FEDSOL: Program User’s Manual and Economic

rwiTMi zation Guide for Solar Federal Buildings Projects

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August 1981

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

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NBSIR 81-2342

»» » FEDSOL: PROGRAM USER'S MANUAL AND ECONOMIC

OPTIMIZATION GUIDE FOR SOLAR FEDERAL BUILDINGS PROJECTS

Jeanne W. Powell

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Economics and Regulatory

Technology Division

Washington, DC 20234

Richard C. Rodgers, Jr.

Consultant in Solar Energy Research,

Development, and Design

Palo Alto, California 94302

August 1981

Sponsored by:

Field Applications Branch

Division of Active Heating and Cooling

Office of Solar Applications for Buildings

U.S. Department of Energy

Washington, DC 20585

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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ABSTRACT

This report provides a user's manual for the FEDSOL computer program and a guide for designing and sizing solar energy projects for Federal buildings.

The life-cycle cost procedures implemented by the computer program and

explained in the report are consistent with the Federal Rules for Life-Cycle

Costing (10 CFR Part 436) as applied to solar energy projects.

The FEDSOL program determines the economically optimal size of a solar energy

system for a user-specified building, location, system type, and set of economic conditions; it conducts numerous breakeven and sensitivity analyses; and it

calculates measures of economic performance as required under the Federal Rules.

The economic model in the program is linked with the SLR (Solar Load Ratio)

design method developed at Los Alamos National Laboratory to predict the performance of active systems. The economics portion of the program can, however,

be used apart from the SLR method, with performance data provided by the user. An environmental data file for 243 U.S. cities is included in the program.

Highly user oriented, the FEDSOL program is intended as a design and sizing

tool for use by architects, engineers, and facilities managers in developing

plans for Federal solar energy projects.

Key words: cost effectiveness; economic optimization; Federal buildings;

life-cycle costing; solar economics; solar energy.

iii
ACKNOWLEDGMENTS

The authors wish to thank all those persons who contributed to the preparation

of this report. Rosalie T. Ruegg served as project leader during the formative

stages of the project and provided substantial editorial and technical assistance to this final report. Much of the material in section 3 of this report

was taken from the Life-Cycle Cost Manual for the Federal Energy Management

Program [1], prepared by Rosalie Ruegg, and Chapter 11 of the Solar Design

Workbook [2], prepared by Rosalie Ruegg, Thomas Sav, and Jeanne Powell.

Dr. Harold E. Marshall, Group Leader of the Applied Economics Group, Dr. Kent

Reed, Group Leader of the Solar Equipment Group, Lynne Charlton of the Solar

Technology Group, Center for Building Technology, and Robert Atkins, Office

of Engineering Standards, National Bureau of Standards also deserve special

thanks for the time they spent in discussing and reviewing this report and for

their many helpful comments.

Special acknowledgment and appreciation are extended to Drs. Norman E. Schnurr

and Bruce D. Hunn of Los Alamos National Laboratory for their encouragment and

technical assistance in incorporating "The Solar Load Ratio Method Applied to

Commercial Building Active System Sizing" [3] within the FEDSOL program and for

reviewing this report.

The authors also wish to thank Mr. William Lemeshewsky of the Department of

Energy, Program Coordinator of the Solar Federal Buildings Program, and

Mr. Robert Lorand of JRB Associates, Inc., Contract Manager, for providing

financial support and guidance to this project.

iv
PREFACE

This report was prepared by the Applied Economics Group, Building Economics and

Regulatory Technology Division, Center for Building Technology, National Engineering Laboratory, National Bureau of Standards (NBS), for the Department of

Energy, Office of Solar Applications for Buildings, under Interagency Agreement

E(49-l )-3800, EA-77-A-01-6010.

The work is in support of the Solar Federal Buildings Program, whose broad

objective is to stimulate the growth and improve the efficiency of the solar

industry by providing funds to Federal agencies for the design, acquisition,

construction, and installation of commercially applicable solar hot water,

heating, cooling, and process systems in new and existing Federal buildings.

The authorizing legislation for the Solar Federal Buildings Program (the

National Energy Conservation and Policy Act of 1978) further ordered that a life-cycle cost analysis conducted in accordance with a uniform methodology

and procedures to be established by the Department of Energy accompany proposals for project funding.

This report provides a comprehensive guide for applying life-cycle cost

analysis to the economic evaluation, design, and sizing of Federal solar energy

projects with FEDSOL, an interactive computer program that is fully consistent

with the methodology and procedures for life-cycle cost analysis established by

the Department of Energy. FEDSOL can be accessed through the Solar Energy

Information Data Bank (SEIDB), the computer time-sharing network operated by

the Solar Energy Research Institute, and is available on magnetic tape from the

National Technical Information Service. The FEDSOL program and user instructions (section 2 of this report) were prepared by Richard C. Rodgers, Jr.,

Consultant in Solar Energy Research, Development, and Design, P. 0. Box 1365,

Palo Alto, California 94302.

v
TABLE OF CONTENTS

Page

ABSTRACT iii

ACKNOWLEDGMENTS iv

PREFACE . . v LIST OF TABLES AND FIGURES viii

1. INTRODUCTION 1

1.1 Background 1 1.2 Purpose and Scope 2

1.3 Approach and Organization 3

2. INSTRUCTIONS FOR OPERATING THE FEDSOL COMPUTER PROGRAM 5

2.1 Overview 5

2.1.1 Thermal (SLR) and Economic Performance Analysis ... 5

2.1.2 Economic Analysis Only 5

2.2 Getting Started 6

2.2.1 Calling Up FEDSOL 6

2.2.2 Getting Acquainted With FEDSOL ..... 7 2.3 Creating a New File 8

2.3.1 Supplying the Required Data 8

2.3.2 Changing Default Values 11

2.4 Running the Analysis 17

2.5 Saving a File 17

2.6 Terminating Execution of FEDSOL 18

2.7 Learning FEDSOL . 18

3. THE LIFE-CYCLE COST METHOD FOR SELECTING SOLAR ENERGY SYSTEMS

FOR FEDERAL BUILDINGS 20

3.1 Comparing Energy Use With and Without Solar 20

3.1.1 Estimating Building Energy Requirements 21

3.1.2 Estimating Energy Savings 22

3.1.3 Estimating Energy Savings with FEDSOL: The SLR

Method . 23

3.2 Identifying Relevant Costs, Assumptions, and Constraints . . 27

3.2.1 Investment Costs 30

3.2.2 Recurring Non-fuel Operation and Maintenance Costs . . 31

3.2.3 Replacement Costs and Salvage Value ... 32

3.2.4 Energy Costs 33

3.2.5 Inflation and the Discount Rate 33

3.2.6 Study Period 35

3.3 Calculating Total Life-Cycle Costs With and Without Solar . . 35

3.3.1 Total Life-Cycle Costs Without Solar 36

3.3.2 Total Life-Cycle Costs With Solar 36

3.3.3 Net Savings 38

3.4 Optimizing System Design ....... 38

3.4.1 Framework for Optimization 38

vi
TABLE OF CONTENTS (cont.)

Page

3.4.2 Maximizing Savings 40

3.4.3 Minimizing Losses 41

3.4.4 What To Do When the Economically Optimal Solar

Energy System Size Is Zero or Very Small 41

3.4.5 Optimizing System Size with FEDSOL 43

3.4.6 Conducting Sensitivity Analyses with FEDSOL 45

3.4.7 Making the Design and Sizing Decision 48

3.5 Calculating Other Measures of Economic Performance 48

4. CASE EXAMPLES ILLUSTRATING THE FEDSOL PROGRAM 51

REFERENCES 74

APPENDICES A1

A - FEDSOL Program Code A1

B - Map and Coded List of Cities in FEDSOL Geographical Data Bank . . B1

C - Discount Formulas Cl

D - The Solar Load Ratio Design Method: Performance Curves and

Schematic Diagrams Dl

E - Illustrations and Explanations of Key Algorithms El

F - Conversion Factors for the Most Common Units Used in Solar

Energy System Design and Evaluation FI

G - Range of Acceptable Values for Input Data G1

vii
LIST OF TABLES AND FIGURES

Page

Tables

2.1 Standard System Types 10

3.1 Thermal Performance for SAMPLE Case 26

3.2 Efficiency Curve Coefficients Used To Characterize the

Generic Types of Flat Plate Collectors 28

3.3 The Standard Active System 29

3.4 Life-Cycle Cost Summary for the SAMPLE Case 44

3.5 Table of Solar Fractions and Net Savings for the SAMPLE Case ... 44

3.6 Breakeven Analysis for the SAMPLE Case 47

Figures

3.1 The Solar Load Ratio Method: A Generalized Design Curve ..... 24

3.2 LCC Trade-Off Between Conventional Energy and Solar Energy .... 39

3.3 Determining the Economically Optimal System Size Through

Minimizing TLCC s>a 39

3.4 Determining the Economically Optimal System Size Through

Maximizing Savings 39

3.5 Minimizing Losses (-NS) Associated with Solar Projects 42

3.6 Sizing Systems When No Optimization Is Possible (A System

Size of Zero Minimizes Net Losses) 42

3.7 Annual Solar Fraction vs. Net Losses - Sample Test Results

for an Office Building System for Space and Service Water Heating

in Four U.S. Cities . 46

viii

!
1 . INTRODUCTION

To design and size solar energy systems for maximum economic efficiency, it is

important to use life-cycle cost (LCC) analysis throughout the planning and

design stages of a project. Federal agencies are required to submit a lifecycle cost evaluation consistent with a prescribed methodology and procedures

for life-cycle cost analyses before undertaking an investment in solar energy.

1.1 BACKGROUND

The National Energy Conservation and Policy Act of 1978 (NECPA) authorized the

Solar Federal Buildings Program (SFBP), a multi-year program designed to promote the use of solar energy and to develop a more efficient solar industry.

The NECPA directed the Department of Energy to develop uniform LCC methods

and procedures to be followed by all Federal agencies in evaluating the cost

effectiveness of potential energy conservation and renewable energy investments in Federally owned and leased buildings. According to Title 5, Part 2,

Sec. 523, of NECPA, these LCC procedures must be applied to projects funded

under the Solar Federal Buildings Program.

The Federal LCC Rule was published in the January 23, 1980 issue of the Federal

Register [4], with energy price data then current. A revision of the Rule,

including new energy price data and other changes pursuant to the Energy

Security Act of 1980, was proposed in the October 27, 1980 issue of the Federal

Register [5] and was published in final form on September 1981 [6]. Further

revisions to the LCC Rule, primarily to update energy prices, will be made

periodically.^ The "Methodology and Procedures for Life-Cycle Cost Analyses"

is Subpart A of Part 436 of Title 10 of the Code of Federal Regulations.

Subpart D of Part 436 sets forth guidelines for the Solar Federal Buildings

Program.

To help implement the LCC methodology and procedures, an LCC Manual [1] has been

prepared. The LCC Manual explains the life-cycle costing method, defines the

terms, describes assumptions and procedures to follow in performing evaluations,

and gives examples. In addition, it provides a set of worksheets, a computer

program, and step-by-step instructions for performing the LCC evaluations of

energy conservation and renewable energy projects for Federal buildings. The

Solar Project worksheets were submitted with proposals for project funding

under the Solar Federal Buildings Program.

1 The status of current energy price data for use in carrying out the Federal

LCC evaluation can be ascertained by contacting Jack Vitullo, Federal Energy

Management Program Office, Forrestal Building, U. S. Department of Energy,

Washington, D.C. 20585. Telephone: 202-252-9471.

^ The reader is referred to the LCC Rules, the LCC Manual [1], and to the

A-2 Cost Data forms for Solar Federal Buildings projects for further information in applying the Federal LCC procedures and computer program contained

in this report to solar projects in Federal buildings.

1
The worksheet evaluations are used as an indication of the relative cost

effectiveness of various candidate projects. The resulting data are useful in

selecting and sizing projects, and add to the body of knowledge concerning the

economic viability of solar investments for Federal buildings.

To promote the economically efficient use of solar energy, the Solar Federal

Buildings Program encourages selection of the system size which gives the greatest total net savings based on a life-cycle cost comparison of alternative solar

energy systems and a reference energy system. 2 Proposals for funding must state

the method of calculation used in optimizing collector area.

A number of solar analysis computer programs with life-cycle cost routines for

system size optimization are available. Unfortunately, use of these programs

to evaluate Federal building projects is difficult, requiring a thorough understanding of the economic models contained in them and considerable manipulation

of data and program output to bring them into conformance with the Federal LCC

Rule and SFBP Rule.^ The worksheets contained in Solar Form A-2 and the computer program in the LCC Manual are convenient for evaluating a single project.

However, using them to evaluate a large number of design/size configurations

requires laborious, repetitive calculations. This process can be streamlined

by using a computerized economic optimization algorithm with a built-in thermal

performance model.

1.2 PURPOSE AND SCOPE

The purpose of this report is to provide an easy-to-use computer program,

FEDSOL, and guide for designing and sizing solar energy projects for Federal

buildings according to required life-cycle cost procedures.

Although the FEDSOL program and guide should be useful to researchers and

students in general in the solar energy field, they are intended primarily as

1 The LCC data for projects funded under the Solar Federal Buildings Program

are available through the Solar Data Center at the National Bureau of Standards. The data may be obtained in hard-copy report form or accessed

interactively through an on-line, data retrieval system [8].

2 A solar project need not be cost effective to be approved for SFBP funding

although its comparative degree of cost effectiveness is one criterion,

accounting for up to 20 percentage points, that is considered in its approval.

"Cost effective" means that the estimated benefits (savings) from a project

exceed its costs, where both are assessed over the life of the project (not

to exceed 25 years) in accordance with the Federal LCC Rules.

3 F-CHART and SOLCOST, for example, contain life-cycle cost routines, including

system size optimization. However, the users' guides provide little information about the life-cycle cost models contained in the programs. The NBS is

currently preparing a report which compares the LCC sections of the following

computer models: F-CHART 3.0, F-CHART 4.0, SOLCOST, BLAST, DOE-2, and FEDSOL

[9].

2
working tools for practicing architects, engineers, facilities managers, and

others engaged in the economic evaluation and design of Federal solar energy

projects

In addition to serving as a user's manual for the FEDSOL program, this guide

describes the model for optimizing the size of a solar energy system according

to the Federal LCC Rules. Since the FEDSOL program contains as default values

the data and assumptions required (or recommended) under the Federal Rules, it

is considerably easier to use for evaluating a Federal project than existing

solar simulation programs with life-cycle cost routines. 1 At the same time,

the life-cycle cost model contained in the program is sufficiently general to

be applicable to a broad range of solar energy investment decisions undertaken

in the public or other non-profit sectors.

Using the solar load ratio (SLR) method for estimating solar energy system

performance, FEDSOL determines the economically optimal size for a solar energy

system and calculates the required life-cycle cost measures of economic performance for the optimal system. It also conducts sensitivity analyses of the

effects on life-cycle costs of oversizing and undersizing systems. For systems

that are not cost effective under the conditions specified, it determines the

energy price assumptions and investment cost assumptions for which the system

would be cost effective.

1.3 APPROACH AND ORGANIZATION

The approach taken in this users' manual and guide is, first, to provide

instructions for operating the FEDSOL computer program and, second, to provide

guidance in understanding the procedure and in applying the computer program

to different kinds of solar projects for Federal buildings.

Section 2 provides a general overview of the thermal and economic analysis

options contained in the FEDSOL program and step-by-step instructions for implementing the program on the SEIDB time-sharing system. Included are instructions

for 1) calling the program, 2) using the program commands, 3) selecting an analysis option appropriate to a specified project, 4) changing the default

values for input variables, 5) rerunning the program with changes in input

values, and 6) saving input data for future use.

Section 3 explains the economic evaluation model for Federal buildings projects

upon which the FEDSOL program is based. It describes the procedures, data, and

assumptions required for conducting a life-cycle cost evaluation of a solar

project undertaken in the Federal sector and provides guidelines for developing

the additional data required.

1 The program will assume these default values unless the user specifies

otherwise

2 For more detailed economic models providing for in-depth analysis of

investments in active and passive solar energy systems for commercial buildings, the reader is directed to references [10, 11, 12, 13]; for models that

treat solar investments for buildings of State and local governments and

non-profit organizations, the reader is directed to references [12, 13, 14].

3
Annotated examples of program input and output listings are provided in section

4. Appendices include a listing of the FEDSOL program code, documentation of

the major algorithms contained in the program, discount formulas referenced in

this report, and a map and coded list of 243 cities for which the program

contains environmental and weather data.

Those who are familiar with the LCC method and the Federal requirements

regarding data and assumptions may wish to proceed directly to the instructions

for operating the FEDSOL computer program in section 2; those who are not may

wish to review section 3, a primer on the method, data, and assumptions, before

going to section 2.

4
2.1 2. INSTRUCTIONS FOR OPERATING THE FEDSOL COMPUTER PROGRAM

OVERVIEW

FEDSOL is a completely interactive, easy-to-use computer program available to

Federal agencies and contractors to Federal agencies in the Program Library of

the Solar Energy Information Data Bank (SEIDB) computer time-sharing system.

This system is operated by the Solar Energy Research Institute through the

TYMNET communications network. No computer programming knowledge or computer

experience is required to use the program.

FEDSOL was designed to evaluate active solar domestic hot water and/or

space-heating systems using the solar load ratio (SLR) method of predicting

performance. Two solar analysis options are available;

1. a Thermal (Solar Load Ratio method) and Economic Performance Analysis,

for situations where both thermal and economic analyses are desired,

and

2. an Economic Analysis Only, for evaluating the economic performance of

projects whose thermal performance is already known or has been projected by some other means.

2.1.1 Thermal (SLR) and Economic Performance Analysis

FEDSOL produces a thermal analysis for the type of "standard" active solar energy

system that you, the program operator, specify. It then uses this thermal analysis as input, along with additional economic information that you are asked to

supply, to perform a life-cycle cost analysis for the system under consideration.

Once this analysis has been generated, you may return to the original data

and change one or more items, then run the analysis again to obtain new results.

You have a choice of pre-specifying the size of the solar energy system or of

solving for the size:

a. you may specify the collector area of the system you wish to analyze,

and FEDSOL will generate the thermal and economic analyses of a system

of that size; or,

b. you may request an optimization analysis, and FEDSOL will determine

the optimal collector area (collector area which results in the lowest

life-cycle cost).

2.1.2 Economic Analysis Only

If you wish to perform an economic analysis only, FEDSOL will accept the preestimated performance of the system as input data along with economic data

for the project. It will then generate an economic analysis from these two sets

of data. You may wish to employ this alternative if you already have a thermal

analysis from another source. You will be asked to supply the annual heating

requirement and annual solar heating fraction obtained from this source.

5
2.2 GETTING STARTED

To access and use FEDSOL, you will need a terminal, an acoustic or direct

connect modem, and a telephone. The modem may be a separate unit or may be

built into the terminal.

For information about accessing the SEIDB System, contact

Mr. Rafael E. Ubico

SEIDB Network Coordinator

Solar Energy Research Institute

1617 Cole Blvd.

Golden, CO 80401

(FTS 327-1032 or 303-231-1032).

The program code, written in BASIC, is reprinted in Appendix A and is

available on tape from

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, VA 22161.

2.2.1 Calling Up FEDSOL

To call up FEDSOL, dial the TYMNET number for your city and fit the telephone

receiver into the acoustic coupler. Be sure that all of the components of your

system are turned ON. The terminal should be set for FULL DUPLEX and upper

case (for alpha entries).

After a brief pause the timeshare system should communicate with your terminal.

You will receive information about log-in procedures when you obtain your

account with the SEIDB system. NOTE: (A carriage return (hereafter referred

to as (CR)) must follow each entry.

After you have completed the "sign on" procedure, the terminal will respond

with the prompt character (*). The next step is to access FEDSOL by entering

- FEDSOL (CR).

Now the terminal will print:

FEDSOL - VERSION 1.0 *** NATIONAL BUREAU OF STANDARDS

COMMAND: N=NEW, 0=0LD, L=LIST, C=CHANGE, R=RUN, S=SAVE,Q=QUIT, H=HELP ?

N allows you to create a completely new file, regardless of data

previously entered;

6
0 calls up any previously saved FEDSOL file when you enter the name of

the file;

C permits you to edit data already present in a file;

L lists the data elements of the current file, along with their current

values

R executes either the economic analysis only or the thermal AND economic

performance analyses;

S saves the data in the current file and allows you to name the file;

Q stops execution of FEDSOL and returns you to system;

H accesses and prints the instructions for using FEDSOL.

You may enter data in either English or Standard International (SI) units. In

addition, once the file has been created using one set of units, you may list

(L) the data or run (R) the program in either that same set of units or the

alternative set. There is no need for the program operator to make any unit

conversions

2.2.2 Getting Acquainted with FEDSOL

Each time you begin a session with FEDSOL you must select either N (New) or 0

(Old). N allows you to create an input file, and 0 retrieves an existing

input file from storage. You may not perform the remaining operations, C, L,

R, or S, until you have used N or 0 to create or access an input file. A

demonstration file for a system for space and service water heating in an office

building in Washington, D.C. is stored permanently under the filename "SAMPLE."

Retrieving an Existing File . The first time you run the program you may wish

to call the demonstration file SAMPLE. This will help familiarize you with the

required input data elements and with the C, L, and R commands.

Select 0 (CR) to retrieve an existing input file. You will be asked for the name of the file you are requesting. Type in SAMPLE (CR) in response to this

prompt. Answer the next prompt, ENGLISH OR SI UNITS (E OR SI)? with E (CR) or

SI (CR), depending on which units you wish to use. The command selection

COMMAND: N=NEW, 0=0LD, L=LIST, C=CHANGE, R=RUN, S=SAVE, Q=QUIT, H=HELP ? will now print again. Select L (CR) to list SAMPLE.

Note carefully the data elements appearing in this SAMPLE listing. These are

the data elements for which you will need to provide values when you create or change your own data files.

Now that you have listed SAMPLE, the command selection will reappear. Select

R (CR) to run the analyses for this SAMPLE input file.

7
After the analyses have been completed and the results printed, the command

selection menu will reappear. Select C (CR) to change any values in the input

file. Type in the number of the line you wish to change (refer to listing)

(CR). The description of the parameter and its current value will be displayed. In response to the LINE NUMBER? query, type in the new value you wish

to use, followed by (CR). When you have completed making changes, you may exit

the change mode by typing a (CR) in response to the LINE NUMBER? query. This

will return you to the command selection. You may wish, for example, to change

the last item (data input #70) in order to generate the "Extended" output (by

entering ”2” as the new value) or the "Summary” output (by entering "3" as the new value)

NOTE: To change units at this (or any) time, first select S (CR) to save the

modified input data file under a filename. Then select 0 (CR) to recall

the file by its name, and enter E or SI (CR) to designate the units you

desire. If you have made changes to the input file since first retrieving it from storage, it is important to use the S command to save the

current input file before you use the 0 command to recall it. Otherwise,

you will lose any changes you have made since retrieving the input file

from storage. Now you may list the file or run the analyses in the new

units

Once having made the desired changes in the data file, you may re-run the

analyses (R) , re-list the input data file (L), save the file in permanent

storage, (S), terminate execution of FEDSOL (Q), or create a new file (N).

NOTE: You may not change a file to describe a system in a different location.

Create a new file to consider a new location or different type of building. FEDSOL will then automatically select the appropriate geographical

and energy price data for the new building and location.

2.3 CREATING A NEW FILE

Select N (CR) from the command selection to create a new file. Be sure first

to save your previous file if you wish to retain it for later reference. If

you have not saved it, the N command will cause that data to be lost.

In creating a new file, you will need to supply a minimum set of data. Once

you have responded to the queries for this data, the program will supply its own default values for the remaining data elements. This enables you to create

a usable data file almost immediately with little chance of error. At this

point, you may list the file (L) to see your new input data along with the

default values for the location you selected. Change (C) any of the data you

wish, or simply run (R) the analyses.

2.3.1 Supplying the Required Data

Once you have given the N command, you will be queried for the following data:

ENGLISH OR SI UNITS? (E OR SI)?

8
Enter E (CR) for English units, SI (CR) for Standard International units.

PERFORMANCE ANALYSIS USING SLR METHOD (Y OR N)?

Enter Y (CR) if you wish a thermal analysis (using the Solar Load Ratio

method) as well as the economic analysis. Enter N (CR) if you want the

economic analysis alone.

ENTER CITY ID NUMBER?

Enter a number from 1 to 243 (CR) to designate the location (or nearest

city in file) for the system you are evaluating. You will find the cities

and their ID numbers listed in Appendix B.

RESIDENTIAL = 1; COMMERCIAL = 2; INDUSTRIAL =3?

Enter 1,2, or 3 (CR). This response determines which set of base-year

fuel prices and energy price escalation rates the program will use. These

values are contained in the energy price data file used by FEDSOL. (Normally this prompt would be used to determine the type of ownership of the

proposed project and the appropriate tax assumptions; however, this distinction is not relevant to this program since it is designed specifically

for Federal buildings.)

THE FOLLOWING DATA ITEMS REPRESENT THE MINIMUM INFORMATION REQUIRED TO CREATE A

USABLE INPUT DATA FILE. ITEMS PRECEDED BY (*T) ARE REQUIRED ONLY IF YOU

REQUEST THE THERMAL-AND-ECONOMIC PERFORMANCE ANALYSIS USING SLR METHOD (ABOVE),

ITEMS PRECEDED BY (*E) ARE REQUIRED ONLY IF YOU REQUEST THE ECONOMIC ANALYSIS

ALONE. ITEMS NOT PRECEDED BY AN ASTERISK ARE REQUIRED IN BOTH CASES.

NOTE: Create a new data file to change from a combined thermal and economic

performance analysis to an economic analysis alone, or vice versa.

Since the two types of analyses require different data, the same data

file cannot be used for both types of analyses.

(*T) TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST)?

Enter a number from 1 to 19 (CR). The 19 "standard systems" are shown in

table 2.1.

(*T) ENTER LOAD TYPE: 1=WATER HTG; 2=SPACE HTG; 3=B0TH?

Enter the appropriate number from 1 to 3 (CR).

(*T) DOMESTIC HOT WATER USAGE?

Enter hot water use (in gallons/day or liters/day) (CR). This prompt will

occur only if you have indicated that your evaluation refers to a water

heating or water/space heating combination system.

9
NOTE: Enter only the numeric value, expressed in the units shown (E or SI as you requested in creating the file). Do not type the units

(gallons/day , MMBtu/Month, etc.).

( *T) MONTHLY SPACE HEATING LOADS?

Enter the 12 values representing the building's monthly space heating

requirements (in MMBtu/month or GJ/month) (CR). Do not adjust for the

operating efficiency of the non-solar heating plant. This prompt will

occur only if you have indicated that the system under consideration is a space heating system or combined water/space heating system.

Table 2.1 Standard System Types

NO.

SYSTEM

TYPE

COLLECTOR

DESCRIPTION

OPERATING

TEMPERATURE, c*F

1 SHW 1 COVER, SELECTIVE 110 OUTLET WATER TEMP.

2 SHW 1 COVER, SELECTIVE 130 OUTLET WATER TEMP.

3 SHW 1 COVER, SELECTIVE 150 OUTLET WATER TEMP.

4 SHW 1 COVER, SELECTIVE 170 OUTLET WATER TEMP.

5 SHW 1 COVER, NON-SELECTIVE 110 OUTLET WATER TEMP.

6 SHW 1 COVER, NON-SELECTIVE 130 OUTLET WATER TEMP.

7 SHW 1 COVER, NON-SELECTIVE 150 OUTLET WATER TEMP.

8 SHW 1 COVER, NON-SELECTIVE 170 OUTLET WATER TEMP.

9 SHW 2 COVERS , NON-SELECTIVE 110 OUTLET WATER TEMP.

10 SHW 2 COVERS , NON-SELECTIVE 130 OUTLET WATER TEMP.

11 SHW 2 COVERS , NON-SELECTIVE 150 OUTLET WATER TEMP.

12 SHW 2 COVERS , NON-SELECTIVE 170 OUTLET WATER TEMP.

13 SHLS 1 COVER, SELECTIVE —

14 SHLS 1 COVER, NON-SELECTIVE

15 SHLS 2 COVERS , NON-SELECTIVE —

16 SHAS 1 COVER, SELECTIVE —

17 SHAS 1 COVER, NON-SELECTIVE —

18 SHAS 2 COVERS , NON-SELECTIVE

19 SH(R) 1 COVER, NON-SELECTIVE ...

SHW = Service Hot Water only, Commercial

SHLS = Space Heating with or without SHW, Liquid System, Commercial

SHAS = Space Heating with or without SHW, Air System, Commercial

SH(R) = Space Heating, Residential

NOTE: Systems 1 through 12 refer to water heating-only systems. Systems

13 through 18 refer to space heating systems or to combined space

and water heating systems. System 19 refers to space heating-only

systems or combined space and water heating systems where the hot

water load is less than 20 percent of the total annual heating

load. For systems other than those listed above, you may obtain a thermal analysis from other sources and use that information as input for the economic analysis.

10
(*E) ANNUAL ENERGY LOAD?

Enter the total annual energy requirement for water heating only (systems

1-12), space heating only, or both (MMBtu/year or GJ/year) (CR). Do not

adjust for furnace efficiency.

(*E) ANNUAL SOLAR FRACTION?

Enter your precalculated annual solar heating fraction (as percent) (CR).

This is the annual percentage value (obtained from another analysis) of

the total annual energy load which is to be supplied by the solar energy

system.

(*E) COLLECTOR AREA?

Specify the area of the solar collector (in square feet or square meters)

(CR) which corresponds to the solar fraction value specified above.

SOLAR ENERGY INVESTMENT - FIXED COST?

Enter the cost (in dollars) (CR) of the portion of the total system cost

which tends to be independent of system size within the size range considered. This may be difficult to determine, but the accuracy of the optimization analysis depends on this breakdown of costs. See section 3.2.1 for

further discussion.

SOLAR ENERGY INVESTMENT - VARIABLE COST?

Enter the size dependent cost of the system (dollars per square foot or square meter of collector area) (CR). See section 3.2.1 for a further

discussion.

TYPE OF FUEL USED IN AUXILIARY SYSTEM?

Enter a number from 1 to 6 (CR) where

l=electric

2=distillate oil

3=residual oil

4=natural gas

5=coal

6=liquid propane gas

TYPE OF FUEL USED IN REFERENCE SYSTEM?

Enter a number from 1 to 6 (CR) as above.

2.3.2 Changing Default Values

Once the above information has been entered, FEDSOL supplements it with default

values for the remaining data elements. You may see these values along with

11
the values you supplied for the required data by listing your file at this

point with the L (List) command. FEDSOL will assume these values unless you

specify other values using the C (Change) command. You may change the value of

any data element by specifying the number of that data item and the new numeric

value in response to the LINE NUMBER? and NEW VALUE? queries.

The entire set of data inputs for the FEDSOL program and the default values are reprinted below. These data elements provide for a life-cycle cost comparison

of a combined solar and auxiliary back-up system with a reference non-solar

system. Items under "Data for Performance Analysis (SLR Method)" will print

only if you requested a performance analysis; items under "Data for Economic

Analysis Only" will print only if you requested an economic analysis alone.

For a further discussion of the individual data elements, see sections 3.1 and

3.2. The range of acceptable values for each data element is shown in

Appendix G.

ENERGY ANALYSIS DATA

DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)

1. Type of Solar Energy System (from coded list)

See table 2.1.

2. Collector Tilt Angle

Number of degrees (from horizontal) that the collector is tilted. To change

the tilt angle, enter the total number of degrees (from horizontal).

DEFAULT = LAT. +10°

3. Optimization Analysis

If you wish an optimization analysis, enter 1. If you do not wish an optimization analysis, enter 2 and specify the collector area being considered

(in data element #4). See section 3.4.5 for a more complete description of the

optimization analysis provided by FEDSOL.

DEFAULT = 1

4. Collector Area

FEDSOL will ignore this value if you have requested an optimization analysis.

DEFAULT = 0 ft 2 (m2

)

5. Minimum Acceptable Solar Fraction

In an optimization analysis, the program will consider only system sizes that

generate a minimum of this annual solar fraction.

DEFAULT = 30 percent

12
6. Operating Efficiency of Auxiliary System

The annual average percentage efficiency of the auxiliary system in meeting the

load specified (space heating, water heating, or both).

