CC BY
9
UDC 621.31
https://doi.org/10.20998/2074-272X.202L6.09
Z.E.Z. Laggoun, H. Benalla, K. Nebti
A power quality enhanced for the wind turbine with sensorless direct power control under different input voltage conditions
Introduction. The quality of electrical energy is essential during disturbances, at the level of power electronic devices will suffer serious operating problems causing dangerous damage. Aim. A new approach to direct power control without grid voltage sensor improves the quality and control of instantaneous active and reactive power converters. Methodology. First, the technique without network voltage sensor with a direct power control based on a switching table, which is a classic approach, is discussed and its performance is analyzed under increasing and decreasing load. In addition, the performance of the proposed technique is also analyzed under the same circumstances and their performance is compared. Originality. The new method consists of a nonlinear grid voltage modulated controller and a conventional controller which guarantees very good results in a polluted network. The proposed method is verified using MATLAB/Simulink. Results. The simulation results under different input voltage conditions show that the proposed method not only has good tracking performance in active and reactive power, but also reduces the current total harmonic distortion to 1.9 %, which is good lower than the requirement for network operation. References 17, tables 2, figures 11. Key words: direct power control, virtual flux, grid voltage modulated, constant switching frequency.
Вступ. Яюсть електроенергп мае важливе значення nid час збогв, на pieHi силових електронних пристрогв будуть мати мкце серйозш проблеми експлуатацп, що викликають небезпечш пошкодження. Мета. Новий nidxid до прямого керування потужтстю без датчика напруги мережг покращуе яюсть та контроль nеретворювачiв миттевог активног та реактивног nотужноcтi. Методологя Спочатку обговорюеться методика без датчика напруги мережi з прямим керуванням потужтстю на оcновi таблиц перемикання, що е класичним тдходом, та аналiзуетьcя його продуктивтсть при збтьшент та зменшент навантаження. Крм того, ефективтсть запропонованог методики також аналiзуетьcя за тих же обставин, i гхня продуктивтсть nорiвнюетьcя. Оригинальность. Новий метод складаеться з нелтшного мережевого контролера з модулящею напруги i звичайного контролера, який гарантуе дуже xорошi результати в забрудненш мережi. Запропонований метод nеревiряетьcя за допомогою MATLAB/Simulink. Результата. Результати моделювання за рiзниx умов вх^дног напруги показують, що запропонований метод не ттьки мае хорошi характеристики вiдcтеження активног та реактивног nотужноcтi, але також знижуе поточний THD до 1,9 %, що значно нижче, нгж вимоги дляроботи мережi.. Бiбл. 17, табл. 2, рис. 11. Ключовi слова: пряме керування потужтстю, вiртуальний потж, модулящя напруги мереж^ постшна частота перемикання.
1. Introduction. Grid-connected converters are widely used in the application of smart grids, Flexible Alternating Current Transmission Systems (FACTS) and renewable energy sources (e.g., wind and solar) and various control methods have been investigated so that converters improve their performance [1].
Many studies have focused on the advanced control of the functioning of renewable energies that have been proposed with the same main objective which is the power quality which focuses on an almost sinusoidal input current waveform with a higher power factor and regardless of the input condition whether balanced or distorted but their different principles.
The instantaneous power theory proposed by Japanese researchers [2] is inspired by the Direct Torque Control (DTC) proposed for asynchronous motors [3]. The Direct Power Control (DPC) strategy has received a lot of attention from researchers in recent years due to its many benefits. They have shown that the use of DPC in various converters and applications whether it be matrix
[4] or Voltage Source Converter (VSC) at two and three levels based on Fuzzy-Q-Learning algorithm is applied
[5] or on active filters [6] is more advantageous.
A DPC switching table has been formulated in which the appropriate switching states are selected from a predefined optimal switching table based on the digitized signals of the instantaneous errors between the commanded and estimated values of active and reactive power extracted by a hysteresis controller and the angular position of the voltage at the terminals of the converter thus guarantees a decoupled control of the powers and good dynamic performance [7].
