NBSIR 83-2658

Solcom: A Computer Program

to Integrate Solar and Conservation

Economics For New Commercial

Buildings

Operations Research Division

Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

lgton D.C. 20234

100

,1156

y 1983

o5-2653 apartment of Commerce

1933 al Bureau of Standards

NATIONAL BUREAU

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NBSIR 83-2658

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SOLCOM: A COMPUTER PROGRAM

TO INTEGRATE SOLAR AND

CONSERVATION ECONOMICS FOR NEW

COMMERCIAL BUILDINGS

Stephen R. Petersen

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Applied Mathematics

Operations Research Division

Washington, DC 20234

January 1 983

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

ABSTRACT

This report provides a methodology, algorithms and a computer program for

determining the minimum life-cycle cost combination of three interdependent

conservation strategies in new commercial buildings. These three strategies

consist of (1) envelope modifications to reduce seasonal and peak load heating

and cooling requirements, (2) heating and cooling plant modifications to

increase their seasonal efficiency, and (3) the use of an active solar space

and water heating system. The resulting computer program, called SOLCOM, can

be run on a microcomputer in three stages.

The SOLCOM program performs a complete life-cycle cost analysis for the active

solar system and for each envelope and plant modification to be considered,

including tax and mortgage effects. The program then determines the optimal

overall conservation investment strategy, including envelope modifications and

the corresponding seasonal and peak load heating and cooling requirements;

space heating, water heating, and space cooling plant efficiencies; and collector size for the active solar heating system.

Key words: building economics, commercial buildings; energy conservation;

engineering economics; heating and cooling equipment; heating

and cooling loads; life-cycle cost analysis; optimization

algorithms; solar heating.

iii
PREFACE

This report describes a computer program, developed at the National Bureau of

Standards, for the simultaneous optimization of a number of interdependent

energy-conservation-related investments in new commercial buildings. At present, this computer program, called "SOLCOM", is still experimental in nature.

It has not been field tested in actual building design exercises. While the

SOLCOM program provides a technically sound basis for the application of a microcomputer to complex economic decisions in new buildings, some improvements

may be needed to make the program more user oriented. Use of the SOLCOM program in actual building design problems must be made at the users own risk.

For a limited time, NBS will provide a copy of the SOLCOM program, for

experimentation and field testing use, by written request if accompanied by a 5 1/4-in "floppy" disk (compatible with the Radio Shack TRS-80 model III microcomputer) and a self-addressed return envelope. Requests should be addressed

to:

Stephen Petersen

Operations Research Division

Bldg. 224, Rm. B120

National Bureau of Standards

Washington, D.C. 20234

iv
ACKNOWLEDGMENTS

The author wishes to thank all those persons who contributed to the review and

final preparation of this report. Particular appreciation is extended to

Robert Chapman, James Barnett and William B. May for their careful review and

many helpful suggestions. The author also wishes to thank Robert Dikkers,

Leader of the NBS Solar Technology Group for his support of this project, and

the Office of Solar Heat Technologies, Department of Energy, for funding this

research. Finally, a special thanks to Brenda Thompson of the CBT Word

Processing Group for typing this report.
TABLE OF CONTENTS

Page

ABSTRACT Ill

PREFACE lv

ACKNOWLEDGMENTS v LIST OF FIGURES vii

LIST OF TABLES vii

1. INTRODUCTION 1

2. THE SOLCOM PROGRAM 5 2.1 WHAT SOLCOM CAN DO 5 2.2 DATA ENTRY FOR SOLCOM 10

2.3 RUNNING THE SOLCOM PROGRAM 11

3. CALCULATION PROCEDURES USED IN SOLCOM 22

3.1 ENERGY ESTIMATING PROCEDURES 22

3.2 SOLAR FRACTION ESTIMATING PROCEDURES 24

4. OPTIMIZATION CRITERIA AND ALGORITHMS 28

4.1 INDEPENDENT OPTIMIZATION CRITERIA 30

4.2 SIMULTANEOUS OPTIMIZATION OF DESIGN VARIABLES 35

4.3 OPTIMIZATION ALGORITHMS USED IN SOLCOM 37

4.3.1 Optimization of Solar Collector Area 38

4.3.2 Optimization of Envelope Modifications, AHR and ACR ..... 43

4.3.3 Optimization of Space Heating Plant Efficiency 47

4.3.4 Optimization of Water Heating Plant Efficiency 48

5. FINANCIAL ANALYSIS METHODOLOGY 50

5.1 CALCULATION OF DISCOUNT FACTORS 50

5.1.1 Cost Escalation Factors 50

5.1.2 Discount Factors 50

5.1.3 Modified Uniform Present Value Factors 51

5.2 GENERAL LCC MODEL FOR CONSERVATION INVESTMENTS IN BUILDINGS .... 51

5.2.1 Non-Energy Costs 51

5.2.2 Energy Costs 56

5.3 CALCULATION OF CUMULATIVE DEPRECIATION FACTORS AND FINANCING

FACTORS 56

5.3.1 Cumulative Depreciation Factors 56

5.3.2 Financing Factors 57

6. SUMMARY 60

REFERENCES 61

APPENDIX A. SOLCOM DATA SHEETS A-l

APPENDIX B. SOLAR LOAD RATIO COEFFICIENTS B-l

APPENDIX C. LISTING OF SOLCOM PROGRAM C-l

vi
LIST OF FIGURES

Page

3.1 Solar fraction vs. collector area for given building

(general form) 25

4.1 Cumulative envelope modification cost as a function of

annual heating requirements (general form) 29

4.2 Plant cost as a function of efficiency (general form) 29

4.3 Solar fraction as a function of collector area and annual

heating requirements (general form) 31

4.4 Total heating-related life-cycle costs: annual heating

requirements variable 31

4.5 Total heating-related life-cycle costs: plant efficiency variable .. 32

4.6 Total heating-related life-cycle costs: collector area variable .... 32

4.7 First derivative of the total cost curve as a function of

collector area (f'(A)) 40

4.8 Convergence algorithms to locate f'(A) = 0 40

LIST OF TABLES

Table 2.1 Sample Output from Overall Optimization Analysis (SI Units) ... 7

Table 2.2 Sample Output from Solar-Only Optimization Analysis

(SI Units) 9

Table 2.3 Supporting File FL2 (SI Units) 14

Table 2.4 Sample Output from Overall Optimization Analysis

(Customary Units) 17

Table 2.5 Supporting File FL1 (Customary Units) 19

vii
'
1 . INTRODUCTION

The large number of design measures for reducing purchased energy use in new commercial buildings can make the final design decision a difficult one. There

are literally hundreds of different energy-conserving methods that can be

incorporated into a new building design, from insulation to energy management

systems. The designer seeks the optimal combination of these measures — not

only in terms of today's energy market, but in terms of his projection of the

future energy market as well. Failure to plan for the future during the design

stage could significantly reduce the economic life of a building. While retrofitting of the building with additional energy conservation features at some point in time may stave off economic obsolescence, these same features can usually be incorporated into the original design at considerably lower cost.

Economic analysis plays an important role in the building design process by

providing systematic and objective decision-making methods for evaluating

energy-saving measures in new buildings. For example, life-cycle cost methods

can be used to determine which of several alternatives is least expensive in

doing a certain job (e.g., reducing heat loss or heat gain through windows to

a specified rate), not only in terms of initial cost but also in terras of maintenance, repair and replacement costs over the building life. Economic analysis can also be used with life-cycle costs and benefits to help to determine

how much of a particular conservation measure should be used, (e.g., how much

insulation should be used in exterior walls). Ultimately, these same analytical methods can be used to determine the economically optimal combination of

all conservation measures to be incorporated into the building design. The

economically optimal combination of conservation measures is defined here as that combination of measures which minimizes total present-value, energyrelated costs over the life of the building (or over a specified study period),

while satisfying required building performance objectives (e.g., thermal

comfort and design aesthetics).

Design measures for conserving energy in new buildings can be classified into

four general categories, each of which competes somewhat with the others in

reducing purchased energy requirements:

(1) envelope or other structural modifications which reduce end-use energy

requirements (e.g., space heating and cooling requirements),

(2) equipment modifications which increase the efficiency of energy

conversion to its end use form,

(3) renewable energy systems which substitute "free" energy available at

the building site (e.g., solar and wind power) for purchased energy

usage, and

(4) energy management systems to cut back or shut down energy using

systems when demand is reduced or eliminated during certain hours of

the day or days of the week.

1
This report explicitly addresses economic optimization procedures for the

first three of these design categories, specifically with regard to space

heating, space cooling, and service water heating. The fourth category

essentially establishes the operational profile for which the first three

categories of conservation measures must be evaluated. As such, energy

management systems are not explicitly considered as a design variable to be

optimized in this report.

A major obstacle to the determination of an overall minimum life-cycle cost

design is the functional interdependence among the first three of these com- peting approaches to energy conservation. For example, as the envelope of the

building is tightened up to reduce space heating loads, smaller purchased

energy savings are attributable to improvements in the heating plant efficiency, or to the addition of a solar heating system. The substitution of

solar heating for conventional heating results in smaller operating cost

savings from both envelope and conventional equipment improvements. And efficiency improvements to conventional space heating equipment reduce the energysaving benefits from improvements in the building envelope and solar heating

system. Determining the optimal allocation of conservation investment among

these three categories must be undertaken simultaneously. This requires a systematic procedure that can be employed within a reasonable amount of time

and with a reasonable amount of effort.

The purpose of this report is to provide a methodology, algorithms, and a supporting computer program that can be used by building design professionals

to determine the optimal amount of conservation investment to be made in each

of these three competing conservation categories. The resulting computer

program, called SOLCOM, is primarily intended for use as a design tool for new commercial buildings with active solar space and water heating equipment.

However, it can be used in the analysis of residential building designs with

active solar heating equipment as well. SOLCOM integrates a wide range of

building and component performance data, cost data and financial analysis

criteria for a specific building design. It then determines the economically

optimal combination of conservation measures, including envelope conservation

features, conventional space heating, water heating, and space cooling equipment efficiencies, and solar heating equipment size. Changes in energy costs,

conservation costs, the discount rate, study period, tax treatments and other

financial analysis criteria can be entered into the program in order to determine the sensitivity of the optimal design configuration to these variables.

A significant amount of thermal performance data and economic-engineering

analysis is needed before the SOLCOM program can be used. Space heating and

cooling requirements, water heating requirements, and peak heating and cooling

loads for the basic building envelope design must be determined, based on an anticipated occupancy profile and the climatic location. Appropriate envelope

modifications must be selected and their impact on heating and cooling requirements and peak loads estimated. Space heating, water heating, and space

cooling plant efficiencies and distribution energy requirements must be determined for each alternative system to be evaluated. Also, specific thermal performance parameters for the solar heating equipment must be known. Building

2
energy analysis programs, such as BLAST *

, DOE-2^, and TRNSYS^ , can be used to

obtain most of these physical performance data requirements. Solar performance

parameters are based on the Solar Load Ratio^ method. The report serves primarily as a users guide to the SOLCOM program. However, the life-cycle cost

and economic optimization methodologies and algorithms used in SOLCOM are thoroughly documented and can be used independently of SOLCOM if desired.

Examples of SOLCOM optimization analyses are shown for a hypothetical building

design but are not intended to provide insight into the relative merits of any

of the conservation methods examined.

This report represents a considerable extension of previous work on simultaneous

optimization of energy conservation measures in buildings. Sav^ has stated the

economic optimality conditions that must be satisfied in order to find a simultaneous solution to the design problem. Balcomb^ has reported a methodology to

determine the optimal mix of conservation and solar energy in building design

for residential applications, but without consideration of domestic hot water,

space cooling or simultaneous optimization of the conventional equipment efficiencies. Noll and Thayer^ have examined graphically the nature of the tradeoff between solar equipment sizing and envelope performance improvements.

Barley^ has developed an algorithm for optimizing both the relative size of

active solar equipment and insulation levels in each portion of a building

independently of the other portions, and includes water heating as well as space heating in the analysis. None of these reports focuses on commercial

building applications, nor do they allow optimization of the heating and

cooling equipment as in SOLCOM. The SOLCOM computer program, which can be run

1 Hittle, D. C., BLAST, The Building Loads Analysis and System Thermodynamics

Program , CEEDO-TR-77-35/CERL-TR-E-119/ADAOA8734 , U.S. Army Construction

Engineering Research Laboratory Systems [CERL], December 1977.

2 DOE-2 Reference Manual (Version 2.1), eds. D.A. York and E. F. Tucker,

LBL-8706 Rev. 1, Lawrence Berkeley Laboratory, Berkeley, CA, and LA-7689-M.

Ver. 2.1., Los Alamos National Laboratory, Los Alamos, N.M. , 1980.

3 TRNSYS - A T ransient Simulation Program. Solar Energy Laboratory, Report 38,

University of Wisconsin, Madison, WI. November 1976.

^ See both Schnurr, Norman M. , Hunn, Bruce D., and Williamson, III, Kenneth D.

,

"The Solar Load Ratio Method Applied to Commercial Building Active Solar

System Sizing," Solar Engineering - 1981 Proceedings of the ASME Solar Energy

Division 3rd Annual Conference on Systems Simulation, Economic Analysis/Solar

Heating and Cooling Operation Results, Reno, Nevada, April 27-May 1, 1981 , American Society of Mechanical Engineers, New York, N.Y., 1981, and Department

of Energy, DoE Facilities Solar Design Handbook , DoE/AD-0006/ 1 , U.S. Government Printing Office, Washington, D.C., 1978.

^ Sav, G. Thomas, "Economic Optimization of Solar Energy and Energy Conservation

in Commercial Buildings," Systems Simulations and Economic Analysis for Solar

Heating and Cooling, Proceedings of the U.S. Department of Energy Conference,

San Diego, CA, June 27-29, 1978, pp. 88-90.

3
on a microcomputer in three stages, provides a ready facility for solving

large-scale design optimization problems not available in these other reports.

Because this report serves primarily as a users guide to the SOLCOM computer

program, the program is described first. In section 2, three SOLCOM subprograms

are discussed, input data requirements are detailed, and examples of the output

are provided. In section 3, the computational procedures used in SOLCOM to

calculate annual energy use in a commercial building are discussed, and the

Solar Load Ratio (SLR) method of calculating solar fractions for 9pace heating

and water heating is outlined.

In section 4, the optimization criteria for determining the least life-cycle

cost combination of conservation measures in a building are examined. Optimization criteria are first presented for determining the optimal value of a single variable in a simple space-heating-only model. Simultaneous optimization methods are then discussed for the same model. Finally, the algorithms

for determining the optimal combination of envelope modifications, the optimal

solar collector area, and the optimal efficiency of the space heating plant and

water heating plant, as used in SOLCOM, are presented.

In section 5, the financial analysis method needed to determine the present

value of all conservation-related costs and energy costs are discussed. This

includes the analysis of initial costs, future operating and maintenance costs,

and salvage (or resale) value, tax adjustments, and mortgage arrangements.

Appendix A provides blank data sheets which can be used to organize the data

input needed to run the SOLCOM program. Appendix B lists the SLR coefficients

of six different active solar heating systems for commercial buildings that can be used in the SOLCOM program. Appendix C provides listings of the SOLCOM

program itself.

6 Balcomb, J. Douglas, "Conservation and Solar: Working Together,"

LA-UR-80-2330 , Los Alamos Scientific Laboaratory, Los Alamos, N.M., 1980.

and "Optimum Mix of Conservation and Solar Energy in Building Design,"

Proceedings of the 1980 Annual Meeting of the AS/ISES, June 2-6, 1980 ; Phoenix, AZ, pp. 1202-1206.

7 Noll, Scott and Thayer, Mark, "Passive Solar Auxiliary, Heat and Building

Conservation Optimization: A Graphical Analysis," Fourth Passive Solar

Conference Proceedings, Kansas City, Oct 3-5, 1979 .

® Barley, C. Dennis, "Load Optimization in Solar Space Heating Systems,"

Solar Energy , Vol. 23, pp. 149-156.

4
2. THE SOLCOM PROGRAM

2.1 WHAT SOLCOM CAN DO

The SOLCOM program was developed primarily to serve as a computer tool for use

by architects, engineers, and building researchers. Its purpose is to determine the economically optimal mix of certain energy conservation measures in a new commercial building design. More specifically, it allows the designer to

evaluate the technical and economic tradeoffs between three competing conservation approaches: (1) improvements in the thermal performance of the building

envelope to reduce space heating and cooling requirements, both in peak load

and annual terms; (2) higher efficiency conventional space heating, water

heating, and space cooling equipment; and (3) more use of active solar heating

equipment

.

The SOLCOM program is written in BASIC computer language and is compatible at

present with the Radio Shack TRS-80 Model III microcomputer (48K RAM) with one

or more disk drives and a compatible line printer with 132-character line

width. 1 The SOLCOM program actually consists of three subprograms which are run in sequence: S0LC0M1 , S0LC0M2, and S0LC0M3. It is assumed that the user

is familiar with the steps required to load and run a BASIC program from a

5 l/4-in disk.

(1) S0LC0M1 is a financial analysis subprogram which computes the present value

cost associated with each design option to be evaluated, including a variety

of tax effects and financing arrangements, over the study period selected by

the user. S0LC0M1 also computes the present value of unit energy costs over

the study period for each energy type specified. All of the conservation

measures to be evaluated, as well as base efficiency data for the conventional

heating and cooling systems are entered in the S0LC0M1 program. Pertinent

cost data, financial analysis assumptions, and borrowing terms, if any, are also entered in S0LC0M1 . The results of S0LC0M1 analysis are stored in an intermediate data file which is then read by S0LC0M2.

(2) S0LC0M2 is an optimization subprogram which determines the minimum

life-cycle cost combination of solar equipment size, conventional equipment

efficiencies, and envelope modifications. S0LC0M2 also determines the corre- sponding annual heating and cooling requirements, peak heating and cooling

loads, and conventional equipment size requirements. It reads in life-cycle

cost data from the intermediate file created in S0LC0M1 . Relevant optimization results and financial analysis data are stored in a second intermediate

file to be passed on the S0LC0M3.

1 Certain trade names and company products are identified in order to

adequately specify the computer equipment used. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the products are necessarily the best available

for the purpose.

5
(3) S0LC0M3 provides the format needed to print out the results of the SOLCOM

analysis. The intermediate file created by S0LC0M2 is read into S0LC0M3. This

data is processed into a comprehensive LCC report, which includes many of the

assumptions, the optimal combination of conservation measures, and the

resulting annual and peak load energy requirements for each end use.

SOLCOM determines the economically optimal solar collector size and space

heating and water heating plant efficiencies in a single run. However, in

order to optimize the space cooling plant efficiency, individual runs of

SOLCOM must be made for each alternative cooling efficiency level considered.

The results of these runs can then be compared manually in order to select

the overall configuration with the lowest total life-cycle cost. (Inclusion of

alternative cooling efficiency levels in a single analysis results in

unacceptably long run times.)

Two different types of analysis can be made with SOLCOM, as specified by the user during execution. The overall optimization mode finds the minimum lifecycle cost combination of envelope modifications, conventional equipment

efficiencies and solar collector area. An example of the output for this

overall optimization is shown in Table 2.1. The sample output first lists many

of the basic assumptions used in the life-cycle cost analysis and then provides

the results of the actual optimization analysis. Note that the life-cycle

costs attributed to the three categories of conservation expenditures do not

include energy costs or savings. Energy costs make up a fourth category of

costs. While the envelope modifications to be included in the optimal design

are printed out in decreasing order of cost effectiveness, their absolute cost

effectiveness (based on the energy savings attributable to each) is not

included in this report.

