the clean alternative renewable energy in rural areas. Mathematical models for both the converter and inverter are presented and simulated. A vector oriented ...
Vector Oriented Control of Voltage Source PWM Inverter as a Dynamic VAR Compensator for Wind Energy Conversion System Connected to Utility Grid Mahmoud M. N. Amin, Student Member, IEEE, O. A. Mohammed, Fellow, IEEE Florida International University, ECE Dept. Energy Systems Research Laboratory
Miami, FL 33174 USA
Abstract— This paper presents analysis, design, and simulation for vector oriented control of threephase voltage source pulsewidth modulation (PWM) inverter which aims to optimize the utilization of wind power injected into the grid. To realize this goal, a digitally controlled converterinverter system is proposed which provides economic utilization of the wind generator by insuring unity power factor operation under different possible conditions, and full control of active and reactive power injected into the grid using a digitally controlled voltage source inverter. The wind energy conversion system (WECS) is represented by three phase selfexcited induction generator (SEIG) driven by a variablespeed prime mover (VSPM) such as a wind turbine for the clean alternative renewable energy in rural areas. Mathematical models for both the converter and inverter are presented and simulated. A vector oriented control scheme is presented in order to control the energy to be injected into the grid. Closedloop control of the converter/inverter utilizes a conventional proportional integral (PI) controller. In order to examine the dynamic performance of the system, its model is simulated and results are analyzed. Simulation results for different disturbance conditions show good performance of this proposed control algorithm. The simulation results are given using MATLAB7/SIMULINK program. Experimental results using DSpace1104 confirm that the good performance of the proposed control system and agree with the simulation results to a great extend. Index Terms— Selfexcited induction generator (SEIG), vector oriented control (VOC), voltage source inverter (VSI), wind energy conversion system (WECS).
R
I. INTRODUCTION ECENTLY,
the wind generation system is attracting attention as a clean and safety renewable power source. The threephase induction machine with a squirrel cage rotor or a wound rotor could work as a threephase induction generator either connected to the utility ac power distribution line or operated in the selfexcitation power generation mode with an additional stator terminal excitation capacitor bank. [16].
Variable speed operation of wind turbines has many advantages that are well documented in the literature [79]. Induction machines have many advantageous characteristics such as high robustness, reliability and low cost. The induction machines may be used as a motor or a generator. Selfexcited
9781424447831/10/$25.00 ©2010 IEEE
induction generators (SEIG) are good candidates for windpower electricity generation especially in remote areas, because they do not need an external power supplies to produce the excitation magnetic fields. [1012]. Threephase voltagesource AC/DC/AC (PWM\) converters have been increasingly used for many applications such as uninterruptible power supply (UPS) systems, boost converters and wind energy conversion systems. The attractive features of them are constant dcbus voltage, low harmonic distortion of the utility currents, bidirectional power flow, and controllable power factor [13][15]. Conventional thyristor phasecontrolled converters with PWM technique have the inherent drawbacks that the power factor decreases as the firing angle increases and that harmonics of the line current are relatively high [16]. Also, the fast power semiconductors used [usually, MOSFET or insulated gate bipolar transistor (IGBT)], are free to switch at frequencies much higher than the mains frequency, enabling the voltage controller to provide an output voltage with fast dynamic response [17]. Nowadays, the voltageoriented control (VOC), which guarantees high dynamics and static performance via internal current control loops, has become very popular and has constantly been developed and improved [18 25]. However, this method depends on using conventional proportional and integral (PI) compensators in the rotating reference frame to produce its control input commands [26]. However, the conventional Pl controllers have the inherent drawbacks that its response is somewhat slower for very fast transients and its control range is limited because its fixed gains [27]. A conventional proportional and integral (PI) compensator can be applied to the variables in the rotating reference frame so as to achieve a zero steadystate error in response to step commands. Then, variables in the rotating reference frame must be restored in the stationary threephase reference frame using the inverse– transformation. In this paper, a vector oriented control strategy for a threephase voltagesource PWM inverter is proposed in the synchronous d–q frame. The mathematical models of the converter in different frames including the synchronous frame are presented. The vector oriented current control technique which is similar to the field oriented control in induction machine is used to control the inverter operation. A Software Phase Locked Loop (SPLL) for phase angle detection of the generator voltage in synchronous reference frame is proposed.
