Modeling and Design of a Grid Connection Control

IEEE I2MTC 2008

Modeling and Design of a Grid Connection Control Mode for a Small Variable-Speed Wind Turbine System L. Mihet-Popa1, V. Groza2, Senior Member, IEEE, O. Prostean1, Member, IEEE and I. Szeidert1 Department of Electrical Machines and Drives, POLITEHNICA University of Timisoara, Romania1 Phone: +40-256-403464, Fax: +40-256-204402, E-mail: [email protected] School of Information Technology and Engineering, University of Ottawa, Canada2

Abstract – In this paper, a variable-speed wind turbine generator system with a vector controlled back-to-back PWM-VSI on the stator side has been modeled, designed and simulated to study its steady state and dynamic behavior. The grid connection control mode of a wind turbine based on a flexible dSPACE digital signal processor system that allows user-friendly code development, monitoring and online tuning is used. The design of an LCL-filter, current controller and DC-link voltage controller are described in detail. The PI-controllers are designed using pole-zero placement technique and the gain of the regulators are found using root locus method. Keywords:

back-to-back PWM-VSI, LCL-filter, induction generator, variable-speed wind turbine.

I. INTRODUCTION The use of cage rotor induction generators (CRIG) with a back-to-back pulse width modulation (PWM) voltage source converter (VSC), for direct grid connection wind energy conversion systems, has become a quite attractive in the last ten years, in both low power and very high power level [1, 3, 5]. Small efficient wind turbines can be used to supply private houses or farms in remote locations in developing countries where low-cost access to the electrical power grid is impractical [1, 5]. Due to the latest developments in power and digital electronics, the market for small distributed power generation systems connected to the domestic grid is increasing rapidly. Increased energy production at low wind speed (6-8 m/s), elimination of the capacitor bank necessary for magnetization, and the possibility for gridconnected and stand-alone operation modes can thus be achieved at the expense of a back-to-back converter with a flexible control [2-3]. The trend is that these systems should be able to work in stand-alone mode but also connected to isolated local grid in parallel with others generators, such as other wind turbines, photovoltaic or diesel generators [1]. The variable speed wind turbines represent a new technology within wind power for large-scale applications and their models have to be set up for making power stability investigations. Therefore, this

concept will be analyzed as follows. Also, the design of the current and voltage controllers and of an LCL-filter are presented. II. SISTEM DESCRIPTION AND MODELING The power configuration of the developed system is depicted in Fig. 1. It consists of a three-phase cage-rotor induction generator, the generator converter to control the speed, a DC-link, and a full-bridge grid converter connected to the grid through an LCL-filter. Three commercial frequency converters (Danfoss-VLT 5022) rated 18.5 kVA/400 V are used [3]. The first one uses a scalar open-loop torque control and is feeding a 15 kW induction motor in order to emulate the wind turbine. The second converter is used as generator converter and uses vector flux control to regulate the speed of the generator and to provide the magnetizing flux for the machine. The last converter is used as grid converter for controlling the active and reactive power independently and is connected to the grid through an LCL-filter. The LCL filter is used because it achieves better current ripple attenuation than L or RL-filters [8]. A. Wind Turbine Emulator The wind turbine rotor is emulated using a standard 6poles 15 kW/400 V cage-rotor induction machine controlled by a commercial frequency converter operated in open-loop torque control mode. The induction motor is mechanically coupled with the induction generator. The wind speed, which is the input of the wind turbine emulator, is calculated as an average value of the fixedpoint wind speed over the whole rotor, and it is implemented via dSPACE digital controller. It takes the tower shadow and the rotational turbulences into account [4, 5]. The aerodynamic model of the wind turbine rotor is based on the power coefficient (Cp), which represents the rotor efficiency of the turbine (aerodynamic efficiency of the blades), also taken from a look-up table. The aerodynamic torque is given by: P 1 Trot = aero = ⋅ ρ ⋅ π ⋅ R 3 ⋅ ueq 2 ⋅ C p ………(1) ωrot 2 ⋅ λ

Fig. 1. Variable-speed wind generator system.

