Vector Control Strategy for Maximum Wind-Power Extraction of a Grid-Connected Wind-Driven Brushless Doubly-Fed Reluctance Generator Mohamed G. Mousa, S. M. Allam, and Essam M. Rashad, senior member IEEE Department of Electrical Power and Machines Engineering, Faculty of Engineering, Tanta University, Egypt E-mail:
[email protected],
[email protected] and
[email protected]
Abstract—This paper proposes a vector-control (powerwinding flux orientation) strategy for maximum wind-power extraction of a grid-connected wind-driven Brushless DoublyFed Reluctance Generator (BDFRG) system. The adopted generator has two stator windings namely; power winding, directly connected to the grid, and control winding, connected to the grid through a bi-directional converter. In addition, a unity power-factor operation is also provided based on the proposed vector-control strategy. Moreover, a soft starting method is suggested to avoid the over-current of the bi-directional converter. A sample of the obtained simulation results is presented to check the effectiveness of the proposed strategy.
, ,
:
dq-axis power-winding currents, A
: : :
gearbox ratio power and control winding resistances, Ω electrical angle of the power-winding flux vector, rad. dq-axis control-winding flux linkages, V.s/rad. dq-axis power-winding flux linkages, V.s/rad. amplitude of the power-winding flux vector, V.s/rad. mechanical angular speed of reference frame, rad./s electrical angular frequency of power winding, Hz BDFRG mechanical rotor angular speed, rad./s wind turbine blade radius, m blade pitch-angle, degree air density, kg/m3
,
:
,
: :
Keywords—Brushless doubly-fed reluctance generator; wind energy conversion system; soft starting; vector control; maximum wind-power extraction
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I. NOMENCLATURE
:
L
: ,
:
,
: : : :
peak mutual inductance between power and control windings, H wind turbine and BDFRG friction coefficient, N.m.s/rad. wind turbine and BDFRG moment of inertia, kg.m2 leakage inductance of control winding, H leakage inductance of power winding, H
:
magnetizing inductance of control winding, H magnetizing inductance of power winding, H power-winding three-phase voltages, V
, ,
: :
dq-axis control-winding voltages, V dq-axis power-winding voltages, V
,
: : :
wind speed, m/s power and control winding frequencies, Hz power-winding three-phase currents, A
:
dq-axis control-winding currents, A
: ,
,
, ,
,
978-1-4673-9130-6/15/$31.00 ©2015 IEEE
: : : :
II. INTRODUCTION Due to the cost increase, limited reserves, and adverse environmental impact of fossil fuels [1], the development of renewable energy sources has been attracting a great attention from researchers. Wind Energy Conversion System (WECS) is one of the top growing renewable energy technologies in the world [2]. The wind energy has proved to be a clean, abundant, and completely renewable source of power. Therefore, it is economical to use the wind energy in producing electric power especially in rural areas [2]. The wind turbine is a very effective component in WECS that converts the wind kinetic-energy into mechanical energy that can be used to derive an electrical generator. The windturbine generator converts the output mechanical energy of the wind turbine into electric power and can be connected either to stand-alone loads or connected to the utility grid. The
squirrel-cage induction generator, doubly-fed induction generator and synchronous generator are the most common generators that have been used in WECS [1]. Wind turbines can be classified into fixed-speed and variable-speed turbines. The main drawback of fixed-speed turbines is that the maximum power-conversion efficiency can be achieved only at a certain wind speed. However, variable-speed wind turbines can achieve maximum power-conversion efficiency over a wide range of wind speeds, since the turbine can continuously adjust its rotational speed according to the wind speed [1]. In order to make the turbine speed adjustable, the wind-turbine generator is normally connected to the utility grid through a power electronic converter. The power rating of the converter is normally the same as that of the generator. This results in increasing the overall system cost [3].
and the secondary winding (called the control winding with pole-pairs) is connected to the grid through a bi-directional acdc-ac converter. The conceptual diagram of the BDFRM is shown in Fig. 1.