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The proportional plus integral (PI) current controllers in dq axes are designed and analyzed to meet the time domain specification: minimum overshot, minimum settling time and minimum steadystate error. A vector current controlled grid connected voltage source inverter (VSI) is proposed as a dynamic VAR compensator system. An analytical model for the VSI connected to the grid with L and LC filter and the operating principle of the proposed vector controllers are introduced. Simulation results for VSI connected to the grid with L and LC filter are presented. This paper is organized as follows. In section I, an introduction to the subject is presented. In Sections II and III a mathematical description and modeling of the system is introduced. In Section IV, simulation and experimental results are presented and analyzed. Finally, Section V presents some conclusions. II. SYSTEM DESCRIPTION Variable speed wind turbine (VSWT) systems are preferred for the higher output power generation. On the other hand, due to the variations of wind speed, direct interfacing of wind energy system to the utility grid gives rise to problems such as voltage fluctuations and flickering. Therefore, synchronization with the grid and stability concerns must be fulfilled. Power electronics systems playing an important position in the overall generation system. The classical scheme of AC/DC/AC conversions is used. In general, the electrical components of VSWT system are generator, rectifier and inverter, and isolation transformer for grid connection. Fig. 1 shows a typical electrical system utilized for grid connected VSWT with the utility grid. The paper will focus on the power electronic conversion scheme that could be used to inject VSWT power into utility grid.
Figure 2. DQ model of an induction machine in the synchronously rotating reference frame (a) daxis (b) qaxis.
In the dq model of the induction machine shown in Fig.2 vds and vqs are the generated voltages along the daxis and qaxis, respectively. The voltage of an induction machine in the synchronous reference frame, which can be obtained from Fig. 2 as follows:
v ds + R s i ds − ω e λ qs + Lls pi ds + Lm pi ds + Lm pi dr = 0 (1) K d − (ω e − ω r )λ qr + R r i dr + Llr pi dr + L m pi ds + L m pi dr = 0 (2)
v qs + R s i qs + ω e λ ds + Lls pi qs + Lm pi qs + Lm pi qr = 0
(3)
K q + (ω e − ω r )λ dr + R r i qr + Llr pi qr + L m pi qs + Lm pi qr = 0 (4)
Where
λds=Lsids+Lmidr λ dr=Lmids+Lridr λqs=Lsiqs+Lmiqr λ qr=Lmiqs+Lriqr
(5)
The voltage equation of the dq model is based on the stator and rotor currents are given as: ( Rs + pLs ) pLm ωe Ls ωe Lm 0 0 − ωe Ls ( Rs + pLs ) − ωe Lm pLm = pLm (ωe − ωr ) Lm ( Rr + pLr ) (ωe − ωr ) Lr 0 pLm − (ωe − ωr ) Lm − (ωe − ωr ) Lr ( Rr + pLr ) 0 iqs Figure 1. Electrical system for grid connected wind energy with the grid
ids
III. SYSTEM MODELING
iqr idr
A. Modeling of SelfExcited Induction Generator The model of an induction generator is helpful to analyze all its characteristics. The induction machine used as SEIG is a three phase squirrelcage machine. In this paper the model, shown in Fig. 2, is used because it provides a complete solution (transient and steady state) of the selfexcitation process.
