Rev. Roum. Sci. Techn.– Électrotechn. et Énerg. Vol. 63, 3, pp. 332–337, Bucarest, 2018

1 (Corresponding Author) Babol Noshirvani University of Technology, Babol, Iran, izanlo_ali@yahoo.com 2 West Distribution Company of Mazandaran, Nowshahr, Iran, mohammad_v_kazemi@yahoo.com 3 Babol Noshirvani University of Technology, Babol, Iran, sagholamian@gmail.com

A NEW METHOD OF PREDICTIVE DIRECT TORQUE CONTROL FOR DOUBLY FED INDUCTION GENERATOR UNDER UNBALANCED

GRID VOLTAGE ALI IZANLO1, MOHAMMAD VERIJ KAZEMI 2, ASGHAR GHOLAMIAN 3

Key words: Doubly fed induction generator (DFIG), Predictive direct torque control (PDTC), Unbalanced stator voltage conditions.

In this paper, a new predictive direct torque control (PDTC) method is presented for doubly fed induction generator (DFIG) under unbalanced grid voltage. In PDTC, the future behavior of the system is first predicted using the system model, the appropriate voltage vector is then selected using an optimized cost function in each control period. This method is simple and has excellent steady-state and transient performance, because uses from both predicted and reference values. The main advantages of proposed method are that all of the voltage vectors examine in cost function and the voltage vector that minimizes cost function will be applied during the next sampling period. Also, two control targets presented for unbalanced condition. The first target eliminates electromagnetic torque oscillation and the second target eliminates active power pulsations. The simulation was conducted on a 1 MW DFIG and results shows the effectiveness and robustness of new DTC method. It can be seen that the torque and flux ripples are reduced and their transient response are within a few milliseconds.

1. INTRODUCTION Wind power is one of the most promising and fastest

growing renewable energy resources. One of the generation systems commercially available in the wind energy market currently is the doubly fed induction generator (DFIG) with its stator winding directly connected to the grid and with its rotor winding connected to the grid through a frequency converter. The DFIG has several advantages including maximum power capture over a wider speed range and decoupled active and reactive power control. It also allows the use of a partially rated converter, which reduces the cost [1].

One of the control strategies is vector control (VC) [2]. The VC method requires complex decoupling and coordinates transformation, resulting in slow transient performance. All these drawbacks will deteriorate the system performance. To overcome the large amount of tuning work and reduce the control complexity in VC, the direct torque control (DTC) [3, 4] and direct power control (DPC) [5, 6] proposed in recent years. More recently, the application of DPC for the DFIG under unbalanced and asymmetric grid voltage condition has also been reported [7–11]. In [7], a new algorithm for generating the power reference for DPC was presented. It was shown that the oscillation term of electromagnetic torque can be eliminated without any sequence extraction. In [8], presented a comparative study between two sensorless methods for DPC of a DFIG under unbalanced grid voltage. In [9], a resonant feedback regulator based control strategy to compensate the point of common coupling (PCC) voltage imbalance for DFIG presented. Paper [10], paper proposes a direct stator current vector control strategy of a DFIG without phase-locked loop (PLL) during network unbalance. Paper [11], paper proposes a coordinated direct power control scheme for the rotor-side converter (RSC) and the grid-side converter (GSC) of the DFIG under unbalanced grid voltage conditions.

DTC is an active research control schemes, which is on the basis of the decoupled control of flux and torque. DTC provides a very fast and precise torque response without a complex field orientation block and inner current regulation loops. The basic principle of DTC is selecting an appropriate voltage vector from a switching table to restrict both torque and flux errors in their respective hysteresis bands that produce torque and flux ripples and also result in a variable switching frequency. To address these limitations, DTC with space vector modulation based on synchronous reference frame transformations, sliding mode and predictive control are reported in the literature [12–15]. Due to the advantages of simple structure and low dependency on the parameters, DTC was widely used in induction motors, but less attention was paid to DFIG.

