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PI Controller parameters design of doubly feed induction generator Based
on Mine Blast Algorithm
Osama El-baksawia, Ahmed Fathyb
a
Department of Electrical Engineering, Faculty of Engineering, Port-said University, Egypt
E-mail: [email protected]
b
Electrical Power & Machine Dept., Faculty of Engineering, Zagazig University, Egypt
E-mail: [email protected]
Abstract:
In this paper, a control strategy optimized by Mine Blast Algorithm (MBA) is applied on a variable speed wind generator
(VSWG) system based on a doubly fed induction machine. The flywheel energy storage system consists of a power electronic
converter supplying a squirrel-cage induction machine coupled to a flywheel. The proposed MBA is applied to evaluate the
optimal parameters of the current PI controller. The proposed objective function is the sum of squared error (SSE) between the
reference and the estimated current in d-q domain. In order to validate the control method; the asymptotic regulation of active and
reactive power is achieved by means of direct closed-loop control of active and reactive components of the stator current vector,
presented in a line-voltage-oriented reference frame. Simulation model demonstrates high dynamic performance and robustness of
the control algorithm for typical operating conditions. The proposed controller is suitable for both energy generation and electrical
drive application with restricted speed variation range.
Keywords: Wind turbine; Doubly fed induction generator; Mine blast algorithm
1. Introduction
The Doubly-Fed Induction Generator (DFIG) is an induction generator with both stator and rotor windings. Nowadays the DFIG
is widely used in variable-speed wind energy applications with a static converter connected between the stator and rotor.
Currently, this topology occupies close to 50% of the wind energy market. A wind turbine generation system (WTGS) generally
comprises of a wind turbine, an electric generator and various control systems. Wind turbine models are also classified as variable
or fixed speed wind turbine based upon their rotational speed [2, 3]. However, the modeling of WTGS is a complex task involving
the modeling of the turbine, the generator and the power converter which ensures that the frequency of the supply voltage is in
conformity with the transmission system. This is because of the generated voltage by the WTGS is never compliant to the grid. In
addition, a control mechanism must be added to regulate the rotor speed which is directly related to the wind speed variations.
Many applications of wind power can be found in a wide power range from a few kilowatts to several megawatts in small scale
off-grid standalone systems or large scale grid-connected wind farms. Due to the lack of control on active and reactive power, this
type of dispersed power generation causes problems in the electrical connected system. Therefore; this requires accurate
modeling, control and selection of appropriate wind energy conversion system.
During the last two decades, the high penetration of the wind turbines in the power system has been closely related to the
advancement of the wind turbine technology and the way of how to control. Doubly-fed induction machines are increasing the
attention for wind energy conversion system during such situation. The main advantage of such machines is that, if the rotor
current is governed applying field orientation control-carried out using commercial double sided PWM inverters, decoupled
control of stator side active and reactive power results and the power processed by the power converter is only a small fraction of
the total system power. So, doubly-fed induction machine with vector control is very attractive to the high performance variable
speed drive and generating applications [1-4]. In this work, Mine blast algorithm (MBA) is applied to evaluate the optimal
parameters of PI controller such that minimizing the sum of squared error between the reference current of DFIG rotor and the
estimated one. The DFIG is driven by variable speed wind generator (VSWG).
2. Mathematical model
2.1 Basic concepts and wind turbine modeling
Wind turbines convert the kinetic energy presented in the wind into mechanical energy by means of producing torque. Since the
energy contained by the wind is in the form of kinetic energy, its magnitude depends on the air density and the wind velocity. The
wind power developed by the turbine is given as follows [1-10]:
1
p=
1
2
cP ρ A V 3
(1)
Where Cp is the power co-efficient, ρ is the air density in kg/m3, A is the area of the turbine blades in m2 and V is the wind
velocity in m/sec. The power coefficient Cp gives the fraction of the kinetic energy that is converted into mechanical energy by the
wind turbine. It is a function of the tip speed ratio λ and depends on the blade pitch angle for pitch-controlled turbines. The tip
speed ratio may be defined as the ratio of turbine blade linear speed and the wind speed
λ=
Rω
(2)
V
By substituting (2) in (1), we have:
𝑝=
1
2
𝑅 3
𝑐𝑃 (𝜆)𝜌 𝐴 ( )
𝑉
𝜔3
(3)
The output torque of the wind turbine Tturbine is calculated by the following equation.
