ELE CTRA
Time Dependent Power Generation Operation Model
User Documentation
Susan Finger
MIT Energy Laboratory Technical Report MIT-EL 79-025
August 1979
Update August 1980
2
I. Introduction
5
II. Operating Instructions
III.
6
A. Time Structure
6
B. Load Curves
6
C. Unit Data
6
D. Case Structure
7
Program Structure
A. Functional Description
1. Cumulative Load Probability Distribution
2. Cumulative Load Frequency Distribution
7
7
7
12
3. Hourly Unit Probability and Frequency
Distribution
12
4. Equivalent Load Probability and Frequency
Distributuion
5. Transmission and Distribution Losses
B. General Block Diagram
IV. Input Files
VII.
17
18
19
A. Card Set Descriptions
19
B. Input Format
20
C. Output Format
26
V. Subroutine Documentation
VI.
16
28
Labeled Common Documentation
41
Sample Run
53
References
1. ELECTRA Input File
53
2. ELECTRA Output File
67
71
List of Figures
1. Creation of load duration curve
2. Conversion from a step function to a piecewise linear function
10
3. Load frequency curve
13
4
Program Summary
TITLE:
ELECTRA, Time Dependent Electric Power Generation Model
AUTHOR:
Susan Finger
PURPOSE: ELECTRA finds the net demand probability and frequency
distributions from an electric utility with time dependent
generators.
METHOD:
The program uses convolution to find the hourly probability and
frequency distributions
SCORE:
The program can handle one customer hourly load curve and up to
four hourly load reduction curves each with up to 8784 hours.
Up to 10 cases can be run, but no one case can have more than 4
distinct units.
A unit can be represented as any multiple of
one of the load reduction curves.
INPUT:
Up to 20 units can be entered.
The program requires general information on how the output
curves are to be structured, the original load curve, the load
reduction curves, the unit characteristics, and the units to be
included in each case.
OUTPUT:
ELECTRA writes load probability and frequency curves into files
to be read by SYSGEN.
There are no reports.
5
I. Introduction
ELECTRA was written so that time dependent power generators could be
included in the production costing model, SYSGEN.1 The methodology
used in ELECTRA is described in greater detail in the accompanying
technical report:
"Electric Power System Production Costing and
Reliability."2 There is also a third program, SCYLLA, that is run
after ELECTRA and SYSGEN that evaluates the worth of the time dependent
power plants to the utility system.3
ELECTRA models time dependent power plants as increases or decreases
in the net load on the system.
Up to four hourly load change curves can
be entered in addition to the original customer demand curve.
The hourly
load curves are converted into load duration curves that represent the
net load with and without the time dependent plants.
A basic assumption in ELECTRA is that the time dependent load
modification does not depend on the output of the other generators.
Therefore, ELECTRA can be used to model generators whose marginal cost is
less than the marginal cost of all the other generators or generators
with a predetermined dispatch strategy that does not depend on the other
generators.
1Finger,
S., SYSGEN, "Production Costing and Reliability Modeling User
Documentation," MIT Energy Lab Technical Report #MIT-EL 79-020, February
1979.
2Finger,
S. "Electric Power System Production Costing and Reliability
Analysis Including Hydro-electric Storage and Time Dependent Power
Plants," MIT Energy Lab Technical Report #MIT-EL-79-006 February 1979.
3Finger,
S., "SCYLLA, Time Dependent Electric Power Generation
Evaluation Model, User Documentation," MIT Energy Lab Technical Report,
forthcoming.
6
II. Operating Instructions
II.A.
Time Structure
ELECTRA can have up to 8784 values in the customer demand curve and
in each of the load modification curves.
It is assumed that the times
for the demand and the modification curves match, e.g., the first value
for each curve corresponds to the first hour in the year.
There can be up to 52 output load duration curves, each with up to
100 values.
The length of time represented by each load duration can be
varied and all output curves do not need to represent the same length of
time.
Currently the output curves are created from sequential values,
e.g. months.
However, with slight modification, the program could create
load curves for weekdays or weekends.
II.B
Load Curves
The customer load curves and the load modification curves can be
input either in standard EEI format or an extended format. The values
are normally given hourly.
If the load modifications decrease the net
load on the system, then the load modifications are entered as positive
numbers.
If the load modifications increase the net load, then they are
entered as negative numbers. Up to four load modification curves can be
entered.
II.C. Unit Data
Each unit is specified by a load modification curve, a scale factor,
a nominal rating, a forced outage rate and a mean time to repair.
The
load modification curve gives the time varying output for a nominal size
generator.
The scale factor is the ratio of the unit's output to the
7
output of the nominal size generator. For example, the first load
reduction curve might represent a 100 MW solar thermal unit and first
plant might be a 200 MW solar thermal unit, and be represented by twice
the output of load reduction curve 1. The forced outage rate is the
fraction of time that the unit is unavailable due to mechanical failure.
The mean time to repair is the expected time that it takes to repair the
unit after it has failed.
There can be up to 20 units, but there can be
at most 4 load modification curves that they reference.
II.D Case Structure
Within a single run, ELECTRA can run up to 10 cases.
have up to 4 distinct units, specified by the unit index.
Each case can
The units can
have the same unit index. All the cases within a run are based on the
same customer load curve and load modification curves.
III
Program Structure
III.A.1
Cumulative Load Probability Distribution (Subroutine ELECDF)
The cumulative load duration curve is created from the hourly load
probability distributions.
First, the probability for each load level is
found using equation (76) from reference (1).
P
Pc(x) = t Pctx It)
(1)
where
Pc(x) = Probability that the customer load = x
Pct(xlt) = Probability that the customer load = x at time t
T = length of the time period.
8
In creating the original customer curve, it is assumed that the customer
demand is deterministic, i.e. Pct(x It)= 1. The load duration curve
is found using the standard method of collapsing an hourly historical
demand curve as shown in figure 1. Analytically, the load duration
curve is found by sorting Pc(x) from the smallest to largest load level
and then summing:
Xmax
Fc(y) =
(2)
Pc(x)
x=y
Fc (y) = load duration curve
where
Xmax = peak demand.