DEFAULT = 60 percent

7. Operating Efficiency of Reference Non-Solar System

The annual average percentage efficiency of the reference non-solar system in

meeting the load specified (space heating, water heating, or both).

DEFAULT = 60 percent

8. Electric Energy as Percent of Useful Solar Energy

Nearly all active solar thermal energy systems require electric energy for pumps

and controls. Because electricity consumption is dependent on system size and

operating time, it is expressed as a percentage of useful solar energy provided

by the system.

DEFAULT = 6 percent

9. Domestic Hot Water Usage

This value will default to zero if you specified 2 (SPACE HTG) in response to

the LOAD TYPE? query.

10. Building Use Schedule

This value is only used in calculating hot water loads. It refers to the

number of days per week the building is in normal (or near-normal) use.

11. Monthly Space Heating Loads

This value will default to zero if you specified 1 (WATER HTG) in response to

the LOAD TYPE? query.

12. Average Daily Horizontal Radiation

These values are supplied by the program. When you select a city in the

geographical data bank and create a new file, the program reads its stored

environmental and weather data for that location. You may change these data by

using the C (Change) command.

13.

Average Ground Water Temperatures

Data are supplied by the program, from the geographical data bank. Values

are entered as quarterly averages for DEC-FEB, MAR-MAY, JUN-AUG, SEP- NOV.

13
The default values for your location should be examined and changed as necessary to adjust for the position and type of water supply facility of the

building under study.

DATA FOR ECONOMIC ANALYSIS ONLY

20. Annual Energy Load

21. Annual Solar Fraction

22. Collector Area

23. Operating Efficiency of Auxiliary System

DEFAULT = 60 percent

24. Operating Efficiency of Reference System

DEFAULT = 60 percent

25. Electrical Energy as Percent of Useful Solar Energy

DEFAULT = 6 percent

LIFE-CYCLE COST DATA

See section 3.2 for a further discussion of these data elements.

BASE YEAR INVESTMENT COSTS

30. Solar Energy Investment - Fixed Cost

31. Solar Energy Investment - Variable Cost

32. Investment Credit (Externality Adjustment)

DEFAULT = 10 percent

33. Investment Cost for Auxiliary System

DEFAULT = $0

34. Investment Cost for Reference Non-Solar System

DEFAULT = $0

FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40. Annually Recurring O&M Cost (percent of investment cost)

14
Do not include electrical energy operating costs.

DEFAULT = 1 percent

41. Replacement Cost and Year

Include repair and replacement costs which are expected to occur on an irregular

basis. Do not include costs covered under item #40. Six values must be entered

when responding to this item. Each replacement cost is to be followed by the

year of its occurrence (number of years after system purchase). Three different

occurrences are allowed for. If there are fewer than three occurrences, enter

zero's for the remaining positions. For example, if replacements of $5000 occur

at 5 years and $7500 at 10 years, then the entry should appear as

5000,5,7500,10,0,0

ALL DEFAULTS = 0

42. Salvage Value at End of Study Period (precent of investment cost)

DEFAULT = 0 percent

AUXILIARY SYSTEM

44. Annually Recurring 0&M Cost (dollars per year)

DEFAULT - $0

45. Replacement Cost and Year

Same format as item #41

ALL DEFAULTS = 0

46. Salvage Value at End of Study Period (dollars)

DEFAULT = $0

REFERENCE NON-SOLAR SYSTEM

47. Annually Recurring 0&M Cost (dollars per year)

DEFAULT = $0

48. Replacement Cost and Year

Same format as item #41.

ALL DEFAULTS = 0

15
49.

Salvage Value at End of Study Period (dollars)

DEFAULT = $0

FUEL COSTS

The base-year energy prices and projected rates of energy price escalation

published by the DoE are contained in the program as default values (see sec- tion 3.2.4). FEDSOL automatically calls the data for the type of building and

location under study. Use the actual price (per MMBtu or GJ) to the agency

undertaking the project, if available.

50. Electricity Price in Base Year

51. Distillate Oil Price in Base Year

52. Residual Oil Price in Base Year

53. Natural Gas Price in Base Year

54. Coal Price in Base Year

55. Liquid Propane Gas Price in Base Year

56. Type of Fuel Used in Auxiliary System

Enter a number from 1 to 6 (CR) where

l=electric

2=distillate oil

3=residual oil

4=natural gas

5=coal

6=liquid propane gas

57. Type of Fuel Used in Reference system

Enter a number from 1 to 6 (CR) as above.

58. Energy Price Escalation (percent per year, excluding inflation)

DISCOUNT RATE AND STUDY PERIOD

60. Real Discount Rate (excludes inflation)

The Federal Rules require a value of 7 percent.

DEFAULT = 7 percent

51. Study Period

16
The value entered will be the period of the life-cycle cost analysis. The

maximum value allowed under the Federal Rules is 25 years.

DEFAULT = 20 years

ANALYSIS OUTPUT

70. 1=STANDARD; 2=EXTENDED; 3=SUMMARY

This item controls the length and content of the analysis report generated by

FEDSOL. The potential output created by FEDSOL consists of the following

sections

1. Table of solar fractions and net savings for a range of system sizes

2. Monthly thermal performance table

3. Life-cycle cost summary table showing breakdown of life-cycle costs

4. Measures of economic performance

5. Simple cash flow analysis: not discounted and not escalated

6. Discounted cash flow analysis: discounted and escalated

7. Breakeven analysis (generated only when net savings are negative) for

investment costs, base-year energy prices, and rates of energy price

escalation.

The standard analysis consists of sections 1 through 4; the extended analysis,

sections 1 through 7. The summary analysis is a one line output showing only

the optimized or prespecified collector area, annual solar fraction, and net

savings

2.4 RUNNING THE ANALYSIS

Once you have called up an old file (0 command) or created a new file (N

command) and made any necessary changes (C command), you may run the analyses

by simply selecting R (CR) from the command selection. The output selections

are described above.

NOTE: If you previously answered Y to the prompt: PERFORMANCE ANALYSIS USING

SLR METHOD (Y OR N)? you will receive both thermal and economic analyses.

If you answered N, you will receive an economic analysis only.

2.5 SAVING A FILE

If you have changed an old file or created a new file without SAVING the

current file, you will lose the data in the current file. Whenever you are satisfied with the data contained in your file, or think you might want to

refer to it later, select the S option from the command selection to SAVE the

file in permanent storage.

17
When you enter the S command (CR), you will be prompted with: STORE DATA UNDER

WHAT NAME? Your response should be a filename of your choosing of up to 7 characters in length (CR). The filename must begin with a letter and contain

alpha-numeric characters only. Certain filenames are forbidden. The user will

be notified if a forbidden filename has been entered. Selecting a name related

to the actual data, such as the name of the city or building in which your

system is located, is helpful for later retrieval. If you have more than one

file for a system, you might want to code it by number, date, or code letter as well as a name, e.g., BDWYP01, BDWYP02 (Broadway Post Office 1st run, 2nd run,

etc.). If an existing file already has that name, the terminal will respond

with: "FILENAME" ALREADY EXISTS. DO YOU WISH TO USE THIS NAME (Y/N)? If a Y

is entered, the current Input data will be entered under this filename and

will REPLACE the file previously stored under that name. If an N is entered,

the current input data will not be saved under this filename, and the command

prompt will appear again. If desired, this data file may be saved under some other valid filename by repeating the SAVE procedure.

NOTE: When you retrieve an existing file from storage, it is called into the

computer's memory, but still remains in the long-term disk storage. You

cannot lose a file that has been permanently saved unless you actually

PURGE it. (This is done after exiting FEDSOL and is a system command.)

If you forget the name of the file you want to use, exit FEDSOL with a Q (CR)

and then type CATLIST (CR). All files saved under your ID number will be

displayed

If you forget these procedures or instructions or need a brief refresher course

on the operation of FEDSOL, type H (CR) to obtain the help instructions. It's

a good idea to use the H command in your first session with FEDSOL and to keep

a copy of the instructions near the terminal.

2.6 TERMINATING EXECUTION OF FEDSOL

Use the Q (Quit) command (CR) to end execution of FEDSOL. The terminal will

respond with

READY

*

Type: BYE (CR) to terminate the session.

Now the timeshare system will log off, telling you the connection time and

the system response units used in this session.

2.7 LEARNING FEDSOL

The following approach is recommended for learning to use FEDSOL:

1. Call upon the program;

2. Select 0 (CR) from the command selection menu;

3. Retrieve the file SAMPLE;

18
4. Run through SAMPLE, listing, making changes, running the analyses, and

saving it under your ID with another name until you are comfortable with

operating the program;

5. Gather the data you need to evaluate your particular solar heating system

and to create your own files. (Keep a copy of the SAMPLE listing to remind

you what data you need to prepare); and

6. When your data are prepared, return to the system, call up the program, and

begin new FEDSOL analyses.

19
3. THE LIFE-CYCLE COST METHOD FOR SELECTING SOLAR ENERGY SYSTEMS FOR FEDERAL

BUILDINGS 1

Life-cycle costing (LCC) is a method of economic evaluation by which all

relevant costs over the life of a project are accounted for when determining

the economic feasibility of projects. It is particularly suited for the evaluation of projects such as energy conservation and solar energy that realize

their benefits primarily through long-run fuel cost avoidance.

Applied to solar energy projects, the Federal life-cycle cost method and

procedures can be summarized in the following five steps:

1) Compare energy use in the building with and without the proposed solar

project

2) Identify the relevant costs, constraints, and assumptions associated

with the project, including the special requirements under the Federal

LCC Rules.

3) Calculate total life-cycle costs of the building with and without use

of solar energy.

4) Using the Federal life-cycle cost procedures, determine the optimal

solar energy system size and design with the lowest life-cycle cost.

5) Calculate other measures of economic performance for this system as needed to determine project priorities and to meet Federal LCC

requirements

An economic model for determining the optimal solar design/size for a Federal

building project is developed graphically and algebraically in this section

within the framework of these steps. This is the model implemented by the

FEDSOL computer program described in section 2. In addition, this section

reviews the options and capabilities in FEDSOL for performing each step of the

analysis.

3.1 COMPARING ENERGY USE WITH AND WITHOUT SOLAR

An essential first step in the life-cycle cost evaluation of a solar energy

project is to determine the end-use energy requirements of the process to which

solar energy is to be applied and the potential contribution of the proposed

solar energy system in meeting these energy requirements. The application

might be space heating, domestic hot water, process water, space cooling, or some combination thereof.

1 Much of parts 3.1, 3.3, and 3.4 extending to 3.4.4 is taken from "Life-Cycle

Cost Evaluation of Solar Energy Investments," Chapter 11 of the Solar Design

Workbook, prepared by Rosalie T. Ruegg , G. Thomas Sav, and Jeanne W. Powell [2].

20
3.1.1 Estimating Building Energy Requirements

Energy requirements for hot water are generally determined by a static heat

balance equation, whereby the energy requirement for water heating in a given

period (Ew) is directly proportional to the hot water demand (D) and to the

difference between the desired water temperature (T<j) and the temperature of

water supplied to the building from the local sanitation system or other water

source (Tj_n ):

Ew = w • c

p

• 0 • (Td - T ln ). (3.1)

The proportionality factors w and c p represent the density of water (8.33 lb/

gal) and specific heat of water (1 Btu/lb/°F), respectively.

The method used to calculate energy requirements for space conditioning should

be tailored to the type of buildings and systems evaluated . ^ In analyzing a small envelope-dominated structure for residential or light commercial use, a steady-state method based on the heat loss coefficient (UA) and degree days is

generally sufficient.^ Larger buildings with complex HVAC systems require more sophisticated transient analysis models which account for hourly differences in

the building thermal capacity, heat generated by solar loading on the building

envelope, and loads generated by mechanical systems, occupants, lights, and

equipment. Examples of energy analysis computer programs with these capabilities are BLAST [15] and DOE-2 [16].

Energy loads for heating or cooling are usually calculated for each month and

then summed to an annual value. ^ Once the annual energy requirement for heating or cooling is known, the annual quantity of non-solar energy required to

meet the load can be calculated based on the energy content of conventional

fuel and the conventional energy equipment efficiency. Algebraically, the

annual quantity of conventional energy required (E) is calculated as follows:

E = _L_ , (3.2)

e

where L represents the annual load for heating or cooling, and e, the annual

efficiency of conventional energy equipment.

For example, assume that the space heating load of a building is 800 MMBtu per

annum, the conventional fuel is oil, and the average annual efficiency of the

furnace is 0.6. Then,

1 For a more extensive overview of methods of evaluating building energy

requirements, see reference [17].

A variable base degree day method is preferred. A simplified method suitable

for a hand calculator is described in reference [18].

O Provided that the same energy source is used, water and space heating loads

each month are summed to determine the total monthly energy requirements for

heating.

21
E = 800 = i 333.

0.6

Thus, it is estimated that 1,333 MMBtu of oil per annum are required for space

heating purposes.

3.1.2 Estimating Energy Savings

The contribution of the solar energy system towards meeting the monthly energy

requirement is a key measure of performance of the solar energy system. It

generally is the major source of savings from undertaking the investment in

solar energy.^

Solar performance is incorporated into the economic analysis by expressing the

useful monthly output of the solar energy system as a fraction of the monthly

energy requirement and then determining the annual solar fraction corresponding

to the total monthly solar contribution. ^ Thus, if the solar energy system is

estimated to deliver a total quantity of useful Btu's per month (Sm), then the

monthly fraction (Fm) of monthly load (Lm) met by solar is

Fm - (3.3)

and the annual fraction is

12

F = ( 2 Lm* Fm)/L. (3.4)

m=l

for m=l, January, m=2, February, etc.

Continuing with our previous example (L = 800 MMBtu), suppose a solar energy

system of a particular design and size is expected to deliver 62.5 percent of

the load for space heating during a year. Then it is expected to deliver

.625 • 800 MMBtu.

If the auxiliary heating system is assumed to be the same type and to have the same operating efficiency as the reference non-solar energy system used alone,

the annual quantity of non-solar (fuel oil, in this example) energy required

would be reduced from 1,333 MMBtu to 500 MMBtu using this solar energy system.

That is, the annual quantity of non-solar energy (fuel oil) required by this

solar auxiliary system (E^) is

E = L(1 - F) = 800 » (1 ~ 0.625) = 500 (3.5) A e (0.6)

! Methods of evaluating non-energy benefits of investments in passive solar

energy are treated in reference [10].

2 In analyzing systems for service hot water only, annual calculations may

often be used.

22
for savings of 833 MMBtu of oil per annum, assuming a constant system efficiency

and a constant building energy load over the study period.

Energy required to operate the solar energy system components, such as electrical energy required to operate the pumps or fans and the control system,

may also be significant to the analysis. Energy costs to operate the solar

energy system reduce the overall savings in fuel from the solar energy system.

In the above example, the solar auxiliary system and the reference non-solar

energy system are, for simplicity, assumed to be identical. This, of course,

need not be the case. If the energy system used as an auxiliary to solar is

different from the reference non-solar energy system, it may use a different

type of fuel and have a different operational efficiency, as well as different

investment and non-fuel operation and maintenance costs.

Furthermore, even if the two systems are identical, the part-load contribution

of the auxiliary solar energy system may cause it to have a lower efficiency

than the reference system. For example, if, in the above example, the system

efficiency dropped from e N

= .6 for the reference non-solar energy system to

e^ = .5 for that same system used as the solar auxiliary, the annual oil

savings, S, would decrease from 833 MMBtu to 733 MMBtu; i.e.,

S = L • (!_“ 11 ~ F >

) = 800 • ( I

" ~ -625)

) = 733 . ( 3 . 6 ) e N

eA

* 6 * 5

3.1.3 Estimating Energy Savings with FEDSOL: The SLR Method

Brief Description . The solar load ratio (SLR) method for active systems is a simplified design method for analyzing solar energy systems in commercial and

residential buildings employing flat plate collectors for space and/or water

heating.^ was developed at Los Alamos National Laboratory by applying correlation analysis to numerous hour-by-hour computer simulations of a reference

system in a large variety of locations performed with the DOE-2 building energy

analysis computer program. The results of the simulation and correlation analyses are a set of "universal" design and sizing curves describing the solar

heating fraction vs. the solar load ratio (SLR), as illustrated in figure 3.1.

The solar load ratio method for active systems in commercial buildings has

recently been revised and extended by Schnurr, Hunn, and Williamson [3] to take

account of advances in energy analysis techniques since the time of the original work reported in the DoE Facilities Solar Design Handbook [19]. The FEDSOL

program incorporates the new set of design curves published in this recent

study. The mathematical equations specifying the curves for 18 system types

(six systems for space heating or combined space and water heating and

! The solar load ratio method is documented in references [3, 19, 20, 21]. For

further information about the general applicability of this method and the

validation tests conducted by Los Alamos National Laboratory, see these

publications

23
Figure 3.1 The Solar Load Ratio Method: A Generalized Design Curve

where SLR = A*l/L and

A = gross collector area;

I = insolation on tilted collector surface, monthly for

space heating or combined space heating and hot water

systems; annually for service hot water only systems;

and

L = energy load to which solar energy is applied, monthly

for space heating or combined space heating and hot

water systems; annually for service hot water only

systems

twelve systems for water heating only) are included within FEDSOL. The complete

set of curves is shown in Appendix D.^

1 The recent Los Alamos study included evacuated tube collectors, as well as flat plate collectors, in its analyses of service hot water systems. Reference [3] includes design curves for service hot water systems with evacuated

tube collectors. However, FEDSOL is limited to systems with flat plate

collectors.

24
Unlike with the original SLR method for commercial buildings, the analysis of

systems for service hot water only is performed on an annual instead of a monthly basis and different performance curves corresponding to the annual

heating degree days are derived for different locations. These changes are due

to research findings showing that 1) a better correlation of solar hot water

system performance to the SLR is obtained on an annual than on a monthly basis

because of the relative uniformity of water heating loads and 2) the performance

of service hot water systems is highly correlated with ambient temperature.

For a given value of the SLR, system performance is better in warmer climates

than in colder climates because of smaller heat losses from the collector and

higher collector efficiencies. The recent Los Alamos study suggests that the

original design curves tend to overstate the performance of systems for hot

water only in locations with substantial heating degree days.

In the recent study, the effect of location on the performance of systems for

space heating was found to be sufficiently small that separate design curves corresponding to different degree day ranges were not required [3]. The major

differences between the original and revised SLR methods as applied to systems

for space heating reflect the lower collector efficiencies assumed in the

recent study. Accordingly, the revised design curves can be expected to yield

somewhat lower solar heating fractions than the original curves.

For the analysis of active systems in residential buildings, the curve-fit

equation developed by Balcomb and Hedstrom for the design and sizing of a standard, residential system for space heating has been included in the FEDSOL

program [21].

The FEDSOL data files contain values for monthly average daily solar radiation,

latitude, the heating degree day range, and average earth temperatures (for

estimating hot water loads) for the 243 cities shown on the map and coded list

printed in Appendix B.l Using the data for the city, collector tilt, and water

usage schedule specified by the user, the program calculates monthly solar

radiation on a tilted surface, estimates the monthly energy requirement for hot

water, combines the monthly energy requirement for hot water with the user

specified monthly energy requirement for space heating, and calculates the SLR

and solar heating fraction for each month. If the system being analyzed is for

service hot water only, the program selects the curve corresponding to the

ambient temperature (degree days) of the location being analyzed and uses annual

calculations for the SLR and solar heating fraction. The program then adjusts

for differences in predicted annual solar fraction provided by the ambient

temperature curve, based on a single-glazed selective collector and design

water temperature of 130°F, and predictions of annual solar fraction for the

type of collector and for the design water temperature specified for study.

1 The solar radiation data contained in the program files are taken directly

from Input Data for Solar Systems , by V. Cinquemani , a report prepared by the

U.S. Dept, of Commerce, National Oceanographic and Atmospheric Administration

for use in energy analysis programs requiring monthly data [22]. These data

are derived from SOLMET weather tapes. Earth temperature data are obtained

from tables of average earth temperatures 1-10 feet below the surface

published by Kusuda and Saitoh [18].

This adjustment procedure is described in detail in reference [3].

25
The user must specify: a) the energy requirements for space heating (by month,

in the case of the SLR analysis; by year, in the case of the economics only

analysis), b) the type of fuel used in the non-solar reference system and aux- iliary system, c) the operating efficiencies of the reference non-solar and

auxiliary heating plants,^- and d) the electricity required to operate the solar

energy system as energy data inputs to the program. Different fuel types and

operating efficiencies are allowed for the reference non-solar system and the

auxiliary system. (The default values for operating efficiencies of both the

reference and the auxiliary systems are 60 percent. Electricity to operate the

solar energy system is expressed as a percent of useful solar energy collected.

The default value is 6 percent.)

The thermal analysis performed by FEDSOL for a sample office building system

for space and water heating in Washington, D.C. is reprinted in table 3.1.^

Table 3.1 Thermal Performance for SAMPLE Case

THERMAL PERFORMANCE

COLLECTOR AREA = 1659.00 SQFT TILT ANGLE = 48.57 DEGREES

SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL

FRACTION H0RZ RAD. COLLECTOR LOAD LOAD SOLAR

(1) (1) (2) (2)

JAN .190 572.00 882.01 71.20 4.58 14.38

FEB .347 815.00 1094.16 42.30 4.13 16.11

MAR .491 1125.00 1272.36 37.90 4.36 20.77

APR .744 1458.00 1384.72 21.60 4.22 19.21

MAY .734 1718.00 1437.81 24.00 4.36 20.82

JUN .690 1900.00 1496.00 28.20 3.41 21.81

JUL .619 1817.00 1470.40 33.90 3.53 23.18

AUG .756 1617.00 1455.68 23.70 3.53 20.60

SEP .791 1340.00 1430.91 20.20 3.57 18.79

OCT .755 1003.00 1316.55 21.00 3.69 18.65

NOV .480 650.00 980.75 28.70 3.57 15.49

DEC .211 481.00 753.07 53.60 4.58 12.28

YEAR .489 406.30 47.53 222.09

(1) = BTU/SQFT-DAY

(2) = MMBtu/MONTH

1 The operating efficiencies of the auxiliary and reference non-solar heating

plants have a large impact on the outcome of the investment in solar energy

because the value of a unit of solar energy delivered increases directly as the operating efficiency of the auxiliary heating system declines. In determining the appropriate auxiliary and reference system operating efficiencies

to use in the life-cycle cost analysis of a solar energy system, care should

be taken to include only those inefficiencies in the auxiliary and reference

systems that are relatively independent of those in the solar energy system.

Do not include, for example, inefficiencies in the heat distribution system of

the building that are common to the solar and auxiliary systems as well as to

the reference system. Differences in efficiencies assumed for the reference

and auxiliary systems should reflect any anticipated part-loading effects

induced by the combined use of solar and auxiliary energy.

2 The input data for this sample project are shown in section 4, case 1.

26
Limitations of the SLR Method * The SLR universal design and sizing curves are

based on standard reference liquid and air systems. The design parameters for

the standard systems simulated in the Los Alamos study were derived from a large number of parameteric optimization studies conducted at Los Alamos

National Laboratory. The collector efficiencies assumed correspond to those

considered typical of collectors of four generic types. Tables 3.2 and 3.3

show the collector performance coefficients and design values for these reference systems. 1 Schematic diagrams are shown in Appendices D.7-D.9.

Use of different design parameters from those used in the Los Alamos simulations

will affect system performance, life-cycle costs for combined solar/auxiliary

heating, and optimal system size. Thus, caution should be taken in using FEDSOL

to predict the solar heating performance of systems with design parameters

significantly different from those assumed in the Los Alamos study.

For evaluating passive systems, systems with combined solar/heat pump, systems

for space cooling, or other systems whose design parameters differ significantly

from those in tables 3.2, and 3.3, it is important that a method suited to

that type of system be used to predict solar performance.^ One can then use FEDSOL to perform an economic analysis by selecting the "economic analysis

only" option and supplying as input data the solar heating fraction derived

apart from FEDSOL by another method and the annual thermal energy load.

Comparison of the SLR Method With Other Methods . When applied to standard

residential systems for space and water heating, the SLR method can be expected

to give similar predictions of solar performance on an annual basis to those

obtained from F-CHART, the design method most widely used, and from SOLCOST [9,

20, 23]. Unlike SOLCOST and F-CHART, the SLR method is designed specifically

for office (or commercial) building systems. It should simulate the size and

demand patterns of these buildings more accurately than these other programs

[20]. Note, however, these studies by Los Alamos National Laboratory have

shown that the SLR sizing curves are not highly sensitive to substantial

differencces in load and use patterns.

3.2 IDENTIFYING RELEVANT COSTS, ASSUMPTIONS, AND CONSTRAINTS3

The life-cycle cost evaluation of an investment in solar energy for a Federal

building requires and assessment of the following kinds of solar-related costs

over the time horizon of the investment: 1) investment costs (capital costs),

1 Considerable sensitivity analyses have been conducted at Los Alamos to

determine the effect of changing these design parameters; however, most of

the resulting data reflect changes occurring when only one parameter is

varied at a time [19]. For further documentation of results of studies

performed at Los Alamos, see references [19, 21].

^ For a discussion of the different types of methods available for predicting

solar heating performance and of recommended applications, see reference [20].

3 These guidelines for identifying costs, assumptions, and constraints are consistent with the Federal LCC Rule [4, 5, 6].

27
Table 3.2 Efficiency Curve Coefficients Used to Characterize

the Generic Types of Flat Plate Collectors3

Type

Transfer

Medium A B

(W/m2 *K) (Btu/h«ft2 *°F)

Single-glazed

,

selective

LIQ 0.705 -5.04 -0.887

Single-glazed

,

nonselective

LIQ 0.780 -7.50 -1.320

Double-glazed

,

nonselective

LIQ 0.643 -5.00 -0.880

Single-glazed

,

selective

AIR 0.550 -4.89 -0.860

Single-glazed

,

nonselective

AIR 0.590 -6.25 -1.100

Double-glazed

,

nonselective

AIR 0.475 -4.15 -0.730

a Collector type is designated by the collector efficiency curve, as specified

by

E = A + Bx,

where

x = (Tf - Ta )/(I)

for

Tf = inlet fluid temperature;

Ta = ambient temperature; and

I = total solar radiation.

The collector efficiency coefficients in this table are intended to correspond

to typical flat plate collectors of each type (single- or double-glazed with

selective or nonselective absorber coatings).

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

Solar System Sizing" [3].

28
Table 3.3 The Standard Active System

Parameter Nominal Value

SOLAR COLLECTOR

Orientation

Tilt (from horizontal)

Coolant flow rate

HEAT EXCHANGER

Effectiveness

Cold site flow rate

STORAGE TANKS

Capacity

Due south

Latitude + 10° a Liquid*5 112.6 kg/h per m2 of collector area

(0.046 gpm per ft2 of collector area)

Air

2 scfm per ft 2 of collection area

(0.0006 L/S per m2 of collector area)

0.70

112.6 kg/h per m2 of collector area (0.046 gpm per ft^ of collector area)

Liquid (storage tank)

73.4 kg of water per m

2 of collector area

(15 lb. of water per ft 2 of collector area)

Air (Rock bed)

0.22 m^ per m2 of collector

(0.72 ft^ per ft2 of collector)

Air (Hot Water Storage Mass)

3.67 kg of water per m2 ft collector

(0.75 lb of water per ft 2 of collector)

Height to diameter ratio 3.0

(Liquid System)

Loss Coefficient 0.28 W/m2 »K

(0.05 Btu/h»ft2 «°F)

Environment temperature 21.1°C (70°F) C

Cold water supply temperature 15.6°C (60°F)

(to BSHW system)

a Parametric studies conducted at Los Alamos showed that for commercial

building systems such as those described in reference [3], latitude + 10° was

the optimal tilt angle for collectors in systems for space heating only or in

combined service hot water and space heating systems; for service hot water

only systems, a tilt angle of latitude + 5° was optimal. These studies also

showed that system performance was relatively insensitive to variations in

collector tilt angle within + 10° of the optimum.

k Water, water /glycol , or nonaqueous collector heat transfer fluid could be

used in liquid system.

c Assumes storage losses do not contribute to meeting the heating load.

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

Solar System Sizing” [3].

29
2) non-fuel operation and maintenance costs, 3) replacement costs, 4) energy

costs, and 5) salvage or resale value net of removal and disposal costs. Since

solar energy systems will generally be used in conjunction with an auxiliary

energy system (e.g., electricity, natural gas, or oil), rather than alone, it

is necessary to consider the costs of both the solar energy system and the

auxiliary energy system to the extent that they differ from the reference nonsolar energy system. The special requirements for Federal building projects

are highlighted with outline boxes in the sections to follow.

To establish a basis for comparison, these same elements of costs must be

assessed for the reference non-solar energy system. As indicated above, costs

which are expected to be approximately the same for the reference system as for

the auxiliary system need not be included because they will be the same regardless of the solar investment decision. Additional costs which need not be con- sidered are "sunk costs.” These are costs incurred prior to the life-cycle cost

analysis, for example, for planning, and preparation of preliminary designs.

3.2.1 Investment Costs

Solar energy investment costs include the costs of design, engineering, purchase,

and installation (exclusive of sunk costs) of the proposed system. Consider

all components necessary for the solar energy system’s operation: 1) solar

collectors, 2) thermal storage, 3) distribution systems (for transporting solar

energy alone), 4) controls, motors, pumps, fans, and other ancillary equipment,

and 5) special building features such as roof and wall modifications. In

evaluating a system for retrofit to an existing building, the costs of building

modifications required to install the solar energy system should be included

among solar energy investment costs.

In evaluating passive systems, the cost of additional thermal mass for exterior

walls or interior spaces in excess of conventional building costs, plus the

cost of movable insulation and sensor controls, should be included among solar

energy investment costs. Capital costs of the auxiliary heating plant and

non-solar reference heating plant and mechanical systems should also be included

in the life-cycle cost evaluation if these costs are different for the solar

and reference buildings.

Federal LCC Rule : 1) Assume the investment costs occur in a lump sum at the

beginning of the base year.-*- 2) Adjust investment costs to 90 percent of their

actual value.

1 The base year is the year in which the life-cycle cost analysis is conducted.

2 The 10 percent investment credit is intended to serve as an interim

adjustment for externality costs, such as the effect of imported oil use on strategic vulnerability, until improved measures are developed.

30
Since the economically optimal solar energy system size depends on the

incremental costs of solar energy and non-solar energy, it is important to make

as accurate a distinction as possible between fixed and variable (size dependent) components of solar energy costs. ^ Fixed costs are costs that are relatively independent of the size of the solar energy system. For example, the

costs of system controls and some minimum set of pumps, heat exchangers, valves,

piping and fittings may remain relatively constant over a substantial initial

range of collector and storage sizes, and hence, be considered fixed costs.

The variable cost is the cost associated directly with each unit of collector

area, plus the corresponding incremental costs of storage and piping.

It is important to note that for solar energy systems with significant fixed

costs, using the average cost per square foot as the measure of investment cost

will significantly underestimate the optimal system size. 3 To simplify the

calculation of the two types of costs, and at the same time to avoid the common

tendency of underestimating the variable unit cost, the fixed cost may be

defined as the cost for the smallest system that is realistic for a particular

application of solar energy, including materials, labor, and design and engineering services; and the variable cost as the corresponding cost for each

additional unit of system size.

FEDSOL contains separate parameters for investment costs for the solar, the

reference non-solar, and the auxiliary energy systems. (The default values for

investment costs for each of these systems are zero. The user must supply

values for solar energy investment costs in order for the program to conduct a life-cycle cost analysis. Values for the reference and the auxiliary systems

need be supplied only if they differ from one another.)

3.2.2 Recurring Non-Fuel Operation and Maintenance Costs

Recurring non-fuel operation and maintenance (O&M) costs are costs other than

for fuel that are expected to recur uniformly in constant dollars every year

over the life cycle of the solar investment.

The trade-offs between solar energy costs and non-solar energy costs are illustrated graphically in section 3.4.1.

Design and engineering typically are placed in this category. However,

design and engineering costs may have both fixed and variable components. A

survey of fee schedules for architectural and engineering services conducted

by the State of Florida in 1977 showed that the basic rate for these services

was dependent upon total construction costs; however, the basic percentage

rate dropped substantially as construction costs increased. The cost of

engineering services, for example, ranged from 15 percent of construction

costs for small projects to 6 percent for multi-million dollar projects [24].

O In a recent study, Los Alamos National Laboratory reports that significant

fixed costs could not be identified for passive systems in residential

buildings, but are expected to be significant for active systems [25]. Cost

estimating equations developed by Honeywell, Inc. for NBS suggest high fixed

costs for large active systems for commercial buildings [11].

