Modeling, Control Design and Simulation of a Grid

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Modeling, Control Design and Simulation of a Grid Connection Control Mode for a Small Variable-Speed Wind Turbine System L. Mihet-Popa, Member, IEEE, and V. Groza, Senior Member IEEE

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. The experimental results demonstrate the performance of the design procedure. A good agreement between simulation and experimental results was obtained. Index Terms-- Back-to-back PWM-VSI, LCL-filter, induction generator, variable-speed wind turbine.

I. INTRODUCTION

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he 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 quite attractive in the last ten years, in both low power and very high power level [1, 6, 7, 9]. Small efficient wind turbines can be used to supply power to houses or farms in remote locations in developing countries where low-cost access to the electrical power grid is impractical [1, 6, 9]. 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 grid-connected and stand-alone operation modes can thus be achieved at the expense of a back-to-back converter with a flexible control [1, 7]. The trend is that these systems should be able to work in standalone mode but also connected to isolated local grid in parallel with others generators, such as other wind turbines, photovoltaic or diesel generators [1, 7]. The variable speed wind turbines represent a new technology within wind power for large-scale applications and their L. Mihet-Popa is with POLITEHNICA University of Timisoara, Romania, (e-mail: [email protected], ) V. Groza is with University of Ottawa, Ottawa ON, (e-mail: [email protected])

models are developed to investigate their power stability. Authors developed such a model which is analyzed and presented hereafter, along with the design of the employed current and voltage controllers and of the LCL-filter. The correctness of the model and its design is confirmed by results obtained both experimentally and by simulations. II. SYSTEM DESCRIPTION AND MODELING The power configuration of the developed system is presented in Fig. 1. It consists of a three-phase cage-rotor induction generator (IG), the generator converter (VC VLT) 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 [7]. The first one (not represented in Fig. 1) feeds a 15 kW induction motor which emulates the wind turbine. The second converter (VC VLT in Fig. 1) is employed as a generator converter and uses the vector flux control to regulate the speed of the generator (IG) and to provide the magnetizing flux for this 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 since it achieves better current ripple attenuation than L or RL-filters [3]. A. Wind Turbine Emulator The wind turbine rotor is emulated using a standard 6-poles 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 IG. The wind speed, which is the input of the wind turbine emulator, is calculated as an average value of the fixed-point wind speed over the whole rotor, and it is implemented via dSPACE digital controller.

Fig. 1. Logic diagram used to estimate the failure intensity

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

The aerodynamic model of the wind turbine rotor is based on the power coefficient C p , which represents the rotor efficiency of the turbine, also taken from a look-up table. The aerodynamic torque is given by: P 1 Trot= aero= ⋅ ρ ⋅ π ⋅ R3 ⋅ ueq 2 ⋅ C p ………….…(1) ωrot 2 ⋅ λ where P aero is the aerodynamic power developed on the main shaft of the wind turbine with the blade radius R, at a wind speed u eq and air density ρ. The blade tip speed ratio λ depends on the rotor speed ω rot , blade radius and wind speed, according to: ω ⋅R …….…………………...(2) λ = rot ueq The power coefficient C p decreases when the wind speed u eq increases (λ small), [9]. 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 Variable Frequency Drive (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 …………...….(3) Telm − Td =J ⋅ dt where T elm represents the electromagnetic torque of induction machine, T d is the driving torque (positive in motoring mode and negative in generating mode), J represents the equivalent moment of inertia for induction machine and the driving mechanism, and Ω r 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. The output of the current controller sets the voltage reference for the control strategy implemented Space Vector Modulation (SVM), which controls the switches of the grid. The synchronization with the grid is achieved by using a Phase-Locked-Loop (PLL). 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 PIcontroller, and thus locking the grid inverter phase to the grid, knowing that for small arguments we can consider [5]: sin ( γ − θ ) ≅ γ − θ = ∆θ ……………………….(4) The signal Δθ 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 ω 0 is feed-forwarded to the output of the PI-controller. D. Model of the LCL-filter The main goal of implementing an LCL-filter is to reduce the current ripple due to the PWM-modulator. In a symmetrical three-phase system an equivalent singlephase LCL-filter can be represented as shown in Fig. 4 a). Parasitic serial resistances of the inductances are ignored; instead that resistance R D is added for reducing the filter damping at its resonance frequency. The mathematical model (s-plane) of the single-phase LCLfilter can be written as follows: iI − iC − iG = 0 uI ( s ) = iI ⋅ LI ⋅ s + uC ………………….….….(5) uG ( s ) =−iG ⋅ LI ⋅ s + uC  1  uC ( s ) = iC ⋅  RD +  ⋅ s CF  

