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Power Stations, Grids and Systems
UDC 621.3 doi: 10.20998/2074-272X.2020.3.08
I. Boukhechem, A. Boukadoum, L. Boukelkoul, R. Lebied
SENSORLESS DIRECT POWER CONTROL FOR THREE-PHASE GRID SIDE CONVERTER INTEGRATED INTO WIND TURBINE SYSTEM UNDER DISTURBED GRID VOLTAGES
Wind turbines with permanent magnet synchronous generator (PMSG) are widely used as sources of energy connected to a grid. The studied system is composed of a wind turbine based on PMSG, a bridge rectifier, a boost converter, and a controlled inverter to eliminate low-order harmonics in grid currents under disturbances of grid voltage. Traditionally, the grid side converter is controlled by using the control VFOC (Virtual Flux Oriented Control), which decouple the three-phase currents indirect components (id) and in quadratic (iq) and regulate them separately. However, the VFOC approach is dependent on the parameters of the system. This paper illustrates a new scheme for the grid-connected converter controller. Voltage imbalance and harmonic contents in the three-phase voltage system cause current distortions. Hence, the synchronization with the network is an important feature of controlling the voltage converter. Thus, a robust control method is necessary to maintain the adequate injection of the power during faults and/or a highly distorted grid voltage. The proposed new control strategy is to use the direct power control based virtual flux to eliminate side effects induced by mains disturbances. This control technique lowers remarkably the fluctuations of the active and reactive power and the harmonic distortion rate. The estimated powers used in the proposed control approach is calculated directly by the positive, negative, and harmonic items of the estimated flux and the measured current without line sensor voltage. References 27, tables 6, figures 13.
Key words: direct power control based virtual flux, disturbances of grid voltage, permanent magnet synchronous generator.
Ветряные турбины с синхронным генератором на постоянных магнитах (PMSG) широко используются в качестве источников энергии, подключенных к сети. Исследуемая система состоит из ветряной турбины на основе PMSG, мостового выпрямителя, повышающего преобразователя и управляемого инвертора для устранения гармоник низкого порядка в токах сетки при возмущениях напряжения сети. Традиционно преобразователь на стороне сети управляется с помощью виртуального потокоориентированного управления VFOC (Virtual Flux Oriented Control), который разделяет трехфазные токи на косвенные компоненты (id) и на квадратичные компоннеты (iq) и регулирует их отдельно. Однако подход VFOC зависит от параметров системы Данная статья иллюстрирует новую схему для контроллера преобразователя, подключенного к сети. Дисбаланс напряжения и содержание гармоник в трехфазной системе напряжения вызывают искажения тока. Следовательно, синхронизация с сетью является важной особенностью управления преобразователем напряжения. Таким образом, надежный метод управления необходим для поддержания адекватной подачи энергии во время неисправностей и/или значительно искаженного напряжения сети. Предложенная новая стратегия управления заключается в использовании виртуального потока на основе прямого управления мощностью для устранения побочных эффектов, вызванных помехами в сети. Этот метод управления значительно снижает колебания активной и реактивной мощности и уровень гармонических искажений. Оценочные мощности, используемые в предлагаемом подходе к управлению, рассчитываются непосредственно по положительным, отрицательным и гармоническим элементам оцененного потока и измеренного тока без напряжения линейного датчика. Библ. 27, табл. 6, рис. 13.
Ключевые слова: виртуальный поток на основе прямого управления мощностью, возмущения напряжения сети, синхронный генератор с постоянными магнитами.
