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THE DESIGN O F A
NATURAL GAS FORECASTING MODEL
PETER RICHARD TOEWS
A RESEARCH PROJECT SUBMITTED I N PARTIAL
FULFILLMENT O F THE REQUIREMENTS FOR THE
DEGREE O F MASTER O F BUSINESS ADMINISTRATION
i n t h e D e p a r t m e n t
of
E c o n o m i c s and C o m m e r c e
@PETER RICHARD TOEWS 1 9 7 6
SIMON FRASER UNIVERSITY
M a r c h 1 9 7 6
A l l r i g h t s reserved. T h i s project m a y n o t be
reproduced i n w h o l e o r i n p a r t , by photocopy o r
other means, w i t h o u t p e r m i s s i o n of t h e au tho r .
NAME : Peter Richard Toews
DEGREE SOUGHT: Master of Business Administration
RESEARCH PROJECT TITLE : The Design of a Natural Gas Forecasting Model
Roger C. Verga , Professor
William C . wedldY, Assistant Professor
DATE OF APPROVAL: @& x, ~ 7 7 6
PARTIAL COP'JtRIGHT LICENSE
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w i t h o u t my w r i t t e n pe rmiss ion .
T i t l e of ~ h e s i s I ~ i s s e r t a t i o n :
THE DESIGN OF A NATURAL GAS FORECASTING MODEL.
Author :
( s i g n a t u r e )
P. R . TOEWS
(name )
March 12th, 1974
( d a t e )
ABSTRACT -
The aim of t h i s work was t o des ign an a n a l y t i c a l n a t u r a l
gas f o r e c a s t i n g model. A gas s u p p l i e r i s confronted with
opposing penal ty c o s t s f o r excess ive and d e f i c i e n t gas s u p p l i e s .
Natural gas consumption is p r imar i ly r e l a t e d t o v a r i a t i o n s i n
t h e weather. The o b j e c t i v e was t o develop a model t o f o r e c a s t
demand wi th an e r r o r no t t o exceed 5 pe rcen t of t h e a c t u a l
demand f o r 95 pe rcen t of a l l f o r e c a s t s .
The b a s i s of t h e model i s a modified m u l t i p l e s tepwise
r eg ress ion program. The procedure c o n s i s t s of ga the r ing
25 independent and 1 dependent v a r i a b l e . A combination of
v a r i a b l e and observat ion weight ing, a s w e l l a s t h e use of dummy
v a r i a b l e s i s appl ied . These v a r i a b l e s a r e subjec ted t o t h e
m u l t i p l e s tepwise r eg ress ion procedure, which r e t a i n s only t h e
s i g n i f i c a n t v a r i a b l e s based on p a r t i a l r e g r e s s i o n using t h e
F test. The r e s u l t i n g c o e f f i c i e n t s a r e app l i ed t o tomorrow's
weather f o r e c a s t i n o rde r t o a r r i v e a t t h e p red ic ted n a t u r a l
gas sendout f o r tomorrow.
A four phase model was developed wi th t h e mul t ip le s tepwise
r eg ress ion performing t h e t h i r d phase. I n excess of 97% of t h e
v a r i a t i o n occuring i n t h e d a t a was accounted f o r by t h e 25
v a r i a b l e s . The model was allowed t o genera te a sample n ine
day period. The mean e r r o r of t h i s sample run was -.7% wi th t h e
h ighes t v a r i a t i o n being - 3 . 3 % .
iii
TABLE OF CONTENTS
............................................. ABSTRACT......... iii
LIST OF TABLES............................................... vi
LIST OF EXHIBITS............................................. vii
........................................ LIST OF ILLUSTRATIONS viii
1 INTRODUCTION ........................................... 1
Generalization
Background
Contractual Commitments
Gas Supply Mix
Model Overview
Significance of Literature in the Field
Previous Research Findings
Objective of the Study
........................................ I1 RESEARCH DESIGN 12
Data Sources
The Analytical Model
Alternatives Tested
Computer Facilities
I
111 THE MODEL DESIGN ....................................... 28
Model Analysis
Data Weighting Validation
Selection of Variables
Future Consideration
Summary
........................................... GLOSSARY OF TERMS 36
BIBLIOGRAPHY ................................................. 37
APPENDIX ................................................... 39
A. Forecasting Model Flow Chart
B. Sample Data Card Listing
LIST OF TABLES
TABLE Page
1 . Error Analysis of Region 4 .......................... 23 2 . Effective Temperature Comparisons .................... 25 3 . Time period model comparisons ........................ 30 4 . Analysis of Variance ................................ 32
................. 5 . Final Variables for Regression Model 38
LIST OF EXHIBITS
EXHIBIT
. 1 . I n l a n d N a t u r a l Gas Co Ltd . System Map ................. .................... 2 . F l u c t u a t i o n i n Annual Temperatures
3 . Annual Temperature P r o f i l e ............................. 4 . Annual Gas S a l e s Volume ................................ 5 . N a t u r a l Gas U t i l i z a t i o n P e r Customer ................... 6 . Regional Day o f t h e Week F a c t o r ........................ 7 . E f f e c t i v e Temperature Formula G a s Sendout Comparison ... 8 . F o r e c a s t i n g Model w i t h o u t Dummy V a r i a b l e s .............. 9 . F o r e c a s t i n g Model w i t h Dummy V a r i a b l e s .................
....... 10 . Sample L i s t i n g o f 1 d a y ' s F o r e c a s t f o r Phase I11
11 . Sample F o r e c a s t Based on 3 Months o f H i s t o r y ........... 1 2 . Sample F o r e c a s t Based on 6 Months o f H i s t o r y ...........
Page
4 5
46
46
46
46
4 7
4 8
51
52
55
69
vii
FIGURE
LIST OF ILLUSTRATIONS
Page
Pictorial Presentation of M o d e l V a r i a b l e s ........... lg
Comparative Graph of Forecasted V e r s u s A c t u a l
Natural Gas Sendout ................................ 24
viii
Page 1
Generalization -
A search for the optimization of a function whose behavior
is more or less unknown to the observer necessarily involves
much experimentation. It was through the direct measurement
of each experiment that this model was derived. The purpose
of this study is to develop and tes,t a natural gas forecasting
model. The usefulness of the model is its value in helping
derive a future nomination* value and its worth to the daily
gas dispatch operations. The design of the model includes
conkinual updating and reformulation of the various variables
on a daily basis so as to avoid obsolescence.
The results have revealed some interesting relationships
between various weather factors and natural gas sendout.
Although this program has not been put into production at the
Inland Natural Gas Company, it is intended that this will occur
when the present computer conversion is completed.
Background
Inland Natural Gas Co. Ltd. is a public utility operating
its distribution system in the interior of British Columbia (see
system map, Exhibit 1, Pg. 45). The customers being served can
*See "Glossary of Terms" Page 36, for definitions of technical . . terms.
Page 2
be c l a s s i f i e d a s t o r e s i d e n t i a l , commercial , s m a l l and l a r g e
i n d u s t r i a l . Peak sales of 148,223,000 c u b i c f e e t occu r r ed on
February 9 , 1975, w i t h t o t a l r e co rded s a l e s f o r t h e y e a r 1975
be ing 35,640,714,000 c u b i c f e e t . The n a t u r a l g a s r e q u i r e d
t o meet t h e s e demands ha s been purchased s o l e l y from Westcoas t
~ r a n s m i s s i o n Company Limited. Beginning i n 1976, peak demands
can be m e t by u s i n g an a l t e r n a t e supp ly from A l b e r t a & Sou the rn
Gas Co. L td . , a l t h o u g h t h i s must b e r e t u r n e d t o them t h e
fo l l owing summer.
The cus tomer b a s e ha s been growing a t a compound r a t e i n
exces s o f 10 p e r c e n t f o r t h e l a s t t h r e e y e a r s (see E x h i b i t 4 ,
Page 46 f o r l o a d p r o f i l e . A major p o r t i o n o f t h e n a t u r a l g a s
s o l d i s used f o r h e a t i n g purposes . A s a r e s u l t , g a s s a l e s
va ry g r e a t l y w i t h t h e wea the r , and it is d i f f i c u l t t o f o r e c a s t
a c c u r a t e l y i n advance what t h e a c t u a l g a s r equ i r emen t s w i l l be .
Weather c a u s e s annua l v a r i a t i o n s i n g a s usage between " c o l d " ,
"normal" and "warm" y e a r s , as i n d i c a t e d i n E x h i b i t 2, Page 46.
I n a d d i t i o n , t h e r e i s a l a r g e s e a s o n a l v a r i a t i o n i n g a s usage
between d i f f e r e n t months o f t h e y e a r a s E x h i b i t 3 shows.
