Environmental Engineering Reference
In-Depth Information
pumped-storage stations (
x
p
) and power served (
s
). A high VOLL implies in
practice that the load will be served unless this is not technically feasible. The aim is
to
nd an optimal vector of power generated
fg
and power served/consumed
fg
that minimizes system costs at any time:
min
x
c
;
x
g
;
x
p
;
s
cðx
c
;
x
g
;
x
p
Þþ d s
ð
Þ
VOLL
f
g
Subject to:
0
x
f
a
f
x
f
;
f
¼
f
c
;
g
;
n
;
w
;
h
;
p
g
;
0
s d
;
d
D
¼
aðD
;
tÞ
d
t þ bðD
;
tÞ
d
V
;
d
R
¼
aðR
;
tÞ
d
t þ bðR
;
tÞ
d
Y
;
R
¼
fW
;
H
;
Pg
;
d
X
¼
aðX
;
tÞ
d
t þ bðX
;
tÞ
d
Z
;
X
¼
C
;
G
;
B
f
g
;
A
t
¼
ðtÞþ
max
B
t
ð
ðtÞ
;
Þ
:
floor
floor
0
The
rst two restrictions set the environment as determined by the operation state of
the physical assets. The components of the power system are subject to limits.
Besides, the power delivered is lower than or equal to the amount demanded. In
other words, served load must fall between zero and total load (it is possible that
some load is not met when cost is minimized).
The last three restrictions are the stochastic differential equations. Demand
fg
has an initial value and evolves seasonally and stochastically over time. The load
factor of
renewable,
intermittent wind- and hydro-based generation stations
f
is governed by a stochastic process. Similarly, the price of each com-
modity (coal, natural gas, and emission allowance) follows another Ito process. The
increments to standard Wiener process d
V
,d
Y
and d
Z
differ. d
Z
also differs for
each commodity
C
;
G
;
B
W
;
H
;
P
g
f
g
along with the terms
aðX
;
tÞ
and
bðX
;
tÞ
.
3 A Heuristic Application to the British Power Sector
To illustrate the model by example we consider a single system that is initially
given and xed, namely Great Britain as of 2012. We abstract from the particular
arrangements of the British wholesale electricity market [
37
], which does not
operate as a pool.
6
The demonstration of our general approach is thus inspired by
GB in that it uses plausible data, but with no claim as to accuracy for GB in detail.
6
The wholesale electricity market is operated within the British Electricity Trading and Trans-
mission Arrangements (BETTA). It is based on voluntary bilateral agreements between generators,
suppliers, traders and customers. In practice BETTA does not set a unique price: the actual price
generators are paid or customers have to pay is different if there is underproduction (for generators)
or overconsumption (for consumers).
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