Control Strategy Analysis and Modelling of the DFIG with ... - IRD India

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Control Strategy Analysis and Modelling of the DFIG with Indirect Matrix Converter in WECS

1Kuldeep Behera, ²Subrat Behera

1,2Electrical Eng., KIIT University, Bhubaneswar, India

Abstract: The indirect matrix converter as induction motor drivers has received considerable attention recently because it is a good alternative to conventional back to back converter. The modulation strategy carried out here is the space vector modulation through MATLAB/

SIMULINK. More over the control strategy is also very much flexible in their operation at any rated power. The closed loop control of DFIG incorporated for the current and voltage control of the rotor is done by the vector control method. The space vector algorithm used for indirect matrix converter for the soft switching. To integrate the system with grid the input and output filters are designed. This method leads to the reduction of losses predominantly increasing the efficiency of output. It is highly effective for wind energy conversion system(WECS).

Keywords: Indirect matrix converter (IMC), Direct matrix converter (DMC), Space vector modulation (SVM), Pulse width modulation (PWM), Space vector pulse width modulation (SVPWM), Doubly fed induction generator (DFIG), Wind energy conversion system(WECS).

I. INTRODUCTION

With increased penetration of wind power into grids DFIG based wind turbines are largely deployed due to their dynamic response and operating with variable wind speed feature. Now a days wind turbines are subjected to variation of load and impact of frequent change in wind speed with respect to the nonlinear behaviour of nature.

Induction motors are frequently used in real world for industrial drive applications. Due to the advantage of bidirectional power flow and controllable power factor the IMC can replace the conventional back to back converter which has been experimentally verified.

Another great advantage of the IMC is the absence of the dc-link capacitor. The design of capacitor was a hard and expensive job in previous days. A usual drawback of this converter scheme is the voltage ratio limitations.

Theoretically the maximum voltage transfer ratio is 87%

of the input voltage with lower order harmonics. But this is not a very significant problem because the rotor voltage depends upon stator voltage with respect to the speed characteristics. L-C filters are used to reduce the harmonics injection in both input and output of converter. And the resistor in combination to filter improve the damping of system.

The main application of IMC here is to control the rotor current of DFIG with variable speed system. In this paper the DFIG fed by indirect space vector modulated

matrix converter is proposed. Only results of simulation are presented.

II. TOPOLOGY

The stator windings of DFIG is directly connected to grid and the rotor windings are connected to grid through the proposed converter called as indirect matrix converter. The IMC consist of GSC (works as current source inverter) and RSC ( works as voltage source inverter).A virtual dc-link is created between the converters by the space vector modulation switching scheme. But physically there is no capacitor between them.

Fig.1: Circuit diagram of DFIG with IMC The system concept is that machine side converter(RSC) controls the speed by controlling the output current, which can be manipulated by the virtual dc-link by adjusting the input to GSC. Thus the power factor can be improved easily. Due to the bidirectional power flow of the converter the rotor circuit of DFIG able to work as a generator both in sub-synchronous and super- synchronous mode. Depending upon the mode of operation the power is either feed to or feed from the rotor. Rotor side converter used to generate or absorb power from grid in order to keep the voltage constant. In steady state we can assume the power of stator side is equal to the rotor power and in both sub-synchronous and super-synchronous mode rotor absorbs power from the converter. The modes are determined from the three phase voltage sequence of the generated rotor voltage.

The frequency of this voltage is equal to the product of grid frequency and the absolute value of slip. If the slip value is negative the machine is running above synchronous speed in the direction of rotating field. If the slip is positive the machine has to be driven by a mechanical power to counteract the torque. It is called the generating mode of machine. The both side

converter have capability of generating or consuming reactive power from grid terminal.

III. INDIRECT MATRIX CONVERTER

Fig. 2. Circuit diagram of Indirect Matrix Converter The source from grid feeds the input terminals of converters where as the output terminals are linked to three phase machine like induction motor. The size of capacitive filter on the voltage feed side and inductive filter on the current feed side are inversely proposal to switching frequency if the MC. The capacitive filter on the voltage- fed side and the inductive filter on the current- fed side represented in the scheme of MC are intrinsically necessary. Their size is inversely proportional to the matrix converter switching frequency.

The IMC is assembled by series connected two mutually anti-parallel connected current link converters and a two level-six switch voltage source converter.

Instead of special sensing mechanism of current and voltage, IMC can commutate offering a reduced complexity of choosing modulation. IGBT with reverse blocking have recently available for construction of bi- polar switch having two anti-parallel connected transistor.

IV. BIDIRECTIONAL SWITCH

To implement the four step strategy the bi-directional switches are designed to control the current flow in the circuit. The fig(2) shows an example of two phase input with a single phase load at output. In steady state both the devices are to be active to allow the current flow.

Considering the current flows in load as shown in fig the upper (SA) is closed.

Fig. 3. Function of 2 level converter

For communication to the lower half (SB), the device SAa2 is in active state but not conducting. So it is turned off. The reverse in case when SBa is conducting. The process is shown in the timing diagram. Time delay is dependent on the device characteristics.

