The diffusion of photovoltaics : background, modeling, calibration and implications for government policy

The Diffusion of Photovoltaics: Background, Modeling, Calibration and Implications for Government Policy

Gary L. Lilien May 1978

MIT ENERGY LABORATORY REPORT - MIT-EL-78-019

PREPARED FOR THE UNITED STATES DEPARTMENT OF ENERGY

Under Contract No. EX-76-A-01-2295 Task Order 37

Note: Charles Allen, Arnold Barnett, Pat Burns, Tom McCormick, Bruce Schweitzer, and Leif Soderberg contributed significantly to the material described in this paper.

APPENDIX 1.1 PV PROGRAM

A.l.1 A Users Guide to the Photovoltaics Simulation System

The photovoltaics simulation system is a self-contained interactive set of computer programs on the Multics system at MIT; It allows the user to exercise the PV model for different sets of parameters by pro-viding general facilities for creating, saving, editing, using, display-ing and deletdisplay-ing sets of parameters. The organization of these sets of parameters reflects the model: the full set of input data is kept in a model, which contains parameters which apply across sectors, such as the cost decline factor, as well as the names of its constituent sectors. A sector, in turn, contains the data that are relevant only to itself, such as average PV installation size. Finally, when a model and its associated sectors are used to perform a simulation, the results are saved in a run, which records all the model and sector input data as well. The commands

in the system are used to manipulate these three types of sets of data, or records.

The actual model is defined by the following key variables and equations:

Xit = number of kwatts of government PV installed in sector

i during time t

Yit = number of Kwatts of private PV installed in sector i during time t

Ct = cost of one Kwatt of PV at the end of period t

-195-*0

Z_i = average number of Kwatts per PV installation in sector i Nit cummulative Kwatts of PV installed in sector i up to

time t

Nt = cumulative production of Kwatts of PV up to time t

No = Kwatts of PV installed before model begins

CO = cost per Kwatt of PV before model begins

X = decimal factor by which cost declines when PV produc-tion doubles

F () = cumulative normal distribution for cost acceptability,

ci

parameterized by and aoc

Ci F

SI

(.) = cumulative normal distribution for successful installa tions acceptability, parameterized by pi and a

i

si

hi = probability of purchase by randomly selected individual in sector i given acceptability

Pio = initial potential market for PV in sector i

Pt = total potential market for PV in sector i at time t

Qi = potential original equipment PV installation that becoifies available per time period

= growth rate of existing market potential in sector i

The equations relating these variables are:

t

N

-

I

(xi+Y

T=

-196-N_t = N + Nit

Pit = (P it-l-Qi)(l+gi) + Qi

1 F l(C₁₎ = probability that cost is acceptable at the beginning of period in sector i. F (N /Zi) = probability that installed PV is

accept-s.

it-

i

able in sector i at the beginning of

period t.

Yit = it- Nit-1/Zi)(1-Fci(Ctt- )) Fsi(Nit-1/Zi) hi Zi

Ct = Co(Nt/No) g2X

These equations describe the model that is embodied in the simulation system. Tables I, II and II (for models, sectors and runs, respectively) show the correspondence between the variable names used here and the names

as they appear in the computer programs and on the output.

In use, the computer and the user exchange information through a com-puter terminal. There is a wide variety of comcom-puter terminals, which have various switches that must be properly set to communicate with Multics. After turning the terminal on, a COM/LCL switch should be on COM, a REMOTE/LOCAL switch on REMOTE, a FULL/HALF switch on HALF, a CONT MSG

switch ON, and a speed switch on HIGH. Once the terminal is ready, you must "dial-up" the computer, that is, establish the telephone link between

-197-it and your terminal. The phone number is 258-8215 for IBM 2741-like ter-minals and 258-8313 for ASCII-type terter-minals. The general procedure is to dial the number; you should get a high-pitched tone in response. Then, depending on the communication system used, push the DATA button or pull up the white button in the handset cradle or insert the handset into the acoustic coupler. On 2741-like terminals, Multics will respond with a two-line message. For ASCII-type terminals, you must type a speed identification character first, followed by a line-feed. Use "s" for 110-baud terminals (11 characters/second), "y" for 150-baud (15 cps) or "o" for 330-band (30 cps). Multics will then respond with its two-line message. Then type

login SMcCormick

and hit carriage return for 2741, line-feed for ASCII. You will then be prompted for the password; enter it, again followed by carriage return for 2741, line-feed for ASCII. After that, Multics will print some login messages and the simulation system's opening message will print. From this point on, everything you type on either kind of terminal should be terminated with a carriage return.

The system will ask if you need the system explained (see attached sample terminal session). If you are familiar with the system, type "no", otherwise type "yes". The system expects the full word "yes" or "no" when-ever it asks you a question, though it generally assumes a "no" answer if anything other than "yes" is typed. If you answered "yes", a brief

description of the commands will be printed. In either case, the system then prints "READY" as a signal that it is awaiting your first command.