Within the program, Fc(x) must be put in the proper format for SYSGEN.
The load duration curve as it is created in equation (2) can have as many
entries as there are hours in the time period, and the curve is a step
function.
In SYSGEN, the probability curve is stored at equal intervals
along the load axis and intermediate values are found using linear
interpolation.
In converting from the step function to a piecewise
linear function, the original shape and total area should be preserved.
The following algorithm is used (see figure 2 for illustration):
1)
Set up the hourly values in the WORK array (done in
ELESET).
Sort the load in decreasing order, storing the
largest value in WORK(IEND).
(The sort is performed in
ELECRV.)
2)
Compute the load curve spacing, DM.
DM = peak demand/NPNT,
where NPNT is the number of points in each final load
duration curve.
(NPNT is input.)
9
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10
Figure 2 CONVERSION FROM A STEP FUNCTION TO A PIECEWISE LINEAR FUNCTION
0
.ta-
.0
Demand (MW)
·
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RES.
Demand (MW)
Accumulated Area = B-A + D - C
i
11
3)
Set ICOUNT = the number of spacings for which the load
duration curve = 1.0 (those values less than the minimum
demand).
Set the load duration curve, CDF, equal to 1.0
from 1 to ICOUNT.
4)
Loop through the WORK array from smallest to largest (from
IEND to 1) using J as the counter.
5)
Compute the distance along the demand axis between WORK(J)
and WORK(J + 1).
Compute the integral number of spacings,
INC,.and the residual, RESX.
6)
If INC = O, then go to 7.
Otherwise, compute the area under the curve, up to the
current counter J that has not yet been included in the
curve.
Compute the change that must be made to PROB(J)
so that all the area is accounted for.
Fill in the load
duration curve, CDF, and increment ICOUNT by the number of
spacings found in step 5.
7)
Compute the residual area from the remainder value, RESX,
and PROB(J), and compute the accumulated distance along the
demand axis which has not yet been included in CDF.
(If
the load levels are closely spaced, several may fall within
an array spacing.)
8)
Increment J. Go to 5 if J is less than NPNT.
9)
Call the area routine from SYSGEN and compute the area
under the CDF curve.
Compute the difference between the
true area and the actual area.
by the percentage error.
Change all non-one values
12
III.A.2
Cumulative Load Frequency Distribution (Subroutine:
ELEBSE)
The load frequency curve is found by counting the number of times
that the original customer load crosses a given load level.
The load
levels that are chosen correspond to the load levels at which the
probability curve is stored.
The number of counts is normalized by the
number of hours in the time period.
(See figure 3.)
A reverse
cumulative curve is then computed.
FQ (Y)
max fq
(x)
(3)
x=y
where fqc =
number of times per hour the load moves from a state
with the load less than x to a state with the load
greater than x.
FQc(x) =
number of times per hour the load enters a state with
load greater than x.
III.A.3
Hourly Unit Probability and Frequency Distributions
(Subroutine: ELEPRB)
The hourly probability density function for the change in load due to
time dependent sources is given in equation (74) of reference 1. Using
convolution:
Rt
where
x 1t) = PRT (x t) + qPRT (x-citlt)
(4)
PRt (x t) = probability that the net change in load, after
plant i is added, equals x at time t
PRt (x t) = probability that the net change in load, before
plant i is added, equals x at time t
1.3
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0)
a
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14
qi = forced outage rate of unit i (independent of time)
Pi = 1-qi
= availability of unit i (independent of time)
cit = power output of unit i at time t.
A similar equation exists for the frequency distribution of the change in
load:
fqRt (x It)= Pi fqRt (xIt)+ q fqRt (x-cit
iPi PRT (xIt)+
where
fqRt (x
(5)
t)
qi PRt (x-citj t)
t) = number of times per hour that the load
enters load state x (frequency that the load change
equals x) at time t after unit i is added
Fq Rt(X t) = frequency that the load change equals x at time t
before plant i is added
1
l.
1
= forced outage occurence rate for unit i
= force outage restoral rate for unit i.
The probability and frequency functions for the load changes are
impulse functions; that is, they have values only at discrete points and
are zero otherwise.
PRt (x )t) =
For the first unit, these distributions are:
P1
if x = Ctl
q1
if x = 0
0
otherwise.
(6)
15
fqRt (x t) =
q1
ctl
ifx
pX?,
(7)
1 if x = 0
otherwise
0o
If a second unit is added, using equations (4)and (5) above, the
distribution becomes:
PRt(x It) =
P1P2
if x = Cti + Ct2
qlP 2
if x = ct2
p1q2
if x = ctl
qlq 2
if x = O
(8)
otherwise
0
XI
P1P2 [X
+
_\
qlP2 [
1+
x2
2]
if x = ct2
fqRt(X It)=
plq2 [
1+
" 2]
if x = Ctl
2
if x = Cti + Ct2
(9)
2
q lq 2
[
1 +
2
if x = O
otherwise
These sequences are generated in ELEPRB using a combinatorial
algorithm.
This algorithm is executed only once because the distribution
themselves do not depend on time.
However, the output of each unit and
the customer load both depend on time, so ELEPRB is called for every hour
to return the net load corresponding to each entry in the hourly
probability and frequency arrays.
The frequency density functions are input as hourly distributions;
i.e., the mean time to repair is given in hours.
The probability
16
functions, however, have to be adjusted by the number of hours in each
time period so that each hour is given equal weight and so that the sum
of the probabilities of all possible states in the time period is equal
to one.
Therefore, whenever ELEPRB is called at the start of a new
The frequency
curve, the probability distribution is adjusted.
distribution is also adjusted since it contains the probability
distribution.
III.A.4.
This is done at the end of ELEPRB.
Equivalent Load Probability and Frequency Distribution
The equivalent load is the sum of the original load minus the load
supplied by the time dependent power plants.