The solar-only optimization mode prints out the annual heating and cooling

requirements, the optimal solar collector area and corresponding solar fraction

for the base envelope configuration and subsequent configurations with cumulative conservation modifications (in the order that these modifications are entered in the supporting data files). An example of this solar-only optimization is shown in Table 2.2. The first line of calculated values pertains to

the base envelope configuration and each subsequent line gives results for a new envelope configuration containing an additional conservation measure. In

order to run the solar-only optimization, the user must specify which of the

space heating and water heating efficiencies contained in the input data files

to use. This solar-only optimization mode is useful for observing the relationship between the optimal collector size and the annual space heating and

water heating requirements for a building. In addition, the solar-only optimization shows the corresponding cumulative envelope modification costs, equipment costs, energy cost, and the total life-cycle cost corresponding to each

alternative envelope configuration. If the envelope modifications are entered

in order of decreasing cost effectiveness, the optimal envelope configuration

includes all conservation modifications up to and including the modification

resulting in the lowest total life-cycle cost. In table 2.2, the total (lifecycle) cost is minimized for a building having a space heating plant efficiency

of 60 percent, a water heating plant efficiency of 60 percent, and a cooling

plant efficiency of 200 percent (i.e., coefficient of performance of 2.0) by

6
Table 2.1 Sample Output from Overall Optimization Analysis (SI Units)

*

**

*

#

*

*

*

**

*

* ANNUAL DISCOUNT RATE AND COST ESCALATION RATES *************************

FROM: 1982 1987 1992

TO: 1986 1991 2001 ************** ****** ****** ****** DISCOUNT RATE 10.007. 10.007. 10.007.

AVERAGE ANNUAL

COST INCREASE:

MAINTENANCE 10.007. 10.007. 10.007.

BLDG VALUE 10.00% 10.007. 10. 007. NATURAL GAS 12.007. 1 1 . 007. 10.007.

ELECTRICITY 10.007. 10.007. 10.007.

BASE YEAR UNIT ENERGY COSTS ***************

*******************************

* PROJECT NAME: TEST PROBLEM (SI UNITS) * RUN DATE : 01 /08/83 00:11:00 * STUDY PERIOD: 20 YEARS (1982 TO 2001) * TAX STATUS: TAX-PAYING BUSINESS * INCOME TAX RATE: FEDERAL=46. 00%> STATE= 5.007. * PROPERTY TAX RATE: 2.007. STATE SALES TAX RATE: 0.007. * CAPITAL GAINS MULTIPLIER: FEDERAL=40. 00%> STATE=40. 007. * SUPPORTING FILE: FL2 *

* ******** * * *********************

END USE ENERGY TYPE UNIT KJ /UNIT UNIT COST ************* *********** ****** ******** :K it SPACE HEATING NATURAL GAS GJ 1000080

WATER HEATING NATURAL GAS GJ 1000000

SPACE COOLING ELECTRICITY KWH 3600

FANS/PUMPS: SOLAR ELECTRICITY KWH 3600

DISTRIBUTION: HTG ELECTRICITY KWH 3600

DISTRIBUTION: CLG ELECTRICITY KWH 3600

$ 9. 478

$9,478

$0. 060

$0. 060

$0,060

$0. 060

7
Table 2.1 (continued)

OPTIMIZATION ANALYSIS ft***#*#*#*#

( 1 )

( 2 )

( 3 )

OPTIMAL ENVELOPE MODIFICATIONS (IN DECREASING ORDER OF COST EFFECTIVENESS)

FIRST LIFE-CYCLE

COST COST*

MODI $1,2)00 $835

M0D2 $1,500 $790

M0D3 $2, 000 $1,054

TOTAL ENVELOPE MODIFICATION COST $4,500 $2,679

APPLICABLE TAX CREDITS $693

NET FIRST COST $3,807

OPTIMAL CONVENTIONAL EQUIPMENT EFFICIENCY:

OUTPUT CAP. SEASONAL FIRST LIFE-CYCLE

( MJ/HR ) EFFICIENCY COST COST*

SPACE HEATING 397 75.007. $10,260 $9, 090

WATER HEATING N/A 75.007. $3,700 $3,956

SPACE COOLING 182 200.007. $6,721 $6,586

TOTAL CONVENTIONAL EQUIPMENT COST $20,681 $19, 632

APPLICABLE TAX CREDITS $231

NET FIRST COST $20, 450

FIRST LIFE-CYCLE

COST COST*

SOLAR HEATING SYSTEM $22,017 $16,581

APPLICABLE TAX CREDITS $3,391

NET FIRST COST $18,626

OPTIMAL COLLECTOR SIZE

SOLAR FRACTION(S):

78.1 SQ. M

SPACE HEATING 18.27.

WATER HEATING 40. 17. COMBINED

FIXED COST

COST PER SQ. M

23.87.

» 1 y 000

$269

(4) ENERGY REQUIREMENTS AND COST:

OUTPUT ENERGY REQUIREMENTS

SPACE HEATING

WATER HEATING

SPACE COOLING

ANNUAL

GJ/YR ) 375

127

149

PEAK LOAD

( MJ/HR ) 269

N/A

149

INPUT ENERGY REQUIREMENTS

SPACE HEATING PLANT

WATER HEATING PLANT

SPACE COOLING PLANT

SOLAR FANS/PUMPS

DISTRIBUTION SYSTEM:

SPACE HEATING

SPACE COOLING

TOTAL ENERGY COST

(5) TOTAL LIFE CYCLE COST

******************

* AFTER-TAX LIFE-CYCLE COST

#*****ANNUAL****** FIRST—YR LIFE-CYCLE

402 GJ NATUR

COST

$3,808

COST*

$43,661

101 GJ NATUR $958 ‘ $10,988

1,015 KWH ELECT $1,261 $12,937

557 KWH ELECT $33 $343

1,775 KWH ELECT . $107 $1,093

705 KWH ELECT $42 $434

$6,209 $69,456

$108,348

8
Table

2.2

Sample

Output

from

Solar-Only

Optimization

Analysis

(SI

Units)

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X 1-1

X

Q O' U"J iH 1—1 vH tH tH 1—1

o. s _j h' CJ

—

O

X

X 3 X

1-H • ©* x II xscos INI Q • --i ll ce cc T-. h

in Ll.

x

x » i"

ill _j a.

qe o O HU)I- II 1-2 CO

cj

x uj o x ii III J D U 2

-J CJ 1 -I 4-

..J < UJ 1- CO O 15 > J <T. w

CJ I- 1 CJ UJ Cl X I- >- X

OE 2 CJ !-

•1 UJ UJ I l l I a

.J CJ to IO CJ

X

O

X LlI i.;.

X

O)

aK

H Q. DL

to o—i cn co

or. ~x •O'O'D'OO 3 *J X X X X X X X X . -CJ C'4 C'4 C-4 C'4 C'4

CJx • ro s i> go X CO '1- Q CD f"-

X

— in in in

x

x

x

—I r—l -i—I rH -H iH

ot ~ s o -h <i

n

©

Xx co C'4 -3 in

x i>x

— C'4

Q UJ

N

XX

xx ro to ro ro 9
using the first three envelope modifications and a solar heating system with

a total collection area of 132.7 m2

, resulting in a total life-cycle cost of

$118,858.

2.2 DATA ENTRY FOR SOLCOM

One supporting data file is needed to run the S0LC0M1 program. This file,

contains cost data, financial analysis assumptions, descriptors of the modifications to be examined, thermal performance data for the basic building and the

envelope modifications, and incident solar radiation data.l All input data are entered directly by the user into the data file using line numbers specified in

the data sheets. Interactive commands are used only for procedural decisions

during execution. The data file can be easily modified using the BASIC edit

mode of the microcomputer. In general, these data files are too long and com- plicated to warrant the use of an interactive file-creating subroutine for

data entry and modification. It is recommended that supporting files be created

separately from the SOLCOM program, saved 2 under their own names, and merged

with the S0LC0M1 program upon execution. This allows a permanent record of the

data file used for a given building analysis and allows it to be rerun at some future time.

SOLCOM analyses can be made in either SI units or conventional units of

measurement. Care must be exercised to use consistent units in the data entry

stage.

Because of the number and diversity of the data requirements needed in the

supporting file, 18 data entry sheets have been prepared to assist the SOLCOM

user. These data sheets are located in Appendix A. Not all of these data

sheets or data entries will be needed for every case, but they cover every

currently allowable input to the SOLCOM program. However, no default values

are provided, so that all relevant data entries must be made. The line

numbering scheme for the data entries does not have to be adhered to rigidly,

but each data point must be entered in the order shown and each data line must

be numbered higher than the one preceeding. The highest data line number that

1 The average daily incident solar radiation, by month, needed to run the

SOLCOM program requires that the angle and orientation of the solar collectors be known and used to modify the available solar radiation on a horizontal plane at the building site. For a discussion of this procedure see Powell, Jeanne W. , and Rodgers Jr., Richard C., FEDSOL: Program User's

Manual and Economic Optimization Guide for Solar Federal Buildings Projects,

NBSIR 81-2342, U.S. Department of Commerce, National Bureau of Standards,

Washington, D.C., August 1981.

2 A data file which is to be merged into a program must be saved in ASCII

format if the TRS-80 microcomputer is used. This is accomplished as: SAVE

"FILE NAME", A. After the S0LC0M1 program is loaded, the command MERGE "FILE

NAME" will pull the file into the program. The user should take care that no other data lines (lines with the word "DATA" after the line number) are in the SOLCOM program before the merge is made.

10
can be used is 19999. The term "DATA" must follow immediately after each line

number as shown. Each data entry must be separated by a comma, but no trailing

commas are permitted. Extreme care must be used in the data entry process

since no error checking routine is presently available. Actual examples of the

supporting data file are shown in section 2.3, along with the corresponding

SOLCOM optimization analysis.

2.3 RUNNING THE SOLCOM PROGRAM

As described in section 2.1, the SOLCOM program is run in three stages:

S0LC0M1 , S0LC0M2 and S0LC0M3, respectively. The TRS-80 microcomputer has two

ways of displaying output data: on the CRT screen (soft copy) and on the

printer (hard copy). The SOLCOM program has user-interactive data input

requests and error messages which show on the CRT screen. Only the final

formatted output from S0LC0M3, and the collector-only optimization analysis in

S0LC0M2, are printed out in hard copy.

To run SOLCOM, S0LC0M1 must first be loaded into the computer memory using the

BASIC "LOAD" command. The supporting data file is then entered (or merged)

into S0LC0M1 (see section 2.2). S0LC0M1 can then be started with a "RUN"

command. When all of the computations are complete (this takes 2-5 minutes),

a message will appear on the CRT screen:

"ENTER TRANSFER FILE NAME FOR S0LC0M2

At this point the user must enter the name of the transfer file to be created

in order to transfer the intermediate results to the S0LC0M2 program. (File names have a maximum of eight letters or numbers and must begin with a letter,

e.g., "0UT1". Do not use the name of another program or file already stored on the same disk or that existing program or file will be erased.) Once the

transfer file is created, the S0LC0M1 analysis is completed. S0LC0M2 can be

automatically run at this point if the user responds affirmatively to the CRT

message:

"DO YOU WANT TO RUN S0LC0M2?

If the user answers negatively, the S0LC0M1 program ends and can then be run again with changes in the supporting data file or with a new supporting data

file.

S0LC0M2 can be run separately (if a transfer file from S0LC0M1 is available) or

by being called in by S0LC0M1 . When S0LC0M2 is run, several user input requests

are made on the CRT screen:

(1) "ENTER TRANSFER DATA FILE NAME FROM S0LC0M1

The user should enter the same name as that entered in S0LC0M1 for transfer file

(e.g., 0UT1), or should enter the name of another file created in a previous run

of S0LC0M1

.

11
(2) "COMPLETE OPTIMIZATION ( 1 ) OR SOLAR COLLECTOR SIZE OPTIMIZATION

ONLY (2)?”

Enter "1" or ”2" as desired (see section 2.1).

If "1" is entered, the computer will request additional input:

"ENTER SEARCH STARTING POINT INDEXES (I,J,W) FOR ENVELOPE, SPACE HEATING

EFF, WATER HEATING EFF"

f.1. 4.L These indexes correspond to the I

L envelope modification, space heating

plant efficiency, and W

1"^ water heating plant efficiency, as described in the

data file used in SOLCOM1 (Data sheets 6, 9, and 11, respectively). Entries

should be separated by a comma. Good guesses as to what the optimal values of

I, J, and W are will help S0LC0M2 converge more rapidly on the optimal

combination of investments.

A second request is made for the complete optimization case:

"ENTER FIRST GUESS FOR THE OPTIMAL COLLECTOR AREA FOR THE STARTING POINTS

USED."

This area (in m^ for SI units or ft^ for conventional units) should be between

the minimum (Ml) and maximum (M2) collector sizes specified in the S0LC0M1 data

file. (See data sheet 15.)

If the solar collector size optimization only option is selected (2), SOLCOM2

requests the following data:

"ENTER INDEXES FOR SPACE HEATING (J) AND WATER HEATING (W) PLANTS."

The user enters 1 for the base heating plant efficiency or the appropriate J

index for any other space heating plant efficiency used in the S0LC0M1 file,

followed by a comma, and the desired value of the W index for the water heating

plant efficiency. No further user input is required. The results of the

solar-only optimization are output by the line printer.

If only the solar collector size optimization output is required, S0LC0M3 is

not needed and no transfer file is created. If the complete optimization

analysis is made in S0LC0M2, a transfer file to S0LC0M3 is needed. SOLCOM

asks:

"ENTER TRANSFER FILE NAME FOR S0LC0M3.

The user enters a file name (e.g. , 0UT2). Then S0LC0M3 is automatically loaded

and run at this point.

SOLCOM3 requires only one input from the user:

"ENTER TRANSFER FILE NAME FROM SOL COM2.

12
The user enters the name of the transfer file used to save the results of the

S0LC0M2 analysis. At this point the results of the complete SOLCOM analysis

will be printed out.

Table 2.1 shows the results from a SOLCOM analysis of a hypothetical office

building, based on the S0LC0M1 input data file shown in table 2.3 (FL2). This

is an example of a run made in SI units. Envelope modifications are hypothetical and are identified here only by arbitrary designators (MODI, M0D2, etc.).

Table 2.2, which shows a solar-only optimization example for the same building,

is also based on the data base In supporting file FL2.

Table 2.4 shows a SOLCOM analysis of the same building, made in conventional

units, with supporting data file shown in table 2.5 (FL1). The same run was made in both SI and conventional units to assist the user in preparing data

files in either measurement system and to show that the results are identical

in terras of optimal design specifications and corresponding costs.

In both of these examples, the auxiliary space heating and water heating plants

are separate. SOLCOM can also be used with a combined space and water heating

auxiliary plant, or for space heating only, by proper specification of variables Ql and Q2 in the supporting file to S0LC0M1. (See data sheet 11.)

13
Table 2.3 Supporting File FL2 (SI Units)

999 REM FILE NAME IS FL2. ANY CHANGES MUST BE SAVED IN ASCII FORMAT.

1(200 REM DATA SHEET 1 1031 DATA FL2

1032 DATA TEST PROBLEM (SI UNITS)

1003 DATA 2 i 1982, 20 » 1 » 46

1004 DATA 5,0,40,40,2

2000 REM DATA SHEET 2

2001 DATA 3

2101 DATA 5,10. 10i 10

2102 DATA 5 « 10. 10. 10

2103 DATA 10. 10. 10. 10

3000 REM DATA SHEET 3

3001 DATA 2

3101 DATA 12.10

3102 DATA 11,10

3103 DATA 10, 10

*•000 REM DATA SHEET 4 4101 DATA 9. 4778, 1000003, NATURAL GAS, GJ

4102 DATA 0.06, 3600, ELECTRICITY, KWH

50:50 REM DATA SHEET 5 5001 DATA 0

6000 REM DATA SHEET 6

6001 DATA 5 6101 DATA 1, MODI- 1000,25,2

6102 DATA 2, M0D2, 1500, 0,

0

6103 DATA 3, MODS, 2000,0,

0

6104 DATA 4, M0D4, 2500, 0,0

6105 DATA 5, MOD5 , 3000, 0,

0

6231 DATA 50,50,25,10,10

6202 DATA 50,50,25,10,10

6203 DATA 50,50,25,10,10

6204 DATA 50,50,25,10,10

6205 DATA 50,50,25,10,10

7030 REM DATA SHEET 7

7100 REM DATA SHEET 7-1

7101 DATA 10,50

7132 DATA 15,50

8000 REM DATA SHEET 8

8031 DATA 15,0

0002 DATA 1 3101 DATA 6.667,6.667,6.667,6.667,6.667

8106 DATA 6.667,6.667,6.667,6.667,6.667

8111 DATA 6.667,6.667,6.667,6.667,6.667

9000 REM DATA SHEET 9

9001 DATA 3,1,2,1.5,4.739

9011 DATA 60,5000,9.4778,100,3

9012 DATA 70,500,25,3

9013 DATA 75,1030,50,0

9021 DATA 50,50,25,0,0

9022 DATA 0,50,25,10,10

9023 DATA 0,50,25,10,10

10030 REM DATA SHEET 10

10100 REM DATA SHEET 10-1

10101 DATA 5,530

10102 DATA 10,500

10103 DATA 15,530

14
Table 2.3 (continued)

117)00

1 3.231

1 IE 33

11011

11012

11013

11021

11022

11023

12003

12100

12101

12102

1 300

0

13001

13002

13303

13101

14030

14031

14032

14101

14106

14111

15003

15031

15002

15003

15101

15102

15103

16000

16001

16002

16101

16136

16111

REM DATA SHEET 11 DATA 2,

2

DATA 3,

1

DATA 60j 3000 > 100i

2

DATA 7052005050

DATA 75550050,0

DATA 505505255050

DATA 0550,2550,0

DA i

A

0,50,25,0,0

REM DATA SHEET 12

REM DATA SHEET 12-1

DATA 8,500

DATA 16,500

REM DATA SHEET 13

DATA 2, 2, 200, 1.2,4. 739

DATA 55100, 9. 4778, 200, 1 DATA 50,50,25,0,0

DATA 105 100

REM DATA SHEET 14

DATA 15,0

DATA 1 DATA 6. 667 , 6. 667 ,6. 667 , 6. 667 , 6. 667

DATA 6. 667,6. 667, 6. 667, 6. 667,6.667

DATA 6.667,6.667,6. 667 , 6 . 667 , 6 . 667

REM DATA SHEET 15

DATA 1030,269.1,2,1,4.739

DATA 29,465,100,3

DATA 50,50,0, 10, 10

DATA 5,500

DATA 10,500

DATA 15,500

REM DATA SHEET 16

DATA 15,0

DATA 1 DATA 6. 667, 6. 667, 6. 667,6. 667,6. 667

DATA 6.667,6.667,6.667,6.667,6.667

DATA 6.667, 6.667,6. 667,6.667,6.667

15
Table 2.3 (continued)

17000 REM DATA SHEET 17

17101 DATA 84. 408.63. 306*42. 204, 21. 102

17105 DATA 21. 102,0,0,0

17109 DATA 21.102,42.204,42.204,84.408

17113 DATA 316.53,158.265,158.265

17201 DATA 10. 521, 10.551, 10.551, 10.551

17205 DATA 10.551,10.351,10.551,10.551

17209 DATA 10.551,10.551,10.551,10.551

17301 DATA 10016,12423,14445,15728

17305 DATA 16330,16989,16693,16534

1730? DATA 16250, 14956, 11140,8551

18000 REM DATA SHEET 18

1809^ REM DATA SHEET 18-1

18100 DATA 1 18101 DATA 4.2204,3.1653,2.1102,1.0551

18105 DATA 1.0551,0,0,0

18109 DATA 1.0551,2.1102,2.1102,4.2204

18113 DATA 21.102,4.2204,4.2204

18199 REM DATA SHEET 18-2

18200 DATA 2

18201 DATA 3.1653,2.1102,2.1102,1.0551

18205 DATA 0,0, 0,0

18209 DATA 1.0551,1.0551,2.1102,3.1653

18213 DATA 15.8264,3.1653,3.1653

18299 REM DATA SHEET 18-3

18300 DATA 3

18301 DATA 2.1102,2.1102,1.0551,1.0551

18305 DATA 0,0, 0,0

18309 DATA 0,1.3551,1.0551,2.1102

18313 DATA 10.551,2.1102,2.1102

18379 REM DATA SHEET 18-4

18400 DATA 4

13401. DATA 1.0551,1.0551,1.0551,0

1 8^05 DATA 8,0, 0,0

'.£409 -DATA 0,2, 1.0551, 1-. 055-1 18413 DATA 5.2755,1.0551,1.0551

18499 REM DATA SHEET 13-5

13500 DATA 5 13531 DATA 1.0551,1.0551,1.0551,0

1S535 DATA 0,0, 0,0

13509 DATA 0,0,1.0551,1.0551

18513 DATA 5-2755,1.0551,1.0551

16
Table 2.4 Sample Output from Overall Optimization Analysis (Customary Units)

a*******************************

* #

* PROJECT NAME: TEST PROBLEM (CUST. UNITS) * * RUN DATE : 01 /0S/83 01:52:13 *

* STUDY PERIOD: 20 YEARS (1982 TO 2001) * * TAX STATUS: TAX-PAYING BUSINESS *

* INCOME TAX RATE: FEDERAL=46. 007., STATE3 5.007. *

* PROPERTY TAX RATE: 2.007. STATE SALES TAX RATE: 0.007. *

* CAPITAL GAINS MULTIPLIER: FEDERAL=40. 007., STATE=40. 007. *

* SUPPORTING FILE: FL1 *

* * ******** * * * * * * * * ********

ANNUAL DISCOUNT RATE AND COST ESCALATION RATES ******** * * * * * * * * ********

FROM: 1982 1987 1992

TO: 1988 1991 2001 ************** ****** ****** ****** DISCOUNT RATE 10.007.