31
Federal LCC Rule : Assume that annually recurring non-fuel operation and

maintenance costs begin to accrue at the beginning of the base year and are evaluated as a lump-sum payment at the end of each year of the study period,

starting at the end of base year.

The annual non-fuel operation and maintenance costs for the solar energy system,

auxiliary system, and reference non-solar system are separate data inputs to

the FEDSOL program. Non-fuel O&M costs for the solar energy system are expressed as a percentage of unadjusted solar energy investment costs, i.e.,

of the total investment costs before applying the externality adjustment. For

non-fuel O&M costs of the auxiliary and reference systems, the user must specify

the actual estimated annual cost, in constant dollar prices of the base year.

(The default value for the solar energy system is 1 percent; for the auxiliary

and reference systems, 0 percent.

3.2.3 Replacement Costs and Salvage Value

Replacement solar energy costs are costs that occur on an irregular basis for

major repair or replacement of damaged or worn out components of the solar

energy system. The estimated repair or replacement cost(s), net of salvage

value of the component(s) replaced, the year(s) of occurrence of repair or replacement ( s) , and the salvage value of the system at the end of the study

period are separate inputs to the FEDSOL program. Solar energy replacement

costs in up to three different years are allowed.

Replacement costs may, of course, arise for components of the reference or auxiliary systems as well as the solar energy system. If major repair or replacement costs (net of salvage value of the components replaced) are expected to be significantly different (in size or timing) for the reference

and auxiliary systems, these costs should be included in the life-cycle cost

evaluation of the solar energy system. FEDSOL contains separate variables for

the costs of replacement parts for the reference and auxiliary systems and

allows for three occurrences of replacement costs for each system. In addition, the program allows the user to specify separate values for the salvage

or resale value of the auxiliary system and the reference non-solar system at

the end of the study period.

Federal LCC Rule : Assume that replacement costs and salvage values are evaluated as lump-sum payments at the end of the year in which they are expected to occur.

(FEDSOL assumes zero values for all replacement costs and salvage values unless

the user specifies otherwise.)

1 The default values of 0 percent for non-fuel O&M costs for the auxiliary and

reference systems should be maintained if non-fuel O&M costs are expected to

be approximately the same for these systems.

32
3.2.4 Energy Costs

Federal LCC Rule : 1) Estimate the quantity of energy delivered annually to the

building boundary with and without use of solar energy. ^ 2) Use actual prices

to the agency undertaking the solar project, or use energy prices published by

the Department of Energy in the LCC Program Rule (and revised periodically) .

3) Use projected annual real rates of fuel price escalation (rates excluding

inflation) published by the Department of Energy in the LCC Program Rule (and

revised periodically) If electricity component prices are used and forecasts

of component price escalations are available from the local utility, they may

be used in pricing electricity. 4) Assume fuel costs are paid annually in

lump-sum payments at the end of each year, starting at the end of the base year.

The energy price data contained in the LCC Program Rule, as revised in the

Federal Register , September 1981, are included in the FEDSOL Program as default

values for the base year fuel prices and rates of energy price escalation for

locations in each of the 10 DoE regions.

3.2.5 Inflation and the Discount Rate

In accounting for project costs, life-cycle costing requires that dollar costs

occurring at different calendar times be adjusted to a common time basis, taking

into account the cost of money over time. This technique is referred to as discounting. Discounting is necessary for a valid economic comparison because

money in hand can be invested to yield a return over time, causing an expenditure or receipt that occurs at some future date not to have the same value as if

it occurred today. This is true whether or not there is price inflation that

changes the value of money over time.

Discounting is accomplished by applying discount formulas—or multiplicative

factors pre-calculated from the formulas—to each item of cost. There are

1 Energy analysis procedures have been discussed in section 3.1.

^ Average prices are now provided for each of 10 DoE regions, by sector —

residential, commercial, and industrial, — and by fuel type — electricity,

distillate, natural gas, residual, and coal [6]. The Department of Energy

(DoE) is developing marginal energy prices adjusted to reflect special subsidies and externalities such as the effect of imported oil use on national

security [26]

3 Projected real rates of energy price escalation (excluding inflation) are provided for each of 10 DoE regions, by sector — residential, commercial,

and industrial —, by fuel type — electricity, distillate, natural gas,

residual, and coal — and based on EIA price projection for four benchmarks —

1980, 1985, 1990, and 1995. They appear in tables C-l through C-ll of the LCC

Rules [6]. Discount factors incorporating the energy price escalation rates

have been developed to simplify the hand calculation of life-cycle energy

costs. These are found in tables B-l to B-ll of the LCC Rules [6]. (These

data are subject to periodic revision.)

33
formulas or factors that can be used to discount each of the various patterns

of cash flow: single future amounts such as replacement costs, recurring

future amounts such as maintenance and repair costs, and escalating future

amounts such as energy costs.

Discounting requires the selection of a discount rate that reflects the

investor's time value of money. The discount rate is used either directly in

the discounting formulas or—if factors are used—to select the appropriate

factor from discount factor tables. If inflation is included in estimates of

future costs and savings, then it must also be included in the discount rate.

Alternatively, if all costs and savings are expressed in constant dollars,

inflation should not be included in the discount rate. Working with constant

dollars and a real discount rate, present prices can be used as estimates of

future prices in constant dollars for those items whose prices can be expected

to inflate at about the same rate as prices in general.

For future amounts that are expected to change at a rate different from the

general rate of inflation, present prices will require adjusting in order to serve as estimates of future prices. In the case of future amounts that are

not subject to price inflation, such as services fixed by contractual agreement,

a price deflator index can be used to convert the future amounts to constant

dollars prior to discounting. In the case of future amounts that are expected

to increase faster than the rate of general price inflation, such as energy

costs, differential price escalation rates can be used to find the future

constant dollar equivalents.

The Office of Management and Budget (OMB) imposes specific requirements which

all agencies must follow in adjusting costs for the time value of money. The

Federal LCC Rule reflects the OMB requirements.

Federal LCC Rule : 1) Estimate all future amounts in constant dollars, i.e., in

terms of the purchasing power of the dollar at the beginning of the base year,

at the time the investment is made; 2) Discount all future amounts to their

present values, using a 7 percent real discount ratejl i.e., the present rate

is assumed to exclude expected inflation.

FEDSOL assumes that all cost inputs and salvage values represent purchasing

power at the beginning of the base year; i.e., that they do not include expected

inflation. The program discounts all future costs using a 7 percent discount

rate unless the user specifies otherwise.

A rate of 10 percent is dictated by the Office of Management and Budget in

Circular A-94 [27]. On June 30, 1980, however. President Carter signed the

Energy Security Act which requires a real discount rate of 7 percent per year

in evaluating energy conservation and renewable energy projects for Federal

buildings [28]. The Federal LCC Rule, as amended, reflects this legislation.

34
3.2.6 Study Period

The study period is the length of time covered by the life-cycle cost analysis.

In comparing alternative energy systems for a given building application, the same study period should be used in evaluating each project and that period

should not exceed the life of the building (or lease).

Federal LCC Rule : Select a study period that does not exceed 25 years.

3.3 CALCULATING TOTAL LIFE-CYCLE COSTS WITH AND WITHOUT SOLAR2

A life-cycle costing approach can be implemented by applying any or all of the

following evaluation techniques or "modes of analysis": 1) total life-cycle

cost (TLCC) analysis, which sums the discounted value of all the equivalent

costs over the investor’s time horizon; 2) net savings (NS) analysis, which

finds the difference between the TLCC’s of a proposed project and its alternative; a 3) savings-to-investment ratio (SIR) method, which indicates by a numerical ratio the size of savings relative to costs; and 4) internal-rate-ofreturn (IRR) technique, which gives the percentage yield on an investment.

Often these life-cycle costing techniques are supplemented by additional

techniques of economic evaluation which focus upon some particular aspect of

the investment, such as the time to payback (PB). Not a full life-cycle

costing technique itself, the payback measure indicates the elapsed time until

cumulative savings (or receipts) are sufficient to cover cumulative costs.

There are two versions of the payback measure that are often used. Discounted

Payback (DPB) takes into account the cost of money through discounting. Simple

Payback (SPB) does not include discounting, nor does it typically include

future escalation in energy prices.

Each of these evaluation techniques has its advantages and disadvantages that

make it particularly appropriate for some purposes and less appropriate for

others. ^ The TLCC and NS techniques are especially useful for designing and

sizing projects, while the SIR and IRR techniques are particularly useful for

assigning priority to projects when the budget is limited. The DPB technique

is useful when project life is very uncertain or when a speculative investment

requires quick recovery of funds. Collectively they form tools of analysis

which can be used in determining the cost-effective design and size of solar

energy systems, the type of auxiliary energy system, the kinds and amounts of

other energy conservation investments to use in conjunction with solar energy,

and, when the budget is limited, the economic priorities that should be

assigned to competing projects.

1 A cut-off for the study period of 30 years was originally adopted in the

Federal LCC Rule. This limit is lowered to 25 years by the provisions of the

Energy Security Act of 1980 [28].

^ The discount formulas referred to in this section appear in Appendix C.

O

~> The advantages and disadvantages and recommended applications of these

techniques are explained in some detail in reference [29].

35
The total life-cycle cost (TLCC) and Net Savings (NS) measures of economic

performance provide the framework for describing the economic optimization

model contained in the FEDSOL program. Other measures of economic performance

required under the Federal LCC Rule are described in section 3.5.

Since solar energy systems will generally be used in conjunction with an auxiliary energy system (electricity, natural gas, oil, etc.), rather than

alone, it is necessary to compare the Total Life-Cycle Costs (TLCC) of the

combined solar energy/auxiliary energy system (TLCC S a ) to the TLCC of a reference non-solar energy system (TLCCW) which would be used in lieu of solar.

If TLCC S a is lower than TLCCW , the solar energy/auxiliary energy system is

more cost effective than the non-solar energy system alone.

3.3.1 Total Life-Cycle Costs Without Solar

TLCCWmay be calculated as follows:

TLCC = P w w

UPW* + I wn w

n + ( 2 t=l

SPW

t

) + (M^ UPW

n

)

- (S • SPW ), w n

(3.7)

where the subscript "w" designates costs of the reference non-solar energy

system; Pw

represents the current price per energy unit of fuel used in the

reference non-solar energy system ($/MMBtu); L, the annual heating load; ew , the average annual efficiency of this system; UPW^ , the uniform present

n worth factor for the specified discount rate and period of study, n, modified

to include projected price escalation rates for the fuel used in this system;

Iw , the initial investment costs for this system; n, the number of years in the

study period; Rw , the costs of replacements of this system net of salvage

value of components replaced in year t; SPWt , the single present worth factor

for the specific discount rate and the year, t, in which the replacement is

expected to occur; Mw , the annually recurring non-fuel operation and maintenance cost for this system; UPWn , the uniform present worth discount factor for

the specified discount rate and period of study; Sw , the estimated salvage value

of this system net of disposal costs at the end of the study period; and SPWn , the single present worth discount factor for the specified discount rate and

last year in the study period.

3.3.2 Total Life-Cycle Costs With Solar

TLCC s>a is determined as follows:

TLCC Sj

= LCC S + LCCa (3.8)

where LCC g represent the life-cycle costs of the solar energy system, and LCCa represents the life-cycle costs of the auxiliary system in a combined solar/

auxiliary system.

36
LCC is calculated in the following manner:^-

LCC

S = Cs + (Vg

• As

) + (M

g

• UPW

n

) + (P

g

• Qg

• UPW^)

n

(3.9)

+ ( Z *s t

• SPWt

) - (S

s

• SPWn ),

j-1

where Cs represents the fixed costs of the solar energy system; Vs , the

variable costs of the solar energy system per unit of solar collector area, As ; Ms , the annually recurring costs of maintaining the solar energy system, UPW

the uniform present worth factor for the specified discount rate and study

period, n; P_, the price of electricity per energy unit; Qs , the quantity of

n»

electricity required annually to operate the fans, pumps, and controls of the

solar energy system; UPWQ , the uniform present worth factor for the specified 'V

discount rate and study period, n, modified to include a set of projected energy

price escalation rates for electricity; Rs , the costs of major replacements to

t the solar energy system net of salvage value of components replaced in year t;

SPWt , the single present worth factor for the specified discount rate and year

t, in which the repair or replacement is expected to occur; S s , the estimated

salvage value of the system at the end of the study period net of removal and

disposal costs; and SPWn , the single present worth factor for the specified

discount rate and the last year in the study period.

LCC a is calculated as follows:

n LCC = P o

• L (1~F) • UPW* + I + ( Z Ra. • SPW_) + (M, • UPW„) a d _ a., a. L t a U

J-l

n (3.10)

designates costs of the auxiliary energy system; P.

- (S • SPW ), a n

where the subscript "< represents the current price per energy unit of fuel consumed in the auxiliary

system; L, the annual heating load; ea , the average annual efficiency of the

auxiliary heating system; F, the annual fraction of the heating load supplied

by solar; UPW* , the uniform present worth factor for the specified discount

n rate and period of study, n, modified to include projected energy escalation

rates for the auxiliary fuel; Ia , the initial investment costs for the auxiliary backup system; Ra , the costs of replacements to the auxiliary system

This equation assumes that solar storage volume and all other variable system

components increase proportionately with installed collector area. Therefore,

the variable cost component (V s ) includes the cost of storage per unit of

collector area, as well as all other variable system costs which increase

proportionately with collector area.

37
net of salvage in year t; SPWt , the single present worth factor for the

specified discount rate and the year, t, in which the replacement is expected

to occur; Ma , the annually recurring non-fuel operation and maintenance cost

of the auxiliary system; UPWn , the uniform present worth discount factor for

the specified discount rate and study period, n; Sa , the estimated salvage of

the auxiliary system net of disposal costs at the end of the study period; and

SPWn , the single present worth discount factor for the specified discount

rate and the last year in the study period.

3.3.3 Net Savings

Assuming that an auxiliary system for the solar energy system is required. Net

Savings (NS) is computed for a given thermal load by subtracting TLCCS a from

TLCCW ; i.e.,

NS = TLCCW- TLCC s>a . (3.11)

3.4 OPTIMIZING SYSTEM DESIGN

The TLCC for each alternative design and size under consideration can be

calculated and compared. The alternative with the lowest TLCC is the most costeffective choice, provided possible differences in comfort and other effects

not quantified in the cost equations do not outweigh the results of the lifecycle cost evaluation.

Similarly, projects can be designed and sized on the basis of their comparative

NS. For example, the NS of a solar energy system of a given design and size can be found by subtracting the TLCC of the combined solar energy/auxiliary

system from the TLCC of the reference non-solar energy system. If a project

has a positive NS, it recovers its full costs plus a surplus, and, hence, is

economically desirable. The system with the highest NS relative to the reference non-solar case is the most cost effective choice, other things being the same

By repeating the procedures described above for a number of system designs and

sizes (including different auxiliary systems), the system design/size configuration with the highest net savings and lowest total life-cycle cost can be

identified

3.4.1 Framework for Optimization

The optimal system design for a given application, building, and location

depends on the trade-off between auxiliary energy costs (LCCa ) and solar energy

system costs (LCC S ) as the size of a solar energy system of a given design is

increased

Consider the trade-off between solar energy system size and auxiliary energy

cost for a system of a given design, as depicted graphically in figure 3.2.

Collector area, as an indicator of overall system size, is shown along the

horizontal axis. Present value costs are shown along the vertical axis. As

collector area increases, the amount of energy supplied by the solar energy

38
Figure 3.2 LCC Trade-off Between

Conventional Energy and

Solar Energy

Figure 3.4 Determining the Economically

Optimal System Size Through

Maximizing Savings

Figure 3.3 Determining the Economically

Optimal System Size Through

Minimizing TLCC s>a

39
system increases. Thus, auxiliary energy usage and LCCa decrease as LCC S increases. The LCC a line is curved toward the origin because additional units

of A generally increase the fraction of the load supplied by solar by ever

smaller amounts, i.e., as additional units of A are installed, the LCC a curve declines at a decreasing rate. LCCS , in contrast, is shown to increase linearly

with A in figure 3.2, as would happen if there were a constant variable cost per

each additional unit of A. C s on the vertical axis indicates those system costs

that are relatively insensitive to system size, that is, the "fixed costs." Cs may be much larger or it could be smaller than portrayed in figure 3.2.

The trade-off depicted in figure 3.2 suggests that there may be a solar energy

system size which just balances the decrease in LCC a with the increase in LCC S as additional units of collector area (A) are installed. At this point TLCC S a would reach a minimum value. This is depicted in figure 3.3, which is identical to figure 3.2 with the addition of the TLCC S a curve. The TLCC S a curve,

obtained by adding LCC a and LCC g vertically, is U-shaped (although other shapes

are possible, depending upon the shape of LCCa and LCCS ). The TLCC S a curve is

shown as first decreasing, reaching a minimum value at A*, and thereafter

increasing. The system size represented by A* collector area is the economically optimal size for the solar energy system. It is economically optimal in

the sense that it minimizes the total life-cycle costs of the combined system,

TLCCSja . Any other size would result in greater TLCC Sja .

3.4.2 Maximizing Savings

Thus far we have considered trade-offs between LCCa and LCC S in order to

determine the total costs of various size combinations of the solar/auxiliary

energy system. Now let us examine the cost effectiveness of the combined

solar/auxiliary energy system relative to the reference non-solar energy system.

Figure 3.4 shows the TLCC curve for the reference non-solar energy system

(TLCCioO%w) > added to the curves of figure 3.3. TLCCiqO%W independent of

collector area because it represents the total life-cycle cost without the

solar energy system. Figure 3.4 also shows the NS curve for the combined

solar/auxiliary energy system of alternative sizes. The NS curve is found by

taking the difference between the TLCCiqO%W curve and the TLCC S a curve. NS

is shown to be initially below the horizontal axis, indicating higher lifecycle costs for small sizes of the combined solar/auxiliary energy system than

for the reference non-solar energy system. NS then increases, rises above the

horizontal axis, and reaches a maximum value for the solar energy system size

designated A*. NS decreases thereafter and losses are incurred for the largest

system sizes. (Other shapes of the NS curve are possible, depending on the

shapes of LCCa , LCC S , and TLCC s>a .)

It is important to note that NS reaches a maximum value at A* coincident with

the minimum value of TLCC S a. Maximizing NS is identical to minimizing TLCC S a in determining the optimal * system size. A*. Only by selecting the economically

optimal size (A*) of the solar energy system will the maximum cost effectiveness of the system be obtained.

40
3.4.3 Minimizing Losses

In the graphic exposition of figure 3.4, NS is positive at A* and, therefore,

the solar energy system is cost effective. It recovers its full cost over the

life-cycle plus some surplus, NS. The value of the surplus is over and above

the opportunity cost of money, since all costs and savings are assumed to have

undergone the discounting procedure.

The collector area which minimizes TLCCS a will not necessarily produce a positive NS. That is, the minimum-cost solar energy system may not be cost

effective relative to the 100 percent non-solar energy system. This situation

is depicted graphically in figure 3.5. The collector size A* in figure 3.5

minimizes TLCC S a , but results in a negative NS, which means a higher lifecycle cost of supplying energy to the building.

If a solar energy system is to be installed regardless of its cost effectiveness,

A* (as depicted in figure 3.5) is the optimally sized system to install, based

on economic efficiency considerations. Although it is not cost effective. A*

is optimal in the sense of minimizing total life-cycle losses (-NS), or "excess

cost," from using solar energy. Any other size for this solar energy system,

other than zero, would result in greater excess cost over the life of the

system than size A*.

This same trade-off procedure could be applied to alternative system designs,

for example, flat-plate collectors versus advanced technology collectors and

air systems versus water systems. The system design and size with the highest

net savings, or the lowest -NS, excess cost, is the economically preferred

solar energy system, other things being equal.

3.4.4 What To Do When the Economically Optimal Solar Energy System Size Is

Zero or Very Small

Figure 3.6 depicts a third possible configuration for the TLCCS a and NS curves.

The TLCC s>a curve is continuously increasing and lies everywhere above the

TLCC^qO%W curve. Thus net losses result for all sizes of the solar energy

system and continuously increase as solar is increased. In this situation, a collector area of zero minimizes losses.

What should one do if the life-cycle cost analysis shows that the optimal

system size is 0 or so small that it does not represent a viable or realistic

design decision? Answers to the following questions provide guidance:

1) Would a different type of system, with different cost and efficiency

profiles, result in different trade-offs between solar costs and auxiliary

energy costs?

2) What is the minimum acceptable solar heating contribution? What is the

cost penalty for selecting the size that will meet the minimum requirement?

Should this minimum solar contribution be used as a minimum size constraint?

41
Figure 3.5 Minimizing Losses (-NS) Associated with Solar Projects

Figure 3.6 Sizing Systems When No Optimization Is Possible (A System

Size of Zero Minimizes Net Losses)

42
3) Can the system size be expanded beyond the minimum acceptable level without

a large increase in dollar losses? That is, is the NS curve steep or flat in

the region of the minimum acceptable size?

4) How sensitive is the outcome of the economic optimization to key

assumptions, for example, investment costs and fuel costs, and how reasonable

are those assumptions? Has sufficient care been taken to differentiate the

solar energy investment costs that are relatively independent of system size

(fixed costs), from those that vary directly with system size (variable costs)?

5) How important is it to the agency to have an alternative energy source?

Are there benefits not accounted for in the life-cycle cost analysis? Do these

expected benefits exceed the excess costs or net losses of a project of acceptable size?

Sections 3.4.5 and 3.4.6 describe special features of the FEDSOL program that

are useful in developing answers to these questions.

3.4.5 Optimizing System Size with FEDSOL

FEDSOL identifies the economically optimal collector area (greater than zero)

by computer search of net savings for a combined solar/auxiliary system relative to a reference non-solar energy system over a wide range of sizes of the

solar energy system.

In essence FEDSOL constructs and scans the NS curve, locates the combined

solar/auxiliary system resulting in highest net savings (or lowest net losses),

and prints out the size, solar fraction, net savings measures for this optimal

system, as illustrated for a sample case—an office building system for service

hot water and space heating in Washington, D.C. —reprinted in table 3.4.1 The

table of solar fractions and net savings results for a range of system sizes is

reprinted in table 3.5.

In FEDSOL, the optimal collector area is determined using an optimization

technique called the "Golden Section Search." The "Golden Section" is a portion of the interval between specified lower and upper bounds, calculated by

taking (SQR(5)-1 )/2 , or approximately 0.618, times the distance between these

bounds. This distance is added to the lower bound and subtracted from the

upper bound to determine the first two points at which to evaluate the net

present value savings of the solar energy investment. The net present value

savings at the two points are compared to determine which is greater, and,

consequently, which end of the interval should move to form a new search interval. The procedure is repeated until the bounds converge on the optimal

collector area.

This method allows one to find a maximum or minimum value, or constrained

optimum, of a function over a specified interval with very few computer

1 The input data for this sample Washington, D.C.,

case 1. case is shown in section 4,

43
Table 3.4 Life-Cycle Cost Summary for the SAMPLE Case

LIFE CYCLE COST SUMMARY

OPTIMAL COLLECTOR AREA = 1659.00 SQFT

OPTIMAL SOLAR FRACTION = .489

SOLAR ENERGY AUXILIARY REFERENCE

SYSTEM SYSTEM SYSTEM

INVESTMENT (ADJ) $ 93792. $ 0 . $ 0.

FUEL $ 2833. $ 61303. $ 120054.

O&M $ 11040. $ 0 . $ 0 . REPLACEMENTS $ 0 . $ 290. $ 767.

SALVAGE $ 4040. $ 0 . $ 0 . TOTAL LCC $ 103626. $ 61593. $ 120820.

Table 3.5 Table of Solar Fractions and Net Savings for

the SAMPLE Case

SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES

AREA SOLAR FRACTION NET SAVINGS

(SQFT)

250.0 .08 $ -56202.

550.0 .18 $ -52749.

850.0 .27 $ -49293.

1250.0 .39 $ -45585.

1700.0 .50 $ -44411.

2300.0 .61 $ -46994.

3050.0 .70 $ -54843.

4200.0 .80 $ -72484.

6350.0 .89 $-114919.

12700.0 .98 $-262959.

iterations. In FEDSOL, the lower bound of this interval initially is set equal

to zero, and the upper bound set equal to the area which produces an annual

solar fraction of approximately 99 percent.

In some cases, the optimization analysis performed by FEDSOL can result in a system too small or too large to be feasible in an engineering or design sense

for the building to which it is to be attached. To avoid the outcome of too

small a system, the minimum acceptable solar fraction input (FEDSOL line number

5) should be used to constrain the optimization analysis to systems with performance capabilities above some minimum acceptable level. 1 Furthermore, the

1 The FEDSOL program sets zero square feet of collector area as the absolute

minimum size constraint. This constraint is adjusted upward by changing the

value of the minimum solar fraction input variable over the range of one to

98 percent solar. The default value is 30 percent.

44
table of solar fractions and net savings in the program output can be examined

for the penalty of selecting a larger or smaller system than optimal on the

basis of life-cycle cost considerations. For many buildings and locations,

there is little change in net savings over a wide range of system sizes and

performance capabilities. In other situations or over other size ranges, the

effects on life-cycle cost and net savings from under- or over-sizing systems

can be major. The maximum feasible system size from an engineering or design

standpoint sets the upper size limit in interpreting the life-cycle costing

results

Consider the following example, illustrated in figure 3.7. The table of net

savings and annual solar fraction results obtained for a similar building and

system in four cities—Washington, D.C., Los Angeles, Phoenix, and Bismarck

are plotted in the figure. 1 Annual solar fraction is plotted as a function of

collector area in the upper quadrant; net losses (negative savings) as a function of collector area in the lower quadrant.

Note that net losses result from the use of solar energy in all four cases. However, in each case, net losses are minimized by a system size greater than

zero. The collector area that minimizes net losses ranges from 628 square feet

in Los Angeles to 1,659 square feet in Washington, D.C. Note further that in

the Bismarck case, the optimally sized system provides only 15 percent of the

annual energy requirement for space and water heating. This fraction is probably smaller than is feasible in an engineering sense. A further examination of

the net losses curve for Bismarck shows it to be relatively flat for collector

areas up to approximately 2,500 square feet, corresponding to a solar fraction

of 22 percent. This suggests that the system could be expanded to 2,500 square

feet with a relatively small economic or cost penalty. On the other hand,

expanding the solar capability system to provide 40-50 percent or more of the

energy load fraction capability would entail a substantial penalty.

3.4.6 Conducting Sensitivity Analyses with FEDS0L

FEDS0L contains a number of features that are useful in examining the

sensitivity of analysis results to specific assumptions and in comparing the

economic performance and optimal sizing of different types of systems.

Breakeven Analysis . The breakeven analysis portion of the program output

provides a comprehensive sensitivity analysis for three key economic input

variables

investment costs for solar energy system (fixed and variable components)

° base-year energy prices

energy price escalation rates.

In the breakeven analysis, these variables are adjusted one at a time, with the

others held at their original values, until the net life-cycle savings from the

solar energy investment equal zero, the minimum conditions for cost

effectiveness

1 The building and system are as described for the sample Washington, D.C.,

case described above.

45
100

80

60

40

20

0

20

40

60

80

too

120

140

160

180

200

220

•e 3.7

2000 4000 6000

COLLECTOR AREA (ft 2

)

8000

Washington, DC —_ phoenix, AZ —— Bismarck, NO

Los Angeles, CA

Annual Solar Fraction vs. Net Losses—Sample Test Results for

an Office Building System for Space and Service Water Heating

in Four U.S. Cities

46
Fuel price escalation rates and investment costs are adjusted by applying

incremental multipliers to the original values. The multiplier which causes

net savings to equal zero is called the breakeven value. The breakeven baseyear fuel price is found by incrementing the original value for the base-year

fuel price until net savings equal zero . Fuel prices and escalation rates

are, of course, adjusted upward; investment costs downward. System size is

reoptimized as prices and escalation rates are adjusted.

Note that FEDSOL conducts this breakeven analysis only when all of the following

conditions apply:

1. the SLR performance analysis has been selected

2. the optimization option has been selected

3. the reference and auxiliary fuel types are the same

4. the extended output option has been selected

5. net life-cycle savings are negative for the original

data and assumptions.

In situations where solar energy currently is not cost effective, this analysis

serves to pinpoint the magnitude of the change required for the optimallysized solar energy system, of the type specified, to become cost effective;

i.e., it shows the "gap" between the current cost conditions and cost

effectiveness

The breakeven analysis for the sample Washington, D.C., project is reprinted

in table 3.6.

I Table 3.6 Breakeven Analysis for the SAMPLE Case

BREAKEVEN ANALYSIS

OPTIMAL AREA = 2585.00 SQFT

SOLAR FRACTION = .647

BREAKEVEN FUEL PRICE = 15.148908 $/MMBtu

BREAKEVEN SYSTEM COST MULTIPLIER = .600340

BREAKEVEN FUEL ESCALATION RATE MULTIPLIER = 1.357

BREAKEVEN FUEL ESCALATION RATES 6.9729 7.1900 12.1557

This breakeven analysis shows that conventional fuel used as auxiliary to solar

must cost at least $15.15/MMBtu for the project to break even, i.e., for net

savings to equal zero, given the conditions assumed. This minimum required

cost can be compared with the default price of oil for commercial use in Washington, D.C., in 1981 of $9.25. Alternatively, given the current price of oil,

the breakeven analysis shows that reducing fixed and variable (per unit) solar

47
energy investment costs to 60 percent of the costs assumed in the base-case

analyses would cause the project to break even. Or, thirdly given the current

price of distillate, investment and other costs assumed in the base-case analyses, the breakeven analysis shows that rates of fuel price escalation 1.36 times

the current projections would be necessary for project savings to equal the

costs.

Note that the optimal solar fraction and optimal system size in the Washington,

D.C. case (project SAMPLE) increase from 49 percent and 1,659 square feet to 65

percent and 2,585 square feet, respectively, as solar energy investment costs

or fuel prices approach their breakeven values. ^ (This can be seen by comparing

tables 3.4 and 3.6.)

Flexibility in Changing Input Data . The FEDSOL user can take advantage of the ease with which FEDSOL* s input data can be changed to develop economic profiles

for making design and sizing decisions. All of the numbered items in the input

data listing can be changed with the C (Change) command. Only if the location,

the type of building, or the type of analysis (SLR or economic analysis alone)

is changed is it necessary to start the program over by stopping execution of

the current file and creating a new file. The summary output can be used to

obtain a quick one-line summary of the results for alternative sets of data and

assumptions (see data item 70, section 2.3.2).

3.4.7 Making the Design and Sizing Decision

By evaluating different types of systems and considering realistic ranges of

values for key economic variables, one can develop a much more complete picture

of the economic consequences of an investment in solar energy than that given

by a single computer run for a single set of assumptions. After weighing the

effects of uncertainties about investment costs, energy prices, and other costs

and after considering engineering practice and architectural considerations,

it remains for the decision maker to exercise a reasoned judgment as to the

most economically efficient design and size under these conditions.

3.5 CALCULATING OTHER MEASURES OF ECONOMIC PERFORMANCE

The Federal LCC Rule requires the savings-to-investment ratio (SIR) and simple

payback (SPB) measures of economic performance in addition to net savings (NS).

The SIR is a numerical ratio calculated with the combined change in energy costs

and non-fuel operation and maintenance costs as the numerator, and the combined

1 Given the particular mathematical model contained in the FEDSOL program, the

breakeven optimal collector area and solar fraction are approximately the same regardless of whether base-year fuel prices, escalation rates, or investment costs are adjusted. Because of this approximate equality and in order to

simplify the program output, a single set of breakeven optimal area and

fraction values is printed.

48
change in investment costs, salvage values, and replacement costs in the

denominator:

SIR = AE - AM * (3.12)

AI - AS + AR

where all amounts are expressed in present value dollars, and E represents

energy costs; M, non-fuel operation and maintenance costs; I, investment costs;

S, salvage value; and R, replacement costs. The delta symbol (A) indicates

that only those changes attributable to the solar energy system need be considered. AE is calculated by subtracting life-cycle energy costs for the combined

solar/auxiliary system from energy costs for the reference system; AM, AI, AS,

and AR are calculated by subtracting the respective life-cycle cost for the

reference system from the corresponding life-cycle cost for the combined solar/

auxiliary system. A SIR value greater than 1 means the project is cost effective. This measure is useful for ranking projects in descending order of their

return per dollar cost and thus assigning priorities to projects competing for

a limited budget, once the optimal size/design for a given project has been

defined using the TLCC or NS measures. (For further explanation see the LCC

Manual [ 1 ] .