𝑇𝑡𝑢𝑟𝑏𝑖𝑛𝑒 =
1
2
𝜌 𝐴𝑐𝑃 𝑉 ⁄𝜆
(4)
Where R is the radius of the wind turbine rotor (m). There is a value of the tip speed ratio at which the power coefficient has a
maximum value [2]. Variable speed turbines can be made to capture this maximum energy in the wind by operating them at a
blade speed that gives the optimum tip speed ratio. This may be done by changing the speed of the turbine in proportion to the
change in wind speed. Fig.1 shows how variable speed operation will allow a wind turbine to capture more energy from the wind
and Fig. 2 shows the Simulink model of the wind turbine. As one can see, the maximum power follows a cubic relationship. For
variable speed generation, an induction generator is considered attractive due to its flexible rotor speed characteristic in contrast to
the constant speed characteristic of synchronous generator.
2.2 Variable speed configuration of DFIG
The variable-speed DFIG wind energy system is one of the main WECS configurations in today's wind power industry. As shown
in Fig. 1, the stator is connected to the grid directly, whereas the rotor is connected to the grid via reduced-capacity power
converters [13]. A two-level IGBT voltage source converter (VSC) system in a back-to-back configuration is normally used.
Since both stator and rotor can feed energy to the grid, the generator is known as a doubly fed generator. The rotor-side converter
(RSC) controls the torque or active/reactive power of the generator while the grid-side converter (GSC) controls the DC-link
voltage and its AC-side reactive power. Since the system has the capability to control the reactive power, external reactive power
compensation is not needed.
Fig.1 Modeling of the wind turbine doubly-fed induction generator
Referring to Fig. 1. The AC/DC/AC converter is divided into two components: the rotor side converter Crotor and the grid-side
converter Cgrid. They are voltage-sourced converters that use forced-commutated power electronic devices (IGBTs) to synthesize
an AC voltage from DC voltage source. A capacitor connected on the DC side acts as the DC voltage source. A coupling inductor
L is used to connect Cgrid to the grid. The three-phase rotor winding is connected to Crotor by slip rings and brushes and the threephase stator winding is directly connected to the grid.
2
The power captured by the wind turbine is converted into electrical power by the induction generator and it is transmitted to the
grid by the stator and the rotor windings. The control system generates the pitch angle command and the voltage command signals
Vr and Vgc for Crotor and Cgrid respectively in order to control the power of the wind turbine, the DC bus voltage and the voltage at
the grid terminals.
An average model of the AC/DC/AC converter is used for real-time simulation. In the average model power electronic devices are
replaced by controlled voltage sources. Vr and Vgc are the control signals for these sources. The DC bus is simulated by a
controlled current source feeding the DC capacitor. The current source is computed on the basis of instantaneous power
conservation principle: the power that flows inside the two AC-sides of the converter is equal to the power absorbed by the DC
capacitor.
The power flow illustrated in Fig. 2 is used to describe the system operating principle. The mechanical power and the stator
electrical power output are:
Pm = Tm ωr
(5)
Ps = Tem ωs
(6)
For a lossless generator; the mechanical equation is:
dωr
= Tm − Tem
dt
In steady-state
Tm = Tem and Pm = Ps + Pr
From where it follows:
Pr = Pm − Ps = Tm ωr − Tem ωs = −sPs
(7)
(8)
(9)
Where is is the generator slip and is defined by:
s=
ωs −ωr
(10)
ωs
Generally the absolute value of slip is much lower than 1 and consequently P r is only a fraction of Ps. Since Tm is positive for
power generation and since ωs is positive and constant for a constant frequency grid voltage, the sign of Pr is a function of the slip
sign. Pr is positive for negative slip (super-synchronous speed) and it is negative for positive slip (sub-synchronous speed). For
super-synchronous speed operation Pr is transmitted to DC bus capacitor and tends to rise the DC voltage. For sub-synchronous
speed operation, Pr is taken out of DC bus capacitor and tends to decrease the DC voltage. C grid is used to generate or absorb the
power Pgc in order to keep the DC voltage constant. In steady-state for a lossless AC/DC/AC converter P gc is equal to Pr and the
speed of the wind turbine is determined by the power Pr absorbed or generated by Crotor. The phase-sequence of the AC voltage
generated by Crotor is positive for sub-synchronous speed and negative for super-synchronous speed. The frequency of this
voltage is equal to the product of the grid frequency and the absolute value of the slip. Crotor and Cgrid have the capability for
generating or absorbing reactive power and could be used to control the reactive power or the voltage at the grid terminals.