AVERAGE ANNUAL

COST INCREASE:

10.007. 10.007.

MAINTENANCE 10.007. 10.007. 10.007.

BLDG VALUE 10.007. 10.007. 10.007.

NATURAL GAS 12.007. 1 1 . 007. 10.007.

ELECTRICITY 10.007. 10.007. 10.007.

BASE YEAR UNIT ENERGY COSTS ***************

END USE ENERGY TYPE UNIT BTU/UNi'T UNIT COST ************* •)r #$£ -X* >£ #*X- £- ****** ******** X* *jc Sf -fr >(- a- ik SPACE HEATING NATURAL GAS THERM 100000 $1,000

WATER HEATING NATURAL GAS THERM 100000 $1 . 002

SPACE COOLING ELECTRICITY KWH 3412 $0. 060

FANS /PUMPS: SOLAR ELECTRICITY KWH 3412 $0,060

DISTRIBUTION: HTG ELECTRICITY KWH 3412 $3. 060

DISTRIBUTION: CLG ELECTRICITY KWH 3412 $3. 0oU

*************************************

17
Table 2.4 (continued)

OPTIMIZATION ANALYSIS ***********

( 1 ) OPTIMAL ENVELOPE MODIFICATIONS (IN DECREASING ORDER OF

FIRST

COST

COST EFFECTIVENESS)

LIFE-CYCLE

COST*

MODI $1,000 $835

MOD2 $1,500 $790

M0D3 $2 , 003 $ 1,054

TOTAL ENVELOPE MODIFICATION

APPLICABLE TAX CREDITS

NET FIRST COST

COST $4,500

$693

$3,807

$2, 679

(2) OPTIMAL CONVENTIONAL EQUIPMENT EFFICIENCY:

OUTPUT CAP. SEASONAL

(MBTU/HR) EFFICIENCY

SPACE HEATING 376 75.007.

WATER HEATING N/A 75.007.

SPACE COOLING 172 200.007.

TOTAL CONVENTIONAL EQUIPMENT COST

APPLICABLE TAX CREDITS

NET FIRST COST

FIRST LIFE-CYCLE

COST COST*

$10? 260 $9, 090

$3, 700 $3,956

$6,721 $6,586

$20,681 $19,632

$231

$20,450

(3) SOLAR HEATING SYSTEM

APPLICABLE TAX CREDITS

NET FIRST COST

FIRST LIFE-CYCLE

COST COST*

$22,050 $16,603

$3,396

$18,654

OPTIMAL COLLECTOR SIZE

SOLAR FRACTION(S):

842.0 SQ.FT.

SPACE HEATING 18.27.

WATER HEATING 40. 17. COMBINED 23.87.

FIXED COST $1 , 000

COST PER SQ.FT. $25

ENERGY REQUIREMENTS AND COST

:

OUTPUT ENERGY REQUIREMENTS ANNUAL PEAK LOAD

(MMBTU/YR) (MBTU/HR)

SPACE HEATING

WATER HEATING

SPACE COOLING

355

120

141

255

N/A

141

INPUT ENERGY REQUIREMENTS ******ANNUAL****** FIRST-'

COST

SPACE HEATING PLANT 3,807 THERM NATUR $3,837

WATER HEATING PLANT 958 THERM NATUR $958

SPACE COOLING PLANT 21,015 KWH ELECT $1,261

SOLAR FANS/ PUMPS

DISTRIBUTION SYSTEM:

558 KWH ELECT $33

SPACE HEATING 1 , 775 KWH ELECT $107

SPACE COOLING

TOTAL ENERGY COST

705 KWH ELECT $42

$6,208

(5) TOTAL LIFE CYCLE COST

******************

* AFTER-TAX LIFE-CYCLE COST

NOTE: MBTU = 1,000 BTU 5 MMBTU = 1,003,000 BTU

LIFE-CYCLE

COST*

$43,651

$10,983

$12,937

$343

$1,093

$434

$69,441

$108,355

18
Table 2.5 Supporting File "FLl" (Customary Units)

799 HL'H HUE NAME IB FLl. ANY CHANGES MUST BE SAVED IN ASCII FORMAT.

i t?ii« i?i:m da ta miri.T \

I m1 DATA FLl

1002 DATA TEST PROBLEM (CUST. UNITS)

1 m

3

DATA 1,1982, 20 , 1 , 46

1004 DATA 5,0,40,40,2

2000 REM DATA SHEET 2

2001 DATA 3

2101 DATA 5,10, 10, 10

2102 DATA 5,10, 10, 10

2103 DATA 10, 10, 10, 10

3000 REM DATA SHEET 3

3001 DATA 2

3101 DATA 12,10

3102 DATA 11,10

3103 DATA 10,10

4000 REM DATA SHEET 4

4101 DATA 1.00, 100000, NATURAL GAS, THERM

4102 DATA 0.06, 3412, ELECTRICITY, KWH

5000 REM DATA SHEET 5

5001 DATA 0

6000 REM DATA SHEET 6

6201 DATA 5 6101 DATA 1, MODI, 1000,25,2

6102 DATA 2, M0D2, 1500,0,0

6103 DATA 3, M0D3, 2000, 3,

0

6104 DATA 4, M0D4, 2500, 0, 0 . 6105 DATA 5, MODS , 3000, 0,

0

6201 DATA 50,50,25,10,10

6202 DATA 53,50,25,10,10

6203 DATA 50,50,25,10,10

6204 DATA 50,50,25,10,10

6205 DATA 50,50,25,10,10

7000 REM DATA SHEET 7 7100 REM DATA SHEET 7-1

7101 DATA 10,50

7102 DATA 15,50

8000 REM DATA SHEET 8

8001 DATA 15,0

8002 DATA 1 8101 DATA 6.667,6.667,6.667,6.667,6.667

8106 DATA 6.667,6.667,6.667,6.667,6.667

8113 DATA 6.667,6.667,6.667,6.667,6.667

9000 REM DATA SHEET 9

9001 DATA 3, 1*2* 1.5,5

9011 DATA 60,5000,10,100,3

9012 DATA 70,500,25,0

93 1 3 DATA 75 , 1 300 , 53,0

9321 DATA 50,50,25,0,0

9022 DATA 0,50,25,10,10

9023 DATA 0,50,25,10,10

103530 REM DATA SHEET 10

13100 REM DATA SHEET 10-1

10101 DATA 5,500

10102 DATA 10,500

10103 DATA 15,500

19
Table 2.5 (continued)

1 1000 REM I 11001 DATA

1 1003 DATA

1101

1

DATA

11012 DATA

11013 DATA

11021 DATA

1 i 022 DATA

11023 DATA

12000 REM I 12100 REM 1 12101 DATA

12102 DATA

13000 REM 1 13001 DATA

13002 DATA

13003 DATA

13101 DATA

14000 REM I 14001 DATA

14002 DATA

14101 DATA

14106 DATA

14111 DATA

15000 REM : 15001 DATA

15002 DATA

15003 DATA

15101 DATA

15102 DATA

15103 DATA

16000 REM I 16001 DATA

16002 DATA

16101 DATA

16106 DATA

16111 DATA

DATA SHEET 11 2.2

3. 1 60i 3000i 100i

2

70i 200i 0i

0

75* 500i 0i0

50i 50i 25 i 0i

0

0i 50i 25i 0i

0

0i 50i 25 i 0i

0

DATA SHEET 12

DATA SHEET 12-1

8i 500

16i 500

DATA SHEET 13

2i 2i 200i 1 . 2i

5

5000! 101200!

1

50i 50i 25 i 0i

0

10 ! 100

DATA SHEET 14

15 1 0

16. 667 1 6. 667 1 6. 667 1 6. 6. 667 i 6. 667 i 6. 667 i 6. 6. 667 i 6. 667 i 6. 667 i 6. DATA SHEET 15

1000! 25i 2i 1.5

320i5000i 100!

3

50! 501 0! 10! 10

5 1 500

10i 500

15i 500

DATA SHEET 16

15 1 0

16 . 667 1 6. 667 1 6 . 667 1 6. 6. 667 1 6. 6671 6. 667 1 6. 6 . 667 1 6 . 667 1 6 . 667 1 6.

667 1 6. 667

667.6.667

667.6.667

667.6.667

667.6.667

667 1 6. 667

20
Table 2.5 (continued)

17000 REM 1DATA SHEET 17

17101 DATA 80, 60i 40i

2

:0 17105 DATA 20i0i0i0

17109 DATA 20i 40i 40i 80

17113 DATA 300i 150i 150

17201 DATA 10i 10i 10i 10

17205 DATA 105 101 101 10

17209 DATA 105 101 101 10

17301 DATA 882 i 1094,

1

272, 1385

1 7305 DATA 1438, 1496, 1470, 1456

1 730? DATA 1431, 1317,931,753

18000 REM DATA SHEET 18

18099 REM DATA SHEET 18-1

18100 DATA 1 18101 DATA 4,3, 2,

1

18105 DATA 1,0,010

1310? DATA 1 , 2, 2,

4

18113 DATA 20,4,4

1819? REM DATA SHEET 18-2

18200 DATA 2

18201 DATA 3,2,2,

1

1S205 DATA 010,0,0

1320? DATA 1 , 1,2,3

18213 DATA 15,3,3

18299 REM DATA SHEET 18-3

1838S DATA 3

1 830

1

DATA 2 , 2 , 1 , 1 18335 DATA 0,0,010

18389 DATA 0 , 1 , 1 ,

2

16313 DATA 10,2,2

18399 REM DATA SHEET 18-4

18480 DATA -il. 18431 DATA 1 , 1 , 1 ,

0

18405 DATA 05 01 05 0

18409 DATA 050, 1, 1

... 18413 DATA 5,1,1

13499 REM DATA SHEET 18-5

18503 DATA 5 18501 DATA 1 , 1 , 1 ,

0

18505 DATA 0, 0, 0, 0

1850? DATA 0,0, 1, 1 18513 DATA 5,1,1

21
3. CALCULATION PROCEDURES USED IN SOLCOM

3.1 ENERGY ESTIMATING PROCEDURES

The methodology used in SOLCOM2 to estimate annual purchased and solar energy

use for space heating, water heating, and space cooling in a commercial building

is described in this section. Purchased energy requirements may be made up of

several different energy types, specified individually by end use. For example,

gas can be specified for space and water heating and electricity for space

cooling. Electricity is always assumed to be used by the HVAC distribution

system and by the fans and pumps in the solar heating equipment. However, only

one type of energy can be specified for any given equipment type. (Switching

among fuels for space heating cannot be handled in the program.)

Annual energy use is estimated separately for each of the following functions:

(1) space heating plant,

(2) water heating plant,

(3) space cooling plant,

(4) fans and pumps: solar equipment,

(5) distribution system: heating, and

(6) distribution system: cooling.

Energy prices can be specified individually for each of these functions, even

if the same energy type is used, so that seasonal differences in utility rate

structures can be reflected. For example, electricity rates are generally

higher in summer than in winter, so that a higher average kWh price may be more appropriate for cooling than for space heating. Because water heating is

required throughout the year, an average annual rate is most appropriate for

this function. (Time-of-use rates cannot be handled by the SOLCOM program.)

Each kWh of electricity used to run the fans and/or pumps in the heating and

cooling distribution system is assumed to result in the generation of 3,600 KJ

(3,412 Btu) of thermal energy. During heating operations this additional

thermal energy helps offset space heating requirements; during cooling operations the additional thermal energy adds to the space cooling requirements.

The distribution system is assumed to provide space heating from both the

conventional space heating plant and the solar heating equipment. The thermal

energy from the fans and/or pumps in the solar heating system itself is

assumed to be included in the useful energy output of that system and not in

addition to that output. Energy use by the distribution system during periods

when no space heating or cooling is required (i.e., for ventilation purposes

only) is not accounted for in SOLCOM. It is assumed that any changes in ven- tilation requirements during these periods resulting from the envelope

modifications made will be insignificant.

The following equations describe the calculation procedures used in S0LC0M2 to

determine annual purchased energy requirements for each of the six functions

listed above.

22
1.

Space Heating Plant

Purchased

Energy

Requirements

(Unitsi/yr)

(1 - EE • DEj) • AHR • (1-FH) • S

HE • Tu/Unit'i

(3.1)

where EE = .0036/kWh if AHR is in GJ or 0.003412/kWh if AHR is

in 106Btu,

DEj = kWh consumed by distribution system per GJ or

106 Btu of AHR,

AHR = annual space heating requirements (in GJ or lO^Btu),

FH = annual solar fraction, space heating,

HE = seasonal efficiency of the space heating plant (useful

thermal output /thermal equivalent input),

Tu/Unitj = thermal content (KJ or Btu) of energy units

purchased for space heating, and

S = 106 .

2.

Water Heating Plant

Purchased

Energy - AWR « (1 - FW) « S (3.2)

Requirements WE • Tu/Unit 2

(UnitS2/yr)

where AWR = annual water heating requirements (in GJ or lO^Btu),

FW = annual solar fraction, water heating,

WE = annual average efficiency of water heating plant, and

Tu/Unit 2 = thermal content (KJ or Btu) of energy units

purchased for water heating.

3.

Space Cooling Plant

Purchased

Energy

Requirements

(UnitS3/yr)

(1 + EE • DE2

)

• ACR • S

CE • Tu/Unit 3

(3.3)

where EE = 0.0036 if ACR is in GJ, or 0.003412 if ACR is in 106Btu

DE2 = kWh consumed by distribution system per GJ or lO^Btu

of ACR,

ACR = annual space cooling requirements (in GJ or lO^Btu),

CE = seasonal efficiency (or seasonal performance factor if

CE>1.0) of space cooling plant, and

Tu/Unit 3 = thermal content (KJ or Btu) of energy units used for

space cooling.

23
4. Solar Heating System: Pumps/fans

Purchased

Energy

Requirements

(kWt^/yr) = [(1 - EE • DE^) • AHR • FH + AWR • FW] • DE3 (3.4)

where DE 3 = kWh consumed by solar heating system per GJ or lO^Btu useful output.

Distribution System: Space Heating

Purchased

Energy

Requirements

(kWh5 /yr)

= AHR • DEi . (3.5)

Distribution System: Space Cooling

Purchased

Energy

Requirements

(kWhfc/yr)

= ACR • DE2

. (3.6)

It should be recognized here that the seasonal efficiencies of the space and

water heating plants are assumed to remain relatively constant as the envelope

is upgraded and the solar fraction is increased. The degree to which this

assumption is realistic depends largely on the type of equipment used, especially with regard to cycling performance. This assumption is not likely to

be realistic if an air source heat pump is used in the heating mode, since the

average air temperature during the on-cycle will be lower as the envelope is

tightened up and the solar fraction increased. In general, it is best to use estimates of seasonal efficiency that are valid for the overall optimal design

of the building, including the solar collector sizing. This may require

several iterations with the SOLCOM program, with a reestimation of the seasonal

efficiencies for the conventional heating and cooling equipment made after one SOLCOM run and used in the next until no significant differences appear.

3.2 SOLAR FRACTION ESTIMATING PROCEDURES

In order to estimate the optimal size of a solar heating system, it is

necessary to be able to determine the annual solar fraction corresponding to

any collector size based on the system type, building heating requirements, and

incident solar radiation. Figure 3.1 shows the general relationship between

the solar fraction and collector area for a particular building installation.

This relationship is characterized by a curve which is relatively straight at

first but gradually increases less and less as the collector area is increased

more and more. Eventually very large increases are needed to produce even small increases in the solar fraction as it approaches 100 percent.

24
Figure 3.1 Solar fraction vs. collector area for given building

(general form)

25
There are a variety of methods available to relate the annual solar fraction to

collector area, with varying degrees of accuracy and computational requirements

These range from complex engineering algorithms which require hourly perfor- mance calculations over the entire year to a single equation with coefficients

representative of a given system type and location. Ideally, a single equation

method, such as that proposed by Lamerio and Bendt ^ would be used in the

optimization analysis. With such an equation the total life-cycle cost curve could be differentiated (either mathematically or numerically) with respect to

collector area to find the collector area for which total cost is minimized.

However, single equation models do not represent the annual performance of a space heating system or combined space and water heating systems well enough

for optimization purposes. The absolute value of the solar fraction may be

reasonably well estimated for any given collector size using a single-equation

method. But, the estimated change in the solar fraction due to the change

in collector area - which is critical to the optimization analysis - does not

appear to be accurate enough to give a reasonable estimate of the optimal

collector size. This is unfortunate, because any alternative requires a separate algorithm to compute the annual solar fraction for a given collector

area, heating load profile, and incident solar gain schedule. Since no continuous function relating solar fraction and collector area results, any optimization algorithm must make multiple entries into the subroutine used to compute

the solar fraction as it converges on the optimal collector area. Since the

determination of an optimal collector area is made repeatedly as the building

envelope is modified and the equipment efficiencies are changed, it is important that the solar fraction algorithm be as efficient as practical. This

essentially precludes the use of hourly or even daily estimates of solar fractions from collector areas. As a practical matter, a monthly calculation procedure is the least aggregated method that is compatible with microcomputer

applications.

The Solar Load Ratio (SLR)^ method for space heating and combined space and

water heating systems is used in the SOLCOM program to estimate solar fractions

from collector areas. This method calculates monthly solar fractions based on

a solar load ratio particular to the building, its location, and collector size

using a set of four coefficients that typify the performance of a known heating

system type. Monthly fractions and heating loads are then aggregated to provide an annual solar fraction. The following two equations are used to find

the monthly solar fraction:

* Lamerio, Gerald F. and Bendt, Paul, "The GFL Method for Sizing Solar Energy

Space and Water Heating Systems," SERI-30, Solar Energy Research Institute,

Golden, Colorado, 1978.

^ Schnurr, Norman M. , Hunn, Bruce D. , and Williamson, III, Kenneth D. , "The

Solar Load Ratio Method Applied to Commercial Building Active Solar System

Sizing," Solar Engineering - 1981 Proceedings of the ASME Solar Energy

Division 3rd Annual Conference on Systems Simulation, Economic Analysis/

Solar Heating and Cooling Operation Results, Reno, Nevada, April 27-May 1,

1981 . American Society of Mechanical Engineers, New York, NY, 1981. See

also Powell and Rodgers' FEDSOL Program User's Manual , Appendix E-2, and U.S.

Department of Energy, DoE Facilities Solar Handbook .

26
F for 0 < Xm < b£ , and (3.1a) ra = b lXm

-b/.X_

Fm

~ 1 ~ b

3 e for > b2

(3.1b)

where Fm * monthly solar fraction,

Xm “ monthly solar load ratio ** AcHf/TL^,

Ac = collector area,

Ht = solar energy per unit area incident monthly on the plane of the

collector,

TLm = monthly combined space and water heating load (net of thermal

output from fans and pumps in distribution system), and

b^ through b4 = system performance coefficients, based on the solar load ratio

method (see appendix A).

The annual solar fraction (F) is then calculated by summing useful monthly

solar energy output and monthly loads and dividing as follows:

12

l Pm • TLm

F = Hz! . (3.2)

12

I TLm

m=l

Appendix B lists system performance coefficients (bj - b^ for several

different solar heating equipment types compatible with commercial buildings.

These coefficients are dimensionless; thus they work equally well with SI and

conventional units of measurement. These coefficients are taken from Powell

and Rodgers, FEDSOL Program User’s Manual . Other coefficients can be substituted for these in the S0LC0M2 program before execution (lines 2460-2690).