The r equ i r emen t o f a l l r e g u l a r or s o c a l l e d " f i rm" cus tomers
must b e s u p p l i e d even on t h e c o l d e s t w i n t e r day , w i t h o u t 1
c u r t a i l m e n t o r i n t e r r u p t i o n s . P l a n t f a c i l i t i e s must , t h e r e f o r e ,
be l a r g e enough f o r t h e s e peak day r equ i r emen t s . his means
t h a t t h e f a c i l i t i e s w i l l n o t be f u l l y u t i l i z e d a t o t h e r t i m e s .
The maximum day sendout h a s i n c r e a s e d from 123,579,000 c u b i c .-
f e e t i n 1973 t o 136,485,000 c u b i c f e e t i n 1974 and 148,223,000
c u b i c f e e t i n 1975. Complex r a m i f i c a t i o n s r e s u l t from demand
p e n a l t i e s , minimum b i l l p r o v i s i o n s and c o n t r a c t u a l commitments
Page 3
listed below, coupled with the fact that the escalating maximum
day sendout must be nominated* one year in advance. An additional
pertinent item stems from the daily fluctuations in revenue due
to varying weather patterns. This variation has created a need
to develop a more satisfactory method of daily forecasting,
which must comply with the following contractual commitments.
Contractual Comni tments
- Nomination of gas (maximum quantity that can he purchased per day) must be submitted by November 1, to be effective
November 1 next year, for a one year term.
- The minimum monthly billing demand is based on 92.5% of the nomination.
- A billing demand penalty in excess of seven fold is incurred for any gas taken in excess of the nomination.
- The yearly minimum that falls under a take or pay category is based on 65% of the nomination (365 x ' \ nomination x .65) .
- Should the minimum billing demand be exceeded, a new minimum billing demand is then established up to the
maximum where the minimum billing demand equals the
nomination. Any gas exceeding the nomination is
penalty gas.
- If it is known today that the quantity of gas required for tomorrow will exceed the nomination, sufficient
advance notice must be given to certain industrial
customers, whose gas supply can then be curtailed for
the followina dav.
Page 4
Gas Supply Mix
In l and has v a r i o u s a l t e r n a t i v e s a v a i l a b l e t o it i n o r d e r
t o meet t h e customer requi rements .
- Basic g a s supply from Westcoast Transmiss ion Company
Limited.
- Peak shaving , which c o n s i s t s , o f t a k i n g gas i n t h e summer
when consumption i s low, and l i q u i f y i n g t h i s gas . I n
t h e w i n t e r t h i s gas i s r e t u r n e d t o t h e l i n e on peak
days , t h u s lowering t h e q u a n t i t y of gas t aken from
Westcoast .
- Using propane, which i s s t o r e d i n r a i l cars. On s e v e r e l y
c o l d days , propane i s mixed w i t h a i r and f ed i n t o t h e
system.
- A l b e r t a gas (any gas bought i n t h e peak w i n t e r pe r iod
must be r e t u r n e d t h e fo l lowing summer).
- Using l i n e pack, which c o n s i s t s o f f o r c i n g more g a s i n t o
t h e m i l e s of p i p e l i n e by i n c r e a s i n g t h e p r e s s u r e through
t h e u s e of compressors. Then on s e v e r e days more gas
i s t aken from t h e system than i s f ed i n t o it from
Westcoast , t h u s reduc ing t h e p r e s s u r e . This has l i m i t e d
u s e s i n c e working p r e s s u r e s must be main ta ined .
Page 5
Model Overview
The model i s based on a modified m u l t i p l e s tepwise
regress ion program developed by S t a t i s t i c s Canada. Various
methods of v a r i a b l e and observat ion weight ing , use of dummy
v a r i a b l e s , a s w e l l a s au to r e g r e s s i v e v a r i a b l e s a r e included.
The s tepwise a lgor i thm performs an eva lua t ion on t h e v a r i a b l e s
based on a p a r t i a l r eg ress ion using t h e F t e s t . The procedure
c o n s i s t s of ga the r ing t h e i n i t i a l d a t a of 6 independent,
11 dummy, and 1 dependent v a r i a b l e . Phase 1 e v a l u a t e s t h e
dependent v a r i a b l e , and genera tes 1 a d d i t i o n a l independent
v a r i a b l e , t h e day of t h e week f a c t o r . The e f f e c t i v e temperature
formula producing t h e lowest e r r o r i s s e l e c t e d by phase 2 , which
c a l c u l a t e s 3 a d d i t i o n a l independent v a r i a b l e s , ( v a r i a b l e s 13,
16 & 18 i n Table 5, Page 3 8 ) . Phase 3 i s en te red wi th 11
dummy v a r i a b l e s , 1 3 independent and 1 dependent v a r i a b l e , which
performs t h e m u l t i p l e s tepwise r e g r e s s i o n procedure, thus
r e t a i n i n g only t h e s i g n i f i c a n t v a r i a b l e s . The f i n a l phase
c o n s i s t s of applying t h e c o e f f i c i e n t s t o tomorrow's weather
f o r e c a s t i n o rde r t o a r r i v e a t t h e p red ic ted n a t u r a l gas sendout.
A f o u r phase model was developed wi th t h e m u l t i p l e
s tepwise r eg ress ion performing t h e t h i r d phase. The combination
of v a r i a b l e s accounted f o r i n excess of 97% of t h e v a r i a t i o n
occurr ing i n t h e d a t a . The model was allowed t o genera te -a
Page 6
sample n i n e day pe r iod . The mean e r r o r o f t h i s sample run w a s
-.7% w i t h t h e h i g h e s t v a r i a t i o n be ing -3.3%. To d a t e , t h e
model has been run i n a tes t mode on ly . However, t h e model ' s
performance has r ece ived accep tance from t h e e n g i n e e r s , who
p lan t o implement it. The model w i l l t h e n become a p roduc t ive
t o o l t o a s s i s t t h e n a t u r a l gas d i s p a t c h e r .
S i g n i f i c a n c e of L i t e r a t u r e i n t h e F i e l d
The l i t e r a t u r e review c o n s i s t e d o f a s e a r c h by t h e a u t h o r
and by t h e P a c i f i c Coast Gas Assoc i a t i on . Th i s combined s e a r c h
covered e x t e n s i v e in format ion on g a s technology from 1960
through 1973. S e v e r a l a r t i c l e s c o n t a i n i n g a n a l y t i c a l approaches
i n i d e n t i f y i n g some of t h e p r i n c i p a l f a c t o r s a f f e c t i n g g a s l oad
were d iscovered . Publ i shed l i t e r a t u r e w a s n o t a v a i l a b l e which
addressed i t s e l f s p e c i f i c a l l y t o t h e nomination o f n a t u r a l gas .
I n a d d i t i o n , a l l of t h e s t u d i e s w e r e conducted i n compara t ive ly
w a r m r e g i o n s i n a r e l a t i v e l y conf ined a r e a .
Page 7
, previous Research Findings
One of t h e e a r l i e r models developed i n 1962 t 1 I * *
desc r ibes an a n a l y t i c a l model t h a t a p p l i e s t h e f i r s t o r d e r
l i n e a r form. I t can be expressed a s :
y = Bo+B X +B X ----- 1 1 2 2 B~ XN
Where y i s t h e dependent v a r i a b l e t o be f o r e c a s t , t h e B ' s a r e
the r eg ress ion c o e f f i c i e n t s determined by t h e l e a s t squares
c r i t e r i o n , t h e X's a r e t h e exogenous v a r i a b l e s . This s tudy
considered t h e l i n e a r weather e f f e c t s from temperature, wind
v e l o c i t y and d a i l y i l lumina t ion . This w a s r e f i n e d by f i t t i n g
a parabol ic curve t o t h e temperature d a t a . A n e g l i g i b l e day of
t h e week c o r r e c t i o n f a c t o r was a l s o included. The equat ion
maintained b e t t e r than 5% accuracy f o r 80% of t h e t ime, b u t
e r r o r s i n t h e magnitude of 1 0 % were introduced from time t o time.
I n 1964 Van Note [ 11 1 used m u l t i p l e l i n e a r c o r r e l a t i o n
with v a r i a b l e s inc luding weighted temperature and a 24 hour
l a g e f f e c t . These were f i t t e d t o a second degree polynomial
equation. E r r o r s i n excess of 6% were f r equen t ly experienced.
I n 1967 Ruskin C 9 1 developed a genera l i zed s imula t ion
model. New f a c t o r s such a s r a t e of temperature change, and
customer c h a r a c t e r i s t i c s which inc lude number and growth of
customers, c l a s s of s e r v i c e and type of s e r v i c e were included.
