1. Wind Farm Energy Optimization using Nested-Loop
Extremum Seeking Controls and Load Reduction
Turaj Ashuri, Ebenesh Rabiraj, Yaoyu Li and Yan Xiao
Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX
75080, USA
Zhongzhou Yang
EXA Corporation, 210 Six Mile Rd, Livonia, MI 48152
E-mail: turaj.ashuri@utdallas.edu
Abstract. A load opimization algorithm is developed to compliment the nested loop
extreemum seeking control. An objective function of the controller is formulated to
accommodate the variations in the load as penalties. The formulated objective function allows
the controller to find the optimal power while mitigating excessive loading on the turbine that
are caused due to the NLESC. The results show a considerable reduction in structual loads and
fatigue loads while preserving the power output of the turbine. Under steady wind conditions
a reduction of upto 25% decrease in peak loads compared to the nested loop extremum seeking
control. Under turbulent wind with a turbulence intensity of 5% we can see a reduction of upto
20% in fatigue loads and upto a 15% decrease in mean loads. This paper also aims to study the
stability and effectiveness of the controller with increase in turbulence intensities.
1. Introduction
In 2015, the US coal-fired power plants experienced a reduction of 12.9 GW in power generation,
while wind energy power generation increased by 9.8 GW 1. This shows that the effects of climate
change have pushed the energy sector to transition into renewable energy with an emphasis on
wind. Although wind energy power generation seems promising, its cost is in general higher
than that from the conventional energy resources. Improving blade design, new manufacturing
techniques, upscaling wind turbines, wind farm optimization, better operation and maintenance
strategies, and advance control algorithms to maximize the energy production are among the
efforts to reduce the cost [1–7].
Maximizing energy production using controls can be performed either at wind turbine or wind
farm level. In the case of wind farms, maximizing the energy output of individual wind turbines
does not guarantee the maximum energy output of the entire farm [8–11]. This is because of the
complex wake interaction among wind turbines that leads to sub-optimal performance of the
wind farm. Talking into account such complex wake interaction is difficult using model-based
control algorithms.
1
US energy information administration, Scheduled 2015 capacity additions mostly wind and natural gas;
retirements mostly coal, http://www.eia.gov/todayinenergy/detail.cfm?id=20292, Retrieved June 9, 2016

2. Model-free control strategies have the advantage of requiring minimal knowledge of the system
under operation. Marden et al. [12] proposed a game theoretic optimization algorithm for
an array of three wind turbines to optimize the energy production of the wind farm. Datta
and Ranganathan [13] proposed tracking the optimal power point, independent of the turbine
characteristics and the air density, by varying the generator speed dynamically using the active
power as a reference. Guo et al. [14] proposed a model predictive controller to assist an
adaptive controller to smoothly track the maximum power point for a wind farm. Gebraad and
Wingerden [15] proposed maximum power point tracking (MPPT) algorithm of the gradient-
ascent and quasi-Newton types to optimize the power output of a three turbine array.
Extremum seeking control (ESC) is a variation of MPPT that tracks the optimum by
perturbing the system with a sinusoidal probing signal to extract gradient information. Johnson
and Fritsch [16] assessed the effectiveness of ESC in a wind farm to maximize the power output
in a low turbulence condition. Yang et al. [17] have optimized the power output of a cascaded
wind turbine array along the prevailing wind direction using the nested-loop extremum seeking
controller (NLESC). These algorithms focus on maximizing the power output of the turbine
without considering the increase in structural loads.
This paper presents a NLESC to maximize the energy production of an array of wind turbines
considering the structural loads imposed on the tower and shaft. The modified NLESC uses the
collective array power coefficient to maximize the power output. Structural loads are applied as
a continuous penalty function for each individual wind turbine power coefficient.
The remainder of this paper is structured as follows. First, the methodology to model the
wind farm wake interaction, and the structure of the NLESC is discussed. Next, the results of
implementing the NLESC on an array of wind turbines is presented. Finally, the conclusion is
presented.
Figure 1: Cascaded NLESC implementation
2. Methodology
A Simulink model of the NLESC is used to control and optimize an array of three wind
turbines [17]. It is dynamically generated using a MATLAB script, based on input parameters
such as mean wind speed, turbulence intensity, and the number and coordinates of each wind
turbine. The model is linked with SimWindFarm (SWF)[18] computational code that is capable
of modeling aerodynamics and wake interactions in a wind farm. Three different wind farm