Introduction. Renewable sources connected to a grid with their inherent intermittent behavior inevitably impose a major challenge to the conception of the controller voltage source converter. The majority of control approaches have equivocal statements according to their performance under conditions of non-ideal voltage grid prevailing in an integrated micro-grid system with renewable energy. Renewable energy production has become a significant development trend for contemporary grids because of environmental concerns. Wind energy is one of the important sources of renewable energy and is a fast-growing technology [1, 2]. There are two types of wind energy systems: the grid-connected system and the stand-alone wind system. Actually, the application of grid-connected is largely preferred to stand-alone wind systems. The most common configuration for MWT systems connected to the grid of less than 20 kW normally consists of a high-pole-pair PMSG supplying a three-phase rectifier followed by a boost converter and an inverter [3]. At the generator terminals, a diode bridge rectifier can be used since no external excitation current is required. The non-controlled rectifier with a boost
converter or supercharged converter serves to regulate the rotor voltage or speed. The interfaces between renewable energy sources and a grid-side have played a crucial role in terms of reliability, the flexibility of connection, and quality of energy and gradually attracted attention from the academic and the industrial worlds these last years. These interfaces can regulate the powers with a constant power factor or constant currents. Various studies of these electronic power interfaces and control methodologies have been largely realized, including the development of schemas of switching to improve the quality of the energy
[4]. Traditionally, the grid side converter is controlled by using the control VFOC (Virtual Flux Oriented Control)
[5] or VOC [6], which decouple the three-phase currents in Direct components (id) and in quadratic (iq) and regulate them separately. A reference frame aligned with the rotary vectors voltage or virtual flux [7]. However, the VFOC or VOC approaches are dependent on the parameters of the system and various simplifying approximations are made; for instance, the magnetic saturation of the inductor is not considered that is, the
© I. Boukhechem, A. Boukadoum, L. Boukelkoul, R. Lebied
inductor is constant whatever of the current values [8]. The three-phase rectifier control approaches in width of impulse can be classified, as quoted in the literature, as vector control (VOC) and direct power control (DPC) [16]. The vector control (VC) can be based on grid side voltage [17-19] or virtual flux (VF) [20] using integral proportional controllers (PI). However, it offers some disadvantages, such as its addiction to the variation of system parameters, and that its performance largely depends on the agreement of the PI parameters. The direct power control strategy (DPC) has become one of the most recent research topics in recent years relying on its fast dynamic response, its a simple structure, and its high power factor [21, 22]. In DPC schemes developed, instant active and reactive powers are directly controlled [24]. This is what we need more than sensors (voltage sensors and AC mains sensors) that not only raises the volume and cost of the system but also lowers the reliability of the system [22]. The grid-connected three-phase rectifier can be seen as a virtual AC motor, its virtual flux link can be used to estimate the voltage of the rectifier [26]. Virtual flux (VF) based schematics are popular in voltage-free controller designs for the following two reasons. The application of VF remains the common benefits of sensorless strategies, such as cost reduction, reliability, and overall improvement. During this time, it eliminates the orientation point limitation for the control system [25] and improves the harmonic tolerance [26]. A more complete comparative study is conducted to evaluate the performance of the system in different grid voltage conditions where the voltage unbalances vary by up to 20 % and the distortion varies by 10 %. The global
magnitude of total harmonic distortion (THD) presented by VF-DPC and the resilient direct power control RV-DPC is always inferior to that of V-DPC [15]. The V-DPC possesses a low immunity to asymmetric and deformed voltage; the VF-DPC shows a better reliability only under distorted grid voltage [15] a new method of VF-DPC control based on the virtual flux estimate Capable of handling these problems; it results in a stable and regular estimated virtual flux with a sectorial detection at a high precision [23].
The aim of this article is to inject all the power provided by a wind turbine based on the PMSG is a three-phase microgrid subjected to various voltage conditions. This document also seeks to propose a new strategy by integrating new theory, Direct Power Control, based on the virtual flux (VF_DPC) to ensure that the injected currents in the three-phase grid emulate the sinusoidal forms even when the grid voltage is no longer ideal.