The SLR method has been modified slightly in the SOLCOM program in order to

provide separate estimates of the annual solar fraction for space heating (FH)

and water heating (FW) when separate conventional heating plants are used. This

is because separate plants will likely have different efficiencies and may even use different types of energy with different costs. The monthly fractions are calculated as shown in equations 3.1a and 3.1b. However, in calculating the

annual fractions, the following equations are used in addition to equation 3.2

to break out FH and FW separately:

12

I Fm • HLm

FH = 5li

12

I H^m

m=l

(3.3) and

12

I Fm

* W^m

FW = Bzl

12

l WLm

ra=l

(3.4)

27
4. OPTIMIZATION CRITERIA AND ALGORITHMS

A relatively simple model of the total heating-related life-cycle cost of a building is used in sections 4.1 and 4.2 to demonstrate the concepts of independent and simultaneous economic optimization criteria. A more complete

exposition of the optimization algorithms used in SOLCOM is provided in section

4.3.

In its most elementary form, the total life-cycle heating-related cost of a solar-heated building can be expressed as

TC = AHR ( 1 ~F

)

. Ke

EFF

UPV* + K + K . + K , , env equip solar* and (4.1)

Ksolar = Kp + Ky • A, (4.2)

where TC = the total present-value of all heating-related costs over the study

period used,

AHR = annual heating requirements (in some units),

F = solar fraction for a given collector area,

EFF = seasonal efficiency of the heating equipment,

Ke = unit price of energy (in the same units used to denote AHR),

UPV* = modified uniform present value factor based on the study period

length, discount rate, and rate of price increase for the energy

type used,

Kenv

= present value cost of all envelope modifications corresponding to

the AHR above,

Kgquip = present value cost of the conventional heating equipment

corresponding to the EFF above,

Kgoiar

= present value cost of solar heating equipment with collector area A that provides the solar fraction F, given the AHR above,

Kp = the fixed cost for the type of solar heating system used, and

Ky = the variable cost per unit of collector area.

Kenv , Keq u ip , and Kso lar include all costs incurred over the study period (e.g.,

initial cost; operating, maintenance and repair costs; tax adjustments), except

for the energy used for heating. In general, it is assumed that the least

costly means of achieving any given level of thermal performance for any given

component modification is used, provided that it does not diminish other perfor- mance requirements of the same components. For example, the insulation material

with the lowest effective cost per unit of thermal resistance would be used

rather than a more expensive material, provided that it satisfied the minimum

technical specifications for insulation materials.

^ While Ky is related to the collector area, it also includes any other

variable costs which occur as a result of scaling up the system (e.g., storage and plumbing costs). Kp and Ky may not be valid over the entire range of

possible collector sizes but should be specified for the region in which the

optimal area is expected to occur.

28
Figure 4.1 Cumulative envelope modification cost as a function of

annual heating requirements (general form)

Figure 4.2 Plant cost as a function of efficiency (general form)

29
In section 4.1, the model described in equation (4.1) is used to formulate

economic optimization criteria for AHR, EFF, and A, independently of one another. Optimization criteria are developed for both continuous and discrete

changes in these three variables. In section 4.2, the same model is used to

formulate simultaneous optimization criteria for both continuous and discrete

functions

.

4.1 INDEPENDENT OPTIMIZATION CRITERIA

In this section, independent economic optimization criteria are formulated for

AHR, EFF, and A. That is, only one variable is optimized at a time while the

other two are held constant.

Initially it is assumed that AHR and EFF are continuous functions of K^y and

Kequip» respectively. Moreover, we assume that AHR decreases at a decreasing

rate as Kenv increases (see figure 4.1) while EFF increases at a decreasing

rate as Kequip increases (see figure 4.2). In general, the solar fraction (F)

increases at a decreasing rate as the solar collector area (A) increases (see

figure 3.1). However, F is also a function of the AHR, since any decrease in

AHR will increase F if A is held constant (see figure 4.3).

The functional relationships between total life-cycle cost and each of the

three independent design variables are shown in figures 4.4, 4.5, and 4.6. In

each of these figures, the total LCC curve is the sum of Kenv , Ke q U^p, Kso i ar and LC energy costs. In each case it is evident that increases in conservation

investment initially reduce life-cycle costs, but that beyond some point,

further increases result in higher life-cycle costs. The point at which the

TLCC function is minimized for each of these three independent variables (AHR'

EFF', and A' in figures 4.4, 4.5, and 4.6, respectively) can be found by

finding the first derivative of equation 4.1 with respect to that variable,

setting the first derivative equal to zero, and solving for the corresponding

value of that variable.

Thus, to determine the optimal AHR (AHR*) and corresponding envelope

modifications, given that EFF and A are fixed, the partial derivative of TC

with respect to AHR is set equal to 0,

3TC

3 AHR

Ke »UPV*

“EFF

(1-F-AHR dF

dAHR)] +

dKenv . Q dAHR ’ (4.3)

and this equation is solved for AHR* . Note that both dF/dAHR and dKe

_ v/dAHR

are needed to solve for the optimal AHR since both the solar fraction (F) and

Kgny change as AHR is changed.

* Second order conditions require that 3'TC/3'AHR be positive in order to assure that 3TC/3AHR = 0 occurs at a minimum point rather than a maximum

point in the TC function. However, as specified, the TC function cannot have

a maximum, so that this second order condition need not be demonstrated.

Similar conditions hold for the total cost functions related to conventional

and solar heating equipment in this report.

30
SOLAR

FRACTION

i

COLLECTOR AREA

Figure 4.3 Solar fraction as a function of collector area and annual

heating requirements (general form)

ANNUAL HEATING REQUIREMENTS

Figure 4.4 Total heating -related life-cycle costs: annual heating

requirements variable

31
P.V.

LIFE-CYCLE

COST

TOTAL LCC

0.6 0.7 0.8 0.9

PLANT EFFICIENCY

Figure 4.6 Total heating-related lifecycle costs: collector area variable

Figure 4.5 Total heating-related lifecycle costs: plant efficiency variable

32

COLLECTOR AREA
To determine the optimal heating equipment efficiency (EFF'), given that AHR

and A are fixed in size, use:

3TC_ . VUrV*-AHR(F-l)

+

dKeoulp _ q

3EFF eff2 dEFF

(4.4)

and solve for EFF'. Finally, to determine the optimal solar collector area

(A 1 ), given that AHR and EFF are fixed, find

3TC =

3A

-K *UPV* «AHR

e EFF

dF

dA + K„ = 0 (4.5)

and solve for A'. However, because of the potentially high fixed cost component

(Kf

) associated with solar heating systems, an additional criterion must be

satisfied. This additional criterion can be stated as

AHR.* F ' • K • UPV* > K„ + Ku

« A', (4.6)

where F' is the optimal solar fraction corresponding to A'. In essence,

equation 4.6 requires that the total energy savings attributable to the optimal

size solar heating system are large enough to amortize not only the variable

cost component but the fixed cost component as well, since the fixed cost

component does not enter the area optimization equation (4.5). If equation 4.6

cannot be satisfied for F' (and the corresponding value of A'), the optimal

solar heating size is zero; i.e., no solar heating is used at all.

If the functional relationships between Kenv and AHR, KeqU^p and EFF, and K. solar»

A, and F are continuously differentiable, the determination of optimal values

for AHR, EFF, and A, independently of one another, is straightforward. The

relationship between K

go 2ar , A and F is generally continuous and thus the optimal A can be found as shown above. However it is impractical to modify most

envelope or mechanical equipment components in any continuous sense. Instead,

discrete modifications (e.g., double glazing, flue damper) are usually incorporated into their designs. In such cases, the optimal level of AHR and EFF

must be determined using discrete evaluation techniques rather than through

mathematical differentiation.

In order to determine the optimal level of AHR, and the corresponding

combination of envelope modifications, independently of EFF and A and using

discrete optimization techniques, the nl discrete envelope modifications to be

considered must be first ranked in decreasing order of cost effectiveness.

That is

-AAHR. »K «UPV* -AAHR, . , *UPV* 1 e

> i±i e (4.7)

AK1 AKi+1 env env

for each envelope modification i = 1, 2, ..., nl-1, where

33
AURjl - the AHR resulting when all envelope modifications 1, 2, i are incorporated into the envelope design,

AAHRi - AHRt - AHR^,

K

A cumulative total cost of all envelope modifications 1, 2, ...i, and env r

AKi„„ - K* - env env env

Equation 4.1 can be restated as

AHR. (1-F.) ^

, TC . = L »K »UPV* + KL„ + K 4 _ + K,

EFF ^env equip solar 1 (4.8)

where TC^ = the total heating-related life-cycle cost of the building when all

envelope modifications 1, 2, ..., i are incorporated into its design.

Now the change in TC per unit change in AHR ( ATC^/ AAHR^ ) can be calculated for

each subsequent modification, i = 2, 3, . .., nl as follows:

ATq

AAHRi

[1 - F1_ 1 - AHRl ( AF t AAHR1

)]

Ke-WV*

+ ^nv,

EFF AAHR1 (4.9)

where F^ = solar fraction corresponding to AHR^ , given A, and

AFi = F^ - Fj[_i (F 0 = solar fraction for unmodified (i.e., base)

envelope configuration).

Since the envelope modifications are ranked in decreasing order of cost

effectiveness, ATC^/AAHRj_ will decrease for each additional modification and

eventually turn negative. At the point where ATC^/AAHR^ turns negative, ATC-l

begins to increase. Therefore, an optimization algorithm is required to find

the last i for which ATC^/AAHR^ is greater than or equal to zero. From a practical standpoint, this is most easily accomplished by evaluating i= 1,2,3 ... stepwise until ATC^/AAHR^ turns negative, and then backing up one step to i',

the optimal integer. (No further modifications need to be evaluated.) The

optimal envelope design contains i' modifications (1,2,..., i').

Similarly, discrete equipment modifications to improve seasonal heating

efficiency can be evaluated using

MCj

AEFFj

where ATCr AHR (F-l) ^ AKeauio

= [ K„ • upv* + , L T7T7T7 - 17 17 IT J C A I7T7T7 EFFj EFFj_i AEFFj

(4.10)

= the change in total life-cycle heating-related cost attributable

to the jth equipment modification, j =2, 3, ..., n2.

EFF^ = the seasonal efficiency of the base space heating equipment.

EFFj

AEFFj

the seasonal efficiency of the upgraded space heating equipment

with cumulative modifications 2, 3, ..., j, and

Effj - EFFj_i

34
If the n2 equipment modifications are ranked in order of decreasing cost

effectiveness, then ATCj/AEFFj will increase as j is increased, and eventually

turn positive. (This is reversed from the envelope modification analysis

because AEFFj has a positive sign while AAHR^ has a negative sign.) The optimization algorithm then can find the optimal j by evaluating j-2,3 ... until

ATCj/AEFFj turns positive, and then backing up one step to j'. (Again, no further modifications need be considered.) The optimal heating equipment

configuration includes j modifications (1,2,..., j’).

Before continuing on to the discussion of simultaneous optimization methods in

section 4.2, two important points should be noted:

(1) The value of the results are limited by the validity of the input data.

Considerable effort prior to the optimization analysis described above is

needed to make sure that the basic envelope design, equipment types, and modifications considered are the most appropriate and cost effective for the overall design objectives. Similarly, the type of solar heating equipment to be

used, the ratio of storage volume to collector area, collector tilt angle, and

other system parameters that affect performance and cost must be carefully

selected in advance. Only the size of the solar heating system is determined

in SOLCOM. However, the total life-cycle cost of buildings with different

typ.es of conventional heating systems, different solar heating systems, and

different approaches to reducing space heating and cooling requirements can be

compared through separate optimization analyses. In this way, the usefulness

of these optimization methods and the SOLCOM computer program can be greatly

expanded.

(2) When an individual component is optimized, independently of the other

components, the life of the component can sometimes be used in the economic

analysis if it is shorter than the life expectancy (or study period) for the

overall building. (This does not hold true if the use of that component essentially "locks in” the replacement decision, in which case the analysis should

be conducted over the entire study period.) However, when two or more components are to be optimized simultaneously, the same study period must be used

for each. This requires a complete schedule of replacement and maintenance

costs over the study period, as well as a careful consideration of the

"salvage" (or resale) value of those components.

An important limitation to the methodology upon which SOLCOM is based is that

any replacement to an original component is assumed to have the same performance characteristics as the original. Thus for instance, if the heating

equipment is replaced at some point during the study period, its efficiency is

assumed to be the same as before, even though it may be logical to increase it

at that time when better information is available and new technologies have

been introduced to improve efficiency or lower costs.

4.2 SIMULTANEOUS OPTIMIZATION OF DESIGN VARIABLES

In section 4.1, the methodology for determining independently the optimal level

of annual space heating requirements (AHR) , heating equipment efficiency (EFF),

and solar collector size (A), was discussed. However, it is apparent from

35
equation 4.1 that the purchased energy usage for space heating is dependent on all three of these design variables. As a result, the change in total lifecycle cost 8 due to a change in any one of these three variables depends in

part on the values assumed for the other two. In order to find the optimal

level for any one, all three must be determined simultaneously.

If the optimal levels of AHR, EFF, and A can be determined mathematically, so that equations 4.3, 4.4, and 4.5 are specified, the simultaneous solution is

relatively straightforward. Since there are three unknowns and three equations,

the optimal level for each design variable can be found by a simultaneous solution of the equation system, using basic algebra to substitute terms.

In practice, however, discrete methods of evaluation are generally more applicable to the determination of optimal AHR and equipment efficiency in a building, while differentiation techniques can be used to find the optimal

collector area. As a result, an iterative process must be used to identify the

optimal combination of design variables. The iterative process described here

is based on the same assumptions about the ranking of the envelope and equipment modifications (in terms of decreasing life-cycle cost effectiveness) outlined in section 4.1. It is actually a series of "nested" optimization

algorithms which can be described by the following interrelated steps:

t STEP 1 : Determine the optimal collector area (A^ j

) and corresponding solar

fraction (F^ , ) , using equations 4.5 and 4.6 for each AHR^ evaluated in STEP

2, and EFFj from STEP 3.

STEP 2 : Determine the optimal AHR (AHR^ ) for each EFFj evaluated in STEP 3,

using:

ATC. , r , AF . , K «UPV* AK1 AA, . 1A = 1 - F]_, , - AHR, . liJ *-g +_env + _ 1_J V

JR. L 1 1 *J 1 ^ AAHR . J J AAHR. TEFF

j

AAHR.

where AAi,j = AiJ - A

i-l.j

AAHR.

AF' = F’ - F’ , and

i,j i,j i-l,J

AHRq = annual heating requirements of unmodified envelope.

(4.11)

for i = 1, 2,..., until ATC-^ j/AAHRj[ turns negative.

AHR-j is then set equal to AHR^_^ (i.e. one step back from the point where

ATCi j/AAHRi turns negative). If i is increased to nl (the total number of

envelope modification identified) without TC^^j/AHR^ turning negative, then

AHRJ is set equal to AHR^. Aj , Fj , and K^nv are the optimal collector

area, solar fraction, and total envelope modification cost, respectively,

corresponding to AHRJ

.

STEP 3 : Determine the optimal heating equipment efficiency (EFF*) using:

36
ATC.

AEFF

ahrJ* eff, , • ( l—F ! ) - ahrJ -1 »EFF , ( 1-F' .),

1 = [ 111 h 1 J J

1

1 »Ke »UPV* L EFFj • EFFj_ 1

J

AKJ AKJ . K„ • AA’ + env + equip + V j

AEFFj AEFFj AEFFj

where AK'

j j j-1

env ^env ^env

»

j j j" 1 ^equlp ^equip ^equip, ana M

j = Aj

A

j

_1 ’

for j= 2, 3, ... until ATCj /AEFFj turns positive.

(4.12)

EFF' is then set equal to EFF-s-j. If j is increased to n2 (the total number of

equipment efficiencies identified) without ATC-j /AEFFj turning positive, then

EFF' is set equal to EFFn2»

The number of iterations required to find optimal values of A, AHR, and EFF can

be considerably reduced if good guesses (based on a priori information) are made

and used as starting points. If the starting points selected for AHR^ or EFFj

result in an increase rather than a decrease in the total cost function, indices

i or j must be decremented until a corresponding decrease in the total cost

function results.

This three-step algorithm can be expanded to find optimal values of other design

parameters which must be evaluated simultaneously with A, AHR, and EFF. For

example, the optimal level of annual cooling requirements and the efficiency of

the cooling equipment may also need to be included in the analysis. In the

following subsection, a more complete description of the optimization algorithm

used in SOLCOM is presented. This includes the determination of optimal water

heating equipment efficiency, and incorporates space cooling considerations and

electric energy used for fans and pumps in the underlying engineering equations

upon which the optimization analysis is based.

4.3 OPTIMIZATION ALGORITHMS USED IN SOLCOM

In this subsection a more comprehensive examination of the optimization

algorithms used in SOLCOM is presented. These include the determination of the

optimal collector area (4.3.1), optimization of envelope modifications with

respect to both space heating and space cooling requirements (4.3.2), optimization of the space heating plant (4.3.3), and optimization of the water heating

plant (4.3.4).

37
4.3.1 Optimization of Solar Collector Area

Collector size is the only one of the design variables optimized in SOLCOM that

is treated continuously, although lower and upper limits on permissible collector size do constrain the solution. Since an equation to relate the annual

solar fractions for space heating (FH) and water heating (FW) to collector area

(A) does not exist, direct dif f erentation of the total life-cycle cost (LCC)

function (which includes the collector area and corresponding solar fraction)

is not possible. Instead, a convergence algorithm, based on the Newton-Raphson

method of successive approximation and numerical difference methods, is used

to find the minimum LCC collector area.

Before the actual convergence algorithm is executed, two tests are made in order

to determine whether the optimal area is equal to either the minimum permissible

or the maximum permissible collector size specified. These tests are made as follows

:

TEST 1 Is the minimum collector size optimal?

The SLR method (section 3.2) is used to estimate solar fractions FH and FW for

Ml (the minimum collector area) and for Ml-Z and Ml+Z. (Z is a discrete interval size used to approximate the first and second derivatives of the total

cost function with respect to A, based on numerical difference techniques.

SOLCOM uses Z = 0.5 m^ in SI calculations and 5 ft^ for conventional unit

calculations). Calculate the total energy and solar equipment cost (TC) for

Ml, Ml-Z, and Ml+Z (Tl, T2 , and T3 respectively) using

TC = KH*HL»(1-FH) + KW*WL»(1-FW) + QT»DE »KS + K_ + K»A (4.13)

HE WE 3 F V

where KH = cost per GJ (10 Btu) for space heating energy x UPV^,

UPV^ = modified uniform present value factor for space heating energy

1

, HE = seasonal efficiency of space heating plant,

HL = net annual heating requirements = AHR (1-EE»DE^),

AHR = annual heating requirements in GJ (lO^Btu),

EE =3.6 MJ/kWh (3412 Btu/kWh),

DE| = kWh per GJ (lO^Btu) AHR required for heating distribution

system,

FH = annual solar fraction, space heating, based on HL,

KW = cost per GJ (10° Btu) for water heating energy x UPVw , k ] UPVW

= modified present value factor for water heating energy ,

1 Modified uniform present value factors are discussed in section 5.1.

38
WE = seasonal efficiency of water heating plant,

WL » annual water heating requirements in GJ (106 Btu) equivalent

temperature rise,

FW “ annual solar fraction, water heating, based on WL,

QT = useful energy output from solar heating equipment (annual) = HL»FH + WL «FW,

DE^ = kWh per GJ (lO^Btu) useful output from solar heating equipment

needed for fans and/or pumps,

KS = cost per kWh for electricity v^sed to run fans and/or pumps in

solar heating equipment x UPV , s UPVS = modified uniform present value factor for electricity used by

solar equipment^,

Kp = fixed cost of solar heating equipment,

Ky = variable cost of solar heating equipment per nr (ft ) of collector

area, and

A - collector area in m^ (ft^).

Calculate Dl (T3-T2) / (2 »Z)

.

(4.14)

Dl is a discrete approximation to the first derivative of the TC function at

A=M1 (f '(Ml)).

If Dl > 0, the optimal collector area would be less than Ml if Ml was not the

minimum permissible area. In this case the optimal area (A') is set equal to

Ml. The net savings (NS) for the solar heating equipment are calculated for

A' = Ml and the corresponding values of FH and FW using:

NS = (KH/HEj)»HLi »FH + (KW/WEw

) »WL«FW - (Kf + KV

«A) - QT »DE 3 «KS (4.15)

where i, j, and w are the indices for the envelope modifications, space heating

equipment and water heating equipment respectively.