where (Paero) is the aerodynamic power developed on the main shaft of wind turbine with the blade radius (R), at a wind speed (ueq) and the air density (ρ). The blade tip speed ratio (λ) depends on the rotor speed (ωrot), blade radius and wind speed, according to: ω ⋅R …….…………………...(2) λ = rot ueq The power coefficient (Cp) decreases when the wind speed (ueq) increases (λ small), [5]. This fact is used in the passive stall controlled wind turbines (our case). B. Induction generator control The generator control (generator converter + controller) is working in closed-loop speed control mode where the speed reference is chosen in order to extract the power from the wind turbine to a certain wind speed. It is used to control mechanical power on the generator shaft. The generator converter (AC/DC) is a sensorless vector controlled (VC) VLT connected to the induction generator and produces voltage on the DC-link, as is shown in Fig. 1. The equation of motion at the induction generator shaft is given by: d Ωr Telm − Td = J ⋅ …………...….(3) dt In which (Telm) represents the electromagnetic torque of induction machine, (Td) is the driving torque (positive in motoring mode and negative in generating mode), (J) represent the equivalent moment of inertia for induction machine and the driving mechanism and (Ωr) is the mechanical rotor angular speed. C. Grid converter control The control structure for grid-connected control mode is shown in Fig. 2. Standard PI-controllers are used to regulate the grid currents in d-q synchronous frame in the inner control loops and the DC-voltage in outer loop. A decoupling of the cross-coupling is implemented in order to compensate the couplings due to the output filter. The reference current in the q-axis of the current loop is set to zero in order to achieve zero phase angles between voltage and current. In this way the unity power factor can be achieved.

Fig. 2. Control structure for grid connected control mode.

The output of the current controllers sets the voltage reference for the control strategy implemented-Space Vector Modulation (SVM), which controls the switches of the grid converter (Fig. 2). The synchronization with the grid is achieved by using a Phase-Locked-Loop (PLL), as can be seen in Fig. 3. The principle of PLL is that the sinus of the difference between the grid phase (γ) and the inverter phase angle (θ) can be reduced to zero using a PI-controller, and thus locking the grid inverter phase to the grid, knowing that for small arguments we can consider [1]:

sin ( γ − θ ) ≅ γ − θ = ∆θ ……………………….(4)

The signal (∆θ) is used as a correction angle. The output of the PI-controller is the inverter output frequency that is integrated to obtain the inverter phase. In order to improve the dynamic response at startup, the nominal frequency of the grid (ω0) is feed-forwarded to the output of the PI-controller. D. Model of the LCL-filter The main goal to implement an LCL-filter is to reduce the current ripple due to the PWM-modulator. In comparison with a standard RL-filter or an L-filter, an LCL-filter is smaller and less expansive and has the same attenuation levels of current ripple than RL-filter [1-2]. In a symmetrical three-phase system an equivalent single-phase LCL-filter can be represented as shown in Fig. 4 a). Parasitic serial resistances of the inductances are ignored; instead that resistance RD is added for reducing the filter damping at its resonance frequency.

Fig. 3. PLL structure used to synchronize the grid converter voltage with the grid voltage.

a)

b) Fig. 4. An equivalent single phase LCL-filter (a), and its model in s-plane (b).

The mathematical model (s-plane) of the single-phase LCL-filter can be written as follows:

iI − iC − iG = 0 uI ( s ) = iI ⋅ LI ⋅ s + uC uG ( s ) = −iG ⋅ LI ⋅ s + uC

………………….…….(5)

 1  uC (s ) = iC ⋅  RD +  s ⋅ CF   From (5) we can get the grid current (iG) and the inverter current (iI):

iI ( s ) =

1 ⋅ ( u I − uC ) s ⋅ LI

1 iG (s ) = ⋅ ( uC − uG ) s ⋅ LG

………………………....(6)

where LI represents the inverter-side inductance, LG is the grid-side inductance and CF is the filter capacitance. From Fig. 4 a) can also be written the next equations:

uI ( s ) = z11 ⋅ iI + z12 ⋅ iG uG (s ) = z21 ⋅ iI + z22 ⋅ iG

…………………………...(7)

