DPC of the Doubly Fed Induction Generator Based on ...

DPC of the Doubly Fed Induction Generator Based on the WECS F. Mazouz 1*, S. Ouchen 2 , A. Bezzou 3, S. Belkacemi 4 1 Electrical Engineering Laboratory LEB, Batna2 University, Algeria. 2 Electrical Engineering Laboratory LGEB, Biskra University, Algeria. 3 Electrical Engineering, Bordj Bou Arreridj University, Algeria. 4 Electronic Engineering, Batna2 University, Algeria. * Mazouz Farida, e-mail: [email protected].

Keywords «Direct Power Control “DPC”», «Doubly Fed Induction Generators “DFIG”», «Wind Enrgy Conversion system “WECS”», «Wind Turbine», «Generator», «Modeling».

Abstract The purpose of this work is to study and model a wind energy conversion system (WECS), based on a double feed induction generator (DFIG), and controlled by direct the powers control (DPC), through a power converter on the rotor side. This technique uses row-side converter voltage space vectors (RSC) in line with an optimal switching table as a function of the stator flux position and the active and reactive power states. Simulation results on a 1.5 MW DFIG, robust, precise and fast dynamic behaviour of the machine.

I.

Introduction

Doubly fed induction generators (DFIG) are extendedly used in modern wind power generation systems due to their variable speed operation, [1], [2], [3] Classical control of grid-connected DFIG is usually based on the orientation of the stator voltage oriented, stator-flux (SFO), or vector control (VC), [4], [5], [6], [7]. Control of instantaneous stator active and reactive powers is then achieved by regulating the decoupled rotor currents, using proportional-integral (PI) controllers, [8], [9]. One main drawback for this control scheme is that the performance highly relies on the tuning of the PI parameters and accurate machine parameters such as stator and rotor inductances and resistances, [8]. The progress of power electronics related to the onset of rapid switches and the development of digital technologies have enabled the control of power full with of high efficient controllers. New control strategies have been proposed such as direct power control (DPC) [10]. Direct Power Control (DPC) provides fast dynamic response, simple structure and proper operation in presence of parameter variations [11]. However, basic DPC suffers large ripple in currents, active and reactive powers. Also, variable switching frequency is another disadvantage of this method. This paper is proposed an approach for synchronization of DFIG by using direct power control (DPC).

II.

System description

This paper presents a direct power control (DPC) of DFIG, which uses one unified switching table to obtain the three vectors [12]. The information of rotor speed is not needed in the process of vector selection. The results prove that the proposed DPC can achieve active/reactive power ripples reduction and quick dynamic response at a low switching frequency. Fig. 1 shows the proposed control algorithm for the DFIG based WECS. In this DPC (Direct Power Control) algorithm, the active and reactive powers are controlled directly by switching the voltage vectors at the rotor side terminals by using VSC. In this control strategy, the rotor position sensor is eliminated by using a position sensor less algorithm as discussed in the following section.

Fig 1: Schematic diagram of DPC for a grid-connected DFIG system.

III.

DFIG model

The dynamic equations of the DFIG in the reference d-q can be written as follows [6], [11], [9]. The voltage equations are given by: 𝑑𝜑𝑑𝑠 − 𝜔𝑠 𝜑𝑞𝑠 𝑑𝑡 𝑉𝑞𝑠 = 𝑅𝑠 𝐼𝑞𝑠 + 𝜔𝑠 𝜑𝑑𝑠 + 𝜔𝑠 𝜑𝑞𝑠 𝑑𝜑𝑑𝑟 𝑉𝑑𝑟 = 𝑅𝑟 𝐼𝑑𝑟 + − (𝜔𝑠 − 𝜔)𝜑𝑞𝑟 𝑑𝑡 𝑑𝜑𝑞𝑟 (𝜔 { 𝑉𝑞𝑟 = 𝑅𝑟 𝐼𝑞𝑟 + 𝑑𝑡 + 𝑠 − 𝜔)𝜑𝑑𝑟

(1)

𝜑𝑑𝑠 = 𝐿𝑠 𝐼𝑑𝑠 + 𝑀𝐼𝑑𝑟 𝜑𝑞𝑠 = 𝐿𝑠 𝐼𝑞𝑠 + 𝑀𝐼𝑞𝑟 𝜑𝑑𝑟 = 𝐿𝑟 𝐼𝑑𝑟 + 𝑀𝐼𝑑𝑟 { 𝜑𝑞𝑟 = 𝐿𝑟 𝐼𝑞𝑟 + 𝑀𝐼𝑞𝑟

(2)

𝑉𝑑𝑠 = 𝑅𝑠 𝐼𝑑𝑠 +

The flux equations are given by:

The arrangement of the equations (1) and (2) gives the expression of the rotor voltages according to the rotor currents by: 𝑀2 𝑑𝐼𝑑𝑟 𝑀2 ) − 𝑔𝜔𝑠 (𝐿𝑟 − )𝐼 𝐿𝑠 𝑑𝑡 𝐿𝑠 𝑞𝑟 2 𝑑𝐼 2 𝑀 𝑀 𝑀𝑉𝑠 𝑞𝑟 𝑉𝑞𝑟 = 𝑅𝑟 𝐼𝑞𝑟 + (𝐿𝑟 − ) + 𝑔𝜔𝑠 (𝐿𝑟 − )𝐼 + 𝑔 𝐿𝑠 𝑑𝑡 𝐿𝑠 𝑑𝑟 𝐿𝑠

𝑉𝑑𝑟 = 𝑅𝑟 𝐼𝑑𝑟 + (𝐿𝑟 −

(3)

The torque equation is represented as follows:

𝐶𝑒𝑚 = 𝑝

𝑀 (𝐼 𝜑 − 𝐼𝑑𝑟 𝜑𝑞𝑠 ) 𝐿𝑠 𝑞𝑟 𝑑𝑠

(4)

The supplied active and reactive powers are defined as follows:

{

𝑃𝑠 = 𝑉𝑑𝑠 𝐼𝑑𝑠 + 𝑉𝑞𝑠 𝐼𝑞𝑠 𝑄𝑠 = 𝑉𝑞𝑠 𝐼𝑑𝑠 − 𝑉𝑑𝑠 𝐼𝑞𝑠

(5)

Adopting the assumption of a negligible stator resistance Rs and the stator flux is constant oriented along the axis, we deduce:

φds = φs

et φqs = 0 𝑑𝜑𝑠 𝑉𝑑𝑠 = =0 { 𝑑𝑡 𝑉𝑞𝑠 = 𝑉𝑠 = 𝜔𝑠 𝜑𝑠

The stator active and reactive power can be expressed as the rotor currents as follows:

(6)

𝑃𝑠 = −𝑉𝑠

𝑀 𝐼 𝐿𝑠 𝑞𝑟

𝑉𝑠2 𝑀 𝑄𝑠 = − 𝑉𝑠 𝐼𝑑𝑟 𝐿𝑠 𝜔𝑠 𝐿𝑠

(7)

From the principal equations we can construct the scheme of DFIG illustrated in figure 2:

Fig 2: Simplified diagram of the DFIG

IV.

Direct Power Control Strategy

DPC method for DFIG is presented for the first time by Takahashi and Depenbrock, [13], [14]. Direct power control is based on the same control principles as the direct torque control technical (DTC). The unique difference is the directly controlled variables. In the case of DTC, the electromagnetic torque and the stator flux are directly controlled, while in DPC, the stator active and reactive powers are directly controlled by selecting the optimum switching state of the converter, [6], [7]. Direct Power Control (DPC) was initially proposed by its simplicity, allowing fast power response without the complex field-orientation block. It doesn’t require the knowledge of the machine parameters, and due to this, shows great robustness, [3]. The method selects appropriate voltage vectors from an optimal switching table, based on the stator flux position and active and reactive power errors. There is no necessity to estimate the rotor flux. The magnitude and angle of the voltage vector can either be increased or decreased by applying appropriate vectors in the α-β plane, [2].

Fig.3: Basic DPC bloc diagram.

The principal of DPC based on the determination of instantaneous rotor vectors in each sampling period regarding desired stator active and reactive powers, [10]. The bloc diagram of the basic DPC strategy is shown in Fig. 3. The computed values of stator active and reactive powers are compared to the corresponding references. The errors are applied to stator active and reactive powers hysteresis regulators, respectively. Outputs of stator active and reactive powers regulators and the phase of the stator flux expressed in the rotor reference are applied to the rotor vector location table block which generates the convenient combinations of the states (ON or OFF) of the inverter power switches, in order to ensure the maintenance of the stator active and reactive power errors within the bands of the hysteresis comparators [10]. The stator flux vector location in rotor reference frame is divided into six sectors as shown in Fig. 4. Stator flux (s r) location in rotor reference frame is denoted with sector number (N), [5]

Fig. 4: Switching-voltage space vectors. Where the binary numbers in the brackets show switching states in the phase sequence (a, b, c). Binary number “1” means top switch is on and “0” means bottom switch is on. Out of these eight voltage vectors, six are active vectors (V1-V6), remaining two are zero vectors (V0, V7). When applying the zero vector, the choice between U0 (000) or U7 (111) depends on the converter legs switching during change of the states, [2].

IV.1 Hysteresis power control The module and the phase of the stator flux referred to the rotor winding are given by:

  r  2  2 s s  s   s )  s  arctan(  s 

(8)

Determining the position  s is essential to select the sector where the flux belongs. The active and reactive powers are controlled by two regulators hysteresis (Fig. 5), the measured values of the powers being estimated from relationships, [15]:

3  P  (Vs I s  Vs I s ) s  2  Q  3 (V I  V I ) s s   s 2 s s

(9)

The real and reactive powers errors are passed through the three level hysteresis controllers, [4], [15], for generating the respective active and reactive power switching states SP (1,0,-1) and SQ (1,0,-1) as shown in Fig. 5. The real and reactive power errors (Perr and Qerr) are estimated as:

 Ps _ error  Ps*  Ps  * Qs _ error  Qs  Qs

(10)

Defines the equation (10) in the αβ references is sufficient to have independent control of power active * * and reactive. This means that for any reference Qs and Ps only the current and the measurement voltage to the stator are needed to implement the DPC. No transformation between vectors commutative and machine dimension converter required, [15].