However, the varying switching frequency results in broadband harmonic spectra, which complicates the design of line filters. To solve the downshift associated with variable frequency operation, various DPC algorithms have been developed for constant switching frequency. One can find various publications studies on how to fix the switching frequency of the DPC. The authors [8] suggest to associate the principle of the DPC with a vector modulation Space Vector Modulation (SVM) in order to obtain a switching frequency constant without the use of a switching table. Other authors [9] combine other technique with DPC to improve the result even more by using Sliding-Mode Control (SMC) it allows to obtain a stabilization response faster than that of the PI controller and a greater robustness. Backstepping improves transient performance [10]. The SVM modulation based on a predictive controller was developed in [11] and even the new method proposed by [12], called Multiple Switching Tables (MST-DPC), performs a real-time selection of the most suitable switching table among four alternatives depending on the operating conditions of the device.
The performance of conventional DPC under unbalanced and/or distorted input voltages deteriorates when this occurs. In recent years, researchers are increasingly interested in control methods to improve the performance of DPC strategies under unbalanced grid voltage conditions. Most solutions to improve the performance of three-phase Pulse Width Modulation (PWM) rectifiers are based on the extraction of the
© Z.E.Z. Laggoun, H. Benalla, K. Nebti
positive/negative voltage/current sequences. These solutions are complicated and difficult to implement for real-time applications since they require a great deal of computation.
In Virtual Flux-based (VF) methods, the VF space vector is obtained by integrating the voltage space vector. The use of a pure integrator induces a shift of the direct current in the estimated VF in order to remedy this drawback. Several methods of practical implementation of VF estimation have been proposed, with the aim of avoiding saturation of the estimated signals. This integration is generally performed via a First Order Low Pass (FLOP) filter to avoid the saturation and DC drift problems associated with pure integrators [13]. The DPC Control Based Virtual Flux (VF-DPC) uses the detected AC line currents and the estimated VF to calculate the input powers. However, FLOP filters lead to amplitude and phase errors. Although these errors can be minimized by reducing the cut-off frequency of the filter, this reduction leads to a reduction in the passband of the filter and therefore to a degradation of its dynamics. And for that, the authors [14, 15] propose a second order generalized integrator (SOGI) estimator exploiting the concept of virtual flow. Recent research in [16] presents a combination of two cascade filters to achieve a VF-based timing scheme, to ensure that the gate currents emulate the desirable sine waveform even when the supply voltage is unbalanced and/or harmonized.
Although the Grid Voltage Modulated Direct Power Control (GVM-DPC) is first introduced in [17], the main contribution of this paper is the proposal for an improvement in the technique using VF incorporated in a DPC scheme (GVM-DPC), for a three-phase PWM rectifier in our case. The results of the simulation of VF-GVM-DPC are compared with GVM-DPC under a polluted network which gives better performance than the classical method. The VF algorithm has an open loop structure and uses the fundamental orthogonal output signals which are obtained directly from the estimation of the fundamental active and reactive powers. This method provides quasi-sinusoidal input current waveform under different input voltage condition and achieves good stability, improves the performance of GVM-DPC.
The goal of the paper is the mathematical analysis and the numerical implementation of an improved method of grid voltage modulated based on direct power control for three phase pulse width modulation rectifiers.
The rest of the paper is organized as follows. In Section 2 the system modeling and the design of the GVM-DPC controls are presented. Section 3 shows the simulation results using MATLAB/Simulink. Finally, conclusions are given in the last Section 4.
2. Virtual flux grid voltage modulated direct power control.
2.1. Modeling VSC.
Figure 1 shows a simplified circuit of a two-level VSC connected to the grid with an LR filter all of these are considered ideal switches. The DC side could be connected to renewable energy sources or energy storage systems with a capacitor C and even at transmission scale High Voltage DC.
