AckermannTh. (ed) Wind Power in Power Systems
Подождите немного. Документ загружается.
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 39 – [1–48/48] 20.12.2004
7:23PM
k
LS
Low-speed shaft stiffness in per unit
k
tot
Total shaft stiffness in per unit
k
f
ð
k
Þ Flicker step factor
k
i
Inrush current factor
k
i
ð
k
Þ Grid-dependent switching current factor
k
spill
Spilled wind energy in percent of wind energy production
k
u
ð
k
Þ Voltage change factor
K Shaft torsion constant
K
p
Pitch angle controller constant
K
HS
High-speed shaft stiffness
K
LS
Low-speed shaft stiffness
K
s
Shaft stiffness
K
v
Voltage controller constant
L
l Turbulence length scale; transmission line length
L Inductance
L
fd
Field inductance
L
m
Mutual inductance
L
sr
Rotor leakage inductance
L
ss
Stator leakage inductance
M
m
G
Mean value of Gaussian distribution
m
x
Mean inflow (hydro power)
m
y
Mean inflow (renewable power source)
N
n Number of points
n
gear
Gear ratio
n
pp
Number of pole pairs
N Maximum number of switchings
N
10
Maximum number of one type of switchings within a 10-minute period
N
120
Maximum number of one type of switchings within a 120-minute period
N
wt
Number of wind turbines
P
p Number of generator poles; pressure
p(t) Power as a function of time
P Active power; win d power production; probability
P
2
Electric power of grid-side converter
P
0.2
Maximum measured power (0.2-second average value)
P
60
Maximum measured power (60-second average value)
P
base
Power base value for use in a per unit system
P
D
Power spectral density; power consumption
P
Dt
Power spectral density of turbulence
Notation xxxix
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 40 – [1–48/48] 20.12.2004
7:23PM
P
G
Additional required power production; generator electric power
P
G
curt
Curtailed active power
P
G
max
Maximum generated power
P
G,Ref
Desired generator electric power
P
L
Power losses on the line; active power of load
P
load
Instantaneous primary electrical load
P
lt
Long-term flicker disturbance factor
P
m
Mean power production
P
mc
Maximum permitted power
P
MECH
Mechanical power of the wind turbine
P
n
Rated power of wind turbine
P
o
Natural load of the line
P
O
Power of moving air mass; standard sea level atmospheric
pressure
P
R
Active power at the receiving end of the line; rated power
P
REF
Generator electric active power reference
P
S
Power delivered from kinetic energy stored in the rotating mass (turbine,
shaft and rotor)
P
st
Short-term flicker disturbance factor
P
T
Power delivered by turbine
P
TL
Transmission limit
P
TOC
(t) Power at time t on the transmission duration curve
P
W
Wind power producti on
P
wind
Instantaneous wind power output
P
WIND
Power of the wind within the rotor swept area of the
wind turbine
P
WPDC
(t) Power at time t on the wind power production duration curve
P
wt
Power extracted from the wind
P
x
Active power of system component x
P
year
Yearly mean price
PðX ¼ xÞ Probability that variable X is equal to x
Q
Q Reactive power
Q
2
Reactive power of grid-side converter
Q
2,Ref
Desired reactive power of grid-side converter
Q
C
Capacitor reactive power; reactive power of compensation
device
Q
Comp
Reactive power of compensation device
Q
G
Generator reactive power
Q
G,Ref
Desired generator reactive power
Q
import
Reactive power absorbed by the network
Q
L
Reactive power of load
Q
n
Rated reactive power of a wind turbine
Q
REF
Generator electric reactive power reference
Q
x
Reactive power of system component x
xl Notation
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 41 – [1–48/48] 20.12.2004
7:23PM
R
r Length along blade (local radius), measured from the hub ðr ¼ 0Þ
r
r
Rotor winding resistance
r
s
Stator winding resistance
r
xy
Cross-correlation
R Resistance; blade length; wind turbine radius; specific gas constant for
air; radius of a cylinder
R
2
Resistance of smoothing inductor
R
fd
Field resistance
R
gas
Gas constant
R
k
Short-circuit ratio at the point of connection
R
r
Rotor resistance
R
s
Stator resistance
S
s Slip; complex frequency
S Apparent power; complex power
