Fourth International Conference on Energy Systems and Developments 2017, Pune, India
February 20 – 24, 2017
DESIGN OF MODEL BASED CONTROL STRATEGY FOR
VARIABLE SPEED WIND POWER GENERATION SYSTEM
Tanuja Sheorey1, Shikha Tripathi 2
1
Mechanical Engineering Department, PDPM Indian Institute of Information
Technology, Design and Manufacturing, Jabalpur-482005, Madhya Pradesh, India
ABSTRACT
Wind energy has grown to be a mainstream energy source. It is the most attractive solution to
the world’s energy challenges. It can make major contribution towards satisfying the global need
for clean renewable energy within the next 30 years. There had been a rapid technological
development in wind power generation over the last decade.
In any locality, available wind speed widely varies across the year. Low wind speed does not bring
any harm to the plant except no power generation; while the high wind speed results in structural
damage to the turbine. Although most wind turbine plants are operating with constant speed, but
variable speed plants are also gaining popularity. The latter has the advantage of maximum
energy capture and longer energy generation by operating the system near 𝐶𝑝,𝑚𝑎𝑥 range by
adopting appropriate control strategy.
In the present paper, a 3-bladed horizontal axis wind turbine model development has been shown.
A complete model based design of the wind turbine plant, comprising of wind turbine,
controller, transmission and generator for a fixed maximum power generation capacity of 2 kW
was carried out. A two level control has been designed for variable speed and variable pitch
operation so that in all operating region, plant works efficiently. The simulation results show
that the controller performs well by accurately adjusting the blade pitch angle so as to set the
power output to the reference value.
Keywords: Wind energy conservation system, wind turbine modeling, control strategy, tip
speed ratio
1. INTRODUCTION
Wind Power is the utilization of air flow for the production of mechanical/electrical
energy. In fact, it is the most attractive solution to the world’s energy challenges. Utilization
of wind energy has become significant, attractive and cost effective. There had been a rapid
development in technology related to wind energy (Burton, T., 2008).

E-mail: tanush@iiitdmj.ac.in
© 2017 ICESD
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Tanuja Sheorey and Shikha Tripathi
According to World Wind Energy Association, worldwide development of wind energy
expanded rapidly with the average annual growth rate of about 31%, making the wind plant
one of the fastest growing industry (WWEA, 2010). Indian wind energy association
mentioned that India's installed wind power recently accounts for 24.677 GW of the 370 GW
of the worldwide installed capacity. India wind energy outlook in its report estimated that the
generation of wind energy could be more than quadruple to 89 MW by 2020 (IWEA). Wind
power accounted for about 69% of total renewable energy capacity or about 8% of the total
installed capacity in India. Owing to technological developments and enhanced installed
capacity, the cost of wind energy is becoming competitive (Sharma, A., et al., 2011).
1.1 Technological development of wind turbine
It consists of wind turbine, generator, transmission, converters and control system. N. Ramesh
Babu et al. have proposed modelling of wind energy conversion systems (WECS), control
strategies of controllers and various maximum power point tracking technologies for efficient
production of wind energy from the available resource. The wind turbine is the basic device
in the WECS for the transmission of the kinetic energy into mechanical energy, connected to
the electrical generator through a gear train. The output of the generator is given to the
electrical grid by employing a controller to avoid the disturbances and to protect the system or
network (Babu, et al., 2013). Figure 1 presents the block diagram of WECS.
Figure 1. Wind energy conservation system
1.2 Variable and constant-speed wind turbines
Depending on the connections between the turbine shaft and the generator, the wind
turbines are categorized as variable speed (VSWT) and constant speed wind turbines
(CSWT). CSWTs are the ones which run at a constant speed irrespective of the wind speed.
VSWTs operate at different RPM for different wind speeds. There is synchronization between
the load and the machine rpm. For VSWTs, the variable frequency outputs of the wind
turbine are connected to the fixed frequency of electrical system through a power electronic
frequency converter. These turbines are very costly due to use of expensive power electronics
filter but operates at maximum efficiency over longer duration of time than CSWTs (Babu, C.
and Mohanty, K. B., 2010). Chang et al. demonstrated that the VSWTs can produce 8% to
15% more energy output as compared to their constant speed counterparts (Bolik, S. M.,
2004).
