending on the source of the coal. The
cost also changes if the coal is first cleaned; cost clean
stream (C), being a higher grade coal, burns cleaner, and
thus less boiler maintenance is required than would be
necessary if stream (M) were used.
5-22
-------
Table 5-10. COMPUTATION OF COEFFICIENTS IN SO,
4
REGULATION CONSTRAINTS FOR 3-PLANT SCENARIO
Variable
Regulation 1:
Al
A1F
Bl
B1F
Cl
GIF
Dl
D1F
DCC1
DCC1F
DCM1
DCM1F
DCR1
DCR1F
Regulation 2:
A2
A2F
B2
B2F
C2
C2F
D2
D2F
DCC2
DCC2F
DCM2
DCM2F
DCR2
DCR2F
Actual Lb
S02/MM Btua
1.28
0.192
1.23
0.1845
1.30
0.195
6.96
1.044
5.47b
0.8205
7.99
1.1985
121.0
18.15
1.28
0.192
1.23
0.1845
1.30
0.195
6.96
1.044
5.47
0.8205
7.99
1.1985
121.0
18.15
Lb S02/MM Btu
Emission Regulations
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
Difference
0.08
-1.008
0.03
-1.0155
0.1
-1.005
5.76
-0.156
4.27
-0.2795
6.79
0.0015
119.8
16.95
-0.52
-1.608
-0.57
-1.6155
-0.5
-1.605
5.16
-0.756
3.67
-0.9795
6.19
-0.6015
119.2
16.35
5-23
-------
Table 5-10 (continued)
Variable
Regulation 3:
A3
A3F
B3
B3F
C3
C3F
D3
D3F
DCC3
DCC3F
DCM3
DCM3F
DCR3
DCR3F
Actual Lb
SO2/MM Btua
1.28
0.192
1.23
0.1845
1.30
0.195
6.96
1.044
5.47
0.8205
7.99
1.1985
121.0
18.15
Lb S02/MM Btu
Emission Regulations
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
1.8
Difference
-0.52
-1.608
-0.57
-1.6155
-0.5
-1.605
5.16
-0.756
3.67
-0.9795
6.19
-0.6015
119.2
16.35
Multiplied by 0.15 when the variable corresponds to a boiler
utilizing an FGD system to reflect an 85 percent removal
efficiency.
See Table 4-2, OPTION C for the sulfur content of the cleaned
coal streams.
5-24
-------
The major difference involves the computation of the co-
efficients in the objective function. Because of the large
size of this network it was necessary to consider transport-
ation costs more carefully. Thus, a matrix was developed
showing travel distances and associated transportation costs
between the various mines and plants. This information is
given in Table 5-11. Table 5-12 shows the previous table in
the units compatible with the other variables for input into
the program, $/MM Btu, and also includes the transportation
costs for the cleaned coal streams. Table 5-13 gives the
costs at the boiler as they depend on the type of coal used.
Tables 5-12 and 5-13 can then be used to compute the co-
efficients for each of the variables in the objective func-
tion. The costs, depending on the source of the coal and its
destination (boiler with or without an FGD system), are
added together to become the cost coefficients for the vari-
able representing that particular path of flow in the ob-
jective function.
Similarly to that done previously, the coefficients in
the SO,, regulation constraint are computed in the following
manner:
sulfur content of coal3 - emission regulation of
boiler (Ib S02/MM Btu)
The output from one run of this scenario is displayed
in Appendix A.
5.4.1 Component Process Scale
The size (capacity) of physical coal cleaning plants
and flue gas desulfurization systems has a major influence
on the capital costs as indicated in equation 2-3. Depend-
ing particularly on boiler age, boiler load factors, and
various economic factors, these capital costs increase
annualized costs of power plant network. The nonlinearities
aSee Table 5-14 and 5-15.
Multiply by 0.15 if boiler utilizes an FGD system to reflect
an 85 percent S02 removal efficiency.
5-25
-------
Table 5-11. TRANSPORTATION COSTS AND DISTANCES
FOR 7-PLANT SCENARIO
Source
A
B
C
D
E
F
G
H
I
J
Plant
1
8.3a
750b
10
1000
10
1500
8.0
100
8.5
150
8.0
100
8.0
100
8.0
100
8.0
300
-
2
8.5
650
10
1150
10
1650
8.0
100
9.5
300
8.0
50
8.0
150
8.0
150
9.0
300
-
3
8.3
700
10
1100
10
1600
8.0
150
9.0
300
8.0
100
8.0
200
8.0
200
8.5
200
-
4
8.2
900
9.5
1000
10
1350
9.0
350
9.0
400
9.0
300
9.0
350
9.0
350
9.0
350
-
5
10
600
9.5
1300
9.5
1800
10
400
9.0
500
10
300
10
400
10
400
8.0
150
-
6
9.0
700
9.5
1200
9.7
1600
8.5
400
8.5
500
8.5
300
8.5
350
8.5
350
8.0
50
-
7
9.5
600
9.5
1300
9.7
1700
10
400
9.0
500
10
300
10
400
10
400
10
10
-
8C
—
-
-
-
-
_
-
-
-
-
Cost coefficient in mills/ton-mile. This is computed by taking
the average of the costs of the modes of transport used weighted
by the portion of the total distance that mode was used. The
costs are as follows: barge - $0.008/ton-mile, rail - $0.010/
ton-mile, truck $0.015/ton-mile.
Distance in miles.
•^
'Purchased power.
5-26
-------
Table 5-12. TRANSPORTATION COSTS, $/MM Btu
FOR 7-PLANT SCENARIO
Mine
A
B
C
D
D
D
D
E
E
E
E
F
F
F
F
G
G
G
G
H
H
H
H
I
H
Coal
stream
—
-
-
-
C
M
R
-
C
M
R
—
C
M
R
-
C
M
R
-
C
M
R
-
-
Plant
1
0.249
0.410
0.920
0.033
0.030
0.047
0.325
0.057
0.048
0.062
0.779
0.035
0.031
0.049
0.469
0.035
0.031
0.049
0.469
0.034
0.031
0.040
0.388
0.107
—
2
0.221
0.472
1.012
0.033
0.030
0.047
0.325
0.127
0.108
0.139
1.742
0.019
0.016
0.024
0.234
0.053
0.047
0.074
0.704
0.051
0.046
0.060
0.582
0.121
—
3
0.232
0.451
0.982
0.050
0.045
0.071
0.488
0.120
0.102
0.132
1.650
0.035
0.031
0.049
0.469
0.070
0.062
0.098
0.938
0.068
0.062
0.080
0.776
0.076
—
4
0.295
0.390
0.828
0.130
0.119
0.186
1.282
0.160
0.136
0.176
2.200
0.127
0.105
0.164
1.585
0.148
0.122
0.192
1.849
0.134
0.121
0.158
1.526
0.141
«.
5
0.240
0.988
0.960
0.166
0.151
0.236
1.627
0.200
0.171
0.219
2.750
0.141
0.116
0.183
0.761
0.170
0.154
0.201
1.938
0.178
0.152
0.202
2.215
0.054
"
6
0.280
0.912
0.853
0.141
0.128
0.200
1.383
0.189
0.162
0.207
2.597
0.120
0.099
0.156
1.497
0.126
0.115
0.149
1.441
0.132
0.113
0.150
1.647
0.121
7
0.240
0.988
0.906
0.166
0.128
0.200
1.383
0.200
0.171
0.219
2.750
0.141
0.116
0.183
.1761
0.170
0.154
0.201
1.938
0.178
0.152
0.202
2.215
0.004
8U
-
—
—
—
—
-
-
—
-
-
—
-
-
-
—
-
-
-
-
-
-
-
-
—
Purchased power.