Fig. 4. Timing diagram of soft switching Advantage of this method is the current conduct in one switch after another switch with no line-line short circuit and load open circuit. The switching losses is reduced by 50% because of this soft switching process.

V. COMMUTATION SCHEME

OF

IMC

The inverter input state and rectifier input state have to be performed in order to avoid short circuit and dead time between transistor turn-on turn-off for a particular switching state. To change from one switching state to another it should to care about that, there should not be any bidirectional path among any input lines having a continuous path for current flow..

A. Space Vector Modulation

A reference voltage is provided using a rotating reference vector. This orientation of reference vector is chosen in order to control the fundamental component of frequency and magnitude in the line side. The most efficient dc link voltage generated by this modulation contains less number of harmonic distortion. The objective of any modulation scheme is to generate variable output with maximum fundamental component and minimum harmonics.

B. DC link Formation

IMC provide freedom in control strategy which reduces the complexity in communication problem. The important technique that has to be considered is that, in the free-wheeling time of inverter stage the rectifier should commutate with zero dc-link current with no overlapping in transistor switching. Thus reduces the losses in switching of the system. Further the number of switches has also reduced and many new topologies are being developed named as SMC, VSMC, USMC etc.

Fig. 5. Behavior of dc-link voltage and three phase input voltage with average dc-link voltage The concept of modulation described here can establish zero dc-link current and the commutation is applicable to IMC. For the maximum output voltage formation one phase input is hold on to positive or negative dc-link bus in a particular interval and phase voltage has highest absolute value shown in table I.

Now instead of considering the total rotating field of the reference vector we will limit our consideration in the interval 0 to π/6. Here the Ua is clamped on with maximum positive voltage and Uac, Uab are two line- line voltage segments. The voltage generated for this state having two different levels assuming the instant average value of current as constant. The total interval (0 to π/6) is denoted by Tp. Further the Tp is divided into many segments depending on the vector selection or switching pattern and denoted by Δ.

TABLE I : OUTPUT VOLTAGE OVER A PERIOD

Ωt Up Un U

0 ... π/6 Ua Ub, Uc Uab, Uac

π/6....2π/6 Ua, Ub Uc Uac, Ubc 2π/6....3π/6 Ub, Ua Uc Ubc, Uac 3π/6....4π/6 Ub Uc, Ua Ubc, Uba 4π/6....5π/6 Ub Ua, Uc Uba, Ubc 5π/6....6π/6 Ub, Uc Ua Uba, Uca 6π/6....7π/6 Uc, Ub Ua Uca, Uba 7π/6....8π/6 Uc Ua,Ub Uca, Ucb 8π/6....9π/6 Uc Ub,Ua Ucb, Uca 9π/6....10π/6 Uc, Ua Ub Ucb,Uab 10π/6....11π/6 Ua, Uc Ub Uab, Ucb 11π/6....12π/6 Ua Ub, Uc Uab, Uac

Now considering the symmetry of the topology the three phase input having angular frequency ω amplitude U1 be;

Ua = U1 cosθ Ub = U1 cos θ−2π

3 Uc = U1 cos θ+2π

3 where

Ua + Ub + Uc = 0

Switching of the rectifier takes place during the free- wheeling interval for the coordinated commutation of rectifier and inverter stage. This can be achieved by turning on the transistor of one leg simultaneously, assuming input currents ia, ib, ic = 0 and Dab+Dac = 1, where Dab, Dac are relative on times for generating Uab, Uac. Simpler commutation can be implemented by changing all switching state of rectifier linking with the inverter free-wheeling interval. In similar way inverter stage can be operated.

ia = Dac + Dab i , ib = − Dab i, ic = −(Dac)i Dac = −ic

ia= −Uc

Ua and Dab = −ib

ia= −Ub Ua Now the result in output can be achieved by two active vectors V(100) and V(110) and either one of the free- wheeling state V(000) or V(111). So we can write dc- link voltage as U = Uac and U = Uab and time period as

∆ab = Dab^Tp₂ , ∆ac = Dac^Tp₂

Fig. 6. Generation of dc-link voltage v and current i within a pulse period

In each voltage segment the pattern of turning on and turning off states of devices are changed considering that there should be only one state change at each time.

And each change in state is denoted by δ.

δ100, ac =^∆100,ac_∆ac and δ100, ab =

∆100,ab

∆ab ...(1) similarly

δ110, ac =^∆110,ac_∆ac and δ110, ab =^∆110,ab_∆ab ...(2) Taking

U100 = 2 3 U and

U110 = 2 3 Ue^jπ/3 the output formed in time Tp/2 is

U^∗= 2 Tp3

2

Uac ∆100, ac + Uab∆100, ab

+ e^jπ3 Uac ∆110, ac + Uab ∆110, ab ...(3) Considering above equations

U^∗= Uac Dac + Uab Dab δ100

+ Uab Dab + Uac Dac e^jπ/3δ110 ...(4) And average value

U = Uab Dab + Uac Dac so

U^∗=²₃ [Uδ100 + U e^jπ3δ110]...(5) C. Dwell Time

Time interval of active switching states can be calculated by directly referring local average values.To calculate on time intervals of active switching states we could directly refer local average value of the dc link voltage. Referring to the dwell time interval of two level inverter i.e.