In which

 1 1  ; z12 = −  RD +  s ⋅ CF s ⋅ CF    1 1 ; z22 = −  RD + s ⋅ LG + z21 = RD + s ⋅ CF s ⋅ CF  z11 = s ⋅ LI +

  

(8)

The transfer function in the s-plane of a single-phase LCL-filter with passive damping can be written as:

H (s) =

iI (s) z22 = = uI (s) z11 ⋅ z22 − z12 ⋅ z21

LGCF s 2 + RDCF s + 1 = LI LGCF s3 + RDCF ⋅ ( LI + LG ) ⋅ s2 + ( LI + LG ) ⋅ s

(9)

E. Control panel The whole control strategy of the wind turbine emulator and control is implemented in MATLAB & Simulink using a dSPACE – DS1103 controller. The dSPACEDS1103 is a mixed RISK/DSP digital controller providing a powerful 64-bit floating point processor for calculations as well as comprehensive I/O capability. A virtual control panel developed in Control Desk [7] that controls the whole system is shown in Fig. 5. The control layout is divided into two parts: generator control and grid converter control. In the generator control panel, the reference for the generator speed and the mechanical power can be set. In the grid-converter control panel the references for the active and reactive power to be transfer to the grid are given. The DCvoltage reference can also be changed in the allowable range. A test control panel for online tuning of the controllers has also been done. It proved to be a very convenient method to fine-tune the PI-controllers in the whole system. III. CONTROL DESIGN Design of the grid connection control mode is based on the mathematical model of the system. Complete controller design (Fig. 2) contains 3 main parts: current controller design, DC-link voltage controller design and LCL-filter design as will be described in the following. A. LCL-filter Design The LCL-filter gives a better attenuation of the switching ripple compared to a classic L-filter as it is a third-order filter (6), and therefore it can be designed using smaller components [1, 8]. The parameters of the controller will be obtained based on the transfer functions of the system modeled in paragraph 2 D. The PI current controller with decoupling is designed using pole-zero placement technique. When designing an LCL-filter the limits on the parameter values should be considered [6]: • the capacitor value (CF) is limited by the tolerable decrease of the power factor at rated power PN (less than 5 %); • the total value of the inductance should be lower than 10 % of the grid impedance (Zb) to limit the DC-link voltage (voltage drops during operation); • the resonance frequency should be included in a range between 10 times the line frequency and one half of the switching frequency in order not to create resonance problems in the lower and higher parts of the harmonic spectrum; • the passive resistors should be chosen as a compromise between the necessary damping and the losses in the system. The passive damping cannot be to low in order to avoid oscillations and the losses cannot be too high to not reduce efficiency.

Considering the reduction of the effectiveness caused by damping resistor chosen value is 1.2 and then grid side inductance is: LG=rLI=1.5 [mH]. The solution of the damping resistance (RD) is based on the impedance of the capacitor at the resonance frequency. Neglecting losses we get:

ωres = f res

LI + LG = 14.7 ⋅103 [rad / s ] LI ⋅ LG ⋅ CF

1 = ⋅ ωres = 2.33[kHz ] 2π

…...(17)

The damping is a compromise between power losses and stability requirements: Fig. 5. Control desk panel for testing the wind turbine control strategy.

Base values are calculated based on line-to-line voltage (EN), nominal power (PN) and grid frequency (ωG):

Zb

(E ) = N PN

2

= 14.55Ω; Cb =

1 = 218.8µ F (10) ωG ⋅ Zb

Total voltage drop on the filter should be less than 10 %, therefore total inductance should be less than:

LTOT =

0.1 ⋅ Z b

ωG

= 4.6mH ……………………..(11)

The resonance frequency is set to half of the switching frequency (fsw=5 kHz): ωres = k ⋅ ω sw = 0.5 ⋅ 2π ⋅ f sw = 15708rad / s …(12) The factor (k) express how far is the switching frequency from the resonance frequency. Adopting 2.7 % impedance for the converter side, a 10 % current ripple can be obtained when using only an Lfilter. With additional LC part the aim is to reduce the ripple at 2 %: Z L = Zb ⋅ 2.7% = 0.393[Ω] …………………..(13) The inverter side inductance (LI) is then:

LI =

ZL

ωG

= 1.25[mH ] ………………………….(14)

Reactive power stored in the capacitor is 5 % of the system power rating, so the maximum capacitor value is:

Cmax =

Q =11[µF];Q = 0.05⋅ PN = 550[VA] (15) ωG ⋅ EN 2

The maximum capacitance within the limits is 11 [µF], and the selected value should be nearly half of that value [1], so that the capacitance of the filter is CF=6 [µF]. The aim is to obtain 20 % ripple attenuation that can be expressed by following equation [1]:

iG (hsw ) 1 = = 0.2 ……………….(16) iI (hsw ) 1 + r (1 − a ⋅ x) where a=LICbωsw2, x=CF/Cb=0.0274, r=LG/LI>1.1.

1 1 RD = ⋅ = 3.79 ≅ 4[Ω] …………….(18) 3 ωres ⋅ CF Bode Diagram of the transfer function (9) of the undamped and damped LCL-filter and of the L-filter is presented in Fig. 6. B. Current Controller Design In order to design the PI current controllers, the transfer function of the LCL-filter (19) is considered as the system plant, and discretized using zero-order hold (zoh) method at a sampling frequency of 5 kHz. This switching frequency was used as a compromise between current ripple, control dynamics, inverter switching losses and dead-time influences. The transfer function of the plant in s-plane is:

G(s) =

iG (s) = uI (s)

RD ⋅ CF ⋅ s +1 = 3 LI LGCF ⋅ s + RDCF ⋅ ( LI + LG ) ⋅ s2 + ( LI + LG ) ⋅ s

(19)

Using zoh equivalent in z-plane:

 G (s)  G ( z ) = (1 − z −1 ) ⋅ Z   …………………….(20)  s  we get the transfer function:

0.0718 ⋅ z 2 + 0.081 ⋅ z + 0.0209 (21) G( z) = 3 z + 0.0932 ⋅ z 2 − 0.7928 ⋅ z − 0.3004

The transfer function of the PI-regulator in z-plane is:

Ts ) TI ………………………(22) z −1

z − (1 − H PI ( z ) = k P ⋅

In Fig. 7 is presented the Simulink model of the current control loop in z-domain and Fig. 8 a) shows zero-pole placements of open-loop without PI-regulator and Fig. 8 b) of closed-loop systems. Figure 8 c) shows the frequency response of the optimize current-loop of the system.

Fig. 6. Bode plot of the damped and undamped LCL-filter and of L-filter (L=2.75 mH).

As can be seen in Fig. 8 a) there are two complexconjugated poles and one real-pole. Because of complex-conjugated poles compensation technique can’t be used. Instead a pole-zero placement technique is used. An integrator time-constant Ts=8 ms is selected as a compromise between good dynamics and still a good noise rejection. The gain kP is selected as dominant pole using root locus method, having a damping of 0.7. In Fig. 8 b) the zeropole placement for optimized closed loop is shown. The dominant poles have now a damping of 0.7 at a frequency of 580 Hz. The gain of the regulator is found to be kP=4.8. The bandwidth is a frequency where the gain of the closed loop is reduced to -3 dB (Fig. 8c) and the phase delay becomes larger than 450 assuming that closed loop behavior can be approximated by a first-order delay element. An approximation of the closed-loop can be done using a first-order transfer function with the bandwidth of 208 Hz, as can also be seen in Fig. 8 c):

H CL ( s ) ≈

Fig. 7. The model of current control loop developed in Simulink.