-198-You then type in the command that you want performed. If you mistype the

command or type a non-existent command, the system will respond: The command XXX does not exist - try again

with XXX replaced by the command you typed. You should then type in a valid command. After the command has finished processing (which may require that you type in information), the system again prints "READY" and awaits your next command. This cycle is terminated when you type the command:

return

which will stop processing and automatically log you off the computer. You will be informed of this by the message:

You will now be disconnected from the computer. Goodbye.

There may be circumstances when you don't want a command to finish an action it has started. For instance, you may start displaying some-thing that is longer than you thought. In any such situation, press the "quit" button on the terminal (which may be labeled "attn" or "break" on some terminals). Whatever the command is doing will stop, "QUIT" will be printed, and then "READY" will be printed to indicate that the next

command may be entered. In certain situations an additional informational message in parentheses will be printed before "QUIT" to inform you of the

status of the records that were being processed. Also, should an unfor-seen error arise, an error message will be printed containing information so the system maintainer can diagnose the error, followed by an artifi-cially created quit signal to return you to command level. Any error mes-sages should be reported promptly to the system maintainer.

There are general conventions that apply to all commands. The format in which they are typed is the command name followed by other information, separated by blanks. For instance,

create model example

would be used to create a model named example. The commands are flexi-ble though; in this example, "create" could be abbreviated to "cr", and any word beginning with "m" could be substituted for "model." Thus

cr m example

create mood example cr money example

would all have the same effect as the previous example. In general, most commands have one or two letter abbreviations, and whenever the next field entered is a type ("model," "sector" or "run"), only the first letter is significant. All names are used as is with no abbreviation allowed. Different types of records are allowed to have the same name (i.e., you can have a model and a sector both named test), but two records of the same type must have different names. The programs check for this and give you a chance to re-enter a different name or overwrite the al-ready existing record if you try (inadvertently or not) to use a dupli-cate name. You can also choose to "cancel" in such circumstances, which means that you are returned to command level as if you never entered the

original command. The programs check to see if you have entered a valid record type, and prompt you if you haven't. For example:

cr x wrong

is answered by:

First argument must be model or sector. Reenter:

You can then type a word beginning with "m" or "s" and create the proper record. If you realize that you don't want to create anything, you can hit "quit" to return to command level. In addition, if you leave out arguments, the programs will prompt you for them. For example:

cr model

is answered by:

Enter model name:

Also several commands allow you to process several records of the same type at once. For instance:

cr mood testl test2 test3

will create three models.

The available commands are:

create - creates models or sectors copy - copies models or sectors modify - modifies models or sectors

delete - deletes models, sectors or runs display - displays models, sectors or runs run - runs a model creating a run

index - lists records on file of a given type

help - prints a brief description of command syntax return - terminates processing, logs you off

The last two commands are self-explanatory and have no arguments. The other seven commands are described below.

create: Syntax: create TYPE NAME1 NAME2 Abbreviation: cr

TYPE: can be model or sector

NAMES: are 0 or more names of records to be created. When this command is invoked it will successively prompt you for all the data items needed to create a model or sector. When the last

item has been entered, a message is issued confirming that the record was created, then the next record (if any) is processed.

copy: Syntax: copy TYPE OLDNAME NEWNAME

Abbreviation: cp

TYPE: can be model or sector

OLDNAME: name of existing record which is to be copied NEWNAME: name that the copy is to saved under

This command copies the record OLDNAME of the indicated TYPE under the name NEWNAME and issues a confirming message. Since the use of this

command is frequently to have several versions of the same record with minor changes, you will then be asked if you want to modify the new record. Answering "yes" is equivalent to issuing the command "modify TYPE NEWNAME."

-202-modify: Syntax: modify TYPE NAME1 NAME2 ...

Abbreviation: m

TYPE: can be model or sector

NAMES: are 0 or more names of records to be modified

When invoked, modify asks for your first subcommand. A dictionary of subcommands is printed by typing "help." Most subcommands are the names of variables that can be changed. To do this, enter the variable name. The program reports back the old value and asks for the new value. Then it prompts you for the next subcommand. There are also subcommands to display the modified record and to finish processing and return to com-mand level.

delete: Syntax: delete TYPE NAME1 NAME2 ... TYPE: can be model, run or sector

NAMES: are 0 or more names of records to be deleted

There is no abbreviation for delete, to avoid accidental deletions. For models and runs, delete checks the index to see if they have been run and displayed, respectively, and asks you to confirm whether you really want to delete these unused records or. not. A confirming message is printed after each deletion.

-203-display: Syntax: display TYPE NAME1 NAME2 ...