5-27
-------
Table 5-13. COST DATA FOR 7-PLANT SCENARIO
Mine
A
B
C
D
D
D
D
E
E
E
E
F
F
F
F
G
G
G
G
H
H
H
H
I
J
Coal
cost
1.60
0.97
0.42
0.70
—
—
—
0.70
_
_
_
0.70
_
_
_
0.70
_
_
_
1.30
_
—
_
3.00
3.00
Coal
stream
—
-
-
-
C
M
R
-
C
M
R
-
C
M
R
-
C
M
R
-
C
M
R
-
-
Coal
cleaning
0
0
0
0
0.10
0.10
0
0
0.10
0.10
0
0
0.10
0.10
0
0
0.10
0.10
0
0
0.10
0.10
0
0
0
Boiler
Operation
and
Maintenance
S/MM Btu
0.2
0.3
0.4
0.2
0
0.2
0.5
0.2
0
0.2
0.5
0.2
0
0.2
0.5
0.2
0
0.2
0.5
0.2
0
0.2
0.5
0.2
0
*
Flue gas
cleaning
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
• 0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0.40
0
ESP
Modification
$/MM Btu
0.065
0.065
0.130
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.065
0
*Included in cost coefficient only if associated with a variable that
represents a boiler utilizing an FGD system.
5-28
-------
Table 5-14. COAL CHARACTERISTICS - 7-PLANT SCENARIO
Mine
A
B
C
D
D
D
D
E
E
E
E
F
F
F
F
G
G
G
G
H
H
H
H
I
J
Coal
stream
-
—
-
—
C
M
R
—
C
M
R
-
C
M
R
—
C
M
R
—
C
M
R
—
"
Sulfur
content
Ib S02/MM Btu
1.28
1.30
1.23
6.76
5.47
7.99
223.40
5.64
3.49
5.24
152.60
8.34
5.32
11.56
219.70
6.21
4.49
7.62
178.90
7.72
4.77
7.47
239.00
1.71
0
Heating
value
Btu/lb
12,500
12,150
8,160
12,074
12,924
10,229
1,229
10,985
12,780
10,261
818
10,502
12,406
6,918
857
11,502
12,729
9,577
1,032
10,971
12,719
9,825
903
11,169
0
% weight
100.0
100.0
100.0
100.0
76.1
14.6
9.3
100.0
68.8
17.0
14.2
100.0
75.2
11.2
13.6
100.0
73.5
16.6
9.9
100.0
25.7
64.4
9.9
100.0
100.0
% Btu
100.0
100.0
100.0
100.0
85.9
13.1
1.0
100.0
82.5
16.4
1.1
100.0
91.3
7.6
1.1
100.0
84.7
14.4
0.9
100.0
31.7
67.4
0.9
100.0
100.0
Table 5-15. S02 EMISSION CONSTRAINTS, LB S02/MM BTU
Plant
Emission
Regula-
tion
1
1.2
2
5.2
3
5.0
4
4.0
5
1.2
6
4.0
7
1.2
8
None
5-29
-------
are particularly important for FGD systems with less than
150 MW throughput capacityb and for coal cleaning plants
with less than 300 tons/hour throughput. To avoid unrealis-
tic cost estimates, lower limits of 50 MW capacity for an
FGD system and 200 tons per hour for coal cleaning plants
have been assumed. The computer model used for FGD incor-
porates an upper limit for s rubbers by providing sets of
equal size scrubber trains in a module for facilities re-
quiring large flue gas desulfurization systems. An upper
limit of 3000 tons per hour has been assumed for coal clean-
ing plants.
The use of flue gas scrubber modules on a boiler is
represented more accurately by a step function than the
linear function which must be used in a linear programming
model. During the iterative procedure, capacity constraints
have been modified as necessary to approximate a step func-
tion, if the optimal solution involved flue gas scrubbing
of less than 25 percent of the boiler effluent gas, the use
of FGD was prohibited entirely at that boiler.
Raw coal sources providing less than 2 percent of
network demand or less than 105 MM Btu/ year were dropped
during subsequent analyses. Transport of small quantities
of coal may cost well in excess of the estimates used.
5.4.2 Derating
The derating of a boiler or set of boilers within a
power plant network results from the energy demand of flue
gas desulfurization systems and/or from the marginal suita-
bility of some low sulfur coal supplies.5 The coal com-
patibility problems are particularly difficult to incor-
porate into the calculation models since the extent of
derating is a nonlinear function of the characteristics of
the coal feed to a particular boiler. Conversely, the
The size of an FGD system is most accurately characterized
by the gas throughput at design gas velocity; however, speci-
fications of size according to the equivalent size boiler
is a more convenient basis for the purposes of this report.
5-30
-------
energy demand can be handled easily as a simple factor in
the overall fuel cost. Both general types of boiler de-
rating must be considered in order to refine the boiler
generation constraints and the boiler energy production
costs.
The combustion of low Btu, high moisture content,
western coals in existing boilers designed for higher qual-
ity coals can result in both materials handling and boiler
operation problems. More material per unit of output power
must be handled when the low Btu coals are burned. Capacity
limitations for crushers, pulverizers, or conveyors may
preclude achievement of design load. Generally these limi-
tations can be overcome by modifying operating practices
(speeding up conveyors) or adding additional equipment.
Boiler operational problems are more difficult to circum-
vent .
The following general operational problems can compli-
cate conversion of existing boilers to low sulfur western
coals.
1. The low Btu, high moisture content, western coals
produce greater quantities of effluent gas,
thereby increasing furnace gas velocity and
pressure losses.
2. Increases in furnace slagging affect the heat
absorption patterns in the lower and upper furnace
areas and result in steam temperature control
problems.
3. The low Btu, high moisture coals reduce furnace/
boiler efficiency.
These boiler operational problems and material handling
limitations can result in a derating from zero to 20 per-
cent. In most cases, derating can be minimized by selec-
tion of coal supplies moderately compatible with the exist-
5-31
-------
ing power plant design. It is conceivable that the optimal
solution derived from the linear programming models will
involve less desirable coals at several of the boilers in a
network. Therefore, it will be necessary to approximate the
nonlinear derating requirements. For simplicity, a function
can be assumed which is based on heating value. As shown in
Figure 5-3, the extent of derating is maintained near zero
in a region around the design point of the original boiler
fuel. As the coal heating vaiue decreases below 10,000
Btu/lb (dry) , the extent of derating increases exponentially
up to a maximum of 20 percent. Slight increases in production
capacity are assumed if the coal quality increases sub-
stantially.
The energy requirements of S02 control systems could
conceivably necessitate an increase in the generating capa-
city of the network. These capital costs have not been
included in the present calculations, but could be approxi-
mated as $400/kW installed.
5.4.3 Particulate Control
As discussed earlier, electrostatic precipitator costs
are dependent on the average sulfur content of the feed
coal. In turn, the feed coal characteristics are a function
of this solution. Therefore, it is necessary to adjust ESP
after each run.
5.4.4 Iterative Procedure
Due to the nonlinearities in some of the cost rela-
tionships used in this study, an iterative procedure is used
to converge to an acceptable solution. Fortunately, the
iterative approach converges quickly with proper selection
of initial conditions. This involves optimizing the scale
of desulfurization facilities and physical coal cleaning
plants.
