Energy and Power Engineering, 2013, 5, 398-403
doi:10.4236/epe.2013.54B077 Published Online July 2013 (http://www.scirp.org/journal/epe)
The Maximum Power Tracking Method and Reactive
Compensation Simulation Research Based on DIgSILENT*
Wei Guo, Dong-mei Zhao
College of Electrical and Electronic Engineering, North China Electric Power University, Beijing, China
Received March, 2013
ABSTRACT
This paper studies about the mechanical part of wind turbine and wind generator operation stability.1) It makes a com-
parative study of two control methods for maximum power tracking: curve fitting method and hill climbing algorithm,
sets up improved control modules in DIgSLIENT and makes comparison research, thus gets the conclusion that the im-
proved control modules of hill climbing algorithm has good effect on MPPT, and it is more desirable in the condition of
steady wind. 2) This paper sets up SVC and STATCOM models and improved control modules in DIgSLIENT, which
are connected to wind power system, verifying the validity of SVC and STATCOM models, and verifying its influence
on wind power plant and system. The results of the study show that STATCOM is more helpful in voltage recovery
when large disturbance of three-phase short-circuit happened in wind power grid, reactive compensation is more effec-
tive.
Keywords: Maximum Power Tracking; Hill Climbing Algorithm; SVC; STATCOM; DIgSLIENT
1. Introduction
With the rapid development of large wind power genera-
tion research, it is more focused that variable speed con-
stant-frequency doubly-fed wind power generation tech-
nology has the feature of variable speed within compara-
bly wide range in maximum power tracking. [7] Dis-
cusses a new and simple control method for maximum
power tracking in a variable speed wind turbine by using
a step-up dc-dc converter [8]. Analyze the wind machine
characteristics and maximum wind power captured prin-
ciple, proposes a control strategy without measuring
wind speed. [5] Reviews the existing maximum wind
energy extraction algorithm and develops an intelligent
maximum power extraction algorithm.
In China, the area that is suitable for large-scale de-
velopment of wind power is in a network terminal. The
power grid structure in this area is comparably weak, so
once connected to grid, large-scale wind power may ap-
pear a series of problems, such as voltage decline, in-
creasing system short circuit capacity, system transient
stability change, etc. Therefore, reactive compensation
for power factor improvement is of great practical sig-
nificance to voltage stability and improving transmission
efficiency. The principle structures and controller models
and dynamic compensation effects of SVC and STAT-
COM have been discussed in [9-11].
2. Mathematical Model
2.1. Wind Turbine Model
Wind turbine is the component that converting winds
energy into mechanical energy. With a certain speed and
angle, the effect of wind makes the paddle rotating, and
thereby the wind energy turns into mechanical energy,
which drives the generator. The process that wind turbine
turn wind energy into mechanical energy is a complex
aerodynamics process, which is quiet difficult to accu-
rately describe. According to Betz' Law, the mechanical
power of wind turbine capture is:
32
0.5 p
P
C  R
(1)
In (1), P is the power of wind turbine capture, ρ is air
density, R is radius of the turbine blade, and v is wind
speed. CP is the wind power utilization coefficient of
wind turbine, and its physical meaning is: the percentage
of energy absorbed from natural wind by wind rotor and
the wind energy contained in undisturbed air within rotor
swept area. CP is the function of tip speed ratio
λ and
pitch angle
β . It could be simulated in the following
nonlinear function [1].
*The National High Technology Research and Development of China
863 Program (2012AA050201).

W. GUO, D.-M. ZHAO 399
12.5/
1
3
116
(,) 0.22(0.45.0)
10.035
[]
0.08 1
i
Pi
i
Ce
R
v

 







 








(2)
2.2. Shaft Model
Shaft drive system mainly includes a wind turbine, over-
drive gearbox and drive shaft, but generally, overdrive
gearbox and wind turbine are equivalent to one mass,
doubly-fed generator is one mass, thus shafting drive
model with two masses is built. As shown in Figure 1:
Two masses model [2]
()
()
GG
GGGG wG
G
ww
wwww wG
w
dw
dt
dwTw k
dt J
dw
d
dwTw k
dJ



















