Effect of Turbulence on FixedSpeed Wind Generators
Hengameh Kojooyan Jafari^{1}
1. Introduction
The influence of wind energy connection to the grid has increased greatly and turbulence or unreliable characteristics of wind energy are expected to produce frequency and voltage changes in power systems and protection system equipment. To prevent these changes, it is necessary to study the working point change due to turbulence. In other papers, the voltage and transient stability analysis have been studied during and after turbulence [2] and the impact of WTGs (wind turbine generators) on the system frequency, inertia response of different wind turbine technologies, and comparison between inertia response of singlefed and doublyfed induction generators have been examined. Moreover study of the frequency change alone was conducted using DigSILENT simulator for FSWTs (fastspeed wind turbines) with onemass shaft model [2].
In this chapter both frequency and grid voltage sag change are presented with MATLAB analytically and also by SIMULINK simulation in FSWTs with one and twomass shaft turbine models to compare both results and a new simulation of induction machine without limiter and switch blocks is presented as a new work. The first part of study is frequency change effect on wind station by SIMULINK that shows opposite direction of torque change in comparison with previous studies with DigSILENT. The second part of study is effect of frequency and voltage sag change on wind station torque due to turbulence in new simulation of induction generator that is new idea.
2. Wind turbine model
The equation of wind turbine power is
where
ρMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeg8aYbaa@37A9@
is air density,
AMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadgeaaaa@36AF@
is area of turbine,
CpMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadoeadaWgaaWcbaGaamiCaaqabaaaaa@37D2@
is power coefficient and
υwMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabew8a1naaBaaaleaacaWG3baabeaaaaa@38D8@
is wind speed.
The C
_{
p
} curve and equation are shown in Fig. 1 and given by equation (2) and (3)
where
θpitch
is blade pitch angle,
λ
is the tip speed ratio described by equation (4). The parameters are given in Table 1.
where R is blade radius.
Figure 1.
Curve of
Cp
for different tip speed ratios
λ
.
The curve of Fig.1 has positive slope before
Cp
_{max} and it has negative slope after
Cp
_{ max}.
3. OneMass Shaft Wind Station Model
Induction machine equation is
Where,
Tm
is the mechanical torque,
Te
is the generator torque,
C
is the system drag coefficient and
J
is the total inertia.
Table 1 shows the parameters of the onemass shaft turbine model and induction generator.
Generator  Wind Turbine 
Rs
= .011Ω 
c1=.44 
Ls
= .000054H 
c2
= 125 
Lm
= .00287H 
c3
= 0 
L′r
= .000089H 
c4
= 0 
R′r
= .0042 [Ω] 
c5
= 0.1 
Jm
=.5 to 20.26 [kgm^{2}] 
c6
= 6.94 
p(#polepairs)
= 2 
c7
= 16.5 
Pn
= 2e6 [w] 
c6
= 0.1 

c9
= .002 

R
= 35 [m] 

A
= πR^{2 }[m^{2}] 

ρ
=1.2041 [kg/m^{3}] 

vw
= 6, 10, 13 [m/s] 

θpitch
= 0 [º] 
 