Vqs +
Vds Kq Kd
(6)
1 i qs dt + V cq t =0 C 1 Vds = ids dt + Vcd t =0 C
V qs =
(7) (8)
The electromagnetic torque is given by: Te = −
3 P Lm (λ dr iqs − λqr ids ) 2 2 Lr
(9)
Where, vqs, vds, iqs, and ids are the stator voltages and currents, respectively. vqr, and vdr are the rotor voltages. qr,
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and dr are the rotor fluxes. Rs, Ls, Rr, and Lr are the resistance and the self inductance of the stator and the rotor, respectively. Lm is the mutual inductance. The mathematical equation that relates the wind turbine output torque with the electromagnetic torque of the induction generator is given by:
Tm = J
d ω m + βω m + Te dt
iqs
−RsLr
(ωe ωr )L ωeLsLr
d ids 1 ωeLsLr −(ωe ωr )Lm = dt iqr L RsLm
2
idr iqs
ωrLsLm
−RsLr
ωrLsLm RsLm
ωrLmLr
ω L −(ωe ωr )LsLr
(ωe ωr )LsLr ωL
LmKq −LrVqs
LmVds −LsKd
d 1 β 1 ω m = T m − ω m − Te dt J J J
di abc (t ) + Ri abc (t ) dt
i c (t ) = i dc (t ) − i L (t ) = C
(14)
dv dc (t ) dt
(15)
(11)
The line voltage, the phase current, and the terminal voltage of the PWM converter can be transformed to a synchronous reference frame using the transformation matrix H(θ ) as follows,
(12)
v abc (t ) = H (θ ).v dq (t )
ids idr
e abc (t ) − v abc (t ) = L
 RrLs
1 LmKd −LrVds + iqr L LmVqs −LsKq
E sin( ω t + 2π / 3)
e c (t )
Referring to Fig.3.c. , the dynamic equation for the output side of the three phase converter system can be written as,
RrLm 2 e m
2 e m
(13)
where E is the maximum amplitude of the generator AC voltage. From Fig.3.b. , the dynamic equation for the input side of the three phase converter system can be written as,
−ωrLmLr
RrLm  RrLs
e a (t ) E sin ω t e b (t ) = E sin( ω t − 2π / 3)
(10)
where ω m, J, and β are the mechanical angular speed of wind turbine, the effective inertia of the wind turbine and the induction generator, and friction coefficient, respectively. From (6)(10), the state equations of the SEIG and turbine can be accomplished as in (11) and (12). 2 m
From the equivalent circuit shown in Fig.4.b, assuming generator voltage is 3phase balanced voltage source and its state equations are
(16)
v dq (t ) = H (θ ).v abc (t ) −1
B. Modeling of Vector Oriented Controlled PWM Converter A power circuit and of a perphase equivalent circuit of a PWM voltagesource converters are shown in Fig. 3. It is assumed that a resistive load RL is connected to the output terminal. Where, (R, L) is the line inductor between generator and the converter terminal, (ea) is the generator phase voltage, (va) is the bridge converter voltage controllable according to the demanded DC voltage level, (ia) is the line current, (idc) is the converter DC output current, (vdc) is the converter DC output controlled voltage, (ic) is the DClink capacitor current, (RL) is the load resistance, and (iL) is the load current.
H −1 (θ ) =
1
cos θ
3 −1
sin θ
3
sin θ cos θ
−1 3 1 3
sin θ cos θ
(17)
And θ is the rotating angle of transformation. Now, the dynamic equation (14) can be transformed directly from the abc frame to the synchronous reference frame resulting in a mathematical model for the PWM converter in a synchronous rotating coordinates,
edq (t ) − v dq (t ) = R.i dq (t ) + L 0 1 0 where M = −1 0 0 0
(a)
didq (t ) dt
− L.ω.M .i dq (t )
(18)
0 0
For more simplification, we assume that the threephase voltage source is balanced without zero sequence component. Therefore, (18) can be written as,
did (t ) − R.id (t ) + L.ω .iq (t ) dt diq (t ) vq ( t ) = eq ( t ) − L − R.iq (t ) − L.ω .id (t ) dt vd ( t ) = ed ( t ) − L
(b)
(c)
Figure 3. AC/DC PWM converter. (a) Power circuit. (b) Perphase input equivalent circuit. (c) Perphase output equivalent circuit.
(19)
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The converter system in Sdomain can be obtained by applying Laplace transformation to the dynamic equations in the synchronous frame directly such as,
[
]
[
]
1 . ed ( s ) − vd ( s ) + ω .L.iq ( s ) Ls + R 1 iq ( s ) = . eq ( s ) − vq ( s ) − ω .L.id ( s ) Ls + R id ( s ) =
For the converter output side,
v dc
RL = .i dc 1 + CR L s
system parameters. The system to be modeled is shown in Fig. 6. In the figure, the grid inductance (Lg) is assumed to be zero. The assumption of the balanced state of the grid is presented, therefore, it can be represented by the state equation as,
u ag (t ) U ⋅ sin ω g t u bg (t ) = U ⋅ sin( ω g t − 2π / 3)
(20)
u (t ) (21)
where vector.