5-32
-------
For the initial computer run the cost coefficients for
FGDs and CCPs are purposely underestimated to maximize the
use of these processes. During each successive run the
coefficients are adjusted upward to match the computer
derived equipment scale of FGDs and CCPs for each power
plant or boiler. This process converges on a solution which
generally consists of the minimum necessary level of flue
gas desulfurization and coal cleaning for each boiler. The
electrostatic precipitator costs are a function of the
average sulfur content into the boiler and must be recal-
culated for each computer iteration in which a change in
average sulfur content is implied. The ESP costs do not
necessarily follow the consistent patterns forced on FGD and
CCP costs. After each run the boilers are derated as
necessary to account for the average heating value of the
feed coal to the boiler. Also, any FGD or CCP units which
do not satisfy minimum size requirements are deleted.
Th.e adjustments listed above result in convergence to
an acceptable solution in several iterations. Once the
technical constraints are satisfied and the cost coeffi-
cients are accurate, the base case can be calculated. This
is the minimum total annualized cost under present system
conditions as obtained through the use of LP. Potential
cost savings can be computed by comparison with base costs.
These savings must be weighed against possible capital costs
for desulfurization systems, coal cleaning plants, and
ESP/boiler modifications. Capital costs are calculated from
the results of the separate estimation models.
The IBM-MPS (Mathematical Programming System) used in
this project provides the capability for sensitivity anal-
yses useful in identifying the most important variables with
respect to total annualized cost. Generally these con-
5-33
-------
straints include the SC>2 emission limitations, network load
factor, and fuel costs. The parameter adjustment procedures
of the MPS will automatically vary the selected cost coeffi-
cient in one set of runs. The results are useful in deter-
mining if the optimum strategy predicted from the base case
run is economical over a wide range of conditions. The
parameter adjustment option : -, a major advantage of the
linear programming technique since the cost per run and/or
the number of runs are substantially reduced.
5-34
-------
6.0 CONCLUSIONS AND RECOMMENDATIONS
The following conclusions are derived on the basis of
several scenarios utilized for demonstrating the application
of linear programming techniques to the determination of a
least cost combined strategy for S0_ control.
1. The linear programming techniques can be used to
determine least cost solutions for reasonably general
scenarios in terms of numbers of coal sources/mines, coal
cleaning plant design and resulting coal characteristics,
and the presence or absence of an FGD system.
2. The cost coefficients, particularly the fuel
costs, are very critical as they determine the structure of
the solution, e.g., which coal sources are used.
3. The emission regulations also play a critical role
in the determination of the optimal solution.
4. Optimal solutions can be obtained as a function of
specific parameters such as FGD or coal cleaning plant
costs, i.e., a sensitivity analysis of the impact of the
parameters on the overall annualized cost.
5. The fact that certain costs are non-linear func-
tions of the amount of coal, the decision variable, does not
deter the usage of a linear programming technique. An
iterative solution converges on the best solution by using
the cost estimate for the nth iteration based on the plant
size implied by the n-1 th iteration, i.e., for the amount
of coal determined by the previous iteration. An alter-
native approach uses the concept of separable programming as
described in the manual.
6-1
-------
6. The uncertainty in certain cost estimates may be
treated by methods described in reference 8 provided some
prior information can be used to infer the probability or
likelihood of certain cost values or a continuous frequency
distribution of these costs.
The following recommendations are made for the purpose
of defining areas for follow :>n studies.
1. A computer program should be written to solicit
and accept data for flexible confiaurations of power plants,
mines, coal cleaning plants, FGD systems, etc. and to per-
form calculations and properly format data for input to the
Mathematical Programming System (MPS). This program would
reduce the likelihood for error inherent in the manual
calculation and input procedure and would permit the data to
be expressed in the most commonly used units.
2. The features of MPS should be more fully exploited
in performing sensitivity analyses and iterative solutions
where costs are nonlinear functions of the amount of coal.
3. The separable programming features of MPS should
also be investigated as this will permit the use of linear
approximations to nonlinear functions.
4. The optimization approach can be applied to both
the capital costs and the annual operating and maintenance
cost. A solution could be obtained by minimizing the total
annualized cost, subject to a limitation on the total
capital cost, or using a multiple objective optimization
approach.
5. More refined cost estimates should be made sub-
sequent to the least cost solution. These costs would foe
determined in the same manner as a utility company would
determine their daily coal requirements, boiler loading,
etc.
6-2
-------
6. The linear programming technique, including the
interactive data input routine, should be converted to run
on EPA's UNIVAC 1110 using the Functional Mathematical
Programming System (FMPS) already installed on the 1110.
6-3
-------
7.0 REFERENCES
1. Coal Washability Analyses and the Use of Coal Cleaning
by TVA to Meet State SC>2 Regulations. Report to U.S.
Environmental Protection Agency, Contract No. 68-2-
1375, Task No. 23; December 1976.
2. Hoffman, L., S. J. Aresco, and C. C. Holt, Jr. "Engi-
neering/Economic Analyses of Coal Preparation with
SC-2 Cleanup Processes for Keeping High Sulfur Coals in
the Energy Market," The Hoffman-Munter Corporation
for U. S. Bureau of Mines, Contract J0155171, November
1976.
3. Mathematical Programming System/360, Version 3, Linear
and Separable Programming - User's Manual (360A-CO-
14x). IBM Corporation, Technical Publications Depart-
ment, October 15, 1971.
4. Flue Gas Desulfurization Process Cost Assessment.
PEDCo Environmental, Inc. Contract No. 68-01-3150,
Task 2, U.S. Environmental Protection Agency, May 1975.
5. Evaluation of the Sulfur Dioxide Emission Compliance
Strategies for the Boston Generating Station, Columbus
and Southern Ohio. Appendix C: Power System Derating
and Energy Penalities. PEDCo Environmental, Inc.
.Contract No. 68-01-4147, Task No. 17, U.S. Environ-
mental Protection Agency, July 1977.
6. Impact of the SO2 Emission Standards Level on the
Method and Costs of Compliance for New Power Plants.
PEDCo Environmental, Inc. Contract No. 68-02-1076,
Task 18, U.S. Environmental Protection Agency; 1976.
7. Wagner, H. M. Principles of Operations Research with
Application to Managerial Decisions. Prentice-Hall,
Inc., 1969.
8. Tummala, V. M. Rao. Decision Analysis with Business
Applications. Intext Education Publishers. New York.
1973.
7-1
-------
8.0 GLOSSARY
The following terms used in this report or its append-
ices are defined in order to aid the reader who may not be
familiar with the technologies discussed.
Combined strategy - The use of multi-stream coal
cleaning in conjunction with flue gas desulfurization and
fuel supply redistribution to achieve compliance with
emission regulations at all plants of a network at a minimum
cost.
Flue gas desulfurization - One or more trains each
of which contains ducting, absorber, holding tank, agi-
tators, recirculation pump(s), demistor, reheater, soot
blowers, ducting shut-off valves, piping, and controls.
Heat rate - A measure of generator thermal efficiency
expressed in Btu/net kWh.
Heavy medium vessel - A device employing a liquid
having a specific gravity higher than water to effect a
gravimetric (float-sink) separation of coal particles from
impurities.
Linear Programming - A mathematical technique designed
to analyze the costs of alternate decisions and to choose
those that permit the best use of resources in the pursuit
of a desireable objective.