Table 1.
Parameters of one mass shaft turbine model and generator.
4. TwoMass Shaft Induction Machine Model
This model is used to investigate the effect of the drive train or twomass shaft, i.e., the masses of the machine and the shaft, according to the equation (8) [3], [4]. In this equation,
Jt
is wind wheel inertia,
JG
is gear box inertia and generator’s rotor inertia connected through the elastic turbine shaft with a
κ
as an angular stiffness coefficient and
C
as an angular damping coefficient.
The angular shaft speed
ωt
can be obtained from equations (6) and (7) [1], [3], [4].
TGMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaaWcbaGaam4raaqabaaaaa@37BA@
is the torque of the machine,
TtMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaaWcbaGaamiDaaqabaaaaa@37E7@
is the turbine torque,
δtMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKnaaBaaaleaacaWG0baabeaaaaa@38B3@
is the angular turbine shaft angle,
δGMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabes7aKnaaBaaaleaacaWGhbaabeaaaaa@3886@
is the angular generator shaft angle,
νMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabe27aUbaa@37A1@
is the inverse of the gear box ratio and
JGMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQeadaWgaaWcbaGaam4raaqabaaaaa@37B0@
and
JtMathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadQeadaWgaaWcbaGaamiDaaqabaaaaa@37DD@
are the inertia of the machine shaft and turbine shaft, respectively.
The Parameters, defined above, are given in Table 2.
This model is described as equation (8).
υ
 1/80 
JG
[kg.m^{2}]  .5 
Jt [kg.m^{2}]  1 
C [Nm/rad^{2}]  1e6 
κ [Nm/rad]  6e7 
Table 2.
Parameters of twomass shaft model.
5. Induction Machine and Kloss Theory
In a singlefed induction machine, the torque angular speed curve of equation (12) [1] is nonlinear, but by using the Kloss equation (13), equations (9), (10), and (11), this curve is linearly modified [1], [2] as shown in Fig. 2. Therefore, the effect of frequency changes in wind power stations can be derived precisely by equation (12) and approximately using equation (13), as shown in Figs. 2–6.
Figure 2.
Electrical torque (nonlinear and linear) versus speed (slip).
Equations (11) and (12) are given in per unit, but the associated resistances are in ohms.
Figure 3.
Mechanical and linear electrical torque versus slip.
Figure 4.
Mechanical and electrical torque versus frequency curves per unit with V
_{sag} = 10%
.
Figure 5.
Mechanical and electrical torque versus frequency per unit with V
_{sag} = 20%.
Figure 6.
Mechanical and electrical torque versus frequency per unit with V
_{sag} = 50%.
Figs. 3, 4, 5, and 6 illustrate that for lower wind speeds of 6 and 10 m/s, as the synchronous frequency f
_{
s
} and V
_{sag} change, the T
_{
e
} and TmMathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaaWcbaGaamyBaaqabaaaaa@37E1@
values of the rotor change in the same direction as the frequency of the network, as shown in Tables III, IV, V, and VI. These figures and tables give the results for V
_{sag} = 0% (i.e., only the frequency changes), 10%, 20%, and 50%. However, for a higher wind speed of 13 m/s, as f
_{
s
} and V
_{sag} change, the T
_{
e
} and
TmMathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsfadaWgaaWcbaGaamyBaaqabaaaaa@37E1@
values of the rotor change in the opposite direction to the changes in the frequency of the network.
For small changes in the slip according to the Kloss approach in equation (13), the torque changes as follows [2]:
Then:
and
or
Thus, the new angular operation speed[2] is
υw

fs= 48 
fs
= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .96050  .1157  1.0005  .1064  1.0405  .0974 
10  .9621  .5337  1.0021  .491  1.0421  .4493 
13  .9631  .7863  1.0035  .8122  1.0439  .8331 
Table 3.
Analytical MATLAB results for different frequencies.
υw

fs
= 48 
fs
= 50 
fs
= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9606  .1156  1.0006  .1064  1.0406  .0974 
10  .9625  .5163  1.0027  .5137  1.0429  .5086 
13  .9738  .7868  1.0043  .8127  1.0448  .8335 
Table 4.
Analytical MATLAB results for
Vsag
= 10%.
υw

fs= 48 
fs= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9607  .1156  1.0007  .1064  1.0407  .0974 
10  .9632  .5163  1.0034  .5136  1.0437  .5085 
13  .9648  .7875  1.0054  .8134  1.0461  .8341 
Table 5.
Analytical MATLAB results for
Vsag
= 20%
υw

fs= 48 
fs= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9618  .1153  1.0018  .1061  1.0418  .0971 
10  .9681  .5161  1.0088  .5131  1.0494  .5076 
13  .9724  .7927  1.0139  .8181  1.0555  .8382 
Table 6.
Analytical MATLAB results for
Vsag
= 50%
6. Simulation of wind generator with frequency change
During turbulence and changes in the grid frequency, the torque speed (slip) curves change in such a way that as the frequency increases, the torque is increased at low wind speeds; 6 and 10 m/s, in contrast to Fig. 6 and decreases at a high speed of 13 m/s [2], as shown in Table 7 and Figs. 7–15.
υw

fs
= 48 
fs
= 50 
fs
= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9619  .1148  1.0019  .1057  1.0418  .0969 
10  .9684  .5179  1.0091  .5134  1.0494  .5076 
13  .9724  .7945  1.0147  .8177  1.0559  .8373 
Table 7.
Simulink simulation results for one and twomass shaft models
Figs. 7–15 show the electrical torque and mechanical speed of the induction machine for the one and twomass shaft turbine models at wind speeds of 6, 10, and 13 m/s to validate Table 7.
Figure 7.
Electrical torque when
$$
= 48 and
$$
= 6m/s.
Figure 8.
Electrical torque when
fs
= 50 and
υw
= 6m/s.
Figure 9.
Electrical torque when
fs
= 52 and
υw
= 6m/s.
Figure 10.
Electrical torque when
fs
= 48 and
υw
= 10m/s.
Figure 11.
Electrical torque when
fs
= 50 and
υw
= 10m/s.
Figure 12.
Electrical torque when
fs
= 52 and
υw
= 10m/s.
Figure 13.
Electrical torque when
fs
= 48 and
υw
= 13m/s.
Figure 14.
Electrical torque when
fs
= 50 and
υw
= 13m/s.
Figure 15.
Electrical torque when
fs
= 52 and
υw
= 13m/s.
7. Simulation of wind station with onemass and twomass shaft turbine models
The results of simulations of a simple grid, fixedspeed induction machine, and onemass and twomass shaft turbines are given in Tables 8 10 and Figs. 16–42. For an induction wind generator using the induction block in SIMULINK with high voltage sag i.e. 50% with frequencies 50 and 52 and
$$
equal to 13, C
_{
p
} becomes negative, and the results are unrealistic. Then results of 50% voltage sag are realistic in new simulation of induction machine in Tables 8 10.
υw