)

The SPB measure computes the elapsed time between the time of the initial

investment and the time at which cumulative savings through reductions in

energy costs, net of other future costs, just offset the initial investment

cost (ignoring the cost of money and energy price escalation). A payback

period equal to or shorter than the study period means that the project is

cost effective according to this measure.

If future costs and savings are estimated to occur in even yearly amounts, the

following formula can be used to determine SPB:

AI

SPB = — = -

AE - AM - AR

(3.13)

where I represents investment costs; E, annual energy costs evaluated at

base-year energy prices^; M, annual non-fuel operation and maintenance costs at

base-year prices; and R annual replacement costs at base-year prices. The bar

above the symbols indicates that the base-year costs have not been discounted

to present value and summed. If future costs and savings are not uniform, the

following equation can be used:

y _ _

Find y, the number of years, such that E (AEl - AMl ~ ARl) = AI. (3.14)

L=1

1 The assignment of values to the numerator and denominator varies, but this

version is widely used and has been adopted for Federal LCC Rule [1, 4].

49
Otherwise, differences are calculated as for the SIR. The SPB is a rough,

approximate measure of economic performance and should not be relied upon as

the primary basis for an investment decision. (For further explanation, see

the LCC Manual [1].)

The FEDSOL program output includes these additional measures in the results of

the life-cycle cost analysis. In addition, it provides two cash flow analyses.

The first shows annual and cumulative dollar values for the undiscounted net

cash flow over each year of the study period. The second cash flow analysis

shows discounted values for the annual and cumulative net cash flow over the

study period. This second cash flow analysis includes the effects of escalation

in fuel prices, while the first does not. (See section 4, case 1.)

50
4. CASE EXAMPLES ILLUSTRATING THE FEDSOL PROGRAM1

This section includes five computer runs of the FEDSOL program. Case 1 illustrates the sample case stored permanently in the program files under the name "SAMPLE" (see section 2). Major elements of the program output are annotated for easy reference.

Case 1. Optimization analysis of an office building system in Washington, D.C.,

for space heating and service water heating.

Case 2. Thermal and economic analysis of a 800 ft^ office building system for

space heating and service hot water in Washington, D.C. (same building

and location as Case 1).

Case 3. Optimization analysis of an office building system for service water

heating only in Washington, D.C. (same building and location as case

1 )

•

Case 4. Optimization analysis of a residential system in Bismarck, N.D. for

space heating and service water heating.

Case 5. Economic analysis only of a residential system for space heating in

Bismarck, N.D. (same building and location as case 4; thermal performance estimate from F-CHART 3.0).

1 The buildings and systems analyzed in the test cases are hypothetical in that

they do not actually exist, nor have they been proposed for construction.

The office building cases are based on a prototypical 3-story office building

of 30,000 square feet with 300 occupants; the residential case, a singlestory detached residence of 1,500 square feet with four occupants. Solar

energy systems costs are based on generalized cost functions for active solar

energy systems prepared by Honeywell, Inc., under contract to the National

Bureau of Standards [11].

51
Case 1

This case shows an building system in

water heating. It

called SAMPLE.

economic optimization analysis of an office

Washington, D.C., for space heating and service

illustrates the use of the demonstration file

FEDSOL - VERSION 1.0 *** NATIONAL BUREAU OF STANDARDS

COMMAND: N=NEW, O-OLD, L-LIST, C=CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? 0

ENTER NAME OF DESIRED FILE »>? SAMPLE

ENGLISH OR SI UNITS (E OR SI) ? E

The demonstrat ion

file SAMPLE is

called from

permanent storage.

COMMAND: N-NEW, COLD, L=LIST, C-CHANGE, R=RUN , S-SAVE, Q-QUIT, H-HELP ? L

ANAIYSIS FOR A FEDERAL OFFICE BUILDING IN WASHINGTON-STERLING, DC ********************************************************

***************** ENERGY ANALYSIS DATA *************** ********************************************************

DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)

1 TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST)

2 COLLECTOR TILT ANGLE

3 OPTIMIZATION ANALYSIS (YES-1 ;NO«2)

4 COLLECTOR AREA .00

5 MINIMUM ACCEPTABLE SOLAR FRACTION 30.00

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM 51.00

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM 51.00

8 ELECTRIC ENERGY AS % OF USEFUL SOLAR ENERGY 6.00

ENERGY REQUIREMENTS DATA

9 DOMESTIC HOT WATER USAGE 300.00

10 BUILDING USE SCHEDULE 5.00

11 MONTHLY SPACE HEATING LOADS - MMBTU/MONTH

JAN 71.20 JUL - 33.90

FEB - 42.30 AUG - 23.70 MAR 37.90 SEP - 20.20 APR 21.60 OCT - 21.00 MAY 24.00 NOV - 28.70

JUN 28.20 DEC 53.60

ENVIRONMENTAL DATA

12 AVERAGE DAILY HORIZONTAL RADIATION - BTU/SQFT-DAY

JAN - 572.00 JUL - 1817.00

FEB - 815.00 AUG - 1617.00 MAR - 1125.00 SEP - 1340.00 APR - 1458.00 OCT - 1003.00 MAY - 1718.00 NOV - 650.00 JUN - 1900.00 DEC - 481.00

13 AVERAGE GROUND WATER TEMPERATURES _ DEGREES F DEC - FEB - 47.0 MAR - MAY = 51.0 JUN - AUG = 66.0

SEP - NOV = 63.0

13.00

48.57 DEGREES

1.00

SQFT

XX

X

X

Input data for

SAMPLE are

listed.

(The coded list

of types of

systems appears

in table 2.1).

52
A**************************************' ***************** LIFE cycle cost data

A**************************************'

BASE YEAR INVESTMENT COSTS

30 SOLAR ENERGY INVESTMENT - FIXED COST

31 SOLAR ENERGY INVESTMENT - VARIABLE COST

32 INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)

33 INVESTMENT COST FOR AUXILIARY SYSTEM

34 INVESTMENT COST FOR REFERENCE NONSOLAR SYSTEM

61577.00 $

25.70 $/SQFT

10.00 Z .00 $

.00 $

FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40 ANNUALLY RECURRING O&M COST (Z OF SYSTEM COST) 1.00 Z

41 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 42 SALVAGE VALUE AT END OF STUDY PERIOD 15.00 Z

AUXILIARY SYSTEM

44 ANNUALLY RECURRING O&M COST .00 $ 45 REPLACEMENT COST AND YEAR

$ 800 AT YEAR 15

$ 0 AT YEAR 0

$ 0 AT YEAR 0 46 SALVAGE VALUE AT END OF STUDY PERIOD .00 $

REFERENCE NON-SOLAR SYSTEM

47 ANNUALLY RECURRING O&M COST .00 $ 48 REPLACEMENT COST AND YEAR

$ 1000 AT YEAR 10

$ 1000 AT YEAR 20

$ 0 AT YEAR 0 49 SALVAGE VALUE AT END OF STUDY PERIOD .00 $

FUEL COSTS

50 ELECTRICITY PRICE IN BASE YEAR

51 DISTILLATE OIL PRICE IN BASE YEAR

52 RESIDUAL OIL PRICE IN BASE YEAR

53 NATURAL GAS PRICE IN BASE YEAR

54 COAL PRICE IN BASE YEAR

55 LPG PRICE IN BASE YEAR

56 TYPE OF FUEL USED IN AUXILIARY SYSTEM

57 TYPE OF FUEL USED IN REFERENCE SYSTEM

16.38 $/MMBTU

9.25 $/MMBTU

6.66 S/MMBTU

3.93 $/MMBTU

1.84 $/MMBTU

.00 $/MMBTU

2.00

2.00

DOE REGION - 3 58 ENERGY PRICE ESCALATION (Z PER YEAR ABOVE INFLATION) - COMMERCIAL

TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9 YRS

ELECTRICITY 5.29 .66 .14 DISTILLATE OIL 2.51 2.67 6.33

RESIDUAL OIL 9.00 2.52 5.56 NATURAL GAS 8.84 2.87 2.75

COAL 6.04 2.36 .90 LPG .00 .00 .00

53
DISCOUNT RATE AND STUDY PERIOD

60 REAL DISCOUNT RATE (EXCLUDES INFLATION) 7.00 X 61 STUDY PERIOD 20.00 YEARS

ANALYSIS OUTPUT

70 1=STANDARD; 2-EXTENDED; 3-SUMMARY 1.00

COMMAND: N=NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP 7 C

LINE NUMBER ? 70

70 1 -STANDARD; 2-EXTENDED; 3-SUMMARY

CURRENT VALUE - 1 NEW VALUE -72

LINE NUMBER ?

COMMAND: N-NEW, 0=0LD. L-LIST, C-CHANGE. R-RUN, S-SAVE, Q-QUIT, K*HELP ? R

* NET SAVINGS - $ -44399 * AREA - 1659 SQFT * SOLAR FRACTION - .489 *

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

kkkkkkkkkkkkkk THERMAL & ECONOMIC ANALYSIS ************** *********************************************************

WASHINGTON-STERLING, DC SYSTEM TYPE = 13

Input #70 is

changed from "1"

to "2" to request

extended analysis

output. A (CR)

is entered in

response to the

line number query

when no further

changes are desired. The Run

command is given.

SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES

AREA SOLAR FRACTION NET SAVINGS

(SQFT)

250.0 .08 $ -56202.

550.0 .18 $ -52749.

850.0 .27 $ -49293.

1250.0 .39 $ -45585.

1700.0 .50 $ -44411.

2300.0 .61 $ -46994.

3050.0 .70 $ -54843.

4200.0 .80 $ -72484.

6350.0 .89 $-114919.

12700.0 .98 $-262959.

THERMAL PERFORMANCE

COLLECTOR AREA = 1659.00 SQFT TILT ANGLE - 48.57 DEGREES

SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL FRACTION HORZ RAD. COLLECTOR LOAD LOAD SOLAR

(1) (1) (2) (2) (2)

JAN .190 572.00 882.01 71.20 4.58 14.38 FEB .347 815.00 1094. 16 42.30 4.13 16.11 MAR .491 1125.00 1272.36 37.90 4.36 20.77 APR .744 1458.00 1384.72 21.60 4.22 19.21 MAY .734 1718.00 1437.81 24.00 4.36 20.82 JUN .690 1900.00 1496.00 28.20 3.41 21.81

54
JUL .619 1817.00 1470.40 33.90 3.53 23.18

AUG .756 1617.00 1455.68 23.70 3.53 20.60

SEP .791 1340.00 1430.91 20.20 3.57 18.79

OCT .755 1003.00 1316.55 21.00 3.69 18.65

NOV .480 650.00 980.75 28.70 3.57 15.49

DEC .211 481.00 753.07 53.60 4.58 12.28 YEAR .489 406.30 47.53 222.09

(1) - BTU/SQFT-DAY

(2) - MMBTU/MONTH

LIFE CYCLE COST SUMMARY

OPTIMAL COLLECTOR AREA *= 1659-00 SQFT

OPTIMAL SOLAR FRACTION - .489

SOLAR ENERGY AUXILIARY REFERENCE

SYSTEM SYSTEM SYSTEM

INVESTMENT (ADJ) $ 93792. $ 0. $ 0.

FUEL $ 2833. $ 61303. $ 120054,

O&M $ 11040. $ 0. $ 0,

REPLACEMENTS $ 0. $ 290. $ 767,

SALVAGE $ 4040. $ 0. $ 0,

TOTAL LCC $ 103626. $ 61593. $ 120820

MEASURES OF ECONOMIC PERFORMANCE

TOTAL LCC WITHOUT SOLAR - $ 120820. TOTAL LCC WITH SOLAR - $ 165219. NET SAVINGS - $ -44399.

SIMPLE PAYBACK TIME - 33.17 YEARS

SAVINGS TO INVESTMENT RATIO - .503

CASH FLOW ANALYSIS

SIMPLE DISCOUNTED

YEAR ANNUAL CUMULATIVE ANNUAL CUMULATIVE

0 $ -93792. $ -93792. $ -93792. $ -93792.

1 $ 2768. $ -91024. $ 2670. $ -91122.

2 $ 2768. $ -88257. $ 2576. $ -88546.

3 $ 2768. $ -85489. $ 2483. $ -86063.

4 $ 2768. $ -82721. $ 2394. $ -83669.

5 $ 2768. $ -79954. $ 2320. $ -81349.

6 $ 2768. $ -77186. $ 2249. $ -79100.

7 $ 2768. $ -74418. $ 2178. $ -76921.

8 $ 2768. $ -71650. $ 2110. $ -74812.

9 $ 2768. $ -68883. $ 2042. $ -72769.

10 $ 3768. $ -65115. $ 2580. $ -70189.

11 $ 2768. $ -62347. $ 2098. $ -68090.

12 $ 2768. $ -59580. $ 2122. $ -65968.

13 $ 2768. $ -56812. $ 2144. $ -63825.

14 $ 2768. $ -54044. $ 2162. $ -61662.

15 $ 1968. $ -52077. $ 1889. $ -59773.

16 $ 2768. $ -49309. $ 2194. $ -57580.

17 $ 2768. $ -46541. $ 2206. $ -55374.

18 $ 2768. $ -43774. $ 2217. $ -53157.

19 $ 2768. $ -41006. $ 2226. $ -50930.

20 $ 19400. $ -21606. $ 6532. $ -44399.

55
BREAKEVEN ANALYSIS

OPTIMAL AREA - 2585.00 SQFT

SOLAR FRACTION - .647

BREAKEVEN FUEL PRICE - 15.148908 $/MMBTU

BREAKEVEN SYSTEM COST MULTPLI ER - .600340

BREAKEVEN FUEL ESCALATION RATE MULTIPLIER - 1.357 BREAKEVEN FUEL ESCALATION RATES 6.9729 7.1900 12.1557
Case 2. This case shows a thermal and economic analysis of a 800 ft^ office

building system for space heating and service hot water in Washington,

D.C. It is based on the file SAMPLE.

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q^JUIT, H-HELP ? C

LINE NUMBER ? 3

3 OPTIMIZATION ANALYSIS (YES-1 ;N0-2)

CURRENT VALUE - 1 NEW VALUE - ? 2

LINE NUMBER ? 4

4 COLLECTOR AREA

CURRENT VALUE - 0 SQFT NEW VALUE - ? 800

LINE NUMBER ? 70

70 1 -STANDARD; 2-EXTENDED; 3-SUMMARY

CURRENT VALUE = 2 NEW VALUE = ? 1

The input data in

SAMPLE are changed

to specify 800 ft^

of collector area and the "standard"

output.

LINE NUMBER ? COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? L

ANALYSIS FOR A FEDERAL OFFICE BUILDING IN WASHINGTON-STERLING, DC

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

***************** ENERGY ANALYSIS DATA *************** ********************************************************

The revised input

data are listed.

DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)

1 TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST)

2 COLLECTOR TILT ANGLE

3 OPTIMIZATION ANALYSIS (YES-1; NO-2)

4 COLLECTOR AREA

5 MINIMUM ACCEPTABLE SOLAR FRACTION

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM

8 ELECTRIC ENERGY AS % OF USEFUL SOLAR ENERGY

13.00

48.57 DEGREES

2.00

800.00 SQFT

30.00 X 51.00 X 51.00 % 6.00 X

ENERGY REQUIREMENTS DATA

9 DOMESTIC HOT WATER USAGE

10 BUILDING USE SCHEDULE

11 MONTHLY SPACE HEATING LOADS - MMBTU/MONTH

JAN - 71.20 JUL - 33.90

FEB - 42.30 AUG - 23.70 MAR - 37.90 SEP - 20.20 APR - 21.60 OCT - 21.00 MAY - 24.00 NOV - 28.70

JUN - 28.20 DEC - 53.60

300.00 GALLONS /DAY

5.00 DAYS /WEEK

ENVIRONMENTAL DATA

12 AVERAGE DAILY HORIZONTAL RADIATION - BTU/SQFT- JAN - 572.00 JUL 1817.00

FEB - 815.00 AUG 1617.00 MAR - 1125.00 SEP 1340.00 APR - 1458.00 OCT 1003.00 MAY - 1718.00 NOV 650.00

JUN - 1900.00 DEC 481.00

57
13 AVERAGE GROUND WATER TEMPERATURES - DEGREES F DEC - FEB = 47.0 MAR - MAY = 51.0

JUN - AUG = 66.0

SEP - NOV = 63.0 ********************************************************

***************** LIFE CYCLE COST DATA *************** ********************************************************

BASE YEAR INVESTMENT COSTS

30 SOLAR ENERGY INVESTMENT - FIXED COST

31 SOLAR ENERGY INVESTMENT - VARIABLE COST

32 INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)

33 INVESTMENT COST FOR AUXILIARY SYSTEM

34 INVESTMENT COST FOR REFERENCE NONSOLAR SYSTEM

FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40 ANNUALLY RECURRING O&M COST (% OF SYSTEM COST) 1.00

41 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 42 SALVAGE VALUE AT END OF STUDY PERIOD 15.00

AUXILIARY SYSTEM

44 ANNUALLY RECURRING O&M COST .00

45 REPLACEMENT COST AND YEAR

$ 800 AT YEAR 15

$ 0 AT YEAR 0

$ 0 AT YEAR 0 46 SALVAGE VALUE AT END OF STUDY PERIOD .00

REFERENCE NON-SOLAR SYSTEM

47 ANNUALLY RECURRING O&M COST .00 $ 48 REPLACEMENT COST AND YEAR

$ 1000 AT YEAR 10

$ 1000 AT YEAR 20

$ 0 AT YEAR 0 49 SALVAGE VALUE AT END OF STUDY PERIOD .00 $

Z

Z

$

$

61577.00 $

25.70 $/SQFT

10.00 Z .00 $ .00 $

FUEL COSTS

50 ELECTRICITY PRICE IN BASE YEAR

51 DISTILLATE OIL PRICE IN BASE YEAR

52 RESIDUAL OIL PRICE IN BASE YEAR

53 NATURAL GAS PRICE IN BASE YEAR

54 COAL PRICE IN BASE YEAR

55 LPG PRICE IN BASE YEAR

56 TYPE OF FUEL USED IN AUXILIARY SYSTEM

57 TYPE OF FUEL USED IN REFERENCE SYSTEM

16.38 $/MMBTU

9.25 $/MMBTU

6.66 $/MMBTU

3.93 $/MMBTU

1.84 $/MMBTU

.00 $/MMBTU

2.00

2.00

DOE REGION = 3 58 ENERGY PRICE ESCALATION (Z PER YEAR ABOVE INFLATION) - COMMERCIAL

TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9

' ELECTRICITY 5.29 .66 .14 DISTILLATE OIL 2.51 2.67 6.33

RESIDUAL OIL 9.00 2.52 5.56 NATURAL GAS 8.84 2.87 2.75

COAL 6.04 2.36 .90 LPG .00 .00 .00

58
DISCOUNT RATE AND STUDY PERIOD

60 REAL DISCOUNT RATE (EXCLUDES INFLATION) 7.00 Z

61 STUDY PERIOD 20.00 YEARS

ANALYSIS OUTPUT

70 1-STANDARD; 2-EXTENDED; 3-SUMMARY

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? R

* NET SAVINGS - $ -49872 * AREA - 800 SQFT * SOLAR FRACTION - .255 *

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

************** THERMAL & ECONOMIC ANALYSIS ************** *********************************************************

No further changes are made. The Run

command is given.

WASHINGTON-STERLING, DC SYSTEM TYPE - 13

SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES

AREA

(SQFT)

SOLAR FRACTION NET SAVINGS

250.0 .08 $ -56202.

550.0 .18 $ -52749.

850.0 .27 $ -49293.

1250.0 .39 $ -45585.

1700.0 .50 $ -44411.

2300.0 .61 $ -46994.

3050.0 .70 $ -54843.

4200.0 .80 $ -72484.

6350.0 .89 $-114919.

12700.0 .98 $-262959.

THERMAL PERFORMANCE

COLLECTOR AREA = 800.00 SQFT TILT ANGLE - 48.57 DEGREES

SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL

FRACTION HORZ RAD. COLLECTOR LOAD LOAD SOLAR

(1) O) (2) (2) (2)

JAN .092 572.00 882.01 71.20 4.58 6.93

FEB .167 815.00 1094.16 42.30 4.13 7.77 MAR .237 1125.00 1272.36 37.90 4.36 10.00 APR .408 1458.00 1384.72 21.60 4.22 10.53 MAY .399 1718.00 1437.81 24.00 4.36 11.30 JUN .360 1900.00 1496.00 28.20 3.41 11.38 JUL .309 1817.00 1470.40 33.90 3.53 11.56

AUG .420 1617.00 1455.68 23.70 3.53 11.44 SEP .458 1340.00 1430.91 20.20 3.57 10.89

OCT .419 1003.00 1316.55 21.00 3.69 10.35

NOV .231 650.00 980.75 28.70 3.57 7.46 DEC . 102 481.00 753.07 53.60 4.58 5.92 YEAR .255 406.30 47.53 115.55

(1) - BTU/SQFT-DAY

(2) - MMBTU /MONTH

59
LIFE CYCLE COST SUMMARY

COLLECTOR AREA = 800.00 SQFT

SOLAR FRACTION = .255

SOLAR ENERGY AUXILIARY REFERENCE

SYSTEM SYSTEM SYSTEM

INVESTMENT (ADJ) $ 73923. $ 0. $ 0

FUEL $ 1474. $ 89487. $ 120054

O&M $ 8702. $ 0. $ 0

REPLACEMENTS $ 0. $ 290. $ 767

SALVAGE $ 3184. $ 0. $ 0

TOTAL LCC $ 80915. $ 89777. $ 120820

MEASURES OF ECONOMIC PERFORMANCE

TOTAL LCC WITHOUT SOLAR = $ 120820. TOTAL LCC WITH SOLAR - $ 170692.

NET SAVINGS = $ -49872.

SIMPLE PAYBACK TIME = 60.55 YEARS

SAVINGS TO INVESTMENT RATIO = .290

60
Case 3. This is an economic optimization analysis of an office building system

for service water heating only in Washington, D.C. A new data file is

established to describe a service water heating system with singleglazed collectors, a selectively coated absorber surface, and water

delivery temperature of 130°F.

COMMAND: N-NEW, 0=0LD, L-LIST, C-CHANGE, R-RUN, S-SAVE,

ENGLISH OR SI UNITS (E OR SI) ? E

PERFORMANCE ANALYSIS USING SLR METHOD (Y OR N)? Y

ENTER CITY ID NUMBER? 52

RES IDENTIAL=1 ; COMMERCIAL-2 ; INDUSTRIAL-3 ? 2

Q-QUIT, H-HELP ? N The user is

queried for the

minimum data

required for a life

cycle cost analysis

THE FOLLOWING DATA ITEMS REPRESENT THE MINIMUM INFORMATION

REQUIRED TO CREATE A USEABLE INPUT DATA FILE. ADDITIONAL

CHANGES CAN BE MADE BY THE CHANGE COMMAND.

TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST) - ? 2

ENTER LOAD TYPE: 1-WATER HTG. 2-SPACE HTG. 3-BOTH - ? 1

DOMESTIC HOT WATER USAGE GALLONS /DAY S3 ? 300

BUILDING USE SCHEDULE DAYS /WEEK “ ? 5

SOLAR ENERGY INVESTMENT - FIXED COST $ « ? 12000

SOLAR ENERGY INVESTMENT - VARIABLE COST $/SQFT - ? 18.00

TYPES OF FUELS USED IN AUXILIARY AND REFERENCE SYSTEMS

1 = ELECTRIC

2 = DISTILLATE OIL

3 = RESIDUAL OIL

4 = NATURAL GAS

5 = COAL

6 = LPG

TYPE OF FUEL USED IN AUXILIARY SYSTEM - ? 1 TYPE OF FUEL USED IN REFERENCE SYSTEM - ? 1

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? L

ANALYSIS FOR A FEDERAL OFFICE BUILDING IN WASHINGTON-STERLING, DC

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

***************** ENERGY ANALYSIS DATA *************** ********************************************************

DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)

1 TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST) 2.00

2 COLLECTOR TILT ANGLE 48.57 DEGREES

3 OPTIMIZATION ANALYSIS (YES-1 ;NO-2) 1.00

4 COLLECTOR AREA .00 SQFT

5 MINIMUM ACCEPTABLE SOLAR FRACTION 30.00 Z

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM 60.00 Z

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM 60.00 Z

8 ELECTRIC ENERGY AS Z OF USEFUL SOLAR ENERGY 6.00 Z

The current data

(user supplied

values and default

values) are listed.

61
ENERGY REQUIREMENTS DATA

9

DOMESTIC HOT WATER USAGE

10 BUILDING USE SCHEDULE

11 MONTHLY SPACE HEATING LOADS - MMBTU/MONTH JAN - .00 JUL - .00 FEB - .00 AUG - .00 MAR - .00 SEP - .00 APR - .00 OCT - .00 MAY - .00 NOV - .00 JUN - .00 DEC - .00

300.00 GALLONS/DAY

5.00 DAYS/WEEK

ENVIRONMENTAL DATA

12 AVERAGE DAILY HORIZONTAL RADIATION - BTU/SQFT-DAY

JAN - 572.00 JUL - 1817.00

FEB - 815.00 AUG - 1617.00 MAR - 1125.00 SEP - 1340.00 APR - 1458.00 OCT - 1003.00 MAY - 1718.00 NOV - 650.00

JUN - 1900.00 DEC - 481.00

13 AVERAGE GROUND WATER TEMPERATURES

DEC - FEB = 47.0 MAR - MAY = 51.0 JUN - AUG = 66.0

SEP - NOV - 63.0

DEGREES F

***************** LIFE CYCLE COST DATA *************** ********************************************************

BASE YEAR INVESTMENT COSTS

12000.00 $

18.00 $/SQFT

10.00 Z .00 $ .00 $

30 SOLAR ENERGY INVESTMENT - FIXED COST

31 SOLAR ENERGY INVESTMENT - VARIABLE COST

32 INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)

33 INVESTMENT COST FOR AUXILIARY SYSTEM

34 INVESTMENT COST FOR REFERENCE NONSOLAR SYSTQ1

FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40 ANNUALLY RECURRING O&M COST (Z OF SYSTEM COST) 1.00 Z

41 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 42 SALVAGE VALUE AT END OF STUDY PERIOD .00 Z AUXILIARY SYSTEM

44 ANNUALLY RECURRING O&M COST

45 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 46 SALVAGE VALUE AT END OF STUDY PERIOD

REFERENCE NON-SOLAR SYSTEM

47 ANNUALLY RECURRING O&M COST .00 $ 48 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 49 SALVAGE VALUE AT END OF STUDY PERIOD .00 $

.00 $

.00 $

62
FUEL COSTS

50 ELECTRICITY PRICE IN BASE YEAR

51 DISTILLATE OIL PRICE IN BASE YEAR

52 RESIDUAL OIL PRICE IN BASE YEAR

53 NATURAL GAS PRICE IN BASE YEAR

54 COAL PRICE IN BASE YEAR

55 LPG PRICE IN BASE YEAR

56 TYPE OF FUEL USED IN AUXILIARY SYSTEM

57 TYPE OF FUEL USED IN REFERENCE SYSTEM

16.38 $/MMBTU

9.25 $/MMBTU

6.66 $/MMBTU

3.93 $/MMBTU

1.84 $/MMBTU

.00 $/MMBTU

1.00

1.00

DOE REGION = 3 58 ENERGY PRICE ESCALATION (% PER YEAR ABOVE INFLATION) - COMMERCIAL

TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9 YRS

ELECTRICITY 5.29 .66 .14 DISTILLATE OIL 2.51 2.67 6.33

RESIDUAL OIL 9.00 2.52 5.56 NATURAL GAS 8.84 2.87 2.75

COAL 6.04 2.36 .90 LPG .00 .00 .00

DISCOUNT RATE AND STUDY PERIOD

60 REAL DISCOUNT RATE (EXCLUDES INFLATION) 7.00 X

61 STUDY PERIOD 20.00 YEARS

ANALYSIS OUTPUT

70 1 -STANDARD; 2=EXTENDED; 3-SUMMARY 1.00

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? C

LINE NUMBER ? 2

2 COLLECTOR TILT ANGLE

CURRENT VALUE = 48.57 DEGREES NEW VALUE - ? 43.57

LINE NUMBER ? 6

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM

CURRENT VALUE = 60 % NEW VALUE - ? 100

LINE NUMBER ? 7

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM CURRENT VALUE = 60 % NEW VALUE - ? 100

LINE NUMBER ?

COMMAND: N-NEW, 0=0LD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? R

* NET SAVINGS = $ -10147 * AREA - 151 SQFT * SOLAR FRACTION - .490 *

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

************** THERMAL & ECONOMIC ANALYSIS ************** *********************************************************

WASHINGTON-STERLING, DC SYSTEM TYPE = 2

Changes are made in

the collector tilt

angle and in the

operating efficiencies of the auxiliary and reference

systems.

The Run command is

given.

63
SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES

AREA

(SQFT)

SOLAR FRACTION NET SAVINGS

20.0 .10 $ -11471.

50.0 .22 $ -10842.

80.0 .32 $ -10455.

110.0 .40 $ -10241.

160.0 .51 $ -10151.

210.0 .59 $ -10286.

280.0 .68 $ -10723.

380.0 .77 $ -11672.

570.0 .87 $ -14097.

1140.0 .98 $ -23409.

THERMAL PERFORMANCE

COLLECTOR AREA - 151.00 SQFT TILT ANGLE - 43.57 DEGREES

SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL

FRACTION HORZ RAD. COLLECTOR LOAD LOAD SOLAR

(1) (1) (2) (2) (2)

JAN * 572.00 869.80 .00 4.58 * FEB * 815.00 1090.37 .00 4.13 * MAR * 1125.00 1286.82 .00 4.36 * APR * 1458.00 1424.45 .00 4.22 * MAY * 1718.00 1498.08 .00 4.36 * JUN * 1900.00 1569.07 .00 3.41 * JUL * 1817.00 1537.68 .00 3.53 * AUG * 1617.00 1506.03 .00 3.53 * SEP * 1340.00 1456.10 .00 3.57 * OCT * 1003.00 1315.43 .00 3.69 * NOV * 650.00 968.90 .00 3.57 * DEC * 481.00 741.58 .00 4.58 * YEAR .490 .00 47.53 23.31

(1) = BTU/SQFT-DAY

(2) - MMBTU/MONTH

LIFE CYCLE COST SUMMARY

OPTIMAL COLLECTOR AREA - 151.00 SQFT

OPTIMAL SOLAR FRACTION - .490

64
SOLAR ENERGY AUXILIARY REFERENCE

SYSTEM SYSTEM SYSTEM

INVESTMENT (ADJ) $ 13246. $ 0. $ 0

FUEL $ 297. $ 5149. $ 10105

O&M $ 1559. $ 0. $ 0

REPLACEMENTS $ 0. $ 0. $ 0

SALVAGE $ 0. $ 0. $ 0

TOTAL LCC $ 15103. $ 5149. $ 10105

MEASURES OF ECONOMIC PERFORMANCE

TOTAL LCC WITHOUT SOLAR - $

TOTAL LCC WITH SOLAR - $ NET SAVINGS - $

10105.

20252.

-10147.

SIMPLE PAYBACK TIME - 62.57 YEARS

SAVINGS TO INVESTMENT RATIO - .234

65
Case 4 This case set up a new data file for a residential system for space

and water heating in Bismarck, N.D. and shows the economic optimiza'

tion analysis for this system.

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? N

ENGLISH OR SI UNITS (E OR SI) ? E

PERFORMANCE ANALYSIS USING SLR METHOD (Y OR N)? Y

ENTER CITY ID NUMBER? 132

RESIDENTIAL-! ; COMMERCIAL*^; INDUSTRIAL-3 ? 1

THE FOLLOWING DATA ITEMS REPRESENT THE MINIMUM INFORMATION

REQUIRED TO CREATE A USEABLE INPUT DATA FILE. ADDITIONAL

CHANGES CAN BE MADE BY THE CHANGE COMMAND.

TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST)

ENTER LOAD TYPE: 1 -WATER HTG. 2-SPACE HTG. 3-BOTH

DOMESTIC HOT WATER USAGE GALLONS/DAY

BUILDING USE SCHEDULE DAYS/WEEK

MONTHLY SPACE HEATING LOADS MMBTU/MONTH

JAN-? 21.12

FEB-? 17.3 MAR-? 14.84 APR-? 7.93 MAY-? 4.06

JUN-? 1.47 JUL-? .22 AUG-? .41 SEP-? 3.02 OCT-? 6.76 NOV-? 13. DEC-? 18.38

SOLAR ENERGY INVESTMENT - FIXED COST $ - ? 10270 SOLAR ENERGY INVESTMENT - VARIABLE COST $/SQFT - ? 17.78

TYPES OF FUELS USED IN AUXILIARY AND REFERENCE SYSTEMS

1 - ELECTRIC

2 = DISTILLATE OIL

3 = RESIDUAL OIL

4 - NATURAL GAS

5 - COAL

6 - LPG

TYPE OF FUEL USED IN AUXILIARY SYSTEM " ? 1 TYPE OF FUEL USED IN REFERENCE SYSTEM - ? 1

- ? 19

- ? 3

- ? 80

- ? 7

The user is queried

for the minimum set

of data.

66
COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? L

ANALYSIS FOR A FEDERAL RESIDENTIAL BUILDING IN BISMARCK, ND

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

***************** energy analysis data *************** ********************************************************

DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)

1 TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST) 19.00

2 COLLECTOR TILT ANGLE 56.46 DEGREES

3 OPTIMIZATION ANALYSIS (YES=l;N0-2) 1.00

4 COLLECTOR AREA .00 SQFT

5 MINIMUM ACCEPTABLE SOLAR FRACTION 30.00 X

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM 60.00 X

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM 60.00 X

8 ELECTRIC ENERGY AS % OF USEFUL SOLAR ENERGY 6.00 X

Current data (user

supplied values

plus default

values) are listed.

ENERGY REQUIREMENTS DATA

9 DOMESTIC HOT WATER USAGE 80.00 GALLONS/DAY

10 BUILDING USE SCHEDULE 7.00 DAYS/WEEK

11 MONTHLY SPACE HEATING LOADS - MMBTU/MONTH

JAN - 21.12 JUL - .22 FEB - 17.30 AUG - .41 MAR - 14.84 SEP - 3.02 APR - 7.93 OCT - 6.76 MAY - 4.06 NOV - 13.00 JUN - 1.47 DEC - 18.38

ENVIRONMENTAL DATA

12 AVERAGE DAILY HORIZONTAL RADIATION - BTU/SQFT-DAY

JAN - 466.00 JUL - 2183.00

FEB - 775.00 AUG - 1876.00 MAR - 1168.00 SEP - 1354.00 APR - 1459.00 OCT - 907.00 MAY - 1848.00 NOV - 507.00

JUN - 2059.00 DEC - 372.00

AVERAGE GROUND WATER TEMPERATURES - DEGREES

DEC - FEB = 33.0 MAR - MAY = 33.0 JUN - AUG = 56.0

SEP - NOV = 51.0

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

***************** life cycle cost data *************** ********************************************************

BASE YEAR INVESTMENT COSTS

10270.00 $

17.78 $/SQFT

10.00 X .00 $ .00 $

30 SOLAR ENERGY INVESTMENT - FIXED COST

31 SOLAR ENERGY INVESTMENT - VARIABLE COST

32 INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)

33 INVESTMENT COST FOR AUXILIARY SYSTEM

34 INVESTMENT COST FOR REFERENCE NONSOLAR SYSTEM

67
FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40 ANNUALLY RECURRING O&M COST (% OF SYSTEM COST) I • 00 %

41 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 42 SALVAGE VALUE AT END OF STUDY PERIOD .00 X

AUXILIARY SYSTEM

44 ANNUALLY RECURRING O&M COST .00

45 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 46 SALVAGE VALUE AT END OF STUDY PERIOD .00

REFERENCE NON-SOLAR SYSTEM

47 ANNUALLY RECURRING O&M COST .00 48 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 49 SALVAGE VALUE AT END OF STUDY PERIOD .00

FUEL COSTS

50 ELECTRICITY PRICE IN BASE YEAR

51 DISTILLATE OIL PRICE IN BASE YEAR

52 RESIDUAL OIL PRICE IN BASE YEAR

53 NATURAL GAS PRICE IN BASE YEAR

54 COAL PRICE IN BASE YEAR

55 LPG PRICE IN BASE YEAR

56 TYPE OF FUEL USED IN AUXILIARY SYSTEM

57 TYPE OF FUEL USED IN REFERENCE SYSTEM

DOE REGION = 8 58 ENERGY PRICE ESCALATION (% PER YEAR ABOVE INFLATION) - RESIDENTIAL

TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9 YRS

ELECTRICITY 5.29 -3.87 -3.06

DISTILLATE OIL 2.54 2.54 6.31

RESIDUAL OIL .00 .00 .00 NATURAL GAS 8.89 .00 1.61 COAL .00 .00 .00 LPG 2.53 2.35 5.99

DISCOUNT RATE AND STUDY PERIOD

60 REAL DISCOUNT RATE (EXCLUDES INFLATION)

61 STUDY PERIOD

7.00 % 20.00 YEARS

16.35 $/MMBTU

9.48 $/MMBTU

.00 $/MMBTU

4.00 $/MMBTU

.00 $/MMBTU

9.44 $/MMBTU

1.00

1.00

$

$

$

$

ANALYSIS OUTPUT

70 1=STANDARD; 2=EXTENDED; 3=SUMMARY 1.00

COMMAND: N=NEW, 0=0LD, L=LIST, C=CHANGE, R«RUN, S=SAVE, Q«=QUIT, H=HELP ? C

LINE NUMBER ? 6

6 OPERATING EFFICIENCY OF AUXILIARY SYSTEM

CURRENT VALUE = 60 % NEW VALUE = ? 100

Input data for

operating efficien

cies of auxiliary

and reference sys68 tems are changed.
LINE NUMBER ? 7

7 OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM

CURRENT VALUE = 60 % NEW VALUE = ? 100

LINE NUMBER ? 45

AUXILIARY SYSTEM REPLACEMENT COST AND YEAR

ENTER SIX VALUES, COST, YEAR, ETC.

? 1250,15,0,0,0,0

LINE NUMBER ? 48

REFERENCE NON-SOLAR SYSTEM

REPLACEMENT COST AND YEAR

ENTER SIX VALUES, COST, YEAR, ETC.

? 1500,8,1500,18,0,0

LINE NUMBER ?

COMMAND: N-NEW, 0=0LD, L-LIST, C“CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP ? R

* NET SAVINGS = $ -7488 * AREA = 269 SQFT * SOLAR FRACTION - .316 *

***************************************************:&

************** THERMAL & ECONOMIC ANALYSIS ************** *********************************************************

BISMARCK, ND SYSTEM TYPE = 19

SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES

AREA

(SQFT)

SOLAR FRACTION NET SAVINGS

100.0 .15 $ -8118.

150.0 .20 $ -7766.

300.0 .34 $ -7501.

400.0 .41 $ -7729.

550.0 .50 $ -8465.

750.0 .60 $ -10003.

1000.0 .69 $ -12517.

1350.0 .78 $ -16800.

2000.0 .89 $ -26135.

4000.0 .99 $ -59701.

THERMAL PERFORMANCE

COLLECTOR AREA - 269.00 SQFT TILT ANGLE = 56.46 DEGREES

SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL

TRACTION HORZ RAD. COLLECTOR LOAD LOAD SOLAR

(1) (1) (2) (2) (2)

JAN .146 466.00 978.51 21.12 2.00 3.38 FEB .212 775.00 1323.48 17.30 1.80 4.04 MAR .296 1168.00 1522.68 14.84 2.00 4.99

The Run command

is given.

69
APR .433 1459.00 1436.03 7.93 1.93 4.27 MAY .668 1848.00 1541.13 4.06 2.00 4.04 JUN .939 2059.00 1589.97 1.47 1.47 2.76 JUL 1.000 2183.00 1739.39 .22 1.52 1.74

AUG 1. 000 1876.00 1747.98 .41 1.52 1.93 SEP .783 1354.00 1592.03 3.02 1.57 3.60

OCT .503 907.00 1428.37 6.76 1.63 4.22

NOV .219 507.00 976.00 13.00 1.57 3.19

DEC .137 372.00 805.09 18.38 2.00 2.79 YEAR .316 108.51 21.02 40.97

(1) - BTU/SQFT-DAY

(2) - MMBTU/MONTH

LIFE CYCLE COST SUMMARY

OPTIMAL COLLECTOR AREA - 269.00 SQFT

OPTIMAL SOLAR FRACTION - .316

SOLAR ENERGY

SYSTEM AUXILIARYSYSTEM

REFERENCE

SYSTEM

INVESTMENT (ADJ) $ 13548. $ 0. $ 0.

FUEL $ 433. $ 15615. $ 22839.

O&M $ 1595. $ 0. $ 0.

REPLACEMENTS $ 0. $ 453. $ 1317.

SALVAGE $ 0. $ 0. $ 0.

TOTAL LCC $ 15576. $ 16068. $ 24156.

MEASURES OF ECONOMIC PERFORMANCE

TOTAL LCC WITHOUT SOLAR - $ 24156.

TOTAL LCC WITH SOLAR » $ 31643. NET SAVINGS - $ -7488.

SIMPLE PAYBACK TIME SB 23.91 YEARS

SAVINGS TO INVESTMENT RATIO - .410

70
Case 5. This case shown an economic analysis only of a residential system for

space heating in Bismarck, N.D. A new file is established with thermal

analysis data from another source (F-CHART 3.0).

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE. Q-QUIT, H-HELP ? N

ENGLISH OR SI UNITS (E OR SI) ? E

PERFORMANCE ANALYSIS USING SLR METHOD (Y OR N)? N

ENTER CITY ID NUMBER? 132

RESIDENTIAL**! ; COMMERCIAL-2; INDUSTRIAL-3 ? 1

The user is queried

for the minimum

data required to

perform an economic

analysis only.

THE FOLLOWING DATA ITEMS REPRESENT THE MINIMUM INFORMATION

REQUIRED TO CREATE A USEABLE INPUT DATA FILE. ADDITIONAL

CHANGES CAN BE MADE BY THE CHANGE COMMAND.

ANNUAL ENERGY LOAD ANNUAL SOLAR FRACTION

COLLECTOR AREA

MMBTU/YEAR - ? 162.78

X “ ? 27.5

SQFT - 7 350

SOLAR ENERGY INVESTMENT - FIXED COST

SOLAR ENERGY INVESTMENT - VARIABLE COST

$ - ? 10270

S/SQFT - ? 17.78

TYPES OF FUELS USED IN AUXILIARY AND REFERENCE SYSTQ1S

1 - ELECTRIC

2 - DISTILLATE OIL

3 - RESIDUAL OIL

4 - NATURAL GAS

5 - COAL

6 = LPG

TYPE OF FUEL USED IN AUXILIARY SYSTEM

TYPE OF FUEL USED IN REFERENCE SYSTEM

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, QM)UIT, H-HELP ? L

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

***************** ENERGY ANALYSIS DATA *************** ********************************************************

The current data

are listed.

DATA FOR ECONOMIC ANALYSIS ONLY

20 ANNUAL ENERGY LOAD

21 ANNUAL SOLAR FRACTION

22 COLLECTOR AREA

23 OPERATING EFFICIENCY OF AUXILIARY SYSTEM

24 OPERATING EFFICIENCY OF REFERENCE SYSTEM

25 ELECTRICAL ENERGY AS % OF USEFUL SOLAR ENERGY

162.78 MMBTU/YEAR

27.50 X 350.00 SQFT

60.00 X 60.00 X 6.00 X ********************************************************

***************** life cycle cost data *************** ********************************************************

base year investment costs

10270.00 $

17.78 $ / SQFT

10.00 X .00 $ .00 $

30 SOLAR ENERGY INVESTMENT - FIXED COST

31 SOLAR ENERGY INVESTMENT - VARIABLE COST

32 INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)

33 INVESTMENT COST FOR AUXILIARY SYSTEM

34 INVESTMENT COST FOR REFERENCE NONSOLAR SYSTEM

71
FUTURE NON-FUEL COSTS

SOLAR ENERGY SYSTEM

40 ANNUALLY RECURRING O&M COST (% OF SYSTEM COST) I. 00 Z

41 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 42 SALVAGE VALUE AT END OF STUDY PERIOD .00 Z

AUXILIARY SYSTEM

44 ANNUALLY RECURRING O&M COST

45 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 46 SALVAGE VALUE AT END OF STUDY PERIOD

REFERENCE NON-SOLAR SYSTEM

47 ANNUALLY RECURRING O&M COST

48 REPLACEMENT COST AND YEAR

$ 0 AT YEAR 0

$ 0 AT YEAR 0

$ 0 AT YEAR 0 49 SALVAGE VALUE AT END OF STUDY PERIOD

FUEL COSTS

50 ELECTRICITY PRICE IN BASE YEAR

51 DISTILLATE OIL PRICE IN BASE YEAR

52 RESIDUAL OIL PRICE IN BASE YEAR

53 NATURAL GAS PRICE IN BASE YEAR

54 COAL PRICE IN BASE YEAR

55 LPG PRICE IN BASE YEAR

56 TYPE OF FUEL USED IN AUXILIARY SYSTEM

57 TYPE OF FUEL USED IN REFERENCE SYSTEM

DOE REGION - 8 58 ENERGY PRICE ESCALATION (Z PER YEAR ABOVE INFLATION) - RESIDENTIAL

TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9

' ELECTRICITY 5.29 -3.87 -3.06

DISTILLATE OIL 2.54 2.54 6.31

RESIDUAL OIL .00 .00 .00 NATURAL GAS 8.89 .00 1.61 COAL .00 .00 .00 LPG 2.53 2.35 5.99

16.35 $/MMBTtl

9.48 $/MMBTU

.00 $/MMBTO

4.00 $/MMBTU

.00 $/MMBTU

9.44 $/MMBTU

2.00

2.00

.00 $

.00 $

.00 $

.00 $

DISCOUNT RATE AND STUDY PERIOD

60 REAL DISCOUNT RATE (EXCLUDES INFLATION) 7.00 Z

61 STUDY PERIOD 20.00 YEARS

ANALYSIS OUTPUT

70 1=STANDARD; 2=EXTENDED; 3-SUMMARY 1.00

72
COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP T 1

* NET SAVINGS - $ -6786 * AREA - 350 SQFT * SOLAR FRACTION - .275 * No changes are

********************************************************* made. The Run

********************************************************* command is given.

BISMARCK, ND

LIFE CYCLE COST SUMMARY

TOTAL ANNUAL LOAD - 162.78 MMBTU/YEAR

COLLECTOR AREA - 350.00 SQFT

SOLAR FRACTION - .275

SOLAR ENERGY AUXILIARY REFERENCE

INVESTMENT (ADJ)

SYSTEM

$ 14844.

SYSTEM

$ 0. SYSTEM

$ 0

FUEL $ 474. $ 27099. $ 37378

O&M $ 1747. $ 0. $ 0

REPLACEMENTS $ 0 . $ 0. $ 0

SALVAGE $ 0 . $ 0. $ 0

TOTAL LCC $ 17065. $ 27099. $ 37378

MEASURES OF ECONOMIC PERFORMANCE

TOTAL LCC WITHOUT SOLAR - $ TOTAL LCC WITH SOLAR - $ NET SAVINGS - $

37378.

44163.

-6786.

SIMPLE PAYBACK TIME 29.78 YEARS

SAVINGS TO INVESTMENT RATIO - .543

COMMAND: N-NEW, O-OLD, L-LIST, C-CHANGE, R-RUN, S-SAVE, Q-QUIT, H-HELP 7 Q

READY. BYE

73
REFERENCES

1. Ruegg, Rosalie T., Life-Cycle Costing Manual for the Federal Energy

Management Program (Washigton, D.C.: National Bureau of Standards, 1980),

NBS Handbook 135.

2. Solar Federal Buildings Program, Solar Design Workbook , Chapter 11,

"Life-Cycle Cost Evaluation of Solar Energy Investments," (Golden, CO.:

Solar Energy Research Institute and Los Alamos National Laboratory, 1981),

SERI/ SP-62-308.

3. 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 , (New York, NY: American Society of Mechanical Engineers, 1981).

4. "Federal Energy Management Programs; Methodology and Procedures for

Life-Cycle Cost Analyses," Federal Register , Rules and Regulations, Vol.

45, No. 16, January 23, 1980.

5. "Federal Energy Management Programs; Methodology and Procedures for

Life-Cycle Cost Analyses, Average Fuel Cost," Federal Register , Rules and

Regulations, Vol. 45, No. 196, 209, October 27, 1980.

6. "Federal Energy Management Programs; Methodology and Procedures for

Life-Cycle Cost Analyses," Federal Register , Rules and Regulations,

September 1981.

7. "Solar Federal Buildings Program Rules," Federal Register , Rules and

Regulations, No. 204, October 19, 1979.

8. Solar Federal Buildings Data Center, User^ Guide , National Bureau of

Standards. In Press.

9. Powell, Jeanne W., and Barnes, Kimberly A., Comparison of Economic

Evaluation Models in Selected Solar Energy Analysis Programs (Washington,

D.C., National Bureau of Standards, 1981). In Press.

10. Powell, Jeanne W., An Economic Model for Passive Solar Designs in

Commercial Environments (Washington, D.C.: U.S. Government Printing

Office, 1980). NBS Building Science Series 125.

11. Ruegg, Rosalie T., Sav, G. Thomas, Powell, Jeanne W., and Pierce,

Thomas E . , Economic Feasibility of Solar Heating and Hot Water for

Commercial Buildings (Washington, D.C.: National Bureau of Standards,

1981). In Press.

74
12 . Ruegg, Rosalie T., Petersen, Stephen R. , and Marshall, Harold E.,

Recommended Practices for Measuring Life-Cycle Costs of Buildings and

Building Systems (Washington, D.C.: National Bureau of Standards, 1980).

NBS Interagency Report 80-2040.

13. Ruegg, Rosalie T., and Sav, G. Thomas, "Microeconomics of Solar Energy,"

Chapter 28, Solar Energy Handbook , eds. Jan F. Kreider and Frank Kreith

(New York, NY: McGraw-Hill Book Company, 1981).

14. Ruegg, Rosilie T., McConnaughey, John S., Sav, Thomas G., and Hockenbery,

Kimberly A., Life-Cycle Costing (Washington, D.C.: U.S. Government

Printing Office, 1978). NBS Building Science Series 113.

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

Program CEED0-TR-77-35/CERL-TR-E-119/ADA048734 (U.S. Army Construction

Engineering Research Laboratory [CERL], December 1977).

16. D0E-2 Reference Manual (Version 2.1), eds. D.A. York and E.F. Tucker

(Berkeley, CA and Los Alamos, NM: Lawrence Berkeley Laboratory and Los

Alamos National Laboratory, 1980), LBL-8706 Rev. 1 and LA-7689-M. Ver. 2.1.

17. Solar Federal Buildings Program, Solar Design Workbook , Chapter 8,

"Building Loads, Energy Requirements, and Characteristics" (Golden, CO:

Solar Energy Research Institute and Los Alamos National Laboratory, 1981),

SERI/ SP-62-308

18. Kusuda, Tamami, and Saitoh, T., Simplified Heating and Cooling Energy

Analysis Calculations for Research Applications (Washington, D.C.:

National Bureau of Standards, 1980). NBS Interagency Report 80-1961.

19. Department of Energy, DOE Facilities Solar Design Handbook (Washington,

D.C.: U.S. Government Printing Office, 1978). D0E/AD-0006/1

20. Solar Federal Buildings Program, Solar Design Workbook , Chapter 10,

"Active System Design and Sizing Methods" (Golden, CO: Solar Energy

Research Institute and Los Alamos National Laboratory, 1981) SERl/SP-62-

308.

21. Energy Research and Development Administration, San Francisco Operations

Office, ERDA* s Pacific Regional Solar Heating Handbook , 2nd edition.

Available from Superintendent of Documents, Washington, D.C., Stock No.:

060-000-00024-7.

22. Cinquemani, V., Owenby Jr., J.R., and Baldwin, R. G., Input Data for Solar

Systems (Asheville, NC: National Climatic Center, 1978).

23. Freeman, T.L., Maybaum, M.W., and Chandra, S., "A Comparison of Four Solar

System Simulation Programs in Solving a Solar Heating Problem," Conference

on Systems Simulation and Economic Analysis for Solar Heating and Cooling,

June 27-29, 1978, San Diego, CA (Washington, D.C.: U.S. Department of

Energy, 1978).

75
24. State of Florida Department of General Services, Division of Construction

and Maintenance, Florida State A/E Guide (Tallahassee, FL, June 1973) [Fee

schedules for engineering and architectural services 1977 update].

25. Roach, Fred, Noll, Scott, and Ben-David, Shaul, "Passive and Active

Presidential Solar Heating: A Comparative Economic Analysis of Select

Designs," Energy: The International Journal (London: The Pergamon Press,

August, 1979).

26. "Federal Energy Management Programs; Methodology and Procedures for

Life-Cycle Cost Analyses," Federal Register , Marginal Prices and Adjustments, Vol. 45, No. 196, October 7, 1980.

27. U.S. Office of Management and Budget, Circular A-94 , "Discount Rate To Be

Used in Evaluating Time-Distributed Costs and Benefits," March 27, 1972.

28. Energy Security Act of 1980, Public Law 96-294, Sec. 405, 96th Congress,

94 Stat. 611.

29. Marshall, Harold E., and Ruegg, Rosalie T., Simplified Energy Design

Economics (Washington, D.C.: U.S. Government Printing Office, 1980). NBS

Special Publication 544.

30. Klein, S.A., "Calculation of Monthly Average Insolation on Tilted Surfaces,

Solar Energy , Vol. 19 (London: Pergamon Press, 1977).

31. Lameiro, Gerald F., and Bendt, Paul, The GFL Method for Sizing Solar

Energy Space and Water Heating Systems (Golden, CO: Solar Energy

Research Institute, 1978), SERI-30.

76
APPENDICES

APPENDIX A - FEDSOL PROGRAM CODE

00100 REM

00110 REM

00120 REM

00130 REM

00140 REM

00150 REM

00160 REM

00170 REM

00180 REM

00190 REM

00200 REM

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

************************* FEDSOL *********************************** *********************************************************************

SPONSOR: NATIONAL BUREAU OF STANDARDS

CENTER FOR BUILDING TECHNOLOGY

APPLIED ECONOMICS GROUP WASHINGTON D.C. VERSION 1.0 MARCH 1981

00210 REM AUTHOR: RICHARD C. RODGERS JR. 00220 REM

00230 REM DESCRIPTION: THE PROGRAM ANALYZES THE PERFORMANCE OF A STANDARD

00240 REM

00250 REM

00260 REM

00270 REM

00280 REM

00290 REM

00300 REM

00310 REM

00320 REM nnnn rfm

SOLAR ENERGY SYSTEM ON A FEDERAL BUILDING. THE PROGRAM

WILL DETERMINE THE COLLECTOR AREA WHICH RESULTS IN THE LOWEST LIFE CYCLE COST AND PERFORM AN ECONOMIC

ANALYSIS OF THIS OPTIMAL AREA OR OTHER SPECIFIED AREA. AN ALTERNATIVE MODE WILL ACCEPT THE THERMAL RESULTS

FROM ANY OTHER SOLAR PERFORMANCE ANALYSIS (FOR NONSTANDARD SYSTEM TYPES) AND PERFORM AN ECONOMIC ANALYSIS

CONFORMING TO THE FEDERAL RULES.

00340 REM

00350 REM MAIN LEVEL

00360 REM

00370 GOSUB 00710

00380 PRINT " FEDSOL - VERSION 1.0 ***" 00390 PRINT " NATIONAL BUREAU OF STANDARDS"

00400 PRINT

00410 PRINT "COMMAND: N=NEW, 0=OLD, L=LIST, C-CHANGE, R-RUN, S«=SAVE,";

00420 PRINT " Q=QUIT, H=HELP

00430 ON ERROR GOTO 00410

00440 INPUT X$

00450 ON ERROR

00460 IF X$ = "N" THEN 00550

00470 IF X$ = "0" OR X$ = "0" OR X$ = "F" THEN 00570

00480 IF X$ *= "C" THEN 00590

00490 IF X$ = "L" THEN 00610

00500 IF X$ = "R" THEN 00630

00510 IF X$ = "H" THEN 00650

00520 IF X$ = "S" THEN 00670

00530 IF X$ = "Q" THEN 00690

00540 GOTO 00410

00550 GOSUB 01010 ' CREATE NEW INPUT FILE

00560 GOTO 00400

00570 GOSUB 02580 ' GET OLD INPUT FILE

00580 GOTO 00400

00590 GOSUB 03010 ' CHANGE INPUT FILE DATA

00600 GOTO 00400

00610 GOSUB 08800 ' LIST CURRENT INPUT FILE 00620 GOTO 00400

00630 GOSUB 04410 ' RUN CURRENT INPUT FILE

00640 GOTO 00400

00650 GOSUB 00870 ' PRINT "HELP" INSTRUCTIONS

00660 GOTO 00400

00670 GOSUB 06170 ' SAVE CURRENT INPUT FILE

00680 GOTO 00400

00690 STOP ' STOP PROGRAM OPERATION

00700 GOTO 00400

A1
00710

00720

00730

00740

00750

00760

00770

00780

00790

00800

00810

00820

00830

00840

00850

00860

00865

00870

00880

00890

00900

00910

00920

00930

00940

00950

00960

00970

00980

00990

01000

01010

01020

01030

01040

01045

01050

01060

01070

01080

01090

01100

01105

OHIO

01120

01130

01140

01150

01160

01165

01170

01180

01190

01200

01210

01215

01220

01230

01240

01250

01260

01270

01280

01290

01300

01310

*********************** DIMENSION *********************************** MARGIN #0,80

Z9 = 0 L$ » "THERE IS NO CURRENT INPUT DATA FILE. USE NEW OR OLD COMMAND TO GET ONE." OPTION BASE 1 DIM Y(12),X(12),K(12),I(19),B(40),V(40) DIM A(12),U(12),P(12) DIM N(12) ,S(12) DIM C(19,4),Q(12),G(12) DIM D$(70),U$(70),D(70) DIM L(12),M$(12),R(20)

DIM E(6,3),H(12),T(70,2) DIM F(6,10),J(12),Z(12) DIM 0(50) DIM A$(100) RETURN

JUMP (ESL(X)-20) REM ********************* INSTRUCTIONS **********************************

FILE #1 = "INSTRUC"

RESTORE #1 MARGIN #0,100

MARGIN #1,100 PRINT

PRINT

IF END#1 THEN 00990 DELIMIT #1 , (CR) INPUT # 1 , A$ ( 1

)

PRINT A$ ( 1

)

GOTO 00940

CLOSE #1 RETURN

REM *********************** DATA INPUT ***********************************

Z9 = 1 PRINT

PRINT "ENGLISH OR SI UNITS (E OR SI)"; ON ERROR GOTO 1040 INPUT U$

IF U$= "E" THEN 01090

IF U$= "SI" THEN 01090 GOTO 01030 PRINT

PRINT "PERFORMANCE ANALYSIS USING SLR METHOD (Y OR N)"; ON ERROR GOTO 1100 INPUT M$

IF M$ » "Y" THEN 01150

IF M$ = "N" THEN 01150

GOTO 01100 PRINT

PRINT "ENTER CITY ID NUMBER";

ON ERROR GOTO 1160 INPUT C9

IF C9 <= 0 THEN 01160

IF C9 > 243 THEN 01160 PRINT

PRINT "RESIDENTIAL=l;COMMERCIAL=2; INDUSTRIAL’S";

ON ERROR GOTO 1210 INPUT SI IF SI = 1 THEN 01270

IF SI = 2 THEN 01270

IF SI = 3 THEN 01270 GOTO 01210

FILE #2 = "DEFALT 1" RESTORE #2 MAT INPUT #2 ,D FILE #3 = "DATA" RESTORE #3

A2
01315

01320

01330

01340

01350

01360

01370

01380

01390

01400

01410

01420

01430

01440

01450

01460

01470

01480

01430

01500

01510

01520

01530

01540

01550

01560

01570

01580

01590

01600

01610

01620

01630

01640

01650

01660

01670

01680

01690

01700

01710

01720

01730

01740

01750

01760

01770

01780

01790

01795

01800

01810

01820

01830

01840

01850

01860

01865

01870

01880

01890

01900

ON ERROR

FOR I - 1 TO C9 INPUT #3,Y3,X1,C$,S$,L1,R1,J8,N1,N2,N3,N4

INPUT #3,Y3 MAT INPUT #3,H NEXT I CLOSE #2

CLOSE #3 FILE #4 = "PRICE" RESTORE #4 FOR J « 1 TO 3 MAT INPUT #4,

IF J <> SI THEN 01470

FOR I =* 1 TO 6 D(49+I) - F(I,R1) NEXT I NEXT J FOR K * 1 TO 3 FOR J 1 TO 3 MAT INPUT #4,F

IF J <> SI THEN 01550

FOR I = 1 TO 6 E(I,K) - F(I,R1) NEXT I NEXT J NEXT K CLOSE #4

D(2) = LI + 10 GOSUB 10220 REM

IF U$*= "E" THEN 01640

GOSUB 13060 REM

FOR M = 1 TO 12 L(M) = 0 K(M) = 0 NEXT M

FOR I - 1 TO 18 R(I) - 0 NEXT I PRINT

PRINT PRINT "THE FOLLOWING DATA ITEMS REPRESENT THE MINIMUM INFORMATION" PRINT "REQUIRED TO CREATE A USEABLE INPUT DATA FILE. ADDITIONAL"; PRINT "CHANGES CAN BE MADE BY THE CHANGE COMMAND."

PRINT

PRINT

IF M$ = "N" THEN 02500 PRINT D$ (1 ) ;TAB(65) ; " - ON ERROR GOTO 1790 INPUT D ( 1

)

IF D ( 1 ) => T ( 1 , 1 ) AND D (1 ) <= T(l,2) THEN 01840 PRINT D$ GOTO 01790 PRINT

PRINT "ENTER LOAD TYPE: 1-WATER HTG. 2-SPACE HTG. 3-BOTH"; PRINT TAB (65)

"; ON ERROR GOTO 1850 INPUT J ON J GOTO 01900,02000,01900

GOTO 01870 PRINT

A3
01910

01920

01925

01930

01940

01950

01960

01970

01980

01990

02000

02010

02020

02030

02035

02040

02050

02060

02070

02080

02090

02100

02110

02115

02120

02130

02140

02150

02160

02170

02180

02190

02200

02210

02220

02230

02235

02240

02250

02260

02265

02270

02280

02290

02300

02310

02320

02330

02340

02350

02360

02370

02380

02390

02400

02410

02420

02430

02440

02450

02460

02470

02480

02490

FOR I = 9 TO 10 PRINT D$(I )

; TAB (52) ;U$(I) ; TAB (65) ; " - ON ERROR GOTO 1920 INPUT D(I)

IF D(I) -> T (I , 1 ) AND D(I) <« T(I,2) THEN 01970 PRINT D$

GOTO 01920

NEXT I PRINT

IF J - 1 THEN 02100 PRINT PRINT "MONTHLY SPACE HEATING LOADS";TAB(52);U$(ll)

FOR I *= 1 TO 12 PRINT M$ (I ON ERROR GOTO 2030 INPUT L (I

)

IF L(I) -> 0 AND L(I) <- 1E7 THEN 02080 PRINT D$

GOTO 02030 NEXT I PRINT

FOR I = 30 TO 31 PRINT D$(I) ;TAB(52) ;U$(I) ; TAB (65) ON ERROR GOTO 2110 INPUT D (I

)

IF D(I) => T(I , 1 ) AND D(I) <= T(I,2) THEN 02160 PRINT D$

GOTO 02110 NEXT I PRINT

PRINT "TYPES OF FUELS USED IN AUXILIARY AND REFERENCE SYSTOiS"

PRINT "1 = ELECTRIC"

PRINT "2 = DISTILLATE OIL" PRINT "3 = RESIDUAL OIL" PRINT "4 = NATURAL GAS" PRINT "5 = COAL" PRINT "6 = LPG" PRINT

FOR I = 56 TO 57 PRINT D$(I) ; TAB (52) ;U$(I) ; TAB (65) ;" - ON ERROR GOTO 2260

INPUT D (I

)

IF D(I) => T(I, 1) AND D(I) <= T(I,2) THEN 02310

PRINT D$ GOTO 02260

NEXT I PRINT

B ( 1 ) = N

B (2 ) = N2

B(3) = N3

B (4) = N4 FOR I = 1 TO 4 IF U$ = "E" THEN 02420

IF B( I ) => (5/9) THEN 02440

B (I ) = (5/9)

GOTO 02440

IF B(I) => 33 THEN 02440

B ( I ) = 33 NEXT I N 1 = B ( 1

)

N2 = B(2)

N3 = B(3) N4 = B (4) RETURN

U

A4
02500

02510

02515

02520

02530

02540

02550

02560

02570

02580REM

02590

02600

02610

02615

02620

02625

02630

02640

02650

02660

02670

02680

02690

02700

02710

02720

02730

02740

02750 REM

02760

02770

02780

02790

02800

02810

02820

02830

02840

02850

02860

02870

02880

02890

02895

02900

02910

02920

02930

02940

02950

02980

02990

03000

03010 REM

03020

03030

03040

03050

03060

03070

03080

03090

03100

FOR I * 20 TO 22 PRINT D$(I) ;TAB(52) ;U$(I) ; TAB (65)

ON ERROR GOTO 2510 INPUT D (I

)

IF D(I) -> T (I,

) AND D(I) <- T(I,2) THEN 02560

PRINT D$ GOTO 02510 NEXT I GOTO 02090 ************************ GET OLD ENTRY ****************************

Z9 - 1 PRINT

PRINT "ENTER NAME OF DESIRED FILE »>";

ON ERROR GOTO 2950 INPUT F$ ON ERROR

IF LEN(F$) > 7 THEN 02720

FOR I - 1 TO LEN(F$) A = ORD(F$(I: I)) IF ( A«>48 AND A<-57 ) OR ( A->65 AND A<«90 ) THEN 02680

GOTO 02720 NEXT I CALL PF ( "GET" , F $ , F $

,

"RRC"

,

K, "NA"

,

J ) I - INT(K)

IF I * 0 THEN 02740 PRINT "FILE NAME *** ";F$;" *** IS INVALID. TRY AGAIN!"

