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esm-course
esm-tutorials
Commits
a0b011e3
Commit
a0b011e3
authored
Jun 13, 2019
by
Fabian Neumann
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tutorial-3: minor corrections in solution
parent
8e12ab8d
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tutorial-3/worksheet/sheet03.tex
tutorial-3/worksheet/sheet03.tex
+2
-2
tutorial-3/worksheet/solution03.pdf
tutorial-3/worksheet/solution03.pdf
+0
-0
tutorial-3/worksheet/solution03.tex
tutorial-3/worksheet/solution03.tex
+7
-7
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tutorial-3/worksheet/sheet03.tex
View file @
a0b011e3
...
...
@@ -123,8 +123,8 @@
\end{axis}
\end{tikzpicture}
\caption
{
Diurnal and synoptic variations of wind and solar power generation
\(
G
^{
N
}_{
w
}
(
t
)
\)
\autoref
{
figref:w
}
and
\(
G
^{
S
}_{
s
}
(
t
)
\)
\(
g
^{
N
}_{
w
}
(
t
)
\)
\autoref
{
figref:w
}
and
\(
g
^{
S
}_{
s
}
(
t
)
\)
\autoref
{
figref:s
}
, and a constant load (all in per-unit)
\(
L
(
t
)
\)
\autoref
{
figref:l
}
.
}
\label
{
fig:variations
}
...
...
tutorial-3/worksheet/solution03.pdf
View file @
a0b011e3
No preview for this file type
tutorial-3/worksheet/solution03.tex
View file @
a0b011e3
...
...
@@ -122,8 +122,8 @@
\end{axis}
\end{tikzpicture}
\caption
{
Diurnal and synoptic variations of wind and solar power generation
\(
G
^{
N
}_{
w
}
(
t
)
\)
\autoref
{
figref:w
}
and
\(
G
^{
S
}_{
s
}
(
t
)
\)
\(
g
^{
N
}_{
w
}
(
t
)
\)
\autoref
{
figref:w
}
and
\(
g
^{
S
}_{
s
}
(
t
)
\)
\autoref
{
figref:s
}
, and a constant load (all in per-unit)
\(
L
(
t
)
\)
\autoref
{
figref:l
}
.
}
\label
{
fig:variations
}
...
...
@@ -180,15 +180,15 @@ For now, assume no power exchange between the regions and that the stores are lo
G
_{
s,storage,dispatch
}^
N
&
=
\max
(
\pm
\Delta
^
N(t))
\\
&
=
\max
(
\pm
[L
^
N(t) - G
^
N
_
w
\cdot
g
^
N
_
w(t)])
\\
&
=
\max
(
\pm
[L
^
N(t) -
\frac
{
A
^
N
_
l
}{
c
_
w
}
\cdot
c
_
w
\cdot
(1+A
_
w
\sin
\omega
_
w t)])
\\
&
=
\max
(
\pm
[L
^
N(t) - A
^
N
_
l
+
A
^
N
_
l A
_
w
\sin
\omega
_
w t)])
\\
&
=
\max
(
\pm
[A
^
N
_
l A
_
w
\sin
\omega
_
w t)])
\\
&
=
\max
(
\pm
[L
^
N(t) - A
^
N
_
l
-
A
^
N
_
l A
_
w
\sin
\omega
_
w t)])
\\
&
=
\max
(
\pm
[
-
A
^
N
_
l A
_
w
\sin
\omega
_
w t)])
\\
&
= A
^
N
_
l A
_
w = 0.9
\cdot
20
\si
{
\giga\watt
}
= 18
\si
{
\giga\watt
}
\end{align*}
In the South:
\begin{align*}
G
_{
s,storage,dispatch
}^
S
&
=
\max
(
\pm
g
_
s
^
S(t))
\\
G
_{
s,storage,dispatch
}^
S
&
=
\max
(
\pm
\Delta
^
S(t))
\\
&
=
\max
(
\pm
[L
^
S(t) - G
^
S
_
s
\cdot
g
^
S
_
s(t)])
\\
&
=
\max
(
\pm
[L
^
S(t) -
\frac
{
A
^
S
_
l
}{
c
_
s
}
\cdot
c
_
s
\cdot
(1+A
_
s
\sin
\omega
_
s t)])
\\
&
=
\max
(
\pm
[L
^
S(t) - A
^
S
_
l + A
^
S
_
l A
_
s
\sin
\omega
_
s t)])
\\
...
...
@@ -219,7 +219,7 @@ For now, assume no power exchange between the regions and that the stores are lo
In the South:
\begin{align*}
e
_{
st
}^
S(t)
&
=
\int
_{
0
}^{
t
}
-
g
_
s
^
S(t')
\;\mathrm
{
d
}
t' =
\int
_{
0
}^{
t
}
A
^
S
_
l A
_
s
\sin
\omega
_
s t'
\;\mathrm
{
d
}
t'
\\
e
_{
st
}^
S(t)
&
=
\int
_{
0
}^{
t
}
-
\Delta
^
S(t')
\;\mathrm
{
d
}
t' =
\int
_{
0
}^{
t
}
A
^
S
_
l A
_
s
\sin
\omega
_
s t'
\;\mathrm
{
d
}
t'
\\
&
= A
^
S
_
l A
_
s
\frac
{
-
\cos
(
\omega
_
s t')
}{
\omega
_
s
}
\Big
|
_
0
^
t = A
^
S
_
l A
_
s
\frac
{
1-
\cos
(
\omega
_
s t')
}{
\omega
_
s
}
\end{align*}
...
...
@@ -271,7 +271,7 @@ For now, assume no power exchange between the regions and that the stores are lo
The minimal (lossless) corresponding cost to supply constant demand by using hydrogen as storage technology are
\begin{align*}
P
_
h
^
S
&
=
120
0
\text
{
\EUR
{}}
\si
{
\per\kilo\watt
}
\cdot
G
_{
storage,dispatch
}^
S + 10
\text
{
\EUR
{}
/kWh
}
\cdot
E
_{
st
}^
S
\\
P
_
h
^
S
&
=
75
0
\text
{
\EUR
{}}
\si
{
\per\kilo\watt
}
\cdot
G
_{
storage,dispatch
}^
S + 10
\text
{
\EUR
{}
/kWh
}
\cdot
E
_{
st
}^
S
\\
&
= 22.5
\cdot
10
^
9
\eur
+ 2.3
\cdot
10
^
9
\eur
\\
&
= 24.8
\cdot
10
^
9
\eur
\end{align*}
...
...
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