Low sulfur coal - Coal having a sufficiently low total
sulfur content so that it can be burned without fuel treat-
ment for pyritic reduction or without flue gas desulfuri-
zation for S02 removal. The term generally applies to coal
supplies of less than an equivalent sulfur content of 1.5 lb
8-1
-------
S02/MM Btu.
Multi-stream coal cleaning - A physical coal cleaning
process in which two or more usable coal streams of dif-
ferent qualities and at least one reject coal stream are
generated.
8-2
-------
APPENDIX A SELECTED COMPUTER RESULTS
ONE PLANT SCENARIO
ROW
N
L
L
L
L
L
L
G
L
L
E
E
E
L
L
L
S
COS!
HINE1
HINE2
M1NE3
WINEU
BOILER1
BOILER2
PLANT
S02A1
S02A2
AW
MW
RW
SUAC
SUHC
SURC
COLUMNS
S1B1
S1B1
S1B1
S1B2
S1B2
S1B2
S1B2F
S1B2F
S1B2J
S2B1
S2B1
S2B1
S2B2
S2B2
S2B2
S2d2F
S2B2F
S2B2F
S3B1
S3B1
S3B1
S3B2
S3B2
S3B2
S3B2i
S3B2F
S3B2F
sue
sue
S4C
SUCA
SUCH
S4CR
SUB1
SUB1
COST
SC2A1
PLANT
COST
SG2A2
PLAKT
COST
S02A2
PLANT
COST
SC2A1
PLANT
COST
S02A2
PLANT
COST
S02A2
PLANT
COST
S02A1
PLANT
COST
S02A2
PLANT
COST
S02A2
PLANT
NH
COST
HINE4
Ab
nu
BW
COST
S02A1
2. 01 WO
2.72000
1.00000
2.01500
.52000
1.00000
2.61500
1.60800
1.00000
1. 63000
2.77000
1.00000
1.63000
.57000
1.00000
2.23000
1.61500
1.00000
1. 75500
2.70000
1.00000
1.75500
.50000
1.00000
2.35500
1.60500
1.00000
. 28000
1.01000
1.00000
1.00000
1.00000
1.00000
1.05000
2.50000
bOILERI
ttlNEl
bUiLEb2
M.NE1
b01LEE2
tiiNE 1
BOiLEfi!
K1HE2
dUiLE&2
fllNE2
b01LER2
flj.NE2
B01LER1
HJ.NE3
faOlLiiH/
hiNE3
BOILER2
U1NE3
RU
AW
SUAC
SUMC
bUHC
BOILEK1
U1NEU
1.000JO
1.000JO
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
.01200
.70800
1.00000
1.00000
1.00000
1.00000
1.00000
A-l
-------
ONE PLANT SCENARIO
S4B1
S4AB1
S4AB1
S4AB1
S4MB1
S4HB1
S4MB1
S4RB1
S4RB1
S4RB1
S4B2
S4B2
S4B2
S4AJ2
S4AB2
S4A32
sun a 2
S4MB2
S4MB2
S4RB2
S4RB2
S4KB2
S4B2F
S4B2F
S 4 B2 r
S4A32i
S4AB2F
S4AB2F
S4HB2F
S4ilB2F
S4HB2F
S4KB2F
S4HB2F
S4RB2F
RHS
RHS
RU5
RHS
RriS
ENDATA
PLANT
COST
S02A1
S4AC
COST
S02A1
S4MC
COST
S02&1
S4FC
COST
S02A2
PLANT
COST
S02A2
S4AC
COST
S02A2
suac
COST
S02A2
S4RC
COST
S02A2
PLANT
COST
S02A2
SUAC
COSI
S02A2
S4MC
COST
S02A2
S4RC
BOILER1
W1NE1
M1NF3
PLAKT
1.00000
. 14000
.20000
1.00000
. 16000
4.54000
1.00000
.5*000
105.00000
1.00000
1.05000
4.70000
1.00000
. 1400o
2.00000
1.00000
. 16000
6.74000
1.00000
. 59000
107.20000
1.00000
1.65000
.82500
1.00000
.74000
1.23000
1.00000
.76000
.51900
1.00000
1. 19000
14.55000
1.00000
34690.00000
70000.00000
70000.00000
69206. 00000
BUlLLh!
PLANT
bOiLLEI
PLANT
bUlLtR!
PL.ANT
r JiLth^:
i1iNh4
b01Lr.h2
PLANT
B01LEh2
PLANT
COlLERi
PLANT
nG iLE-fa*.
dlN EU
iiOILtR2
PLAN!
bOlLhK2
PLANT
B01Lt.R2
PLANT
COILEK2
M1SE2
ftlW E4
1 .00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.0JOOO
1.00000
1.00000
1.00000
1.00000
1.00000
86724. OOllOO
70000.00000
70000.00000
A-2
-------
SECTION 1 - ROMS
AT
b..
Al-Ti V1T *
.LO.tH L1IUT.
HIM 1
4 HtNLJ
5 HINFU
6 B01L£8 1
7 BOILEB2
8 PLAkT
9 S02A1
10 SU2A2
1 1 AH
12 NU
13 kV
14 5MAL
15 b4HC
Ib b«RL
SECTION 2 -
NUnbtK .COU,lib.
17 S1B1
IB SI fit'
19 S1B2f
20 b«!B1
21 S2b2
22 s2a/:P
23 S3B1
24 S3B2
25 b3B2P
26 S4C
27 SMC*
2d bica
29 S4CJ)
30 Stbl
31 j«ibl
32 5 until
33 S4BB1
34 S4B2
35 S44B2
36 SUHB2
37 S4«o2
38 btiB2F
39 S4AL21'
u 0 b'UHD^ f
41 b'4tn2r
us
OS
UL
Ob
LL
UL
OL
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UL
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b*iV1 1.d7720
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6b5. 87720-
COLUMNS
AT
LL
LL
LL
LL
LL
LL
LL
LL
LL
BS
Bb
tab
Bb
BS
BS
LL
LL
LI.
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LL
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BS
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...ACTIKITY...
.
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1.05000
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1. 19000
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NONE
NONE
• ONE
69206.00000
NONE
NOIIE
NOHt
NONE
NONE
NONE
70000.00000
70000.00000
70000. 00000
70000.00000
34690.00000
86724.00000
NONE
.
•
•
.
.
.UPPER LI BIT. .DUAL iLTIVITI
1.00UOO
.30912
1.52806-
.06758
.14780
1.09246
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1.09246
.84477
LIMIT.
. UPPE6 LI HIT.
HONE
tone
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
NUNE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
. IEOUCEO COST.