Fig. 1. Representation of a VSC connected to wind turbine generator
The relationship among the VSC output voltages, the grid voltages, and the output currents in the stationary reference frame by using the Clark transformation can be expressed as:
bf = R ■
+ L ^ Ï +
Uß = R ■ iß + L ■-
di
ß dt
(1)
+ V„
where Ua and Up indicate the VSC output voltage; ia and ip indicate the output currents; Vga and Vgp indicate the grid voltage in ap frame, and L and R are the filter inductance and resistance, respectively.
2.2. Modeling VF.
The concept of VF is based on the voltage integral and can be applied as an estimation method for voltage-sensor-less control of VSCs:
*aß = I U,
f Uaßdt = I
R ■ iaß + L ■-
di
aß
dt
+ V„
dt , (2)
where x¥aß is the estimated VF.
The use of the proposed Dual Virtual Flux Phase Locked Loop (DVF-PLL), based on the cascade of two adaptive filters illustrated in Fig. 2, is an optimized solution.
Fig. 2. The diagram of the proposed Dual Virtual Flux estimator
The DVF-PLL filter function is based on the estimated voltage and measurements current. First, the voltage reference signals are expressed in the stationary reference frame (ap). Then the resistive voltage drop included in the model is subtracted. The latter is shifted in phase (90°) and gains unity for the fundamental frequency used to estimate the VF components with the second-order-low-pass filters. The estimated components of the VF are separated in positive and negative sequences with the same transfer function as that used for the estimation of the VF components. By using the estimated VF components in the stationary reference frame, the flux angles can be estimated by using a conventional PLL. The cutoff frequency is equal to 50 Hz and only the positive
sequence is used to ensure adequate operation under faulty network conditions [16].
2.3 Fuzzy Controller for PLL. To have good PLL control performance, especially in case of voltage disturbance variation and load disturbance the PI controller will be replaced by a fuzzy controller. The schematic diagram of this control is given in Fig. 3.
Fig. 3. The PLL fuzzy control
The fuzzy regulator uses two inputs. He first input is the error between the reference and the measured value of the quadratic voltage Vq. The second one represents the variation of this error.
These two signals are expressed by:
je = Vqref («)" Vq (
[Ae = e(n)- e(n -1),
where e and Ae are the error of the quadratic voltage and its variation of the error.
For fuzzification, we used triangular membership functions for the error. We chose the seven fuzzy sets: NL (negative large), NM (negative middle), NS (negative small), ZE (zero), PS (positive small), PM (positive middle), PL (positive large). The rate of change AEw includes 3 fuzzy subsets, it is not necessary to subdivide it, because it is changing quickly in DPC. Output membership KP and KI, both contain four fuzzy subsets as shown in Fig. 4. There are total of 21 rules as listed in Table 1.
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Input variable "dEv"
0.005 0.01 0.015
Output variable "Ki"
a b
Fig. 4. The fuzzy membership functions of input (a) and output (b) variables
Table 1
Fuzzy rules
KP ^^ KI Em
NL NM NS ZE PS PM PL
AE N L M S M S M L
Z S M L M S Z
AE Z L M L Z L M L
Z S M L M S Z
AE P L M L Z L M L
Z M L L L M Z
respectively can be expressed as a function of variations in network voltage and output current as follows:
d dV
— = iß' ^ +
dP dt dQ I dt
= in
dt dt
diß ' dt diß ' dt
- in
dt
dVß
+ i
ß
dVß V da.