Modeling Of The Wind Conversion. In the suggested system of energy, the PMSG is plugged to the grid through an inverter assisted by a rectifier bridge and a boost converter (Fig. 1). The rectifier consisted of diodes that convert the AC output voltage from PMSG to a DC voltage. The boost converter increases the output rectifier voltage at a regulated DC level. The boost converter regulates the speed of the generator or the active power of the generator to capture the maximum power of available wind energy. The grid-side converter (GSC) is then utilized to control the DC link voltage and transfer all the active power provided by the turbine to the grid.
Dioilc'^liridst' Boost converter Grid Side converter
""""" W-t—e*-
Cdc
-A/V- L Filter
Fig. 1. The system under study comprising PMSG assisted with diode rectifier and boost converter
Wind Turbine Modeling. The wind turbine is three-dimensional, with complex shapes in movement, inundated in a stream air; it changes over the wind's motor vitality and conveys mechanical force portrayed by a rotating speed and mechanical torque. The dynamic force accessible to the turbine is given by:
P» = 2 FsSVl = | pnR V, (1)
where p is density of air (1.25 kg/m3), S is area swept by the turbine (m2), R is turbine radius (m), Vm is wind speed (m/s).
Aerodynamic shaft power is given by:
Pturb = CpPm = 1 pnR VCp (A, 0), (2)
where Cp is the power coefficient which is a function of the pitch angle of rotor blades and of the tip speed ratio; 0 is orientation angle of the blades; A is specific speed
A =
aturbR
Vm
(3)
where aturb is speed of the turbine.
Modeling of PMSG. The model of PMSG in d-q transformation is given by the accompanying voltage framework condition
Vd = -RsId - Ld dJd +aLnIn;
dt
d
(4)
Vq =~RsIq - Lq~tI9 + ®LdId + ®Pf.
(5)
The electromagnetic coupling
pd = Ld'd+Pf ;
{Pq = Lq'q,
where Ld is stator inductance in d-axis, Lq is stator inductance in q-axis, Lq and Ld are supposed independent of 0, pf is magnet flux.
Equation (6) represent the expression of electromagnetic torque:
Vd RsId Cem
= f p\Ld-Lq )tfq + iqPf
d~tId + ^LqIq; (6)
Vq =- RsIq - LqdtIq + WLdId + W(Pf,
in which Cem = 312-p-cpf -Iq, where p is the pole pair number; Rs is stator resistance; Vd and Vq are stator voltage components; Id and Iq are stator current components.
Control Of Boost Converter. At the output of certain renewable sources (such as wind systems) in general, the voltage generated is not enough to ensure the proper functioning of the inverter. For this, a DC/DC boost converter must be used, built with electronic semiconductor devices, an inductor and a capacitor in parallel [12]. The wind generator is tied to a boost converter, and its input voltage is controlled so that the wind generator delivers the maximum power to its output terminals. The boost converter is connected between the output terminals of the non-controlled rectifier and the input of the inverter, as shown in Fig. 2.
Fig. 2. Structure and principle control of an AC / DC converter
The essential role of the boost converter is to convert the variable input DC voltage, due to different operating conditions, to a suitable constant DC voltage. The DC link voltage can be maintained constant at the reference value by adjusting the duty cycle of the converter. In doing so, the DC voltage is controlled to sufficient and non-fluctuating levels so that maximum power is injected under better conditions through the grid side inverter. The control framework of the DC-DC boost converter is founded on the use of the PI controller to keep the DC link voltage at the reference value as shown in Fig. 2. The voltage/current input/output relationship of the boost converter can be written as [13].
Direct Power Control Based On Virtual Flux (VF_DPC). In this situation, the direct power control based on the virtual flux (DPC-VF) is used instead of the direct power control (DPC). This control technique greatly lowers the fluctuations of the active and reactive power and the harmonic distortion rate THD, keeping the advantage of control without the line voltage sensor. In the VF concept, the virtual AC motor is assumed from the behavior of grid voltages and AC side coupling impedance with inductance L in series with equivalent resistance R. As a result, L and R are analogous to the leakage inductance and the stator resistance of an AC motor, respectively [26]. The control of the active (Pref)
and reactive (Qref) power are compared with the estimated active and reactive power values (Pes and Qes) by hysteresis controllers, respectively. The output digitized signals (SP) and (SQ) and the vector position (09) make it possible to select the appropriate voltage vector according to the switching table defined in [24].