.61224
.41008
.64927
.22386
.01769
.46324
.35359
. 15304
.58972
.09263
6.46682
.21660
.47289
14.90618
.12261)
1.81244
A-3
-------
NAME
ROWS
N COST
G NETWORK
I FJD1
L FGD2
I FGD3
1 PLANT1
I PLANT2
1 PLANT3
1 PLANTS
I MINEA
L HINEB
1 MI NEC
L MINED
1 MINES
1 REG1
I PEG2
L EEG3
L CLEAN
L niDDLING
I REJECT
E DCC
E DCM
E DCP
COLUMNS
A1
A1
A1
A1F
A1F
A1F '
A2
A2
A2
A2F
A2F
A2F
A3
A3
A3
A3F
A3F
A3F
B1
B1
B1
B1F
B1F
B1F
B2
B2
B2
B2F
3 PLANT
STRATA
COST
REG1
NETWORK
COST
FEG1
NETWORK
COST
REG2
NETWOFK
COST
REG2
NETWORK
COST
P.EG1
NETWORK
COST
REG 3
NETWORK
COST
REG1
NETWORK
COST
FEG1
NETWORK
COST
REG2
NETWORK
COST
SCENARIO
2.6450C
.C8CCO
1.CCOCO
3.2U5CC
1. CO 000
1.CCCCC
2.6450C
.520CC
1.CCOCO
3.465CO
l.bCSOC
1.PCCGG
2.6U5uO
.520CO
1.CCOCO
3.1750C
1.60803
1.00000
2.37COO
.C3000
1. GO COO
2.97CCO
1.01000
1.00CCO
2.370CO
.57CCC
1.00COC
3. 190CC
A-4
MINEA
PLANT1
hINEA
PLANI1
I'LANI^
PLANTS
PLANTS
HINEA
PLANTS
PLANI1
PL AN 11
FOD1
MINEb
PLANT2
HINEB
1.0GCCO
1.COOOC
ooooc
ocooc
occco
COCOu
1.GCCOO
1.03CCO
1.COOCO
1.COOOO
1.COCCO
1.COOOO
1.COOOC
1.00000
1.000CO
1.000CO
1.00COO
oococ
.oocoo
00000
,00000
,00000
1.00000
-------
3 PIANT SCENAFi:
B2F
B2F
B3
B3
B3
B3F
B3F
B3F
C1
C1
C1
C1F
C1F
C1F
C2
C2
C2
C2F
C2F
C2F
C3
C3
C3
C3F
C3F
C3F
D1
D1
D1
D1F
D1F
D1F
D2
D2
02
D2F
D2F
D2F
D3
D3
D3
D3F
D3F
D3F
E4
E4
DCC1
DCC1
DCC1
DCC1F
DCC1F
DCC1F
DCC2
DCC2
RE32
NETWOFK
CCS1
ft EG 3
NETWORK
COST
FEG3
NETWORK
COST
REG1
NETWOt-K
COST
REG1
NETWOPK
ccsr
PEG 2
NETWORK
COST
FEG2
NETWORK
COST
3EG3
NETWORK
ccsr
REG 3
NETWOFK
COS-
BEG 1
NETWORK
C03I
REG1
NETWORK
COST
REG2
NETWOFK
COST
REG2
NETWORK
COST
FEG3
NETWORK
COJT
REG3
NETWORK
COST
NETWORK
COST
FEG1
CLEAN
COS!
REP, 1
CIEAN
COST
REG2
1.61bjC
1.CCTv,0
2.37CCG
.57COC
1.0CCOO
2.90COO
1.t15CC
1.CCCCO
2.2U5CG
. 1COOO
i.OOfGC
2. 814500
1.CC50C
I.CC^G^
2.2U50C
.5GOCC
1.0CCCO
3.C65CC
1.6C5CO
1.CCCOC
2.2a5CO
.SC-COC
1 . C C C C C
2.7750C
l.bCSGC
1 . C C C 0 C
1.U930C
5.76COC
1 . 0 C C G C
2.C9^0C
. 156CC
1.COCOC
1.U9:OC
5. 16 COG
1.CCCOC
2.31CCC
.75600
1.CCOOO
1.U90CO
[>. 160CC
1.00000
2.C2CCC
.756CO
1 . C C C C C
3.0CCOC
1.0COOC
.58COO
4.2700C
1.0COOO
1 .18COT
.37900
1.COCCO
.56CCC
3 . 6 7 C C C
tlAM^
t'^'J*.
MINEB
PLANT3
WIN Eb
PL A NT 3
FuD3
MINEC
t-LnNH
ftiJEC
F L A N T 1
FJD1
KINLv.
PLAM2
WINEC
P- AN" 12
rGD2
rtiNEc
PLANIJ
rtlNEC
PLANI3
I Ju3
MINED
PLANI1
OINED
PL AN 11
FG J1
BIN Ei)
i-LANT^
hlN£D
PL AN 1 2
FGD2
WINED
PLANT3
ftxNEU
PLAN13
FGD3
ftlNEE
PLANTu
tiZIWORK
PLANT1
NETWORK
PLANT1
FGD1
h£l WORK
PLANI^i
i.conoc
1.CGOCO
1.CCOOC
l.OCncc
-COOOC
.^CCoO
• CCCOC
ocooc
1.CCOCO
LGOCtC
1.COOCO
1.CCCCO
1.COOOC
1.CCDCO
1.CDCGO
1.000CC
1.CGOCO
1.CGOCC
I.CCCuC
1.COCCC
1.COCCO
1. C C 0 C C
1.COGCO
1.000GC
1.COOOC
1.0GOOO
1.GCOCC
1.00CGO
I.OCOoO
1.COCCC
1.00CGC
1.0GCOC
1.COCOC
1.00000
1.00000
1.COOOO
1.0COGO
1.00000
1.00000
1.00000
1.0&CCC
1.0CCCO
1.0COOO
1.00000
1.CGOOO
A-5
-------
3 PLANT 5CENAF 10
DCC2
DCC2F
DCC2F
DCC2F
DCC3
DCC 3
DCC 3
DCC3F
DCC3F
DCC3F
DCM1
DCM1
DCM1
DCM1F
DCM1F
DCM1F
DCM2
DCM 2
DCM2
DCM2F
DCM2F
DCM2F
DCM3
DCM 3
DCM3
DCM3F
DCM3F
DCM3F
DCR1
DCR1
DCP1
DCP1F
DCR1F
DCF1F
DCR2
DCP2
DCS2
DCP2F
DCR2F
DCP2F
OCR 3
DCR3
DCP3
DCR3F
DCR3F
DCR3F
DC
DC
DC
DCC
DCC
DCM
DCM
OCR
CLEAN
C OS I
CLEAN
COST
REG3
CLEAN
COST
PEG 3
CLEAN
COST
REG1
MIDDLING
COST
PEG1
MIDDLING
COST
REG2
MIDDLING
COST
REG/:
MIDLLING
COST
REG3
MIDDLING
COST
RZG3
MIDDLING
' COST
REG1
REJECT
COST
REG1
REJECT
COST
REG2
REJECT
COST
REG2
REJECT
CCST
REG 3
REJECT
COST
REG 3
REJECT
COST
DCC
OCR
DCC
COST
DCM
COST
OCR
1 . 0 G C 0 C
1 a f "* n "
1 . ^ O >J U V
.979C :
1 o r r ,i r
• • V v, w v
. 5 d C C G
3.6700C
1 . r f 0 C C
1 1 1 r< f r
' • 1 1 \j L '
.9790:
1 0 <* 1 Ci ^
' • * - « n r
i • w I. ^ y \
6. 19CCC
1.00COO
1.32:00
.6C200
i.c:oco
1.43CCC
11 9. 8 COCO
1.00COC
2.C3COO
1o.95CCO
1.COOOC
119.2CCOO
1.0COCO
2.25COC
16.35COO
1.0CGOC
1.U300C
1iy.20CCj
1.CCOCO
1.96CCO
1f .35CCC
1.CCOCO
.7CGOC
.b590C
.C10CG
1.000GC
. 1970C
1.COOOC
.19300
1.0CCOO
Ncl w'Or. h
PLANI2
* ^* L) iL
it LI ti 0 f\ K
PLANT J
PLAAI13
1 1 • ' i
r b u J
N h I «IO J* K
PLAN: 1
Nil' kv'Oi K
PLaN 11
Ff- -«
OU 1
NET^IGPK
i ^
Nil Wui-K
/* ^
r uL2
NElWOf K
PL A NT 3
PLAMJ
FJD3
PLANT1
NET WORK
PLANI1
NEIWOaK
NETWORK
NEI JOtK
PLANT3
PLANIJ
FGD3
flINED
DCM
LLLdK
MIDDLING -
REJECT
i.corcc
1 . G o r c o
1 . C 0 C 0 C
1 . C G r o G
1.CCCCG
1.0CCGO
1 .00000
1.: jccc
1.CCOCC
1.COOCC
1.GOGGG
1. GOOOO
1.COCOC
1 . C G C C C
1. GO iCC
1 .COCCO
1.0COOC
1.CCOCC
1.0GOGG
1 . 0 G C C C
1 .CCGOC
1. COCCO
1.GOCCO
1.00000
1.000CO
1.COCOO
1.0COOO
1.00000
1.GCCOO
1.0000C
1.000GC
1.COCGC
1.000CO
1.000CO
1.000CC
1.COOOO
1.0COOO
1.000CO
.13100
1.000CO
1.00000
1.0COCO
A-6
-------
3 PLANT SCENARIO
SHS
HHS NETWORK 7278.00000 i-JI;1 353C.COCCC