(3)
In (3), “w”“G”respectively stand for turbine and
generator:
θ is the torsion angle of shaft, K is stiffness
coefficient, Jw and JG are the inertia time constant of
wind turbine and generator, δw andδG are the damping
coefficient of wind turbine and generator rotor, Tw is the
mechanical torque of wind rotor and TG is the mechani-
cal torque effected on rotor shaft of generator. It is
known that two masses model of differential variables
have four, this will increase the workload, so that influ-
ence the simulation speed, therefore we need to simplify
the shaft model, a simplified model is that the two inertia
time constant are equal to one:
W
eq G
J
JJN  (4)
where: N stand for Gear box of variable ratio. So that one
mass model equation:
G
eqw GG
dw
J
TT w
dt

 (5)
Figure 1. Shaft model diagram..
2.3. Wind Turbine Model
Considering DFIG stator transient process and transient
state of system, the increasing of system order is time-
consuming, it is necessary to lower the order of generator.
As electromagnetic transient state of stator is much rapid
than that of rotor, and have less effect on transient stabil-
ity of generator, so transient process of stator is ignored,
that is, the change of the stator magnetic chain is zero.
The voltage equation of DFIG in the two phase synchro-
nous speed rotating coordinate system is converted
as[3,4]:
sdssqs sd
sqssds sq
rdrdsrqr rq
rqrqsrdrrq
uRi
uRi
up sRi
up sRi




 



 

 

(6)
Equation (5) and (6) are combined, a third order equa-
tion of wind generator is set. As a third Order model
could fully reflect the characteristics of wind power gen-
eration in system transient state, precision is acceptable,
and calculation speed is fast, and In the DIgSLIENT,
wind generator mechanical and electrical transient model
is to use the third order model.
3. Wind Energy Capture
3.1. Method Introduced
The common control method of MPT could be classified
into three types [5]: Tip Speed Ratio, Power Signal
Feedback, and Hill-climbing Search. This paper tries to
compare wind MPPT control by listing two different
realization methods in DIgSLIENT.
Method 1[6]: curve fitting method, the optimal power
curve of the wind turbine is fitted to the wind turbine
speed ω as the independent variable, Power P is the po-
lynomial expression of the speed ω, the generator rota-
tional speed ω and the power P is a one-to-one relation-
ship. Back stepping the actual active output of the wind
generation, we can get the corresponding optimal speed
as the speed reference value, input the value to speed
controller to get the optimal power reference value, and
then input to the active control system of doubly-fed
generation as the reference active power value. Speed
controller role: the difference of the speed reference val-
ue and the measured values of the generator speed is the
error value, the value input PI controller to obtain active
power reference value. If the actual speed is equal to ref-
erence speed value, speed controller input signal is 0
which means it doesn't work; if not, speed controller will
conduct continuous control until the wind generator out-
put the corresponding optimal power. So the realization
of the function the maximum wind power capture is in
turn depend on the maximum power tracking module,

W. GUO, D.-M. ZHAO
400
speed controller and doubly-fed motor power control. As
shown in Figure 2:
Method 2[7, 8]: constant step hill climbing algorithm
is local optimization algorithm, The specific algorithm is
as follows: First of all, the initial reference motor speed
ω and active power P are given. Secondly, by observing
the changes in P and ω, compare with previous P and ω
to get the trend of the P and ω to decide positive and
negative of the step: If the trends of the two variables are
the same, then the calculated out step is positive. At last,
the current step plus the previous cycle of reference value
will get a new reference value.
Implementation: in the control cycle interval n and n-1
time in the control cycle, Sampling the P and ω and Ob-
servation of the current P and ω. If P increases, main-
taining step ωstep direction, or else makes the step length
ωstep inverting. Finally, the current ωstep plus the previous
cycle of reference speed command will obtain a new ref-
erence value, the reference speed value input to speed
controller and reference active power value is obtained
by the PI controller, and then input to the active power
controller of the DFIG. As shown in Fi gure 3:
Calculation △P,△ωand the next moment of refer-
ence speed:
()( 1)
()( 1)
()(1)()( )
ref refstep
dP Pn Pn
dw wnwn
wnwnsignPsignww