Design of model based control strategy for variable speed wind power generation system 3
1.3 Objectives and outline of paper
The objective of the work was to develop mathematical model of wind turbine,
aerodynamic modelling of mechanical and electrical parts using MATLAB and control
strategy. Section two describes mathematical modelling of a WECS based on wind conditions
of the locality. The work has been carried out to investigate the values of system parameters
of horizontal axis wind turbine (HAWTs). The designed model is validated by evaluating its
performance. In section three, simulation results of the implemented MATLAB model for a
particular wind speed pattern have been incorporated. It also deals with the formulation of the
control strategy. The advantages and attributes of this method for wind energy system have
been explored. Section four summarizes the research findings and presents recommendations.
2. MATERIALS AND METHODS
Modern wind turbine generator system consists of wind wheel with horizontal axis of
rotation having three blades, a high speed asynchronous generator and a gear box (Burton, T.,
2008). Wind turbines are also equipped with a blade pitch angle control system which enables
the control of power that is being generated from the wind turbine (WWEA, 2010). In this
work, a 3-bladed horizontal axis wind turbine has been modelled. Considering the highest
wind speed of around 11 m/s in a locality, wind turbine was designed for a capacity of 2 kW.
The designed model is validated by evaluating performance and comparing with existing
models. The work has been carried out to investigate the values of system parameters of
HAWTs.
2.1. Design of wind turbine
Utility scale turbines are available in the ratings ranging from few kilowatts to several
thousand kilowatts. Wind velocity plays an important role in determining the rating of the
wind turbine. The power that can be extracted from plant holds a cubic relationship with the
wind velocity. Therefore, a small increase in wind velocity will bring large change in
available power.
Wind patterns are employed in simulations for predicting and analyzing the performance
of wind turbine. In this work various wind patterns representing seasonal variation of wind at
Sagar Island have been considered for simulation (Grant, I., 2005).
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Tanuja Sheorey and Shikha Tripathi
Figure 2. Wind Patterns in terms of velocity (m/s) vs Number of days, (a) rainy season, (b) winter,
(c) summer season, (d) over a year
2.2.Wind power law
Wind velocity at two different heights from the ground can be given by Eq. (1).
𝑧
𝛼
𝑉0 = 𝑉∞ [𝑧 ]
𝑔
(1)
where 𝑉0 =velocity at elevation 14m ‘z’, 𝑉∞ = Reference wind velocity at 2m height, ‘𝑧𝑔 ’
α=empirically derived coefficient that varies depending on the stability of the
atmosphere. For human inhabited area, its value is taken as 0.27.
For a tower height of 14 meters, wind velocity is given by:
(2)
14 0.27
𝑉𝑜 = 6.75 [ ]
𝑚/𝑠
2
Thus, 𝑉0 = 11.415 𝑚/𝑠
Axial Interference Factor, denoted by 𝑎 is defined as the fractional decrease in the wind
velocity between the free stream and the energy extraction device, namely rotor by Eq. (3).
Interference factor is also a function of  which is the ratio of the coefficient of the drag to the
coefficient of lift and ϕ, the angle of the relative wind with respect to the rotor plane (Babu,
C. and Mohanty, K. B., 2010) as given in Eq. (4).
Design of model based control strategy for variable speed wind power generation system 5
𝑎=
𝑉0 − 𝑉1
𝑉0
1
= 2 + 𝑠𝑒𝑐𝜙(𝐺 + √(𝐺 + 𝐻 2 )
𝑎
where,
(3)
(4)
 𝑠𝑒𝑐𝜙
𝐺 = 2(𝑡𝑎𝑛𝜙−)
𝐻=
𝑡𝑎𝑛𝜙
(𝑡𝑎𝑛𝜙 − )
(5)
(6)
For the purpose of calculation they are taken as of 𝜙 = 45° and  = 0.01 [Glauert
Momentum Vertex Theory].
Substituting, values of 𝜙 & ,
𝐺 = 7.14249 × 10−3 and 𝐻 = 1.0101
Putting the values of G and H, a comes out to be 𝑎 = 0.2904
Figure 3. Reduction in wind velocity as it passes through wind turbine
Using Eq. (3) velocity at the inlet of energy extraction device can be found out as
𝑉1
0.290404 = 1 −
11.415
So, the magnitude of velocity entering the wind turbine, 𝑉1 = 8.1 𝑚/𝑠. Figure 3 depicts
reduction in wind velocity as it passes through wind turbine blades.