RHS FGD2 133C.OCCCC r^3 bSaO.OOCCO
RHS FLAM1 3CCC.CCCCC i-LA;J^ 116C.COCOO
HHS PIANT3 SoCC.COCOC PLANT-* 1213C.&CCOG
RHS HINtA 1213C.CCXO niN^B 1213C.CCCCO
FHS WINEC 1213C.COCCC KINED 1213C.tOCOO
PHS MINEL 12130.OC-CCC
RANGES
FANGEF PLANT1 15CC.OCOO' KiNT^ SbC.COCOC
RANGEn P1ANT3 28'lC.COCoC
ENDATA
A-7
-------
3 PLANT SCINAHO
TCTTOJI i - ;ous
1
2
3
u
5
6
7
8
15
11
12
15
1b
17
18
19
20
21
22
23
COST
NETkOFK
FGD1
PLANT1
PLAI-T2
PLAKT3
PLAVT1
I1IMA
HINTS
UINEC
13 MINED
i
ccoc:
o9US
OCOOO
cccoc
i/OCOO
.10.EP LI.1IT.
.UPPEP LIBIT.
67*t. 3C 115
12130.COOCC
U13C.OCCCC
53J3. -J9885
1^130.00000
7278.
1500.
5BC.
28CO.
NON E
cocoo
NON E
NONE
NONE
CCCOO
CCOOt
oocoo
NONE
NONE
NONE
NONE
NON:
NONE
KONZ
NONE
HONE
NONE
NONE
NONE
353C
133C
65UC
3000
11bC
5bCO
1213C
12130
12130
12130
12130
1213C
NONE
NONE
. CCOOO
.OCOOO
.COCOO
.ocooo
.o:oco
.ococo
.CDCOO
.coooo
.00000
.cccco
.coooo
.00000
.
t
,
t
f
. DOAL ACTIVITY
1.00000
1.93113-
.13121-
.22361-
. 12906
.17452
. 11359
.93725
.68251
.18951
3 PLANT SCBNJoIO
'ECTIOV 2 - CJLUMNS
. COL.OHN.
AT
.ACIIVIT*...
21
25
*6
27
28
29
30
31
32
33
34
35
36
37
38
39
10
11
«2
• 3
«1
• 5
«6
47
«a
19
50
51
52
53
5«
55
56
57
58
59
63
61
62
63
61
65
66
67
68
69
70
A1
A1F
A2
A2F
A3
A3F
B1
B1F
B2
32F
B3
B3F
C1
C1F
C2
C2F
C3
C3F
D1
D1F
D2
D2F
D3
D3F
£1
DCC1
DCC1F
DCC 2
DCC2F
DCC 3
DCC3F
DCH1
DCH1F
DCH2
DC 112 f
DC13
DCH3F
DCR1
DCR1F
DCR2
DCE2F
DCB3
DCP3F
DC
DCC
ocn
DCS
LL
LL
LL
LL
LL
LL
LL
LL
LL
LI
LL
LL
LL
LI
BS
LL
LI
LL
LL
LL
LI
LL
LL
BS
LL
BS
BS
BS
LL
BS
LL
LL
LL
LL
LL
LL
BS
LL
LL
LL
LL
LL
LL
BS
BS
BS
BS
510.H556U
3950.322UU
1377.7156U
69. 5u <436
U7U.B9365
372.78391
28*5.67871
211(1.113801
372.78391
28.05679
COST..
2.615CC
3.21500
2.6U5C&
3.165CO
2.615CC
J.175CC
2.370CO
2.970CO
3.190CO
2.J7COO
2.90000
. .LOUER LI HIT.
2.D15CC
2.2H5CO
3.C65CO
2.215CC
2.775CO
1.19003
2.L9CCO
1.190CC
2.31000
1.19000
2.C20CO
3.0COOO
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1.18COO
.58CCO
1.1COCO
.58000
1.110CO
.79000
1.39000
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1.61000
.79000
1.320CO
1.13000
2.03COO
1.130CO
2.25000
1.13000
1.96000
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.OPPEB LIBIT.
HONE
NOME
NONE
not.;
NONE
(ONE
NONE
HONE
HONE
KOBE
DONE
NONE
NOME
NONE
NONE
NONE
NONE
NONE
NONE
IOKE
NONE
NONE
NONE
NONE
NONE
NONE
NONE
DONE
NONE
NONE
• ONE
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NONE
NONE
NONE
NONE
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NONE
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NONE
NONE
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NONE
NONE
(ONE
. EEDDCED COST.
.58699
1.01657
.39651
1.02663
.65181
1.05822
.30554
.77131
.11278
.75011
.37113
.78213
.18957
.61696
.62715
.25108
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.16505
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l'.06587
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100192
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.00391
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.24150
1*Ia2305
2.14923
20.07510
2.9*567
13.0J583
1.68307
A-8
-------
APPENDIX B
STATEMENT OF THE PROBLEM IN MATHEMATICAL TERMS
The subject of this study has been coal burning power
plants of one or more electric utilities. In particular,
the study has considered alternative control methods for
compliance with S0~ emission limitations affecting coal
burning activities. The control methods considered included
flue gas desulfurization, physical coal cleaning, low sulfur
coal, and blending of coals. These methods have been dis-
cussed earlier.
From the broadest point of view, the objective of the
study was to identify a methodology to aid in selection of
the method or combination of methods which would meet the
SO- emission limitations and satisfy other- constraints with
the least possible total cost. Thus the problem is one of
constrained optimization.
The- number of location of coal mines and power plants
were taken to be given.
The initial effort attempted to address selection of
locations for physical coal cleaning plants (CCP) and flue
gas desulfurization (FGD) systems. The FGD systems must
be located at the power plants they are to serve. However,
CCP's could be located anywhere, at least theoretically.
This generality makes the problem very difficult to formu-
late mathematically.
Even if the CCP's are only allowed at coal mines,
the problem is very complex. It is a form of zero-one pro-
gramming in that there are tow possible values at each coal
mine or power plant (i.e., either the mine does or does not
have a CCP, and either the power plant does or does not
have an FGD).