3. controllers are used for this research, a baseline controller distributed with SWF, a NLESC to
maximize the wind farm power output, and a NLESC to maximize the wind farm power output
with load penalties. These are explained next.
2.1. Simulation Platform
SWF is a powerful toolbox that provides an environment to develop new control algorithms. It
is capable of simulating wakes for turbines with an in-built NREL5MW turbine model [19]. This
is done by dynamically generating a wind field based on the input parameters specified in the
MATLAB script. The model allows extraction of two moments, including the shaft and tower
moment. The shaft moment (Mshaft) can be measured from a third order drive train model.
The drive train is modeled as a pair of rotating shafts through a gearbox.
˙Ω =
1
Irot
Mshaft − φKshaft − ˙φBshaft (1)
˙ω =
1
Igen
−Mgen +
1
N
φKshaft + ˙φBshaft (2)
˙φ = Ω −
1
N
ω (3)
where, Kshaft is the torsional spring constant and Bshaft is the viscous friction of the gearbox
of gear ratio N. φ is the torsion angle of the shaft and, Irot and Igen are the rotor and generator
inertias.
Further, the tower deflection(z) is modeled as a second order spring-damper system
(equation 4)from which the tower moment(Mtow) can be measured.
¨z =
1
Mtow
(Ftow − Ktowz − Btow ˙z) (4)
where, Ktow is the spring constant of the tower and Btow is the damping term.
SWF is also capable of performing fatigue calculations. The fatigue postprocessor utilizes
Mcrunch to perform calculations including, rainflow counting and damage equivalent load for
the tower and the shaft [20].
2.2. Controller
The performance of the controller that incorporates load optimization is justified by comparing
it against the baseline controller of the NREL5MW turbine and the NLESC algorithm. The
different control algorithms that are used are mentioned below.
2.2.1. Baseline Control
During region 3 operation, the baseline control has a constant generator power reference. Using
a gain scheduled proportional integrator control algorithm, the blade pitch is actuated to control
the rotor speed. During region 2 operation, the blade pitch is kept constant, while the generator
power is estimated using the generator speed as an input. The estimation is done using a simple
lookup table. In the simulation performed, only the region 2 control scheme is active.
2.2.2. Nested-Loop Extremum Seeking Control
The ESC strategy as shown in Figure 2, employs a gradient based search technique to find a
maximum in the input signal. A dither signal (fdither = asin(ωt)) is added to the input of the
plant as a sinusoidal probing signal (ud = u + fdither) to excite it. THe output of the plant is
represented as,
y = l(ud) = l(u + asin(ωt)) = l(u) +
∂l
∂u
asin(ωt) + ... (5)

4. × Low pass Filter Integrator
High pass Filter Wind Turbine
fdem = sin(ωt) fdither = asin(ωt)
+
u
udy
+
Figure 2: Block diagram of the ESC for a single wind turbine
A high pass filter is used to remove the DC term (l(u))while retaining the harmonics. A
demodulation signal (fdem = sin(ωt)) converts the first harmonic to a DC component. This
demodulation signal is proportional to the gradient. The higher order terms are then removed
using a low pass filter while retaining the DC component. An integrator is used to eliminate
any steady state error present to reach zero gradient.
In the case of steady wind, the input chosen is the aerodynamic power. As there are no
variations in the wind speed, the change in power is a direct consequence of the control signal.
However, in the case of turbulent wind, the aerodynamic power is a function of the variation in
the wind speed over time. This makes it difficult to isolate the variation in the power due to the
control signal. Thus we aim to optimize the coefficient of power instead. The coefficient of power
is extended to operate in a nested-loop configuration as the Array Power Coefficient(APC). This
is based on a similar approach by Corten et al. [21] and justified by Yang et al. [17]. APC is
defined as the ratio of sum of aerodynamic power of the turbine(i) and all the n turbines in it’s
wake, to the estimated power. This can be represented as,
Ki
p =
Pi + j
n=1 Pn
a
1
2ρAU3
(6)
where, Ki
p is the APC of the ith turbine, Pj
a is the aerodynamic power of the most downstream
turbine in the wake of turbine i. A trasportation delay is implemented to compensate for the
time taken for the wake to travel to the downstream turbine. The estimated power is calculated
using the measured wind speed in front of the upstream turbine i and for the following j number
of turbines in its wake, a transport delay, Ti is applied to the wind speed of the upstream turbine.
Therefore for any time t, the APC can be written as,
Ki
p(t) =
Pi(t − T) + j
n=1 Pn
a (t − T)
1
2ρAU(t − Ti))3
(7)
Any residual fluctuations in the APC signal due to the changes in wind speed appear as high
frequencies in the signal which can be mitigated using a moving average filter. This signal is
used as an input to the controller optimize the power output of the wind farm.
2.2.3. Load optimized NLESC