Fig.2. Power flow in DFIG
3
2.3 Doubly fed induction motor model
Using the flux ψds , ψqs and current Idr , Iqr as state variables and under assumption of linear magnetic circuit, the equivalent twophase model of the doubly fed induction motor, represented in a rotating reference frame (d, q) linked to the stator voltage is:
Vds = R s Ids +
Vqs = R s Iqs +
dψds
dt
dψqs
Vdr = R r Idr +
Vqr = R r Iqr +
dt
dψdr
− θṡ ψqs
(11.a)
− θṡ ψds
(11.b)
dt
dψqr
dt
− θṙ ψqr (11.c)
− θṙ ψdr (11.d)
ψds = Ls Ids + MIdr
(11.e)
ψqs = Ls Iqs + MIqr
(11.f)
ψdr = Lr Idr + MIds (11.g)
ψqr = Lr Iqr + MIqs (11.h)
Tm = Te + J
dω
dt
+ fω
(11.j)
Where Ird, Irq, ψds, ψqs, ωm and ωs are the components of rotor currents, stator fluxes, angular speed and Park transformation speed,
respectively. Wherever they come in, the subscripts s and r refer to the stator and rotor, respectively. That is, R s and Rr are the
stator and rotor resistances; Ls and Lr are the self-inductances; Msr denotes the mutual inductance between the stator and rotor
windings; p designates the number of pole-pair, J is the inertia of the motor-load set, F is the friction coefficient and TL is the load
torque. The remaining parameters are defined as follows: when the stator voltage is linked to the d-axis of the frame we have Vds
= Vs and Vqs = 0, the stator and networks currents will be related directly to the active and reactive power. An adapted control of
these currents will thus permit to control the power exchanged between the motor and the grid.
4. Proposed Control model
4.1 Mine blast Optimization algorithm
Mine blast algorithm (MBA) is one of the most recent meta-heuristic optimization algorithms; it has been proposed by Sadollah et
al. [1]. The MBA is motivated from the observation of mine bomb explosion that produces thrown pieces of shrapnel and collides
with other one in the same mine field; this action is helping in exploring a new mine bomb. Finally; the most explosive mine
located at optimal location resulting in best objective function has been evaluated. The first step in the MBA methodology is
defining an initial point called shot point, x0k where k is the number of shot points, it produces number of shrapnel pieces, N s,
which are represented the individuals in the population. The location of exploding mine by the shrapnel pieces is calculated as
follows:
x(j+1) k = xe(j+1) k + exp (−√
m(j+1) k
d(j+1) k
) ∗ xj k
j = 0, 1, 2, … . , (Ns − 1)
(12)
Where xe(j+1)k is the exploding mine bomb location, m(j+1)k and d(j+1)k are the direction and the distance of the generated thrown
shrapnel pieces in each iteration and xj k is the solution at iteration k.
The value of xe(j+1)k can be calculated as follows:
xe(j+1) k = dj k × rand × cos(θ)
(13)
Where rand is a random number in range [0, 1], θ is the angle of the shrapnel pieces and it is equal to 360/N s.