This s tudy in t roduces t h e idea of s c a l i n g a v a r i a b l e such a s
wind s o it can be included a s a dichotomous v a r i a b l e . A major
he he numbers i n parentheses r e f e r t o t h e r e fe rences i n t h e Bibliography, Page 37.
Page 8
f i n d i n g of t h i s s t u d y is t h a t t h e r e l a t i o n s h i p o f environmental
changes t o g a s sendout i s non l inea r . Th i s i n c l u d e s t h e
growth of t h e g a s l o a d w i t h r e s p e c t t o t i m e , s i n c e t h e customer
growth i s more l i k e l y t o occur d u r i n g t h e summer c o n s t r u c t i o n
season than du r ing t h e w in t e r . S ince t h e g a s l oad accumulated
from r e s i d e n t i a l c o n s t r u c t i o n i s d i f f e r e n t from t h a t of
commercial, t h e growth w i l l b e s e a s o n a l l y d i f f e r e n t . Economic
changes a f f e c t i n g produc t ion schedu le s and t h e day t o day mix
of commercial and r e s i d e n t i a l customers add more complexi ty t o
t h e d a i l y sendout .
I n 1968 Hingorani and Marcynski 1 5 I developed a model
u s ing a non s t a t i o n e r y t ime series and a c r o s s p roduc t v a r i a b l e
of wind v e l o c i t y m u l t i p l i e d by tempera ture . The use of t h e
t i m e s e r i e s model was in tended t o i n t r o d u c e economic and
environmental e f f e c t s i n a d d i t i o n t o weather . A f o r e c a s t
e r r o r as h igh a s 10 p e r c e n t of t h e g a s l oad was exper ienced.
I n 1973 Haenel t 4 1 developed a model u s i n g t h e m u l t i p l e
s t epwise r e g r e s s i o n technique as t h e base . A geometr ic we igh t ing
f a c t o r was a p p l i e d t o t h e d a t a t o i n t r o d u c e an a u t o r e g r e s s i v e
t i m e s e r i e s e f f e c t . I n a d d i t i o n , a n o p t i m a l weight ing f a c t o r
was in t roduced , which minimized t h e sum of t h e squared e r r o r . 1
The model y i e l d e d 9 5 p e r c e n t of a l l f o r e c a s t s w i t h i n + 5.36 -
p e r c e n t of a c t u a l , which i s a c o n s i d e r a b l e improvement ove r
p rev ious models.
Page 9
i i I n a l l of t h e s t u d i e s , on ly a p o r t i o n of t h e y e a r ' s d a t a ?
was s e l e c t e d f o r model l ing. Many used d a t a from t h e prev ious
yea r and a l l excluded ho l idays and non t y p i c a l g a s days . A l l
p a r t i t i o n e d t h e d a t a , and w i t h i n t h e s e p a r t i t i o n s assumed t h e
e f f e c t s of t h e v a r i a b l e s t o have a nea r l i n e a r r e l a t i o n s h i p
wi th g a s l oad .
The most d i f f i c u l t and impor t an t p e r i o d f o r f o r e c a s t i n g
is t h a t of t h e w i n t e r h e a t i n g season. I t i s h e r e t h a t t h e
peak day i s encountered, and it i s t h i s sendout t h a t has t h e
g r e a t e s t e f f e c t on y e a r l y c o s t s . I f t h e d i s p a t c h e r selects
t o o low a nomination v a l u e , revenues w i l l b e reduced. I f h e
chooses t o o h igh a va lue , c o n s i d e r a b l e p e n a l t i e s cou ld be
r e a l i z e d .
The use o f mathemat ical models i n f o r e c a s t i n g d a i l y g a s
load i s l i m i t e d th roughout t h e i n d u s t r y . P a s t model response
t o s h o r t t e r m t r e n d s i n t h e economy o r from changes i n
customer h a b i t s have been u n s a t i s f a c t o r y . Thus, obso lescence
of t h e f o r e c a s t i n g equa t ion f r e q u e n t l y r e s u l t s . The
a v a i l a b i l i t y of i n fo rma t ion and t h e c o s t o f a c q u i r i n g t h i s
i n fo rma t ion must be cons idered . I t is e v i d e n t t h a t con t inuous
d a i l y f o r e c a s t i n g over a pe r iod o f t i m e w i l l b e necessary t o
demonstra te t h e u s e f u l n e s s of t h i s t o o l .
Page 10
k 4
o b j e c t i v e of t h e Study
The main framework of c o u r s e , i s t o d e s i g n a model t h a t t
w i l l f o r e c a s t t h e demand of n a t u r a l g a s t h a t w i l l be needed ! ! tomorrow. The need has been c r e a t e d due t o t h e i n c r e a s i n g i : complexity of t h e g a s system o p e r a t i o n s . A s can be seen from
t h e system map ( E x h i b i t 1, Page 4 5 ) , t h e o p e r a t i n g r eg ion
covers i n exces s of 700 m i l e s , which c r o s s e s two mountain <
ranges . Consequently, ve ry d i s t i n c t wea ther p a t t e r n s a s w e l l
a s geograph ica l p e c u l i a r i t i e s e x i s t . A c o l d f r o n t moving a c r o s s
such a v a s t a r e a i n t r o d u c e s d i v e r s i t y between t h e peak days i n
v a r i o u s towns. The r a m i f i c a t i o n s encountered w i t h m u l t i p l e
gas s u p p l i e s , demand p e n a l t i e s and minimum b i l l p r o v i s i o n s and
advance n o t i f i c a t i o n of customers t o be c u r t a i l e d have c r e a t e d
t h e need t o develop a more s a t i s f a c t o r y method of f o r e c a s t i n g
sendout . The fo l lowing o b j e c t i v e s are s t a t e d :
(1) Design a model w i t h a f o r e c a s t e r r o r n o t t o exceed
5% of t h e a c t u a l demand f o r 95 p e r c e n t o f a l l f o r e c a s t s .
The b e n e f i t h e r e w i l l b e i n s u b s t a n t i a t i n g a d i s p a t c h e r ' s
c a l c u l a t i o n p l u s a s s i s t i n g i n n o t i f y i n g customers i n
t i m e t o a f f e c t c u r t a i l m e n t f o r t h e fo l lowing day. \
( 2 ) Sources of d a t a must be r e a d i l y a t t a i n a b l e and must be
t ime ly s o t h a t t h e s e can be a c t e d upon f o r t h e
fo l lowing day. The n a t u r e o f t h e c u r r e n t c o n t r a c t
s i t u a t i o n r e q u i r e s 8 hours n o t i c e t o t h e i n t e r r u p t i b l e *
Page 11
customers , and improvement i n p r e d i c t i o n s could
i n c r e a s e t h e s e c u r i t y of t h e system. S i n c e t h e
c o n t r a c t day beg ins a t 8 a . m . , t h i s means t h a t
customers must be n o t i f i e d by midn igh t i f c u r t a i l m e n t
is t o b e e f f e c t i v e f o r t h e f o l l o w i n g day.
Cons ide ra t ions w i l l b e g iven i n t h e model d e s i g n t o
p rov ide f o r p o s s i b l e f u t u r e o b s o l e s c e n c e o f v a r i a b l e s
which a r e no longe r s i g n i q i c a n t .
An a d d i t i o n a l problem a s s o c i a t e d w i t h g a s d i s p a t c h is
t h a t o f s e l e c t i n g a nominat ion v a l u e which w i l l become
e f f e c t i v e one y e a r hence. T h i s r e q u i r e s f o r e c a s t i n g
f u t u r e wea ther a s w e l l as f u t u r e demand. A p r o b a b i l i s t i c
approach t o t h e u n c e r t a i n t y o f wea the r can b e ach ieved
by us ing t h e Monte-Carlo s i m u l a t i o n method. The
s imu la t ed tempera tures must have t h e s a m e s t a t i s t i c a l
p r o p e r t i e s a s a c t u a l t empefa tu re s . By u t i l i z i n g
p a s t h i s t o r i c a l d a t a c o n s i s t i n g o f t h e extremes and
t h e d a i l y mean tempera tures i n c o n j u n c t i o n w i t h a
random number g e n e r a t o r , a sample set of s imu la t ed
tempera tures can be d e r i v e d . Using t h i s d a t a a s a
base , it i s p o s s i b l e t o f o r e c a s t f o r t h e subsequent
y e a r i n o r d e r t o a r r i v e a t a nomina t ion va lue .
However, a l though t h i s i s a s t a t e d o b j e c t i v e , t h i s w i l l
n o t be r e a l i z e d i n t h i s s tudy . I t is in t ended t h a t
t h e d a i l y f o r e c a s t i n g model w i l l b e i n p roduc t ion and
accep ted b e f o r e ' t h i s phase w i l l b e a t t empted .