1 1 = 0.76[ms] (23) ; Tet = 1 + s ⋅ Tet 2π ⋅ fbw

C. DC-Link Voltage Controller Design Voltage controller design uses the mathematical model of DC-link and can be designed in s-plane because time constants of the plant are much bigger than the sampling time (Ts). Cascade connected DC-link voltage controller will be designed using symmetric optimum in order to reject disturbances on the DC-link voltage. The current of DC-link (iDC) can be calculated using power balance between DC and AC side as follows:

uDC ⋅ iDC =

3 ( ud ⋅ id + uq ⋅ iq ) ………………....(24) 2

When the grid converter (active rectifier) operated with unity power factor (iq=0), therefore iDC is expressed as:

iDC = a)

b)

3 ud ⋅ id ⋅ = K DC ⋅ iD ……………………...(25) 2 uDC

Selecting the operating point of controller ud=326 V and uDC=700 V, we obtain:

K DC =

3 ud ⋅ = 0.7 ………………………….…(26) 2 uDC

The transfer function (tf) of DC-link is:

H DC ( s) =

uDC ( s) 1 …………………….(27) = iDC ( s) s ⋅ CDC

If the transfer function of current loop is approximated by a first order tf ( H CL ( s ) = 1/(1 + s ⋅ Tei ) ), we can get the transfer function of the plant: c) Fig. 8. The pole-zero placements of open-loop (a) and closed-loop (b) of the system, and Bode Diagram of the optimize current-loop c).

H0 (s) = HDC (s) ⋅ HI (s) = KDC ⋅

e−s⋅τ0 (28) s ⋅ CDC ⋅ (1+ s ⋅ Tet )

where τ0 represents the sampling delay time ( τ 0 = K DC ⋅ (1/ f s ) = 0.7 ) and time constant Tet=4.8 ms was obtained in last paragraph. The transfer function of PI-regulator in s-plane is:

 1 + s ⋅ Ti  H PI ( s ) = k P ⋅   ………………………...(29)  s ⋅ Ti  When CDC>>(τ0+Tet), optimal symmetry criterion to design parameters of the PI-controller can be used [8]:

Ti = 4 ⋅ (Tet +τ 0 ) = 0.02; kP =

CDC (30) 2 ⋅ kDC ⋅ (τ 0 + Tet )

The gain of voltage controller is verified using root locus of open-loop transfer function (tf) in s-plane, where delay is replaced by a tf with the time delay τ0. In this way the open-loop transfer function becomes:

H0 (s) =

k ⋅ (1+ sTi ) kDC ⋅ P (31) s ⋅ CDC ⋅ (1+ s ⋅Tei ) ⋅ (1+ s ⋅τ0 ) sTi

Block diagram of the DC-link voltage control loop implemented in MATLAB & Simulink is depicted in Fig. 9 and root locus and Bode Diagram are presented in Fig. 10. As can be seen in Fig. 10 optimal gain selected by using root locus method is kP=0.35 and the bandwidth of the closed loop is 13 Hz. The parameters obtained for DClink voltage controller are: kP=0.35 and Ti=20 ms.

IV. CONCLUSION In this paper a variable-speed wind turbine concept using cage rotor induction generator connected to the grid through an LCL-filter has been modeled and simulated in MATLAB & Simulink. The paper has also analyzed the design of an LCL-filter, current and voltage controllers based on the mathematical model of the system. The main aim was to provide a design procedure for the filter and the controllers to study the stability and the dynamic response of the overall system. The design procedure has been tested in simulation and the desired current ripple attenuation has been achieved for the test system parameters. The cage rotor induction generator was connected to the grid through a vector controlled back-to-back PWM-VSI inverter and an LCL-filter. Using this configuration is possible to increase the energy production especially in the low wind range, up to 1 MW per unit, eliminate the capacitor bank for reactive power compensation and allow both grid-connection and stand-alone operation modes. A flexible development platform with DS1103 dSPACE was used to implement and test a control strategy for 11 kW variable-speed wind turbines. The most relevant feature of the system is the ability to develop the control strategy entirely in MATLAB & Simulink and test it using dSPACE platform in a short time. A further research topic in the field of design of a LCLfilter is the development of a more embedded design procedure taking into account EMI disturbances. REFERENCES

Fig. 9. Block diagram of the DC-link voltage control loop.

a) b) Fig. 10. Root locus of open-loop with selected gain k p=0.35 (a) and frequency response (Bode Diagram) of closed-loop (b).

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