S
base
Base power, in per unit system
S
n
Rated apparent power of a wind turbine
S
park
Nominal apparent power of wind farm
S
rG
Generator rated apparent power
S
k
Short circuit power
S
N
Nominal three-phase power of the induction generator
S
T
Transformer power capacity
S, SðtÞ Spa ce vector
S
a
(t) Instantaneous (momentaneous) value of a quantity for phase a
S
b
(t) Instantaneous (momentaneous) value of a quantity for phase b
S
c
(t) Instantaneous (momentaneous) value of a quantity for phase c
S
d
, S
d
(t) Direct axis of a space vector SðtÞ
S
q
, S
q
(t) Quadrature axis of a space vector SðtÞ
S
r
, S
r
ðtÞ Space vector SðtÞ referred to the rotor reference frame
S
r,a
Instantaneous (momentaneous) value of a quantity for phase a in rotor
reference frame
S
r,b
Instantaneous (momentaneous) value of a quantity for phase b in rotor
reference frame
S
r,c
Instantaneous (momentaneous) value of a quantity for phase c in rotor
reference frame
S
rd
Real part of S
r
S
rq
Imaginary part of S
r
S
s
, S
s
ðtÞ Space vector SðtÞ referred to the stator reference frame
S
s,d
Real part of S
s
S
s,q
Imaginary part of S
s
T
t Time
t
C
Temperature
Notation xli
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 42 – [1–48/48] 20.12.2004
7:23PM
t
TL
Number of hours over which the transmission limit is exceeded
T Time; torque; temperature
T
1
Cost for subscription per kW per year
T
2
Price of excess power per kW per year
T
base
Base value of torque, in per unit system
T
damping
Damping torque of the shaft
T
e
Torque of generator (electrical)
T
eg
End time of wind speed gust
T
el
Electrical air gap torque of the induction generator
T
er
End time of wind speed ramp
T
h
Time period
T
m
Mechanical torque produced by the wind turbine
T
MECH
Mechanical torque of the wind turbine
T
p
Duration of voltage variation caused by a switching operation
T
sg
Start time of wind speed ramp
T
shaft
Incoming torque from the shaft connecting the induction generator with
the wind turbine
T
torsion
Elasticity torque of the shaft
T
wr
Torque of wind turbine
U
u Voltage; integration variable
u(t) Voltage as a function of time
u
N
Nominal voltage
u
s
r
Stator voltage in the rotor reference frame
u
r
r
Rotor voltage in the rotor reference frame
u
s
s
Stator voltage in the stator reference frame
U Voltage
U
1
Fixed voltage at the end of the power system
U
2
Terminal voltage
U
2
Terminal voltage magnitude
U
2;Ref
Desired terminal voltage magnitude
U
DC
DC-link voltage
U
DC,Ref
Desired DC-link voltage
U
h
Harmonic voltage
U
i
Voltage of bus i
U
min
i
Minium voltage at bus i
U
LL
Phase-to-phase voltage
U
M
Maximum voltage amplitude
U
max
Maximum voltage
U
min
Minium voltage
U
N
Root mean square value of the phase-to-phase voltage
of a machine
U
n
Nominal phase-to-phase voltage
U
R
Generator rotor voltage; voltage at the receiving end
U
REF
Generator stator voltage reference
xlii Notation
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 43 – [1–48/48] 20.12.2004
7:23PM
U
S
Generator stator voltage; voltage at the sending end
U
t
Terminal voltage
V
v Wind speed
v
a
Annual average wind speed
v
ci
Cut-in wind speed
v
R
Rated wind speed
v
t
Rotor tip speed
v
w
Wind speed at hub height of the power system
v
w
(t) Wind speed at time t
v
wa
Average value of wind speed
v
wg
Gust component of wind speed
v
wr
(t) Ramp component of wind speed
v
wt
Turbulence component of wind speed
V Wind speed
V
rel
Relative wind speed
V
tip
Speed of the blade tip
V
WIND
Wind speed
V(x) Value of water inflow
W
W Yearly energy production
W
spill
Spilled energy
W
W
Energy generated by wind farm
X
x Power transmission; water inflow
x
r
l
Leakage reactance of the rotor
x
s
l
Leakage reactance of the stator
x
m
Mutual reactance between the stator and rotor windings
x
r
Rotor self-reactance
x
s
Stator self-reactance
X Reactance; power flow; cable length
X
2
Reactance of smoothing inductor
X
D
Direct axis reactance
X
Q
Quadrupol axis reactance
Y
Y Generated wind power
Y
e
Lumped admittance of long transmission line
Z
z Altitude above sea level
z
0