Page 12
V a r i a b l e 1
I1 RESEARCH D E S I G N
Data Sources -
C u r r e n t l y , t h e d i s p a t c h f u n c t i o n i s performed on a manual
b a s i s . U n t i l r e c e n t l y , a l l weather i n fo rma t ion t h a t t h e
d i s p a t c h e r r e q u i r e d was r ece ived v i a t e l e x . I n December 1974,
a P.D.P. 11/40 p roces s c o n t r o l computer w a s i n s t a l l e d . The
f i r s t pa se of i t s development w a s t h e moni tor ing of t h e t e l e x
l i n e t o c a p t u r e any weather d a t a pe , r ta in ing t o r e g i o n s s e rved
by t h e d i s t r i b u t i o n system. The unique code of t h e weather d a t a
i s t r a n s l a t e d and p r i n t e d i n a r e a d a b l e format . I t i s from t h i s
source t h a t t h e independent v a r i a b l e s f o r t h i s model o r i g i n a t e .
The o b j e c t i v e of t h e model i s t o f o r e c a s t tomorrow's
sendout . Weather d a t a i s r ece ived hour ly , w i t h f o r e c a s t s
r ece ived a t 5 a.m., 10 a.m., 2:30 p.m., 7:30 p.m. and 10:30 p.m.
These f o r e c a s t s c o n s i s t of g e n e r a l p u b l i c i n fo rma t ion , w i t h an
o u t l i n e of g e n e r a l area e x p e c t a t i o n s . I n a d d i t i o n , a 2:30 p.m.
s p e c i a l f o r e c a s t i s r ece ived from t h e wea ther o f f i c e i n d i c a t i n g
\ , t o n i g h t ' s low, tomorrow's h igh , and t h e low tomorrow n i g h t .
should t h e r e be a d r a s t i c change i n t h e wea the r , r e v i s e d f o r e c a s t s
w i l l be i s s u e d a t any t i m e .
The d i f f e r e n t v a r i a b l e s i nc luded f o r each day a r e l i s t e d
i n Table 5.
- A Cons tan t f a c t o r .
V a r i a b l e s 2-12 - These v a r i a b l e s are dummy v a r i a b l e s and
a r e used t o s i g n i f y d i f f e r e n t wea ther r eg ions . T h i s
Page 13
i s necessary i n order t o account f o r t h e s e p a r a t e
e f f e c t s on t h e gas sendout which a r e p e c u l i a r t o
each region .
Var iables 13-15 - These v a r i a b l e s form t h e au to regress ive
s e r i e s . The temperature is measured i n degrees Ce l s ius ,
whi le t h e opera t iona l v a r i a b l e i s measured i n m i l l i o n s
of cubic f e e t of gas. The v a r i a b l e s a r e i n t e r v a l
sca led over a continuous 'range.
Var iables 16-18 - These v a r i a b l e s a r e c a l c u l a t e d weighting
v a r i a b l e s .
Var iables 1 9 - 2 4 - These v a r i a b l e s a r e t h e o r i g i n a l
independent v a r i a b l e s rece ived from t h e P.D.P. 11/40.
When o p e r a t i o n a l , t h e s e w i l l be t h e f o r e c a s t s f o r t h e
fol lowing day.
Var iable 25 - Is t h e dependent v a r i a b l e c o n s i s t i n g of t h e
a c t u a l gas sendout.
Addit ional v a r i a b l e s such a s cloud cover , i l l u m i n a t i o n and \
p r e c i p i t a t i o n were considered. The au thor d i d n o t have an
opportuni ty t o determine t h e e f f e c t on sendout from t h e s e
weather v a r i a b l e s , s o no conclusion can be reached a s t o t h e
b e n e f i t t h a t could be der ived from t h e i n c l u s i o n of t h e s e
v a r i a b l e s . The reason f o r excluding t h i s d a t a was t h a t it was
e i t h e r s u b j e c t t o human i n t e r p r e t a t i o n t o t r a n s l a t e it t o a
numerical va lue , o r was unava i l ab le f o r a l l of t h e r eg ions
.under cons ide ra t ion , o r both.
Page 1 4
I t i s known from h i s t o r i c a l d a t a w i t h i n t h e Company t h a t
a s p r i n g and f a l l t r a n s i t i o n p o i n t o c c u r s , i . e . , t h e s l o p e of
t h e demand v e r s u s wea ther i s d i f f e r e n t f o r w i n t e r t han f o r
summer. However, as mentioned e a r l i e r , t h e c r i t i c a l requ i rement
f o r e x a c t sendout i s n o t p r e s e n t du r ing t h e s e t r a n s i t i o n p e r i o d s ,
s o a l though it i s recognized , t h i s problem w i l l n o t be pursued
i n t h i s s tudy .
Some of t h e earl ier models w e r e des igned by c o n s i d e r i n g
one v a r i a b l e a t a t i m e and f i n d i n g t h e optimum s o l u t i o n , f i x i n g
t h e r e l a t i o n s h i p w i t h demand and t h e n c o n s i d e r i n g t h e nex t
v a r i a b l e . Although t h e m u l t i p l e r e g r e s s i o n model a l l ows c r o s s
c o r r e l a t i o n s , t h e s e can be removed by p l a c i n g d i f f e r e n t l e v e l s
of tests on each independent v a r i a b l e . The f a c t t h a t n a t u r a l
gas demand i s dynamic would tend t o i n d i c a t e t h a t models w i t h
f i x e d v a r i a b l e s a r e s l a t e d f o r obso lescence .
I f a l l t h e v a r i a b l e s a r e c o n t i n u a l l y made a v a i l a b l e t o
t h e M u l t i p l e Stepwise Regress ion Program, on ly t h o s e v a r i a b l e s
which b e s t a i d i n e x p l a i n i n g t h e v a r i a t i o n i n a c t u a l g a s sendout
w i l l b e chosen f o r any one f o r e c a s t .
The b e s t se t of v a r i a b l e s i s con t inuous ly chosen by
re-examining t h e i n t e r r e l a t i o n s h i p s between t h e v a r i a b l e s . The
model w i l l t h u s i n c l u d e d i f f e r e n t combinat ions of v a r i a b l e s
depending upon v a r i o u s economic o r s e a s o n a l c y c l e s .
Page 15
The following is a description of the final variables
included in the model:
- One constant factor. - Eleven dummy variables allowing a separate description of each weather region.
- Yesterday's effective temperature, which is derived from a formula based on the weighted average temperatures of
the past 4 weeks (see Page 1,7 Item iii, for the effective
temperature formula used).
- Yesterday's average temperature which is computed from the 24 hourly temperatures.
- Yesterday's sendout consisting of the natural gas load in millions of cubic feet.
- Wind times corrected average temperature consisting of the wind speed in knots times tomorrow's forecasted
average temperature. \
- Day of the week factor consisting of a constant percentage determined by the actual day of the week being forecasted
(see Exhibit 6, Page 47 for sample) . - Change in effective temperature consisting of the difference between the previous day's and yesterday's
effective temperature.
- High temperature consisting of the high forecast for tomorrow.
- Low temperature consisting of the low forecast for tomorrow.
Page 16
- Average temperature consisting of the forecasted average for tomorrow.
- Wet bulb average determined by the dispatchers tomorrow.
- Daylight hours consisting of the hours between
for
sunrise
and sunset for tomorrow.
- Wind speed consisting of forecasted wind for tomorrow.
The Analytical Model
A Multiple Regression Program with modified variables was
' used in the formulation of the model. The program used was
developed by Statistics Canada C 10 3. A very useful text
relating to multiple regression was one written by Draper and
Smith 1 2 1.
, The steps employed by the foreCasting model are as follows: \
\
'\ Step 1 -
Step 2 -
Segregate historical data by region, and analyze
each region for day of the week variations.
Discount the day of the week variation, and
analyze which formula of effective temperature
produces the least error. The effective temperature
is intended to show a warming or cooling trend.
In addition, it also accounts for temperature
latency* ofbuildings as well as human psychological
factors.
Page 17
The three different effective temperature formulas were
taken from a study conducted by F. G. Van Note t 11 1.
Where a + b = 1
T~ = Today's average temperature
T ~ - 1 = Yesterday's average temperature
T~ = Effective temperature
T~ , ~ - l = Yesterday ' s effective temperature
Where WK = Average tem6erature in the week.
The optimal formula is then used to calculate other effective
temperature related variables.