B-l
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In addition to the zero-one problem, the amount of
coal from each source used at each plant is a significant
variable affecting capital costs and operating costs as well
as the constraints.
It was felt that arbitrary or heuristic selection of
the locations of CCP's would permit formulation of the
remaining problem, determination of coal amounts, as a linear
programming package. This formulation would have the dis-
tinct advantage of permitting i e use of powerful^ existing
computer solution packages such as IBM's Mathematical
Programming System (MPS).
B-l LINEAR PROGRAMMING FORMULATION
PEDCo Environmental's cost models were run for several
different cases to determine the relationship of annualized
cost of CCP's and FGD's to coal throughput or capacity.
The cost curves were found to be approximately linear over
a wide enough range to use linear programming. If the
solution puts values outside this range, then coefficients
can be adjusted and the solution recomputed.
The general linear programming formulation is expressed
as: minimize total cost subject to the set of constraints.
The total cost includes costs of (1) raw coal at the mine,
(2) transportation to the power plants or CCP's, (3) coal
cleaning, (4) transportation from CCP's to power plants,
and (5) FGD's and ESP's (electrostatic precipitators) where
applicable. Constraints employed included power plant (or
boiler) capacity, network demand, SO2 emission limitations,
and coal washability characteristics. Other optional
constraints utilized were mine capacity and derated boiler
capacity when FGD was used.
A more specific discussion of the formulation will be
facilitated by use of the network representation.
B-2
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B-2 NETWORK REPRESENTATION
The network representation is a useful structure for
formulating a large class of mathematical problems. A
network consists of sets of nodes representing resources
and/or facilities, and arcs representing possible routes the
resources might take, connecting various pairs of the nodes."
In the coal cleaning problem, coal mines, coal cleaning
plants, and power plants are represented by nodes in the
network. Arcs connecting these nodes are used to represent
possible routes of coal. The network for a three mine, two
plant scenario is shown in Figure B-l.
1
B
IF
2F
CCP
CR
Figure B-l. Three mine, two plant network
B-3
-------
In Figure B-l the nodes representing coal mines are
lettered A, B, and C. CCP designates the node representing
a coal cleaning plant. Note that only coal from mine C
may be sent to the CCP (representing a situation in which
the coals from mines A and B are clean enough that physical
coal cleaning is not desirable). The nodes CC, CM, and CR
designate three output streams of -'he CCP: clean, middling,
and reject, respectively, so that the routing of these
streams can be represented in ,e network.
In order for the model to determine where FGD systems
are used and to what extent, each power plant node is re-
placed by two nodes. These nodes can be envisioned as two
boilers at the same plant, one with FGD and one without,
and otherwise identical. In actuality a single boiler with
an FGD can have some of the gases directed to the FGD and
the rest vented directly to the ambient air. However, the
two-boiler situation is easier to model. At plant 1, let
the boiler without FGD be designated by node 1 and the
boiler with FGD be designated by node IF, and similarly
for plant 2.
B-3 FORMULATION OF LINEAR COST FUNCTION AND CONSTRAINTS
Independent Variables
An independent variable can be associated with each
of the arcs in the network. Each variable is to represent.
the flow of coal along that route. The units chosen for
these variables were MM Btu since these units are appropriate
both for measuring demand and emission limitations. Quan-
tities expressed in tons or pounds are easily converted to
MM Btu when the heating values are known. The cost function
and constraints are linear expressions of the independent
variables, wherein the coefficient of each independent
variable is a constant.
B-4
-------
Cost Function
Several functions for the various cost components were
defined and summed to obtain coefficients of the independent
variables for use in the objective functions. All costs were
converted to $/MM Btu. The cost of raw coal at each mine
was applied to the flow along each arc originating at
that mine. Transportation costs reflected distances and
mode of transportation and were assigned to each arc from
mine to boiler or CCP and to each arc from a CCP output
(i.e., CC, CM, or CR) to a boiler. No transportation costs
are incurred on arcs from CCP to CC, CM, or CR as these
routes are totally within the coal cleaning plant. These
arcs from CCP to CC, CM, and CR were, however, assigned
the coal cleaning costs, except that normally the reject
stream was not considered a saleable product and was not
assigned any portion of the coal cleaning cost. Finally,
if any boiler had an FGD or ESP or both, those costs were
allocated to all arcs terminating in the node representing
that boiler.
Table B-l lists all arcs and indicates the cost com-
ponents allocated to flows along those arcs.
Constraints
This section discusses the constraints used in a basic
model. Ways of adjusting these constraints to reflect
various real situations will be discussed later. These
basic constraints include several less than or equal rela-
tions: plant capacity, boiler capacity, mine capacity,
emission limitations, and usage of CCP output. There is
one greater than or equal constraint: network demand.
We have also included a set of equality constraints de-
scribing the coal cleaning process. The constraints ef-
fecting each arc are shown in Table B-l.
For each plant, the sum of all flows into either node
for that plant must be less than or equal to the plant
B-5
-------
Table B-l. ARCS AND COST COMPONENTS ALLOCATED TO FLOWS
Al
A2
A3
Bl
B2
B3
Cl
C2
C3
A1F
A2F
A3F
B1F
B2F
B3F
C1F
C2F
C3F
CPCCP
CCPCC
CCPCM
CCPCR
CC1
CC2
CC3
CM1
CM2
CM 3
CR1
CR2
CR3
CC1F
CC2F
CC3F
CM1F
CM2F
CM3F
CR1F
CR2F
CR3F
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trnas+ESP
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trans+ESP
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans+ESP+FGD
Coal+Trans
Cleaning
Cleaning
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Trans+ESP+FGD
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Boiler
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Mine
Min
Mine
Mine
Mine
Mine
Mine
Mine
Cleaning
Cleaning
Cleaning
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Conservation
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
so2
S02
S02
SO2
SO2
so2
S02
S02
S02
S02
S02
so-,
so|
S02
so2
S02
S02
S02
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Plant
Cleaning
Conservation
Conservation
Conservation
Boiler Plant Network
Boiler Plant
Boiler Plant
Boiler Plant Network
Boiler Plant Network
Boiler Plant Network
Boiler Plant Network
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Boiler Plant
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
Network
S02
SO2
S02
S02
SO2
S02
S02
S02
SO2
S02
S02
SO,
S02
SO2
SO2
S02
S02
S02
B-6
-------
capacity, expressed in MM Btu. The coefficient of each
variable is 1.
The sum of all flows into each boiler node must be less
than or equal to the capacity (in MM Btu) of the boiler or
boilers represented by that node. The coefficient of each
variable representing a flow into a boiler node is 1 in the
constraint for that node.
The sum of all flows from a mine must be less than or
equal to the capacity of the mine. The coefficient of each
variable representing the flow from a particular mine is 1
in the constraint for that mine.
The Ib of S02/MM Btu burned at a particular plant must
be less than or equal to the emission limitation (in Ib
SO-/MM Btu) established by regulation. This relation must
be transformed, however, to fit the units used in the linear
programming formulation. The left-hand side is computed by
multiplying the amount (in MM Btu) of each coal stream
burned 'at a given plant by the Ib of SO- produced by burning
each MM Btu; this product is divided by the total amount of
coal burned at the plant to give the actual emission rate in
Ib S02/MM Btu.