ß dt '
ß m diß --iß--•
dt ß dt
ß
(5)
If we consider a non-distorted grid, the following relationship could be obtained
2.4 Modeling DPC. Line current and VF components are used in power calculations. It should be noted that electrical resistance is included in the estimation process VF, they can be calculated by the following expressions:
[P = m-(wa-iß-Vß-n)
|Q = ®( ia+Vß-iß} ()
where P is the estimate active power. Q is the estimate reactive power; m is the angular frequency of the grid fundamental wave; Va, Vß, ia, iß are respectively the virtual flow and the currents in the reference aß.•
By deriving (3) with respect to time, instantaneous variations in active and reactive power dP/dt and dQ/dt
dV
dt
ß;
dV
dt
(6)
where rn = 2• n •f is the angular frequency of the grid voltage and f is the frequency of the grid voltage.
By substituting (4) in (5), the state-space model of the active and reactive powers is obtained as follows:
dP = -L-PQ + 7' ^(a-Uß+Vß Ua)-V2g )
= - R dt " L dQ „ R
dQ = „. p - LQ+L ( Uß + Vß •Ua\
(7)
where / \ ~Ta(t )" T1 sin(®j t+(h )
Tg =a2 -(Ta +Tp) Tp(( ) T1 cos(®j -1+01 )
2.5 Grid voltage modulated direct power control.
As mentioned in point (6), our main idea is to decouple the outputs from the inputs. The definition of the control inputs of the GVM is given as follows:
\oq =a-i^a-Ua+^p-Up)
The space-state model of the active and reactive powers becomes again as follows:
(8)
dP R n „ 1 / ,T,2Ï
-=-R..Pß+L
dQ n R „ 1
- = a- P---Q + —-OQ.
dt L L Q
(9)
A controller is designed to let the active and reactive powers track their references. Define errors of the active and reactive powers as follows:
(ep = Pref - P;
\eQ = Qref - Q,
where Pref and Qref are the active and reactive power references, respectively.
(10)
UP = Tg + R. P + L-a-Q + LoP ;
Feedforward Feedback
Uq =lO,.L-P + R-Q + L-Oq ,
Feedforward Feedback
(11)
where UP and Uq are the new control inputs; uP and uq are the feedback control inputs.
If the feedback control inputs are designed as follows:
Op = Pref + KP - eP + KP - J eP (()dt + KP - sgn(eP );
(12)
ISq = Qref + Kq ■ eQ + Kq - J eQ (i)di + Kq ■ sgn(eq ) 0
where &P and §q are the new control inputs; KP and Kq
are controller gains.
If we consider a non-distorted grid, the following relationship could be obtained
Ta-1 (( ) T1 sin(®1 -1 + t 01 )) " A) "
Tp-1(() T1 cos(a1-t+ 01 ) + Bo _
+ Z, (13)
with
Z = 1
n=2
Tn - sin(an -1 + dn ) Tn - cos(an -1 + 9n )
where is the magnitude of the «th term; mn its pulsation; 6n its initial phase; A0 and B0 are, respectively, the DC offsets of and is the magnitude of
fundamental components of the and
While the fundamental VF value is expressed as follows:
where ca1 and d1 is the magnitude components, pulsation and initial phase of fundamental.
Based on the grid voltage (13), the GVM inputs can be represented as follows:
Up UQ
sin(a-1 + di ) - cos(a-1 + ) cos(a-1 + &1 ) sin(a-1 + )
1 rt
T
P.
(15)
The original control inputs can be calculated as follows:
Ua =
UP =
Ta UP -TP 'UQ
T 2
Tg
TPUP - Ta • UQ T2
(16)
Figure 5 shows the block diagram of the proposed method.
Fig. 5. Structure of VF-GVM-DPC controller
3. Simulation results. In order to provide a complete comparison work, the classical control and the proposed method are exposed to disturbed voltages which are implemented with the help of MATLAB / Simulink software. In a first step, a voltage unbalance and injection of the 7th order harmonic are created and included in phase A at a cost of 20 %. Then, harmonics 5 and 7 with an amplitude of 20 % is applied. A voltage unbalance of 20 % and a 5th order harmonic of 20 % are created and included in phase A. Finally, which is the worst case that can occur with mains voltages, an asymmetrical disturbance with harmonics 5 and 7 with an amplitude of 20 % is applied. We define the power fluctuation and the total harmonic distortion (THD) factor of input current as comparative criteria to demonstrate the superiority of the proposed strategy using simulation results. During all simulations, the Qref is kept at zero to ensure the functioning of the Unit Power Factor, which is an indispensable criterion.