Figure 3 shows the maximum power point tracking (MPPT) control charts for the optimal torque control method respectively. The torque reference multiplied by the speed of the turbine (wt) gives the optimal power reference. As shown in Fig. 3, the maximum power of the wind turbine is calculated from the equation [Pref = Tre/-wt] which represents the power reference injected into the grid.
0)t i
COt
Fig. 3. Block diagram of MPPT Optimal torque control
Model of Grid Side Converter. The vector of virtual flux can be estimated from the integration of the vector of grid voltages eap as indicated follow in equation (8).
The voltages of the converter (Fig. 4) are estimated in the block ais follows
V =
v sa
Vsj
Vdc *(Sa ~{Sb + Scft
= ^Vdc x(Sb - Sc ),
(7)
where Sa, Sb, and Sc are the switching states of the rectifier and (Vsa, Vsf) are the AC side voltages of the converter. Vdc is rectified voltage.
The components of the virtual flux are calculated as follows:
' dla
dt
(Psa = J(Vsa+ L^dda~)dt ;
<Psp = J (Vs^+ L^jL )dt
(8)
dt
where Vs^ap) is the voltage at the output of the inverter at the a, P mark; ia and ip are grid currents in the Concordia.
AC-Side L R eb
/YYYMA/V—©—I
L R ec '
Fig. 4. Simplified representation of a three-phase PWM inverter
The virtual flux concept has been developed for a better estimate of instantaneous active and reactive power in AC-free sensor operation. The use of an ideal integrator for computing the virtual flux produces a DC offset. According to (7) and (8) the integrator can be used to
estimate the virtual flux, but the initial value of the flux has to be estimated first, this complicates the simulation and the DC offset could be produced easily [14]. The virtual line stream observer (Fig. 5) shows that the new algorithm responds faster than traditional control.
Vsp N N
S+Wc S+Wc •I
(9)
Fig. 6. Virtual flux plane 12 sectors The position of the VF vector
dN = tan
Psp
Psa
is used in the VF-DPC scheme to select the appropriate converter voltage vector according to the switch table defined in Table 1.
Table 1
Switching Table
Sp 01 02 03 04 05 06 07 08 09 010 011 012
1 0 V5 V6 V6 V1 V1 V2 V2 V3 V3 V4 V4 V5
1 V3 V4 V4 V5 V5 V6 V6 V1 V1 V2 V2 V3
0 0 V6 V1 V1 V2 V2 V3 V3 V4 V4 V5 V5 V6
1 V1 V2 V2 V3 V3 V4 V4 V5 V5 V6 V6 V1
according to the theory of symmetrical decomposition, an unbalanced and distorted three-phase system can be decomposed into three symmetrical components: the positive sequence, the negative sequence, and the zero sequence.
In fixed reference systems the flux and the measured current are expressed as
sa = (Psa ~^Psa ^^j«)'
(10)
Fig. 5. The virtual line flux linkage observer
The active and instantaneous reactive powers are observed in the (power observer block) by the measurement of the line current and the observation of the virtual flux components in equation [9]. Instant active and reactive powers can be estimated as
|Pes = a(Psa x V ~PsP X 'sa )'
\Qes = a(Psa x 'sa + Psp x 'sp ).
There is a change in the sector. These sectors may be expressed as follows (Fig. 6)
T n
(N - 5)— X eN X (N - 4)—.
6 6
Psp =\ptp+psp+phsp)
'sa ('sa +'sa +'sa)
'sp = (p + 'sp + 'hP )
(11)
According to the theory of symmetric decomposition:
[ Xa
" X+" 1 1 a a2
X - = 3 1 a2 a
Xb Xc
(12)
here the indices (+) and (-) indicate the positive sequence
' 2T
}
the zero sequence
and the negative sequence, a = e is X = X - X+ - X-.
