54
1
1
0 02
0 03
1
3
λ λ
β
β
i
= −
− +
.
.
(3.51)
Consequently, the dynamic mode of wind energy production is shown in a circuit
diagram considering the nonlinear nature of the open-circuit voltage (V oc ) where R p
represents the self-discharge resistance, R ic and R id are the internal resistance which
compensates resistance of the electrolyte, R co and R do are the voltage drop for the
charge and discharge process, and C o represents the double-layer capacitance
behavior of the battery during charge and discharge [30–32].
Simply, this open-circuit voltage is a nonlinear function of the temperature (T)
and discharge current (I B ) and thus this energy can also be stored as (E cd ). Thus, this
model used here initially calculates current (I B ) to confirm the maximum available
energy stored which is determined by V oc and SOC, calculated as the power generation by wind energy as P wg (t) ≥ P load (t), and the storage capacity at any given time
(t) is expressed as
C t C t
P t P t P t
t
bat
b at
PV
wg
load
cad
cha
( ) =
−
( )+ ( )+ ( )− ( )
(
)
1
η
η
∆
(3.52)
where C bat (t) and C bat (t − 1) are the available battery capacity at time (t) and (t − 1).
P PV is the power generation rate, P wg is the power generated by wind turbine
generator, P load (t) is the power consumed at load t, t is the simulation time step
(Δt = 1 h), η cad is the efficiency of AC/DC converter, and η cha is the energy efficiency.
Here, wind energy has been finally estimated as, i.e., (η inv P wg (t) + P PV (t)) ≥ P load
(t), the extra storage of energy as
C t C t
P t
P t P t
bat
b at
dech
PV
load
wg
inv
( ) =
−
( )+
( )−
( )− ( )
1
1
η
η
∆t
(3.53)
where η dech is the energy rate efficiency, η inv is the inverter efficiency, C is the capacity of energy at any time t, and C bat (t) is constrained by C bat min ≤ C bat (t) ≤ C bat max
where C bat min and C bat max are minimum and maximum allowable energy storage
capacity.
Simply, this stored wind energy system can be stand-alone, or grid connected.
Stand-alone systems need to have generation and storage capacity large enough to
handle the load while in a grid-connected system the storage device can be relatively smaller as deficient power can be obtained from the grid [24, 33]. A gridconnected hybrid can supply electricity to both load and utility grid. However, when
connected to grid, proper power electronic controllers are required to control voltage, frequency and harmonic regulations, and load sharing.
3 Wind Energy
1
1
0 02
0 03
1
3
λ λ
β
β
i
= −
− +
.
.
(3.51)
Consequently, the dynamic mode of wind energy production is shown in a circuit
diagram considering the nonlinear nature of the open-circuit voltage (V oc ) where R p
represents the self-discharge resistance, R ic and R id are the internal resistance which
compensates resistance of the electrolyte, R co and R do are the voltage drop for the
charge and discharge process, and C o represents the double-layer capacitance
behavior of the battery during charge and discharge [30–32].
Simply, this open-circuit voltage is a nonlinear function of the temperature (T)
and discharge current (I B ) and thus this energy can also be stored as (E cd ). Thus, this
model used here initially calculates current (I B ) to confirm the maximum available
energy stored which is determined by V oc and SOC, calculated as the power generation by wind energy as P wg (t) ≥ P load (t), and the storage capacity at any given time
(t) is expressed as
C t C t
P t P t P t
t
bat
b at
PV
wg
load
cad
cha
( ) =
−
( )+ ( )+ ( )− ( )
(
)
1
η
η
∆
(3.52)
where C bat (t) and C bat (t − 1) are the available battery capacity at time (t) and (t − 1).
P PV is the power generation rate, P wg is the power generated by wind turbine
generator, P load (t) is the power consumed at load t, t is the simulation time step
(Δt = 1 h), η cad is the efficiency of AC/DC converter, and η cha is the energy efficiency.
Here, wind energy has been finally estimated as, i.e., (η inv P wg (t) + P PV (t)) ≥ P load
(t), the extra storage of energy as
C t C t
P t
P t P t
bat
b at
dech
PV
load
wg
inv
( ) =
−
( )+
( )−
( )− ( )
1
1
η
η
∆t
(3.53)
where η dech is the energy rate efficiency, η inv is the inverter efficiency, C is the capacity of energy at any time t, and C bat (t) is constrained by C bat min ≤ C bat (t) ≤ C bat max
where C bat min and C bat max are minimum and maximum allowable energy storage
capacity.
Simply, this stored wind energy system can be stand-alone, or grid connected.
Stand-alone systems need to have generation and storage capacity large enough to
handle the load while in a grid-connected system the storage device can be relatively smaller as deficient power can be obtained from the grid [24, 33]. A gridconnected hybrid can supply electricity to both load and utility grid. However, when
connected to grid, proper power electronic controllers are required to control voltage, frequency and harmonic regulations, and load sharing.
3 Wind Energy