The two compared methods are simulated under conditions shown in Fig. 6.
The following simulation results are obtained using the values of the parameters given in Table 2.
100
100
0.44 0.46 0.48 0.5 0.5 0.52 0.54 0.56
c d
Fig. 6. The different voltage source condition applied to the rectifier: (a) - unbalanced and harmonic 7 to 20 %; (b) - harmonic 5 and 7 to 20 %; (c) - unbalanced and harmonic 5 to 20 %; (d) - harmonic 5 and 7 to 20 % asymmetric;
System parameters used in simulation
Table 2
Parameters Symbol Values Parameters Symbol Values Parameters Symbol Values
The resistance of reactors R 0.56 a DC-bus capacitor C 1100 |F Switching frequency F í sw 7500 Hz
Load resistance RL 68.6 a The line-to-line AC voltage E 85 V DC-bus voltage VDC 180 V
Inductance of reactors L 19.5 mH Frequency F 50 Hz Sampling period Ts 20 |us
Figure 7 shows the results for GVM-DPC:
• (a) - the bus voltage curve;
• (b) - the grid current;
• (c) - the estimated voltages Uap\
• (d) - the superimposition current i and voltage V in phase A;
• (e) - the active P and reactive Q powers.
üb 1ÖU & 175 O
>> 170
^ r < 5
C 0 0)
b -5
U
i i 1 1 1 1 1 1 1 —DC1-
___Y^ V V V V'TVTV^
1 1 1 1 1 1 1 t, s
iifipill WWM m$m M -X- b ^
0.2
100
> O
So »
c3
-50
„100
ftlíRl 'ñb/th ti \ ïïh fiht I * up
¿wwwwwWmW mm MM WWW
- i i i 3.2 0.25 0.3 0.35 1 1 1 0.4 0.45 0.; 1 ' H i 0.55 0.
1 _ -0- Va _ Ka^J y> Kf Kf t, s
0.25
-r~
0.35
—T~
0.45
-r~
AaaaaaaaAa^
-www<>iUUUL<>^
£ o Cu
CO
w
02 025 03 0.35 04 045
Fig. 7. The simulation results GVM-DPC
Figure 8 shows the results for VF-GVM-DPC:
• (a) - the bus voltage curve;
• (b) - the grid current;
• (c) - the estimated virtual flux x¥ap\
0.55
HZ
P(W) Q(Var)
hJV\J\!\J)hJ\\J№
• (d) - the superposition current i and the voltage V in phase A;
• (e) - the active P and reactive Q powers.
a
b
c
d
e
t, s -
1 1 1 1 1 1 1 DC U
1 r
1 1 t, s
P(W) Q(Var)
Fig. 8. The simulation result VF-GVM-DPC
The distribution of Fig. 7 is the same as that of Fig. 8. We can see in Fig. 7 the GVM-DPC which leads to fluctuations in the voltage curve of the bus. In addition, the grid current is affected by disturbed grid voltage conditions, with a high THD rate, which reduces the accuracy of the estimates of active and reactive power as can be seen in Fig. 7. In addition, the DC bus seriously oscillates around 5 V and the system does not operate under a unit power factor which is a very important criterion during our comparison.
On the other hand, we can see in Fig. 8 VF-GVM-DPC which gives us the current and the voltage are in phase. Although there are still some low order harmonics, we can observe that they have a limited influence compared to that of Fig. 7. The oscillations of the vector component of the estimated flux are sinusoidal and out of phase without disturbance and fluctuation.