After substituting the flux and the current by their values indicated in (10) and (11), the results of the active and reactive powers can be grouped as follows
Pes = ax
P P ■ Phi)x(l+ '- 'h
Ps a + Psa + Psa )x ¡(.IP + 'sp+ ''sp )-(P + P~sp + PhSp )x )(a + ha + ''sa )
(P+a x '+p - P+p x '+a )+ [Pa x '-p - P-p x ha )+
I h h h h \ I + ^ + ^ ^ + Psa x 'sp - Psp x 'sa)+ Psa x 'sp - Psp x 'sa)+
+ (P+a x 'p - P+p x 'sa )+ (sa x '+p - Psp x '+a )h
I - h - h W h ■+ h ■+ ^
+ [Psa x 'sp - Psp x 'sa)+ Psa x 'sp - Psp x 'sa)+ + (ax hp-Phspx 'sa)
(13)
Qes =ax
+ - h IPsa + Psa + Psa
Qes = ® x
)x (''sa + 'sa + 'sa )+
(P+p +P-p +Psp)x ((p + hp + 'kspp
Cp)+(Pax lsa + P-px 'sp)+ )+)P+ax 'sa + Psp x hp) )+(ax 'sa + Psp x '+p)
Psa x 'sa + Psp x Í t
+ (P(ax sa + P%x 'sp)+(ax sa + Pspx 'sp+ + (sax 'sha + P+spx 'sp)+(Psax 'sa +Psp x 'sp +
■ h , - -h I . I h ■+ , h p+P
+ Psax sa + Pspx 'sp+Psax sa + Pspx 'sp+
h - h -+ Psax 'sa+Pspx 'sp
(14)
The target control of the DPC strategy is to eliminate the negative and harmonic components of the current, so we can force
Modified Direct Power Control (M DPC) for Converter. When the grid is unbalanced and harmonized,
'sa 'sp 'sa 'sp 0 .
hp
(15)
Leading to
Pes = ® x
+
Pneg = cxWsax lsß'
Psß
x iç
Q
neg
:cx№sax l+a+P-ßx l+ß
(16)
where Pneg and Qneg represent the interaction between the negative sequence and the positive sequence of flux and currents that generate oscillation in active and reactive power with a frequency of 2œ.
So we have
Phar = cx Ua x Cß -
x i„
Qha
■■ cox
h •+ fPsa x lsa
h •+ + Psßx l
sß
(17)
where Phar and Qhar represent the interaction between the harmonic parts of the flux and the positive sequence of the currents.
It can be seen from equations [16, 17] that if we want to eliminate the effect of the negative and harmonic components of the unbalanced and deformed grid, the active and reactive power of compensation can be obtained as
Pcom = cxWsax lsß '
h •+ fsa x lsß ' h+
h+ ■ psß x lsa
(18)
Qcom =cx Wsa x lsa + Psß x lsß+ psa x lsa + Psß x lsß
Figure 7 shows the overall configuration of the direct power control without a voltage sensor based on the virtual flux.
Fig. 7. Control block diagram of the grid-side converter
of the wind turbine
Simulation Results. In order to verify the performance of the optimal VF-DPC proposed on a two-level voltage source inverter, simulation studies were performed in the Matlab/Simulink environment under various grid voltage conditions. All the results are obtained at the maximum power Pre/[W] and Qrf of 0 [VAR].
The simulation model is Kollmorgen 6 kW industrial synchronous machine [27]. The values of the turbine and the PMSG used parameters are given in Appendix in Table A.1 and Table A.2. The converter power and its monitoring algorithm are also implemented and included in the model. The sampling time used for the simulation is 2-10-5 s.
Test 1. Maximum Power Generation injected.