Fig.5: Active and reactive power hysteresis comparators

IV.1 Switching Table Selection of appropriate vector applied to the rotor side converter is presented by the following table (Table 1), this table permit to control the active and reactive power exchanged with grid [4], [7], [16].

Table I: Optimal switching Table for Direct Power Control of DFIG. Sp

-1

Sq

Stator flux position

0

1

-1

0

1

-1

0

1

-1

0

1

1

V3

V4

V5

V3

V0

V5

V2

V1

V6

2

V4

V5

V6

V4

V7

V6

V3

V2

V1

3

V5

V6

V1

V5

V0

V1

V4

V3

V2

4

V6

V1

V2

V6

V7

V2

V5

V4

V3

5

V1

V2

V3

V1

V0

V3

V6

V5

V4

6

V2

V3

V4

V2

V7

V4

V1

V6

V5

V.

Simulation results

The following figures show the simulation results of the direct control of the active and reactive powers of the DFIG. For a different period of time, the reference value of the active power was varied in order to study the effectiveness of the control technique applied to the wind system, t = 0.7s, the reference in reactive power is adjusted To zero so that the power factor of the stator is kept unitary.

Puissance Active (Ps)

5

2

x 10

Ps P ref

5

x 10 0

Ps (Watt)

Peak due to the sudden change in reactive power

-5

-2

-10

-4

-15 0.695

0.7

0.705

-6

5

-8

0

-5

-10

-10 0.295

-12

-14

x 10

0

0.3

0.1

0.305

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

temps (s)

Fig.6: Active power 1

x 10

Reactive Power (Qs)

5

Qs Q ref 0

-1

5

5

0

-2

Qs (Watt)

x 10

-5 -3 -10 0.695

0.7

0.705

-4

-5

-6

-7

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (s)

Fig.7: Reactive power. Stator Current (Is) 3000 Isa Isb Isc

2000 1st change in active power 2000

0

-2000 0.25

Is abc (A)

1000

0.3

0.35

0

-1000 5000 -2000 2nd variation of the active power

0

-5000 0.65 -3000

0

0.1

0.2

0.3

0.4

0.7

0.5

time (s)

Fig.8: Stator Current.

0.75 0.6

0.7

0.8

0.9

1

Rotor current (Ir) 3000

5000

Ira Irb Irc

2nd variation of the active power

0 2000 -5000 0.68

0.7

0.72

Ir abc

1000

0

-1000 2000 0 -2000

1St change in active power

-2000 -3000

0

0.1

0.3

0.32

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (s)

Fig.9: Rotor Current. The figures (Figure 6 and Figure 7), Showing the active and reactive powers, the two powers are well adapted to the variations in applied reference, At t=1.3s and t=0.7s, we notice the influence of the sudden change of the active power on the stator and rotor currents ( Figure 8 and Figure 9), the two currents are well adapted to the variations of the active power with sinusoidal shapes and almost without harmonics. The variation of the reactive power directly influences on the active power with a peak which is seen in figure 6.

VI.

Conclusion

In this paper, an approach has been proposed to control the DFIG-based wind system. A direct power control (DPC) technique was used to test the robustness of the latter. The study of the principles of the structure of the DPC control in the production casing has been developed from ideal operating conditions where the effect of the stator resistance is neglected. In addition, the switching frequency is variable and difficult to control due to the use of hysteresis controllers. This is one of the main disadvantages of DPC. In order to improve the control performance of the wind conversion chain, we have introduced the concept of direct control of the active and reactive powers by monitoring the variation of reactive power. The simulation results obtained are very satisfactory.

VII. Simulation Parameters Table II: Turbine parameters. Balde radius, R Number of blades Gearbox ratio, G Moment of inertia, J

35.25 m 3 90 1000 Kg.m2

Viscous friction coefficient, f Cut-in wind speed Cut-out wind speed Nominal wind speed, v

0.0024 N.m.s-1 4 m/s 25 m/s 16 m/s

Table II: DFIG parameters. Rated power, Pn Stator rated voltage, Vs Rates current, In Rated DC-link voltage UDC Stator rated frequency, f Number of pair of poles, P

1.5 MW 398/690 V 1900 A 1200 V 50 Hz

Stator resistance, Rs Rotor resistance, Rr Stator inductance, Ls Rotor inductance, Lr Mutual inductance, M

0.012 Ω 0.021 Ω 0.0137 H 0.0136 H 0.0135 H

2

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