Step 3 - An increasing wind at the same temperature has a greater chilling effect. This effect is only
noticed below 15O Celsius. The formula as supplied
by the Inland Natural Gas Dispatcher is:
CHILLF = t(TD - 15) X W1 Where TD = Average temperature Celsius
W = Wind speed in knots
Step 4 - E s t a b l i s h t h e twenty-five v a r i a b l e s f o r each
region f o r t h i s day, t ak ing i n t o account t h e
va lues e s t a b l i s h e d i n t h e previous t h r e e s t e p s .
S tep 5 - Subjec t a l l of these v a r i a b l e s t o m u l t i p l e
r eg ress ion , which f i n d s t h e v a r i a b l e no t y e t i n
t h e r eg ress ion with t h e h i g h e s t F va lue , and i f
t h i s i s above t h e necessary l e v e l , adds t h e v a r i a b l e
t o t h e equation. Then t h e r e g r e s s i o n equat ion i s
t e s t e d f o r t h e v a r i a b l e wi th t h e lowest F va lue ,
t h i s v a r i a b l e being removed i f it i s below t h e
s i g n i f i c a n t l e v e l . I f s t i l l s i g n i f i c a n t , t h e
equat ion i s t e s t e d wi thout t h i s lowest v a r i a b l e
t o f i n d a lower e r r o r var iance . I f s o , t h e v a r i a b l e
i s d e l e t e d , ( s e e Appendix B, Page 4 0 f o r flow c h a r t ) .
S tep 6 - Using t h e c o e f f i c i e n t s e s t a b l i s h e d , inc lude
c u r r e n t f o r e c a s t s f o r tomorrow f o r each of t h e
r eg ions , and d e r i v e a gas sendout by region.
(Exhib i t 1 2 , Page 72 is an example of t h e f i n a l
r e p o r t . Figure 1 p r e s e n t s a p i c t o r i a l overview
of where t h e v a r i a b l e s a r e der ived from, and how
t h e y come toge the r i n t h e model).
r i g . I. - P i c t o r i a l P r c a c n t n t i o n of Model Voriablcs
Indcpcmdent Var iab les
. calculated
and Store
Page 20
The v a r i a b l e s i n r e g r e s s i o n e q u a t i o n s u s u a l l y t a k e v a l u e s
o v e r some con t inuous range. However, t h i s model must a ccoun t
f o r t h e s e p a r a t e d e t e r m i n i s t i c e f f e c t s on t h e r e sponse due
t o t h e e f f e c t o f d i f f e r e n t wea ther r e g i o n s . V a r i a b l e s which
h e l p d i s t i n g u i s h d i f f e r e n t l e v e l s o f r e s p o n s e a r e c a l l e d dummy
v a r i a b l e s . I n o r d e r t o d e a l w i t h r r e g i o n s , (r-1) dummy
v a r i a b l e s a r e i n c l u d e d i n t h e r e g r e s s i o n a n a l y s i s . For example,
i f 3 r e g i o n s w e r e i n c l u d e d , t h e n dummy v a r i a b l e s would be
i nc luded a s fo l l ows :
X1 X2
1 0 = r e g i o n 1
0 1 = r e g i o n 2
0 0 = r e g i o n 3
The g e n e r a l form o f t h e model i s a s fo l l ows :
n y ( t ) = Bo + ----- b . x . ( t ) +-----
1 1 + b p k (t)
+ ----- b . y . (t) +----- 1 1 b k ~ k ( t )
+ ----- b . 2 . (t-t . ) +----- 1 1 1
A Where y i s t h e dependent v a r i a b l e t o b e f o r e c a s t e d , t h e
b ' s a r e t h e l e a s t s q u a r e c o e f f i c i e n t s de te rmined by t h e model
f o r each f o r e c a s t , t h e x v a r i a b l e s a r e t h e dummy v a r i a b l e s
r e q u i r e d t o i d e n t i f y each r e g i o n , t h e y v a r i a b l e s a r e t h e
exogenous series, and t h e z ( t - t i ) v a r i a b l e s are a u t o r e g r e s s i v e
v a l u e s o f t h e f o r e c a s t e d series i t s e l f .
P a g e 2 1
A s a m p l e c a l c u l a t i o n f o r r e g i o n 4 f o r F e b r u a r y 22 is:
V a r i a b l e - # V a r i a b l e D e s c r i p t i o n
2 Reg ion 1
4 R e g i o n 3
5 R e g i o n 4
6 R e g i o n 5
C o e f f i c i e n t V a r i a b l e D a t a
. I 3 1 9 5 9 - 0
1 . 5 1 5 1 7 0
7 R e g i o n 6 . l l 1 3 1 4 - 0
1 0 R e g i o n 9 .121379 - 0
11 R e g i o n 1 0 .0928959 0
1 2 R e g i o n 11 . I 2 0 1 8 2 - 0
1 3 Y e s t e r d a y ' s E f f e c t i v e t e m p e r a t u r e .00308867 - 6.3-
1 4 Y e s t e r d a y ' s Avg. Temp. ,0212799 .6-
1 5 Y e s t e r d a y ' s s e n d o u t .860937 2 .999
1 6 Wind x Temp. .00010965 2 1 7 . 1 I
1 7 Day o f t h e Week F a c t o r .751174 .969 t
I
1 8 C h a n g e i n E f f e c t i v e Temp. .0571149 1 .6 - I
1 9 E f f e c t i v e Temp. .0102688 4.7-
20 F o r e c a s t e d High Temp. .0181356 - 5 .0
2 1 F o r e c a s t e d Low Temp. .0192658 - .6-
22 F o r e c a s t e d Avg. Temp. .0192827
23 F o r e c a s t e d W e t B u l b .OX47737
24 F o r e c a s t e d D a y l i g h t H r s . . 369423 1 0 . 1
2 5 F o r e c a s t e d Wind .00668735 - 1 3 .
C o n s t a n t .go258 - 1
( # I s 3 , 8 & 9 were d r o p p e d d u e t o p a r t i a l F b e i n g i n s i g n i f i c a n t )
Page 22
n F e b r u a r y 22 Y = 2.765
The a c t u a l s e n d o u t f o r r e g i o n 4 f o r F e b r u a r y 22 was
2.735, t h u s t h e forecast r e s u l t e d i n a r e s i d u a l error o f
TABLE 1
Page 23
ERROR ANALYSIS OF REGION 4
Actua l Fo recas t ed Res idua l 02/22/75 2.735 2.765 .030-
Average % e r r o r -. 28%
Average Residual -.004
Standard Devia t ion .085
However, it should be no ted t h a t t h e key e lement of succes s
of t h i s model does n o t r e l y on f o r e c a s t i n g each r eg ion
i n d i v i d u a l l y , b u t r a t h e r on p r e d i c t i n g t h e requi rement f o r t h e
e n t i r e system. Although c e r t a i n i n d i v i d u a l r e g i o n f o r e c a s t s
were beyond t h e a c c e p t a b l e c r i t e r i a , t h e combining of t h e
11 r e g i o n s i n t h e system forms a normal d i s t r i b u t i o n whose mean
was w e l l w i t h i n t h e s t a t e d o b j e c t i v e (see E x h i b i t 11, Page 69).
An i n d i c a t i o n of t h e model" a b i l i t y t o p r e d i c t t u r n i n g
p o i n t s , and a comparison of Fo recas t ed Versus Actua l Na tu ra l
Gas Sendout i s shown i n F igu re 2.
Page 24
Fig. 2 - Comparative Graph of Forecas ted Versus Actual Sendout
Region 4
Forecasted f ----. Ir
1 Actual
Day of t h e Week (February 2 2 - March 02)
Page 25
Alternatives Tested
Although many alternatives were tested, only a few of
the significant variables and their associated effect on the
final formula will be discussed.
As indicated earlier and as evidenced by the system map,
an extensive area is being served by the distribution system.
The solution to treating the diverse weather patterns was to
divide the system into 11 distinct regions.
Another distinct pattern idenkified was the consistent
variation in consumption based on the day of the week. An
example of these variations can be seen in Exhibit 6, Page 47.
Discounting a major upheaval such as a strike, indications
were that consumption by region, for the same day of the week,
tended to be quite stable.
Earlier mention was made of the different formulas used
in arriving at the effective temperature. Exhibit 7, Page 48
shows three sample runs made from the same basic data, with
only the effective temperature formula changed.
TABLE 2
EFFECTIVE TEMPERATURE COMPARISONS
Effective Effective Effective Temperature Temperature Temperature Formula 1 Formula 2 Formula 3
Multiple Correlation Coefficient
Error of Standard Deviation
Regression F
Page 26
The method used i n a l l of t h e t e s t i n g w a s t o va ry t h e d a t a
on one v a r i a b l e o n l y , t h u s de te rmin ing whether t h e e f f e c t of
t h i s one v a r i a b l e w a s p o s i t i v e o r nega t ive .