(22)
U ⋅ sin( ω g t + 2π / 3)
g c
g is the angular frequency of the grid voltage
The converter plant model in S domain representation is shown in Fig. 4. ed +
Vd
Converter Controllers & Vector Controller

1 LS+R
+
3ed idc id
2Vdc
RL 1+CRLS
Vdc
wL
PWM
wL 
Vq
+
1 LS+R
Fig. 5. The main electric circuit of the VSI connected to the utility grid
iq
eq
Figure.4. Converter model block diagram
According to the converter dynamic equations in synchronous frame,(19), there are coupling terms between these equations which degrade the dynamic performance (slow the controller transient and cause high overshoots) of the system. These terms are the coupling q current componenet (ω Liq) and generator voltage on the daxis equation, ed , while coupling d current component ( ω Lid) and eq on the qaxis. The vector controller will decouple these terms, giving the ability to control each current component separately without any effect from the other component. The block diagram of the vector controlled PWM converter is shown in Fig. 5.
Fig. 6. Simplified circuit of a grid connected VSI, where the focus is on the Lfilter.
The AC side of the inverter system is modeled by the differential equations for 3phases such that,
L
di abc (t ) g + Ri abc (t ) = v abc (t ) − u abc (t ) dt
(22)
By using vector notation, the last equation can be written in the stationary frame such as,
L
di αβ (t ) dt
g + Riαβ (t ) = vαβ (t ) − u αβ (t )
(24)
Equation (24) can be written in the rotating reference frame synchronized with grid voltage as,
IV. SYSTEM MODELING A. Vector Oriented Controlled PWM Converter The main circuit of the VSI connected to a three phase public grid is shown in Fig. 5. An inductance L works as line filter is mounted between the utility grid and the VSI having an internal resistance R. The phase potentials of the VSI denoted as va(t), vb(t), and vc(t). The phase potentials of the utility grid denoted uag(t), ubg(t), and ucg(t). The currents flowing from the DClink to the VSI denoted as ia(t), ib(t), and ic(t), while the DClink current and voltage are denoted as idc(t), and Vdc(t) respectively. In order to design a VSI control systems, mathematical models are important tools for predicting dynamic performance and stability limits of different control lows and
L
di dq (t ) dt
+ ( R + jω g L )i dq (t ) = v dq (t ) − u dqg (t )
(25)
The decoupled equation can be written in the state space form as, dX = A ⋅ X − B ⋅Y dt
(26)
where the state vector and the input vector are defined by
[
X = id
[
Y = Vd
Vq
iq
], T
u dg
(27)
u qg
]
T
(28)
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respectively, the system matrix and the input matrix are given by
A= B=
−R/L
ωg
− ωg
−R/L
1/ L
0
0 1/ L
− 1/ L 0
, 0
− 1/ L
(29)
(30)
dV dc (t ) = i dc (t ) − i L (t ) dt
(31)
V. THE PROPOSED CONTROL SYSTEM The schematic diagram of the VSI connected to the grid and its vector current controller is shown in Fig. 7. A. Proposed VOC VSI as dynamic VAR compensator Until recently, most wind power plant and utility have utilized capacitor banks to correct power factor to near unity. The capacitors are switched in and out by means of mechanical contactors. Unfortunately, because these contactors are relatively slow, they are unable to react to sudden momentary dips in voltage commonly seen in weak grid and can add greater stress to the utility grid. Vector oriented control VSI is proposed here as a dynamic VAR compensator system. Dynamic VAR systems detect and instantaneously compensate for voltage disturbances by injecting leading or lagging reactive power at key points on power transmission grids. Through the VAR control system, reactive power is supplied to the grid in a fraction of second, regulating the system voltage and stabilizing weak grid. A controller measures utility line voltage compares it to the desired level, and compute the amount of reactive power needed to bring the line voltage back to the specified range. The active and reactive power in the synchronous frame given by, 3 j [u d (t ) ⋅ i d (t ) + u qj (t ) ⋅ i q (t )] 2 3 Q (t ) = [u qj (t ) ⋅ i d (t ) − u dj (t ) ⋅ i q (t )] 2
(
)
(
)