Brushless Doubly-Fed Machine (BDFM) is a special form of slip recovery machines that reduce the capacity of the required converter to be used if the required speed-control range is limited. This will lead to a significant reduction in the drive-system cost [4]. Therefore, the use of this type of machines would be a cost-effective one that should be used in variable-speed WECS. The Brushless Doubly-Fed Induction Machine (BDFIM) and the Brushless Doubly-Fed Reluctance Machine (BDFRM) are the two main competitors attracting most of the attention from researchers [5]. The rotor design of both BDFIM and BDFRM ensures robustness, reliability, and maintenance-free operation. However, the efficiency of the BDFRM is expected to be superior to the BDFIM due to the lack of rotor copper losses [5]. Therefore, the Brushless Doubly-Fed Reluctance Generator (BDFRG) is found to be the most attractive one for variable-speed WECS.
The ' ' signs denote the same (+ve. sign) and opposite (ve. sign) sequence of the control winding with respect to that of the power winding respectively.
The background and fundamental structure of the BDFRM was described in [6]-[7]. In addition, the machine dynamic model has already been established in [7] based on the space-vector theory. On the other hand, some research works have concentrated on the development of BDFRG in WECS [8]-[9]. Moreover, in order to extract the maximum power from the wind turbine, different control techniques are proposed [8]-[9]. Among them, the vector-control technique which is considered to be one of the most favorable control strategies for high performance operation [9]-[10]. This control technique offers the control of both the electromagnetic torque and the reactive power of the generator in a completely decoupled fashion [10]. In this paper, the vector-control technique is suggested for maximum wind-power extraction under wind-speed variations of a grid-connected wind-driven BDFRG system. In addition, a soft starting method is presented to avoid the converter overcurrent. III. MAIN CONSTRUCTION OF BDFRM The BDFRM has two stator windings with different number of poles in order to avoid direct transformer coupling between the two windings. In addition, the stator windings must differ by more than one to avoid unbalanced magnetic pull on the rotor [5]. The primary winding (called the power pole-pairs) is directly connected to the grid winding with
The number of poles of the reluctance rotor is governed by the summation of the pole-pairs of the two stator windings in order to get a rotor position dependent mutual coupling between the two stator windings. The resultant mutual inductance variation with rotor position causes a change of coenergy as well as torque production [5]. The electromechanical energy conversion can occur only at a particular speed [6]. This speed is given by: 2
1
Fig. 1. Conceptual diagram of the BDFRM
IV. GRID-CONNECTED WIND-DRIVEN BDFRG SYSTEM Fig. 2 illustrates a simple configuration of the proposed grid-connected wind-driven BDFRG system. The wind turbine is mechanically coupled to the rotor shaft of the BDFRG through a step-up gearbox.
Fig. 2. Grid-connected wind-driven BDFRG system
Due to a reduced power rating of the control winding converter, the starting current of the control winding should be limited below the rated value of the used converter. In order to achieve a good soft starting, the BDFRG is started as an induction machine by shorting the control winding terminals using the auxiliary switches S1 and S2 shown in Fig. 2. In other words, S1 is closed and S2 is opened during this period up to reaching a speed approximately equals the rated value. Then, the bi-directional converter is switched into the control windings by closing the switch S2 and opening the switch S1. In order to enable the bi-directional power flow between the grid side and the control winding, the grid-side converter, shown in Fig. 2, should be controlled. A step-down transformer, shown in Fig. 2, is required to match the voltage
level between the DC link and the grid-side terminals. The main objective of the grid-side converter is to keep the DC link voltage at a constant appropriate level regardless of the magnitude and direction of the control-winding power. A. Wind Turbine Characteristics The wind turbine is used to convert the kinetic energy associated with the wind energy into mechanical energy. The mechanical power captured from the wind energy by the wind turbine can be expressed as [11]: ,
0.5
7
where 8
2
The turbine tip-speed ratio,
is given by: 3
9 In addition, the corresponding flux linkage relations are given by:
can be In addition, the wind-turbine power coefficient, written, in terms of the turbine tip-speed ratio, λ and the blade pitch-angle, β as [11]: ,
0.5176
116
10
21
0.4
5
0.0068
where 4
where 1
1 0.08
0.035 1
11
5 L
The mechanical output torque of wind turbine is given by: 6 Fig. 3 shows the characteristics of the wind turbine power coefficient with the tip-speed ratio at different values of the blade pitch-angle. It is clear from the figure that there is a certain value of the tip-speed ratio at which the power coefficient is maximized. This value is known as the optimal value of the tip-speed ratio, λopt. Hence, a maximum mechanical power can be obtained from the wind turbine.