F i n a l l y , t h e dummy v a r i a b l e s w e r e i n t roduced t o account
f o r t h e 11 d i s t i n c t weather r eg ions . E x h i b i t 9 , Page 52 i n d i c a t e s
t h e s l i g h t improvement i n e x p l a i n i n g v a r i a t i o n s i n t h e dependent
v a r i a b l e by t h e i n c l u s i o n of t h e d e t e r m i n i s t i c e f f e c t s o f t h e
dummy v a r i a b l e s . This i s a by-product of t h e weather d a t a , which
had t o be submi t ted r e g i o n a l l y . A r e g i o n by r e g i o n f o r e c a s t i s
a l s o provided.
Without Dummy V a r i a b l e s With Dummy V a r i a b l e s
R~ .98253 .98424
E r r o r of S td . Devia t ion .523918
E r r o r Mean .001191
Computer F a c i l i t i e s
The same equipment was used th roughout t h e development and
d e s i g n o f t h e model. Many d i f f e r e n t programs and methods of
manipula t ing t h e d a t a were a t tempted b e f o r e s e t t l i n g w i t h t h e
program developed by S t a t i s t i c s Canada. ,
A l l a c c e s s t o t h e Simon F r a s e r 370/155 computer was through
a remote t e rmina l . Data was submi t ted i n t h e form of c a r d s
through a 2501 c a r d r e a d e r . The r e p o r t s w e r e produced on a
Telex 5403 p r i n t e r . These t e r m i n a l s are l o c a t e d i n t h e academic
b u i l d i n g a t Simon F r a s e r Un ive r s i t y .
Page 27
The o r i g i n a l t es t d a t a and sample r u n s c o n s i s t i n g of
3 months of d a t a r e q u i r e d a 120K reg ion of memory.
as t h e t ime span of t h e d a t a base w a s i n c r e a s e d t o
per iod of December 1 7 t h t o June 22nd, it was found
memory s i z e had t o be i nc reased t o a 240K reg ion .
However,
t h e l o n g e s t
t h a t t h e
T h i s was
due t o t h e f a c t t h a t a l l t h e d a t a was k e p t i n memory i n a
ma t r ix , r a t h e r t h a n us ing a u x i l l i a r , ~ s t o r a g e dev ices .
Consequently, t h e r u n s were ve ry f a s t , r e q u i r i n g about one
minute t o execute .
The l o c a t i o n of t h e t e r m i n a l s made it neces sa ry t o keypunch
t h e weather d a t a and a s s o c i a t e d dependent v a r i a b l e s . This
d a t a was t h e n t r a n s p o r t e d t o t h e t e r m i n a l s , where t h e computer
runs could be performed. Although t h i s was accomplished i n
o r d e r t o d e s i g n t h e model, it i s c e r t a i n l y n o t p r a c t i c a l f o r
d a i l y f o r e c a s t i n g from a d i s p a t c h e r ' s v iewpoin t . Mention a s
t o t h e implementat ion of t h i s model w i l l b e made i n a l a t e r
s e c t i o n .
Comparison of E x h i b i t 11, Page 69 and E x h i b i t 1 2 , Paqe 72
a l s o i n d i c a t e s t h a t t h e l onge r h i s t o r i c a l d a t a b a s e d i d n o t
produce r e s u l t s w i t h t h e same accuracy a s t h e s h o r t e r t i m e span.
Thus it i s i n t e r e s t i n g t o n o t e t h a t t h e l onge r t i m e span i s
more expens ive t o ma in t a in , by r e q u i r i n g more memory and computer
t i m e , w h i l e producing poorer r e s u l t s .
Page 28
I11 THE MODEL DESIGN
Model Ana lys i s -
Typ ica l d a t a weight ing and a r r i v a l a t t h e f o r e c a s t t a k e i
t h e fo l lowing form. The l a s t d a y ' s a c t u a l wea ther v a r i a b l e s
and g a s sendout a r e added t o t h e d a t a base f o r each r eg ion .
The e a r l i e s t o b s e r v a t i o n s ( c o n s i s t i n g of 1 day of d a t a ) a r e
d e l e t e d , s o t h a t a c o n s t a n t t i m e frame is mainta ined. This
new d a t a base is analyzed t o de te rmine t h e day of t h e week
f a c t o r f o r each r eg ion . The e f f e c t i v e t empera tu re which
produced t h e l owes t e r r o r i s t h e n chosen. Now t h e o t h e r
independent v a r i a b l e s a r e gene ra t ed , which become i n p u t t o t h e
m u l t i p l e r e g r e s s i o n . The r e s u l t i n g c o e f f i c i e n t s a r e combined
w i t h t h e f o r e c a s t e d weather f o r tomorrow, from which t h e new
f o r e c a s t f o r tomorrow's sendout f o r a l l r e g i o n s r e s u l t s i n t h e
t o t a l sendout f o r t h e n e x t 24 hours .
Many of t h e p a s t models u s e a c o r r e c t i o n f a c t o r from l a s t
y e a r , o r a weigh t ing t o r e f l e c t p r ev ious weather p a t t e r n s .
The a u t h o r contends t h a t t h i s i s i r r e l e v a n t , and p o s s i b l y
mis lead ing . A s an example, peak days i n t h e p a s t 3 y e a r s
occur red on February 8 , 1973, January 10 , 1974 and February 9 ,
1975. I f t h e cor responding day from t h e p rev ious y e a r had been
al lowed t o i n f l u e n c e t h e c u r r e n t f o r e c a s t , it is e v i d e n t t h a t
an e r r o r would have been in t roduced i n t o t h e model.
I n ana lyz ing E x h i b i t 11, Page 69 it can be seen t h a t t h e
pe rcen tage e r r o r s f o r each i n d i v i d u a l r e g i o n a r e q u i t e h igh ,
and vary q u i t e cons ide rab ly . However, t h e v a r i a t i o n between
r e g i o n s is random, w i t h t h e f l u c t u a t i o n s n e t t i n g o u t t o an
a c c e p t a b l e f o r e c a s t f o r t h e e n t i r e system f o r one day.
Page 29
The m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t has been used a s
t h e measure of t h e succes s of t h e r e g r e s s i o n e q u a t i o n i n
exp la in ing t h e v a r i a t i o n of t h e d a t a . The observed mean
square r a t i o is s t a t i s t i c a l l y s i g n i f i c a n t , i n d i c a t i n g t h a t
t h e v a r i a t i o n i n t h e d a t a , which has been accounted f o r by
t h e equa t ion , i s g r e a t e r t h a n would be expected by chance.
Examining t h e r e s i d u a l s from E x h i b i t 1 0 , Page 55 g i v e s
no i n d i c a t i o n of t i m e dependent nonrandomness o r unusual
behavior . Occasional spo rad ic p o i n t s r ang ing t o s e v e r a l s t a n d a r d
e r r o r s a r e observed f o r c e r t a i n o b s e r v a t i o n s . No s p e c i f i c
exp lana t ion has been uncovered t o account f o r t h e s e d e p a r t u r e s .
Fu r the r r e s e a r c h w i l l be neces sa ry t o de te rmine t h e cause ,
and d e r i v e a v a r i a b l e which w i l l a ccoun t f o r t h e s e spo rad ic
p o i n t s . However, it should be noted t h a t c o n t r a r y t o s e v e r a l
p a s t s t u d i e s , no d a t a p o i n t s such as h o l i d a y s o r weekends
w e r e removed. With t h e t r e n d towards f l e x i b l e hour s , a
s h o r t e r work week, and o p t i o n s r e g a r d i n g h o l i d a y s , it was
f e l t t h a t p o s s i b l e maximum exposure t h a t a d i s p a t c h e r could
be s u b j e c t e d t o should be shown. However, i n t h e c a s e of
n a t i o n a l h o l i d a y s , a l though t h i s day w a s f o r e c a s t e d , i n
p r a c t i c e such a h o l i d a y should b e suppressed i n t h e d a t a base ,
t o p reven t f u t u r e f o r e c a s t s from be ing b i a sed .
Page 30
Data Weighting V a l i d a t i o n -
Two d i f f e r e n t t i m e p e r i o d s w e r e t e s t e d t o de t e rmine t h e
i n f l u e n c e o f h i s t o r i c a l e v e n t s on tomorrow's s endou t . Both
sets i n c l u d e d t h e same v a r i a b l e s and began a t t h e same t i m e .
The a c t u a l e r r o r v a l u e s were c a l c u l a t e d as a c t u a l g a s s endou t
minus t h e f o r e c a s t e d sendout . T h i s d i f f e r e n c e was t a k e n a s
a p e r c e n t o f a c t u a l g a s sendout .
