33 Optimal Design and Operation of a Residential Hybrid Microgrid …
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33.2 Mathematical Modeling of the Proposed System
33.2.1 Wind Power Generation
The amount of power output of a wind turbine is directly proportional to the wind
speed, which can be calculated using the following formula (Dhundhara et al. 2018):
P wt (V) =
⎧
⎪ ⎨
⎪ ⎩
P r (V−V CIN )
V rat −V CIN
, V CIN ≤ V ≤ V rat
P r ,
V rat ≤ V ≤ V CO
0,
V ≤ V CIN and V ≥ V CO
(33.1)
where,
P r
Constant power [kW]
V CIN Cut-in speed [m/s]
V rat Rated wind speed [m/s]
V CO Cutout speed [m/s].
V = V ref
H
H ref
α
(33.2)
V referes to the wind speed at the height of H. V ref is the wind speed measured
at the reference height, H ref , and α, which is the power-law exponent (Hiendro et al.
2013).
P wt =
ρ
ρ 0
P wt (ST P)
(33.3)
where, P wt (ST P) is the wind turbine power output at standard temperature and
pressure [kW]. ρ shows the actual air density [kg/m
3 ]. ρ 0 is defined “the air density
at standard temperature and pressure (1.225 kg/m
3 ). Table 33.1 gives the technical
specifications of the Air dolphin pro wind turbine which was used in this study.
Table 33.1 Wind turbine
input data (Zephyr
AIRDOLPHIN Introduction.
http://www.shida-kk.com/ima
ges/Airdolphin.pdf)
Constant power [kWh]
2.3
Cut-in wind speed [m/s]
2.5
Cut out wind speed [m/s]
20
Height [m]
30.5
Height of wind speed measurement (high) [m]
80
Height of wind speed measurement (low) [m]
10
Air density on sea surface [kg/m 3 ]
1.225