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Tanuja Sheorey and Shikha Tripathi
Applying Bernoulli’s equation at upstream and downstream of the rotor blades, and
solving it, velocity at the exit can be obtained. Eq. (7) provides exit velocity.
(7)
𝑉2 = 𝑉0 (1 − 2𝑎)
Substituting values, 𝑉2 = 4.785 𝑚/𝑠
The power that can be extracted from wind at a particular site can be written by Blade
Momentum theory. The power extracted and the power output can be obtained by Eqs. (8)
and (9) respectively.
1
(8)
𝑃𝑤 = 𝐶𝑝 (𝜆, 𝛽)𝜌𝐴𝑣 3
2
1
𝑃𝑜 = 𝜌𝐴𝐶𝑝 (, 𝛽)𝑣 3
2
(9)
where  is the air density & 𝐴 is the area swept by the rotor blades.  is the expected
electrical and mechanical combined efficiency (0.9 would be a suitable value) [Grant, I.,
2005]. Air density, expressed as a function of the turbine elevation, H is given by Eq. (10).
(10)
𝜌 = 𝜌0 − 1.194 ∗ 10−4 𝐻
where 𝜌0 = 1.225 𝑘𝑔/𝑚3 is the air density at sea level at temperature
T=150C
𝜌 = 1.225 − (1.194 ∗ 10−4 ∗ 400) 𝑘𝑔/𝑚3
Air density, 𝜌 = 1.1723 𝑘𝑔/𝑚3
Using Eq. (9), the area swept by the blades can be calculated.
2𝑃0
𝐴=
𝜌𝐶𝑝 𝑉𝑜3
The wind turbine has been designed for 2 kW (𝑃𝑜 ). The expected power coefficient 𝐶𝑝 is
considered as 0.4 (Grant, I., 2005). The radius of the rotor shaft comes out to be, 𝑅 =
1.499 𝑚𝑒𝑡𝑟𝑒𝑠
Thus, the total power of 2 kW would be produced by the turbine having rotor diameter,
𝑑 = 2.798 𝑚𝑒𝑡𝑟𝑒𝑠.
Pressure difference that is created at the turbine rotor because of the wind flow is given
in Eq. (11),
(11)
∆ 𝑝 = 𝜌𝑉2 [𝑉0 − 𝑉1 ]
∆𝑝 = 19.4 𝑁𝑒𝑤𝑡𝑜𝑛/𝑚2
A turbine extracts wind energy, causing the difference in momentum of air streams
between the upstream and downstream sides which leads to development of axial thrust on
the rotor. It is given as
𝑇 = 𝑎𝑟𝑒𝑎 𝑠𝑤𝑒𝑝𝑡 𝑏𝑦 𝑟𝑜𝑡𝑜𝑟 𝑏𝑙𝑎𝑑𝑒𝑠 ∗ ∆𝑝
𝑇 = 136.944 𝑁𝑒𝑤𝑡𝑜𝑛𝑠
Design of model based control strategy for variable speed wind power generation system 7
2.3.Tip speed ratio
Tip speed ratio (TSR),  is defined as the ratio of the tangential speed at the tip of blade
to the actual velocity of the wind. In this case the power is fed by the turbine to the grid
through generator. Thus, the frequency of power generation is fixed through the power grid.
TSR is obtained using Eq. (12).
𝜔𝑅
𝑣𝑇𝐼𝑃
=
=
(12)
𝑣
𝑣𝑤𝑖𝑛𝑑
where  = angular velocity of blades (rad/sec) (Eqs. (13) and (14)),
R = radius of the rotor (metres), v = wind speed (m/s)
2𝜋𝑁
60
120𝑓
𝑁=
𝑃
𝜔=
(13)
(14)
where f is the frequency which is fixed to 50 Hz for generation and transmission and P is
the number of poles, P is taken as 8.
Substituting the values,
𝜔 = 36 𝑟𝑎𝑑/𝑠𝑒𝑐
𝜆=
36 ∗ 2.799
8.1
TSR, 𝜆 = 12.44
Betz's law states that it is possible for a turbine to capture more than 59.3% of
the available kinetic energy of the wind. The factor 0.593 is referred as Betz's coefficient.