In this paper proposed a new predictive DTC with power compensation schemes for power quality improvement under unbalanced grid voltage for DFIG. It has many merits, such as reduced torque and flux ripples, constant switching frequency, and excellent steady state and transient responses. Performance of predictive direct torque control under unbalanced stator voltage has not been reported in literatures yet. Therefore, this paper investigates the operation of DFIG under these voltage conditions using predictive DTC strategy.

2. DFIG ANALYSIS The mathematical equations for a DFIG can be expressed

in the stationary frame (αβ frame) using complex vectors. These are now well known but for completeness they are quoted below [7].

tIRV s

sss dd

(1)

rrr

rrr tIRV

j

dd (2)

rmsss ILIL (3) rrsmr ILIL (4)

2 Ali Izanlo, Mohammad Verij Kazemi, Asghar Gholamian

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,Im

23

Im23 *

srsrm

srme

Lp

LpT (5)

where the phasors and variables are define as:

rs VV , stator, rotor voltage vectors;

rs II , stator, rotor current vectors;

rs , stator, rotor flux linkage vectors;

sr ,,1 synchronous, rotor and slip angular frequency;

mL magnetizing inductance;

rs LL , stator, rotor leakage inductance;

rs LL , stator, rotor self-inductance;

rs RR , stator, rotor resistance;

eT electromagnetic torque; p number of pole pairs;

leakage coefficient, )/(1 2mrs LLL ;

* conjugate complex.

3. PDTC OF DFIG PDTC has been extensively used in control of induction

motor, but it is rarely reported as being used in the control of DFIGs. In [13, 14] a method of PDTC was applied for a DFIG, but, only results were presented for balanced condition and unbalanced condition was not considered. In PDTC, the future behavior of the system is first predicted using the system model, the appropriate voltage vector is then selected using an optimized cost function in each control period.

According to (5), the torque derivative can be expressed as

tt

Lpt

T srs

rm

ed

dd

dIm23

dd *

**

. (6)

By substituting the derivative of the stator and rotor flux from (1) and (2) into the equation (6) and neglecting rotor and stator resistance, electromagnetic torque derivative in the stationary frame can be found as

*** .).(Im23

dd

rssrrrme VjVLpt

T

TV

VLp

tT

sr

srrsrm

e

).Im(

).Re().Im(23

dd

*

**.

(7)

And rotor flux can be derived in a similar manner as

rrrr

r Vt

.Re1d

d * , (8)

where 22 rrr . It can be seen that the DFIG is

modelled using the torque and rotor flux as the state variables and the rotor voltages as input. Based on this discrete time model, the torque and rotor flux at the next sampling instant can be predicted from

skk TTTT .1 (9)

srk

rk

r T.1 , (10) where Ts is sampling period. Now, we should define a cost function. The best cost function for this issue is

),(abs

)(abs 1

1

kref

kref

k

TTfunctionCost + (11)

where k is a constant coefficients. At first the voltage vectors (V1 to V6) placed in the (12) and then T and

r calculated by using (7) and (8). Finally, the values of 1kT and 1 k

r calculated and the voltage vectors that minimized the cost function used in the next period.

.)6,...,1( e.32 3

)1(j

kVVk

dck

r (12)

Note that the amount of krV for V0 and V7 is zero. In

DTC the voltage vector is determined according to a switching table. Thus, the selected vector is not necessarily the best one in terms of reducing torque and rotor flux ripples. But, in PDTC all the possible voltage vectors are evaluated in every sampling period. Therefore, better steady state performance and enhanced dynamic response can be obtained.

The block diagram of PDTC method of DFIG shown in Fig. 1. In first, the required parameters measured and then by using of (3) and (4) the value of r and s are calculated. In the next step the effect of all the voltage vectors on the torque and rotor flux determined and finally

1keT and 1 k

r with refT and refr sent to the cost

function and the best voltage vectors selected for switching of rotor side converter (RSC).

Fig. 1 – Schematic diagram for PDTC of DFIG.

The main objective of the grid side converter (GSC) is to maintain a constant dc link voltage and it is controlled using a similar method as the dc voltage controller in [15].

4. TORQUE COMPENSATION STRATEGIES UNDER UNBALANCED CONDITION

In this section, the control strategies that produces constant stator active power and electromagnetic torque will be analyzed.