The hourly distribution of
the equivalent load is:
PEt(Y
t) = E
Pct(x
(10)
t) PRt (Y-x t)
Then, the time independent distribution is:
E
PE ()
E
Pt (x
t)PRt (y-xI
t),
(11)
and the cumulative is:
FE(Y)
PE (x)
(12)
The cumulative distribution is converted into a linear curve using the
algorithm given in section III.A.1 for the customer curve.
The hourly equivalent frequency curve is given by:
fqEt(y I t) =
[Pc(x I t) fqRt (-x
+ fqc (x
t)
t) PRt (y-x j t)]
(13)
17
This summations to convert fqEt to a time independent cumulative are
the same as for the probability distributions.
III.A.5. Transmission of Distribution Losses (Subroutine ELECTD)
ELECTD is a proxy for transmission and distribution loss and
reliability analysis for decentralized generation.
If the original
customer demand includes demand due T&D losses, then when decentralized
generation is used, these losses are not incurred.
ELECTD computes the
change in demand due soley to the reduction in losses.
Currently the
marginal loss factor is entered for five demand levels given as a
percentage of the peak demand.
linear interpolation.
Intermediate values are found using
18
Input Common
Data
Yes
Case Counter
E
a)
Stop
No
Yes
·\·
·IC·
C
Iricrement the Curve
Counter
,
No
Set Up Hourly Probability
and Frequency Curves for
the Time Dependent
;
Generators
.
Write the Curves
to the Output
Files
|
I
!
Convert the Cumulative
Discrete Load Curve to
a Piecewise Linear
Curve
- ·
*No
a)
Set Up Hourly Load
Reduction Curve for
the Time Dependent
Generators
4-,
C
c
:3
0
0
=3
0
I -,
cC:
Cr
a,
Convolve the Hourly
Frequency Curve into
the Cumulative
Frequency Curve
E
I-
C:
III.
Add the Hourly Arrays
to the Cumulative
Arrays
rrays
B. General Block Diagram
19
IV.
8/80
Input File
IV.A
Card Set Description
File Unit
Number
File
Name
Card
Number
10
IGEN
A/1-5
A/ 1/1
A/2/1
A/2/2
A/2/3
Information to be Supplied
Input:
A/2/4
A/2/5
A/2/6-9
10
IGEN
B/1/1
B/2/1
B/3/1-4
General Information
Debug options
Print options
Operating options
Loading order option,
spinning reserve
Class identifiers
Year dollars information
Report headings
General Information
Start, end of planning
horizon
Number of sub-periods, hours
per week
Number of weeks in a
sub-period
13 sub-periods per card
B/4-5
Time Dependent Unit Information
25
ICL S
C
Class data
11
LOADC
D
Customer Load Data
12
LOADDD
F
Load Reduction
13
ITD
F
T+D Data
30
IPLNT
G
Unit Data
22
IBUG
ELECTRA debug file
60-69
ICRV
Load duration curves for cases
1 to 10
70-79
IFRQ
Frequency curves for cases 1 to
10
80-89
ICOR
Correlation curves for cases 1
to 10
Output:
20
IV.B
Input Format
Card
Columns
Variables
Format
A/1
42
50
52
54
IDEBUG (21)
IDEBUG (22)
IDEBUG (23)
IDEBUG (24)
IDEBUG (25)
IDEBUG (26)
IDEBUG (27)
L1
L1
L1
L1
L1
L1
L1
64
MCORR
L1
72
MEEI
L1
A/2/2
16
MFREQ
L1
A/2/3
blank card (SYSGEN information)
44
46
48
A/2/1
A/2/4
Description
Debug Option for:
ELEBSE
ELECDF
ELECIN
ELECRV
ELEFRQ
ELEPRB
ELESET
If TRUE, load-generation
correlation matrix is
printed.
If TRUE, load input is
read in standard EEI
format.
If MFREQ=T, the frequency
curves are computed.
2-5
ITDP
A4
7-10
ICHY
A4
Alpha identifier for
time dependent units.
Alpha identifier for
conventional hydro unit.
(See card E/2/1.)
12-15
ISTO
A4
Alpha identifier for
storage units. Normally
17-20
IBASE
A4
22-25
INTR
A4
Alpha identifier for base
load class (see card
E/2/1). Normally set to
'BASE'.
Alpha identifier for
intermediate class.
Normally set to 'INTR'.
27-30
IPEAK
A4
Normally set to ' CHY'.
set to ' STO'.
A/2/5
blank card (SYSGEN information)
Alpha identifier for
peaking class. Normally
set to 'PEAK'.
21
Card
A/26
Columns Variables
2-41
TITLE(1-10)
Format
10A4
Description
Report Heading. A 40
character title
(including blanks) to
appear at the top of each
page of each report.
A/2/7
2-41
TITLE(11-20)
10A4
Title Page Heading. A 40
character head to appear
on the title page.
A/2/8
2-41
TITLE(21-30)
10A4
Title Page Heading. A
second 40 character
heading to appear on the
title page.
A/2/9
2-41
TITLE (31-40)
10A4
Title Page Heading. A
third 40 character
heading to appear on the
title page.
B/l/l
2-5
ISY
I4
7-10
IEY
I4
Start year of planning
horizon (e.g. 1985).
End year of planning
horizon (e.g. 1995).
NTP
I2
(ISY < IEY)
12-13
Number of time periods
(years) in study (e.g.
10).
[1 < NTP < 34]
Note: NTP = IEY-ISY+1
39-44
HOURS
F6.1
46-50
DR
F5.3
Number of hours in a time
peiod (e.g. 8736).
Discount rate used in
present worth
calculations.
[DR > 0.0]
B/2/1
2-3
NSTP
I2
5-10
HRWEEK
F6.1
Hours in aweek (e.g.
168.)
WKDAY
A4
Alpha identifier used for
reporting the length of
HRWEEK (e.g. WKDAY =
Number of time
sub-periods. A
sub-period may represent
a week, a month, a 4-week
period, or any other
fraction of a year.