Now A' = Ml if NS ^ 0, and (4.16a)

A' = 0 if NS < 0. (4.16b)

If Dl < 0, then the optimal area must be greater than Ml. Proceed to TEST 2.

If Dl = 0, use equations 4.15 and 4.16a or 4.16b to find A'.

TEST 2 Is the maximum collector size optimal?

The SLR method is used to estimate FH and FW for M2 (the maximum permissible

collector area), and for M2-Z and M2+Z. Calculate total energy and solar equipment cost corresponding to areas M2, M2-Z, and M2+Z (Tl, T2 , T3, respectively)

using equation 4.13. Calculate Dl = (T3-T2)/(2 »Z)

.

39
If D1>0, the optimal collector size must be less than M2. Proceed to

convergence algorithm below.

If D1<0, the optimal area must be greater than M2. A' is set equal to M2 and

net savings for A = M2 are calculated using equation 4.15.

Now A' = M2 if NS ^ 0, and (4.17a)

A' = 0 if NS < 0. (4.17b)

If D1 = 0, use equations 4.15 and 4.17a or 4.17b to find A'.

Convergence Algorithm

The convergence algorithm is used only when it is known that the optimal

collector area (A') lies between Ml and M2, the minimum and maximum permissible

collector areas, respectively. A' can generally be found in a few iterations

using the Newton-Raphson method of successive approximation. The actual number

of iterations needed depends on both the proximity of the starting point to A' and the slope of the solar fraction curve at A'. (As the slope of the solar

fraction curve becomes relatively flat, more iterations will generally be

needed for convergence.)

From equation 4.5 it is known that the first derivative of the total cost

function at A' is zero (f'(A') = 0). Since the total cost function (equation

4.13) is U-shaped, f'(A) must be negative for values of A less than A' and

positive for values of A greater than A’. Figure 4.7 shows the general shape

of the f'(A) function. The optimization algorithm must converge on the point

where the f'(A) function changes from negative to positive (i.e., where

f'(A') = 0).

The Newton-Raphson method is very efficient at converging on f'(A) =0. An

initial guess as to A', Ak

(Ml < Ak < M2), is made. The second derivative of

the TC function at Ak (F"(Ak ) is approximated numerically by calculating D2 as follows

:

D2 = (T3-2 »T1+T2 ) /Z2

, (4.18)

where Tl, T2 , and T3 are total costs calculated at Ak , Ak-Z and Ak+Z,

respectively. The calculation of Ak+i , the trial solution to A', is made using

Ak+1 = Ak

" f'(Ak )/f"(Ak ), (4.19a)

or numerically

Ak+1 = Ak

“ D1/D2. (4.19b)

In essence, Ak+i is the point at which a line drawn tangent to f'(Ak ) intersects

the horizontal axis, as shown in figure 4.8. This process is repeated, substituting Ak+i for Ak , until the difference between Ak and Ak+^ converges to some specified tolerance level, say 1 m^ (~10 ft^). The last trial value obtained

with such a tolerance will generally be within 0.1 m^ (~1 ft^) of the actual

optimum and is used as A'

.

40
COLLECTOR AREA

Figure 4.7 First derivative of the total cost curve as a function of

collector area (f'(A))

COLLECTOR AREA

Figure 4.8 Convergence algorithms to locate f’(A) = 0

41
Since the calculation of FH and FW for any given collector area, space heating

load, water heating load, and equipment efficiency level requires the solution

of several equations in a monthly model, it is important that convergence be

rapid. Rapid convergence is also important because this optimization algorithm

is repeated many times as envelope modifications are analyzed and equipment

efficiencies (space heating, water heating, and space cooling) are changed.

When the initial guess for Akis within 5 nr (~50 ft^) of A', this algorithm

can usually locate A' in one iteration. Under most conditions, convergence can

be obtained in four iterations or less. However, several modifications have

been made to this convergence algorithm, as used in SOLCOM, to improve its performance under certain conditions which might otherwise slow it down:

(1) Test for D2>0 . The numerical approximation of f'CA^), D2 , should have a positive value over the entire f'(A) function. That is, each additional unit area of collector yields a smaller increase in the solar fractions than the one before. (This is the second order condition needed to ensure that f'(A) = 0 occurs at the minimum point on the TC curve.) It is possible that discontinuities in the empirical relationship between the solar fraction and collector

area will result in a negative value for D2 at some value of Ak , causing divergence from, rather than convergence on, A'. If D2 is found to be negative, Ak

is increased by 2»Z and D2 is recomputed in order to move it out of the region

of discontinuity.

It is conceivable that, for a particular type of solar heating system, or for a different model of solar heating performance than the SLR method used here, an additional unit of collector area may yield a larger increase in the solar

fraction than the one preceding, at least initially when the solar fraction is

very low. The optimal collector area cannot occur in this region (as long as the unit cost of collector area (Kv ) is constant) since energy savings are increasing faster than costs. The second derivative of the total cost function

will be negative throughout such a region, again preventing convergence on A'

Increasing Ak by 2«Z (as discussed above) will eventually move Ak out of this

region. However, by specifying Ml (the minimum collector size) large enough to

keep Ak out of this region, this potential problem can be avoided altogether.

( 2 ) Test for Ml < Ak+i < M2.

If Ak+^ < Ml, set Ak+i = Ml.

If A^-fi > M2, set Ak-f^ = M2.

( 3

)

Test for M3 < Ak+i < M4 #

In order to increase the rate of which the Newton-Raphson method converges to

A' in some cases, it is useful to dynamically specify new lower and upper

bounds (M3 and M4 , respectively) on Ak+^ , as follows:

If D1 for Ak < 0, set M3 = Ak ; if D1 for Ak > 0, set M4 = Ak

.

Then, if Ak+1 < M3 , set Ak+1 to (M3 + M4)/2;

if Ak+i > M4, set Ak+j to (M3 + M4)/2.

42
(4) Estimating A^ using A* from previous optimization.

As a general rule, if the total annual heating requirements are reduced by some given percentage, the optimal collector area will decrease by the same percentage and the corresponding solar fraction will remain unchanged^. This relationship is not exact if the percentage reduction in heating loads is not the same

for each month of the year, nor if water heating loads (which remain constant)

are included. However, this rule can be very helpful in determining a starting

point for the convergence algorithm as AHR are reduced in the envelope optimization analysis. Usually only one iteration is needed to find the optimal

collector area for a new AHR once the optimal area for the previous envelope

configuration has been determined.

The starting point to find A{+x for HLi+x , given A{ for HL^ , where x is a positive or negative integer representing the number of envelope modifications

added to or subtracted from the configuration with HLj[, is computed in SOLCOM as as follows:

Ai+x

Ai [HLi+x #KH/HE + WL’KW/WE + FT(HL1+X + WL)*DE

3 *KS]

HL1 »KH/HE + WL »KW/WE + FTCffl^ + WL)*DE

3 »KS (4.20)

where FT = annual solar fraction for combined space and water heating (total

output/total load).

No general rule exists for estimating the change in optimal collector area due

to a change in energy prices or changes in conventional equipment efficiency.

(In fact, the amount of change in optimal collector area due to a change in

energy price depends in part where on the solar fraction curve the optimal

fraction lies before the change is made, and the shape of the curve.) Since no expedient approximation rule could be worked out, the optimal collector area computed for a given HL and WL, based on HEj and WE^ is used as the starting

point in SOLCOM to search for the new optimal area as HE and WE are increased

or decreased.

4.3.2 Optimization of Envelope Modifications, AHR and ACR

The general search procedure used in SOLCOM to find the optimal combination of

envelope modifications to reduce space heating loads is similar to that outlined in section 4.2 (Steps 1 and 2). However, the actual optimization

algorithms used in SOLCOM are more comprehensive than the general search procedure in that the total cost function is expanded to include reductions in

annual cooling requirements (ACR), separate space and water heating plants and

solar fractions, and electricity usage for fans and/or pumps in both the

heating/cooling distribution system and the solar heating equipment. Approximation techniques are used to provide a more efficient starting point for the

search algorithm in order to reduce the number of times the optimal solar

collector size must be determined. Ranking of the envelope modifications in

1 Sav, G. Thomas, "Economic Optimization of Solar Energy and Energy Conservation

in Commercial Buildings."
decreasing order of cost effectiveness is also verified in this part of SOLCOM,

and if necessary, redetermined as the space heating plant efficiency changes.

The total cost function in SOLCOM can be expressed as follows:

TC = ECSH + ECWH + ECSC + ECS + ECDH + ECDC + PCSH + PCWH (4.21) + PCSC + MCE + SSC,

TC = total life cycle heating- and cooling-related costs,

ECSH = LC energy cost for space heating plant,

ECWH = LC energy cost for water heating plant,

ECSC = LC energy cost for space cooling plant,

ECS = LC electricity cost for space heating equipment,

ECDH = LC electricity cost for distribution system, heating,

ECDC = LC electricity cost for distribution system, cooling,

PCSH = LC plant cost, space heating,

PCWH = LC plant cost, water heating,

PCSC = LC plant cost, space cooling,

MCE = total LC envelope modification costs, and

SSC = LC solar heating system costs.

Life-cycle energy costs are found by multiplying annual energy use for each

function by the cost per unit for the type of energy used (as of the beginning

of the study period), a modified uniform present value factor (UPV*), and an after-tax equivalence (ATE) factor. Computation of annual energy use for each

of the six energy use functions above is detailed in equations 3.1 through 3.6

in section 3. Computation of the UPV* and ATE factors is explained in sections

5.1 and 5.2. Unit energy costs are selected by the user to represent actual

energy costs at the building site. Computation procedures to find the lifecycle costs of all equipment and envelope modifications, including initial

costs as well as future costs and savings (e.g., maintenance, replacements,

resale value and tax savings) are also detailed in section 5.

As each envelope modification is brought into the analysis, all of the cost

elements in equation 4.21 (except for the water heating plant) may change.

Modifications that reduce AHR will likely reduce the design heating load (DHL)

allowing the use of a smaller space heating plant. The same envelope modification may lead to a reduction (or possibly an increase) in the annual cooling

requirements (ACR) and the design cooling load (DCL) as well, resulting in a change in the size of the space cooling plant. As the AHR are reduced, a smaller solar collector size (if any) will be optimal, but solar fraction for

water heating will be increased. Changes in AHR and ACR also result in

proportional changes in distribution energy requirements.

The algorithms used in SOLCOM to determine the optimal combination of envelope

modifications are divided into several stages:

(1) ranking of envelope modifications,

(2) first approximation to optimum, and

(3) actual determination of optimum.

44
( 1 ) Ranking of Envelope Modifications

Each of the envelope modifications analyzed in SOLCOM must be ranked in

decending order of life-cycle cost effectiveness or the optimization algorithm

will fail. The incremental energy savings (in terms of AAHR, ADHL, MCR, and

ADCL) entered into the program have ideally been determined in this order since

there is some interdependence among the modifications. That is, when the

incremental energy savings attributable to the i

tri modification (Mj) are calculated for a specific building using a load determination model, all of the more cost-effective modifications (Mi, M2 , •••, M^-i) have already been incorporated,

while all of the less cost-effective modifications (M^+j, Mi+2> **• Mn l) have

yet to be considered.

However, the proper economic ranking of the modifications may change as the

plant efficiencies are changed or the solar fraction for space heating (FH)

changes. Ideally, the optimal values for each of these parameters should be

used when establishing the initial ordering of the modifications. Since these

values are obviously not known at the outset, an informed estimate must be made

for each. If the ranking of modifications determined in the SOLCOM analysis

differs significantly from the ranking used in estimating the energy savings

(especially for modifications near the cut-off point in the optimization) it

may be wise to recalculate the energy savings based on this new ranking and

rerun SOLCOM with the new data.

The SOLCOM program initially evaluates the list of envelope modifications, in

the order entered, to determine the AHR, DHL, ACR, and DCL as each additional

envelope modification is incorporated into the building design. Based on the

initial search values (specified by the user), SOLCOM calculates an optimal

collector area and corresponding solar fractions. Using these initial search

values and solar fractions, SOLCOM then steps through the list of nl envelope

modifications to make sure they are ranked in decending order of cost effectiveness, based on a benefit-cost ratio (R^: i= 1, 2, •••, nl), so that

R1 2. R2 2.

* *

* 2. Rnl > whera

Ri = [AHLi »((l-FH)»KH/HE + DE3 *KS°FH) + AAHRt ‘DEj «KDi

+ ACLi*KC/CE + AACRi *DE 2 -KD2 + AMHi«HO»VCHE (4.22)

+ AMC^ •CO»VCCE] / AMCEi

and where

1

KD^ = cost per kWh for heating distribution system x UPV* for same,

KD2 = cost per kWh for cooling distribution system x UPV* for same,

AACR^ = change in annual cooling requirements in GJ (10^ Btu) due to i

tl1 modification,

ACLi = AACRi *(l+EE*DE2 )

,

1 Other variables are described in section 4.3.1
DE 2 kWh per GJ (lO^Btu) ACR required for cooling distribution system,

AMH-l = (DHLi - DHL^-i ) ( 1 - EE»DEj) , AMCi - (DCLi - DCL^-i ) ( 1 + EE*DE2 ),

DHL^ design heating load (MJ or 10 Btu) for envelope with modifications

1 through i,

DCL^ = design cooling load (MJ or lO^Btu) for envelope with modifications

1 through i,

HO = oversizing factor for heating plant,

CO = oversizing factor for cooling plant,

VCHE » variable cost per MJ (lO^Btu) output capacity for heating plant,

VCCE variable cost per MJ (lO^Btu) output capacity for cooling plant,

and

AMCE^ = MCE^ - MCE^_i , the incremental cost of the i

c ^ modification.

This ranking procedure is based on the assumption that the optimal solar

fraction(s) remain unchanged as the AHR are reduced, as discussed in section

4.2. While this assumption is not exactly correct, it is so close that any

difference would rarely affect the resulting ranking. (An extra step in the

search procedure in SOLCOM is designed to catch an error here if this assumption causes a misordering of envelope modifications.)

If the order in which the modifications are initially entered does not satisfy

this ranking criteria, it is changed internally in SOLCOM until it does. Note,

however, that the values entered for AAHR, ADHL, AACR, and ADCL for any given

modification do not change. In fact, if these values were to be recalculated

in the load determination program based on this new order, there would probably

be some difference from the original estimates because of the interdependent

nature of the envelope modifications. For this reason, if the final ordering

of the modifications (printed out after the optimization analysis) differs

significantly from the initial ordering used to find AAHR^, AADHL^, AACR^, and

ADCL^, especially for the last few modifications included in the optimum configuration, serious consideration should be given to recalculating the value of

these changes in the new ordering.

(2) First Approximation to Optimum Combination of Envelope Modifications

A first approximation to the optimum combination of envelope modifications is

sought in order to reduce the number of iterations for which the collector

area must be optimized as SOLCOM steps through i = 1, 2, ... nl. This first

approximation is based on the assumption that the optimal solar fractions

remain unchanged as the envelope is modified and that the optimal collector

area can be approximated using equation 4.20 above. The collector size is

first optimized for the starting point designated by the user or determined in

a previous iteration. Then TC^ and TC^-i are determined using equation 4.21,

46
with approximate values substituted for the collector area and solar fractions

if the exact value is not known from a previous iteration. The difference is

calculated as

DTt - TCi - TCi-i . (4.23)

t* Vi If DTj > 0, so that total costs increase as the i tn modification is brought in,

i is decremented by 1 until either (a) DT^ 0 , in which case all modifications

1 , 2 , ..., i are cost effective, or (b) i “ 1 and DT^ > 0 , in which case no modifications are cost effective.

f. l_ If DT^ _< 0, so that total costs decrease or remain constant as the i

modification is brought in, i is incremented by 1 until either

(a) DT-t > 0 , in which case all modifications 1 , 2 , ... i -1 are cost effective

(but i is not), or (b) i = nl and DT^ £ 0 , in which case all nl modifications

are cost effective.

(3) Actual Determination of Optimum Combination of Envelope Modifications

At this point a first approximation to the optimum combination of envelope

modifications has been found and it will serve as the starting point to find

the actual optimum combination. In practice, this first approximation usually

is the actual optimum as well but it must be verified and adjusted if not.

Starting with the last cost-effective modification determined above (say the

i*"^), TC^ and TC^_^ are recalculated using the actual optimum solar fractions

and collector areas for AHRj_ and AHR^-^ ( as detailed in section 4.3.1). The same evaluation procedures for DT-^ discussed in ( 2 ) above are used to find the

actual optimum combination of modifications, but the solar collector area must

be reoptimized with each step if it is unknown.

One additional check is made, however, to ensure that an error in the ranking

of modifications does not terminate the optimization search prematurely. (The

possibility of an error was discussed in (1) above.) The search algorithm goes one step past the termination point in order to ensure that the modifications

are ranked properly at this critical point, i.e., the total cost continues to

increase. If a ranking error is detected, the modifications are reordered and

the search process is then continued as described above.

4.3.3 Optimization of Space Heating Plant Efficiency

Up to five space heating plant efficiencies may be specified in S0LC0M, listed

in order of increasing efficiency. The incremental benefit-cost ratio (Rj)

for each increase in efficiency must be smaller than the one preceding it, i.e.

> R

3 >

•** > rJJ 2

• (4.24)

This benefit-cost ratio is calculated as follows:

47
R

j

_1

HE HE 1

APCSH

J-l (4.25)

j

where HE i th

J APCSH

= seasonal efficiency of the j

« PCSH. - PCSH, the incremental LCC of the j uu plant relative

to tne (j-1)*^ plant.

space heating plant, and

th

If R*? £ R

1? - , the j

1"*1 plant is dropped out of the optimization analysis since

it cannot be optimal. The incremental LCC of the (j+l) th plant (APCSHj +1 ) is

then increased to include APCSHj , and n2 is decreased accordingly.

The search algorithm to find the optimal HEj (j m 1, 2, ..., n2) in SOLCOM is

analogous to the search algorithm used to find the optimal envelope configuration. Equation 4.21 is used to calculate TCj and TCj_i , given WE, for the

starting point specified (1 < j _< n2). The optimal combination of envelope

modifications, optimal collector area and corresponding solar fractions are determined for both HEj and HEj_i and are used in the determination of TCj and

TCj_i, respectively. The difference in total life cycle costs, DTj , is

computed as:

DTj = TCj - TCj-} . (4.26)

If DTj > 0, j is decremented by 1 until either

(a) DTj <^0, in which case HEj is optimal or

(b) j=2 and DTj > 0, in which case HEj is optimal.

If DTj 0, then j is incremented by 1 until either

(a) DTj > 0, in which case HEj_i is optimal, or

(b) j = n2 and DTj < 0, in which case HEn2 is optimal.

At this point, the optimal efficiency for the space heating plant and the

corresponding optimal combination of envelope modifications and collector area have all been identified, given WE, the efficiency of the water heating plant.

If space heating and water heating are provided by the same plant, then WE is

assigned the same value as HEj (j = 1, 2, ... n2) in SOLCOM. In this case, no further iterations are needed, for WE is optimized at the same time as HE. If

the water heating plant is separate, and more than one efficiency level is to

be considered in the SOLCOM analysis, the optimization algorithm for the water

heating plant must be executed.

4.3.4 Optimization of Water Heating Plant Efficiency

The search algorithm to find the optimal water heating plant efficiency is

essentially the same as the search algorithm used for the space heating plant

above. WE^ is the efficiency of the basic water heating plant. WEw

(w = 2,

3, ..., n3) is the efficiency of the Wfc ^ improved plant. The incremental

benefit-cost ratio (Rj7 ) for each increase in efficiency must be smaller

48
than the one preceding it, i.e..

r

2 > R

3 > > R

n3*

This benefit-cost ratio is similar to equation (4.25):

(4.27)

1 1

,w , WEw

kw ~ <1

APCWI^

(4.28)

where WEw

= average efficiency of the w*"*

1 water heating plant, and

APCWH^ = PCW1I - the incremental LCC of the w**1 plant relative

to the (w-1)*-^ plant.

If R^ £ Rw+i» the wth plant is dropped out of the optimization analysis

since it cannot be optimal. The incremental LCC of the (w+l) th plant (APCW^j)

is then increased to include APCWT^, and n3 is decreased accordingly.

An initial starting point for w (1 < w n3) is specified by the user during the

execution of S0LC0M2. The optimal heating system efficiency, combination of

envelope modifications, and collector area and the corresponding total LCC (TCW

and TCw_i) are determined for both WEw and WE^j, as described in sections

4. 3. 1-4. 3. 3.