Abbreviation: dp

TYPE: can be model, sector or run

NAMES: are 0 or more names or records to be displayed This command prints the requested records on the terminal, one at a time. For a run, display asks you if you want model, sector, both or. neither input variables printed (again, only the first letter is

signifi-cant, so "m", "s", "b" or "n" is sufficient), and give you the same choice for output variables. Successively answering "b", "b" will print every-thing, "n", "n" will print noevery-thing, "s", "s" will print only

sector-specific input and output variables (which depend on model input variables however), etc.

run: Syntax: run MODELNAME RUNNAME

Abbreviation: r

MODELNAME: name of the model to be run

RUNNAME: name that the output will be saved under

After the model is run, the program prints a confirming message and asks if you would like to have the run displayed. Answering yes is equiva-lent to issuing the command "display run RUNNAME".

index: Syntax: index TYPE

Abbreviation: i

TYPE: can be model, sector, run or all

-204-If TYPE is "all" or left blank, index prints a table of all records created and still on file giving their name, their type, and for models and runs, under the heading "Used?", an indication of whether they have been run and displayed yet. If TYPE is model, sector or run, a table

restricted to only that type of record is printed with no type column but retaining the "Used" column.

To clarify these ideas an annotated terminal session is attached, followed by a complete listing of the program.

-YI

d . ,·

-205-TABLE I: Model Correspondences

English Concept Name

Number of Sectors Number of time periods

Initial cost Cost decay rate

Initial installed Kwatts of

PV Name of sector i Government investment in sector i at time t Symbolic Notation C0 A N0

Xit

PL/I Variable Name mname n tmax initcost costdecay initwatt sn(i) govinv(i,t) Modify Mnemonic name n tmax initcost costdecay initwatt secname(i) govinv(i,t)

-206-TABLE II: Sector Correspondences

English Concept Name

Average PV installation size (Kwatts)

Initial existing poten-tial market (Kwatts) Growth rate of existing

potential market

Potential for original equip-ment installation per time period (Kwatts)

Purchase probability given acceptance

Mean of cost distribution

Symbolic Notation Z. PiO Qi h. 1 PL/I vari-able name sname avgsize initpotinst buildrate newinst ppurch cmean Pci Modify mnemonic name avgsize initpotin buildrate newinst ppurch costmean

Std. dev. of cost distribu-tion

Mean of successes

distribu-tion Std. dev. of successes distribution cdev costdev imean

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-210-APPENDIX 2

FACTOR STRUCTURE COMPARISON: AGRICULTURAL SECTOR

With Choffray and Lilien's [13] modification of the Chow test, when we compare the evaluation criteria of A against C we must also look at the evaluation of the combined group, (A + C). Actually, we are

comparing A and C with (A + C) to determine equality; our null hypoth-esis is that the groups are, in fact, equal. Defining:

N(1-R2) X N-2q

C =

nl(l-RP1)+

n

2

(1-R

22

)

q

where,

2 2

R' R2 = squared multiple correlations associated with the p1' p2 estimation of factor p in sample 1 and 2 respectively

2.

R = squared multiple correlation associated with factor p in pooled sample

nl,,n₂ = number of responses in sample 1 and 2 respectively

N = n + n2

q = number of items

When the value of C exceeds the corresponding F statistic at the appropriate level of significance, the null hypothesis of equality is rejected.

Group A = Pre-test and post-test survey Group B = pre-test survey only

Group C = post-test survey only

-211-APPENDIX 2 (continued)

TABLE 1

For comparison of A and C:

Factor C F F

p .90 . 95

1 0.41 1.72 2.01

2 0.42 1.72 2.01

3 1.79 1.72 2.01

null hypothesis is accepted at the .95 level

TABLE 2

For comparison of B and C:

Factor 1 2 3 C F p .90 2.62 1.72 2.53 1.72 0.22 1.72 F_. 9 5 2.01 2.01 2.01 .F9 9 2.75 2.75 2.75 FF _{9 9} 2.75 2.75 2.75

null hypothesis is rejected at.the .95 level

-212-APPENDIX 3: FACTOR STRUCTURE COMPARISON: RESIDENTIAL SECTOR

TABLE 1

COMPARISON OF GROUP 1 AND GROUP 2

Factor 1 2

3

C

P

5.76

10.58

3.34

F.

.g..9 0

1.72

1.72

1.72

F.9 5

2.01

2.01

- 2.01

F .9*7

2.75

2.75 2.75

Null Hypothesis of equality is rejected

COMPARISON OF GROUP 3 AND GROUP 4

Factor

2 3 C

P

0.94 2.42 1.24

F.

9 0 1.72 1.72 1.72 F._{9 5}

2.01

2.01

2.01

F.99 2.75 2.75 2.75

Null Hypothesis is rejected at the .95 level

-213-APPENDIX 3 (continued): TABLE 2

MODIFIED CHOW TEST

COMPARISON OF GROUP 1 AND GROUP 4

C

P

Factor

I

2

3

2.44

. 3.72

-8.88

F .90 1.72 1.72

1.72

F,_{9 5}

2.01

2.01

2.01

Null Hypothesis of equality is

rej

COMPARISON OF GROUP 2 AND GROUP 3

C

p

Factor

1

2

3

6.57

1.92

0.88

F.90

1.72

1.72

1.72

F.9

5

.95

2.01

2.01

2.01

Null Hypothesis of equality is rejected

-214-F .99

2.75

2.75

2.75

F.99

.99

2.75

2.75

2.75

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