Roughness length
Z Impedance; desired power transmission
Notation xliii
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 44 – [1–48/48] 20.12.2004
7:23PM
Z
c
Transmission line surge impedance
Z
e
Lumped impedance of long transmission line
Z
l
Load impedance
Z
L
Line impedance
Z
LD
Load impedance
Greek symbols
Exponent; reference angle
Pitch angle; reference angle
const
Fixed blade angle
ref
Blade reference angle
Torsional displacement between shaft ends
P Differences between consecutive production values
d=dt Pitch speed
Pitch angle
base
Base value of pitch angle, for use in per unit system
base, el
Electrical base angle
g Generator rotor angle
’ Angle between terminal voltage and current
’
LD
Load angle
cos ’
LD
Load power factor
Tip-speed ratio
opt
Tip-speed ratio corres ponding to the optimal rotor speed
Average
Air density
AIR
Air density
xy
Correlation between x and y
ðzÞ Air density as a function of altitude
Standard deviation of Gaussian distribution; total leakage factor
load
Standard deviation of load time series
m
Position of wind turbine
total
Standard deviation of net load time series
wind
Standard deviation of wind power production time series
V
Characteristic time constant of induced velocity lag
’ Angle of incidence; phase angle
’
1
Phase angle of voltage source of DFIG rotor converter or PMG converter
cos ’
min
Expected minimum power factor at full load
Flux linkag e
base
Base flux
k
Network impedance phase angle
pm
Amount of flux of the permanent magnets mounted on the rotor that is
coupled to the stator winding
s
rd
Direct axis of the stator flux in rotor reference frame
s
rq
Quadrature axis of the stator flux in rotor reference frame
xliv Notation
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 45 – [1–48/48] 20.12.2004
7:23PM
r
rd
Direct axis of the rotor flux in rotor reference frame
r
rq
Quadrature axis of the rotor flux in rotor reference frame
s
s
Stator flux in the stator reference frame
s
r
Stator flux in the rotor reference frame
r
r
Rotor flux in the rotor reference frame
! Angular frequency; angu lar speed
!
base
Base value of rotational speed, in per unit system
!
base, el
Electrical base angular speed
!
g
Speed of machine
!
G
Generator rotor speed
!
G, Ref
Disired generator rotor speed
!
gen
Generator rotor rotat ional speed
!
m
Angular speed of the wind turbine; angular frequency of generator
(mechanical)
!
N
Angular speed (e.g. 2f
N
)
!
turb
Turbine rotational speed
!
turb, opt
Optimal turbine rotational speed
!
wr
Angular frequency of wind turbine
Notation xlv
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 46 – [1–48/48] 20.12.2004
7:23PM
Units
SI Units
Basic unit Name Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
SI-derived units
Unit Name Unit Symbol
Area square meter m
2
Volume cubic meter m
3
Speed or velocity meter per second m/s
Acceleration meter per second squared m/s
2
Density kilogram per cubic meter kg/m
3
Specific volume cubic meter per kilogram m
3
/kg
Current density ampere per square meter A/m
2
Magnetic field strength ampere per meter A/m
Derived units with special names and symbols
Unit Name Unit Symbol In SI Units
Frequency hertz Hz s
1
Force Newton N m kg s
2
Pressure pascal Pa m
1
kg s
2
Energy, work, quantity of heat joule J m
2
kg s
2
Power watt W m
2
kg s
3
Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 47 – [1–48/48] 20.12.2004
7:23PM
Electromotive force volt V m
2
kg s
Apparent power volt ampere VA m
2
kg s
3
Reactive power var var m
2
kg s
3
Capacitance farad F m
2
kg
1
s
4
A
2
Electric resistance ohm m
2
kg s
3
A
2
Electric conductance siemens S m
2
kg
1
s
3
A
2
Magnetic flux weber Wb m
2
kg s
2
A
1
Magnetic flux density tesla T kg s
2
A
1
Inductance henry H m
2
kg s
2
A
2
SI prefixes
Prefix Symbol Value Prefix Symbol Value
Atto a 10
18
Kilo k 10
3
Femto f 10
15
Mega M 10
6
Pico p 10
12
Giga G 10
9
Nano n 10
9
Tera T 10
12
Micro m 10
6
Peta P 10
15
Milli m 10
3
Exa E 10
18
Units xlvii
//INTEGRAS/KCG/PAGINATION/WILEY/WPS/FINALS_14-12-04/0470855088_01_PREA01.3D – 48 – [1–48/48] 20.12.2004
7:23PM