DTW is then calculated as

DTW = TCw - TCw-!. (4-29)

If DTW > 0, then w is decremented by 1 until either:

(a) DTW 0, in which case WEw is optimal, or

(b) w = 2 and DTW > 0, in which case WE^ is optimal.

If DTW <^0, j is incremented by 1 until either

(a) DTW > 0, in which case WEw_i is optimal, or

(b) w = n3 and DTW <^0, in which case WEn3 is optimal.

Optimal values have now been determined for the collector area and corresponding

solar fractions; for envelope modifications and corresponding AHR, ACR, DHL, and

DCL; and for space heating and water heating system efficiencies. In addition

the total LCC associated with the overall conservation investment has been calculated. If it is desirable to determine an optimal cooling system efficiency

(CE) as well, separate runs of SOLCOM can be made with each CE to be evaluated,

along with its corresponding cost data. The CE resulting in the lowest overall

total LCC indicates the optimal overall configuration, including CE.

49
5. FINANCIAL ANALYSIS METHODOLOGY

In this section the methodology used in SOLCOM1 to determine life-cycle costs

for each of the envelope modifications, plant efficiency improvements, and the

solar heating system, as well as for energy costs, is detailed. Tax treatments

(including depreciation and tax credits), resale value, inflation, and financing

arrangements are also discussed.

5.1 CALCULATION OF DISCOUNT FACTORS, COST ESCALATION FACTORS, AND UPV* FACTORS

The SOLCOM program requires that annual cost escalation rates be specified

individually for several different categories of expenditures. These categories

include individual energy types, operating and maintenance costs and conservation measure costs. These cost escalation rates, and the discount rate used to

convert future costs to present value, can be changed during the study period

to better track long terra expectations of inflation and opportunity costs.

The methods used to convert annual price escalation rates and discount rates to

cumulative escalation factors and discount factors are detailed in the following

sections

5.1.1 Cost Escalation Factors

The cost escalation factor for any given year i (CEF^) represents the ratio of

the cost for a given cost element at the end of year i to its cost at the

beginning of the study period (i.e., the beginning of year i). Cost escalation

factors for each cost category are computed as follows:

CEF0 = 1 (5.1a)

CEF^ = CEF i_ 1

• ( 1 + CER^ for i = 1 , 2 , . . . , N (5.1b)

where CER^ = the cost escalation rate in year i, and

N = length of the study period (in years).

5.1.2 Discount Factors

The discount factor for any given year i represents the ratio of the present

value of a given dollar amount to the actual dollar amount incurred in year i

for a given cost element. The discount factor is computed as follows:

DF 0 = 1 (5.2a)

DFi = DFj-i/U + DRi) for i = 1, 2, ..., N (5.2b)

where DF^ = discount factor in year i, and

DR^ = discount rate in year i.

50
5.1.3 Modified Uniform Present Value Factors

The modified uniform present value factor (UPV*) is used to find the present

value of a stream of related costs (or savings) which occur annually over the

study period (N), increasing (or decreasing) at some known rate. UPV* factors

are used in SOLCOM to determine the present value of annual energy expenditures

for each energy type and the present value of annually recurring operating and

maintenance costs. Since the discount rate may not be constant over the entire

study period, UPV* factors are computed using the following summation formula

(instead of a closed-form equation):

N

UPV* = l CEF i

« DF

i

. i=l

5.2 GENERAL LCC MODEL FOR CONSERVATION INVESTMENTS IN BUILDINGS

5.2.1 Non-Energy Costs

Conservation measures to improve the overall energy efficiency of a new building

generally have life-cycle costs (LCC) significantly different from their first

cost alone. The LCC of any given conservation measure (distinct from its energy

cost implications) is made up of a number of cost elements, each attributable

specifically to that measure, as follows:

LCC = FC + ST - CT + AROM + NAROM + PT - RV + RT - TS (5.3)

where FC = ST

CT

AROM = NAROM =

PT

RV

RT

TS

first cost,

sales tax,

investment or conservation tax credits,

annual recurring operating and maintenance costs,

non-annual recurring operating and maintenance costs, including

replacement cost,

property taxes,

resale value,

capital gains and depreciation recapture taxes, and

income tax savings (from ST, AROM, NAROM, PT, depreciation,

and interest payments, if any).

and all costs are expressed in life-cycle, present-value dollar terms.

If the investment is financed, then

FC = DP + MP, (5.4)

where DP = down payment (at beginning of study period), and

MP = present value of all principal and interest payments, and

TS is adjusted to include tax savings from interest payments.

The following calculation methods are used in SOLCOM to compute a LCC factor

for each measure which incorporates each of these cost elements. (Note that

51
all cost elements, except O&M-related costs, are calculated in SOLCOM as a percentage of the first cost. O&M-related costs can be calculated either as a percentage of the first cost or independently of first cost.) Each of these

factors is computed once in the S0LC0M1 subprogram and then transferred to

the S0LC0M2 subprogram.

(1) First Cost (FC) This variable is entered directly into the data list of

S0LC0M1. If FC is financed, see subsection 5.3.2 which describes financing

factors

(2) Sales Tax (ST)

ST = FC • AP • TX, (5.5)

where AP = percentage of first cost to which sales tax is applicable ( %/ 1 00 )

and

TX sales tax rate ( % / 1 00 )

(3)

Investment or Conservation Tax Credits (CT)

These tax credits are assumed to be realized at the end of the first year.

State tax credits are adjusted to reflect increased Federal tax liability.

Thus

CT = CTF + CTS , (5.6)

CTF

= (FC + ST)*CF»DF 1 , and (5.7)

CTg = (FC + ST) »CS(-TF) *DFj

(5.8)

where CTp = Federal tax credit,

CTg = state tax credit (net),

CF = Federal tax credit rate (%/100),

CS = state tax credit rate (%/100),

DFi = discount factor at end of year 1, and

TF = Federal tax rate (%/100).

(4)

Annually Recurring 0 & M Costs (AROM)

AROM = ARC • UPV*, (5.9)

where ARC = annual recurring cost (in base-time dollars) and

UPV* = UPV* for 0 & M costs.

52
(5)

Non-Annually Recurring O&M Costs (NAROM)

NN

NAROM - i-1

l NRq.CEF^.DF^, (5.10a)

where NN = number of non-annually recurring costs,

NRC^ = amount of i Ln non-annually recurring cost (in base-time dollars),

CEFy^ = cost escalation factor for O&M expenditures in year yi,

DFyi = discount factor for year yi, and

yi = year of occurrence of i

fc ^ cost (base year =* 1).

Capital replacement costs are included in the NAROM cost element, which results

in their treatment as a tax deductable expenditure in the year of occurrence,

rather than capital expenditure which must be depreciated over time. A more comprehensive analysis would incorporate a depreciation schedule for capital

replacements. However, it is unlikely that current depreciation schedules will

still be in use at the time a replacement is made.

(6)

Property Taxes (PT)

Property taxes are based on an assumed linear reduction in real asset value

from first cost to remaining value (in constant dollars) at the end of the

study period and a corresponding increase in nominal value due to the general

rate of increase in prices for such measures. They are calculated as though

they are paid at the beginning of each year, based on the asset value at that

time, but the tax savings are discounted from the end of the year. Property

taxes attributable to any given conservation measure can be set to zero by

setting PP = 0 for that measure.

(7)

Resale Value (RV)

Resale value is the remaining value of each conservation measure at the end

of the study period, whether the building is to be sold, torn down, or held.

RV can be set equal to zero by setting RP=0.

(5.10b)

where PP = assessment rate for the particular measure (%/100),

TP = property tax rate (%/100),

RP = remaining value factor for measure at end of study period (in base

year dollars), and

CEF? = cost escalation factor for conservation measures in year i.

RV = FC • RP • CEF§ • DFn

. (5.11)

53
(8) Capital Gains and Depreciation Recapture Taxes (RT)

Capital gains tax and depreciation recapture tax are calculated for both the

state and Federal government if the nominal resale value (SP) of a given con- servation measure is greater than its first cost less cumulative straight-line

depreciation. RT can be set equal to zero by specifying CG^ - 0 for Federal

tax purposes and CG 2 0 for state tax purposes. (CG^ and CG2 are Federal

and state capital gains factors, respectively, in data sheet 1.) Depreciation

computations are discussed in subsection 5.3 below.

Capital gains tax liability to Federal (CGF) and state (CGS) tax agencies are calculated using the positive difference between the nominal resale value of an asset and its first cost as follows:

CGF = [SP-FC] • TF • CGj • DFN

for (SP>FC), (5.12a)

CGS = [SP-FC] • TS • ( 1-TF )

• CG2

• DFN

for (SP>FC), (5.12b)

where SP = FC • RP • CEFjj,

TF = Federal income tax (marginal), and

TS = state income tax state (marginal).

Depreciation recapture tax liability (RTf and RT S for Federal and state,

respectively) varies according to the type of property and appropriate recapture rulel . One of three different rules may apply:

(a) Recapture Rule 1: The positive difference between the nominal resale value

(SP) and the remaining basis (first cost less cumulative depreciation) is taxed

as ordinary income.

RTf = (FC-RB f )

• TF • DFN for SP _> FC , or (5.13a)

RTf = (SP-RBf) • TF • DFn for FC > SP > RB f , and (5.13b)

RT S = (FC-RB S )

• TS(l-TF) • DFN

for SP ^ FC, or (5.14a)

RTS = (SP-RBg) • TS(l-TF) • DFN

for FC > SP > RB S , (5.14b)

where RBf = FC-CDf, remaining basis using Federal depreciation schedule,

CDf = cumulative depreciation using Federal depreciation schedule,

RB S = FC-CDS , remaining basis using state depreciation schedule, and

CDS = cumulative depreciation using state depreciation schedule.

1 A good overview of depreciation guidelines and recapture rules is available

in the Commerce Clearing House, Editorial Staff Publication, " Economic

Recovery Tax Act of 1981, Law and Explanation , Chapter 2 ("Business Tax

Incentives"), Chicago, Illinois, August 1981.

54
(b) Recapture Rule 2: The positive difference between the nominal resale value

and the remaining basis is taxed as capital gains.

RT f - (FC-RB f )

• TF • CG! • DFN for SP > FC, or (5.15a)

RT f - ( SP--RB f )

• TF • CG t

• DFN

for FC > SP > RB f , and (5.15b)

RT S = (FC-RB g )

• TS • CG2 • (1-TF) • DFN for SP ^ FC , or (5.16a)

RTS = (SP-RB s )

• TS • CG2 • (1-TF) • DFN for FC > SP > RB f

. (5.16b)

(c) Recapture Rule 3: The positive difference between the nominal resale

value and the remaining basis (first cost less straight-line depreciation) is

taxed as capital gains. Any excess depreciation claimed through use of an accelerated method of depreciation is taxed as ordinary income.

RT

f = [(FC-RB^'CGj + (RBf-RBf

)

] «TF »DFN for SP>FC, (5.17a)

RTf = [(SP-RBj ).CG

X + (RBf-RBf )]«TF»DFN for FC>SP>RBf, or (5.17b)

RTf = ( SP-RBf

) • TF • DF

n for RB^>SP>RB f

, and (5.17c)

RT

g = [ (FC-RBg ) *CG

2 + (RBg-RBs )]«TS(l-TF)*DFN

for SP>FC , (5.18a)

RT

S = [ (SP-RBg ) *CG2 + (RBg-RBs

) ]-TS(1 -TF)«DF

n

for FC>SP>RBj, or (5.18b)

RT

g = (SP-RBs )»TS(1-TF)»DFn

for RBg>SP>RB

g

, (5.18c)

I where RB^ = remaining basis using straight-line depreciation rules, Federal and

t RB

g = remaining basis using straight-line depreciation rules, state.

(9) Income Tax Savings

Present-value income tax savings are computed in S0LC0M1 as follows:

(a) Tax savings from sales tax payments (TSgX ):

TS SX = ST«(TF + TS(1-TF))*DF 1

. (5.19)

(b) Income tax savings from annually recurring O&M (TS^qj^):

tsAROM = AROM ( TF + TS(l-TF)). (5.20)

(c) Income tax savings from non-annually recurring O&M (TSjjarom) :

TSNarom

= NAROM (TF + TS(l-TF)). (5.21)

(d) Income tax savings from property tax payments (TSpX ):

(Property taxes are assumed to be paid at the beginning of the

year but not realized as tax savings until the end of the year.)

55
TS (5.22) pt = FC»PP»TP[ l [ 1— (——-) ( 1-RP) ]

DF-jJ .(TF+TS( 1-TF) )

i-1 N

(e) Income tax savings from depreciation (TSpEp):

TSdep - DDpTF + DD2 *TS(1-TF). (5.23)

where DD^ = present value of cumulative depreciation, Federal, and

DD2 “ present value of cumulative depreciation, state.

(The methodology used to compute cumulative depreciation is detailed in

section 5.3 below.)

(f) Income tax savings from interest payments (TSint):

TSINT

3 IN * * (TF+TSO-TF)), (5.24)

where In' = present-value of interest payments, discounted from end of year.

(The methodology used to compute interest payments is detailed in section

5.3 below.)

5.2.2 Energy Costs

In addition to the life-cycle costs of the specific conservation measures examined in SOLCOM, life-cycle costs must be calculated for each energy type

used in the building. Life-cycle energy costs are computed in terms of the

cost per GJ or lO^Btu of each energy type purchased per year each year over

the study period.

ECt = $/U±

• UPV* (5.25)

where EC^ = present-value life cycle cost of i*-*

1 energy type per GJ (10^ Btu)

per year for N years,

£ $/U^ = cost per GJ (10° Btu) of energy type i at beginning of study period,

and

UPV^ = modified uniform p. v. factor for the i tn energy type.

Tax savings for energy type (TSE:j_) are computed as

TSEi = ECi (TF + TS(l-TF)). (5.26)

5.3 CALCULATION OF CUMULATIVE DEPRECIATION FACTORS AND FINANCING FACTORS

5.3.1 Cumulative Depreciation Factors

Cumulative depreciation factors for each of the three conservation investment

classes (envelope modifications, conventional heating and cooling equipment

improvements, solar equipment) are calculated for both Federal and state income

56
tax purposes. These cumulative depreciation factors are calculated from

depreciation schedules entered into the S0LC0M1 program. (Separate depreciation schedules for Federal and state tax purposes can be entered if warranted;

otherwise, the depreciation factor for state taxes is the same as that computed

for Federal tax purposes.

The depreciation schedule has the form Dj , D2 , •••, Dm

where = the ratio of depreciation allowance to first cost in year i (i = 1,

2 , . . . , M) , and

M = the number of years in the study period, or the depreciation period,

whichever is shorter.

Cumulative depreciation factors are calculated both in present value (i.e.,

discounted) and nominal (i.e., non-discounted) terms as follows:

M

DA = l Di • DFi, and (5.27)

i=l

M

DD = l Di, (5.28)

i=l

where DA = the present-value cumulative depreciation factor, and

DD = the nominal cumulative depreciation factor.

In addition, a straight-line cumulative depreciation factor (SC) must be

calculated if depreciation recapture rule 3 is used and the resale value of the

investment is greater than the remaining basis (SP > FC-DD) at the end of the

study period. This is calculated as

SL = 1 for N > M, or (5.29a)

SL = N/DL for N < DL, (5.29b)

where N = the length of the study period, and

DL = the actual length of the depreciation period for a given class of

assets

5.3.2 Financing Factors

All of the conservation measures evaluated in SOLCOM are considered to have the same financing terms, if any. Three different financing alternatives can be

specified in SOLCOM:

(1) fully amortized loan with equal payments in each time period,

(2) interest-only payments at periodic intervals (of equal length) but not less

than one per year); principal paid back at end of loan life, and

(3) principal and interest deferred to end of loan period.

57
While a longer loan life than the time horizon can be specified, any unpaid

principal is assumed to be paid back at the end of the study period. A down

payment factor (DP), the ratio of initial payment to actual first cost

(including sales tax) for a given conservation measure is specified in the

input data file (see data sheet 5.) The loan amount factor is then computed as (1-DP).

Computation procedures to find the present value factor for principal and

interest payments are as follows:

( 1 ) Loan Type 1 (Amortized)

(a) Loan payment factor (CR):

CR = LI/LN » (1+LI/LN) LN * LL

(5.30)

(1 + LI/LN) ln#ll-1

where LI * annual interest rate (nominal),

LN = number of payments per year, and

LL = loan life (in years).

(b) Present-value factor for loan payments discounted from time of

payment (LI):

LI

LM

(1-DP)* l CR*

i-1

(i+dr]/ln) ln — -i

r

1

i * DF i-i

DR

1 /LN*(l+DRi /LN) LN

where DR^ = LN* ( l+DRi

) 1/LN - LN, and

LM - LL or study period, whichever is shorter.

(5.31)

(5.32)

(DR{ is the nominal equivalent of the effective discount rate in year i, DR^.

If LN = 1, DR{ and DR^ are equivalent.)

(c) Present-value factor for interest payments discounted from end of year

(L2):

LM LN

L2 = I

• DF

i l

I i,k (5.33)

i=l k=l

where I i>k = P i>k-1 * LI/LN, i-1, 2, .. ., LM (5.34)

k=l, 2, .. ., LN

Pl,o = (5.35)

p i ,o = Pi-1.LN» 1=2,3, ..., LM (5.36)

p i,k = pi,k-l + Ii,k " CR(l-DP), k-1, 2, ..., LN (5.37)

58
(d) If the loan life is greater than the study period (LL > N) then the

present value of the remaining principal (L3) must be calculated:

L3 - Plm,lN * DFN (5.38)

(2) Loan Type 2 (Interest Only)

(a) Present-value factor for interest payments discounted from time of

payment (Ll):

LM LI (1+Dr!/LN) ln-1

Ll = (1-DP) l — • —;—± • DFi_i (5.39)

i=l LN DRi /LN»( 1+DR^/LN)^

(b) Present-value factor for interest payments discounted from end of year

(L2):

LM

L2 = (1-DP) l LI • DFi (5.40)

i=l

(c) Present-value for remaining principal at end of loan period (L3):

L3 = (1-DP) • DFlm (5.41)

(3) Loan Type 3 (Interest and Principal Deferred)

(a) Present-value factor for interest payments made at end of loan period

(Ll):

Ll = ( 1-DP) [( 1 + LI) LM - l] • DFlm (5.42)

(b) Present-value factor for remaining principal at end of loan period

(L3):

L3 - (1-DP) • DFlm (5.43)

59
6 . SUMMARY

This report provides a methodology, algorithms, and a computer program to

determine simultaneously the lowest life-cycle cost combination of energyconserving envelope modifications, equipment efficiencies, and size of an active solar heating system for a new commercial building. These three com- peting approaches to energy conservation in a new building design must be

analyzed simultaneously because they are functionally interdependent. That is,

a change in any one will significantly affect the energy savings attributable

to each of the others. The computer program, called SOLCOM, can be used by

design professionals on a microcomputer. Considerable financial analysis and

thermal performance data is required to run the program. The thermal perfor- mance data will require extensive engineering analysis of the appropriate con- servation modifications and of the active solar heating system design prior to

the use of the SOLCOM program.

This report represents a significant advance over previous studies which

evaluated solar heating systems and other energy conservation methods in

buildings in a systematic manner. The economic optimization algorithm for

determining the size of a solar heating system, based on the Newton-Raphson

method of successive approximation, greatly decreases the amount of computer

time needed to converge on an optimal collector size. This algorithm makes the use of a microcomputer to solve the simultaneous optimization problem a practical choice.

However, only a hypothetical building is used in this report to demonstrate

the application of the SOLCOM program. In order to demonstrate the usefulness

of this program to professionals engaged in commercial building design, actual

building and system performance data are needed. As active solar heating

systems become more attractive to commercial building developers during the

next decade, an expansion of this report to include realistic examples of

design problems and their solutions would greatly increase the value of the

SOLCOM program.

60
REFERENCES

Balcorab, J. Douglas, "Conservation and Solar: Working Together," LA-UR-80-2330

,

Los Alamos Scientific Laboratory, Los Alamos, N.M. , 1980.

Balcomb, J. Douglas, "Optimum Mix of Conservation and Solar Energy in Building

Design," Proceedings of the 1980 Annual Meeting of the AS/ISES, June 2-6, 1980 , Phoenix, AZ, pp. 1202-1206.