5. Load optimization is done by penalizing the objective function of the NLESC based on the
structural loads. The penalty function is formulated such that the loads are a variation of
the APC. The objective function with load optimization is thus formulated as a multiplicative
penalty and is represented as,
K = Kp(1 − Kload) (8)
where K is the load optimized objective function which is a function of the APC (equation 7)
and the load coefficient, KLoad.
To formulate the load coefficient, we intend to normalize the structural loads that we consider
as a part of the penalty function. The structural loads include the tower moment and the shaft
moment. The tower moment is usually in the order of 107Nm and the shaft moments are in the
order of 106Nm. The normalization ensures that we give an equal weight to both the structural
loads initially. As we optimize of power output below rated speed, the maximum loads at rated
speed are chosen as a factor to normalize the loads. The load coefficient for any turbine i can
be represented as,
Ki
load =
wi
1 × Mi
shaft
M∗
shaft
−
wi
2 × Mi
tower
M∗
tower
w3 (9)
where Mi
shaft and Mi
tower represent the shaft and tower moments. M∗
shaft and M∗
tower are the
maximum shaft and tower moment at rated wind speed (11.4 m/s). The values of these moments
are 4.2e6Nm and 9e7Nm respectively. Each normalized load is then weighted individually using
wi
1 and wi
2 and also together using wi
3.
Initially the weights wi
1 and wi
2 are chosen to be 1 for all turbines and, the wi
3 is adjusted
such that the load coefficient penalizes the power is effective. The independent weights are then
tuned such that all the turbines see a decrease in loads.
At any time t, from equations 7 and 9 we get,
Ki
(t) =
Pi(t − T) + j
n=1 Pn
a (t − T)
1
2ρAU(t − Ti))3
1 −
wi
1 × Mi
shaft(t)
M∗
shaft
−
wi
2 × Mi
tower(t)
M∗
tower
w3
(10)
In figure 3 the objective K1(t) is shown for a mean wind speed of 8m/s with a turbulence
intensity of 5%. The signal, especially for upstream turbines contain noise that is a consequence
of the turbulence in the wind speed and its summation over the nested loop and even a sudden
decrease in the load coefficient. There are also spikes in the signal (marked with circles) which
could compromise the stability of the controller. To mitigate this a saturation block is introduced
to extract region of most relevance from the objective function before the introduction of a
moving average filter.
3. Result
The first subsection deals with load optimization is carried out for the steady wind condition.
In the steady wind condition, wind speeds of 6m/s and 8m/s are analysed. In the consequent
subsection turbulent conditions are analysed. The results of 8m/s wind with a 5% and 10%
turbulence intensity are studied.
3.1. Steady wind
In the case of the 8m/s steady wind, the gains are 1.5e-8, 2.5e-8, 5e-6 respectively for the first,
second and third turbine for the NLESC. The dither amplitudes are 0.05, 0.03, 0.10 respectively
The time periods for the dither frequencies chosen are 2800s, 1400s and 80s respectively. The
gains of the load optimized NLESC are 3e-9, 7e-9, 5e-6 respectively. All the other parameters

6. Figure 3: The noise in the objective function of turbine 1 is shown for a mean wind speed of
8m/s and a turbulence intensity of 5% . The signal is conditioned using a saturation with a
range[1.05, 1.18]. A moving average filter is applied to the saturated signal.
remain the same. The optimal torque gain for the NLESC is about 3.05, 2.77, 2.4KNm/rpm2
respectively and for the load optimized NLESC is 2.9, 2.83, 2.4KNm/rpm2 respectively as seen
in figure 4. The results from figure 5 shows that there is a negligible loss in power output but a
significant decrease in ultimate loads on the turbine. The percentage change in ultimate loads
on the turbine are shown in figure 6.
In the case of the 6m/s the gains chosen are 3.7e-7, 3.1e-8, 5e-6 for the NLESC and the load
optimized NLESC. The rest of the parameters are the same as that of the 8m/s condition. At
lower wind speeds the NLESC is able to extract much more power from the wind. The results
are similar to the 8m/s case. Though the percentage decrease of power is higher, it is still
capable of reducing a significant amount of loads on the turbine.
3.2. Turbulent wind
In the case of turbulent wind, the weights are set to w1 = [1, 1, 1] and w2 = [1, 1, 1] initially.
w3 is varied until the effect of the load is significant. By following this procedure w3 is chosen
to be 0.1. For a wind speed of 8m/s at a turbulence intensity of 5%, the objective function, as
shown in figure 3, uses a moving average filter that have time periods of 1800s, 850s and 35s for
turbines 1, 2 and 3 respectively. Similarly, the time periods for the dither frequencies chosen
are the same as those used for the previous cases. The Integrator gains used are larger, when
compared to those used for the steady wind case due to the fact that we use the coefficient of
power instead of the aerodynamic power. The gains chosen are 0.023, 0.01 and 1 respectively.
The DEL for the shaft and tower are shown in figure 12a and 12b respectively. In this case
where the weights are evenly split between the turbines the DEL of the load optimized control
scheme lies between the baseline and the NLESC. Another consideration is that the first turbine
experiences higher loading due to the higher wind speeds. To reduce the load on the first turbine
even further, with a primary focus on the shaft, we can alter the weight w1 = [1.03, 1, 1] while
keeping the other weights the same.
The torque gain obtained for the modified weight is shown in figure 14. The DEL, as shown in
figure 15a and 15b sees a reduction in the loads on the first turbine preserving the performance