[1 < NSTP < 52]
12-15
'WEEK', if HRWEEK = 168.0)
8/80
22
Card
Columns
Variables
Format
Description
B/3/1
2-3
NWEEKS(1)
I2
5-6
NWEEKS(2)
I2
8-9
NWEEKS(3)
I2
Number of weeks in
sub-period 1
Number of weeks in
sub-period 2
Number of weeks in
sub-period 3
38-39
NWEEKS(13)
I2
Number of weeks in
sub-period 13
B/3/2
Same format as card
B/3/1/ Information
pertains to sub-periods
14-26. Used only if
there are more than 13
sub-periods.
B/3/3
Same format as card
B/3/1/ Information
pertains to sub-periods
27-39. Used only if
there are more than 26
sub-periods.
8/3/4
Same format as card
B/3/1/ Information
pertains to sub-periods
40-52. Used only if
there are more than 39
sub-periods.
8/4
2-3
NCASE
I2
Number of runs with time
dependent units
[0 < NCASE < 20]
B/5/1
2-3
NOTD
I2
Number of time dependent
units in the first case.
B/5/2
2-3
IDTD(1)
I2
Unit index of the first
time dependent unit in
case 1.
8/80
23
Card
Columns Variables
Format
Description
NPLNT (1)
I2
Number of units with
index IDTD(1) in the
first case.
20-21
IDTD(4)
I2
23-24
NPLNT(4)
I2
Unit index of the fourth
time dependent unit in
case 1.
Number of units with
index IDTD(4) in the
first case.
5-6
Cards B/5/1 and 2 are repeated for each time dependent case until NCASEs
have been entered.
Group C/2 contains the class information and cross-reference table. Each
unit in the system will have a class number (j)which refers to the
information for the jth class, which is listed on the jth card in this
group.
C/l/l
2-3
NCLASS
12
Indicates the number of
generation classes to be
input. Each generation
class wil occupy one card
in Group 2. [1 < NCLASS
< 34].
C/2/1
2-5
ICLASS(1,1)
A4
Class name of Class 1.
Can be any character
string up to 4 characters
long including blanks.
NOTE: For storage class
ISTO must be entered in
columns 2-5 (as defined
on Card A/2/4).
7-10
ICLASS(1,2)
A4
Class type of Class 1.
'BASE' = Base loaded unit.
'INTR' = Intermediate
unit.
'PEAK' = Peaking unit
NOTE: SYSGEN uses the
class types in setting up
the order under many of
its loading order options.
Card sets D and E can be entered in either of two formats. If MEEI is
set to true on card A/2/1, then the following format is used:
8/80
24
Card
Columns
Variables
Format
Description
D/1
21-25
26-30
CSTLD(1)
CSTLD(2)
F5.0
F5.0
Customer demand in hour 1
Customer demand in hour 2
76-80
CSTLD(12)
F5.0
Customer demand in hour 12
Card D/1 is repeated until an entry has been made for each hour in the
time period.
E/1
21-25
CRVRED(1,1)
Load change for curve 1
in hour 1.
76-80
CRVRED(1,12)
Load change for curve 1
in hour 12.
Card set E/1 is repeated until an entry has been made for each hour.
The value of NINC on card B/2/1 determines the number of load reduction
curves to be read. Each curve follows immediately after the preceding
one and is numbered in the order it is read.
If NINC is set to zero, card set E is not required.
If MEEI is set to false, then the following format is used:
D/1
2-7
8-13
68-73
CSTLD(1)
CSTLD(2)
F6.0
F6.0
Customer demand in hour 1
Customer demand in hour 2
CSTLD(12)
F6.0
Customer demand in hour 12
The same format is repeated for Card Set E.
F/1
4-5
NLEVEL
I2
Number of TaD loss entries
[1 < NLEVEL < 10]
F/2
2-7
DLEVEL (1)
F6. 0
8-13
14-19
DLEVEL(2)
DLEVEL (3)
F6.0
F6.0
56-61
DLEVEL(10)
F6.0
Load level 1 (as fraction
of peak load)
Load level 2
Load level 3
Load level 10 (as
fraction of peak load)
25
8/80
Card
Columns
Variables
Format
Description
F/3
2-7
PLOSS (1)
F6.0
8-13
PLOSS(2)
F6.0
Marginal losses at load
level 1.
Marginal losses at load
level 2.
56-61
PLOSS(10)
F6.0
Marginal losses at load
level 10.
12-14
IC
I3
Class number for unit 1.
Cross-references to data
in Group E/2
15-16
NVPT
12
61-67
ATTR
F7.3
TCAP(1)
F7.1
FOR (1)
F6.3
G/1/1
[1 < ICLNUM < NCLASS]
G/1/2
2-8
19-24
Number of vaTve points
for unit 1.
Mean time to repair after
failure for unit 1 (hours)
[O < ATTR < HOURS]
Total MW capacity of unit
1. Used only if MXVPT =
1.
Forced outage rate for
unit 1[O < TFOR < 1.0]
G/1/3
Note:
1-3
NCRV(1)
I3
5-10
RNUM(1)
F6.1
Curve number for the time
dependent unit.
Capacity multiplier for
the time dependent unit.
This is all the information required for time-dependent
units. If other units are included in the plant file in
SYSGEN format, their data will be skipped and all the
time-dependent units will be processed.
26
IV.C Output Format
The only outputs from ELECTRA are the load duration and frequency
curves in SYSGEN format.
(See reference 2, card sets C and D).
Two
separate files are written for each case.
Card
Columns Variables
Format
Description
C/1
2-5
NPNT
I4
Number of points in each
load shape
C/1/1
2-3
6-11
NUMYR
PEAK
I2
F7.1
12-16
IOUT
I5
Year number
Peak demand for the first
output curve
Output curve number
Card C/1/1 is repeated for every output curve in current case
C/2/1
2-3
NOUTC
I2
Number of output load
shapes
C/3/1
2-11
CDF(1, 1)
F10.8
14-23
CDF(1, 2)
F10.8
26-35
CDF(1, 3)
F10.8
38-47
CDF(1, 4)
F10.8
50-59
CDF(1, 4)
F10.8
First entry in the first
load duration curve in
current case
Second entry in the first
load duration curve
Third entry in the first
load duration curve
Fourth entry in the first
load duration curve
Fifth entry in the first
level duration curve
Card C/3 is repeated until all NPNT points have been written.