2 u dj (t ) ⋅ P r (t ) + u qj (t ) ⋅ Q r (t ) , 3∏ (34) 2 r j r j r i q (t ) = u q (t ) ⋅ P (t ) − u d (t ) ⋅ Q ( t ) 3∏ 2 2 Where ∏ = u dj (t ) + u qj (t ) , and Pr(t), Qr(t) are the active and reactive power commands. With the assumption of zero reactive power command, the current command equations can be simplified such that 2 ⋅ P r (t ) 2 ⋅ V dc ⋅ i dcr (t ) i dr (t ) = = , (35) 3 ⋅ u dj (t ) 3 ⋅ u dj (t ) i dr (t ) =
The DC side of the system is modeled by the equation,
C
voltage are calculated. Consequently, the current controllers are trying to bring the actual currents to its references. So far is how the controller could be constructed. The reference currents iqr, and idr could be calculated from the power equation (32), such that,
i qr (t ) = 0 From the state equation (7), the current controllers can be constructed such that v dr (t ) = u dj (t ) − ω g Li q (t ) + R ⋅ i d (t ) + U dv , (36) v qr (t ) = u qj (t ) + ω g Li d (t ) + R ⋅ i q (t ) + U qv where vdr(t) and vqr(t) are the daxis and qaxis voltage commands respectively, Udv and Uqv are the effective voltage commands. The coupling term between the daxis and qaxis cancelled out by feedforward is controller. The effective voltage commands are obtained by using PI controller such that U dv = k ip ⋅ [i dr (t ) − i d (t )] + k ii ⋅ [i dr (t ) − i d (t )]dt U qv = k ip ⋅ [i qr (t ) − i q (t )] + k ii ⋅ [i qr (t ) − i q (t )]dt
(37)
where kpi, and kii are the proportional and integral gains of the current controllers respectively.
P (t ) =
(32)
The power of the DC side is given by,
Pdc = V dc ⋅ i dc
(33)
The basic principle of the vector oreinted control method is to control the instantaneous active and reactive grid currents and, consequently, the active and reactive power, by separate controllers independently of each other. The grid voltages and currents are first sensed. By means of the software phase locked loop (SPLL), the grid phase angle and frequency can be detected in order to synchronize the VSI output with grid. The demanded amount of power is first estimated from the utility grid at the desired power factor, in consequence, the reference currents in a synchronous frame synchronized with grid
Fig. 7.
Schematic diagram of the proposed VOC VSI connected to the grid
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B. Gridconnected VSI with LC filter The perphase equivalent circuit for the VSI connected to the grid with LC filter is shown in Fig. 8. The inverter dynamic should have additional voltage controller in front of the current controller to control the filter capacitor voltage.
so it can be used here. The overall VSI controllers are shown in Fig. 9.
Fig. 8. VSI with LC filter equivalent circuit.
According to the equivalent circuit, the system dynamic equations can be written as,
Lf
di abc (t ) c = v abc (t ) − R f i abc (t ) − u abc (t ) dt c (t ) du abc j = i abc (t ) − i abc (t ) dt
Cf
(38) (39)
The three phase model of the system transformed to a synchronous reference frame, where the d axis is oriented with the grid voltage vector, can be described by the state equations, d i d (t ) = v d (t ) − R f i d (t ) − u dc (t ) + ω g L f i q (t ) , dt d Lf i q (t ) = v q (t ) − R f i q (t ) − u qc (t ) − ω g L f i d (t ) , dt d c Cf u d (t ) = i d (t ) − i dj (t ) + ω g C f u qc (t ) , dt d c Cf u q (t ) = i q (t ) − i qj (t ) − ω g C f u dc (t ) , dt Lf
(40)
(41)
Fig. 9. VSI with LC filter controller’s diagram.
VI. SIMULATION AND EXPERIMENTAL RESULTS In order to investigate the VSI connected to the grid with the proposed VOC algorithm, a simulation program using Simulink™ was carried out using simulation parameters shown in Table I. The SVPWM presented in this paper has been used with a 5 KHz switching frequency. VOC strategy discussed in section III is utilized in the simulation. Two inner PI controllers are used as current controllers; one for the dcomponent and the other for the qcomponent. The outer PI is the voltage controller. A low pass filter with LC elements and 280 Hz cutoff frequency is connected before the isolation transformer in order to have clean power injection. Fig. 10 shows Schematic diagram of the overall proposed WECS control system connected to grid. The induction machine is listed in Table II in the appendix. Photograph for the experimental proposed WECS connected to the utility grid is shown in Fig. 11.