Multiplying the left-hand side by the denominator, the
amount of coal burned, yields the total amount of S0_ pro-
duced. Multiplying the emission limitations on the right-
hand side by the total amount of coal burned results in the
allowable SO2 production at that level. This resulting
right-hand side may be subtracted from both sides to obtain
a constant right-hand side (zero) which is then in the
standardized form necessary for input in MPS. The relation
now states that excess S0? production (actual S0~ pro-
duction less allowable SO™ production) must be less than
or equal to zero.
B-7
-------
The above inequality applies when no FGD is used to
remove S0_ after combustion. For every boiler with FGD, the
corresponding term in the expression for actual S0_ pro-
duction must be reduced by the efficiency of the FGD system,
assumed to be 85 percent in this study. Thus, each such
term is multipled by 0.15 since only 15 percent of the S0~
produced by combustion is re"1 ^ased into the atmosphere when
FGD is used.
Network theory requires that for every node with flows
both in and out, there be a conservation constraint pro-
hibiting any creation or destruction of the commodity in the
flow, i.e., total flow in must equal total flow out. In
our network, such nodes are the nodes associated with the
outputs of the coal cleaning plant, CC, CM, and CR. To
allow for disposal of some of this coal, a node could be
created as a sink for unused coal. To simplify our network,
however, we have chosen to use inequality constraints at CC,
CM, and CR, i.e., flow out, must be less than or equal to
flow in. It is understood that the difference between flow
in and flow out represents unused coal. NOTE: without a
sink for unused coal and arcs from appropriate nodes it is
impossible to model the cost of storage, transportation, or
disposal of unused coal.
Network demand is a greater than or equal to constraint.
The sum of the outputs of all plants (or boilers) must be
greater than or equal to the network demand in MM Btu. The
output of any boiler is equal to the input in MM Btu mul-
tiplied by the efficiency of the boiler. The coefficient in
this constraint of each variable representing the flow into
any boiler would be unity if the efficiency of that boiler
were 100 percent.
B-8
-------
The set of constraints controlling the output of the
coal cleaning plant reflects the washability characteristics
of the coal being cleaned. When coal with known character-
istics is cleaned, the amount of coal output in each stream
per unit of raw coal can be predicted. This amount can be
expressed in units of pounds of feed. Since we are assuming
three output streams, the amount going to CC is a certain
fraction of the flow into CCP, the amount going to CM is
another fraction, and the amount to CR is the remainder.
The heating values of the output streams are different from
that of the input stream as a result of removal of sulfur
and ash from the clean and middling streams. The con-
straints must be expressed in terms of MM Btu. The flow
going to CC is equal to the fraction of the feed rate (in
lb/100 Ib feed) times 100 multiplied by the flow into the
CCP converted to pounds by dividing by the heating rate (in
Btu/lb) of the input stream. This flow is converted from
pounds to MM Btu by multiplying by the heating value of the
clean output stream. The coefficient of the variable repre-
senting the flow from CCP to CC may be given as -1, so that
all variables are on the left-hand side of the equality
constraint and the right-hand side is zero. The coefficient
of the variable representing flow into the CCP is the frac-
tion of the feed rate going to the clean stream (in lb/100
Ib feed) multiplied by 100 times the ratio of the heating
value of the clean output stream to the heating value of the
input stream. Constraints on the flows going to CM and CR
are formulated similarly.
B-4 MODIFICATIONS TO THE BASIC MODEL
The model described above was found to be quite flex-
ible to variations imposed to take into account additional
aspects of the real situation.
B-9
-------
Boiler Derating
The efficiency of a boiler can be reduced when an FGD
system is employed. This reduction is called derating. The
RHS representing boiler capacity for boilers with FGD's (IF,
2F, . . .) can be reduced accordingly.
The model can be allowed to .^se FGD for any portion of
the total capacity at a given olant by proper assignment of
capacities. Let node 1 represent the combined capacity of
all boilers at plant 1 if no FGD systems are used; then the
capacity at node 1 will be equal to the total plant capa-
city. The capacity at node IF may equal the total capacity
of all boilers with FGD's, derated by a factor representing
the decreased efficiency due to the FGD's. The sum of the
flows to node 1 and node IF will be less than or equal to
the plant capacity because all of these flows are in the
plant capacity constraint.
Mine Capacity
The mine capacity constraints are somewhat arbitrary.
It may be hard to determine or estimate the capacity of a
mine to deliver coal at a certain rate. If it is desired
that limited mine capacity affect the solution, the capacity
of each mine may be set slightly higher than the total
network demand.
Purchased Power
Often, when a utility company cannot meet the demand
with its own power plants, it will purchase power from
another utility company. This can be represented in the
model by a dummy mine node and dummy plant node disjoint
from the rest of the network. The flow to this dummy plant
is included in the network demand constraint, but there are
no mine capacity, plant capacity, boiler capacity, or emis-
sion limitations on this arc. The cost associated with this
B-10
-------
arc is the cost of the purchased power. This cost is high
enough that the flow on this arc will be positive only if
network demand cannot be met from other sources.
B-ll
-------
TECHNICAL REPORT DATA
,' ''lease read Instructions on the reverse be/ore completing/
t REPORT MO
EPA 450/3-78-045
4 TITLE ANDSUBTITLE
Linear Programming Derived Optimization Strategies for
Control of SO^ From Coal-Fired Power Plants
7 AUTHOR(S)
Richards, John; Nelson, A. Carl; Hardy, Albert
8 PERFORMING ORGANIZATION REPORT NO
9 PERFORMING ORGANIZATION NAME A\D ADDRESS
PEDCo Environmental, Inc.
11499 Chester Road
Cincinnati, Ohio 45246
3 RECIPIENT'S ACCESSION NO
5 REPORT DATE
November 1977
6 PERFORMING ORGANIZATION CODE
10 PROGRAM ELEMENT NO
11 CONTRACT/GRANT NO.
68-02-1452, Task No. 12
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Air Quality Planning and Standards
Strategies and Air Standards Division
Research Triangle Park, N. C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Contract Report
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Project Officers: Constancio F. Miranda and Rayburn M. Morrison
16. ABSTRACT
p
r
A linear programming (LP) technique has been used to determine a least cost
control strategy for a network of coal-fired power plants. The general
strategy consists of multi-stream coal cleaning in conjunction with the use of
low sulfur coal supplies and flue gas desulfurization. The use of linear programming
is demonstrated to be, a convenient mechanism to rapidly identify the most
economically attractive fuel redistribution/SO, control options. The structure of
the technique is a transshipment model. The simplex alorithm is used to
determine the minimum of an objective function which includes the major cost com-
ponents of interest. Non-linear cost functions are handled with a heuristic approach.
The LP results for two hypothetical power plant networks suggest that the use
of flue gas desulfurization and coal cleaning as a combined strategy yields a reduc-
tion in SOp compliance costs if moderate capital costs can be tolerated. For a 3
plant system with a combined capacity of 1150 MW, the LP solution resulted in an
incremental capital cost of 36.5 million and an 11 percent reduction in total
annualized costs. Annualized costs for a large network of 7 plants (combined capacity
12,970 MW) could potentially be reduced 4.5 percent. This saving results from a 30
percent reduction in annualized S0? compliance costs.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air pollution
Electric utility power plants
Steam generating units
Sulfur oxides
Sulfur oxides control strategies
Pollution control costs
Economics
Air Pollution Control
Coal
Power Plants
^IBUTION STATEMENT
Unlimited
19 SECURITY CLASS (This Report)
Unclassified
21 NO OF PAGES
126
2O SECURITY CLASS (Tills page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
C-l
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DATE DUE
'JUN •>
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