GOTO 02610

#1 INPUT DATA «««««««««

FILE #1 - F$

»»»»»»>> READ FILE

ON ERROR GOTO 02980 MAT READ #1,D MAT READ #1,H MAT READ #1,L READ #1,N1,N2,N3,N4 MAT READ #1,R MAT READ 4»1,E READ #1,R1,L1,S1,J8

READ #1,C$,S$,M$,U$

CLOSE #1 ON ERROR

GOSUB 10220 PRINT

PRINT" ENGLISH OR SI UNITS (E OR SI)"; ON ERROR GOTO 2890 INPUT U$

IF U$ = "E" THEN 02950

IF U$= "SI" THEN 02940

GOTO 02890 GOSUB 13060 RETURN PRINT "DATA IN ";F$;" IS INVALID" CLOSE ifl GOTO 02610

* ************************ edit *************************************

IF Z9 = 1 THEN 03050 PRINT L$ RETURN

PRINT

PRINT "LINE NUMBER";

ON ERROR GOTO 04400

INPUT X

ON ERROR

P - X

A5
03110

03120

03130

03140

03150

03160

03170

03180

03190

03200

03210

03220

03230

03240

03250

03260

032 70 03280

03285

03290

03300

03310

03320

03330

03340

03350

03360

03370

03380

03390

03395

03400

03410

03420

03430

03440

03450

03460

03470

03480

03490

03495

03500

03510

03520

03530

03540

03550

03560

03570

03580

03585

03590

03600

03610

03620

03630

03640

03645

03650

03660

03670

03680

03690

03700

IF X >= 0 THEN l04400

IF X <> INT(X) THEN 03050

IF X < 1 OR X :> 70 THEN 03050

IF X => 1 AND :X «= 10 THEN 133280

IF X *= 11 THEN 03360

IF X = 12 THEN 03460

IF X *= 13 THEN 03560

IF X => 20 AND X <- 25 THEN 03280

IF X «> 30 AND X <« 34 THEN 03280

IF X “> 40 AND X <= 42 THEN 03820

IF X => 44 AND X <« 46 THEN 03980

IF X => 47 AND X <» 49 THEN 04140

IF X => 50 AND X <- 57 THEN 03280

IF X - 58 THEN 04300

IF X *=> 60 AND X <= 61 THEN 03280

IF X - 70 THEN 03280

GOTO 03050 PRINT P;" ";D$(P)

II - D(P) PRINT "CURRENT VALUE = ";D(P);" ";U$(P>;" NEW VALUE - ON ERROR GOTO 3290 INPUT D(P)

IF D(P) «> T(P, 1) AND D(P) <- T(P,2) THEN 03050 PRINT D$

D(P) = II GOTO 3285 PRINT

PRINT "MONTHLY SPACE HEATING LOADS - U$(P)

FOR I = 1 TO 12 PRINT M$(I)

ON ERROR GOTO 3390 INPUT L(I)

IF L(I) => 0 AND L(I) <= 1E7 THEN 03440 PRINT D$

GOTO 03390 NEXT I GOTO 03050 PRINT PRINT "AVERAGE DAILY HORIZONTAL RADIATION - U$(P) FOR I - 1 TO 12 PRINT M$(I)

ON ERROR GOTO 3490 INPUT H(I)

IF H(I) => 0 AND H (I ) <= 3E3 THEN 03540 PRINT D$

GOTO 03490 NEXT I GOTO 03050 PRINT PRINT "AVERAGE GROUND WATER TEMPERTURES - ";U$(P) PRINT M$(12) ; " TO M$(2);

ON ERROR GOTO 3580 INPUT N

IF U$ = "E" AND N1 => 33 AND N1 <= 212 THEN 03640

IF U$ = "SI" AND N 1 => 5/9 AND N1 <= 100 THEN 03640

PRINT D$

GOTO 03580 PRINT M$(3) ; " TO M$(5);

ON ERROR GOTO 3640 INPUT N2

IF U$ = "E" AND N2 => 33 AND N2 <» 212 THEN 03700

IF U$ = "SI" AND N2 => 5/9 AND N1 <- 100 THEN 03700

PRINT D$ GOTO 03640 PRINT M$(6) ; " TO M$(8);

A6
03705

03710

03720

03730

03740

03750

03760

03765

03770

03780

03790

03800

03810

03820

03830

03840

03850

03860

03870

03875

03880

03890

03900

03910

03920

03930

03940

03950

03960

03970

03980

03990

04000

04010

04020

04030

04035

04040

04050

04060

04070

04080

04090

04100

04110

04120

04130

04140

04150

04160

04170

04180

04190

04195

04200

04210

04220

04230

04240

04250

04260

04270

04280

04290

ON ERROR GOTO 3700 INPUT N3

IF U$ = "E" AND N3 => 33 AND N3 <= 212 THEN 03760

IF U$ = "SI" AND N3 => 5/9 AND N3 <=* 100 THEN 03760 PRINT D$

GOTO 03700 PRINT M$(9) ; " TO M$(ll);

ON ERROR GOTO 3760

INPUT N4

IF U$ = "E" AND N4 => 33 AND N4 <= 212 THEN 03050

IF U$ = "SI" AND N4 => 5/9 AND N4 <- 100 THEN 03050

PRINT D$ GOTO 03760 PRINT

PRINT "SOLAR ENERGY SYSTEM"

IF P = 41 THEN 03860 GOTO 03280 PRINT "REPLACEMENT COST AND YEAR - " PRINT "ENTER SIX VALUES, COST, YEAR, ETC."

ON ERROR GOTO 3870 INPUT R(1),R(2),R(3),R(4),R(5),R(6)

1$ = "NO ERROR"

FOR I = 1 TO 5 STEP 2 IF R(I ) => 0 AND R(I) <= 1E8 THEN 03920 ELSE 03930

IF R(I+1) => 0 AND R(I+1) <- D(61 ) THEN 03950 PRINT D$

1$ = "ERROR" NEXT I IF 1$ = "ERROR" THEN 03870

GOTO 03050 PRINT PRINT "AUXILIARY SYSTEM"

IF P - 45 THEN 04020 GOTO 03280 PRINT "REPLACEMENT COST AND YEAR”

PRINT "ENTER SIX VALUES, COST, YEAR, ETC."

ON ERROR GOTO 4030

INPUT R(7),R(8),R(9),R(10),R(11),R(12)

1$ *= "NO ERROR" FOR I = 7 TO 11 STEP 2 IF R(I) -> 0 AND R(I ) <« 1E8 THEN 04080 ELSE 04090

IF R(I+1) «> 0 AND R(I+1 ) <« D(61 ) THEN 04110

PRINT D$

1$ = "ERROR" NEXT I IF 1$ = "ERROR" THEN 04030

GOTO 03050 PRINT PRINT "REFERENCE NON-SOLAR SYSTEM"

IF P = 48 THEN 04180

GOTO 03280 PRINT "REPLACEMENT COST AND YEAR"

PRINT "ENTER SIX VALUES, COST, YEAR, ETC."

ON ERROR GOTO 4190 INPUT R(13 ) , R(14) , R(15) , R(16), R(17), R(18)

1$ = "NO ERROR"

FOR I - 13 TO 17 STEP 2 IF R(I) -=> 0 AND R (I ) <= 1E8 THEN 04240 ELSE 04250

IF R(I+1 ) => 0 AND R(I+1 ) <= D (61 ) THEN 04270 PRINT D$

1$ - "ERROR" NEXT I IF 1$ = "ERROR" THEN 04190

GOTO 03050

A7
04300

04310

04315

04320

04330

04340

04350

04360

04370

04375

04380

04390

04400

04410

04420

04430

04440

04450

04460

04470

04480

04490

04500

04510

04520

04530

04540

04550

04560

04570

04580

04590

04600

04610

04620

04630

04640

04670

04680

04690

04 700 04710

04720

04730

04740

04750

04 760 04770

04780

04790

04800

04810

04820

04830

04840

04850

04860

04870

04880

04890

04900

PRINT "ENERGY PRICE ESCALATION (X PER YEAR ABOVE INFLATION)"

PRINT "1-ELEC; 2-DIST OIL; 3-RES OIL; 4-NAT GAS; 5-COAL; 6-LPG; O-FINISHED"

ON ERROR GOTO 4310

INPUT I IF I = 0 THEN 03050

IF I -> 1 AND I <- 6 THEN 04370 PRINT D$

GOTO 04310 PRINT "ENTER THREE VALUES: 1ST 4 YRS, NEXT 5 YRS, AFTER 9 YRS"

ON ERROR GOTO 4370 INPUT E(I,1),E(I,2),E(I,3)

GOTO 04310 RETURN

REM ************************** ANALYSIS***************************

IF Z9 - 1 THEN 04450 PRINT L$ RETURN

IF U$ = "E" THEN 04470

GOSUB 13490

J9 = D (1

)

X5 - 0 IF M$ - "N" THEN 06020 GOSUB 11700 GOSUB 08230

GOSUB 04800

IF D (3 ) = 2 THEN 04580

GOSUB 05750 GOSUB 05490

A5 = A9 GOTO 04590

A9 = D (4) GOSUB 12190 GOSUB 13800 GOSUB 14410

C5 = C9

F5 = F9 GOSUB 15130

IF D (70) = 1 THEN 04750

IF D(3) = 2 THEN 04710

A9 = A5 GOTO 04720

A9 = D (4) GOSUB 12190 GOSUB 13800 GOSUB 14410

IF U$ = "E" THEN 04770

GOSUB 13060

IF D (70) = 3 THEN 04790

GOSUB 06660 RETURN

REM

VI = C(J8, 1) V2 = C(J8, 2) V3 = C(J8,3)

V4 - C(J8,4)

V5 = 1.4 REM

REM

IF J9

IF J9

IF J8

CALCULATE TEN SOLAR FRACTIONS FOR 10 EVENLY

AREAS FROM .1 TO .95 AND DETERMINE TOTAL LCC

» 19 THEN 05020

> 12 THEN 05000

> 1 THEN 04930

SPACED COLLECTOR

FOR EACH.

A8
04910 E - 1E6*X9*L0G(2*C(1,3))/(C(1,4)*Z8)

04920 GOTO 05040

04930 A - -.5*(V1*(V2~2)*EXP(-V2*V5) + V3*(V4~2)*EXP(-V4*V5)

)

04940 B - V1*V2*EXP(-V2*V5) + V3*V4*EXP(-V4*V5)

04950 C - .5 - V1*EXP(-V2*V5) - V3*EXP(-V4*V5)

04960 V6 - (-B + SQR((B~2)-4*A*C))/(2*A)

04970 V7 - V6 + V5

04980 E - 1E6*X9*V7/Z8

04990 GOTO 05040

05000 J7 - J9 + 1 05010 GOTO 05030

05020 J7 - 15 05030 E - 1E6*X(3)/(2*C(J7,2)*Z(3)*N(3))

05040 A1 - E 05050 A9 - A1 05060 GOSUB 12190

05070 FI- F9

05080 A2 - 8*A1

05090 A9 - A2

05100 GOSUB 12190

05110 F2 - F9

05120 GOSUB 13800

05130 Cl « ( A2* ( -LOG ( 1 —F 1 ) ) - Al*(-LOG(l-F2) ) ) / (A2*Ai*2 - A1*A2~2)

05140 C2 - ((Al~2)*(-LOG(l-F2)) - (A2~2)*(-L0G(1-F1)) ) / (A2*A1~2 - A1*A2*2)

05150 IF A1 <- 50 THEN 05220

05160 IF A1 <- 100 THEN 05240

05170 IF A1 <- 200 THEN 05260

05180 IF A1 <- 500 THEN05280

05190 IF A1 <- 5000 THEN 05300

05200 R9 - 100 05210 GOTO 05310

05220 R9 - 1 05230 GOTO 05310

05240 R9 - 5 05250 GOTO 05310

05260 R9 - 10 05270 GOTO 05310

05280 R9 - 25 05290 GOTO 05310

05300 R9 - 50 05310 FOR F - 1 TO 9 05320 C3 - LOG( 1-(F/10)

)

05330 A(F) - (-C2+SQR((C2~2)-4*C1*C3)) / (2*C1)

05340 A(F) - R9*INT( (A(F) /R9)+. 5 ) 05350 A9 - A(F)

05360 GOSUB 12190

05370 P (F) - F9

05380 GOSUB 14410

05390 U (F) - C9

05400 NEXT F 05410 A( 10) - 2*A(9)

05420 A( 10) - R9*INT( (A(10)/R9)+.5 ) 05430 A9 - A( 10)

05440 GOSUB 12190

05450 P(10) - F9

05460 GOSUB 14410

05470 U(10) - C9

05480 RETURN

A9
05490 REM

05500 REM

05510

05520

05530

05540

05550

05560

05570

05580

05590

05600

05610

05620

05630

05640

05650

05660

05670

05680

05690

05700

05710

05720

05730

05740

05750 REM

05760 REM 05770 REM

05780

05790

05800

05810

05820

05830

05840

05850

05860

05870

05880

05890

05900

05910

05920

05930

05940

05950

05960

05970

05980

05990

06000

06010

06020 REM

06030 REM

06040

06050

06060

06070

06080

06090

06100

06110

06120

06130

06140

06150

06160

CALCULATE AREA FOR AREA CORRESPONDING TO MIN SOLAR FRACTION

IF F9 -=> D(5)/100 THEN 05720

X5 = 1 C3 = LOG (1-(D(5)/100))

A9 - (-C2+SQR( (C2'"2)-4*C1*C3) ) / (2*C1

)

GOSUB 12190

IF (F9*100) < (D(5)-.4) THEN 05590

IF (F9*100) > (D(5)+.4) THEN 05670 RETURN

A8 = A9

A9 = 1 • 1*A9 GOSUB 12190

IF (F9*100) < (D (5)-. 4) THEN 05590

IF (F9*100) > (D(5)+.4) THEN 05650 RETURN

A9 = (A8+A9) /2 GOTO 05610

A8 = A9

A9 = . 9*A9 GOSUB 12190

IF (F9*100) < (D (5 )-. 4) THEN 05730

IF (F9*100) > (D(5)+.4) THEN 05670 RETURN

A9 * (A84A9) /2 GOTO 05690

THE OPTIMAL COLLECTOR AREA WILL NOW BE FOUND

B 1 = 0 B2 = A( 10) G = (SQR(5)-l)/2 R = B2-B1

IF R <= 1 THEN 05990

T1 = B2 - R*G

T2 = B1 + R*G

A9 = T1 GOSUB 12190

GOSUB 14410

PI = C9

A9 «= T2 GOSUB 12190

GOSUB 14410

P2 = C9

IF P2 < PI THEN 05950

GOTO 05970

B2 = T2 GOTO 05810

B1 = T

GOTO 05810

AO = INT(Bl)

A9 = AO

RETURN

PERFORM ECONOMIC ANALYSIS ON NON-STARDARD ANALYSIS

X9 = D(20)

F9 = D (21 ) /100

A9 = D (22)

D (6) = D (23)

D (7 ) = D (24)

D(8) = D (25) GOSUB 13800 GOSUB 14410 GOSUB 15130

IF U$ = "E" THEN 06150 GOSUB 13060 GOSUB 06660 RETURN

A10
06170

06180

06190

06200

06210

06220

06225

06230

06240

06250

06260

06270

06280

06290

06300

06310

06320

06330

06340

06350

06360

06370

06380

06390

06400

06410

06420

06430

06440

06450

06460

06470

06480

06490

06500

06510

06520

06530

06540

06550

06560

06570

06560

06590

06600

06610

06620

06630

06640

06650

06660

06670

06680

06690

06700

06710

06720

06730

06740

06750

06760

06770

06780

06790

06800

06810

06820

06830

06840

06850

REM ************************* SAVE DATA **************************

IF Z9 = 1 THEN 06210 PRINT L$ RETURN

PRINT

PRINT "STORE DATA UNDER WHAT NAME";

ON ERROR GOTO 6650

INPUT X$

IF X$ = "FEDSOL" OR X$ - "DATA" THEN 06300

IF X$ = "DEFALT 1" OR X$ - "PRICE" THEN 06300

IF X$ - "INSTRUC" OR X$ - "SAMPLE" THEN 06300

GOTO 06320 PRINT "FILE NAME *** ";X$;" *** IS INVALID. TRY AGAIN!"

GOTO 06220 PRINT "FORBIDDEN NAME. USE ANOTHER NAME!"

GOTO 06220

IF LEN (X$) > 7 THEN 06280

FOR I = 1 TO LEN (X$) A = ORD(X$ (1:1))

IF ( A=>48 AND A<-57 ) OR ( A«>65 AND A<-90 ) THEN 06370

GOTO 06280 NEXT I FILE //I = X$

RESTORE #1 MAT WRITE 01, D MAT WRITE 01 ,H MAT WRITE 01 ,L WRITE 01,N1,N2,N3,N4 MAT WRITE 01, R MAT WRITE 01 , E WRITE 01,R1,L1,S1,J8

WRITE 01,C$,S$,M$,U$

CLOSE 01 CALL PF ( "SAVE" , X$ , X$ , "RRC" ,K1,"NA",J)

I = INT(Kl)

IF I » 0 THEN 06650

IF I • 5 THEN 06540

GOTO 06280

PRINT X$; " ALREADY EXISTS. DO YOU WISH TO USE THIS NAME (Y/N) "j ON ERROR GOTO 06650

INPUT Y$

ON ERROR

IF Y$ - :, N” THEN 06650

IF Y$ - "Y" THEN 06610

GOTO 06540 CALL PF ( "REPLACE" , X$ , X$ , "RRC" , K2 , "NA" , J

)

II - INT (K2) IF II - 0 THEN 06650

GOTO 06280 RETURN REM *********************** PRINT REPORT *******************************

IF M$ - "Y" THEN 06800 PRINT PRINT " *********************************************************"

PRINT " ****************** ECONOMIC ANALYSIS ******************"

PRINT " *********************************************************"

PRINT PRINT C$;", ";S$

PRINT " —

PRINT "LIFE CYCLE COST SUMMARY" PRINT PRINTUSING 06780, D(20),U$(20)

: TOTAL ANNUAL LOAD - ######.## <#########

GOTO 07320 PRINT

PRINT

PRINT " a********************************************************"

PRINT " ************** THERMAL & ECONOMIC ANALYSIS ***************

PRINT " a********************************************************"

PRINT

All
06860

06870

06880

06890

06900

06910

06920

06930

06940

06950

06960

06970

06980

06990

07000

07010

07020

07030

07040

07050

07060

07070

07080

07090

07100

07110

07120

07130

07140

07150

07160

07170

07180

07190

07200

07210

07220

07230

07240

07250

07260

07270

07280

07290

07300

07310

07320

07330

07340

07350

07360

07370

07380

07390

07400

07410

07420

07430

07440

07450

07460

07470

07480

07490

07500

07510

PRINT C$;", ";S$ PRINT "SYSTEM TYPE «";D(1) PRINT PRINT " PRINT "SOLAR FRACTION AND NS FOR A RANGE OF SYSTEM SIZES" PRINT

PRINT " AREA SOLAR FRACTION NET SAVINGS" PRINT " (";U$(4) PRINT

FOR I - 1 TO 10 PRINTUSING06970, A(I) ,P(I) ,U(I)

: ######.# #.«# $#######. NEXT I PRINT

PRINT

PRINT

PRINT "THERMAL PERFORMANCE"

PRINT PRINTUSING 07050, A9,U$(4),D(2)

: COLLECTOR AREA =* ######.## <###/#### TILT ANGLE - ##. ## DEGREES

PRINT PRINT " SOLAR AVG DAILY INCIDENT SPACE WATER USEFUL' PRINT " FRACTION HORZ RAD. COLLECTOR LOAD LOAD SOLAR" PRINT " (1) (1) (2) (2) (2)" PRINT

FOR M =* 1 TO 12 IF J9 < 13 THEN 07150

PRINTUSING 07160, M$(M) ,G(M) ,H(M) ,Z(M) ,L(M) ,K(M) ,Q(M) GOTO 07180

PRINTUSING 07170, M$(M) ,H(M) ,Z(M) ,L(M) ,K(M)

:<#### #.### ####.## ####.## ####.## ####.## ####.##

:<#### * ####.## ####.## ####.## ####.## * NEXT M

PRINTUSING 07200, F9,L9,K9,Q9

: YEAR #.### #######.## #####.## #######.*# PRINT

PRINT " (1) PRINT " (2) PRINT

PRINT

";U$(12)

”;U$(11)

PRINT " PRINT "LIFE CYCLE COST SUMMARY" PRINT

IF X5 ** 1 THEN 07320

IF D(3) » 1 THEN 07380

A9 = D (4) PRINTUSING 07330, A9,U$(4)

: COLLECTOR AREA - #########.## <########

PRINTUSING 07350, F9

: SOLAR FRACTION = #.### PRINT

GOTO 07430

PRINTUSING 07390, A5,U$(4)

; OPTIMAL COLLECTOR AREA - #######.## <#######

PRINTUSING 07410, F5

: OPTIMAL SOLAR FRACTION - #.### PRINT PRINTUSING 07590

PRINTUSING 07600 PRINT PRINTUSING 07610, "INVESTMENT (ADJ)",P6,D(33) ,D(34) PRINT PRINTUSING 07610, "FUEL", G3,G2,G1 PRINT PRINTUSING 07610, "O&M",M3, M2, Ml PRINT

A12
07520

07530

07540

07550

07560

07570

07580

07590

07600

07610

07620

07630

07640

07650

07660

07670

07680

07690

07700

07710

07720

07730

07740

07750

07760

07770

07780

07790

07800

07810

07820

07830

07835

07840

07850

07855

07860

07870

07880

07890

07900

07910

07920

07930

07940

07950

07960

07970

07980

07990

08000

08010

08020

08030

08040

08050

08060

08070

08080

08090

08100

08110

08120

08130

08140

08150

08160

08170

D8180

08190

PRINTUSING 07610, "REPLACEMENTS", H3,H2, HI PRINT

PRINTUS ING 07610," SALVAGE" , Z 3 , Z 2 , Z

PRINT PRINTUSING 07610, "TOTAL LCC" , J3, J2, J1 PRINT PRINT

: SOLAR ENERGY AUXILIARY

: SYSTEM SYSTEM

: <################ $#######. $#######. PRINT " PRINT "MEASURES OF ECONOMIC PERFORMANCE"

PRINT PRINTUSING 07680, J1 PRINTUSING 07690, J4

PRINTUSING 07700, C9

: TOTAL LCC WITHOUT SOLAR - $#########.

: TOTAL LCC WITH SOLAR = $#########.

: NET SAVINGS = $#########. PRINT

: SAVINGS TO INVESTMENT RATIO - ##.###

IF P8 -> 0 THEN 07760 PRINT "SIMPLE PAYBACK TIME - NEVER"

GOTO 07780

PRINTUSING 07770, P8

: SIMPLE PAYBACK TIME - ###.## YEARS

PRINT PRINTUSING 07720, R8 PRINT

IF D(70) = 1 THEN 08220 PRINT " PRINT "CASH FLOW ANALYSIS"

PRINT

PRINT " SIMPLE

PRINT " YEAR ANNUAL CUMULATIVE

PRINT

T2 - X8

T3 = X7 PRINTUSING 07930, 0,X8,T2,X7,T3

FOR Y - 1 TO N5 T2 - T2 + 0 (Y)

T3 - T3 + V(Y)

PRINTUSING 07930, Y,0(Y),T2,V(Y),T3

: ## $#######. $#########. $#######

NEXT Y PRINT

PRINT

IF C9 > 0 THEN 08220

IF D(3) - 2 THEN 08220

IF M$ » "N" THEN 08220

IF D(56) <> D(57) THEN 08220 PRINT " PRINT "BREAKEVEN ANALYSIS"

PRINT PRINTUSING 08050, A6,U$(4)

: OPTIMAL AREA - ######.## <#######

PRINTUSING 08070, F6

: SOLAR FRACTION - #.### PRINT PRINTUSING 08100, Q4,U$(50)

: BREAKEVEN FUEL PRICE - ###.###### <########

PRINT PRINTUSING 08130, Y1

: BREAKEVEN SYSTEM COST MULTPLIBR - #.######

PRINT PRINTUSING 08160, A3

: BREAKEVEN FUEL ESCALATION RATE MULTIPLIER - ##.

PRINTUSING 08180, W(l) ,W(2) ,W(3)

: BREAKEVEN FUEL ESCALATION RATES ##.#### ##. PRINT

REFERENCE

SYSTEM

$#######.

DISCOUNTED" ANNUAL CUMULATIVE"

$########.

###

#### ##.####

A13
08200

08210

08220

08230

08240

08250

08260

08270

08280

08290

08300

08310

08320

08330

08340

08350

08360

08370

08380

08390

08400

08410

08420

08430

08440

08450

08460

08470

08480

08490

08500

08510

08520

08530

08540

08550

08560

08570

08580

08590

08600

08610

08620

08630

08640

08650

08660

08670

08680

08690

08700

08710

08720

08730

08740

08750

08760

08770

08780

08790

08800

08810

08820

08830

08840

08850

08860

08870

PRINT

PRINT RETURN

REM ********************** LOAD CALCULATION *************************

REM

K9 - 0 B(l) - N1

B(2) - N1

B(3) - N2

B (4) - N2

B(5) - N2

B(6) = N3

B(7) = N3

B (8) - N3

B(9) - N4

B(10) - N4

B(ll) - N4

B(12) - N1 KD - 110 1(2) - 130

1(3) - 150

1(4) - 170

1(5) - 110 1(6) - 130

1(7) > 150

1(8) - 170

1(9) = 110 1(10) •» 130

1(11) * 150 1(12) - 170 FOR I >- 13 TO 19 1(1) - 130 NEXT I FOR M - 1 TO 12 K(M) - 0 NEXT M

IF J9 > 12 THEN 08600 FOR M - 1 TO 12 L (M) - 0 NEXT M

FOR M - 1 TO 12 K(M) - D(9)*D(10)*(N (M) / 7 )*8 . 3*(I (D (1) )-B(M)

)

K(M) - K(M) /1000000

K9 - K9 + K(M) NEXT M

REM

REM REM

REM

REM

REM REM

X9 - 0 L9 - 0 FOR M

X(M) - L(M) + K(M)

X9 - X9 + X(M)

L9 - L9 + L(M) NEXT M

RETURN

REM ******************** PROMPTED INPUT *******************************

IF Z9 - 1 THEN 08840 PRINT L$ RETURN

IF M$ =* "N" THEN 09280 PRINT PRINT "ANALYSIS FOR A FEDERAL ";T$(S1);" IN ";C$;", ";S$ PRINT

B(M) - MONTHLY GROUND WATER TQtPERATURE

I(D(1)) - WATER HEATER SET TEMPERATURE

D (9) - GALLONS /DAY USAGE

D (10) - DAYS/WEEK USAGE

N(M)/7 - NUMBER OF WEEKS IN EACH MONTH

K(M) - DHW MONTHLY LOAD IN MMBTU/MONTH

K9 - ANNUAL DHW LOAD IN MMBTU/YEAR

A14
08880 PRINT " ***************************************************

08890 PRINT " ***************** ENERGY ANALYSIS DATA **********

08900 PRINT " ***************************************************

08910 PRINT

08920 PRINT "DATA FOR SOLAR PERFORMANCE ANALYSIS (SLR METHOD)"

08930 PRINT

08940 FOR I - 1 TO 8 08950 PRINTUSING 08970, I,D$(I) ,D(I)

08960 PRINT " ";U$(I)

08970: ## <################################################ #######.##

08980 NEXT I 08990 PRINT

09000 PRINT " 09010 PRINT "ENERGY REQUIREMENTS DATA" 09020 PRINT

09030 PRINTUSING 08970, 9,D$(9) ,D(9)

09040 PRINT " ";U$(9)

09050 PRINTUSING 08970, 10, D$(10) ,D(10)

09060 PRINT " ";U$(10)

09070 PRINT " 11 MONTHLY SPACE HEATING LOADS - ";U$(11)

09080 FOR I - 1 TO 6 09090 PRINTUSING 09180,M$(I) ,L(I) ,M$(I+6) ,L(I4$)

09100 NEXT I 09110 PRINT

09130 PRINT "ENVIRONMENTAL DATA"

09140 PRINT

09150 PRINT " 12 AVERAGE DAILY HORIZONTAL RADIATION - ";U$(12)

09160 FOR I - 1 TO 6 09170 PRINTUSING 09180,M$(I) ,H(I) ,M$(I4«) ,H(I+6)

09180: <##### - ####.## <##### - ####.##

09190 NEXT I 09200 PRINT

09210 PRINT " 13 AVERAGE GROUND WATER TEMPERATURES - ";U$(13)

09220 PRINTUSING 09260,M$(12) ,M$(2) ,N1

09230 PRINTUSING 09260, M$(3) ,M$(5) ,N2

09240 PRINTUSING 09260,M$(6) ,M$(8) ,N3

09250 PRINTUSING 09260, M$(9) ,M$(11) ,N4

09260: <### - <### - ###.#

09270 IF M$ - "Y" THEN 09400

09280 PRINT

09290 PRINT

09300 PRINT " *******************************************

09310 PRINT " ***************** ENERGY ANALYSIS DATA ***************"

09320 PRINT " **********************************************************

09330 PRINT

09340 PRINT "DATA FOR ECONOMIC ANALYSIS ONLY"

09350 PRINT

09360FOR I - 20 TO 25 09370 PRINTUSING 08970, I,D$(I) ,D(I)

09380 PRINT " ";U$(I)

09390 NEXT I 09400 PRINT

09410 PRINT " ********************************************************N 09420 PRINT " ***************** LIFE CYCLE COST DATA ***************"

09430 PRINT " **********************************************************

09440 PRINT

09450 PRINT "BASE YEAR INVESTMENT COSTS"

09460 PRINT

09470 FOR I - 30 TO 34 09480 PRINTUSING 08970, I,D$(I) ,D(I)

09490 PRINT " ";U$(I)

09500 NEXT I 09510 PRINT

09520 PRINT " •' 09530 PRINT "FUTURE NON-FUEL COSTS"

09540 PRINT

09550 PRINT "SOLAR ENERGY SYSTEM" 09560 PRINTUSING 08970, 40, D$ (40) ,D(40)

09570 PRINT " ”;U$(40)

A15
09580 PRINT " 41 REPLACEMENT COST AND YEAR"