The system utilizes an inner control loop to control the current through the filter inductor, and an outer control loop to control the filter capacitor voltage, which in turn will be applied to the primary terminals of the isolation transformer between the grid and the inverter. The capacitor voltage could be controlled by controlling the filter inductor current since the injected current, idqj, may be considered as a disturbance. Therefore, the controller could be constructed such that,
i dr (t ) = i dj (t ) − ω g C f u qc (t ) + U dc
(42)
i qr (t ) = i qj (t ) + ω g C f u dc (t ) + U qc
where idr(t) and iqr(t) are the daxis and qaxis current commands respectively, Udc and Uqc are the effective current commands. If PI controller is used, udqc(t) could be controlled such that, r
[ [u
r
] (t ) − u (t ) ]dt
U dc = k cp ⋅ [u dc (t ) − u dc (t )] + k ic ⋅ u dc (t ) − u dc (t ) dt cr q
U = k ⋅ [u (t ) − u (t )] + k ⋅ c q
c p
c q
c i
cr q
c q
Fig. 10. Schematic diagram of the overall proposed WECS control system connected to grid.
(43)
where kpc, and kic are the proportional and integral gains of the capacitor voltage controllers respectively. The inner current controller has the same dynamics as the controller of L filter discussed in section A, (Eqns.34, and 35),
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Fig. 13. Reference wind speed applied to emulator. Fig. 11. Photograph for the experimental proposed WECS connected to the utility grid.
A. Wind speed variation In order to evaluate the performance of proposed emulator in turbulent wind speed condition an experimental test has been carried out. The wind speed could be constant, or varying in a form of pulses, sinusoidal, or step change. Actually wind speed almost has a random variation according to the wind turbine location and its atmospheric conditions, but they can be set to operate within a given variation of speed. Fig. 12 shows the monthly average wind speed at La Venta station. After making fitting to these real data then we can get approximation for Wind speed versus time as shown in Fig. 13.
B. gridconnected VOC VSI with L filter In order to estimate the power injection characteristics, two types of tests are carried out. The first is active power injection without any reactive power compensation. The second is injection of active power with reactive power compensation (lagging or leading). The terminal phase and line voltage of the VSI in abc frame are shown in Fig. 14a,b, and Fig. 15a,b respectively. However the wind speed is variable according to the previous wind characteristics in Fig. 13, the output voltage has the rating of 208 v, 60 Hz which is synchronized with the utility grid rating.
(a)
Fig. 12. Monthly average wind speed at La Venta station.
(b) Fig. 14. Phase voltage of the VSI in abc frame (a) simulation. (b) experimental.
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Va volt Vb volt Vc v olt
200 0 200 1.25
1.255
1.26
1.265
1.27 1.275 1.28 Time 5ms/div
1.285
1.29
1.295
1.3
1.255
1.26
1.265
1.27 1.275 1.28 Time 5ms/div
1.285
1.29
1.295
1.3
1.255
1.26
1.265
1.27 1.275 1.28 Time 5ms/div
1.285
1.29
1.295
1.3
200 0 200 1.25
Because the injected power is only active, the current appears in phase with grid voltage as shown in Fig. 16. The harmonic spectrum using fast Fourier transform (FFT) analysis for the injected current are shown in Fig. 17. From Fig. 17, it is clearly appear that the current harmonics is small (THD=1.9%) due to using the Lfilter.
200 0 200 1.25
Fundamental (60Hz) = 1.569 , THD= 1.90% 1.2 Mag (% of Fundamental)
(a)
1 0.8 0.6 0.4 0.2 0
0
2
4
6 8 10 Harmonic order
12
14
16
Fig. 17 The harmonic spectrum of the injected current.
(b) Fig. 15. Line voltage of the VSI in abc frame (a) simulation. (b) experimental.
The VSI phase voltage accompanied with the switching harmonics and its harmonic spectrum are shown in Fig. 18, 19. 200
Figure 16 shows the first test of the injection power. A step change to the demanded active power and the actual is shown in Fig. 16 keeping the reactive power equal zero.
0 200
uag ia A m p
2
2.005 2.01 2.015 2.02 2.025 2.03 2.035 2.04 2.045 Time (s)
uag v olts &
(a)
ia
time
sec
(a)
(b) Figure 18. Inverter phase voltage to be connected to the grid with only L filter
From Fig. 19, it is noticed that the phase voltage has a large harmonic contents (THD=34.83%) due to the high switching frequency (5 KHz) of the VSI. (b) Fig. 16. Grid phase voltage and injected current. (a) simulation. (b) experimantal
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Mag (% of Fundamental)
2 1.5 1 0.5 0
0
2
4
6 8 10 Harmonic order
12
14
16
Fig. 19 The harmonic spectrum of the phase volatge.