Card sets C/3/2 - C/3/NOUTC are the same format as C/3/1. These card sets
follow one another directly without any spacing cards in between. Each case
is written to a separate file.
The frequency data is written to a separate file. Its format is identical to
that of C/3. There are no cross reference cards in the frequency file. In
SYSGEN, the curves are assumed to match the load duration curve file with the
matching name. The frequency curves are assumed to be given in the same order
as the load duration curves and to have the same number of points.
The correlation matrix is written to a separate file also. This file is
designed to interface with a long-range planning model that requires the joint
distribution of load and time dependent output. Its current format is 7F1L8
27
Eleven values are reported for each load level.
These values correspond to
Probability time dependent generation = y given the load > x
for y are 0, .1 capacity, .2 capacity, ..., capacity.
-
. The values
28
V. Subroutine Documentation
NAME
ELECTRA
TYPE
MAIN
SYSTEM
SYSGEN
UPDATE
7/2/79
DESCRIPTION
ELECTRA is the main routine
ARGUMENTS
None
COMMONS
/ELEGEN/, /ELEIOS/, /DEBUGS/
SUBROUTINES
ELECIN, ELESET
LOGIC
1) Set up input file numbers.
2) Call ELECIN to set up common data blocks.
3) Loop through all cases calling ELESET for each output
curve.
4) Stop.
ERRORS
IFLG = -98 Error in call to subroutine
IDEBUG
None.
29
NAME
ELEBSE
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
8/8/79
DESCRIPTION
ELEBSE computes the load and frequency curves for the base case.
ARGUMENTS
NAME
IFLG
IOUT
IFIRST
ILAST
COMMONS
/ELEGEN/, /ELETDF/, /ELECVE/, /DEBUGS/
SUBROUTINES
ELECRV, ELECWT
LOGIC
1)
2)
3)
4)
5)
6)
7)
8)
9)
ERRORS
DEBUG:
DESCRIPTION
error code (returned)
output curve number
first hour in the curve
last hour in the curve
TYPE
1*4
1*4
1*4
1*4
Set the base case load curve, CDF, and frequency curve,
FLOAD, to zero.
Set the WORK array equal to the original customer demand.
Set the PROB array equal to one divided by the number of
entries. Compute the area under the curve and find the
minimum and maximum load.
If the frequency curves are not required, go to 6)
otherwise, divide the load curve into strata, and count the
number of times the load crosses each stratum from below.
Accumulate the counts in the FREQ array.
Divide the number of counts by the number of hours in the
curve. The division is performed in a separate operation
due to the rounding errors that occur if it is performed as
part of step 3.
Call ELECRV to create the cumulative load curve, CDF.
Set CLOAD equal to CDF so that it can be saved for the
succeeding cases.
Call ELECWT to write the curves to the output files.
Return.
IFLG = -97
Number of possible probability states greater
than allowed.
IFLG = -98
Error in call to subroutine.
If IDEBUG (21) = True, print the curve number, peak demand, minimum
demand, and the unsorted load curve. If the frequency option is
true, print the hour, load level, stratum value, and cumulative
frequency value. Print the frequency count curve.
30
NAME
ELECDF
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
7/2/79
DESCRIPTION
ELECDF creates the reverse cumulative load curve for the
equivalent net load
ARGUMENTS
NAME
DESCRIPTION
TYPE
IFLG
Error flag (returned)
output curve number
number of points in the
work array
peak demand in MW for
curve IOUT (returned)
total actual energy
demand in MWH for curve
IOUT (returned)
total computed area in
MWH under curve IOUT
(returned)
I*4
IOUT
IEND
PEAK
ENERGY
AREA1
COMMONS
1*4
1*4
R*4
R*4
R*4
/ELEGEN/, /ELECVE/, /DEBUGS/, /DEMAND/, /MAXMUM/
SUBROUTINES
AREADM (from SYSGEN)
LOGIC
1) Set up array counters and the /DEMAND/ and /MAXMUM/
common from SYSGEN.
2) Set the probability curve = 1 for all values less than
the minimum load.
3) Loop through the sorted WORK array that contains each
possible load level to find the probability of the load
level corresponding to the equally spaced intervals.
(See section III.A.1).
4) Set the probability array in /DEMAND/ equal to the
computed curve
5) Call AREADM and compute the difference between the
actual area and the area computed using linear
interpolation. Correct each term in the new array by
the percent error.
6) Return.
ERRORS
IFLG = - 96
Too many points in the new probability
curve
IFLG = - 98
Error in call to subroutine
31
ELECDF (cont.)
DEBUG
If IDEBUG (22) = True, print the peak demand. For each new
point, print the current WORK index; the probability
corresponding to the current load level and the load level
above it; the current position in the new probability
array, CDF; the difference between the current load level
and the previous one, RESIDUAL X (the distances along the
load axis); the accumulated distance between the last CDF
point created and the last load level, ACCUMULATED X; and
the residual area under the curve that has not yet been
accounted for.
32
NAME
ELECIN
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
7/31/79
DESCRIPTION
ELECIN reads the input files into the labeled common blocks.
ARGUMENTS
NAME
IFLG
COMMONS
/GGENRL/, /GCLASS/, /SYSDAT/, /TDPLNT/, /ELEGEN/, /ELECVE/,
/ELECLS/, /ELETDF/, /ELEIOS/, /ELECOR/, /DEBUGS/
SUBROUTINES
IRANGE
LOGIC
Read general information from file 10 into the
/GGENRL/, /SYSDAT/, and /ELEGEN/ comnons.
2) Read class data from file 25 into /GCLASS/ commons.
3) Read plant data from file 30 into /TDPLNT/.
4) Read T&D data from file 13 into /ELETDF/.