fs= 48 
fs= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9624  .1152  1.0024  .106  1.0423  .097 
10  .9703  .516  1.0111  .5128  1.0519  .5071 
13  .9757  .795  1.0176  .8201  1.0595  .8399 
Table 8.
Simulation results by SIMULINK for one and two mass shaft model for
Vsag
= 10%
υw

fs= 48 
fs= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .963  .1151  1.003  .1059  1.043  .0969 
10  .973  .5159  1.014  .5125  1.055  .5066 
13  .9799  .7977  1.0223  .8226  1.0648  .842 
Table 9.
Simulation results by SIMULINK for one and two mass shaft model for
Vsag
= 20%
υw

fs= 48 
fs= 50 
fs= 52 
ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

ωm[pu]

Te[pu]

6  .9674  .114  1.0074  .1048  1.0474  .0959 
10  .9933  .5146  1.0364  .5096  1.0796  .502 
13  1.0248  .8239  1.0474  .8347  1.0917  .85 
Table 10.
Simulation results by SIMULINK for one and two mass shaft model for
Vsag
= 50%
Figure 16.
Torquetime in per unit while
Vsag
= 10% and
υw
= 6m/s,
fs
=48
Figure 17.
Torquetime in per unit while
Vsag
= 10% and
υw
= 10m/s,
fs
= 48
Figure 18.
Torquetime in per unit while
Vsag
= 10% and
υw
= 13m/s,
fs
= 48
Figure 19.
Torquetime in per unit while
Vsag
= 20% and
υw
= 6m/s,
fs
= 48
Figure 20.
Torquetime in per unit while
Vsag
= 20% and
υw
= 10m/s,
fs
= 48
Figure 21.
Torquetime in per unit while
Vsag
= 20% and
υw
= 13m/s,
fs
= 48
Figure 22.
Torquetime in per unit while
Vsag
= 50% and
υw
= 6m/s,
fs
= 48
Figure 23.
Torquetime in per unit while
Vsag
= 50% and
υw
= 10m/s,
fs
= 48
Figure 24.
Torquetime in per unit while
Vsag
= 50% and
υw
= 13m/s,
fs
= 48
Figure 25.
Torquetime in per unit while
Vsag
= 10% and
υw
= 6m/s,
fs
= 50
Figure 26.
Torquetime in per unit while
Vsag
= 10% and
υw
= 10m/s,
fs
= 50
Figure 27.
Torquetime in per unit while
Vsag
= 10% and
υw
= 13m/s,
fs
= 50
Figure 28.
Torquetime in per unit while
Vsag
= 20% and
υw
= 6m/s,
fs
= 50
Figure 29.
Torquetime in per unit while
Vsag
= 20% and
υw
= 10m/s,
fs
= 50
Figure 30.
Torquetime in per unit while
Vsag
= 20% and
υw
= 13m/s,
fs
= 50
Figure 31.
Torquetime in per unit while
Vsag
= 50% and
υw
= 6m/s, fs
$$
= 50
Figure 32.
Torquetime in per unit while
Vsag
= 50% and
υw
= 10m/s,
fs
= 50
Figure 33.
Torquetime in per unit while
Vsag
= 50% and
υw
= 13m/s,
fs
= 50 in new simulation of wind generator
Figure 34.
Torquetime in per unit while
Vsag
=10% and
υw
= 6m/s,
fs
= 52
Figure 35.
Torquetime in per unit while
Vsag
=10% and
υw
= 10m/s,
fs
= 52
Figure 36.
Torquetime in per unit while
Vsag
= 10% and
υw
= 13m/s,
fs
= 52
Figure 37.
Torquetime in per unit while
Vsag
= 20% and
υw
= 6m/s,
$$
= 52
Figure 38.
Torquetime in per unit while
Vsag
= 20% and
υw
= 10m/s,
fs
= 52
Figure 39.
Torquetime in per unit while
Vsag
= 20% and
υw
= 13m/s,
fs
= 52
Figure 40.
Torquetime in per unit while
Vsag
= 50% and
υw
= 6m/s,
fs
= 52
Figure 41.
Torquetime in per unit while
Vsag
= 50% and
υw
= 10m/s,
fs
= 52
Figure 42.
Torquetime in per unit while
Vsag
= 50% and
υw
= 13m/s,
fs
= 52 in new simulation of wind generator
8. New Simulation of Induction Machine
Figs. 33 and 42 show the results of new simulation of the induction machine model illustrated in Fig. 43 [1]. The new simulation, which has no limiters and switches, is used because at high grid voltage dropdown or sag, the Simulink induction model does not yield realistic results.
Figure 43.
Induction machine Model in
dqo
system
The new simulation of induction machine is in
dqo
system and synchronous reference frame simulation on the stator side; n (Transfer coefficient) is assumed to be 1. Circuit theory is used in this simulation, and it does not have saturation and switch blocks, unlike the MATLAB–SIMULINK Induction block. In Fig. 43,