T =^V_V^ref

dc sin π

−α 3 sinπ

3 Ts...(*) where

U = V_dc, U2∗= U^∗and U2∗= Vref

Therefore

δ100 = 3^U_U ^2∗cos π

+6 α ...(6)

and

δ110 = 3^U_U ^2∗ sinα...(7) From (6) , (7) and (*)

∆100, ac = −1 3

U^∗

U²Tp cos π

+6 α Uc

∆100, ab = −1 3

U^∗

U²Tp cos π

+6 α Ub

∆100, ac = −1 3

U^∗

U²Tp sinα Uc

∆100, ab = −1 3

U^∗

U²Tp sinα Ub

In similar way we can calculate the dwell time for all intervals from π/6 to 2π/6, 2π/6 to 3π/6...11π/6 to 2π.

We can observe that the output voltage formed is √3/2 times of U1. Therefore the modulating index of complete analysis can be taken as

M = U U1≤ 3

2

Fig. 7. Sector diagram comprising of vectors

VI. CLOSED LOOP MODELING OF DFIG

By referring to the equivalent circuit of the induction generator and applying kirchhoff's law

V_ds = r_sI_ds−ω_sλ_qs +_dt^dλ_ds V_qs = r_sI_qs +ω_sλ_ds +_dt^dλ_qs

Vdr = rrIdr− ωs−ωr λ_qr + d dtλdr

Vqr = rrIqr + ωs−ωr λdr +d dtλqr

Where,

Vds , Vqs = d-axis , q-axis stator voltage respectively, V_dr , V_qr = d-axis , q-axis rotor voltage,

I_ds , I_qs = d-axis , q-axis stator current, Idr , Iqr = d-axis , q-axis rotor current, λ_ds ,λ_qs = d-axis , q-axis stator fluxes, λdr ,λqr = d-axis , q-axis rotor fluxes, r_s , r_r = stator and rotor resistance,

ωs = Rotational speed of synchronous reference frame.

The main requirement of vector control strategy is to control the speed and torque of machine thus the power can be controlled. The control has an advantage of independent control of stator flux and electromagnetic torque. It is possible by changing the three phase rotating frame to two phase stationary reference frame.

Generally we follow the Park's transformation to change the frame of reference(abc to dq).

λ_ds λqs

λdr λ_qr

=

L^s 0 Lm

0 Ls 0

L^m

0 0^m

L_m L^r

0

0 Lm

00 L r

ids

i_qs idr i_qr

Vds

Vqs = Rs 0 0 Rs id

iq + d dt

λds

λqs + 0 −ωe

ωe 0 λds

λqs Te=3

2PLm iqsidr− idsiqr λs = Lmims = Stator flux,

λr = Rotor flux,

Ls, Lm, Lr =Stator, magnetizing and rotor inductance vs and is = Stator voltages and currents

vr and ir = Rotor voltages and currents Rr and Rs = Rotor and stator resistances

ωe and ωr = Synchronous and rotating angular frequencies

ωslip = ωe − ωr

Fig. 8: Vector control scheme of DFIG connected with grid

The reference frame is orientated along the stator flux vector. The position of the stator flux vector (θe) is obtained from the stator flux α–β components as

θ_e = tan⁻¹λ_β λ_α

The magnitude and position of the reference rotor vector voltage for each output converter is given by

Ir= i_α^∗2+ i_β^∗2 θe= tan⁻¹i_β

i_α

VII. RESULTS AND DISCUSSION

The proposed control scheme of indirect matrix converter is verified in a open loop condition first with RL load connected. The open results are also shown below. After getting sinusoidal waveform we have gone for the closed loop control of DFIG with IMC. The vector control algorithm is carried out using MATLAB/SIMULINK software. The results shown below are with wind speed 11m/s

Fig. 9(a)

Fig. 9(b)

Fig. 8(a): Nature of generated dc-link voltage waveform and Fig. 8(b): The output current of converter when connected in open loop with RL load.

Fig. 9: Rotor current fed to machine

Fig. 10: Active power(upper) and reactive power (lower) of the rotor side

Fig. 11: Grid side current fed to stator

Fig: 12: Active power(upper) and reactive power (lower) of the stator side

Fig.13: Rotor current fed to machine

VIII. CONCLUSION

A control strategy for modulation of Indirect Matrix converter has been experimentally verified. The sizing of capacitor has been omitted ,thus results in reduction of cost. Also stabilize the frequency variations. Though more number of switches are used, but the switching losses can be reduced by this soft switching control algorithm which is experimentally verified. Further to reduce the harmonics and better performance the PLL loop can be applied to the control mechanism. Controller mechanism can be designed in a better way to increase efficiency in WECS.

ACKNOWLEDGEMENT

We Would like to thank all faulty members of School of Electrical Engineering, KIIT university for all their technical advice. Also gladly thanks to all staff members of the department for helping in implementing the experimental rig used during research.

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