In MBA; there are two processes for searching the optimal solution; the exploration and exploitation processes. The exploration
one is conducted when the exploration factor (γ) is greater than the iteration number (k). In this process the exploding mine bomb
location can be evaluated as follows:
xe(j+1) k = dj+1 k × cos(θ), n = 0, 1, 2, … . , (Ns − 1) (14)
dj+1 k = dj k × (|randn|)2
(15)
4
The exploitation process is conducted in case of γ less than k; this process is responsible for converging to the optimal solution;
this is done by gradually reducing the initial distance of shrapnel pieces through a reduction constant, α, which is defined by the
user. The reduction in the initial distance is calculated as follows:
dj−1 k
dj k =
(16)
k
α
exp( )
In this process the location of exploded mine bomb is calculated using eqn. (13) while the distance and shrapnel pieces are
calculated as follows:
2
2
dj+1 k = √(x(j+1) k − x(j) k ) + (F(j+1) k − F(j) k ) ,
m(j+1) k =
k
F(j+1) −F(j)
j = 0, 1, 2, … . . , (Ns − 1) (17)
k
(18)
x(j+1) k −x(j) k
Where F is the value of fitness function at location x. The flow chart of MBA algorithm is shown in Fig. 3.
Start
Initialize the MBA
parameters Ns, γ , α and k
Set iteration number j=0
No
γ>k
Yes
Calculate the distance of shrapnel pieces
and their locations Eqns. (14 and 15)
Generate the shrapnel pieces and compute
their improved locations Eqn. (12)
No
Fj
+1
< Fj
Yes
Update the shrapnel piece
Calculate the distance of shrapnel pieces and
their locations Eqns. (13and 16)
Reduce the distance of the shrapnel pieces
adaptively Eqn. (16)
Convergence criteria
satisfied?
Yes
Optimal solution is obtained
End
Fig. 3 The proposed steps of the MBA algorithm
4.2 Design of the proposed PI controller
In this paper the proposed MBA technique is applied to evaluate the optimal parameters of proportional integral (PI) controller in
the side of rotor of doubly-fed induction generator driven by wind turbine; the main objective is to minimize the sum of squared
error between the measured current in d-q plane and the reference one. The mathematical formula of the proposed constrained
objective function can be expressed as follows:
𝜀𝑑 = 𝐼𝑑𝑟 − 𝐼𝑑
𝜀𝑞 = 𝐼𝑞𝑟 − 𝐼𝑞
𝐽(𝑥) = 𝑉𝑟 = (𝐾𝑝 +
(19)
(20)
𝐾𝐼
𝑆
2
) ∗ ∑(𝜀𝑑 + 𝜀𝑞 )
Subjected to inequality constraints as follows:
5
(21)
𝐾𝑃 𝑚𝑖𝑛 < 𝐾𝑃 ≤ 𝐾𝑃 𝑚𝑎𝑥
𝐾𝐼 𝑚𝑖𝑛 < 𝐾𝐼 ≤ 𝐾𝐼 𝑚𝑎𝑥
(22.a)
(22.b)
Where εd and εq are the errors in d-axis current and q-axis current respectively, Idr and Iqr are the reference currents of d and q
currents respectively, Id and Iq are the measured currents of d and q currents respectively, Vr is the controlling voltage fed to the
DFIG rotor voltage, Kp and KI are the parameters of the PI controllers under design, Kpmin and Kpmax are the minimum and
maximum limits of the proportional gain and KImin and KImax are the minimum and maximum limits of the Integral gain. In this
paper the limits are selected as 𝐾𝑃 𝑚𝑖𝑛 = 0.01, 𝐾𝑃 𝑚𝑎𝑥 = 2, 𝐾𝐼 𝑚𝑖𝑛 = 1 and 𝐾𝐼 𝑚𝑎𝑥 = 15.
5. Results and analysis
Simulink library is used to model the system under study; the system comprises 6 wind turbines each provides 1.5 MW feed
doubly fed induction generator, the wind farm is connected to 25 kV, 60 Hz grid. The model of the proposed control circuit of the
DFIG rotor is given in Fig. 4. The proposed MBA is used to determine the optimal parameters of the PI controller such that
minimizing the SSE between the measured and desired currents in dq plan. The controlling parameters of the MBA are given in
Table 1.
