Environmental Engineering Reference
In-Depth Information
Generation capacity
.
S
stands for a given particular powe
r
station, and its actual
electricity generation is denoted by
x
with an upper bound
x
.
The coal (
c
), natural gas (
g
), and nuclear (
n
) fuel technologies in our model are
prone to failure. We adopt a set of binary (Bernoulli) random variables for the
possibility of any one contingency. We thus assume that each stat
io
n
S
of type
c
;
g
;
n
; ...;
C
st
an
ds for
coal plants, irrespective of whether they are operative or not. Note that
C
is not
f
g
is in service for a fraction
K
of the year. Here
c
¼
1
xed; it can change ov
er
time due to openi
ng
s or closures on a planned schedule.
Similarly,
g
¼
and
n
¼
refer to gas and nuclear plants.
1
; ...;
G
1
; ...;
N
We do not consider that wind (
w
), natural-
ow or hydro (
h
), and pumped storage
(
p
) stations can be
. All the intermittences for whatever reasons are modeled
through the stochastic behavior of the load factor. The theoretical model assumed is
an IGBM:
'
off
'
d
W
t
¼
k
W
ðW
m
W
t
Þ
d
t þ r
W
W
t
d
Y
t
;
d
t þ r
H
H
t
d
Y
t
d
H
t
¼
k
H
ðH
m
H
t
Þ
;
d
t þ r
P
P
t
d
Y
t
d
P
t
¼
k
P
ðP
m
P
t
Þ
:
The standard notation for reversion speed, long-term value, and volatility holds
(wind:
k
W
,
W
m
, and
r
W
; hydro:
k
H
,
H
m
, and
r
H
; pumped storage:
k
P
,
P
m
, and
r
P
).
Generation from wind, natural
ow and pumped storage stations is seasonal. Our
simulations assume a seasonal behavior for renewable electricity, so the seasonality
in each load factor must be previously identi
ed (from historical time series).
across all its tech-
We can de
ne the activity vector
a
a
c
;
a
g
;
a
n
;
1
;
1
;
1
nologies
f
¼
. Aggregate output electricity, denoted
x
, comprises
generation from all its energy sources
f
¼
f
c
;
g
;
n
;
w
;
h
;
p
g
f
c
;
g
;
n
;
w
;
h
;
p
g
:
X
x
x
f
¼
x
c
þ x
g
þ x
n
þ x
w
þ x
h
þ x
p
:
f
The maximum power that can be generated at a given time (
t
) by coal plants is
a
c
x
c
. Therefore, the aggregate output electricity is bounded from above.
2.2 Economic Environment
Demand
-
side costs
. According to Foley et al. [
15
], in liberalized electricity markets
the sale of electricity at a pro
t is the main business focus with value of lost load
(VOLL) playing a larger part than energy not served (ENS) (which was a key factor
in the era of the state monopoly). Short run marginal cost-based pricing is generally
not high enough to ensure this, so equilibrium involves a degree of ENS priced at
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