In this test, the purpose of the algorithm is to follow the
developed permanent
from a magnet
maximum power of the system. Fig. 8 and 9 show several results obtained.
Figure 8 shows the system response for a gradual change in wind speed from 9 m/s to 7.5 m/s to 8 m/s then back to 9.5 m/s. It can be seen in Fig. 8,d that the electromagnetic torque of the generator Tg also follows the reference torque of the turbine Tm. Figures 8,c and 8,e show that the voltage of the PMSG varies with wind speed as well as the DC voltage at the output of the rectifier. Figure 8,f shows that the current is controlled according to the MPPT strategy and can be better regulated to reach the optimum current. Figure 8,g illustrates that the DC capacitor voltage (Vdc) reaches its reference quickly to 700 V using the proposed power factor correction controller (PFC). The PFC attests its capability to give a fast response time and to pursue the reference voltage regardless of the variation in wind speed.
Figure 9 shows the performance of the converter with a balanced and free-harmonic voltage (Fig. 9,a and 9,6). Figure 9,c and 9,d exhibit that the injected current in
the range is controlled to be sinusoidal and balanced. Figure 9,g and 9,h indicate that the estimated active and reactive powers are identical to the measured power.
Fig. 8. System response for a change of wind speed at 9 m/s to 7.5 m/s to 8 m/s to 9.5 m /s: (a) rotor speed; (b) output power; (c) voltage generator; (d) torque reference and generator electromagnetic torque; (e) output voltage rectifier; f current boost converter; (g) voltage boost converter; (h) zoom of voltage boost converter
This indicates that the applied virtual flux DPC has high performance. The injected currents rise and drop according to the variation of the wind speed and thus the
power. It can easily be shown that the dynamic response for a brusque change in the speed level is preferable for the proposed system.
Tlrae[s]
Fig. 9. Performance of the VF_DPC in a balanced and non-distorted grid during different periods of wind variation: (a) grid voltage; (b) zoom grid voltage; (c) grid current injected; (d) zoom grid current; (e) current injected with the grid voltage; (f) the estimated active and reactive power; (g) the active power estimated at the measured power; (h) the reactive power estimated at the measured reactive power
Test 2. Simulated Transient Responses in Various Grid Voltage Conditions.
1. Without Compensation. In order to check the implementation of the VF_DPC on a two-level voltage source inverter, simulations were performed under various grid voltage conditions. Four grid voltage states are applied. Initially, the main voltages are balanced and sinusoidal, afterward, a voltage unbalance of 30 % is created. secondly, the amplitude of each phase voltage is
restored. But, the 5th and 7th harmonics with an amplitude of 20 % are added to the fundamental. Hence, the grid voltages are balanced but distorted. Finally, the worst case of grid voltages, both unbalanced and distorted of 20 % and harmonic 7th of 20 %, is also included in the last condition. The curves in Fig. 10 are three-phase mains voltages, three-phase mains currents, active and reactive power. For further justification, comprehensive quantitative analyses were performed for grid voltages
P[W]-Q[VAR] grid current[A] grid voltage[V]
е. a
5*
m
Table 3
Currents THD
Case Balanced Unbalanced 30 % Distorted 5th and 7th 20 % Unbalanced and distorted 7th 20 %
THD 1.7 % 1.73 % 0.25 % 2.26 %
From Table 3, it is clear that the proposed control satisfactorily compensates for distortions and imbalances under all three-phase grid conditions demonstrating the superiority and performance of the proposed control.
0.3 Time[sl
Fig. 12. Performance of the proposed VF_DPC in an unbalanced and distorted grid during different periods of wind variation: (a) grid voltage and current injected; (b) active power compensation; (c) reactive power compensation; (d) reactive and active power estimated and injected into the grid
Figure 12,d reveals that both active and reactive powers are well controlled. The reactive power is controlled to be zero to get a unity power factor. Figure 12,b and 12,c show the estimation block response of compensation powers. The use of this control process removes the effect of harmonic content and unbalanced voltages on the currents. We also note that the compensating powers of the distorted part are almost null in the case of harmonics in voltages, Figure 12,b and 12,c) [0.3 s 0.55 s].