09590 PRINTUSING 09620, R(l) ,R(2)

09600 PRINTUSING09620,R(3) ,R(4)

09610 PRINTUSING 09620, R(5) ,R(6)

09620: $###### AT YEAR ##

09630 PRINTUSING 08970, 42, D$(42) ,D(42)

09640 PRINT " ";U$(42)

09650 PRINT

09660 PRINT "AUXILIARY SYSTEM" 09670 PRINTUSING 08970, 44, D$(44) ,D(44)

09680 PRINT " ";U$(44)

09690 PRINT " 45 REPLACEMENT COST AND YEAR"

09700 PRINTUSING 09620, R(7 ) ,R(8)

09710 PRINTUSING 09620, R(9) ,R(10)

09720 PRINTUSING 09620, R(ll) ,R(12)

09730 PRINTUSING 08970, 46, D$(46) ,D(46)

09740 PRINT " ";U$(46)

09750 PRINT

09760 PRINT "REFERENCE NON-SOLAR SYSTEM" 09770 PRINTUSING 08970, 47, D$(47) ,D(47)

09780 PRINT " ”;U$(47)

09790 PRINT "48 REPLACEMENT COST AND YEAR" 09800 PRINTUSING 09620, R(13) „R(14)

09810 PRINTUSING09620, R(15),R(16)

09820 PRINTUSING 09620, R(17) ,R(18)

09830 PRINTUSING 08970, 49, D$(49) ,D(49)

09840 PRINT " ”;U$(49)

09850 PRINT

09860 PRINT " 09870 PRINT "FUEL COSTS" 09880PRINT

09890 FOR I » 50 TO 57 09900 PRINTUSING 08970, I, D$(I) ,D(I)

09910 PRINT " ";U$(I)

09920 NEXTI

09930 PRINT

09940 PRINT "DOE REGION - ";R1 09950 PRINT 58 ENERGY PRICE ESCALATION (Z PER YEAR ABOVE INFLATION) - 09960 PRINT

09970 PRINT " TIME PERIODS: 1ST 4 YRS NEXT 5 YRS AFTER 9 YRS" 09980 PRINTUSING 10030, "ELECTRICITY" ,E(1 , 1) ,E(1 , 2) ,E(1, 3) 09990 PRINTUSING 10030, "DISTILLATE OIL",E(2, 1) ,E(2, 2) ,E(2, 3) 10010 PRINTUSING 10030, "RESIDUAL OIL",E(3, 1) ,E(3,2) ,E(3,3)

10015 PRINTUSING 10030, "NATURAL GAS" ,E(4, 1) ,E(4, 2) ,E(4, 3)

10020 PRINTUSING 10030, "COAL" ,E(5, 1) ,E(5, 2) ,E(5, 3)

10025 PRINTUSING 10030, "LPG",E(6, l) ,E(6,2) ,E(6,3)

10030 <############## ###.## ###.## ###.##

10040 PRINT

10050 PRINT " 10060 PRINT "DISCOUNT RATE AND STUDY PERIOD"

10070 PRINT

10080 PRINTUSING 08970, 60, D$(60) ,D(60);

10090 PRINT " ";U$(60)

10100 PRINTUSING 08970, 61 ,D$(61 ) ,D(61 )

10110 PRINT " ";U$(61)

10120 PRINT

10130 PRINT " 10140 PRINT "ANALYSIS OUTPUT"

10150 PRINT

10160 PRINTUSING 08970, 70, D$(70) ,D(70)

10170 PRINT

10180 PRINT

10190 RETURN

;S$(si)

A16
10200 REM ************************ CHANGE UNITS TO SI UNITS ************' 10210 RETURN

10220 REM *************** DEFINITION OF VARIABLES **********************

10230 RESTORE

10240 D$(l) * "TYPE OF SOLAR ENERGY SYSTEM (FROM CODED LIST)"

10250 D$(2) - "COLLECTOR TILT ANGLE"

10260 D$(3) - "OPTIMIZATION ANALYSIS (YES-1 ;NO-2)"

10270 D$ (4) - "COLLECTOR AREA"

10280 D$ (5 ) = "MINIMUM ACCEPTABLE SOLAR FRACTION"

10290 D$(6) - "OPERATING EFFICIENCY OF AUXILIARY SYSTEM"

10300 D$(7) - "OPERATING EFFICIENCY OF REFERENCE NONSOLAR SYSTEM"

10310 D$(8) = "ELECTRIC ENERGY AS Z OF USEFUL SOLAR ENERGY"

10320 D$(9) =* "DOMESTIC HOT WATER USAGE"

10330 D$(10) - "BUILDING USE SCHEDULE"

10340 D$(20) - "ANNUAL ENERGY LOAD"

10350 D$ (21 ) - "ANNUAL SOLAR FRACTION"

10360 D$(22) -"COLLECTOR AREA"

10370 D$ (23) - "OPERATING EFFICIENCY OF AUXILIARY SYSTEM"

10380 D$ (24) - "OPERATING EFFICIENCY OF REFERENCE SYSTEM"

10390 D$(25) - "ELECTRICAL ENERGY AS Z OF USEFUL SOLAR ENERGY"

10400 D$(30) - "SOLAR ENERGY INVESTMENT - FIXED COST"

10410 D$(31) - "SOLAR ENERGY INVESTMENT - VARIABLE COST"

10420 D$(32) - "INVESTMENT CREDIT (EXTERNALITY ADJUSTMENT)"

10430 D$ (33) - "INVESTMENT COST FOR AUXILIARY SYSTEM"

10440 D$ (34) - "INVESTMENT COST FOR REFERENCE NONSOLAR SYSTEM"

10450 D$ (40) - "ANNUALLY RECURRING O&M COST (Z OF SYSTEM COST)"

10460 D$(42) - "SALVAGE VALUE AT END OF STUDY PERIOD"

10470 D$ (44) - "ANNUALLY RECURRING O&M COST"

10480 D$(46) - "SALVAGE VALUE AT END OF STUDY PERIOD"

10490 D$ (47) - "ANNUALLY RECURRING O&M COST"

10500 D$ (49) - "SALVAGE VALUE AT END OF STUDY PERIOD"

10510 D$ (50) - "ELECTRICITY PRICE IN BASE YEAR"

10520 D$ (51 ) - "DISTILLATE OIL PRICE IN BASE YEAR"

10530 D$ (52) - "RESIDUAL OIL PRICE IN BASE YEAR"

10540 D$(53) - "NATURAL GAS PRICE IN BASE YEAR"

10550 D$ (54) - "COAL PRICE IN BASE YEAR"

10555 D$ (55) - "LPG PRICE IN BASE YEAR"

10560 D$ (56) - "TYPE OF FUEL USED IN AUXILIARY SYSTEM"

10570 D$(57) - "TYPE OF FUEL USED IN REFERENCE SYSTEM"

10580 D$ (60) - "REAL DISCOUNT RATE (EXCLUDES INFLATION)"

10590 D$ (61 ) - "STUDY PERIOD"

10600 D$(70) - "1-STANDARD; 2-EXTENDED; 3-SUMMARY"

10610 D$ - "DATA OUT OF RANGE. TRY AGAIN!"

10620 J9 - D(l)

10630 Q1 - D(49+D(5/>)

10640 Q2 - D(49+D(56))

10650 Q3 - D(50)

10660 U$(l) - " " 10670 U$ (2) - "DEGREES"

10680 U$(3) - " " 10690 U$ (4) - "SQFT"

10700 U$ (5) - "Z" 10710 U$ (6) - "Z" 10720 U$ (7 ) - "Z" 10730 U$(8) - "Z"

10740 U$ (9) - "GALLONS/DAY"

10750U$(10) - ,tDAYS/WEEK"

10760 U$(ll) - "MMBTU/MONTH"

10770 U$(12) - "BTU/ SQFT-DAY"

A17
10780 U$ (13) - "DEGREES P” 10790 U$ (20) - "MMBTU/YEAR"

10800 U$ (21 ) - "Z" 10810 U$(22) - "SQFT"

10820U$ (23) - "Z" 10830U$ (24) » "Z" 10840 U$(25) - "Z" 10850 U$(30) - "$"

10860 U$ (31 ) = "$/SQFT"

10870 U$(32) - 10880 U$(33) * "$"

10890 U$(34) = "$"

10900 U$ (40) = "Z" 10910 U$ (42) = "Z” 10920 U$(44) = "$"

10930 U$ (46 ) = "$"

10940 U$ (47) = "$"

10950 U$ (49) = "$"

10960 U$ (50) = "$/MMBTU"

10970 U$ (51 ) = "$/MMBTU"

10980 U$(52) =* "$/MMBTU"

10990 U$(53) = "$/MMBTU"

11000 U$(54) = "$/MMBTU"

11010 U$ (55) = "$/MMBTU"

11020 U$(56) - " " 11025 U$ (57) - " " 11030 U$(60) = "Z" 11040 U$ (61 ) = "YEARS"

11050 U$ (70) = " " 11060 S$(l) = "RESIDENTIAL"

11070 S$(2) = "COMMERCIAL"

11080 S$(3) =* "INDUSTRIAL"

11090 T $ ( 1 ) = "RESIDENTIAL BUILDING"

11100 T$(2) =» "OFFICE BUILDING"

11110 T$ (3 ) = "INDUSTRIAL FACILITY"

11120 M$(l) = "JAN" 11130 M$(2) =c "FEB" 11140 M$(3) =* "MAR"

11150 M$(4) - "APR" 11160 M$(5) - "MAY"

11170M$(6) - "JUN"

11180 M$(7) - "JUL"

11190 M$(8) - "AUG"

11200 M$(9) a "SEP"

11210 M$(10) = "OCT"

11220 M$ (11) . "NOV" 11230 M$(12) » "DEC" 11240 MAT READ C 11250 DATA .366, .573, 1.026, .713 11260 DATA .815, .470, .185, 2.003

11270 DATA .570, .336, .430, .946 11280 DATA .783, .327, .217, 1.429

11290 DATA .638, .269, .362, .966 11300 DATA .438, .159, .562, .740

11310 DATA .092, .080, .908, .690 11320 DATA .652, .328, .348, 1.074

31330 DATA .819, .308, .181, 2.020
11340 DATA .819, .248, . 181, 2 .342

11350 DATA .652, .328, . 348, 1 .074

11360 DATA .627, .255, . 373, 1 .239

11370 DATA .660, .278, . 340, 1 .011 11380 DATA 1.478, .317, 1 .314, .613

11390 DATA 1.581, .291, 1 .298, .555 11400 DATA 1.605, .287, 1 .302, .550

11410 DATA 1.187, .415, 1 .360, .830

11420 DATA 1.177, .426, 1 .392, .872 11430 DATA 1.314, .371, 1 .353, .739

11440 MAT READ N 11450 DATA 31,28, 31,30,31 ,30,31 ,31 ,30,31 ,30,31

11460 MAT READ Y 11470 DATA 17,47, 75,105,135,162 ,198,228, 258,288, 318,:344 11480 FOR I: 1 TO 70 11490 READ X$,T(I,1),T(I,2)

11500 NEXT I 11510 DATA #1. 1, 19, #2, 0, 90, #3, 1, 2. #4, 0, 1E6

11520 DATA #5, 0, 100, #6, o. 1E3, #7, 0, 1E3, #8, 0, 100 11530 DATA #9, 0, 1E6, #10, 1, 7, #11, o. o. #12, 0, 0

11540 DATA #13, 0, 0, #14, o. 0, #15, 0, o. #16, 0, 0

11550 DATA #17, 0, 0, #18, o. o. #19, 0, 0, #20, 0, 1E6

11560 DATA #21, 0, 100, #22, 0, 1E6, #23, 0, 100, #24, 0. 100

11570 DATA #25, 0, 100, #26, o. o. #27, 0, o. #28, 0. 0

11580 DATA #29, 0, 0, #30, o. 1E8, #31. 0, 1E4, #32, 0, 100 11590 DATA #33, 0, 1E8, #34, o. 1E8, #35. 0, o. #36, 0, 0

11600 DATA #37, 0, 0, #38, o. 0, #39, 0, o. #40. o. 100

11610 DATA #41, 0, 0, #42, o. 100, #43, 0, 0, #44, o. 1E7 11620 DATA #45, 0, 0, #46, o. 1E8, #47, 0, 1E7, #48, o. 0

11630 DATA #49, 0, 1E8, #50, o. 1E3, #51, 0, 1E3, #52, 0, 1E3

11640 DATA #53, 0, 1E6, #54, o. 1E3, #55, 0, 1E3, #56, 1. 6 11650 DATA #57, 1, 6, #58, 0, o. #59, 0, o. #60, 0, 100 11660 DATA #61, 1, 40, #62, o. o. #63, 0, o. #64, 0, 0

11670 DATA #65, 0, 0, #66, o, 0, #67, 0, o. #68, 0. 0

11680 DATA #69, 0, 0, #70, 1, 3 11690 RETURN

11700REM *********** CALCULATE SOLAR RADIATION ON TILTED SURFACE ************

11710 REM

11720 PI - 3.1415926

11730 P2 - 57.295779

11740 19 -428.9

11750 S = D(2

)

11760 L - LI 11770 Z8 = 0 11780 FOR M - 1 TO 12 11790 N - Y (M) 11800 D1 - 23.45*SIN(360*(2844N)/(365*P2))

11810 W1 - -TAN (L /P 2

) *TAN (D 1 /P 2

)

11820 IF W1 > .999 THEN 11870

11830 IF W1 < -.999 THEN 11850

11840 GOTO 11890

11850 W1 = PI 11860 GOTO 11900

11870 Z (M) = 0 11880 GOTO 12040

11890 W1 = (Pl/2) - ATN(W1/((1-W1~2)~.5))

11900 G = (24/Pl)*I9*( 1+. 033*C0S (360*N/(365*P2) )

)

11910 G = G * ( COS (L/P2)*COS (D1/P2)*SIN(W1)+W1*SIN(L/P2)*SIN(D1/P2) ) 11920 K = H(M)/G

11930 D = 1.00 - 1 . 13*K

11940 W2 - -TAN( (L-S) /P2)*TAN (D1/P2)

11950 W2 = (Pl/2) - ATN(W2/( (1-W2''2)~.5))

11960 IF W1 < W2 THEN 11990

11970 W3 = W2

11980 GOTO 12000

A19
11990

12000

12010

12020

12030

12040

12050

12060

12070

12080

12090

12100

12110

12120

12130

12140

12150

12160

12170

12180

12190

12200

12210

12220

12230

12240

12250

12260

12270

12280

12290

12300

12310

12320

12330

12340

12350

12360

12370

12380

12390

12400

12410

12420

12430

12440

12450

12460

12470

12480

12490

12500

12510

12520

12530

12540

12550

12560

12570

12580

12590

12600

12610

12620

12630

W3 = W1

J - COS ( (L-S) /P2)*C0S (D1/P2)*SIN (W3) + W3*SIN((L-S)/P2)*SIN(D1/P2)

J = J / ( COS (L/P2)*COS (D1/P2)*SIN(W1 ) + W1*SIN(L/P2)*SIN(D1/P2) ) J (M) = (1-D)*J + D*( 1+COS (S/P2))/2 + . 2*( 1-COS (S/P2) ) /2

Z (M) = J (M)*H(M)

Z8 = Z8 + Z(M)*N(M) NEXT M

REM 19 = SOLAR CONSTANT REM N = DAY OF YEAR

REM S = COLLECTOR TILT ANGLE IN DEGREES REM D1 - SOLAR DECLINATION ANGLE IN DEGREES

REM W1 = SUNSET ANGLE ON HORIZONTAL SURFACE IN RADIANS

REM W2 = SUNSET ANGLE ON TILTED SURFACE IN RADIANS REM W3 = MINIMUM OF W1 AND W2

REM K = K SUB T REM D = RATIO OF AVG HORIZ DIFFUSE TO AVG HORIZ TOTAL RADIATION

REM J = RATIO OF BEAM ON TILTED SURFACE TO BEAM ON HORIZ SURFACE REM J (M) = RATIO OF AVG DAILY RADIATION ON TILTED TO HORIZ SURFACE REM Z(M) = AVERAGE DAILY RADIATION ON TILTED SURFACE (BTU/SQFT*DAY) RETURN REM ************* SOLAR LOAD RATIO CALCULATION ********************

REM

REM ENTER WITH COLLECTOR AREAEQUAL TO A9 REM EXIT WITH F9, Q(M) , F(M), Q9, L9

REM

Q9 = 0 IF J9 - 19 THEN 12920

IF J9 > 12 THEN 12780 REM ***** SYS 1 THRU SYS 12 DHW ONLY *****

S9 = Z8*A9/(1E6*K9)

IF J8 > 1 THEN 12350

IF S9 > C(l,l) THEN 12330

K1 = C ( 1

, 2)*S9

GOTO 12360

K1 = 1 - C(1,3)*EXP(-C(1,4)*S9)

GOTO 12360

K1 = 1 - C(J8, 1)*EXP(-C(J8,2)*S9) - C(J8,3)*EXP(-C(J8,4)*S9)

ON J9 GOTO 12370,12400,12430,12460,12490,12520,12550,12580,12610,12640,12670,12700

El = 7 E2 = 11 GOTO 12720

El = 8 E2 = 11 GOTO 12720

El - 9 E2 - 11 GOTO 12720

El - 10 E2 - 11 GOTO 12720

El *= 7 E2 - 12 GOTO 12720

El = 8 E2 = 12 GOTO 12720

El = 9 E2 « 12 GOTO 12720

El - 10 E2 - 12 GOTO 12720

El - 7 E2 = 13 GOTO 12720

A20
12640 El = 8 12650 E2 - 13 12660 GOTO 12720

12670 El = 9 12680 E2 = 13 12690 GOTO 12720

12700 El = 10 12710 E2 - 13 12720 K2 = 1 - C(8, 1)*EXP(-C(8,2)*S9) - C(8,3)*EXP(-C(8,4)*S9)

12730 K3 = 1 - C(E1,1)*EXP(-C(E1,2)*S9) - C(E1,3)*EXP(-C(E1,4)*S9)

12740 K4 = 1 - C(E2,1)*EXP(-C(E2,2)*S9) - C(E2,3)*EXP(-C(E2,4)*S9)

12750 F9 - K1 + (K3-K2) + (K4-K2

)

12760 Q9 - F9*K9

12770 RETURN

12780 REM ***** SYS 13 THRU SYS 18 SPACE + :DHW COMBINED

12790 J7 = J9 + 1 12800 FOR M - 1 TO 12 12810 IF X(M) « 0 THEN 12870

12820 S (M) = Z (M) *A9*N (M) / ( 1E6*X (M)

)

12830 IF S (M) > C(J7, 1) THEN 12860

12840 G (M) = C(J7,2)*S(M)

12850 GOTO 12870

12860 G(M) = 1 - C(J7,3)*EXP(-C(J7,4)*S(M))

12870 Q(M) = G(M)*X(M)

12880 Q9 = Q9 + Q(M)

12890 NEXT M

12900 F9 = Q9/X9

12910 RETURN

12920 REM ***** SYS 19 - SPACE HEATING RESIDENTIAL *****

12930 FOR M = 1 TO 12 12940 G(M) - 0 12950 IF X(M) *= 0 THEN 13010

12960 S (M) = Z (M) *A9*N (M) / ( 1E6*X (M) ) 12970 IF S(M) > 5.66 THEN 13000

12980 G(M) -= 1.06 - 1 . 366*EXP (-. 55*S (M) ) + .306*EXP(-1.05*S(M))

12990 GOTO 13010

13000 G (M) = 1 13010 Q(M) - G(M)*X(M)

13020 Q9 = Q9 + Q(M)

13030 NEXT M

13040 F9 = Q9/X9

13050 RETURN

13060 REM *********** CHANGE UNITS FROM ENGLISH TOSI UNITS ****************

13070 U$ (4 ) = "M2" 13080 U$ (9 ) = "LITERS/DAY"

13090 U$ ( 1 1 ) = "GJ /MONTH"

13100 U$(12)= "MJ/M2-DAY"

13110 U $ ( 1 3 ) = "DEGREES C" 13120 U$(20) - "GJ/YEAR"

13130 U$(22) - "M2" 13140 U$ (31 ) ="$/M2"

13150 D(4) = D(4)*. 092903

13160 D(9) = D(9)*3. 78544

13170 D(20) = D(20)*l. 05506

13180 D(22) = D(22)*. 092903

13190 D (31 ) = D (31 ) / . 092903

13200 FOR I = 50 TO 54 13210 U$ (I ) - "$/GJ"

13220 D(I) » D(I)*(1/1. 05506)

13230 NEXT I 13240 FOR M = 1 TO 12 13250 L (M) = L(M)*1. 05506

13260 K(M) - K(M)*1. 05506

13270 X (M) « X(M)*1. 05506

13280 Q(M) = Q(M)*1. 05506

13290 H(M) “ H(M) /88.05

13300 Z(M) - Z(M)/88.05

13310 NEXT M

A21
13320 N 1 = (Nl-32)*5/9

13330 N2 = (N2-32)*5/9

13340 N3 = (N3-32)*5/9

13350 N4 = (N4-32)*5/9

13360 FOR I = 1 TO 10 13370 A( I ) = A(I)*. 092903

13330 NEXT I 13390 A9 = A9*. 092903

13400 A5 = A5*. 092903

13410 A6 - A6*. 092903

13420 AO = AO*. 092903

13430 K9 = K9*l. 05506

13440 L9 = L9*l. 05506

13450 X9 = X9*l. 05506

13460 Q9 = Q9*l. 05506

13470 Q4= Q4/1. 05506

13480 RETURN

13490 REM *************** CHANGE UNITS FROM SI TO ENGLISHUNITS ************

13500 U $ ( 4 ) = "SQFT"

13510 U$(9) = "GALLONS/DAY"

13520 U$ ( 1 1 ) = "MMBTU/MONTH"

13530 U$ ( 12 ) = "BTU/SQFT-DAY"

13540 U $ ( 1 3 ) = "DEGREES F" 13550 U$(20) = "MMBTU/YEAR"

13560 U$(22) = "SQFT"

13570 U$ (31 ) = "$/SQFT"

13580 D(4) = D(4)/. 092903

13590 D(9) = D(9)/3. 78544

13600 D(20) = D(20)/l. 05506

13610 D(22) = D(22)/. 092903

13620 D (31 ) = D(31)*. 092903

13630 FOR I = 50 TO 54 13640 U$(I) = "$/MMBTU"

13650 D (I ) = D(I)*1. 05506

13660 NEXT I 13670 FOR M = 1 TO 12 13680 L (M) = L(M)/1. 05506

13690 K(M) = K(M)/1. 05506

13700 X (M) = X(M)/1. 05506

13710 Q(M) = Q(M)/1. 05506

13720 H(M) = H(M)*88.05

13730 Z (M) - Z(M)*88.05

13740 NEXT M

i ntn SI — v« 1 »9/' 5)4-32

13760 N2 = (N2*9/5)432

13770 N3 - (N3*9/5)432

13780 N4 = (N4*9/5)432

13790 RETURN

13800 REM ******************** LIFE CYCLE COST ANALYSIS ********************

13810 REM PART 1 OF LCCA

13820 N5 = D (61

)

13830 15 = D (60) /100

13835 16 = N5

13836 IF 15 = 0 THEN 13850

13840 16 = (((1+I5)~N5)-1) / (I5*((14I5)~N5))

13850 17 = 1 / (1+I5)~N5

13860 GOSUB 13880

13870 GOTO 14030

13880 REM YEAR BREAKS FOR MFW FUEL FACTOR

13890 IF N5 *=> 9 THEN 13990

13900 IF N5 => 4 THEN 13950

13910 M( 1 ) = N5

13920 M(2) = 0 13930 M(3) - 0 13940 GOTO 14020

A22
13950 M(l) - 4 13960 M(2) - N5 - 4 13970 M(3) = 0 13980 GOTO 14020

13990 M( 1 ) - 4 14000 M(2) - 5 14010 M(3) « N5 - 9 14020 RETURN

14030 REM REFERENCE SYSTEM

14040 T5 = D(57)

14050 Q1 = D(49+T5)

14060 GOSUB 14260

14070 D1 = D 14080 Ml - D(47)*I6

14090 HI - R(13)/((l+I5rR(14))+R(15)/((l+I5)~R(16))+R(17)/((l+I5rR(18))

14100 Z1 = D(49)*I7

14110 REM AUXILIARY SYSTEM

14120 T5 = D(56)

14130 Q2 = D (49+T5)

14140 GOSUB 14260

14150 D2 = D 14160 M2 = D(44)*I6

14170 H2 - R(7 ) / ( ( 1+I5)~R(8) ) + R(9)/( (1+I5)^R(10) ) + R(11)/((1+I5)^R(12>)

14180 Z2 = D(46)*I7

14190 REM SOLAR SYSTEM

14200 T5 = 1 14210 Q3 = D(50)

14220 GOSUB 14260

14230 D3 - D

14240 H3 - R( 1 )/( (1+I5)~R(2) ) + R(3)/((1+I5)“R(4)) + R(5)/((1+I5)~R(6))

14250 RETURN

14260 REM MOD NPW FACTOR FOR FUEL PRICE

14270 1(1) - E(T5, 1)/100

14280 1(2) *= E(T5, 2)/100

14290 1(3) = E(T5, 3)/100

14300 D = 0 14310 D5 = 1 14320 FOR J = 1 TO 3 14330 IF I(J) - 15 THEN 14360

14340 D4 = D5*((1+I(J))/(I5-I(J)))*((1+I5)~M(J)-(1+I(J))~M(J)>/(1+I5)~M(J)

14350 GOTO 14370

14360 D4 = D5*M( J)

14370 D5 = D5*((1+I(J))/(1+I5))~M(J)

14380 D = D + D4 14390 NEXT J 14400 RETURN

14410 REM PART 2 OF LCCA

14420 REM REFERENCE SYSTEM

14430 G1 = 1 00*Q 1 *X9*D 1 /D ( 7

)

14440 J1 = D (34) + G1 + Ml + HI - Z1 14450 REM AUXILIARYSYSTEM

14460 G2 = 100*Q2*(1-F9)*X9*D2/D(6)

14470 J2 - D (33) + G2 + M2 + H2 - Z2

14480 REM SOLAR SYSTEM

14490 P5 = D (30) + D(31)*A9

14500 P6 = (1-(D(32)/100))*P5

14510 E3 = D (8)*F9*X9/100

14520 G3 = Q3*E3*D3

14530 M3 - P5*D (40)*I6/100

14540 Z3 - D(42)*P5*I7/100

14550 J3 - P6 + G3 + M3 + H3 - Z3

14560 J4 - J2 + J3

14570 C9 - J1 - .14 14580 RETURN

A23
14590

14600

14610

14620

14630

14640

14650

14660

14670

14680

14690

14700

14710

14720

14730

14740

14750

14760

14770

14780

14790

14800

14810

14820

14830

14840

14850

14860

14870

14880

14890

14900

14910

14920

14930

14940

14950

14960

14970

14980

14990

15000

15010

15020

15030

15040

15050

15060

15070

15080

15090

15100

15110

15120

15130

15140

15150

15160

15170

15180

15190

15200

REM SET UP FOR ANNUAL DISC CASH FLOW

X6 ** 0 FOR N5 = 1 TO D (61

)

GO SUB 13880

GO SUB 14260

B(N5) = D NEXT N5

N5 - D(61

)

RETURN

REM DISC CASH FLOW * FOR I - 1 TO N5

V ( I ) - 0 NEXT I FI » Q1*X9*100/D(7)

F2 » Q2*( 1-F9)*X9*100/D (6)

F3 = Q3*F9*X9*D (8 ) / 1 00 X7 = D(34) - (D(33)+P6)

T5 = D ( 5 7

)

GOSUB 14590 FOR Y = 1 TO D(61

)

IF Y = 1 THEN V(l) - F1*B( 1

)

IF Y > 1 THEN V(Y) - F1*(B(Y)-B(Y-1))

NEXT Y T5 = D(56)

GOSUB 14590 FOR Y = 1 TO D(61)

IF Y = 1 THEN V(l) - V(l) - F2*B(1)

IF Y > 1 THEN V(Y) - V(Y) - F2*(B(Y)-B(Y-1))

NEXT Y T5 « 1 GOSUB 14590 FOR Y = 1 TO D(61)

IF Y » 1 THEN V(l) - V(l) - F3*B(1)

IF Y > 1 THEN V(Y) - V(Y) - F3*(B(Y)-B(Y-1))

NEXT Y FOR I - 2 TO 12 STEP 2 IF R (I ) - 0 THEN 14970

V(R(I)) - V(R(I)) - R(I-1)/((1+I5)“R(I))

NEXT I FOR I - 14 TO 18 STEP 2 IF R(I) » 0 THEN 15010

V (R(I) ) - V(R(I)) + R(I-1)/((1+I5)-R(I))

NEXT I FOR Y - 1 TO N5

V(Y) - V(Y) + D(47)/((1+I5)~Y)

NEXT Y FOR Y - 1 TO N5

V(Y) - V(Y) - D(44)/((1+I5)~Y)

NEXT Y FOR Y - 1 TO N5

V(Y) = V(Y) - D(40)*(P5/100)/((1+I5)~Y)

MPVT V iUjai A V(N5) - V (N5) + Z2 +Z3 - Z1 RETURN

REM ********************* FINANCE DETAIL *****************************

:* NET SAVINGS - $######## * AREA - ###### SQFT * SOLAR FRACTION -.###*

:* NET SAVINGS - $######## * AREA - ###### M2 * SOLAR FRACTION -.###*

IF U$ - "E" THEN 15190

PRINTUS ING 15 1 50 , C9 , A9* . 092903 , F9

GOTO 15210

PRINTUSING 15140, C9,A9,F9

GOSUB 14680

A24
15210 REM

15220

SAVINGS TO INVESTMENT RATIO ' R8 « (G1-G2-G3+M1-M2-M3) / (P6+D (33)-D(34)+Zl-Z2-Z34H2+H3-

15230 IF R8 > 0 THEN 15250

15240 R8 - 0 15250 REM QTMDT 17 DAVRAPF TTM17 15260 FI - Q1*X9*100/D(7)

15270 F2 = Q2*(1-F9)*X9*100/D(6)

15280 F3 « Q3*F9*X9*D(8)/100

15290 X8 = D(34) - ( D (33) + P6 ) 15300 FOR Y - 1 TO N5

15310 O(Y) - (Fl+D (47) ) - (F2-H)(44) ) - (F3-H) (40)*P5/100)

15320 NEXT Y

15330 FOR Y = 2 TO 12 STEP 2 15340 IF R(Y) - 0 THEN 15360

15350 0(R(Y)) = 0(R(Y)) -R(Y-l)

15360 NEXT Y 15370 T2 = 0 15380 FOR Y *= 14 TO 18 STEP 2 15390 IF R(Y) = 0 THEN 15410

15400 0(R(Y)) = 0(R(Y)) + R(Y-l)

15410 NEXT Y

15420 Y = 0 15430 T2 = 0 15440 T 1 = T2

15450 IF Y = 0 THEN T2 = T2 + X8

15460 IF Y > 0 THEN T2 - T2 + O(Y)

154 70 IF T2 > 0 THEN 15510

15480 IF Y = N5 THEN 15530

15490 Y = Y + 1 15500 GOTO 15440

15510 P8 = Y - (T2/ (T2-T 1 )

)

15520 GOTO 15550

15530 T2 = T2 - X8

15540 P8 = -X8/ (T2/N5)

15550 0 (N5) = 0(N5) + D (46 ) + D(42)*P5/100 - D(49)