7. and the load reduction on the second and third turbine. The DEL gives a look at fatigue caused
by the load while the mean loads as shown in figures 3.2 and 3.2 show the overall change in
the loads imposed on the turbine. The mean loads are calculated after 5000s assuming that the
NLESC and the load optimized NLESC have reached a stable condition.
The challenging aspect of the NLESC, with and without the load optimized algorithm, is
high turbulence conditions. In the case of higher turbulence the input of the controller, as
discussed earlier in figure 3, is to remove the variation in the power due to the wind. Higher
turbulence causes larger variation in the wind and even larger variation in the power. This tends
to compromise the integrity of the controller.
For a mean wind speed of 8m/s and a turbulence intensity of 10% the moving average is
chosen to be more aggressive. The average is taken over 190s, 100s, 4.3s respectively for the
NLESC and 190s, 100s, 5.3s respectively for the load optimized NLESC. This affects the time the
controller takes to react to a change in the loads and thus the effectiveness is reduced. In figure
18, at about 1400s there is a considerable dip in the windspeed. Due to a narrower averaging
of the input of the third turbine, the change in the torque gain, as seen in figure 19b is much
more noticeable. These variations may cause the controller to become unstable if not taken into
account.
For the NLESC the gains are chosen to be 0.020,0.005,0.2 respectively. The gains are lower
than those chosen for the 5% turbulence to maintain the stability of the controller. The dither
frequency is the same as the previous cases while the dither amplitudes are chosen to be
0.5,0.3,0.8 respectively. Similarly, the gains for the load optimized NLESC are 0.008,0.004,0.2
and the dither amplitudes are the same as those chosen for the NLESC. the weights are chosen
as w1 = [1.2, 1, 1.1], w2 = [1.05, 1, 1] and w3 = 0.1.
The results show a similar trend to that seen for the 5% turbulence. The DEL are in some
cases marginally higher than the NLESC but maintains it close to or upto 6% less than the
baseline loads. The mean loads are maintained at upto 35% lower tha the baseline load. The
power output is also marginally lower than the NLESC but is still about 2% greater than the
baseline power.
(a) Torque gain for NLESC (b) Torque gain for load optimized NLESC
Figure 4: Optimal torque gain at a steady wind speed of 8m/s for 16000 seconds

8. (a) Total power of 3 turbines (b) Percentage change of power of each turbine
Figure 5: Power for a steady wind speed of 8m/s for 16000 seconds for different controllers and
the percentage change in power between them.
(a) Tower moment (b) Shaft moment
Figure 6: Percentage change of the maximum moments for a steady wind speed of 8m/s for
16000 seconds for different controllers.
(a) Torque gain for NLESC (b) Torque gain for load optimized NLESC
Figure 7: Optimal torque gain at a steady wind speed of 6m/s for 16000 seconds

9. (a) Total power of 3 turbines (b) Percentage change of power of each turbine
Figure 8: Power at a steady wind speed of 6m/s for 16000 seconds for different controllers and
the percentage change in power between them.
(a) Tower moment (b) Shaft moment
Figure 9: Maximum moment at a steady wind speed of 6m/s for 16000 seconds for different
controllers.
Figure 10: Tower moment of turbine 1 over a period of 30000 seconds for a wind speed of 8m/s
and a turbulence intensity of 5% using the different control schemes.