According to the [7], in unbalanced condition electromagnetic torque and stator active power by forgoing of the stator resistance can be written as follows

)( PPPPs DCBAP (13)

)(23

PPPPs

e DCBApT

. (14)

Predictive direct torque control for doubly fed induction generator 3

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Notice that AP and BP are constant in steady state since they are composed of the same sequence product. However, the terms CP and DP oscillate with s2 pulsation, because they are composed of positive and negative sequence products.

4.1. TORQUE AND ROTOR FLUX OSCILLATION CANCELLATION STRATEGY (TARGET 1)

In order to obtain constant electromagnetic torque and

rotor flux, the both of them reference must be kept constant,

thus the torque ripples must be zero, i.e.

0 PP DC . (15)

As a result, the required torque for compensation become

)(23

PPs

constref BApTT

. (16)

In other words, in PDTC strategy torque and rotor flux are directly controlled and their reference are a dc term, therefore torque and rotor flux should be constant. This means the oscillating terms of the torque in PDTC will be zero. In result, mechanical stress on the gearbox and core losses is reduced. Also, according to the (13) and (14), even if the electromagnetic torque pulsation can be removed by the unbalanced PDTC, the stator active power pulsation will still exist.

4.2. ACTIVE POWER OSCILLATION CANCELLATION STRATEGY (TARGET 2)

This objective is to mitigate the stator active power oscillation when the network is unbalanced. According to (13), only way to achieve constant stator active power is by imposing

0 PP DC . (17)

As a result, the required torque for compensation become

)2(23)2(

23

Ps

constPs

constref DpTCpTT

. (18)

Since the condition for stator active power oscillation cancellation in (18) is not related to rotor flux, no compensation is needed for the rotor flux; that is

0 refr .

The torque compensation strategies under unbalanced grid voltage condition are shown in Fig. 2. The positive and negative sequence of current and voltage stator extracted from notch filter and then are used for generate the compensation terms. Compensation term added to the original constant torque reference to produce the new reference, which are fed into the PDTC controller.

Fig. 2 – Torque compensation strategies under unbalanced grid voltage.

6. SIMULATION RESULTS To check feasibility of the proposed strategy, simulation

results were carried out by using Matlab/Simulink. The main characteristics of the simulated system are shown in Table 1. The simulated generator is a 1 MW DFIG, and the scheme of the implemented system is shown in Fig. 3. During simulation, a sampling frequency of 20 kHz was used for the proposed control strategy and the bandwidths of the torque and rotor flux hysteresis controllers were set at ± 4 % of the rated generator power of 1 MW. Amount of dc-link capacitance is 16000 μF and the nominal converter dc-link voltage was set at 1200 V.

Fig. 3 – Scheme of the simulated system.

Table 1 Parameters of the DFIG simulated

Rated power 2 MW Stator voltage 690 V

Stator/rotor turns ratio 0.3 Rs 0.0108 pu

Rr 0.0121 pu (referred to the stator)

Lm 3.362 pu Lσs 0.102 pu Lσr 0.11 pu (referred to the stator)

Lumped inertia constant 0.5 Number of pole pairs 2

Figure 4 shows the comparison between two method

PDTC and conventional DTC in balanced condition. Rotor speed in this section is 0.8 p.u. Various torque and rotor flux steps are also applied, i.e., torque and rotor flux references are changed from 0.4 to – 0.4 p.u at 0.25 s and from 0.9 to 1.1 Wb at 0.24 s, respectively. As it is seen, the performance of the PDTC method is better in comparison with conventional DTC. It has many merits, such as reduced torque and flux ripples, constant switching frequency, and excellent steady state and transient responses. For a better comparison of these methods, total harmonic distortion (THD) values for two methods are presented in Table 2. The experiment was done for three states: sub-synchronous speed, super-synchronous speed and variable speed. In PDTC method, the amount of stator currents ripples is less.

In this paper we define tTTT ref d)( 2 and

tref d)( 2 in definite time span to subtly

consider the ripples of the torque and rotor flux. The values of these parameters for different cases in the 0.1 to 0.8 seconds are presented in Table 3.