The s h o r t e r t i m e span was found t o improve t h e model
s i g n i f i c a n t l y by r e d u c i n g t h e f o r e c a s t e r r o r . T h i s i s due t o
t h e f a c t t h a t c o n d i t i o n s d u r i n g t h e p a s t s e v e r a l weeks a r e much
more r e l e v a n t t h a n c o n d i t i o n s s ay . f o u r months ago. The l o n g e r
t i m e span a l lowed t o o much we igh t i ng t o b e p l a c e d on o l d e r
h i s t o r i c a l d a t a . E x h i b i t 11, Page 69 and E x h i b i t 12 . Page 72
c o n t a i n a sample o f t h e d i f f e r e n t t i m e p e r i o d s .
TABLE 3
~ i m e P e r i o d Model Comparisons
D e c . 17 - Feb. 22
Mean P e r c e n t E r r o r - . 7
Standard ~ e v i a t i o n
M u l t i p l e C o e f f i c i e n t of De te rmina t ion
S e l e c t i o n o f V a r i a b l e s
D e c . 17 - June 28
3.0
.704
The f i n a l se t o f v a r i a b l e s are shown i n Tab l e 5. A s c an
be s een from E x h i b i t 1 0 , Page 55 t h e s e v a r i a b l e s accoun ted f o r
i n exce s s o f 9 8 % o f t h e v a r i a t i o n i n t h e dependen t v a r i a b l e .
A d d i t i o n a l v a r i a b l e s such a s c l o u d c o v e r , p r e c i p i t a t i o n and
Page 31
wind direction were also considered. These variables were
discarded due to the fact that they were either not available
in all of the areas, were subject to human interpretation,
and also were most prone to forecasting error from the
weather bureau.
A human psychological factor is evidenced by the fact
that the thermostat is not set as high on the first day of
a cold spell, as it is on the 3rd or 4th day of continuing
cold. The effective temperature was intended to account
for this fact. In all of the variations of testing performed,
the effective temperature, yesterday's effective temperature,
and the change in effective temperature remained significantly
high and were never excluded from the equation.
. One of the other significant effects that the model was
intended to allow for was the speed of temperature change.
This was accomplished by showing <he high, low and average
temperatures, and the change of temperatures from the
previous day. Although hourly readings are received, it
can be seen how massive the data base would become if a11 of
these variables were accumulated by the hour for each region.
According to J. M. Wetz C 2 1 , the range of values of ,
the observed F ratio should be considerably greater than the
selected percentage point of the F distribution. The
inaccuracy of a regression equation derives from the regression
lack of fit and pure error. The F ratio consists of the
(regression mean square)/ (residual mean square) . The test of
Page 32
lack of fit and the satisfactory results for F(21, 715,.05)
= 1.56 are
Source of Variation
Regression
Rcsidual
Total
shown in the following table:
TABLE 4
Analysis of Variance
Degrees of Surn of Mean Square Freedom Squares
Page 33
I V CONCLUSION
presen t Model Design
A s evidenced by Exh ib i t 11, Page 69 t h e f o r e c a s t i n g model
has m e t t h e o r i g i n a l o b j e c t i v e s . The work i n t h e s tudy has
been designed around t h e d i spa tch ing philosophy of t h e Company.
The v a r i a b l e s s e l e c t e d have been chosen on t h e b a s i s of
a v a i l a b i l i t y and t ime l iness t o t h e d i spa tch ing personnel .
The b a s i c philosophy of t h e model has been t o l eave it
open ended. I n t h i s manner, it i s intended t h a t a s economic
and personal h a b i t s change, t h e model w i l l dynamically a d j u s t
t h e c o e f f i c i e n t s . I n a d d i t i o n , should any of t h e v a r i a b l e s
become i n s i g n i f i c a n t due t o changes such a s consumer h a b i t s
o r economic cond i t ions , t h e v a r i a b l e s w i l l simply drop from
t h e r e g r e s s i o n equat ion.
The d i s p a t c h e r w i l l have t o o p e r a t e t h e system under
appropr ia t e guidance and c o n t r o l s , i n o r d e r t o ga in confidence
i n t h e f o r e c a s t i n g system. The f o r e c a s t i n g des ign must work
i n t h e environment which a c t u a l l y e x i s t s i n o rde r t o prove
t h e a p p l i c a t i o n .
The model i s modular i n des ign , and provides p rogress ive
information of t h e d a t a t h a t i s s e l e c t e d . Although a number
of v a r i a b l e s must be entered by t h e d i s p a t c h e r , they a r e a l l
based on information a v a i l a b l e t o him. The one disadvantage
is t h e cons ide rab le computer c a p a c i t y r equ i red t o d e r i v e t h e
f o r e c a s t i n g c o e f f i c i e n t s . ..
Page 34
Fu tu re Cons ide ra t ions
E a r l i e r mention was made of t h e u s e o f t h e computer
f a c i l i t i e s e x i s t i n g a t Simon F r a s e r U n i v e r s i t y . I t is in t ended
t h a t t h e model w i l l b e implemented i n t h e fo l lowing manner.
The weather d a t a o r i g i n a t i n g from Toronto w i l l b e c a p t u r e d
by a PDP 11/40. The PDP i s a l s o c o n t r o l l i n g t h e t e l e m e t r y
l i n e s i n d i c a t i n g a c t u a l gas sendout . The PDP w i l l be l i n k e d
t o a Univac 90/30 c o n s i s t i n g of i 3 1 ~ of memory and 120 m i l l i o n
b y t e s of o n l i n e d i s c s t o r a g e . The 90/30 w i l l p o l l t h e PDP
and r e c e i v e from it both t h e t e l e m e t r y and weather d a t a .
The d i s p a t c h e r i s l i n k e d w i t h t h e 90/30 v i a a ~ n i s c o p e 200
ca thode r a y tube . Through t h e t e r m i n a l , t h e d i s p a t c h e r can
r e q u e s t t h e f o r e c a s t program, which w i l l prompt him f o r
the necessary f o r e c a s t e d weather d a t a f o r each r eg ion . When
t h e f i n a l v a r i a b l e i s r e c e i v e d , t h e s e are l i n k e d w i t h t h e
a c t u a l d a t a r e c e i v e d from t h e PDP 11/40 and a f o r e c a s t w i l l b e
genera ted . his w i l l be d i s p l a y e d back t o t h e d i s p a t c h e r
on h i s t e rmina l . The d a t a b a s e w i l l b e a u t o m a t i c a l l y
updated a s a c t u a l d a t a is r e c e i v e d from t h e PDP.
It i s e v i d e n t t h a t f u r t h e r r e s e a r c h w i l l b e neces sa ry
t o improve t h e model t o account f o r unknown v a r i a t i o n s , and
f o r d r a s t i c changes t h a t cou ld occur . S i n c e t h e computing
f a c i l i t i e s w i l l be a v a i l a b l e , t h i s w i l l probably be accomplished
by ma in t a in ing a p a r a l l e l set of v a r i a b l e s which w i l l
Page 35
SUMMARY
The primary intent of the study was to design a model
which would assist dispatching personnel in forecasting daily
natural gas sendout. The first problem was formulating an
analytical model which would simulate the natural gas
environment. Statistical measures had to be applied to
determine the significance of the model results.
The first phase consisted of removing non-weathcr effects,
such as day of the week, after the system had been segregated
into distinct weather regions. Then data weighting had to
be applied to help determine which factors produced the most
relevant forecast. These factors were finally subjected to
Multiple Regression Analysis. The final resulting model
consisting of the variables listed in Table 5 included the
use of the dummy variables which helped to account for the
unique influence from each geographical region.
Although considerable work has gone into the formulation
of the model, much remains to be proven, as the model is
actually implemented and proves itself in a real time working
environment. Only a bit of a byte has been taken out of the
entire spectrum of accurate natural gas forecasting.
GLOSSARY OF TERMS
B a s e Load -
I n t e r r u p t i b l e Cus tomers -
Nominat ion -
Sendou t -
T r a n s i t i o n Zone -
Tempera ture Latency -
The p o r t i o n of t h e sendout t h a t i s
Page 36
r e l a t i v e l y c o n s t a n t , w i t h some v a r i a t i o n s
from day t o day due t o work schedu le
and customer h a b i t s .
An i n d u s t r i a l customer whose gas supply
may be c u r t a i l e d , fo l lowing a s p e c i f i e d
number of hours of advance n o t i c e .
The maximum d a i l y volume of gas t h a t
t h e s u p p l i e r i s o b l i g a t e d t o p rov ide
t o t h e Company, and t h e b a s i s f o r
c o n t r a c t u a l minimums and " t a k e o r pay"
c l a u s e s .