Thus, Betz Coefficient is the maximum efficiency that can be attained by the system. In case
of wind turbine, the Betz’s coefficient is referred as the Coefficient of Power (Cp). Cp is a
function of two parameters namely the speed ratio () and the pitch angle () (Babu, C. and
Mohanty, K. B., 2010). Based on previous research Cp is given as:
𝐶𝑝 (, ) = 𝐶1 (
1
𝑖
=
𝐶2
𝑖
− 𝐶3  − 𝐶4) 𝑒
−𝐶5
𝑖
1
0.035
−
 + 0.08𝛽 1 + 𝛽 3
+ 𝐶6 
(15)
(16)
where the coefficients C1 = 0.5176, C2 = 116, C3 = 0.4, C4= 5, C5= 21, and C6 = 0.0068
Power that can be extracted from the wind depends on the wind speed and hence the tip
speed ratio, for a fixed rotor size and the rotation speed. Cp is also a function of pitch angle, .
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Tanuja Sheorey and Shikha Tripathi
For various values of , the wind turbine performance analysis was done by plotting Cp vs .
Figure 4 shows a plot between Cp & for various  values.
Figure 4. Characteristic Plot of 𝑪𝒑 (𝝀, 𝜷) 𝒗𝒔 𝝀
From the plot it is clear that for any  value, COP i.e. the efficiency with which the
turbine will extract power would be optimum within a small  range. Beyond this range,
extracted power would be very low owing to greater losses. Also, it can be seen clearly that
pitch angle has significant effect on maximum Cp for a particular operating range of .
The actual power output from wind turbine can be obtained using Eq. (17),
𝑃𝑜 = 𝑃𝑤 ∗ 𝐶𝑝 (, 𝛽)
(17)
1
𝑃𝑜 = 2 𝐶𝑝 (𝜆, 𝛽)𝜌𝐴𝑣 3
Substituting values we get, 𝑃𝑜 = 396.95 𝑊𝑎𝑡𝑡𝑠.
For developing the rated power of 2 kW, the wind speed required at the blades can be
found out:
1
2000 = ∗ 0.4 ∗ 1.17 ∗ 0.9 ∗ 7.055𝑣 3
2
𝑣 3 = 1346.09159
𝑣 = 11.02 𝑚/𝑠
Thus , the rated power is obtained at the wind speed of about 11 m/s.
3. RESULTS AND DISCUSSION
A model based design of the wind plant, comprising of wind turbine, controller,
transmission and generator was taken next. Although most wind turbine plants are operating
Design of model based control strategy for variable speed wind power generation system 9
with constant speed but variable speed plants are also gaining popularity (WWEA, 2010). The
latter has the advantage of longer energy generation by operating the system near Cpmax range
by adopting appropriate control strategy. A control strategy hence plays an important role in
wind turbine plant operation. A model based design of the plant with two level control was
carried out in MATLAB®.
3.1. Coefficient of performance
The coefficient of performance of a wind turbine is a measure of how efficiently the
wind turbine converts the energy of the wind into electricity. For a given turbine design, Cp is
function of TSR and pitch angle. In the present work, the equations used for the calculation of
Cp are based on previous research paper (Babu, N. R. and Arulmozhivarman, P., 2013).
The variation of COP with TSR is shown in Figure 5. Similar trend was obtained by N.
Ramesh Babu for VSWT. A maximum COP of 0.35 was attained at TSR of 9.75. It means
with the variation of wind speed, if TSR can be maintained at 9.75, the plant will operate with
maximum efficiency. Since, the TSR varies with the wind speed so it is not possible to
operate the turbine with fixed TSR. Hence to maintain good efficiency, a range of TSR is
selected for wind turbine operation. In the present study, TSR range of 7-12 is considered
(marked by shaded region) which corresponds to the variation of Cp in the range of 0.3-0.35.
The controller restricts the TSR within this range.
Figure 5. Coefficient of power vs Tip speed ratio
3.2. Control strategy
The control strategy indicates the control techniques used at various wind speeds. In
order to obtain maximum energy from wind, the optimum angular speed and power of turbine
need to be set. In the present work, control strategy was designed first with variable speed
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Tanuja Sheorey and Shikha Tripathi
operation and then variable pitch control was added. The variable speed, variable pitch
WTGS include two control levels.