The performance of the system will be further analyzed under unbalanced grid voltage condition. The grid voltage unbalance which programmed for this experiment is shown in Fig. 5 (Vsa = 555 < 0, Vsb = 484.2 < –113, Vsc = 557.5 <

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–231). Torque and rotor flux references are changed from 0.4 to –0.4 p.u at 0.25 s and from 0.9 to 1.1 Wb at 0.24 s, respectively. Performance of predictive direct torque control under unbalanced stator voltage has not been reported in literatures yet. Therefore, this paper investigates the operation of DFIG under these voltage conditions using predictive DTC strategy.

Figure 6 divided into two modes. In mode 4.1 used from target 1 and mode 4.2 used from target 2. The target 1, is torque and rotor flux oscillation cancellation strategy, and target 2, is stator active power oscillation cancellation strategy.

In 4.1 mode: from Fig. 6a&b it can be seen that, torque and rotor flux are tracking their reference values. Figure 6c

shows the stator active power that has a lot of ripples, because the stator active power oscillation cancellation strategy is not used in this mode. Figure 6d shows the three phase stator current that are unbalanced and nonsinusoidal.

In 4.2 mode target 2, i.e., stator active power oscillation cancellation strategy, was selected as the control objective. Figure 6a shows the electromagnetic torque tracking behavior in order to cancel the stator active power oscillation. The electromagnetic torque is oscillating from 0.24 s, because the terms of 2CP or 2DP added to it. Figure 6c shows that the stator active power oscillations removed from 0.24 s. It can be seen from Fig. 6d, the stator currents from 0.24 s are still unbalanced, but have became sinusoidal.

     

     

     

    Fig. 4 – Comparison between simulation results in two states: PDTC [A] and Convential DTC [B]:

a) electromagnetic torque (p.u); b) rotor flux (Wb); c) stator active power (p.u); d) three phase stator currents (p.u).

Table 2 The value of THD for three phase stator currents in different condition

Isc (%) Isb (%) Isa (%) Proposed methods Rotor speed 0.51 0.52 0.48 DTC 0.8 p.u 0.14 0.16 0.21 PDTC 0.56 0.53 0.41 DTC 1.2 p.u 0.12 0.15 0.20 PDTC 0.53 0.51 0.48 DTC 1.2 to 0.8 p.u 0.14 0.17 0.19 PDTC

Table 3 Comparison of the distributions of the torque and rotor flux errors for 0.1 < t < 0.8

Proposed method Torque & rotor flux errors

0.8 p.u 1.2 p.u 1.2 to 0.8 p.u

DTC ∆T 0.005878 0.006042 0.006541 Δψ 0.001425 0.001478 0.001485

 

PDTC ∆T 0.002159 0.003245 0.003306 Δψ 0.000552 0.000546 0.000518

Predictive direct torque control for doubly fed induction generator 5

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7. CONCLUSION This paper proposes a novel predictive DTC method with

excellent transient and steady state performance. In first PDTC was developed and by using a cost function the best voltage vector was selected for switching of RSC. In continue PDTC method combined with two new compensation schemes. One of them is torque oscillation cancellation and other is power oscillation cancellation scheme. Simulation results illustrated accuracy of the proposed PDTC method under balanced and unbalanced grid voltage condition and show good performance of proposed method during variation of references of torque and rotor flux and wind speed. The torque and rotor flux and stator current ripples are reduced and the transient responces of them are within a few milliseconds and THD of stator current is suitable.

ACKNOWLEDGMENTS The authors would like to thank the anonymous

reviewers for their valuable comments and suggestions that helped to improve the quality of this manuscript.

Received on April 11, 2017

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Fig. 5 – Unbalanced grid voltage.

   

 

   

 

Fig. 6 – Comparison between simulation results in two states: (target 1 (4.1) and target 2 (4.2))], by applying PDTC method: a) electromagnetic torque (p.u); b) rotor flux (Wb); c) stator active power (p.u); d) three phase stator currents (p.u).

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