5) Read load data from file 11 into /ELECVE/.
6) Read load reduction data from file 12 into /ELECVE/.
7) Convert demand levels, entered as fraction.
8) Return.
ERRORS
IFLG = -97
IFLG = -98
DEBUG
If IDEBUG(23) = True, echo print the input.
DESCRIPTION
error code (returned)
TYPE
1*4
1)
End of file on input unit
Error in call to subroutine
33
NAME
ELECPK
TYPE
FUNCTION
SYSTEM
ELECTRA
UPDATE
5/24/79
DESCRIPTION
ELECPK returns the smallest non-positive value in the load
reduction curve. That is, if all entries are positive,
ELECPK returns zero. If entries are negative, ELECPK
returns the peak negative value.
ARGUMENTS
NAME
ICRV
IFIRST
ILAST
COMMONS
/ELECVE/
SUBROUTINES
None
LOGIC
1)
2)
3)
ERRORS
None
DEBUG
None
DESCRIPTION
curve number
starting array value to
be searched
last array value
TYPE
1*4
I*4
1*4
Set ELECPK = 0.0.
Loop through CRVRED(i,ICRV) from i = IFIRST to i =
ILAST. If CRVRED(i,ICRV) is less than ELECPK, set
ELECPK = CRVRED(i, ICRV)
Return.
34
NAME
ELECRV
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
7/2/79
DESCRIPTION
ELECRV sorts the load array from largest to smallest using
a bubble sort and computes the cumulative probability for
each load level.
ARGUMENTS
NAME
IFLG
IOUT
IEND
PEAK
ENERGY
AREA
TYPE
DESCRIPTION
1*4
(returned)
flag
error
1*4
output curve number
1*4
the
in
entires
number of
probability array
peak demand for curve IOUT R*4
(returned)
R*4
total energy demand for
curve IOUT computed from
the created piecewise linear
curve (returned)
R*4
total energy demand for
IOUT computed from the
input curve (sent)
COMMONS
/ELEGEN/, /ELECVE/, /DEBUGS/
SUBROUTINES
ELECDF
LOGIC
1)
2)
3)
4)
ERRORS
Use a bubble sort to order the load from largest to
smallest and store the sorted curve in the WORK array.
Compute the cumulative probability for each load level.
Call ELECDF to create the piecewise linear cumulative
load duration curve.
Return.
IFLG = -97
IFLG = -98
DEBUG
Probability value greater than one or less than
zero
Error in call to subroutine
If IDEBUG(24) = True, print the curve number, end point,
and the probability distribution
35
NAME
ELECTD
TYPE
FUNCTION
SYSTEM
ELECTRA
UPDATE
5/24/79
DESCRIPTION
ELECTD returns the marginal loss factor for the given
demand level.
ARGUMENTS
NAME
DEMAND
COMMONS
/ELETDF/
SUBROUTINES
None
LOGIC
1)
2)
ERRORS
None
DEBUG
None
DESCRIPTION
Customer demand
TYPE
R*4
Use linear interpolation to find the marginal loss
rate from the input loss rates.
Return.
36
NAME
ELECWT
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
ELECWT writes the probability and frequency curves to the
output file.
ARGUMENTS
NAME
IFLG
ICASE
PEAK
ENERGY
IOUT
DESCRIPTION
error code (returned)
case number
peak demand (MW)
energy demand (MWH)
output curve number
COMMONS
/ELEGEN/, /ELECVE/, /ELEIOS/, /ELCOR/
SUBROUTINES
None
LOGIC
1)
2)
3)
43
5
6)
7)
8
ERRORS
None
DEBUG
None
TYPE
1*4
1*4
R*4
R*4
1*4
Write the case number, ICASE, and number of points in
each curve, NPNT, at the top of the file
For each curve, write the peak, the energy, and the
curve number to file ICRV.
Write the frequency curves to file IFRQ.
Write the correlation curve to file ICOR.
If this is not the last curve in the case, then RETURN.
Otherwise, write all the load duration curves to file
ICRV below the peak and curve number information.
Increment all the output files by 1.
Return.
37
NAME
ELEFRQ
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
8/2/79
DESCRIPTION
ELEFRQ computes the equivalent frequency distribution for
the load plus the generation in the current hour.
ARGUMENTS
NAME
IFLG
IOUT
IHOUR
DESCRIPTION
error flag (returned)
output curve number
current hour
COMMONS
/ELEGEN/, /ELECVE/, /ELECHR/, /DEBUGS/
SUBROUTINES
None
LOGIC
1)
2)
3)
4)
TYPE
1*4
1*4
1*4
If frequency curve is not required, then return.
Loop through the points of the output curve
For each point in the output curve, perform the
frequency convolution (see Section III.A.4)
Return.
ERRORS
None
DEBUG
If IDEBUG (25) = true, print the output curve, hour,
and new frequency distribution.
38
NAME
ELEPRB
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
ELEPRB computes the hourly probability and frequency
density functions.
ARGUMENTS
NAME
IFLG
ICASE
IOUT
IHOUR
COMMONS
/TDPLNT/, /ELEGEN/, /ELECVE/, /ELECHR/, /ELECOR/, ELECLS/,
/DEBUGS/
SUBROUTINES
ELECTD
LOGIC
1)
2)
3)
4)
5)
6)
7)
8)
DESCRIPTION
error flag (returned)
case number
output curve number
current hour
TYPE
1*4
1*4
1*4
1*4
If this is the first hour, initialize the probability
and frequency arrays.
If there are no units for the current case, then
RETURN.
Set the T&D loss factor equal to the loss multiplier
for the customer load in the current hour.
Initialize the load array to zero.
Loop through all the classes for the current case.
Find the load reduction curve, JCRV, the number of
plants, IPLNT, the forced outage occurrence rate, and
the load reduction for the class in the current hour.
Loop through all possible combinations for the current
class and compute the new load and, in the first hour,
the proability and frequency distributions. (The
distributions are independent of time and need only be
computed once.)
At the end of the computation of curve, IOUT,
normalize the probability and frequency arrays by the
number of hours in the output curve.