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

From (5) we can get the grid current i G and the inverter current iI: 1 iI ( s )= ⋅ ( uI − uC ) s ⋅ LI ……………………….....(6) 1 iG ( s )= ⋅ ( uC − uG ) s ⋅ LG where L I represents the inverter-side inductance, L G is the grid-side inductance and C F is the filter capacitance. From Fig. 4 a) the following equations can also be written: uI ( s ) = z11 ⋅ iI + z12 ⋅ iG …………………………...(7) uG ( s ) = z21 ⋅ iI + z22 ⋅ iG where  1 1  −  RD + ; z12 =  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 LCLfilter with passive damping can be written as: iI ( s ) z22 H = ( s) = = uI ( s) z11 ⋅ z22 − z12 ⋅ z21 …..(9)

=

LG CF s 2 + RD CF s + 1 LI LG CF s 3 + RD CF ⋅ ( LI + LG ) ⋅ s 2 + ( LI + LG ) ⋅ s

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 dSPACE-DS1103 is a mixed RISC/DSP digital controller providing a powerful 64bit floating point processor for calculations as well as comprehensive I/O capability. A virtual control panel developed in Control Desk [8] 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 DC-voltage 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.

Fig. 5. Control desk panel for testing the wind turbine control strategy and for monitoring and on-line tuning the parameters.

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, DClink voltage controller design and LCL-filter design, as it 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, and therefore it can be designed using smaller components [6]. The parameters of the controller will be obtained on the base of the transfer functions of the system modeled in paragraph II.D. The PI current controller with de-coupling is designed using pole-zero placement technique. When designing an LCL-filter, the limits on the parameter values should be considered [4]: • the capacitor value C F is limited by the tolerable decrease of the power factor at rated power P N (less than 5 %); • the total value of the inductance should be lower than 10 % of the grid impedance Z b 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. Base values are calculated based on line-to-line voltage E N , nominal power P N and grid frequency ω G : 2 ( EN ) = 14.55Ω; C = 1 = 218.8µ F ….(10) Zb = b PN ωG ⋅ Z b Total voltage drop on the filter should be less than 10 %, therefore total inductance should be less than: 0.1 ⋅ Z b = LTOT = 4.6mH ……………………..(11) ωG The resonance frequency is set to half of the switching frequency (f sw = 5 kHz): ωres =k ⋅ ωsw =0.5 ⋅ 2π ⋅ f sw =15708rad / s …(12)

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The factor k expresses how far the switching frequency from the resonance frequency is. Adopting 2.7 % impedance for the converter side, a 10 % current ripple can be obtained when using only an L-filter. With additional LC part the aim is to reduce the ripple at 2 %: 0.393[Ω] …………………..(13) ZL = Z b ⋅ 2.7% = The inverter side inductance (L I ) is then:

ZL = 1.25[mH ] ……………………….(14)

ωG

1 ⋅ ωres = 2.33[kHz ] 2π The damping is a compromise between power losses and stability requirements: 1 1 RD = ⋅ = 3.79 ≅ 4[Ω] …………….(18) 3 ωres ⋅ CF The Bode Diagram of the tf (9) of the undamped and damped LCL-filter and of the L-filter is presented in Fig. 6. Figure 7 shows the current attenuation using LCL-filter. f res =

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’s plant, and sampled 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 controlled subsystem in s-plane is: iG ( s ) RD ⋅ CF ⋅ s + 1 …(19) G = (s) = uI ( s)

LI LG CF ⋅ s + RD CF ⋅ ( LI + LG ) ⋅ s + ( LI + LG ) ⋅ s 3

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Using zoh equivalent in z-plane we get the transfer function: 0.0718 ⋅ z 2 + 0.081 ⋅ z + 0.0209 ……………....(20) 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 …………………………………..(21) z −1

z − (1 − ) kP ⋅ H PI ( z=

Fig. 6. Bode plot of the damped and undamped LCL-filter and of L-filter (L=2.75 mH). 20 10

ii [A]

Reactive power stored in the capacitor is 5 % of the system power rating, so the maximum capacitor value is: Q Cmax = = 11[ µ F ]; 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 [6], such that the capacitance of the filter is C F = 6 μF. The aim is to obtain 20 % ripple attenuation that can be expressed by the following equation [5]: iG (hsw ) 1 = = 0.2 ……………….(16) iI (hsw ) 1 + r (1 − a ⋅ x) where a = L I C b ω sw 2, x = C F /C b = 0.0274, r = L G /L I > 1.1. Considering the reduction of the effectiveness caused by the damping resistor, the chosen value is 1.2 and then the grid side inductance is: L G = rL I = 1.5 mH. Neglecting losses we get: LI + LG ω= = 14.7 ⋅103 [rad / s ] res …...(17) LI ⋅ LG ⋅ CF

0 -10 -20 0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

0.14

0.105

0.11

0.115

0.12 t [s]

0.125

0.13

0.135

0.14

20 10

ig [A]

= LI

0 -10 -20 0.1

Fig. 7. Comparison between inverter current (ii) and grid current (ig) using LCL-filter.