Barley, C. Dennis, "Load Optimization in Solar Space Heating Systems," Solar

Energy , Vol. 23, pp. 149-156.

Commerce Clearing House, Economic Recovery Tax Act of 1981, Law and

Explanation , Chicago, Illinois, 1981.

Department of Energy, DoE Facilities Solar Design Handbook , DoE/AD-0006/1

,

U.S. Government Printing Office, Washington, D.C., 1978.

Hittle, D. C., BLAST, The Building Loads Analysis and System Thermodynamics

Program , CEEDO-TR-77-35/CERL-TR-E-1 19/ADA048734 , U.S. Army Construction

Engineering Research Laboratory Systems [CERL] , December 1977.

Lameiro, Gerald F. and Bendt , Paul, The GFL Method for Sizing Solar Energy

Space and Water Heating Systems , SERI-30, Solar Energy Research Institute,

Golden, Colorado, 1978.

Noll, Scott and Thayer, Mark, "Passive Solar Auxiliary, Heat and Building

Conservation Optimization: A Graphical Analysis," Fourth Passive Solar

Conference Proceedings, Kansas City, October 3-5, 1979 .

Powell, Jeanne W., and Rodgers Jr., Richard C., FEDSOL: Program User's Manual

and Economic Optimization Guide for Solar Federal Buildings Projects , NBSIR

81-2342, U.S. Department of Commerce, National Bureau of Standards, Washington,

D.C., August 1981.

Ruegg, Rosalie T., Sav, G. Thomas, Powell, Jeanne W. , and Pierce, E. Thomas,

Economic Evaluation of Solar Energy Systems in Commercial Buildings:

Methodology and Case Studies , NBSIR 82-2540, U.S. Department of Commerce,

National Bureau of Standards, Washington, D.C., July 1982.

Sav, G. Thomas, "Economic Optimization of Solar Energy and Energy Conservation

in Commercial Buildings," Proceedings of the U.S. Department of Energy

Conference, San Diego, CA, June 27-29, 1978 , pp. 88-90.

Schnurr, Norman M. , Hunn, Bruce D., and Williamson, III, Kenneth D., "The Solar

Load Ratio Method Applied to Commercial Building Active Solar System Sizing,"

Solar Engineering - 1981 Proceedings of the ASME Solar Energy Division 3rd

Annual Conference on Systems Simulation, Economic Analysis/Solar Heating and

Cooling Operation Results, Reno, Nevada, April 27-May 1, 1981 , American Society

of Mechanical Engineers, New York, N.Y., 1981.

61
TRNSYS - A Transient Simulation Program , Solar Energy Laboratory, Report 38,

University of Wisconsin, Madison, WI , November 1976.

York, D. A., and Tucker, E. F., DOE-2 Reference Manual (Version 2.1) , LBL-8706

Rev. 1 and LA-7689-M. , Lawrence Berkeley Laboratory, Berkeley California, and

Los Alamos, National Laboratory, Los Alamos, N.M. , 1980.

62
APPENDIX A

SOLCOM DATA SHEETS

1. PROJECT IDENTIFICATION AND ECONOMIC PARAMETERS

2. DISCOUNT RATES AND PRICE ESCALATION RATES BY TIME INTERVALS

3. ENERGY PRICE ESCALATION RATES BY TIME INTERVAL Y(I)

4. ENERGY COST DATA

5 . MORTGAGE DATA

6. ENVELOPE MODIFICATION IDENTIFICATION DATA

7. NON-ANNUALLY RECURRING O&M COSTS - ENVELOPE MODIFICATIONS

8. DEPRECIATION DATA FOR ENVELOPE MODIFICATIONS

9. SPACE HEATING EQUIPMENT DATA

10. NON-ANNUALLY RECURRING O&M COSTS - SPACE HEATING PLANT IMPROVEMENTS

11. WATER HEATING PLANT DATA

12. NON-ANNUALLY RECURRING O&M COSTS - WATER HEATING PLANT IMPROVEMENTS

13. SPACE HEATING SYSTEM DATA

14. DEPRECIATION SCHEDULE FOR CONVENTIONAL HEATING AND COOLING PLANTS

15. SOLAR HEATING SYSTEM DATA

16. DEPRECIATION DATA FOR SOLAR HEATING EQUIPMENT

17. BASIC ENVELOPE PERFORMANCE DATA, WATER HEATING REQUIREMENTS, AND INCIDENT

SOLAR RADIATION

18. REDUCTIONS IN HEATING AND COOLING LOADS DUE TO ENVELOPE MODIFICATIONS

A1
DATA SHEET 1

PROJECT IDENTIFICATION AND ECONOMIC PARAMETERS

01001

01002

DATA

DATA

FI $

01003 DATA »

N$

» > >

01004 DATA

MM

*

Y0

>

TH

» TT> TS TX CG( 1

CG(2)

Variable Description

Fl$ File name

N$ Project title

MM Measurement base:

MM = 1: conventional units (e.g. Btu, gallons),

MM = 2: SI units (e.g., J(oules), liters).

Yf) First year of occupancy

Occupancy is assumed to occur on January 1 and all initial

costs are incurred on that date. January 1 of year Y0 is

the base time to which all future costs are discounted.

TH Time horizon, or the length of the study period in years

(0 < TH £ 50).

TT Tax status of owner:

TT = 1 : tax paying,

TT 3 2: tax exempt.

If TT = 1, all initial costs (except sales tax) are depreciated;

all future costs, sales tax, and interest payments are tax

deductible in the year of occurrence. Tax credits are computed

as of the end of the first year. If TT = 2, no tax deductions,

depreciation, or tax credits are allowed; no property taxes are paid.

TG Federal income tax rate (%).

TS State income tax rate (%).

TX Sales tax rate (%).

CG(1) Percent of capital gains subject to income taxation at ordinary

income tax rate - Federal taxes (currently 40%).

CG(2) Same as CG(1) but for state taxes.

TP Property tax rate (%).

The property tax rate is applied to the assessed value of each

conservation measure. The assessment rate is specified individually for each measure.

ATHIS PAGE PURPOSELY LEFT BLANK.

DATA SHEET 2

DISCOUNT RATES AND PRICE ESCALATION RATES

BY TIME INTERVAL

02001 DATA

IN

Line

Number

• • TXT ** Y(I) R1(I) R2(I) R3(I)

'IN’ entries

only

02101 DATA I = 1

02102 DATA H CM W

02103 DATA 1=3

02104 DATA M

II

02105 DATA 1 = 5

02106 DATA 1 = 6

02107 DATA r*» it M

02108 DATA M

II 00

02109 DATA 1=9

02110 DATA I = 10

continue as needed

02150 DATA I = 50
Variable Description

IN

Y(I)

R1(I)

R2(I)

R3(I)

Number of time intervals for which a discount rate and price

escalation rates are entered (see lines 2101-2150 and

3101-3150). (0 < IN < 50.)

The discount rate and price escalation rates for

certain cost elements can be varied from time

interval to time interval.

Length of the 1^ time interval (in whole years) for which

a discount rate and price escalation rates are given.

The sum of all Y(I), I - 1, 2, . .., IN, must be at

least as great as the length of the study period

(TH).

Discount rate in the 1^ time interval (%).

Annual rate of increase in operating and maintenance costs in

I

c ^ time interval (%).

Annual rate of increase in the cost of conservation measures,

including solar equipment, in the I^ time interval (%).
DATA SHEET 3

ENERGY PRICE ESCALATION RATES

BY TIME INTERVAL Y(I)

3001 DATA

EN only* EN entries * -*• Line

Number R4(I,1) R4(I,2) R4(I,3) R4(I,4) R4(I,5) R4(I,6)

continue as needed

03130 DATA

IN

entries

only**

I = 1

1 = 2 1=3

1 = 4

1 = 5

1 = 6

1 = 7

1 = 8

1 = 9

I = 10

I = 50

Variable Description

EN Number of energy types to be entered.

The same energy types with different unit

prices (e.g. , electricity for space heating

at winter rates and electricity for cooling

at summer rates) are counted separately.

(0 < EN _< 6)

R4(I,K) Annual rate of increase in the energy type

price in I^ time interval (%).

* EN entries corresponding to number of energy types specified in line 3001.

** IN entries corresponding to number of time intervals used in Data Sheet 2.

A5
DATA SHEET 4

ENERGY COST DATA

EN

entries only* Line * Number KE(K) TU(K) EN$(K) EM$(K) +

04101 DATA

04102 DATA

04103 DATA

04104 DATA

04105 DATA

04106 DATA

K

K

K

K

K

K

1

2

3

4

5

6

Variable Description

KE(K) Cost per unit of energy type K (in base-time dollars).

TU(K) Thermal units per unit of energy type K, in KJ (Btu);

e.g. 3 ,600KJ/kWh (3,412 Btu/kWh).

EN$(K) Name of Kth energy type.

EM$(K) Name of unit used for K

th energy type (e.g. kWh,

liter, gallon).

* EN entries corresponding to number of energy types entered in Data Sheet 3.

ADATA SHEET 5

MORTGAGE DATA

05101 DATA

LT

Skip the following if LT = 0

05002 DATA , , , LL LN LI DP

Variable Description

LT

LL

LN

LI

DP

Loan type designator:

LT = 0: no loan

LT = 1 : amortized loan,

LT = 2: interest only loan,

LT = 3: interest and principal deferred loan.

Life of loan (years)

Number of payments per year.

Nominal interest rate per year (%)

Down payment as a percent of initial cost

(including sales tax).

ATHIS PAGE PURPOSELY LEFT BLANK

DATA SHEET 6

ENVELOPE MODIFICATION IDENTIFICATION DATA

06001 DATA

Line

Number

N1

EN ( I

)

E$(I) EC(I , 1

)

EA(I)

N1

entries

NE(I) only

I = 1

1 = 2

1 = 3

1 = 4

1 = 5 1=6

1 = 7

1 = 8

1 = 9

I = 10

N1

Line entries

Number EP(I) ET(I) ER(I,1) EG(I) ES(I) only

1

06201 DATA

06202 DATA

06203 DATA

06204 DATA

06205 DATA

06206 DATA

06207 DATA

06208 DATA

06209 DATA

06210 DATA

I = 1

1 = 2 1=3

1 = 4

1 = 5

1 = 6

1 = 7

1 = 8

1 = 9

I = 10

Variable Description

N1 Number of envelope modifications to be entered

EN(I)

(0 < N1 _< 10).

Code number for 1^ modification (0 < EN(I) < 100).

E$(I)

EC(l , 1

)

EA(I)

This code number is used again in data sheet

18-1 to match thermal performance data to the

appropriate modification.

Name of 1^ envelope modification.

Initial cost of the envelope modification.

Annual recurring O&M (AROM) cost for the

I

1-*1 envelope modification (in base time dollars).*

Enter actual cost (EA(I) > 1) or the ratio

of AROM cost to EC(I , 1 ) (EA(I) < 1).

NE( I) Number of non-annually recurring (NAROM) costs (e.g.,

repair or replacement costs) to be entered for the I envelope modification.

EP(l) Assessment rate for property tax computation

purposes for the I*1 ' 1 envelope modification

(percent of actual value).

ET(I)

ER(I)

If the conservation measure is not expected

to increase property taxes, set EP(I) = 0.

Percent of EC(I,1) which is subject to sales tax.

Resale value of the I^ envelope modification at

end of study period, as a percent of EC(I,1),

unadjusted for inflation.

This resale value is the value this measure

EG(I)

would add to the selling price of the

building at the end of the study period,

whether or not the building is to be sold.

Federal investment or energy tax credit for the

ibh modification, as a percent of EC(I,1).

ES(I) Same as EG(I), but for a state tax credit.

* Annual recurring O&M costs do not include energy costs in this report
DATA SHEET 7-1

NON-ANNUALLY RECURRING O&M COSTS - ENVELOPE MODIFICATIONS

Separate data sheet required for each envelope modification I for which NE(I) > 0

No data needed if NE(I) = 0

Line

Number* YI(I,K) Y2(I,K)

NE(I)

entries

only

+

K - 1

K - 2

K - 3

K = 4

K - 5

K » 6

K 7

K - 8

K - 9

K - 10

K - 11

K = 12

K = 13

K * 14

K - 15

K = 99

* Note - use the following schedule to assign line numbers:

I line numbers I line numbers

1 07101 - 07199 6 07601 - 07699

2 07201 - 07299 7 07701 - 07799

3 07301 - 07399 8 07801 - 07899

4 07401 - 07499 9 07901 - 07999

5 07501 - 07599 10 08001 - 08099

A- 10
Variable Description

Y1(I,K) Year of occurrence of NAROM cost to

envelope modification (base year » 1).

NAROM is assumed to occur on the last day

of year Y1(I,K).

Y2(I,K) Amount of NAROM cost (in base-time dollars)

Enter actual cost (Y2(I,K) > 1) or ratio of

K

th NAROM cost to EC(I,1) (Y2(I,K) < 1).

Note: Use ratio, not percent.

A— 1
DATA SHEET 8

DEPRECIATION DATA FOR ENVELOPE MODIFICATIONS

08001 DATA

DG ED

Skip lines 08002 - 08141 if DG - 0.

08002 DATA

rr(g)

Line DY(Fed . Env.)

Number DG entries only

08101 DATA

08106 DATA

08111 DATA

08116 DATA

08121 DATA

08126 DATA

08131 DATA

08136 DATA

08141 DATA

Skip lines 0£

08198 DATA

Skip lines 0J

08199 DATA

]

Line

Number

3198 - 08241 if ED = 0.

DS

3199 - 08241 if DS = 0.

*R(S)

DY(State, Env.)

DS entries only •*

08201 DATA

08206 DATA

08211 DATA

08216 DATA

08221 DATA

08226 DATA

08231 DATA

08236 DATA

08241 DATA

years

years

years

years

years

years

years

years

years

years

years

years

years

years

years

years

years

years

I- 5 6-10

II- 15

16-20

21-25

26-30

31-35

36-40

41-45

1-5

6-10

11-15

16-20

21-25

26-30

31-35

36-40

41-45

A- 12
Variable Description

DG Number of years over which any envelope modification is to

be depreciated - Federal schedule.

ED Depreciation code for state tax purposes:

ED 0: state depreciation schedule is same as Federal,

ED °* 1: state depreciation schedule is different from

Federal.

RR(G) Depreciation recapture rule code - Federal tax*:

RR = 1 any positive difference between the actual selling

price at the end of the study period and the

remaining basis (first cost less cumulative depreciation) is taxed as ordinary income.

RR = 2 The same positive difference is taxed as capital

gains.

RR = 3 Any positive difference between the actual selling

price and the remaining basis computed using

straight-line depreciation is taxed as capital

gains. The difference between cumulative depreciation computed using the depreciation schedule

entered and the straight-line method is taxed as ordinary income.

DY(fed,env.) Percent of initial envelope modification cost to be

depreciated in each year (1, 2, ..., DG) - Federal tax.

DY is entered for each year in the depreciation

schedule. Any type of depreciation schedule can

be entered (e.g. straight-line, sum-of-years

digits, etc).

DS Same as DG, but for state depreciation schedule.

RR(S) Depreciation recapture rule for state tax (see above).

DY(state, env.) Same as DY(fed,env.) but for state depreciation schedule.

* The Economic Recovery Tax Act of 1981 is fairly explicit about which of

these methods to use for different building classes. Even if the building

is not to be sold at the end of the study period, there is still a potential liability of this amount that may partially offset the resale value.

However, depreciation recapture and capital gains liability at the end of

the study period can be set to zero by setting RR(G) = 2, CG(1) = 0,

RR( S) = 2, and CG(2) = 0.

A- 13
DATA SHEET 9

SPACE HEATING EQUIPMENT DATA

09001 DATA » » > •

09011 DATA

N2

»

HB

t

DB( 1

>

HO

>

DE( 1

HE( 1) HF HV HA( 1

NH(1)

Line

Number HE( J) HC( J , 1

HA( J) NH( J)

N2-1

entries

only

+

09012 DATA J a 2

09013 DATA J = 3

09014 DATA J =» 4

09015 DATA J * 5

Line

Number HP( J) HT( J) HR( J ) HG(J) HS( J)

09021

09022

09023

09024

09025

N2

entries

only

+

J = 1

J = 2

J = 3

J = 4

J = 5

A-14
Variable Description

N2

HB

DB( 1

)

HO

DE( 1

)

HE( 1

HF

HV

HA( 1

)

NH(i)

HE( J)

HC ( J , 1

)

HA( J)

NH( J)

HP( J)

HT( J)

HR( J)

HG( J)

HS( J)

Number of alternative space heating plants to be entered (0 < N2 5).

Index of energy type used by space heating plant. HB corresponds to

K in data sheet 4, i.e., HB = 1 for energy type designated as EN$ ( 1 ) , etc.

Index of energy type used by distribution system for space heating.

This energy type will always be electricity, but the proper index

number (K in data sheet 4) must be designated.

Oversizing ratio for space heating plant (nominal capacity/design

heating load).

kWh consumed per GJ (lO^Btu) of heating output by fans and/or

pumps in distribution system.

Seasonal energy efficiency (output/input ) of base space heating

plant, measured before entering distribution system (percent).

Initial fixed cost of base space heating plant (i.e., that portion

of the total cost not sensitive to output capacity).

Initial variable cost of base space heating plant, in dollars per

MJ (10-^Btu) nominal output capacity.

AROM cost for base heating plant (in base-time dollars). Enter

actual cost (HA(1) >_ 1) or ratio of AROM cost to total initial

cost (HA(1) < 1).

Number of NAROM entries for base space heating plant.

Seasonal energy efficiency of the space heating plant (percent)

HE(J) > HE (J-l), i.e., each new plant is more efficient than

the one before (using the same energy type).

Additional initial cost of space heating plant relative to the

(J-l)*-*1 plant. Enter actual cost (HC(J,1) 1) or ratio of additional cost to base plant cost (HC(J,1) < 1).

AROM cost (in base-time dollars) due only to the improvement in

efficiency from HE(J-l) to HE(J).

Number of NAROM entries for the increase in efficiency from

HE(J-l) to HE( J)

.

Assessment rate for property tax computation purposes for the base

space heating plant (J=l) or the J

c “ modification (J>1), as a percent of actual value.

Percent of the initial cost of the base space heating plant (J=l) or modification (J>1) subject to sales tax.

Resale value of the base plant (J=l) or modification (J>1) at

end of the study period as a percent of its initial cost,

unadjusted for inflation.

Federal investment or energy tax credit for base heating plant

(J=l) or jth modification (J>1) as a percent of its initial

cost.

Same as HG(1), but for state tax credits.

A- 15
-t>

lo

ro

DATA SHEET 10-J

NON-ANNUALLY RECURRING O&M COSTS - SPACE HEATING PLANT IMPROVEMENTS

Separate data sheet required for each space heating plant improvement

for which NH(J) > 0. No data needed if NH(J) = 0.

* Note:

Line

Numbers* Y3(J,K) Y4(J,K)

NH( J)

entries

only

+

K - 1

K - 2

K - 3

K - 4

K *» 5

K = 6

K - 7

K = 8

K = 9

K = 10

K = 99

Use the following schedule to assign line numbers:

J line numbers

1 10101 - 10199

10201 - 10299

10301 - 10399

10401 - 10499

5 10501 - 10599

A- 16
Variable Description

Y3(J,K) Year of occurrence of K1-*1 NAROM cost to base space heating

plant (J**l) or modification ( J> 1 ) • Base year * 1.

NAROM is assumed to occur on last day of year Y3(J,K).

Y4(J,K) Amount of NAROM cost (in base-time dollars). Enter

actual cost (Y4(J,K)>^ 1) or ratio of NAROM cost to

incremental cost of plant (Y4(J,K)<1). Note: When

J=l, incremental cost is cost of base plant, i.e., incremental cost = HF + HV • CAP, where CAP = nominal output

capacity in MJ (10^ Btu).

A- 17
DATA SHEET 11

WATER HEATING PLANT DATA

11001 DATA , Q1 Q2

Skip all the following unless Ql a 2 and Q2 = 2.

11002 DATA

Line

Number

N3

WE(W)

WB

WC(W,1) WA(W) NW(W)

N3

entries

only*

4-

11011 DATA W = 1

11012 DATA W = 2

11013 DATA W = 3

11014 DATA s u

11015 DATA W = 5

Line

Numbe r WP(W) WT(W) WR(W) WG(W) WS(W)

11021 DATA

11022 DATA

11023 DATA

11024 DATA

11025 DATA

* N3 entries corresponding to water heating plant numbers.