10. Figure 11: Shaft moment of turbine 1 over a period of 30000 seconds for a wind speed of 8m/s
and a turbulence intensity of 5% using the different control schemes.
(a) DEL for shaft (b) DEL for tower
Figure 12: Percentage change in damage equivalent loads for turbulent wind with a mean wind
speed of 8m/s and turbulence intensity of 5% for a period of 30000 seconds using the weights
w1 = [1, 1, 1] and w2 = [1, 1, 1].
(a) Mean shaft moment (b) Mean tower moment
Figure 13: Percentage change in mean moments for turbulent wind with a mean wind speed of
8m/s and turbulence intensity of 5% for a period of 30000 seconds using the weights w1 = [1, 1, 1]
and w2 = [1, 1, 1]. The mean loads are calculated from 5000s for all controllers.

11. (a) Torque gain of NLESC (b) Torque gain of load optimized NLESC
Figure 14: Torque gains for turbulent wind with a mean wind speed of 8m/s and turbulence
intensity of 5% for a period of 30000 seconds using the weights w1 = [1.03, 1, 1] and w2 = [1, 1, 1].
(a) DEL for shaft (b) DEL for tower
Figure 15: Percentage change in damage equivalent loads for turbulent wind with a mean wind
speed of 8m/s and turbulence intensity of 5% for a period of 30000 seconds using the weights
w1 = [1.03, 1, 1] and w2 = [1, 1, 1]
(a) Mean shaft moment (b) Mean tower moment
Figure 16: Percentage change in mean moments for turbulent wind with a mean wind speed
of 8m/s and turbulence intensity of 5% for a period of 30000 seconds using the weights
w1 = [1.03, 1, 1] and w2 = [1, 1, 1]. The mean loads are calculated from 3500s for all controllers.

12. (a) Total power output (b) Percentage change in power output
Figure 17: Power output shown on a windfarm level of the three control algorithms and a per
turbine evaluation of the percentage change in power output using the load optimized NLESC
for turbulent wind with a mean wind speed of 8m/s and turbulence intensity of 5% for a period
of 30000 seconds using the weights w1 = [1.03, 1, 1] and w2 = [1, 1, 1]..
Figure 18: Wind speed over a period of 30000s for a wind speed of 8m/s and a turbulence
intensity of 10% at the rotor of each turbine.
(a) Torque gain of NLESC (b) Torque gain of load optimized NLESC
Figure 19: Percentage change in mean moments for turbulent wind with a mean wind speed
of 8m/s and turbulence intensity of 10% for a period of 30000 seconds using the weights
w1 = [1.2, 1, 1.1] and w2 = [1.05, 1, 1]. The mean loads are calculated from 5000s for all
controllers.

13. (a) DEL for shaft (b) DEL for tower
Figure 20: Percentage change in damage equivalent loads for turbulent wind with a mean wind
speed of 8m/s and turbulence intensity of 10% for a period of 30000 seconds using the weights
w1 = [1.2, 1, 1.1] and w2 = [1.05, 1, 1].
(a) Mean shaft moment (b) Mean tower moment
Figure 21: Percentage change in mean moments for turbulent wind with a mean wind speed
of 8m/s and turbulence intensity of 10% for a period of 30000 seconds using the weights
w1 = [1.2, 1, 1.1] and w2 = [1.05, 1, 1]. The mean loads are calculated from 5000s for all
controllers.
(a) Total power output (b) Percentage change in power output
Figure 22: Power output shown on a windfarm level of the three control algorithms and a per
turbine evaluation of the percentage change in power output using the load optimized NLESC
for turbulent wind with a mean wind speed of 8m/s and turbulence intensity of 10% for a period
of 30000 seconds using the weights w1 = [1.2, 1, 1.1] and w2 = [1.05, 1, 1].

14. 4. Conclusion and future work
Based on the results we can see that the utilizing NLESC does impose structural loads on the
turbine while maximizing the power. The steady wind simulations provided us a proof for the
theory and this is further applied in the case of the turbulent wind. The introduction of the
loads as a penalty function to the power coefficient mitigates the increase in loads due to the
NLESC with negligible decrease in the power. Though the power output is on average upto
0.5% lower than the NLESC, it comes with upto 30% decrease in the mean loads and upto 20%
decrease in the fatigue loads imposed on the turbine. The results are however subject to the
quality of the wind.
At higher turbulence intensity the decrease in the loads reduces. This is because the
NLESC and it’s load optimization is tedious to control at these conditions. This brings up
the requirement to smoothen the input of the controller such that it does not a function of the
wind. This requires the use of a moving average filter over larger sample times. This makes the
controller stable at the cost of slower response to changes in the APC.
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