3.2.1. First level of control
With the wind speed increasing, increase in power output is allowed till rated value is
reached. Also TSR need to remain within the optimum window, hence rotor speed will be
increasing. Once the rated output is reached, controlled variation of rotor speed is done by
the controller. At this stage the control is done by restricting the rotor speed. Turbinegenerator coupling model implemented in Matlab is uded for the purpose. It is observed that
speed varies about a nominal rotor speed of 31 rpm. Figure 6 shows the braking
characteristics of the wind turbine. ‘a-d’ represents various stage of power generated by the
plant, Pe. It is the primary objective for all the wind turbines to maintain this characteristic. In
the present design the generated braking pattern was found to follow the standard
characteristics.
Figure 6. Typical power Vs Wind speed characteristics of wind turbine
‘a’ shows the cut-in speed which is the speed below which the machine does not produce
power due to inertia effect of the machine. For the present work, 3 m/s is set as the cut-in
speed. In many modern designs the aerodynamic torque produced at the starting condition is
quite low and the rotor has to be started by an auxiliary device (motor as generator) at the cutin wind speed.
As the wind speed rises above 3 m/s, power developed by the wind turbine starts
increasing. ‘b’ corresponds to the operation at normal wind speed. ‘1’ shows power of 400
Watts is obtained at 6 m/s. In this region, system operates in variable speed mode, the power
output is below the rated power. The blade pitch angle of zero is held constant during this
mode. The turbine operation is done by varying rotor speed so as to capture maximum power
available in the wind. The rated power point is achieved at a specific (constant) value of the
Design of model based control strategy for variable speed wind power generation system 11
TSR. Therefore, to track the maximum power limit point, the rotational speed has to be
changed continuously in accordance with the wind speed. As explained in section 2.2, for a
chosen value of TSR and prevailing wind speed, rotor speed can be calculated by equation
𝜆 = 𝜔𝑅/𝑣. In the proposed wind turbine model, the rated power of 2 kW is developed at
wind speed of 11m/s at the tip speed ratio of 9.75 and the rotor speed of 36 rpm.
‘c’ corresponds to the mode of operation at higher wind speeds. In this region, the rated
power of the turbine has been developed and the power output is kept constant at the
maximum value allowed by the electrical components. At ‘4’ and ‘5’, the theoretical power
developed by the wind is about 6 kW and 15 kW respectively. Such a large value may cause
damage to the structure as it can’t withstand this high wind loads. Thus, in this region after
the attainment of the rated power, the second level of control is employed.
‘d’ shows a particular furling wind speed at which the power generation is shut down and
the rotation is stopped in order to protect the system components. Thus, the aerodynamic
power of the blades is limited by employing brakes.
3.2.2. Second level of control
The turbine operates in variable speed and variable pitch mode. The main aim here is to
hold power constant at its rated value which is achieved by varying blade pitch angle as well
as rotor speed. The controller will pitch the blades towards wind direction. Speed of the rotor
and generator is maintained around a nominal value. At high wind speeds, the rotor speed is
maintained in the nominal range and the pitch angle is incremented in steps of 1 degree, and
corresponding value is selected which provides the rated power. A pitch actuation mechanism
is required to be employed.
Figure 7. Control of power through pitch angle variation
Figure 7 shows the application of strategy for maintaining rated power. When the system
is operated without any control, the main aim of the system is to obtain maximum efficiency
and thus the pitch angle is fixed as zero, which can be clearly seen from the above plot. Till
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Tanuja Sheorey and Shikha Tripathi
the development of the rated power, the plant operates in variable speed mode only and the
pitch angle is fixed to zero degrees. Once the system has attained its capacity, the plant starts
operating in the variable speed and variable pitch mode. As shown in the figure, the power
continues to increase but the controller opposes the changing value and the excess power is
stalled by changing the pitch angle. Hence, the rated power output remains constant to 2kW.
As shown in figure the power obtained at 13m/s is 4 kW which reduces to 2 kW by the
change of pitch angle through the controller.
Low value of Cp (0.2195) is observed in this region as the power is restrained to the rated
value which is far less than the presently available power from the wind. The rotor stalls
power in this region by bringing in second level control.
4. CONCLUSION
In the present work a horizontal axis, variable speed, variable pitch wind turbine
modelling has been done using Matlab. A two level control strategy was implemented to keep
speed fluctuations to the minimum as well as not to allow power output beyond rated value.
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