N3

entries

only*

4-

W = 1

W = 2

W = 3

W = 4

W * 5

A- 18
Variable Description

Ql

Q2

N3

WB

WE(W)

WC(W,1)

WA(W)

NW(W)

WP(W)

WT(W)

WR(W)

WG(W)

WS(W)

Water heating plant code:

Ql = 1 if space heating and water heating are provided by

the same plant;

Ql = 2 if space heating and water heating are provided by

separate plants.

If Ql = 1 , no entries are needed for water heating plant.

In either case, solar heating equipment provides both space

and water heating. (If Q2 = 1, Ql is ignored; use Ql = 0.)

Solar equipment code:

If Q2 = 1 , solar equipment does not provide service hot

water;

If Q2 = 2, solar equipment provides both space and water

heating.

When Q2 = 1 , there is no need to evaluate the water heating

plant or water heating requirements because they are functionally independent from the simultaneous optimization

problem.

Number of alternative water heating plants to be entered

(0 < N3 < 5).

Index of energy type used by water heating plant.

WB corresponds to K in data sheet 4, i.e.,

WB = 1 for EN$ ( 1 ) , etc.

Seasonal energy efficiency of the W^ water heating plant

(W=l for base plant), percent (WE(W) > WE(W-l)).

For W = 1, initial cost of the base plant.

For W > 1, additional initial cost due to increase in efficiency from WE(W-l) to WE(W).

AROM cost for the base plant (W=l) or the improvement in

energy efficiency from WE(W-l) to WE(W).

Enter actual cost (WA(W) 1) or ratio of AROM to WC(W,1)

(WA(W) < 1).

Number of NAROM entries for W^ plant.

Assessment rate for property tax computation purposes for the

base water heating plant (W=l), or Wfc h modification (W>1),

as a percent of actual value.

Percent of the initial cost of the base water heating plant

(W=l), or Wth modification (W>1), subject to sales tax.

Resale value of base plant (W=l), or Wt^1 modification (W>1),

at the end of the study period as a percent of its initial

cost, unadjusted for inflation.

Federal investment or energy tax credit for base water heating

plant (W=l), or Wfc ^ modification (W>1), as a percent of its

initial cost.

Same as WG(W), but for state tax credits.

A- 19
cn

m

DATA SHEET 12-W

NON-ANNUALLY RECURRING O&M COSTS - WATER HEATING PLANT IMPROVEMENTS

Separate data sheet required for each water plant

improvement for which NW(W) >0. No data needed

if NW(W) “ 0.

NW(W)

Line entries

Number* Y5(W,K) Y6(W,K) only

+

12X01 DATA K = 1

12X02 DATA K = 2

12X03 DATA K = 3

12X04 DATA iA

12X05 DATA K = 5

12X06 DATA K = 6

12X07 DATA K = 7

12X08 DATA FI II OO

12X09 DATA K = 9

12X10 DATA K = 10

continue as needed

12X99 DATA K = 99

* Note: Use the following schedule to assign line numbers

W line numbers

1 12101 - 12199

2 12201 - 12299

12301 - 12399

12401 - 12499

12501 - 12599

A-20
Variable Description

Y5(W,K) Year of occurrence of K^*1 NAROM cost to base

water heating plant (W"l) or Wt^ modification

( W> 1 ) . Base year «* 1.

NAROM is assumed to occur on last day of year

Y5(W,K).

Y6(W,K) Amount of K

1-*1 NAROM cost (in base-time dollars).

Enter actual cost (Y6(W,K)>1) or ratio of

NAROM cost to incremental cost of Wt^1 water

heating plant (WC(W,1)), (Y6(W,K)<1).

A-21
DATA SHEET 13

SPACE COOLING PLANT DATA

13001 DATA > > • CB DB(2) CE CO

13002 DATA » t t CF CV CA NC

13003 DATA > t f CP CT CR CG

Skip the following if NC - 0:

Line

Number Y7(K) Y8(K)

NC

entries

only

I

K - 1

K - 2

K - 3

K = 4

K 5

K - 6

K - 7

K = 8

K - 9

K = 10

K 99

DE(2)

CS

A-22
Variable Description

CB Index of energy type used by space cooling plant.

CB corresponds to K in data sheet 4, i.e.,

CB - 1 for EN$( 1 ) , etc.

DB(2) Index of energy type used by distribution system for

space cooling. This energy type will always be electricity, but the proper index number (K in data sheet

4) must be designated.

CE Seasonal efficiency (or coefficient of performance) for

space cooling plant (before entering distribution

system, (%)).

CO Oversizing ratio for space cooling equipment (nominal

capacity/design cooling load). (Note: Use ratio, not

DE(2)

percent .

)

kWh consumed per GJ (lO^Btu) of cooling output by fans

CF

and/or pumps in the distribution system.

Initial fixed cost of space cooling plant (i.e., that

portion of total cost not sensitive to output capacity).

CV Initial variable cost of space cooling plant in dollars

per MJ (10 3 Btu) nominal output capacity.

CA AROM cost for space cooling plant (in base-time dollars).

Enter actual cost or ratio of AROM to total initial

cost

.

NC

CP

Number of NAROM entries for space cooling plant.

Assessment rate for property tax computation purposes

for the space cooling plant as a percent of actual

value.

CT Percent of the initial cost of the space cooling plant

subject to sales tax. Note: Initial cost = CF + CV« CAP, where CAP = nominal output capacity

in MJ (103 Btu).

CR Resale value of space cooling plant at end of study

period as a percent of its initial cost, unadjusted

for inflation.

CG Federal investment or energy tax credit for space

heating plant, as a percent of its initial cost.

CS

Y7(K)

Same as CG, but for state tax credits.

Year of occurrence of Kfch NAROM cost to space cooling

Y8(K)

plant. Base year =1.

NAROM is assumed to occur on last day of year Y7(K).

Amount of K

1^ NAROM cost (in base-time dollars).

Enter actual cost (Y8(K) < 1) of ratio of K*1 ^1 NAROM

cost to initial cost of space cooling plant (Y8(K)<1).

A-23
DATA SHEET 14

DEPRECIATION SCHEDULE FOR CONVENTIONAL HEATING AND COOLING PLANTS

14001 DATA

DG HD

Skip lines 14002 - 14111 if DG ** 0.

14002 DATA

RR(G)

DY(fed., plant)

Line

Number DG entries only

14101 DATA

14106 DATA

14111 DATA

years 1-5

years 6-10

years 11-15

Skip lines 14198 - 14211 if HD - 0.

14198 DATA

DS

Skip lines 14199 - 14211 if DS = 0.

14199 DATA

RR( S)

DY(state, plant)

Line

Number DS entries only *

14201 DATA

14206 DATA

14211 DATA

years 1-5

years 6-10

years 11-15

A-24
Variable Description

DG

HD

RR(G)

DY(fed, plant)

DS

RR(S)

DY( state, plant)

Number of years over which any plant or plant modification

is to be depreciated - Federal schedule.

Depreciation code for state tax purposes:

HD *= 0: state depreciation schedule is same as Federal.

HD *° 1 : state depreciation schedule is different from

Federal.

Depreciation recapture rule code - Federal tax

(See data sheet 8 for codes).

Percent of initial plant cost (or plant modification cost)

to be depreciated in each year (1, 2, ..., DG) - Federal

schedule.

Same as DG, but for state depreciation schedule.

Depreciation recapture rule for state income tax.

Same as DY(fed, plant), but for state depreciation

schedule.

A-25
DATA SHEET 15

SOLAR HEATING SYSTEM DATA

15001 DATA 9 9 9 SF SV SB SO

15002 DATA > 9 9 Ml M2 SA NS

15003 DATA 9 • 9 SP ST SR SG

Skip the following if NS ° 0:

NS

Line entries

Number Y9(K) Y0(K) only

+

15101 DATA K = 1

15102 DATA n CM

15103 DATA K - 3

15104 DATA K = 4

15105 DATA K = 5

15106 DATA K = 6

15107 DATA K - 7

15108 DATA &

ii 00

15109 DATA K = 9

15110 DATA K = 10

continue as needed

15199 DATA K = 99

DE(3)

SS

A-26
Variable Description

SF

SV

SB

SO

DE( 3 )

Ml

M2

SA

NS

SP

ST

SR

SG

SS

Y9(K)

Y0(K)

Initial fixed cost of solar heating equipment.

Initial variable cost of solar heating equipment, in dollars per ra^ (ft^) of collector area. Index of energy type used by fans and/or pumps in solar heating

equipment.

Electricity is always used but the proper index (with appropriate kWh price) must be designated. SB corresponds to K in

data sheet 4, i.e., SB = 1 for EN$(1), etc.

Solar heating system code.

Coefficients for six different solar heating systems which

can provide space heating and service hot water are stored

in the SOLCOM program. The system code designates which of

these are to be used. The user must be sure that the cost

data entered into S0LC0M1 for the solar heating system is

consistent with the system type designated here.

SO = 1 : liquid system, 1 - cover, selective.

SO = 2: liquid system, 1 - cover, non-selective.

SO = 3: liquid system, 2 - cover, non-selective.

SO = 4: air system, 1 - cover, selective.

SO = 5: air system, 1 - cover, non-selective.

SO = 6: air system, 2 - cover, non-selective.

kWh consumed per GJ (lO^Btu) of useful heat provided by the

solar heating system to run fans and/or pumps.

Minimum permissible collector size in m^ (ft^).

Maximum permissible collector size in m^ (ft^).

AROM cost for solar equipment (in base-time dollars).

Enter actual cost (SAM) or ratio of AROM to total

first cost (SAM).

Number of NAROM entries for solar heating equipment.

Assessment rate for property tax computation purposes for the

solar heating equipment as a percent of actual value.

Percent of the initial cost of the space cooling plant subject

to sales tax. Note: Initial cost = SF + SV • AREA, where

AREA = collector area in m^ (ft^).

Resale value of solar heating equipment at end of study period

as a percent of its initial cost, unadjusted for inflation.

Federal investment or energy tax credit for solar heating equipment, as a percent of its initial cost.

Same as SG, but for state tax credits.

Year of occurrence of NAROM cost to solar heating equipment.

Base year =1. NAROM is assumed to occur on last day of year

Y9(K).

Amount of Kt^1 NAROM cost (in base-time dollars).

Enter actual cost (Y0(K) _> 1 ) or ratio of Kt^1 NAROM cost to

initial cost of solar heating equipment (Y0(K)<1).

A-27
DATA SHEET 16

DEPRECIATION DATA FOR SOLAR HEATING EQUIPMENT

16001 DATA , DG SD

Skip lines 16002 - 16113 if DG =

16002 DATA

rr(g)

0 .

DY(fed, solar)

Line

Number DG entries only -*

16101 DATA

16106 DATA

16111 DATA

Skip lines 16201 - 16213 if SD = 0.

16198 DATA

DS

Skip lines 16202 - 16213 if DS = 0.

16199 DATA

RR( S)

years

years

years

DY(state, solar)

Line

Number DS entries only *

16201 DATA

16206 DATA

16211 DATA

years

years

years

-5

-10

1-15

-5

-10

1-15

A-28
Variable Description

DG Number of years over which solar heating equipment is to

be depreciated - Federal schedule.

SD Depreciation code for state tax purposes

SD = 0: state depreciation schedule is same as Federal.

DD = 1 : state depreciation schedule is different

from Federal.

RR(G) Depreciation recapture sale code - Federal tax.

(See data sheet 8 for codes.)

DY(fed, solar) Percent of initial solar equipment cost to be depreciated

in each year (1, 2, ... DG) Federal schedule.

DS

RR( S)

DY(state, solar)

Same as DG, but for state depreciation schedule.

Depreciation recapture rule for state income tax.

Same as DY(fed, solar), but for state depreciation

schedule.

A-29
DATA SHEET 17

BASIC ENVELOPE PERFORMANCE DATA,

WATER HEATING REQUIREMENTS, AND INCIDENT SOLAR RADIATION

Line

Number HL(0,M), M 3 1 to 12

17101 DATA

17105 DATA

17109 DATA

17113 DATA 9 > MH(0)

" CL(0) MC(0)

Line

Number WL(M)

M = 1 to 12

17201 DATA

17205 DATA

17209 DATA

Jan., Feb., Mar., Apr.

May, June, July, Aug.

Sept., Oct., Nov., Dec

Jan., Feb., Mar., Apr.

May, June, July, Aug.

Sept., Oct., Nov., Dec

Line

Number IR(M), M = 1 to 12

17301 DATA

17305 DATA

17309 DATA

Jan., Feb., Mar., Apr.

May, June, July, Aug.

Sept., Oct., Nov., Dec

A-30
Variable Description

HL(0,M) Monthly space heating requirements (output) for base building

(before the envelope modifications are brought in), M = 1, 2,

, 12, in GJ (10°Btu).

MH(0) Maximum hourly space heating load for the year, in MJ

( 103 Btu)

.

CL(0) Annual cooling requirements (output) for the base building, in

GJ (10 6Btu).

MC(0) Maximum hourly space cooling load for the year, in MJ

(10 3 Btu).

WL(M) Monthly water heating requirements, in GJ (lO^Btu),

M = 1, 2, ... , 12.

IR(M) Daily average incident solar radiation on tilted collector

surface in M^ month, in KJ/m^ (Btu/ft^), M= 1, 2, ..., 12.

A-31
DATA SHEET 18-1

REDUCTIONS IN HEATING AND COOLING LOADS

DUE TO ENVELOPE MODIFICATIONS

Separate data sheet required for each envelope modification.

18X00 DATA

El(l)

Line

Number DH(I,M), M = 1 to 12

18X01 DATA

18X05 DATA

18X09 DATA

Jan., Feb., Mar., Apr.

May, June, July, Aug.

Sept., Oct., Nov., Dec.

18X13 DATA

Dl(l) dcTD D2(l)

Note: Use the following schedule to assign line numbers:

I line numbers I line numbers

1 18101 - 18113 6 18601 - 18613

2 18201 - 18213 7 18701 - 18713

3 18301 - 18313 8 18801 - 18813

4 18401 - 18413 9 18901 - 18913

5 18501 - 18513 10 19001 - 19013

A-32
Variable Description

EI(I)

DH( I ,M)

D1(I)

DC(I)

D2(I)

Code number for the it*1 envelope modification, corresponding

to EN(I) in data sheet 6. Every envelope modification on data sheet 6 must have a corresponding data sheet here.

Reduction* in monthly space heating requirements due to the

it*1 envelope modification, in GJ (lO^Btu), M = 1, 2, ...,

12 . Reduction* in maximum space heating load due to the it*1 envelope modification, in MJ/hr (lCpBtu/hr)

.

Reduction* in annual cooling requirements due to the it*1 envelope modification, in KJ (lO^Btu).

Reduction* in maximum space cooling load due to the it*1 envelope modification, in KJ/hr (lO^Btu/hr).

* Reductions in heating or cooling requirements are entered as positive numbers.

If an increase in heating or cooling requirements results from any envelope

modifications, use a negative sign. (Some modifications, e.g. solar screening,

may reduce cooling requirements but increase heating requirements, and vice

versa.

)

A-33

APPENDIX B. SOLAR LOAD RATIO COEFFICIENTS

Solar load ratio coefficients for six different "standard" solar heating

systems that can provide both space and water heating in commercial buildings

are referenced in the SOLCOM optimization program. The use of these coefficients is explained in section 3.2. These coefficients are as follows^:

System Type

Liquid Systems

1. 1-cover,

2. 1 -cover,

3. 2-cover,

Air Systems

1. 1-cover,

2. 1-cover,

3. 2-cover,

selective

non-selective

non-selective

selective

non-selective

non-selective

B1 B2

0.317 1.478

0.291 1.581

0.287 1.605

0.415 1.187

0.426 1.177

0.371 1.314

B3 B4

1.314 0.613

1.298 0.555

1.302 0.550

1.360 0.830

1.392 0.872

1.353 0.739

1 Source: Powell, Jeanne W. and Rodgers, Jr., Richard C., FEDSOL: Program

User’s Manual and Economic Optimization Guide for Solar Federal Buildings

Projects , NBSIR 81-2342, U.S. Department of Commerce, National Bureau of

Standards, Washington, D.C., August 1981.

B-l

APPENDIX C LISTING OF SOLCOM PROGRAM

C-l
I

z

oNHH

cc0

1

UJr

rH s 1-

in w s H-l w _J tH 3

- C'4 X \

S X. x CL 1-

t—

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C-32
01. Summary date

Yr. Mo. Day

8 2 0 9 3 0

04. Software date

Yr. Mo. Day

8 2 0 9 3 c

FEDERAL INFORMATION PROCESSING STANDARD SOFTWARE SUMMARY

02. Summary prepared by (Name and Phone)

Stephen R. Petersen (301) 921-3701

05. Software title

SOLCOM

06. Short title SOLCOM

03. Summary action New Replacement Deletion Kl

Previous Internal Software ID

07. Internal Software ID None

08. Software type

Automated Data g

System

Q Computer Program

q

Subroutine/Module

09. Processing mode

jpfc Interactive Batch

| | Combination

10. General Computer Systems

Q Support/ Utility

~| Scientific/Engineering

Bibliographic/Textual

Application area

Management/

Business

Process Control

Specific

Other

Economic optimization of

energy-related building

designs

11. Submitting organization and address Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

12. Technical contact(s) and phone

Stephen R. Petersen

(301) 921-3701

13. Narrative

The SOLCOM program was written to demonstrate the use of economic optimization

algorithms for integrating solar and other energy conservation features into new commercial building designs. These algorithms will be useful to design

engineering teams who must determine the proper size of an energy conservation

budget in a new building and its allocation among competing solar and conservation

investments. It is intended to be used on a microcomputer with 48K memory,

one disk drive, and 132 character line printer.

14. Keywords building design; commercial buildings; energy conservation; engineering economics

heating and cooling equipment; heating and cooling loads; life-cycle cost analysis;

optimization algorithms; solar heating

15. Computer manuf'r and model Radio Shack

TRS-80 Model III

16. Computer operating system

TRSDOS

17. Programing language(s)

BASIC

18. Number of source program state- ments 1800

19. Computer memory requirements

48K Ram

20. Tape drives 0

21. Disk/Drum units 1

22. Terminals

1

23. Other operational requirements

Line printer

24. Software availability

Available Limited m

In-house only

25. Documentation availability

Available £3

Inadequate In-house only

I

26. FOR SUBMITTING ORGANIZATION USE

185-101 Standard Form 185

1974 July U S. Dept, of Commen-^

(FIPS Pub. 3
N BS-1 14A (Rb.. «. U.S. DEPT. OF COMM.

4.

1 . BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR 2 REPORT NO.

NBSIR 83-2658

. Performing Organ. Report NoJ 3.

TITLE AND SUBTITLE

Publication Date

v February 1983

SOLCOM: A Computer Program to Integrate Solar and Conservation Economics for New

Commercial Buildings

5. AUTHOR(S)

Stephen R. Petersen

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS _

DEPARTMENT OF COMMERCE 7

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Type of Report & Period Covered

Final

Office of Solar Heat Technologies

Department of Energy

Washington, D.C. 20545

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gnificant Information. If document includes a significant

bibliography or literature survey, mention it here) This report provides a methodology, algorithms and a computer program for determining

the least life-cycle cost combination of three interdependent conservation strategies

in new commercial buildings. These three strategies include (1) envelope modifications

to reduce seasonal and peak load heating and cooling requirements, (2) heating and

cooling plant modifications to increase their seasonal efficiency, and (3) the use of an active solar space and water heating system. The resulting computer program, called

SOLCOM, can be run on a microcomputer in three stages.

The SOLCOM program performs a complete life-cycle cost analysis for the active solar

system and for each envelope and plant modification to be considered, include tax and

mortgage effects. The program then determines the optimal combination of envelope

modifications and the resulting seasonal and peak load heating and cooling requirements;

the optimal space heating, water heating, and space cooling plant efficiencies; and

the optimal collector size for the active solar heating system.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

building design; commercial buildings; energy conservation; engineering economics;

heating and cooling equipment; heating and cooling loads; life-cycle cost analysis;

optimization algorithms; solar heating

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

P^-Unlimited

| | For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

138

15. Price

(5tXj<Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $14.50

U S COMM- D C 6043-P80