In the second test to investigate the controller performance and the capability of the system assumption of demanded active and reactive power is considered such that, Pr = 500 watt over the test period. Qr = 500 VAR from the start till 2 sec, and reversed to a positive reference (Qr = 500 VAR) after that. The change between the modes of supplying and extracting reactive power is very clear with grid current and voltage waveforms as shown in Fig. 20. From the start until 2 sec, the VSI is considered as a capacitive load supplies reactive power to the grid. After that, the VSI absorbs reactive power from the grid causing the current to lag the voltage.
C. Gridconnected VOC VSI with LC filter The capacitor voltage controller should give the value to be injected through the isolating transformer. For simplification, the transformer is assumed to have a ratio of 1:1. An LC filter with cutoff frequency of 205 Hz is used in the simulation. The simulation parameters are shown in Table II. The in phase injected current with grid and capacitor voltages (iaj, uag, uac), the harmonic content of the injected current and filter capacitor voltage are shown in Figs. 21,22. Not like the L filter, the voltage waveforms are very clean. Fig. 21 shows the synchronization between the grid voltage and the filter capacitor voltage where they are almost the same. From Fig. 22, it is clearly shown that there is a significant change in the harmonic content for the output voltage of the WECS where the THD% decreases from 34.83% with Lfilter to be almost negligible as 0.28% with LC filter. 200
uac ia/20 uag
uag
150
ia
100 uac, uag ,ia
Fundamental (60Hz) = 169.4 , THD= 34.83% 2.5
50 0 50 100 uac
150 200 1.1
1.11
1.12
1.13
1.14
1.15 Time sec
1.16
1.17
1.18
1.19
1.2
(a)
uag volts, ia Amp
uag
ia
Time
sec
(a)
(b) Fig. 21. VSI response with LC filter for the grid and capacitor voltage with the injected line current to be connected to the grid . (a) Simulation. (b) experimental
(b) Fig. 20. Step response in the reactive power to be injected to the grid. (a)simulation. (b) experimental.
(a)
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TABLE II INDUCTION MOTOR IM PARAMETERS
Mag (% of Fundamental)
Fundamental (60Hz) = 169.9 , THD= 0.28% 0.4
Symbol
0.3
hp Vn
Output power Nominal voltage,
0.2
rpm In Vf Rr Rs Lls Llr Lm J
Nominal speed Nominal currnt Field voltage Rotor resistance Stator resistance Stator selfinducatnce Rotor selfinducatnce Mutual inductance Moment of inertia
0.1 0
0
2
4
6 8 10 Harmonic order
12
14
16
(b) Fig. 22. The harmonic spectrum analysis with LC filter to be connected to the grid. (a) Injected current harmonic content. (h) Filter capacitor voltage harmonic content.
Quantity
Value 1/2 208 v LL 1800 3.5 A 125 v 3.592 6.294 0.0168 H 0.0168 H 0.464 H 0.03338 Kg.m2
VII. CONCLUSION In this paper; the dynamic mathematical model of the wind energy conversion system has been derived. The vector oriented control grid connected voltage source inverter has been investigated for high performance control operation. The simulation results showed how the control scheme succeeded in injecting the wind power as active or reactive power in order to compensate the grid power state. All results obtained confirm the effectiveness of the proposed control system for the SEIG feeding Threephase bridge rectifiers and connected to grid through VOC VSI. An experimental setup has been designed and implemented including a DS1104 R&D controller board as an interface element, and all the interfacing circuits to the analog power circuits. The complete wind energy conversion system has been tested and the experimental results showed good transient and steady state performance for each section as well as the overall system and agree with the simulation results to a great extend. APPENDIX TABLE I SIMULATION PARAMETERS FOR VSI WITH L & LCFILTER Symbol
Quantity
Value
fg Vdc
Grid frequency DC link voltage
60 Hz 350 v
Lf Rf Cf fsw k pi kii k pc kic
Filter inductance Filter resistance Filter capacitance Switching frequency Current controller gain Current controller gain Voltage controller gain Volatge controller gain
24 mH 2 40 µf 5 KHz 100 1000 0.07 0.7
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