 
(7)
where: if x≥0,sign(x) = 1; if x＜0,sign(x) = -1.
Repeating the appeal process: change generator speed,
until the unit output power is no longer sensitive to sys-
tem parameter.
Figure 2. MPT and Speed controller model structure.
Figure 3. hill climbing algorithm structure diagram.
If power change is zero, the system has achieved the
current wind speed of the maximum power point.
3.2. Example Comparison
1) The MPPT condition in constant wind speed 13 m/s,
the comparison of two MPPT results:
Conclusion: The coordinate system in the above two
graphs ranges from 0.8984 to 0.8992. Results can be seen
that the precision of the two methods has met the re-
quirements, because the interval range retains 3 digits
after the decimal point. In the curve fitting method, out-
put power reference still presents approximate linear in-
crease in a very small range; while in the hill climbing
algorithm, the reference presents slight fluctuations. It is
obvious that the wave output in the hill climbing algo-
rithm is more stable, making the active output of wind
turbine followed active power reference more stable,
which solve the problem that power is output fast and
smoothly in the stable wind speed condition.
2) The MPPT condition: 0 s -17 s wind speed keeps 10
m/s, 17 s wind speed jump to 15 m/s, the comparison of
two MPPT results:
Conclusion: Large changes in wind speed, hill climb-
ing algorithms fluctuations are much larger than the
curve fitting method from the Figure 6 and Figure 7. At
Figure 4. Pref value output by curve fitting method.
Figure 5. Pref value output by hill climbing algorithm.
Figure 6. Pref value output by curve fitting method.

W. GUO, D.-M. ZHAO 401
Figure 7. Pref value output by hill climbing algorithm.
17 s, the wind speed suddenly increases. In the hill
climbing algorithm, the output power reference value
fluctuations from 0.9p.u. to 0.975 p.u., however, in the
curve fitting method, the output reference value just
fluctuations from 0.899p.u. to 0.92 p.u.. But, in the hill
climbing algorithm, over time is short, and it takes ap-
proximately 30 seconds to reaches a steady state, while
in the curve fitting method it’s about 40 seconds to reach
a steady state. So it can be concluded that the constant
step hill climbing algorithm applies winds less volatile
condition, and the wind turbine of the inertia can not be
too large, otherwise not timely tracking to the best power
point.
4. Reactive Compensation
In the short circuit fault process, the wind generator will
trigger rotor protection, which will make the wind gen-
erator asynchronous running in a short time. Thus, the
continuous wind generator running need to absorb a large
amount of reactive power, which can reduce the grid
stability and the power factor of system, and in addition,
the increase of line loss. Therefore, reactive compensa-
tion will have a great practical significance of improving
the steady-state and dynamic performance of wind power
generation system. This paper will make brief introduc-
tion and analog simulation of the control of two reactive
compensation devices SVC and STATCOM which are
widely applied.
4.1. STATCOM
The STATCOM's basic principle is the self-commutated
bridge circuit that is connected with capacitor, through
resistance and reactance or direct connects to the grid.
According to the DC voltage of the capacitance and AC
voltage of the access point, properly adjust the amplitude
and phase of the AC output voltage of the bridge circuit
to make absorption or generation reactive current of the
circuit meet the system requirements, thus achieve the
purpose of dynamic reactive power compensation.
As Figure 8 shown, observing the amplitude and the
phase of the AC voltage signal of the STATCOM con-
nected bus. The amplitude difference with the set refer-
ence value, differences through the PI control become the
signal which can control the PWM, but firstly the signal
need connect to a limiter, then input to the PWM. At the
same time, the phase angle of the phase-locked loop
measurements that is use to make modulation wave syn-
chronized with the system. Both of them control PWM,
so that the phase of the PWM output modulated wave
change to Trigger fully controlled devices (GTO/IGBT)
which is in each leg of the three-phase inverter bridge off
or on. So the AC side of STATCOM changes its reactive
current to follow the command current Iref.
4.2. SVC (Static Var Compensator)
The SVC system is a combination of a shunt capacitor
bank and a thyristor controlled shunt reactance (TCR).
The capacitors in the capacitor bank could be switched
with thyristors (TSC) or could be permanently connected
(MSC). Through TSC, reactive power compensation is
into reasonable classification, get a hierarchical reactive
power change. In addition, TCR can absorb continuous
reactive power. If absorbing the whole reactive power is
needed, disconnect all TSCs. For coordinated control
TSC and TCR, the system can get continuous reactive
power output.
As Figure 9 shown, The SVC bus is installed voltage
measurement, the measuring voltage is in turn sent to
Lead lag correction link、Proportional lead lag correction
link and inertial element, through the selector compari-
son with output results of a comparator, select one to
input to the SVC interface and output the firing angle
which can open or close the TCR and signal to control
the number of TSC. In DIgSLIENT, we need to set out
Figure 8. STATCOM control block diagram.
Figure 9. SVC control block diagram.

