CHEN
et al.
: POWER SYSTEM CAPACITY EXPANSION UNDER HIGHER PENETRATION OF RENEWABLES CONSIDERING FLEXIBILITY
6243
In light of the system reliability requirement, the total in-
stalled capacity should be no less than the required capacity
limit:
M
k
i
=1
¯
I
i
k
+
λ
w
k
·
¯
I
w
k
+
λ
s
k
·
¯
I
s
k
≥
D
max
k
(10)
where
λ
w
k
and
λ
s
k
are the capacity credits for wind and so-
lar power in region
k
, respectively;
D
max
k
represents the total
capacity requirement to maintain reliability standards. For sim-
plicity in the modeling, we use fixed capacity credits for wind
and solar respectively, although the value of capacity credit for
wind and solar is non-linear with respect to the total capacity.
D. Modeling for the Operation and Investment for Storage
A novel linear simulation model for energy storage is pre-
sented in this section to represent the costs and constraints asso-
ciated with their investment and operation, considering multiple
geographical areas and different storage types.
The overall costs for storage systems include both amortized
investment and operational costs formulated as:
C
es
=
N
a
k
=1
N
e s
z
=1
a
p,z
k
·
¯
I
p,z
k
+
a
e,z
k
·
¯
I
e,z
k
+
c
es,z
k
·
T
t
=1
p
dis,z
t,k
+
p
ch,z
t,k
·
Δ
t
(11)
where
a
p,z
k
and
a
e,z
k
are the power-specific and energy-specific
amortized investment costs for the
z
th
category of energy stor-
age in region
k
. The power-specific cost is related for example
to the rotating synchronous machines in a pumped hydro unit,
or to the power electronic rectifier/inverters in a battery stor-
age system, or to the costs for anodes and cathodes in the case
of flow battery [17]. The energy-specific cost is related to the
reservoir for a pumped hydro system [18] or to the cost for the
solution included in a flow battery.
c
es,z
k
is the operational cost
for the
z
th
category of energy storages in region
k
. The opera-
tional cost is proportional to both the charging and discharging
power.
¯
I
p,z
k
and
¯
I
e,z
k
define the corresponding maximum power
and energy capacities for the newly installed storage systems.
They satisfy:
¯
I
p,z
k
≥
0
,
¯
I
e,z
k
≥
0
(12)
0
≤
p
dis,z
t,k
≤
¯
I
p,z
k
(13)
0
≤
p
ch,z
t,k
≤
¯
I
p,z
k
(14)
The energy balances of electric storage systems are repre-
sented by:
e
es,z
t
+1
,k
=
e
es,z
t,k
+
γ
ch,z
es
·
p
ch,z
t,k
·
Δ
t
−
1
γ
dis,z
es
·
p
dis,z
t,k
·
Δ
t
−
γ
self,z
es
·
e
es,z
t,k
(15)
where
γ
ch,z
es
,
γ
dis,z
es
and
γ
self,z
es
indicate respectively the charg-
ing/discharging efficiency and energy loss (self-discharge) rate
for the
z
th
category of energy storages;
e
es,z
t,k
represents the en-
ergy level at time
t
for the
z
th
category of energy storage in
region
k
, constrained by the installed capacity:
ν
−
z
es
·
¯
I
e,z
k
≤
e
es,z
t,k
≤
¯
ν
z
es
·
¯
I
e,z
k
(16)
where
ν
−
z
es
and
¯
ν
z
es
represent the minimum and maximum levels
of residual energy in the storage system respectively. For certain
types of storage systems, deep-discharge will significantly re-