Fig. 8 presents the Simulink model of the current control loop in z-domain. Fig. 9 a) shows zero-pole placements of the openloop system without PI-regulator and Fig. 9 b) of the closedloop system. Figure 9 c) shows the frequency response of the optimized current-loop of the system. As can be seen in Fig. 9 a) there are two complex-conjugated poles and one real-pole. Because of the complex-conjugated poles compensation technique cannot be used; instead, a pole-zero placement technique is used. Fig. 9 b) shows the zero-pole placement for optimized closed loop. 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 k P = 4.8 and the integrator time-constant Ts = 8 ms.

Fig. 8. The model of current control loop developed in Simulink.

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b)

 1 + s ⋅ Ti ) kP ⋅  H PI ( s=  s ⋅ Ti

 …………………………(29)  

When C DC >> (τ 0 +T et ), optimal symmetry criterion to design parameters of the PI-controller can be used [8]: CDC ….(30) 4 (Tet + τ 0 ) = 0.02; k P = Ti =⋅ 2 ⋅ k DC ⋅ (τ 0 + Tet ) The gain of voltage controller is verified using the root locus of the open-loop transfer function (tf) in the s-plane, where delay is replaced by a tf with the time delay τ 0 . Hence the open-loop transfer function becomes: k ⋅ (1 + sTi ) .…(31) k DC c) = ⋅ P H 0 (s) Fig. 9. The pole-zero placements of open-loop (a) and closed-loop (b) of the s ⋅ CDC ⋅ (1 + s ⋅ Tei ) ⋅ (1 + s ⋅τ 0 ) sTi system, and Bode Diagram of the optimize current-loop c). The block diagram of the DC-link voltage control loop The bandwidth is a frequency where the gain of the closed implemented in MATLAB & Simulink is depicted in Fig. 10 loop is reduced to -3 dB (Fig. 9c) and the phase delay becomes and root locus and Bode Diagram are presented in Fig. 11. larger than 450 assuming that closed loop behavior can be approximated by a first-order delay element [5]. An approximation of the closed-loop can be done using a firstorder transfer function with the bandwidth of 208 Hz, as can also be seen in Fig. 9 c): 1 1 H CL ( s ) ≈ ; Tet = = 0.76[ms ] ….(23) 1 + s ⋅ Tet 2π ⋅ fbw Fig. 10. Block diagram of the DC-link voltage control loop.

C. DC-Link Voltage Controller Design Voltage controller design uses the mathematical model of DClink and can be designed in s-plane because the time constants of the controlled subsystem are much bigger than the sampling period (Ts). The cascade connected DC-link voltage controller is designed using symmetric optimum in order to reject the disturbances on the DC-link voltage. The current of DC-link (i DC ) can be calculated using power balance between DC and AC side as follows: 3 uDC ⋅ iDC = ud ⋅ id + uq ⋅ iq ………………....(24) 2 When the grid converter (active rectifier) operated with unity power factor (i q =0), i DC is expressed as: 3 ud ⋅ id iDC = ⋅ = K DC ⋅ iD ……………………...(25) 2 uDC Selecting the operating point of controller u d = 326 V and u DC = 700 V, we obtain: 3 u 0.7 ………………………….…(26) K =⋅ d =

(

DC

)

2 uDC

The transfer function (tf) of DC-link is: uDC ( s ) 1 …………………….(27) H= = DC ( s ) iDC ( s ) s ⋅ CDC If the transfer function of the current loop is approximated by a first order tf ( H CL ( s )= 1/(1 + s ⋅ Tei ) ), one can get the transfer function of the controlled subsytem:

H 0 ( s) =H DC ( s) ⋅ H I ( s) =K DC ⋅

e− s⋅τ 0 …(28) s ⋅ CDC ⋅ (1 + s ⋅ Tet )

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

a) b) Fig. 11. Root locus of open-loop with selected gain k p = 0.35 (a) and frequency response (Bode Diagram) of closed-loop (b).

As can be seen in Fig. 11 the optimal gain selected by using root locus method is k P = 0.35 and the bandwidth of the closed loop is 13 Hz. The parameters obtained for the DC-link voltage controller are: k P = 0.35 and T i = 20 ms. IV. SIMULATIONS VERSUS EXPERIMENTAL RESULTS A simulation model was built in order to verify the validity of the designed controllers and the LCL-filter. The simulation model was implemented using MATLAB & Simulink. Simulation results are used for implementation and to verify the wind generator system model that we developed. There are two modes of operation of the grid converter, rectifying mode (Fig. 12 b) and generating mode (Fig. 12 a). The figure 12 shows the phase current (i a ) and phase voltage (u a ) at nominal load in steady-state in both operation modes.