A t e r m used , to r e p r e s e n t t h e amount of
g a s d e l i v e r e d from a system. I t i s t h e
dependent v a r i a b l e i n t h e equa t ion .
A t e r m used t o d e s c r i b e a s e c t i o n of
t h e e q u a t i o n where t h e c o r r e l a t i o n
becomes poor.
A p h y s i c a l a t t r i b u t e o f a b u i l d i n g
whereby it w i l l r e q u i r e from 2 4 t o 4 8
hours t o r e a d j u s t t o a r a p i d e x t e r n a l
environmental change i n temperature .
Page 37
Bib l iography
Barn, M.D. and W. J. Gunderson, "Load F o r e c a s t i n g and Dispa tch ing f o r D i s t r i b u t i o n Companies". Paper p re sen ted a t t h e 1962 American G a s A s s o c i a t i o n Conference, Houston, Texas (CEP-62-16) . Draper, N.R. and H. Smith, Applied Regress ion Ana lys i s . N e w York. John Wiley & Sons, I n c . , 1966.
Ger tz , M.L. "Development and U t i l i z a t i o n of Load Sendout Fo recas t ing" . Paper p re sen ted a t t h e 1968 American Gas Assoc i a t i on Dispa tch ing Workshop.
Haenel, R .D . , "An Analys i s and Model f o r F o r e c a s t i n g Dai ly N a t u r a l Gas Load", Masters D i s , s e r t a t i o n , Northrop I n s t i t u t e of Technology, Inglewood, C a l i f o r n i a , 1973.
Hingorani , G. and L. F. Marcynski, "Sendout F o r e c a s t i n g Technique Development and U t i l i z a t i o n " . Paper p re sen ted a t t h e 1968 American Gas A s s o c i a t i o n Conference, Cleveland, Ohio (68-T-41).
Luecke, M.C., "Gu ide l ines on Developing a Succes s fu l Model". Management ~ d v i s e r , January-February, 1973.
Naylor, T.M. and J. L. B a l i n t f y . Computer S imula t ion Technique. John Wiley & Sons, I n c . , 1966.
R i v e t t , P . , P r i n c i p l e s of Model Bui ld ing : The Cons t ruc t ion of Models f o r Decis ion Analys i s . The Mendy's P r e s s , Bath.1972
Ruskin, V.W. "S imula t ion o f Companies by Models". Paper p re sen ted a t t h e 1970 Canadian Gas A s s o c i a t i o n Conference, Vancouver, B.C.
S t a t i s t i c s Canada, "General Purpose M u l t i p l e Regress ion Program." Program documentation made a v a i l a b l e through Simon F r a s e r Un ive r s i t y .
Van Note, F.G. " S t a t i s t i c a l and Computer Ana lys i s of t h e E f f e c t of Weather on Gas Sendout". A.G.A. Opera t ing S e c t i o n Procedures , 1964.
Wilde, D . J . Optimum Seeking Methods, N e w J e r s e y : P r e n t i c e - H a l l , I n c . , 1964.
No.
1
Page 38
TABLE 5
Variables for Regression Model
Variable
Exogenous
Region 1
Region 2
Region 3
Region 4
Region 5
Region 6
Region 7
Region 8
Region 9
Region 10
Region 11
Yesterday's effective temperature
Yesterday's average temperature
Yesterday's sendout
Wind x corrected average temperature
Day of the week factor
Change in effective temperature
High Temperature in Celsius
Low temperature in Celsius
Average temperature in Celsius
Wet bulb average
Daylight hours
Wind speed in knots
Actual gas load in MMCF
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APPENDIX B
Check For I Val id E n t r i e s
Page 40
A P P S N D I X B (Cont'd)
Calculate E f f e c t i v e
Var iables By 171 1 I n s e r t Next
NO i E f f e c t i v e > Temperature
Formula L ----
Var iab les /------------- 1 New Var iab les
pou t i n e By Region
Page 41
APPENDIX B (Cont'd)
Page 4 2
I ----v-- E d i t Paranw tcr Cards i
A P P E N D I X B (Cont'd)
Page 4 3
\
$.-.
F V a l u c Vnr inh1 .e i n Equation
' V a l u e
-. -. - i
V a r i a n c e M i n u s Above L*<i
V a r i a b l e
*
APPENDIX B (Cont'd)
Page 4 4
- - - . . . - -- -- - - Reformat Grouped Var i ab l e s an
1 d
F Leve l
- I -- -
I
4 -- Punch i
\ , v a r i a b l e tL
.i,Coeff i c ien ' t s
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l o r e c a s t Data I
f C a l c u l a t e 1 - . -- --. . f ~ e n d o u t From I ( v a r i a b l e 4 I - - - j) ICoeff ic ient-s -,
p f i c i e n t s ' 1 /
SYSTEM MAP C . ....a
WALL
IlLinSON - NOPE CIICTKYHD 1' FT. ST. JOllN lL1.1p.
MACKLNLIE LAKE ). MACKENllC TCl lP .
PRINCE GEOhOE > PRINCE GEOllGE TEMP.
QUCSXEL I. QUCCNZL I L M P .
WlLLlAUS LAKC f. WILLIAMS LAK): TEMP.
I00 MILE IIllilOC LAC L A HACIIL ) WILLIAMS LAKE TEMP.
MERRITT 3 LYTTON TEIIP.
EXHIBIT 2 ,
. - . . " . .. ..', " .,.....- J
AREA TEMPERATURES
BASE0 ON 30 YEAR AVERAGE Clln~alology fJrvslon. hfoloorlogrc.ll Branch
Don~~nron Oopl. ol Tronsporl
COLDER Normal Avorngo System Degree Days 7565
WARMER 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974
YEAR ENDED JUNE 30 . . i 9.. . I - - . .-ur. . .. .. ., .-- . ..-.... .--. d
E X H I B I T 4 .
36
34
COMMERCIAL 32 30
28
28
P 0 24 H 22
U 0
20
cn 18 Z
3 16
14 5i 12
10
8 6
4
2
1065 1 x 0 lMi7 1 x 8 1069 1970 1971 1072 1073 1874
YEAR ENDED JUNE 30 L:. .. . . - . . ." .- . ... A . D . -* .. ..l
Page 46
NORMAL. Bawd on 30 yvnr uverngo. DEGnEE DAY. hlca:.wo 01 lllc oxlonl wh~cli Ihu mcan dally lempcrjturu rolls ~ O I O W (is ' Fol~runhcll.
JULY AUG. SEPT. OCT. NOV. OEC. JAN. FEB. MAR. APRIL MAY JUNE
MONTHS OF YEAR ENDED JUNE 31 1973
~ a ' z Z ~ - ~ X ~ w 4 1
EXHIBIT 5
E X H I B I T 6 Page 47
R E G I O N 1 - 3 MNTHS DFMAND P R F O I C T I O N M n D F L
D A Y O F WFEk FACTOR W I T H MON = 100.0 t TllF = 1011-4
WFD = 1 0 2 . 0 THR = 100.6 F R I = 106.9 S A T = 1 0 1 . 2 SON = 1 0 6 . 7
R E G I n N 2 - 3 MNTHS D F M A N n P K F n I C T I O N M n D F L
D A Y O F WEEK FACTf lR W l T H Mf lN = 100.0 TlJE = 1 0 1 . 7 w E n = 1 0 4 . 5 THR = 106.7 F R I = 1 1 3 . 9 SAT = 107.4 Sl lN = 9 7 - 5
R E G I O N 3 3 MNTHS DEMAND P R E D I C T I O N MODEL . -
D A Y OF WEEK F A C T n R b I T H MON = 100.0 TIJE = 1 0 4 . 7 WFD = 1 0 8 . 1 THR = 108 .9 . F R I = 1 0 9 . 5 <AT = 1 0 8 - 5 SlJN = 1 0 4 . 7
R E G I O N 4-3 MNTHS DEMAND P R E D I C T I O N M n n F L
I 11 11
4 1ll1l
D A Y O F WEEK FACTOR W I T H MON = 100.0 1 1 1
,_-_ _I ___-_-___ -__- - TUE = 101.6 - - -. WED = 101.8 THR = 1 0 0 . 5 F R I = I n h - 1 S A T = 96.9
R E G I O N 5-3 MNTHS DEMAND P R E D I C T I O N MODFL
D A Y O F MEEK FACTOR W I T H MON = 100.0 -- - - - . -- - - -- - . - -- TOE = 1 0 2 . 6 WED = 1 0 7 . 1
L THR = 1 0 7 . 7 rn F R I = 1 0 3 . 5
S A T = 9 8 . 4 - - - _ - - - - - * . .. A C l l h l - 0 1 3
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