Figure 9 shows the bus voltage stabilizers at about minus 2 V and the system is operating at unity power factor.
Figure 10 shows the difference between the application of an SRF-PLL and a PLL which operates on the basis of a fuzzy logic controller to detect the fundamental frequency positive sequence component of the mains voltage in unbalanced and distorted conditions as well as fast and smooth tracking.
/
3 2
1 2 3 - DC № - DC № - DC № til R Ui R* 1.5 til R"2 t, s
i/ 1
1 2 3 - DC w - DC iv - DC iv th L th L*1 5 th 1*2 t, s
Fig. 10. The difference between Synchronous Reference Frame
based Phase Locked Loop and proposed fuzzy-PLL
From Fig. 11 we can note that the THD rate of the network current has been improved compared to traditional control while respecting the standard of the electrical network. To highlight the contribution of the oscillatory terms, first of all, the results of the proposed control structure are shown in Fig. 2. The design and optimization process were carried out in the same manner as the procedure presented above. This result expressly shows how the components of the low order harmonics (5 and 7) with symmetrical and asymmetrical fault of the network voltage affect the network current. To summarize the results, Fig. 11 below presents an analysis based on the current THD of the VF-GVM-DPC strategies studied in this article.
■UJ UJ U.iJ U.O 7 U.O J \t.y U.7J
b
Fig. 9. System parameters influence on the evolution of the DC bus voltage: R (a); L (b)
a
b
c
e
t, s ::
t, s
a
Fig. 11. Fast Fourier Transform analysis showing THD in source current of the proposed method:
a) ideal network voltage conditions;
b) unbalance and injection of the 7th order harmonic;
c) injection harmonics 5 and 7;
d) an asymmetrical disturbance with harmonics 5;
e) an asymmetrical disturbance with harmonics 5 and 7
4. Conclusions.
This paper presented the mathematical analysis and the numerical implementation of an improved method of Grid Voltage Modulated based on Direct Power Control or we introduced them for three phase rectifiers. The main objectives of the proposed control strategy are to obtain sinusoidal input currents under different input voltage conditions and to maintain the DC bus voltage at the level required as part of the improvement of the wind chain.
In these situations, harmonic components appear on the grid voltage, which causes distortion and current imbalance if the power reference is kept constant. However, the use of the proposed Virtual Flux-Grid Voltage Modulated method has the same control structure as the classic Grid Voltage Modulated, except for the use of virtual flux instead of voltages, which results in the optimization of the cost, since the voltage sensors will not be used, which is based on the principle of disturbance rejection, makes it possible to obtain an input current of low THD compared to the conventional method.
The proposed control method could offer many advantages and allows to obtain good performances with a THD of 1.7 % under ideal conditions and during disturbances it varies between 2.06 % to 2.81 % which respects the standard, without forgetting with a load lower calculation, without it being necessary to specify the power calculation term, nor to extract the positive / negative voltage sequence. We can therefore say that this control method is able to improve the quality of the input current.
Conflict of interest. The authors declare that they have no conflicts of interest.
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Received 15.10.2021 Accepted 18.11.2021 Published 03.12.2021
Zakaria El Zair Laggoun1, PhD Student,
Hocine Benalla', Doctor of Electrical Engineering, Professor,
Khalil Nebti1, PhD, MCA,
1 Laboratory of Electrotechnics of Constantine (LEC),
Mentouri Brothers University, Constantine 1,
Campus Ahmed Hamani Zerzara,
Route d'Ain el Bey, Constantine, 25000, Algeria,
e-mail:
[email protected] (Corresponding author),
How to cite this article:
Laggoun Z.E.Z., Benalla H., Nebti K. A power quality enhanced for the wind turbine with sensorless direct power control under different input voltage conditions. Electrical Engineering & Electromechanics, 2021, no. 6, pp. 64-71. doi: https://doi.org/10.20998/2074-272X.202L6.09.