Table 1 the controlling parameters of MBA
Number of shrapnel pieces
50
Reduction factor (α)
1.5712
Number of function evaluations
10000
No. of iterations
100
The final optimal values of PI parameters are Kp=1.65113573084045 and KI=14.8735145784575; the final minimum error is
1.61175341920802e-06 A. the response of MBA is shown in Fig. 5 while the change of shrapnel distances with number of
iterations is shown in Fig. 6.
Fig. 4 Simulink model of DFIG rotor control circuit
6
Fig. 5 The change of fitness function with number of iterations
Fig. 6 The variation of shrapnel distance with the number of iterations during MBA execution
The simulation results for output wind turbine are shown in Figs. 7.a, 7.b, 7.c and 7.d. These curves represent the turbine power
characteristics (turbine output power versus turbine speed), pitch angle, wind speed and mechanical angular velocity. It is obvious
that at t= 5 sec PI controller is set to start, there are a strong variation in the rotor speed from 0.8 pu to 1.22 pu du to the variations
of wind speed from 8 to 14 m/s as shown in Figs. 7.c and 7.d. The wind speed curve as shown in Fig. 7.c represents a rise in wind
speed within the interval for 5 to 12 second. So, an automatic rise in pitch angle from zero to 0.78 as well as the rotor speed
followed. The graph of pitch angle is controlled to overcome the speed variation and oscillation. Figs. 8.a, 8.b, 8.c and 8.d show
the DC voltage, active power, reactive power and mechanical torque. Fig. 8.a shows the DC voltage is constant at t= 20 second,
active power as shown in Fig. 8.b is variation between 2 to 9 MW and constant at 9MW. While reactive power as shown in Fig.
8.c is varied between -0.02 to -0.68 MVAR and then became constant at -0.68 MVAR. In Fig. 8.d the torque is constant after 20
second at 0.73 pu. Furthermore, Figs. 9.a, 9.b, 9.c, 9.d, 9.e and 9.f show the current plant, voltage plant, the active and reactive
power generated. As well as speed motor and voltage bus generated. The first two sub-Figs. 9.a and 9.b the current and voltage
generated, the current is constant at 0.9665 pu and voltage is constant at 0.9972 pu. The active power exhibits some strong
oscillations within the range of -6 to 0.5 MW. The reactive power is constantly at 1.3 MVAR at t= 19 second. While the graph of
speed motor is constant at t=20 second and equal 0.9933pu. Finally voltage bus of grid is constant at 1.0014 at t=20 second.
7
Fig. 7.a Turbine power characteristics
Fig. 7.b Pitch angle control
Fig. 7.c Speed wind
Fig. 7.d Rotor speed
8
Fig. 8.a Wind turbine DC voltage
Fig. 8.b Wind turbine ative power
Fig. 8.c Wind turbine reactive power
Fig. 8.d Mechanical torque
9
Fig. 9.a Current plant
Fig. 9.b Voltage plant
Fig. 9.c Wind turbine active power
Fig. 9.d Wind turbine reactive power
10
Fig. 9.e Speed motor
Fig. 9.f Wind turbine voltage bus
6. Conclusion
This paper presents a model and simulation of variable speed wind turbine using DFIG under Matlab/Simulation. The model of a
wind turbine-generator system equipped with a doubly-fed induction generator which is developed in a Matlab/Simulink
environment. It simulates the dynamics of the system from the turbine rotor, where the kinetic wind energy is converted to the
mechanical energy, to the generator, which transforms the mechanical power to electrical power, and then to the grid connection
point, where the electric power is fed into the grid. An analytical model of wind turbine was presented and power coefficient
characteristics were investigated. Furthermore, a graphical model of 6 MW wind farm was built with enhanced control of speed
using PI controller with MBA algorithm. At first when the control system was not applied, the rotor speed was very unstable but
after 5s and also due to a perfect tuning of the PI controller with MBA algorithm, results were the best in terms of stability of the
rotor speed versus the wind variation. The rotor speed was merely constant after 20s despite the wind speed was still varying
within the range of 5m/s to 12m/s. On the other hand, the voltage generated as well as the reactive and active powers were also
good performance.
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