Return.
ERRORS
IFLG = - 97
DEBUG
If IDEBUG (26) = true, print case number, output curve
number, total number of plants in the case, number of
possible states. For each class, print the class number,
number of plants in the class, reduced load, availability,
forced outage rate, lambda and mu. At the end of the
computation for IOUT, write the new probability density
function.
Probability out of range
39
NAME
ELESET
TYPE
SUBROUTINE
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
ELESET sets up the probability and load arrays to sorted by
ELECRV and converted to load and frequency curves by ELECDF.
ARGUMENTS
NAME
IFLG
ICASE
IOUT
IFIRST
ILAST
DESCRIPTION
error code (returned)
case number
output curve number
first hour in curve
IOUT
last hour in curve IOUT
TYPE
1*4
1*4
1*4
1*4
1*4
COMMONS
/TDPLNT/, /ELEGEN/, /ELECVE/, /ELECHR/, /ELECOR/, /ELECLS/,
/DEBUGS/
SUBROUTINES
ELEPRB, ELEFRQ, ELECRV, ELECWT, ELECPK, ELEBSE
LOGIC
1)
2)
3)
4)
5)
6)
7)
8)
ERRORS
If ICASE = 1, then call ELEBSE to set up base case
curves.
Compute new peak and curve spacing.
Initilize curves to zero.
Loop through all hours calling ELEPRB and ELEFRQ to
get the hourly probability and frequency density
functions. For each hour compute all possible
combinations of load and generation and, from these,
set up the working arrays to be sent to ELECRV.
Create the reverse frequency curve by looping
backwards through the frequency density function and
summing.
Call ELECRV to create the reverse cumulative
probability function.
Call ELECWT to write the curves to the output file.
Return.
IFLG = - 95
IFLG = - 96
IFLG = - 98
DEBUG
Number of points in the working array exceeds
the maximum
Number of combinations in any hour exceeds the
maximum
Error in call to subroutine
If IDEBUG (27) = true, print the curve number and the
unsorted work array.
40
NAME
IRANGE
TYPE
SUBROUTINE
SYSTEM
LOLEV
UPDATE
4/23/79
DESCRIPTION
ARGUMENTS
IRANGE checks the range of integer variables.
NAME
DESCRIPTION
TYPE
IFLG
error code (returned)
variable to be tested
lowest permissible
value
highest permissible
value
program name
variable name
1st subscript if IVAR
is in an array
2nd subscript
3rd subscript
4th subscript
1*4
IVAR
ILOW
IUP
PRNAM
VRNAM
IS1
IS2
IS3
IS4
COMMONS
SUBROUTINES
LOGIC
ERRORS
I*4
1*4
A*8
A*8
1*4
I*4
1*4
1*4
None
None
1) Test variable.
2) If out-of range, set IFLG, and print message.
3) Return.
IFLG = -10
IFLG = -11
IFLG = -12
DEBUG
I*4
None
Variable out of range
Invalid subscripts
IUP less than ILOW
41
VI.
Labeled Common Documentation
NAME
/DEBUGS/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/DEBUGS/ contains the debug control variable.
ARGUMENTS
NAME
IBUG
IDEBUG(40)
DESCRIPTION
TYPE
output file for debut print 1*4
Logical variables for debug L*4
print
21
22
23
24
25
26
27
=
=
=
=
=
=
=
ELEBSE
ELECDF
ELECIN
ELECRV
ELEFRQ
ELEPBR
ELESET
42
NAME
/ELECHR/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELECHR/ contains the hourly probability, frequency, and
load data.
ARGUMENTS
NAME
PHOUR(64)
FHOUR(64)
CHOUR(64)
NPRB
DESCRIPTION
Probability distribution
of the load change
Frequency distribution of
the load change
Load change corresponding
to each probability level
Number of load change
Levels.
TYPE
R*8
R*8
R*4
1*4
43
NAME
/ELECLS/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELECLS/ contains data on the cases to be run.
ARGUMENTS
NAME
NUM(10)
DESCRIPTION
total number of plants in
TYPE
1*4
case i
IDTD(10,4)
unit indices for up to
four plants, to be in-
cluded in case i
NPLNT(10,4) number of units identical
to IDTD(i,j) to be inclu-
ded in case i.
1*4
1*4
44
NAME
/ELECOR/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELECOR/ contains the load-load reduction correlation curve.
ARGUMENTS
NAME
MCORR
SPACE3
DESCRIPTION
TYPE
Logical variable to control L*4
whether correlation curve
is computed
Interval at which corR*4
relation curve is stored
SPACE3 = peak rating/10.
CORR (100, 11
Correlation curve
R*4
45
NAME
/ELECVE/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELECVE/ contains the input and output curves.
ARGUMENTS
NAME
DESCRIPTION
Probability array containing
the probability of each
possible load level for
the current output curve.
CSTLD(8784)
Original hourly customer
demand
CRVRED(8784,4) Load change curves.
Working array for sorting
WORK(8784)
the probability curves
Final load duration curves
CDF(100,52)
for the current case
CLOAD(100,52) Final load duration curves
for the base case.
Frequency duration curve for
FREQ(100)
the current output curve of
the current case
FLOAD(100,52) Frequency duration curves for
the base case
SPACE1
Length of each spacing in
the base case load duration
curve
SPACE2
Length of each spacing after
the load change is added
IMIN
Array counter where minimum
load is stored
PROB(8784)
TYPE
R*8
R*4
R*4
R*4
R*4
R*4
R*4
R*4
R*4
R*4
I*4
46
NAME
/ELEGEN/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELEGEN/ contains general information on the ELECTRA run.