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In the grid – connection mode, basically all the available power, which can be extracted from the wind turbine, is injected into the grid. Fig. 13 illustrates an acquisition of data at steady-state using an oscilloscope (TDS 540) at nominal load (11 kW) in generating mode (Fig. 13 a) and in motoring mode (13 b). In rectifying mode phase voltage (u a ) is in phase with phase current (i a ), while the difference in generating mode is 90 degrees. The DC-link voltage controller maintains the DC-link voltage almost constant when applying a disturbance of nominal load (DC-link voltage drop is under 4 %). The correspondence between simulations (Fig. 12) and experiments (Fig. 13) at steady-state is good and confirms the correctness of the design of the control system.

V. DISCUSSION AND 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 LCLfilter, 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 both experimentally and by simulation, and the desired current ripple attenuation has been achieved for the test system parameters. The simulations were compared with experimental results and a good consistency was achieved. Both simulation results and experimental results confirm successful design of the wind generator system. A further research topic in the field of design of a LCL-filter is the development of a more embedded design procedure taking into account EMI disturbances. Both simulation and experimental models can be used for further development in the field of low – harmonics elimination, especially in the case of distorted grid.

a)

VI. REFERENCES Periodicals:

b) Fig. 12. Simulated grid phase current and voltage at nominal power (11 kW) generating mode, (a) and rectifying mode, (b).

[1] R. Teodorescu and F. Blaabjerg, “Flexible control of small wind turbines with grid failure detection operating in stand-alone and gridconnected mode”, IEEE Transactions on Power Electronics, vol. 19, No. 5, pp. 1323 – 1332, September 2004. [2] L. Mihet-Popa, F. Blaabjerg and I. Boldea, ”Wind Turbine Generator Modeling and Simulation where Rotational Speed is the Controlled Variable”, IEEE-IAS Transactions on Energy Conversion, January / February 2004, Vol. 40, No. 1.. [3] M. Liserre, F. Blaabjerg and S. Hansen, ”Design and Control of an LCL-filter-Based Three-Phase Active Rectifier”, IEEE Transactions on Industry Applications, Vol. 41, No. 5, September/October 2005, pp. 1281-1291.

Books: [4] A. Tewari, Modern Control Design with MATLAB and Simulink, New York: Wiley, 2002. [5] D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives”, Oxford University Press, 1996.

Papers from Conference Proceedings: a)

[6] L. Mihet-Popa, V. Groza, O. Prostean and I. Szeidert, “Modeling and Design of a Grid Connection Control Mode for a Small Variable-Speed Wind Turbine System”, 2008 IEEE International Instrumentation and Measurement Technology Conference Proceedings-I2MTC, 12-15 May, Vancouver-Canada, 2008, pp. 288-293. [7] L. Mihet-Popa, V. Groza, G. Prostean, I. Filip and I. Szeidert, “Variable speed wind turbines using cage rotor induction generators connected to the grid”, Proceedings of EPC 2007, vol. III, , pp. 271 – 279, Montreal-Canada 2007. [8] L. Mihet-Popa, “Wind Turbines using Induction Generators connected to the grid”, Ph. D Thesis, The POLITEHNICA University of Timisoara-Romania, October 2003.

Dissertations: b) Fig. 13. Phase current (i a ), phase voltage (u a ) and DC voltage (U DC ) at nominal load in generating mode, (a), and in rectifying mode (b), acquired by an Oscilloscope.

[9] R. Otterbach, T. Pohlmann, “DS1103 PPC controller board-rapid prototyping with combined RISK and DSP power for motion control”, Proceedings of PCIM’98, Nurnberg-Germany.

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VII. BIOGRAPHIES Lucian Mihet-Popa received the B.S. degree, M.S. degree and Ph.D. degree from the POLITEHNICA University of Timisoara, Timisoara, Romania, in 1999, 2000 and 2003, respectively, all in electrical engineering. He is currently working as Associate Professor in the Department of Electrical Machines and Drives, Timisoara, Romania. He has visited Aalborg University, Denmark, in 2000, 2001 and 2002 and Siegen University, Germany in 2004 as a guest researcher. He received in 2005 the second prize paper award of the IEEE Industry Applications Society. His research interest includes control and modeling of induction machines, detection and diagnosis of faults, especially for wind turbine applications. Voicu Groza received the B.S. degree and Ph.D. degree from the POLITEHNICA University of Timisoara, Romania, in 1972 and 1985, respectively. He is currently working as Associate Professor in School of Information Technology and Engineering, University of Ottawa. His research interest includes real-time embedded systems, distributed intelligent instrumentation and smart sensors networks.