15560 IF M$ = "N" THEN 16520

15570 IF D ( 3 ) = 2 THEN 16520

15580 IF C9 => 0 THEN 16520

15590 IF D(56) <> D(57) THEN 16520

15600 IF D(70) = 1 THEN 16520

15610 IF D(70) *> 3 THEN 16520

15620 REM BREAKEVEN FUEL PRICE

15630 N7 = Q2

15640 P4 = C9

15650 B3 - Q2

15660 B4 = B3 + N7

15670 P3 = P4

15680 Q1 « B4 15690 Q2 - B4 15700 IF D(56) > 1 THEN 15720

15710 Q3 = B4 15720 GOSUB 05750

15730 P4 = C9

15740 IF P4 > 0 THEN 15760

15750 GOTO 15650

15760 Q4 •= B3 + ( -P3*(B4-B3)/ (P4-P3) ) 15770 Q1 “ Q4

15780 Q2 - Q4

15790 IF D(56) > 1 THEN 15810

15800 Q3 «= B4 15810 GOSUB 05750

15820 IF ABS (C9) < 1 THEN 15930

15830 P3 - C9

15840 B3 = Q4

15850 B4 *= B3 - 2*C9*( (B4-B3) /(P4-P3) )

A25
15860

15870

15880

15890

15900

15910

15920

15930

15940

15950

15960

15970

15980

15990 16000

16010

16020

16030

16040

16050

16060

16070

16080

16090

16100

16110

16120

16130

16140

16150

16160

16170

16180

16190

16200

16210

16220

16230

16240

16250

16260

162 70 16280

16290

16300

16310

16320

16330

16340

16350

16360

16370

16380

16390

16400

16410

16420

16430

16440

16450

16460

16470

16480

16490

16500

16510

16520

Q1 = B4 Q2 - B4

IF D(56) > 1 THEN 15900

Q3 = B4

GOSUB 05750

P4 = C9

GOTO 15760 REM

REM BREAKEVEN FUEL ESCALATION RATE

T5 = D ( 56

)

FOR I * 1 TO 3 J(I) - E(T5, I) NEXT I A1 = Q4*D2

A2 « 1 A3 = 1 . 3*A2 FOR I - 1 TO 3 W(I) = A3*(J(I)+10)

W(I) *= W(I)-10

I (I ) = W(I)/100

NEXT I GOSUB 14300

IF N7*D -> A1 THEN 16110

A2 = A3

GOTO 16010

A4 = A3

IF ABS (N7*D-A1 ) < .01 THEN 16230

A3 “ (A2+A4)/2

FOR I - 1 TO 3 W(I) >= A3*(J (I)+10)

W(I) = W(I)-10

1(1) - W(I)/100

NEXT I GOSUB 14300

IF N7*D -> A1 THEN 16110

A2 -= A3

GOTO 16120 REM BREAKEVEN SYSTEMCOST —

A9 = A5

P3 - C5

GOSUB 13800

55 - D (30) 56 - D (31

)

Y1 - D(49+D(56) )/Q4

D(30) - S5*Y1

D(31 ) = S6*Y

GOSUB 05750

P4 = C9

Y2 = 1 + P3*(1-Y1)/(P4-P3)

P3 = P4

D (30) - S5*Y2

D(31 ) = S6*Y2

GOSUB05750

P4 - C9

57 - (Y1-Y2)/(P4-P3)

Y1 = Y2 + P4*S7

D(30) = S5*Y1

D (31 ) = S6*Y1 GOSUB 05750

P3 - C9

IF ABS (P3) < 1 THEN 16490

Y2 = Y1 + 2*P3*S7

GOTO 16360 REM

D(30) = S5

D (31 ) = S6 RETURN
I 2K-l

C/2 w' MHM

CJmXMQzw

Oh3

B1
2

3

4

56

78

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

CODED LIST OF CITIES IN FEDSOL GEOGRAPHICAL DATA BANK

City State Latitude

ADAK AK 51.53

ANNETTE AK 55.02

BARROW AK 71.18

BETHEL AK 60.47

BETTLES AK 66.55

BIG DELTA AK 64.00

FAIRBANKS AK 64.49

GULKANA AK 62.09

HOMER AK 59.38

JUNEAU AK 58.22

KING SALMON AK 58.41

KODIAK AK 57.45

KITZEBUE AK 66.52

MCGRATH AK 62.58

NOME AK 64.30

SUMMIT AK 63.20

YAKUTAT AK 59.31

BIRMINGHAM AL 33.34

MOBILE AL 30.41

MONTGOMERY AL 32.18

FORT SMITH AR 35.20

LITTLE ROCK AR 34.44

PHOENIX AZ 33.26

PRESCOTT AZ 34.39

TUSCON AZ 32.07

WINSLOW AZ 35.01

YUMA AZ 32.40

ARCATA CA 40.59

BAKERSFIELD CA 35.25

CHINA LAKE CA 35.41

DAGGETT CA 34.52

EL TORO CA 33.40

FRESNO CA 36.46

LONG BEACH CA 33.49

LOS ANGELES CA 33.56

MOUNT SHASTA CA 41.19

NEEDLES CA 34.46

OAKLAND CA 37.44

POINT MUGU CA 34.07

RED BLUFF CA 40.09

SACRAMENTO CA 38.31

SAN DIEGO CA 32.44

SAN FRANCISCO CA 37.37

SANTA MARIA CA 34.54

SUNNYVALE CA 37.25

COLORADO SPRINGS CO 38.49

B2
City Code City State Latitude

47 DENVER CO 39.45

48 EAGLE CO 39.39

49 GRAND JUNCTION CO 39.07

50 PUEBLO CO 38.17

51 HARTFORD CT 41.56

52 WASHINGTON-STERLING DC 38.57

53 WILMINGTON DE 39.40

54 APALACHICOLA FL 29.44

55 DAYTONA BEACH FL 29.11

56 JACKSONVILLE FL 30.30

57 MIAMI FL 25.48

58 ORLANDO FL 28.33

59 TALLAHASSEE FL 30.23

60 TAMPA FL 27.58

61 WEST PALM BEACH FL 26.41

62 ATLANTA GA 33.39

63 AUGUSTA GA 33.22

64 MACON GA 32.42

65 SAVANNAH GA 32.08

66 BARBERS POINT HI 21.19

67 HILO HI 19.43

68 HONOLULU HI 21.20

69 LIHUE HI 21.59

70 BURLINGTON IA 40.47

71 DES MOINES IA 41.32

72 MASON CITY IA 43.09

73 SIOUX CITY IA 42.24

74 BOISE ID 43.34

75 LEWISTON ID 46.23

76 POCATELLO ID 42.55

77 CHICAGO IL 41.47

78 MOLINE IL 41.27

79 SPRINGFIELD IL 39.50

80 EVANSVILLE IN 38.03

81 FORT WAYNE IN 41.00

82 INDIANAPOLIS IN 39.44

83 SOUTH BEND IN 41.42

84 DODGE CITY KS 37.46

85 GOODLAND KS 39.22

86 TOPEKA KS 39.04

87 WICHITA KS 37.39

88 LEXINGTON KY 38.02

89 LOUISVILLE KY 38.11

90 BATON ROUGE LA 30.32

91 LAKE CHARLES LA 30.07

92 NEW ORLEANS LA 29.59

93 SHREVEPORT LA 32.28

94 BOSTON MA 42.22

95 BALTIMORE MD 39.11

B3
City Code City State Latitude

96 PATUXENT MD 38.17

97 BANGOR ME 44.48

98 CARIBOU ME 46.52

99 PORTLAND ME 43.39

100 ALPENA MI 45.04

101 DETROIT MI 42.25

102 FLINT MI 42.58

103 GRAND RAPIDS MI 42.53

104 HOUGHTON MI 47.10

105 SAULT SAINT MARIE MI 46.28

106 TRAVERSE CITY MI 44.44

107 DULUTH MN 46.50

108 INTERNATIONAL FALLS MN 48.34

109 MINNEAPOLIS-ST. PAUL MN 44.53

110 ROCHESTER MN 43.55

111 COLUMBIA MO 38.49

112 KANSAS CITY MO 39.18

113 SPRINGFIELD MO 37.14

114 ST. LOUIS MO 38.45

115 JACKSON MS 32.19

116 MERIDIAN MS 32.20

117 BILLINGS MT 45.48

118 CUT BANK MT 48.36

119 DILLON MT 45.15

120 GLASGOW MT 48.13

121 GREAT FALLS MT 47.29

122 HELENA MT 46.36

123 LEWISTOWN MT 47.03

124 MILES CITY MT 46.26

125 MISSOULA MT 46.55

126 ASHEVILLE NC 35.26

127 CAPE HATTERAS NC 35.16

128 CHARLOTTE NC 35.13

129 CHERRY POINT NC 34.54

130 GREENSBORO NC 36.05

131 RALEIGH-DURHAM NC 35.52

132 BISMARCK ND 46.46

133 FARGO ND 46.54

134 MINOT ND 48.16

135 GRAND ISLAND NE 40.58

136 NORTH OMAHA NE 41.22

137 NORTH PLATTE NE 41.08

138 SCOTTSBLUFF NE 41.52

139 CONCORD NH 43.12

140 LAKEHURST NJ 40.02

141 NEWARK NJ 40.42

142 ALBUQUERQUE NM 35.03

143 CLAYTON NM 36.27

144 FARMINGTON NM 36.45

B4
ty Code City State Latitude

145 ROSWELL NM 33.24

146 TRUTH OR CONSEQUENCES NM 33.14

147 TUCUMCARI NM 35.11

148 ZUNI NM 35.06

149 ELKO NV 40.50

150 ELY NV 39.17

151 LAS VEGAS NV 36.05

152 LOVELOCK NV 40.04

153 RENO NV 39.30

154 TOWOPAH NV 38.04

155 WINNEMUCCA NV 40.54

156 YUCCA FLATS NV 36.57

157 ALBANY NY 42.45

158 BINGHAMPTON NY 42.13

159 BUFFALO NY 42.56

160 MAS SENA NY 44.56

161 NYC (CENTRAL PARK) NY 40.47

162 NYC (LA GUARDIA) NY 40.46

163 ROCHESTER NY 43.07

164 SYRACUSE NY 43.07

165 ADRON-CANTON OH 40.55

166 CINCINNATI OH 39.04

167 CLEVELAND OH 41.24

168 COLUMBUS OH 40.00

169 DAYTON OH 39.54

170 TOLEDO OH 41.36

171 YOUNGSTOWN OH 41.16

172 OKLAHOMA CITY OK 35.24

173 TULSA OK 36.12

174 ASTORIA OR 46.09

175 BURNS OR 43.35

176 MEDFORD OR 42.22

177 NORTH BEND OR 43.25

178 PENDLETON OR 45.41

179 PORTLAND OR 45.36

180 REDMOND OR 44 .16

181 SALEM OR 44.55

182 ALLENTOWN PA 40.39

183 ERIE PA 42.05

184 HARRISBURG PA 40.13

185 PHILADELPHIA PA 39.53

186 PITTSBURGH PA 40.30

187 WILKES-BARRE-SCRANTON PA 41.20

188 PROVIDENCE RI 41.44

189 CHARLESTON SC 32.54

190 COLUMBIA SC 33.57

191 GREENVILLE-SPARTANBURG SC 34.54

192 HURON SD 44.23

193 PIERRE SD 44.23

B5
Lty Code City State Latitude

194 RAPID CITY SD 44.03

195 SIOUX FALLS SD 43.34

196 CHATTANOOGA TN 35.02

197 KNOXVILLE TN 35.49

198 MEMPHIS TN 35.03

199 NASHVILLE TN 36.07

200 ABILENE TX 32.26

201 AMARILLO TX 35.14

202 AUSTIN TX 30.18

203 BROWNSVILLE TX 25.54

204 CORPUS CHRISTI TX 27.46

205 DALLAS TX 32.51

206 DEL RIO TX 29.22

207 EL PASO TX 31.48

208 FORT WORTH TX 32.50

209 HOUSTON TX 29.59

210 KINGSVILLE TX 27.31

211 LAREDO TX 27.32

212 LUBBOCK TX 33.39

213 LUFKIN TX 31.14

214 MIDLAND-ODESSA TX 31.56

215 PORT ARTHUR TX 29.57

216 SAN ANGELO TX 31.22

217 SAN ANTONIO TX 29.32

218 SHERMAN TX 33.43

219 WACO TX 31.37

220 WICHITA FALLS TX 33.58

221 BRYCE CANYON UT 37.42

222 CEDAR CITY UT 37.42

223 SALT LAKE CITY UT 40.46

224 NORFOLK VA 36.54

225 RICHMOND VA 37.30

226 ROANOKE VA 37.19

227 BURLINGTON VT 44.28

228 OLYMPIA WA 46.58

229 SEATTLE-TACOMA WA 47.27

230 SPOKANE WA 47.38

231 WHIDBEY ISLAND WA 48.21

232 YAKIMA WA 46.34

233 EAU CLAIRE WI 44.52

234 GREEN BAY WI 44.29

235 LA CROSSE WI 43.52

236 MADISON WI 43.08

237 MILWAUKEE WI 42.57

238 CHARLESTON wv 38.22

239 HUNTINGTON wv 38.22

240 CASPER WY 42.55

241 CHEYENNE WY 41.09

242 ROCK SPRINGS WY 41.36

243 SHERIDAN WY 44.46

B6
APPENDIX CDISCOUNT

FORMULAS* 3 o

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O 3 u

O CO 3 CM CM CO CO

a o JJ •H to 3 3 O 1 o ftM 3 iM to 3 3 3 3 3 MM 3 3 3 0

33 W) MM mm 3 Mm 0 3 3 3 0 3 3 CM 33 3 + 1 + 1 O 3 3 O O 3 Eo 3 3 •H T—

3 3 O O 3 3 4M 0 0 3 3 3 3 3 4J 0 r—

33 J—

33 V4 3 a iH 3 «* 3 3 3 • a mm 3 31 3 iH mm CD • a mm JO 3 3 o O 33 3 3 3 O 3 cn CD o -* -t 0 3 3 3 0

Mm o 3 3 O 3 3 3 3

4-1 •H 3 iM •H 3 3 CD 3 3 3 3 0 3 3 iH 3 3 3 3 3 3 4-1 to 3 3 3

Mm 33 iH 3 3 3 3 3 to to CD 3 3 O a a 3 * 3 r-M .3 3 CD ”3 31 3 i 3 4-> 3 CM COW 4-1 CD 3 MM 3 3 i—i 3 3 3 3 3 3 3 O 3 3 3 4-1 3 II 3 3 3 3 3 1 33 3 0 3 CO 4J 4-1 3 > a 3 3 > 33 3 > £ 3 3 X CD 3 3

•H

X 3 3 •H 3 •H •H 3 3 •H 3 3 3 o 3 to a O 3 MM O a. 3 mm 3 pH CM 33

r* 3 3 3 4-1 J3 CD 3

JO 4J 3 U

4-1 3m IM 3 3 O Pm 4-1 >M O S 3 3 5 0 'o 3

4J 4-1 ft Me

O 3 4-1 3 O 3 o

rH 3 3 mm Pm CD o 3 CD o •H pp •H 3 3 & 3 S 3 w 33 3 3 CM 3 CM 33 0 3 CO CM J3 s: 3 O CM w s-x 33 4-1 !Z 0 3 3 4-1 3 ft •H O

i—

o Mm [3 II M MM •H 3 •H 33 33

•H 3 O

CO C3 S *

Cl

APPENDIX D - THE SOLAR LOAD RATIO DESIGN METHOD: PERFORMANCE CURVES AND

SCHEMATIC DIAGRAMS

D.l Design Curves for Various Degree-Day Ranges, Service Hot Water Only,

Commercial Buildings

D.2 Design Curves for Various Delivery Temperatures, Service Hot Water Only,

Commercial Buildings

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

System Sizing" [3].

D1
COLLECTOR TYPE

r S»

g;.

o

I«j

SINGLE-BLAZED SELECTIVE SINGLE-GLAZED NONSELCCTIVE DOUBLE-GLAZED NONSELCCTIVE

BSHM SYSTEM MATER SUPPLY TEMP. - 54C I130T)

i.a 2.0 3.0 4.0 vo

ANNUAL SOLAR LOAO RATIO (SLR!

e.o 7.0 o.o

D.3 Design Curves for Various Collector Types, Service Hot Water Only,

Commercial Buildings

8

D.4 Design Curves for Various Collector Types, Space Heating, Liquid Systems,

in Commercial Buildings

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

System Sizing" [3],

D2
D.5 Design Curves for Various Collector Types, Space Heating, Air Systems,

in Commercial Buildings3

D.6 Design Curve for Space Heating System, Residential Building^

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

System Sizing" [3],

^SOURCE: ERDA'S Pacific Regional Solar Design Handbook [21],

D3
TCMPCftlNC VALVl

D.7 Schematic Diagram of Standard Service Hot Water Systems

POD DULONG

smet ICATING

D.8 Schematic Diagram of Standard Space Heating (or Combined Space and

Service Water Heating) Liquid System

D.9 Schematic Diagram of Standard Space Heating (or Combined Space and

Service Water Heating) Air System

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

System Sizing" [3].

D4
APPENDIX E - ILLUSTRATIONS AND EXPLANATIONS OF KEY ALGORITHMS

E.l CALCULATION OF AVERAGE SOLAR RADIATION ON A TILTED SURFACE

In order to use the Solar Load Ratio (SLR) design method, or other methods

based on monthly calculations, such as F-CHART, it is necessary to estimate the

solar radiation incident on the collector surface monthly, from average daily

values. The total solar radiation incident on any surface is the sum of the

direct beam, diffuse, and reflected components. The radiation model used in

FEDSOL to calculate monthly values for the average daily total radiation is

that devised by Liu and Jordan and improved upon by Page and Klein [30]. It is

limited to south-facing surfaces.

The only data required by this model are: 1) the slope of a collector surface,

2) the ground reflectance near the collector, 3) the monthly average daily total

horizontal solar radiation (measured), and 4) the latitude of the site. This

model is summarized below:

Let

H-p = total monthly average daily solar radiation on a tilted surface, and

HT

= R«H,

where

H = monthly average daily total solar radiation on the horizontal surface,

R = ratio of the monthly average total daily solar radiation on a tilted

surface to that on a horizontal surface, and

R = (1 - (HD/H))RB + (HD

/H) [1 + cos(S) ] /2 + p [1 - cos(S) ] /2

Then:

H(1 - (HB /H))Rg = monthly average daily beam component on a tilted

surface

,

H(Hd

/H)[ 1 + cos(S)]/2 = monthly average daily diffuse component on a tilted

surface, and

H»p[l - cos(S)]/2 = monthly average daily reflected component on a tilted surface.

The monthly average total daily solar radiation, H, has been measured for over

250 sites around the United States. The solar radiation data used by FEDSOL

was obtained from Input Data for Solar Systems [22].

FEDSOL uses the value of 0.2 for ground reflectance, p. This value may tend

to underestimate incident radiation on tilted collectors at sites where there

is snow cover during winter months. However, the error should be small and

may be expected to result in only a slightly conservative estimate of solar

fraction.

(Hd

/H) and Rg are calculated with the following equations:
(HD

/H) ratio of monthly average daily diffuse radiation to daily

average total radiation on a horizontal surface,

(Hd

/H) = 1-1.13 Kt ,

rb

r

b

where

5

L

6

6

n

kt

kt

( Ro)n

(^o)n

sc

ratio of monthly average daily beam radiation on a tilted surface

to daily beam radiation on a horizontal surface,

cos(L-S) cos(6) sin(w *) + w_ ' sin(L-S) sin(5) a a——— —

cos(L) cos(6) sinCoj^) + ws sin(L) sin(6)

slope of collector surface (tilt angle),

latitude

,

solar declination angle,

23.45 sin[360(284+n)/365]

,

day of the year,

ratio of monthly average daily total radiation to the

extraterrestrial daily solar radiation (both horizontal),

H/(H0 ) n ,

extraterrestrial daily solar radiation on a horizontal surface

on day n,

(24/tt)I sc [l+.033cos(360n/365) ] [cos(L)cos(5)cos(ujs ) +

ms sin(L) sin(5)],

solar constant (1353 watts/sq. meter),

sunset hour angle on horizontal plane, radians,

arccos [ - tan(L)tan(6) ],

sunset hour angle on tilted surface, radians, and

minimum of u)s and arccos [ - tan(L-S) tan( 6) ].

In order to evaluate K^, and therefore (Hd

/H), it is necessary to know the

average monthly extraterrestrial radiation. The equation above for (H0 ) n calculates the value for only one day of the year. It is necessary either to

calculate (HQ ) nfor each day of the month and average all the days to one average monthly value or to use a day within the month which yields a value

near the average value. Klein has determined that the following days give good

results

E2
month Julian Day

Jan - 17

Feb - 47

Mar - 75

Apr - 105

May - 135

Jun - 162

Jul - 198

Aug - 228

Sep - 258

Oct - 288

Nov - 318

Dec - 344

As described for FEDSOL, this method is designed for collectors facing due

south. However, collectors which face within 20 degrees east or west of south

can be evaluated with this radiation model without significant error.

E3
E.2. CALCULATION OF RANGE OF SYSTEM SIZES AND SOLAR FRACTIONS

OVERVIEW:

The table of solar fractions and net savings for a range of system sizes

included in the FEDSOL program output is derived using a mathematical model

that combines elements of the GFL(G-CHART) design method [31] with the SLR

design method [3, 19, 21] taking advantage of the simplicity of the annual

methods such as the former and the greater flexibility and accuracy of monthly

analysis methods such as the SLR or F-CHART.

A primary assumption of the GFL method, as derived by Lameiro and Bendt, is

that the annual performance (annual solar fraction, f a ) for any active solar

energy system for service hot water, space heating, or combination thereof, can

be described by the following equation [31]:

-(RA + SA2

) f a " 1 - e (E.2.1)

where A is the collector area and R and S are constants that can be calculated.

If one knows the annual solar fractions associated with any two collector areas

for a system, the SLR method can be used to generate two initial predictions

of annual solar fraction. These two pairs of collector areas and annual solar

fractions are then employed to C4lculate R and S, and finally an expression is

developed to determine the area required to give any desired solar fraction

(see eq. (E.2.5)). Lastly, the SLR method is employed to obtain more accurate

annual solar fraction solutions for the collector areas identified with GFL

method

By expressing the annual solar fraction as a function of collector area, one

can print a table of system sizes and solar fractions (as in the FEDSOL program

output) or plot a curve of solar fraction vs. collector area. Moreover, when

combined with a model for life-cycle cost analysis, the model provides the

basis for a very fast method of calculating the economically optimal collector

area.

SHW SYSTEMS (TYPES 1-12)

Earlier versions of the SLR method and the initial version of the FEDSOL

program expressed the monthly solar fraction of SHW (service hot water) systems

as a function of the monthly SLR. The annual solar fraction was calculated from

the results of the twelve monthly calculations.

The recently revised SLR method expresses the annual solar fraction for service

hot water only systems as a function of the annual SLR [3]. With this revised

method, it is possible to calculate the annual solar fraction directly from the

annual SLR and, hence, from the collector area. However, the combined GFL - SLR

approach was still useful in generating a series of collector areas, solar fractions, and net savings values for which solar fractions are evenly spaced over a range from 10 percent to 90 percent.

E4
The SLR annual solar fraction equation for SHW systems has the form

fa

= 1 -a2x _a4 x

a

a

x e

z a - a

3 e

4 a (E.2.2)

where

fa = annual solar fraction,

xa

= annual solar load ratio = A^, Ha /Qa , ^ = collector area,

Ha

= solar energy per unit area incident annually on the plane of the

collector, and

Qa = annual SHW load.

In order to calculate the area required to produce a desired solar fraction,

one may guess an area, solve equation (E.2.2) to obtain a solar fraction, guess

a new area larger or smaller depending on the outcome of the first guess, and

solve the equation again, until the area which gives the desired solar fraction

is found. An alternative method, that adopted in FEDSOL, is to solve equation

(E.2.2) for xa and hence Ac

. Unfortunately, it is not a simple matter to solve

this equation for xa as a function, of fa. However, for reasons which will become

obvious later, it is necessary only to solve the equation for fa equal to .5.

This has been done by expanding a Taylor's series about a = 1.4, using only the

first three terms of the series to approximate the function fa when the value of

f a is near 0.5:

"1 • 4a 2 —1 • 4a a 1 .4a 2 “l .4a a fa (*

a

) = 1 “ a

i e ~ a3 e + [ a

i a2 e + a3a

4

a ] (x

a-1.4)

-1.4a 2 -1.4a, 2 + .5 [a^a

2 e

z + a^a^e q

] (x

a~1.4)

Setting f = .5 and solving for xa gives

x_ =

[ - B + (B2 - 4AC )

5

] 2A

+ 1.4

where

—1 • 4a 2 — 1.4a,

A = .5 [ a

i a2 e ^ + a

3a4 e

4

] »

1 .4a 2 —1 .4a,

B = a^a

2 e + a^a^e 4

, and

-1.4a 2 -1.4a,

C .5 — a-^e a^e

E5
and

xa

= ^ Ha/Qa and

^50 = xa Qa^a

because xa was solved for f = 0.5.

We now have a good estimate of the collector area which will give this system a 50 percent solar fraction. This value, A50 , is put into equation (E.2.2) and

the equation is solved for f

fl

. The value of f a will be close to .5, which is

all that is necessary at this point. The area (A 50 ) and its corresponding solar

fraction are denoted as A^ and respectively. Another area, A2, is obtained

by multiplying A-j_ by 8 . There is nothing special about the number 8 except

that it causes A2 to be significantly larger than A^ . (Smaller numbers cause computational problems at a later point in the procedure.) The new area A2

is put into equation (E.2.2) and the equation is solved again for f a

. The solar

fraction associated with area A2 is labeled F2. Recalling equation (E.2.1) and

expressing it as two equations with two unknowns!

“(RA1 + SA1 2

) Fl = 1 - e , and

-(RA2 + SA2 2

) F2 = 1 - e

N. The two equations can be solved for R and S:

R = Al 2

[ -ln(l-F2) | - A22

1 -ln(l-Fl) ]

_ and (E . 2 . 3 ) A1 2A2 - Al A22

S = A2 [ -ln(l-Fl) ] - Al [ -ln(l-F2) ] . A12A2 “ Al A22

Finally solving equation (E.2.1) for A gives

A = -S + [S 2 - 4 R ln( l/(l"fa

) ) ]* 5

.

(E.2.4)

(E.2.5)

Once S and R have been calculated for a specific solar energy system, it

becomes a quick matter to determine the collector area which will give any

desired solar fraction. For example, if a system with a solar fraction of

.65 were desired, equation (E.2.5) would be solved simply with f a=.65 to

determine the required area (Ac ).

The FEDSOL program uses the above method to predict collector areas corresponding

to annual solar fractions of .1, .2, 3, up to .9. Each collector area predicted

with this method is then put into equation (E.2.2) to obtain the exact annual

solar fraction according to the SLR method.

E 6
SPACE HEATING SYSTEMS (TYPES 13 - 19)

The SLR design for space heating systems does not give annual results directly.

Calculations must be performed monthly and the annual solar fraction determined

from those results. The same is true with F-CHART. The following method is

particularly useful for this situation.

The SLR method for space heating systems calculates monthly solar fractions

with the following equations

fm = b^xm for 0 < xm < b2 , and (E.2.6a)

fm

= 1 - b3e~^4xm for xm > b

2 » (E.2.6b)

where

fm = monthly solar fraction,

xm = monthly solar load ratio = Ac HT/Qm,

Ac = collector area,

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

collector, and

Qm = monthly load.

It is possible to solve equation (E.2.6b) for xm

in terms of fm

. Recalling

that xm = H-ji Ac /Qm , the following equation will predict the area required to

give any specified monthly solar fraction:

. . Qm

• i« (b3 /a-fn) ) b

4 *1

However, an annual, not a monthly fraction is needed. Drawing on past

experience, we know that if a space heating system has an annual solar fraction

near 50 percent, the average of the February and March monthly fractions is in

nearly all cases within 1 percent of 50 percent. This observation is exploited

here. For simplicity, we assume that the collector that provides a solar fraction of 50 percent in March will also give approximately a 50 percent solar

fraction on an annual basis:

A _

QMar ln ( 2#b3

)

• b

4 H

T Mar

We call this area Al. Area A1 is evaluated with the SLR subroutine for twelve

months to determine an annual solar fraction Fl. Then area Al is multiplied by

E7
8, as before, to yield the new area A2. Area A2 is evaluated with the SLR

subroutine for twelve months and an annual solar fraction F2 determined, also

as before. Again, we have two equations and two unknowns:

-(RA1 + SAl 2

) FI = 1 - e , and

“(RA2 + SA2 2

) F2 = 1 - e

and these equations are solved for R and S as before:

R - Al2

[ -ln(l-F2) | - A22[ - ln(l-Fl) ]

_ and

A1 2A2 - Al A22

S = A2 [ -ln(l-Fl) ] - Al [ -ln(l-F2) ]

> A1 2A2 - Al A22

Solving equation E.2.1 for Ac yields

-S + ( S

2 - 4 R ln( l/(l-fa

) ) ]* 5

We then determine the areas corresponding to the series of solar fractions .1,

.2, .3, up to .9, and submit each of these areas to the SLR subroutine for a more exact prediction based on monthly calculations.

\

E8
APPENDIX F - CONVERSION FACTORS FOR THE MOST COMMON UNITS USED IN SOLAR

ENERGY SYSTEM DESIGN AND EVALUATION

Length: 1 inch (in) = 25.4 millimeters (mm)

1 foot (ft) = 0.3048 meter (m)

Area: 1 ft 2 = 0.092903 m2

Volume:

Fluid Capacity:

Temperature

1 ft 3 = 0.028317 m3

1 gallon (gal) = 3.78541 liters (L)

1°F = 9/5°C + 32

Temperature

Interval

1°F = 5/9°C or K

Mass

1 pound (lb) = 0.453592 kilogram (kg)

Mass per unit

length: 1 lb/ft = 1.48816 kg/m

Mass per unit area

1 lb/ ft 2 = 4.88243 kg/m2

Mass per unit

volume1 lb/f

3 = 16.0185 kg/m3

Energy:

Heat flow rate:

Specific heat:

1 Btu = 1.05506 kilojoules (kJ)

1 Btu/h = 0.293071 Watt (W)

1 Btu/ (lb)(°F) = 4.1868 kJ/(kg)(K)

U-value1 Btu/(ft 2 )(h)(°F) = 5.67826 W/(m2 )(K)

Energy per

unit area: 1 Btu/ ft 2 = 0.011357 MJ/m2

FI
APPENDIX G - RANGE OF ACCEPTABLE VALUES FOR INPUT DATA

DATA ITEM MINIMUM VALUE (SI) MAXIMUM VALUE (SI)

1 1 19

2 0 90

3 1 2

4 0 1,000,000

5 0 100

6 0 1,000

7 0 1,000

8 0 100

9 0 1,000,000

10 1 7 11 0 10,000,000

12 0 3,000

13 33(5/8) 212(100)

20 0 1,000,000

21 0 100

22 0 1,000,000

23 0 100

24 0 100

25 0 100

30 0 100,000,000

31 0 .. 10,000

32 0 100

33 0 100,000,000

34 0 100,000,000

40 0 100

41 0 100,000,000

42 0 100

44 0 10,000,000

45 0 100,000,000

46 0 100,000,000

47 0 10,000,000

48 0 year < study period 100,000,000

49 0 100,000,000

50 0 1,000

51 0 1,000

52 0 1,000

53 0 1,000,000

54 0 1,000

55 0 1,000

56 1 6

57 1 6

58

60

any number (+/-)

0 100

61 1 40

70 1 3

G1
NBS-114A irev. 2 -80 ) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2342

2. Performing Organ. Report NoJ 3. Publication Date

4.

TITLE AND SUBTITLE

FEDSOL: Program User's Manual and Economic Optimization Guide for Solar

Federal Buildings Projects

5.

AUTHOR(S)

Jeanne W. Powell and Richard C. Rodgers, Jr.

6.

PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Department of Energy

Washington, D.C. 20585

10.

SUPPLEMENTARY NOTES

_J Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) This report provides a user's manual for the FEDSOL computer program and a guide

for designing and sizing solar energy projects for Federal buildings. The lifecycle cost procedures implemented by the computer program and explained in the

report are consistent with the Federal Rules for Life-Cycle Costing (10 CFR Part

436) as applied to solar energy projects.

The FEDSOL program determines the economically optimal size of a solar energy

system for a user-specified building, location, system type, and set of economic

conditions; it conducts numerous breakeven and sensitivity analyses; and it

calculates measures of economic performance as required under the Federal Rules.

The economic model in the program is linked with the SLR (Solar Load Ratio)

design method developed at Los Alamos National Laboratory to predict the

performance of active systems. The economics portion of the program can, however,

be used apart from the SLR method, with performance data provided by the user.

An environmental data file for 243 U.S*. cities is included in the program.

Highly user oriented, the FEDSOL program is intended as a design and sizing tool

for use by architects, engineers, and facilities managers in developing plans

for Federal solar energy projects.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

economic optimization; life-cycle costing; solar economics; solar energy.

13.

AVAILABILITY

fyj^Unlimited

| | For Official Distribution. Do Not Release to NTIS

f | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

124

15. Price

$ 11.00

USCOMM-DC 8043-P80
I

1I