ARGUMENTS
NAME
NHOUR
NINC
NOUTC
NPNT
NCASE
NOTD
NHRS(52)
MFREQ
DESCRIPTION
Total number of hours in the
input curves
Number of load reduction
curves
Number of output curves in
each case
Number of points in each
output curve
Number of cases to be run
Number of time dependent
units
Number of hours in each
output curve
Logical control for frequency
calculations
TYPE
1*4
1*4
1*4
1*4
1*4
1*4
1*4
1*4
47
8/80
NAME
/ ELEIOS/
TYPE
LABELED COMMON
SYSTEM
ELECTR A
UPDATE
8 /21/79
DESCRIPTION
/ELEIOS/ contains the input and output file numbers
ARGUMENTS
NAME
IGEN
LOADC
LOADD
ITD
ICRV
IFRQ
ICOR
IPLNT
ICLS
DESCRIPTION
Input file for general informati on
(Card Set A and B)
Input file for general
customer load
(Card Set D)
Input file for load 1*4
change data
(Card Set E)
Input file for TaD loss
multiplers
(Card Set F)
Output file for load duration
cu rve
Output file for frequency
cu rve
Output file for correlation
each case
Input file for plant informati on
(Card Set G)
Input file for class information
TYPE
I*4
1*4
1*4
1*4
I*4
1*4
1*4
1*4
48
NAME
/ELETDF/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/ELETDF/ contains the marginal loss factors
ARGUMENTS
NAME
NLEVEL
DLEVEL(10)
PLOSS(10)
DESCRIPTION
number of loss levels input
demand levels
marginal loss factor for
corresponding demand level
TYPE
1*4
R*4
R*4
49
NAME
GCLASS
TYPE
LABELED COMMON
SYSTEM
GEM/SYSGEN
UPDATE
4/23/79
DESCRIPTION
ARGUMENTS
/GCLASS/ contains class data that pertain to all
units in a class
NAME
DESCRIPTION
TYPE
NCLASS
Number of classes
1*4
NCLSVR
Number of variables
associated with each
class in the ICLASS
table
1*4
ICLASS(J,1)
ICLASS(J,2)
ICLASS( J,3)
ICLASS(J,4)
ICLASS(J,5)
Class name
Class type
Not used in SYSGEN
Not used in SYSGEN
Cross reference to
O&M escalation rate
Cross reference to
fuel cost escalation
rate
Not used in SYSGEN
Cross reference to
immature forced outage
rate multipliers table
Not used in SYSGEN
Not used in SYSGEN
Not used in SYSGEN
A*4
A*4
1*4
1*4
1*4
ICLASS(J,6)
ICLASS(J,7)
ICLASS(J,8)
ICLASS(J,9)
ICLASS(J,10)
ICLASS(J,11)
NFORML
Number of sets of
immature
forced outage rate
multipliers
1*4
1*4
1*4
I*4
1*4
I*4
NIMYRS
Number of years in
each set
1*4
of immature forced
outage rate multipliers
FORML(10,10)
Immature forced outage 1*4
rate multiplers table
50
NAME
GGENRL
TYPE
LABELED COMMON
SYSTEM
GEM/SYSGEN
UPDATE
4/23/79
DESCRIPTION
ARGUMENTS
/GGENRL/ contains general information about the
current GEM run.
NAME
DESCRIPTION
TYPE
ISY
Starting year of
planning horizon
(integer)(e.g. 1985)
*4
I'
IEY
Final year of the
planning horizon
(integer)
*4
I:
NTP
I *4
Number of yearly
time periods
[=(IEY-ISY)+1] (integer)
NUMWK(12)
Not used in SYSGEN
HOURS
Number of hours per
year (real number)
(hours)
R*4
DR
Discount rate
(fraction)
R*4
TITLE(40)
R*4
Name of the current
run (words 1 to 10
appear at top of each
reoport)
ECOENV
Not used in SYSGEN
A*4
51
NAME
SYSDAT
TYPE
LABELED COMMON
SYSTEM
SYSGEN
UPDATE
4/23/79
DESCRIPTION
ARGUMENTS
/SYSDAT/ contains general system information.
NAME
DESCRIPTION
NOSTNS
Number of units in
1*4
the system
Number of hours in a R*4
week
Maximum percent of any R*4
plant that counts
toward spinning reserve
HRWEEK
PERCNT
RES
ERVE
If ERVE = 'PER', then
RES = percent of load
that is kept in
spinning reserve
If ERVE = 'PER', then
the spinning reserve
is RES percent of
the load
TYPE
R*4
A*4
If ERVE = 'ABS' then
spinning reserve is kept
.at a constant level of
RES megawatts.
If ERVE = 'MAX', then
spinning reserve is set
equal to the largest
plant on line (see
section III.K)
WKDAY
WKDAY = 'WEEK' or
ITDP
ICHY
ISTO
IBASE
INTR
IPEAK
'DAY'. Used only in
reporting as a reminder
of how HRWEEK is set
(see section II.B)
Alphabetic test
A*4
variables set in
A*4
input card set
A*4
A/2/2
A*4
A*4
A*4
A*4
52
NAME
/TDPLNT/
TYPE
LABELED COMMON
SYSTEM
ELECTRA
UPDATE
8/21/79
DESCRIPTION
/TDPLNT/ contains information on the time dependent power
units
ARGUMENTS
NAME
DESCRIPTION
NCRV (20)
load reduction curve
1*4
number for the plant
number of units in the plant R*4
(scale factor for the values
in NCRV)
nominal size of the plant
R*4
R*4
forced outage rate of the
plant
R*4
average forced outage
occurrence rate for the
plant
RNUM(20)
TCAP(20)
FOR(20)
AVFORR(20)
TYPE
53
VII.
Sample Run
VII.
1. ELECTRA Input File
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References
1) Finger, S., SYSGEN, "Production Costing and Reliability Modeling User
Documentation," MIT Energy Lab Technical Report , #MIT-EL 79-020, August
1979.
2) Finger, S. "Electric Power System Production Costing and Reliability
Analysis Including Hydro-electric Storage and Time Dependent Power
Plants," MIT Energy Lab Technical Report #MIT-EL-79-006 February 1979.
3) Finger, S., "SCYLLA, Time Dependent Electric Power Generation
Evaluation Model, User Documentation," MIT Energy Lab Technical Report,
forthcoming.