LM
is the magnetic mutual inductance, and
r
and
L
are the ohm resistance and selfinductance of the
dqo
circuits, respectively. The machine torque is given by equation (19). In this equation,
id,qs
and
λd,qs
, the current and flux parameters, respectively, are derived from linear equations (20)–(23); they are sinusoidal because the voltage sources are sinusoidal.
Where
P
is poles number,
λds
and
λqs
are flux linkages and leakages, respectively, and
iqs
and
ids
are stator currents in
q
and
d
circuits of
dqo
system, respectively.
Then
i
matrix produced by the
λ
matrix is given by equation (20).
where the inductance matrix parameters are given by (21), (22), (23).
The linkage and leakage fluxes are given by (24) to (29).
To create the torque in equation (19), it is necessary to determine the currents in equations (30)–(33) from the stator and rotor currents by using current meters.
9. Conclusion
As frequency changes and voltage sag occurs because of turbulence in wind stations in ridethrough faults, the system’s set point changes. The theoretical and simulation results results are similar for one mass shaft and two mass shaft turbine models. At lower wind speeds; 6 and 10 m/s, the directions of the changes in the new working point are the same as those of the frequency changes. At a higher wind speed; 13 m/s, the directions of these changes are opposite to the direction of the frequency changes. Simulation results of high grid voltage sag with SIMULINK induction block has error and new simulation of wind induction generator in synchronous reference frame is presented without error and in 50% voltage sag, new simulation of wind generator model has higher precision than that in 10% and 20% voltage sags; however, this model can simulate wind generator turbulence with voltage sags higher than 50%. Although results of new simulation of induction machine with wind turbine for 50% voltage sag and frequencies 50 and 52 have been presented in this chapter.
10. Nomenclature
P=
Generator power
ρ=
Air density
A=
Turbine rotor area
Cp=
Power Coefficient
υw=
Wind speed
θpitch=
Pitch angle
Te=
Electrical torque
Tm=
Mechanical torque
J = Inertia
ωm=
Mechanical speed
C=
Drag coefficient
ν=
Gear box ration
R=
Blade radius
Rs
= Stator resistance
Ls
$$
= Stator inductance
$$
Lm
= Mutual inductance
$$
L′r
= Rotor inductance
R′r
= Rotor resistance
p=
Pole pairs
κ= Stiffness
λr,s=
Rotor and stator flux
Kr,s=
Rotor and stator park transformation in synchronous reference frame
ir,s=
Rotor and stator current
vr,s=
Rotor and stator voltage
11. Future Work
The new simulation of induction generator will be tested by new innovative rain turbine theory and model of the author.
Acknowledgements
I appreciate Dr. Oriol Gomis Bellmunt for conceptualization, Discussions and new information and Dr. Andreas Sumper for discussions about first part of chapter, with special thanks to Dr. Joaquin Pedra for checking reference frame and starting point in new simulation of induction machine.
References
1 
Paul C. Krause,
1986
Analysis of Electric Machinery
MCGrawHill, Inc.
2 
A. Sunmper, O. GomisBellmunt, A. SudriaAndreu, et al.
2009
Response of Fixed Speed Wind Turbines to System Frequency Disturbances
ICEE Transaction on Power Systems
24
1
181
192
3 
A. JunyentFerre, O. GomisBellmunt, A. Sunmper, et al.
2010
Modeling and control of the doubly fed induction generator wind turbine
Simulation modeling practice and theory journal of ELSEVIER
1365
1381
4 
Z Lubosny,
2003
Wind Turbine operation in electric power systems
Springer publisher