W. GUO, D.-M. ZHAO
402
the minimum and maximum reactive power and control
mode of the Static Var Components system separately.
4.3. Example
Using DIgSLIENT simulation, Wake effect between the
various units of the wind farm is not considered in the
simulation, and the assumption that wind conditions
which is loaded into each wind turbine is same, so that
10 wind driven generations can be equivalent to 1. In
wind farms, wind turbines whose rated voltage are 690 V,
through the terminal transformer step up to 10 kV, and
then connect to the Low voltage bus of wind farm,
through the 1 km transmission lines to wind farms
booster station and stepped up to 110 kV, finally using
20 km transmission cable connect to the external power
grid, as shown below:
As shown in Figure 10, wind farms 10 kV low voltage
bus respectively access the same capacity of the two
kinds of reactive power compensation equipment, but
separate simulation run. In a condition of given wind
speed of 13 m/s, the short-circuit fault occurs in the mid-
dle of the transmission line which is on the second
booster station 110 kV side, and set the fault type three-
phase short-circuit fault: voltage drops to 0.39 p.u., fault
starts at 5 s, continued 100ms till the fault is cleared, this
paper mainly observes the bus voltage, reactive power
compensation equipment issued and compares and ana-
lyzes the results.
1) STATCOM reactive power compensation (Figures
11,12)
2) SVC reactive power compensation (Figures 13,14)
Figure 10. Single-line schematic diagram of the system.
Figure 11. bus bar voltage waveform after compensation.
Figure 12. Reactive power of compensation.
Figure 13. Bus bar voltage waveform after compensation.
Figure 14. Reactive compensation(amount in absolute value).
The results of simulation analysis:
1) Compared with without compensation equipment
situation, during the fault，STATCOM improves the
voltage from 0.39 p.u. to 0.503 p.u., and generates a large
amount of reactive power about 20 Mvar. In the fault
clearing time 5.2 s, reactive power has a great impact,
because the voltage recovery needs a lot of reactive
power. STATCOM dynamic compensation prevent the
wind driven generator which run as a asynchronous gen-
erator due to the low voltage protection action, absorp-
tion power grid more reactive power and make the volt-
age stability variation.
2) SVC output reactive power is proportional to the
square of the connected bus voltage. Therefore, during
the fault, bus bar voltage reduction makes SVC compen-
sating reactive power reduction, Voltage is just raised
from 0.39 p.u. to 0.403 p.u. Once the fault clearance,
SVC will improve the compensation capacity from 14.35
Mvar rise to about 20 Mvar, so as to help the system re-
covery voltage.

W. GUO, D.-M. ZHAO
403
3) From the chart, we know that SVC and STATCOM
can control reactive power, effectively maintain system
voltage stability, improve the system power factor, etc. In
contrast, STATCOM has obvious advantages: STAT-
COM compensation effect is better, more amount of
compensation and Since the SVC is group for cut, after
fault clearance, longer time is need to compensating re-
active power. But the control of STATCOM is more
complicated, and the cost of the frequency converter is
higher.
5. Conclusions
This paper finishes two parts on the DigSILENT:
1) It sets up two kinds of methods for the MPT mod-
eling simulation: the curve fitting method and hill climb-
ing algorithm, and improves the hill climbing algorithm
control, the conclusion is: output in the hill climbing al-
gorithm is more stable and converges faster so that the
hill climbing algorithm is better than the curve fitting
method.
2) It sets up the SVC and STATCOM modeling simu-
lation, compare and analyze these two kinds of equip-
ment in the power grid fault cases, and the dynamic re-
sponse of STATCOM compensation capacity is bigger,
the effect is more apparent.
This conclusion has certain reference and guidance for
practical engineering application.
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