The following relations show how to compensate with only negative power. We have
Phar — ax [fSa x 'S+ß - x '+a )\ = 0;
Qhar — ax
So, it becomes
[a
üS+a + Ppx 'S+ß\
Vsß
Sa x 'sß -Vsß x 'sa)\;
= 0.
Pcom =®x [(psa x iß- - x '+
Qcom — ®x
+ +r" +
sa x 1
Figure 13 shows the simulation results with only negative power compensation.
0.3
Time[s]
Fig. 13. The performance of VF_DPC with only negative power compensation: (a) grid voltage; (b) grid current; (c) active and reactive powers
Figure 13 shows that this method (compensation with negative powers) gives almost the same results similar to the previous method in terms of THD as shown in Table 4, except that a delay in response is estimated for one period. This is shown in Figure 13,6.
Table 4 presents the THD percentage of two periods of each condition applied.
Table 4
Currents THD
Case Balanced Unbalanced 30 % Distorted 5th and 7th 20 % Unbalanced and distorted 7th 20 %
THD 1.7 % 1.9 % 2.22 % 2.53 %
Conclusion.
This article proposes a strategy of controlling a micro wind turbine based on a PMSG by injecting maximum power and adapting to all disturbances that occur in the grid.
For this, a new control strategy VF_DPC is suggested for the grid converter. Thanks to the efficiency of the proposed controller, the three-phase grid currents are effectively regulated to be balanced and sinusoidal with very low direct current component despite deformed and unbalanced grid voltages. All the results are obtained at the maximum power of the wind turbine Pref [W] and Qf of 0 [VAR].
The total harmonic distortion and the direct current component of the grid current are still kept very low and completely comply with European Standard (EN 50160) and IEEE Standard 519.
The simulation results gave 2.26 % for umbalanced and distorted voltage. In addition to good steady-state performance, this controller also provides a very fast dynamic response under the reference variation. The use of this control process removes the effect of harmonic content and unbalanced voltages on the currents.
The proposed current control scheme can be implemented without the need for grid-side voltage sensors; it can be easily integrated into the grid with reduced cost.
APPENDIX
Table A.1
Parameters of wind turbine
Parameter Symbol Value
Power P, 7.5 kW
Radius R 3.24 m
Rated wind speed N 296 rpm
Wind speed range V t- V y cut-in y max 4-12 m/s
Inertia J, 7.5 kg-m2
Friction coefficient B, 0.06 N-m-s/rad
Micro grid parameters: Vrms = 230 V, Rs = 0.1 Q, Ls = 0.01 H, N = 50.
Table A.2
Parameters of PMSG
Parameter Symbol Value
Rated power Pg 6 kW
Rated torque Tg 40 N-m
Rated current I 12 A
Rated speed v 153 rad/sec
Number of poles P 10
Magnet flux linkage pm 0.433 Wb
Armature resistance Ra 0.425 Q
Stator inductance Ls 8.4 mH
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Received 10.02.2020
Ismail Boukhechem1, Ph.D.,
Ahcen Boukadoum1, Doctor of Electrotechnical, Professor, Lahcene Boukelkoul1, Doctor of Electrotechnical, Rima Lebied1, Ph.D.,
1 Electrotechnical Laboratory Skikda (LES),
University 20 August 1955,
26 Road El Hadaiek 21000, Skikda, Algeria.
e-mail: [email protected],
How to cite this article:
Boukhechem I., Boukadoum A., Boukelkoul L., Lebied R. Sensorless direct power control for three-phase grid side converter integrated into wind turbine system under disturbed grid voltages. Electrical engineering & electromechanics, 2020, no. 3, pp. 48-57. doi: 10.20998/2074-272X.2020.3.08.