Among the possible electromagnetic torque expressions, the following can be chosen for its importance from the view point of vector control [10]: 12 The electromechanical equation of the overall wind-driven BDFRG system referred to generator side can be expressed as: 13 On the other hand, the active and reactive power expressions of the power and control windings are given by: 14 15 16
Fig. 3. Characteristics of the wind-turbine power coefficient with the tipspeed ratio at different values of the blade pitch-angle
B. System Dynamic Modeling In an arbitrary reference frame, the BDFRG dq-model is expressed as [3]: The dq-axis voltage equations of the power and control windings can be written as:
17 V. PROPOSED VECTOR-CONTROL STRATEGY One of the most important advantages of the vectorcontrol technique applied on the BDFRG is that the electromagnetic torque and the reactive power of the power winding can be achieved in an inherently decoupled fashion [10]. Generally, the vector control of the BDFRG is based on
with the dthe alignment of the total power-winding flux, axis of the power-winding flux. In other words and based on this flux orientation, the d-axis component of the powerwinding flux, and the total power-winding flux, are ) and the q-axis component of the powerequal ( equals zero ( 0). Fig. 4 shows the winding flux, phase-axis relationship of the BDFRG in the case of the proposed power-winding flux orientation. Therefore, it can be stated that the main principle of the power-winding flux orientation is the estimation of the total power-winding flux vector.
Based on the proposed power-winding flux orientation, the following importance expressions, aiding with (12) and (15), can be easily obtained. 22 23 It can be clearly observed from (22) that the instantaneous electromagnetic-torque control can be easily achieved via controlling the q-axis control-winding current, . Moreover, equation (23) proves that the reactive-power control of the power winding is realized by controlling the d-axis control. This is attributed to the approximately winding current, as a result constant level of the total power-winding flux, of the direct connection of the power-winding terminals to the grid-side terminals. It can be concluded from (22) and (23) that the machine electromagnetic torque and the reactive power of the power winding became completely decoupled based on the proposed power-winding flux orientation technique. In this paper, the proposed control technique is used to extract maximum power from the wind turbine under different wind-speed variations.
Fig. 4. Phase-axis relationship of the BDFRG for the proposed powerwinding flux orientation
In order to estimate the magnitude and the angle of the power-winding flux vector ( and ), the αβ-axis powerwinding voltage and current components should be firstly obtained as follows:
0
0
18 √
√
VI. MAXIMUM WIND-POWER EXTRACTION BASED ON THE PROPOSED VECTOR-CONTROL STRATEGY In order to extract the maximum power from the wind turbine, the tip-speed ratio must equal its optimal value. Therefore, the generator speed should vary with wind-speed variations to maintain the tip-speed ratio at that proper value according to (3). Moreover, it is obvious from (1) that for a constant power-winding frequency (grid connected), the control-winding frequency should be varied to vary the rotor speed of BDFRG. Fig. 5 shows the main structure of the proposed control strategy for maximum wind-power extraction.
19 √
√
from which, the αβ-axis power-winding flux components can be calculated as:
20 Hence, the magnitude and the angle of the power-winding flux vector can be obtained as:
21
Fig. 5. Main structure of the proposed control technique for maximum windpower extraction
In order to extract the maximum power from the wind turbine, the electromagnetic-torque command of the BDFRG, should be determined at the optimal value of the tip-speed
ratio and the corresponding maximum value of wind-turbine power coefficient. In order to provide a unity power-factor operation, the is reactive-power command of the power winding, adjusted to be equal zero. After getting the command values and , the qdaxis command components of the control-winding current, and , can be easily determined aiding with (22) and (23) respectively.
[10] up to 3 seconds. Then, the partially power-rating converter is switched into the control windings. During this period the proposed control algorithm is already activated for extracting maximum power from the wind turbine along with wind-speed variations. The response of the control-winding phase-current during different periods is shown in Fig. 8. It can be observed that the converter over-current is completely avoided when the converter is switched into the control windings after a small short-circuit period of 3 seconds.
From which, the abc-axis command components of the can be obtained and compared control-winding current, . Hence, the with the corresponding actual currents, resulting errors are controlled using a hysteresis-band current controller for getting the appropriate gating signals of the machine-side converter. VII. SIMULATION RESULTS In order to confirm the validity of the proposed control technique, a sample of simulation results is introduced. The presented simulation results are obtained based on a six/twopole, 4.5 kW BDFRG driven by an appropriate wind turbine. All data related to the overall system parameters are listed in the appendix section [10]-[12]. It can be observed from Fig. 3 that the optimal tip-speed equals 8.1 and the ratio of the employed wind turbine equals 0.48 corresponding maximum power coefficient, at zero value of blade pitch-angle. The torque-speed profile of the proposed wind-driven BDFRG is presented in Fig. 6 indicating the optimal values of BDFRG mechanical-torque and the corresponding rotor speed according to the optimal tip-speed ratio.
Fig. 8. Response of the control-winding phase-current
Under the same wind-speed variations, shown in Fig. 7, the generator rotor-speed response and the corresponding electromagnetic torque are shown in Fig. 9. Moreover, the response of wind-turbine power coefficient is shown in Fig. 10.
Fig. 9. BDFRG rotor-speed response and the corresponding electromagnetic torque
Fig. 6. Torque-speed profile of the proposed wind-driven BDFRG
The capability of maximum wind-power extraction using the proposed vector-control technique has been studied for wind-speed variations shown in Fig. 7.
Fig. 7. Wind-speed variations
Firstly, the BDFRG is freely accelerated with shortcircuited control-winding terminals for soft starting purpose
Fig. 10. Wind-turbine power coefficient
It can be observed from Fig. 9 that the generator electromagnetic-torque tracks the optimal values, shown in Fig. 6, for maximum wind-power extraction. In addition, a constant level of the power coefficient at its maximum value can be also observed as illustrated in Fig. 10. This ensures the effectiveness of the proposed control strategy to maintain the tip-speed ratio at its optimal value under wind-speed variations. Table I summarizes the system behaviour under different operating conditions including both the soft starting period and the period of maximum wind-power extraction based on the proposed control strategy.
TABLE I.
SUMMARY OF THE PRESENTED SIMULATION RESULTS UNDER DIFFERENT OPERATING CONDITIONS Proposed Control Technique for Maximum Wind-Power Extraction
Operating Region
BDFRG Soft Starting
Time (s)
0 to 3
3 to 10
10 to 17
18 to 26
Wind speed (m/s)
4.5
4.5
5.5
6
Control-winding frequency (Hz)
-2.283
6.5
-3.167
-8
BDFRG rotor-speed (rpm)
784.25
652.5
797.5
870
Power coefficient of wind turbine
0.423
0.48
0.48
0.48
BDFRG electromagnetictorque (N.m)
-14.74
-20
-30
validated the capability and effectiveness of the proposed control strategy for maximum wind-power extraction under wind-speed variations. APPENDIX BDFRG Parameters [10]: 380 V, 50 Hz, Y-connected
Fig. 11. Active and reactive power of the generator power-winding
It can be clearly noted from Fig. 11 that the reactive power of the generator power-winding is approximately not affected by wind-speed variations and is maintained constant and equals zero to ensure a unity power-factor operation. It can be concluded, based on the proposed control strategy, that the control of both the BDFRG electromagnetictorque and the reactive power of generator power-winding is effectively achieved in a completely decoupled fashion. VIII. CONCLUSIONS This paper has proposed a vector-control strategy of a grid-connected wind-driven Brushless Doubly-Fed Reluctance Generator (BDFRG) for maximum wind-power extraction under wind-speed variations. The proposed control technique has been based on the alignment of the total power-winding flux with the d-axis of the power-winding flux. In addition, a unity power-factor operation has been also achieved via adjusting the reactive-power command of the power winding to be equal zero. On the other hand, the employed converter over-current has been completely avoided aiding with the suggested soft starting method. All presented results have
(Ω)
(Ω)
(H)
(H)
(H)
Rotor Inertia (kg.m2)
7.5
3.781
2.441
0.41
0.316
0.3
0.2
Wind Turbine Parameters [12]:
-35
On the other hand, the response of the active and reactive power of the generator power-winding is shown in Fig. 11. The negative sign associated with the electromagnetic torque and the corresponding active power of the power winding, shown in Fig. 9 and Fig. 11 respectively, proves that the machine is effectively in generating mode.
Rated Current (A)
Rated Power
Turbine Radius
Wind Speed Range
Turbine Inertia
(kW)
(m)
(m/s)
(kg.m2)
6.0
4.0
2 – 12
1.5
Gearbox Ratio
7.5
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