A control scheme for improving the efficiency of DFIG at low wind speeds with fractional rated converters

Electrical Power and Energy Systems 70 (2015) 61–69

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A control scheme for improving the efficiency of DFIG at low wind speeds with fractional rated converters Venkata Rama Raju Rudraraju, Chilakapati Nagamani, G. Saravana Ilango ⇑ Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu 620015, India

a r t i c l e

i n f o

Article history: Received 21 May 2014 Received in revised form 12 January 2015 Accepted 31 January 2015 Available online 21 February 2015 Keywords: Wind energy conversion system Variable speed generator Doubly fed induction generator Extending speed range Stator short circuited operation

a b s t r a c t This study proposes a scheme for extending the low speed range of operation of a Doubly Fed Induction Generator (DFIG) without down grading the efficiency. Also, only fractional rated converters are employed. The technique involves two operational modes for the generator. When the rotor speed is between 70% and 130% of the synchronous speed, the machine is operated in the normal Doubly Fed Induction Generator (DFIG) mode and when the rotor speed falls below 70%, it is operated in Stator Short Circuited (SSC) mode. The switch-over from the DFIG mode to the SSC mode is carried out at a threshold speed to maintain the efficiency of generator with the same fractional rated converters. The computer simulations on a typical DFIG (250 kW) in Matlab/Simulink environment illustrate that the range of efficiency improvement is from zero to 15%. Further, the experimental results on a 2.3 kW DFIG set up are also illustrated to demonstrate the efficacy of the scheme. Ó 2015 Published by Elsevier Ltd.

Introduction With the depleting natural resources, increase in energy demand and global warming, exploitation of renewable energy sources is growing at a fast pace since last decade. Of the renewable energy sources, wind energy is attractive options as 100 kW–8 MW wind turbines are commercially available. An overview and comparison of wind turbine generators are presented in [1–3]. Variable speed wind turbines have increased energy capture compared to fixed speed wind turbines. Among the variable speed wind turbines DFIGs are widely used due to the advantages such as four quadrant operation, decoupled power control, fractional rated converters and reduced mechanical stresses [4–7]. As the operating speed of DFIG is limited to 30% above and below synchronous speed, the rating of power converters used are typically 30% of the machine rating. Studies [8–10] presented the steady state analysis of DFIG for wide speed operation. The rotor voltage is linearly proportional to the slip (0.49 p.u. for a wind speed of 5 m/s at a slip of 0.47) while the aspect of efficiency is not examined [8]. The active power delivered is controlled by varying the angle between the stator and rotor voltages and magnitude of rotor voltage [9]. Increased rating

⇑ Corresponding author. Tel.: +91 4312503259. E-mail addresses: [email protected] (V.R.R. Rudraraju), cnmani@nitt. edu (C. Nagamani), [email protected] (G.S. Ilango). http://dx.doi.org/10.1016/j.ijepes.2015.01.032 0142-0615/Ó 2015 Published by Elsevier Ltd.

of the power converter is implied at speeds below 70% of synchronous speed [10]. Maximum Power Point Tracking (MPPT) scheme [11] was independent of the turbine parameters and air density where the peak power points in the P–x curve corresponds to dP/dx = 0 while [12] presented the implementation of speed mode control for tracking the peak wind power. In [13] MPPT was implemented using characteristic power curve. The optimal power reference curve was obtained by finding the optimal mechanical power and generator speed for a given wind speed. Generally, the efficiency of induction generator is low at low wind speeds. Efficiency of induction generator, synchronous generator and PMSG were compared in [14] for different wind speeds. The efficiency of induction generator is lower compared with that of other machines, particularly at low rotor speeds. A method to calculate losses, power and efficiency of wind turbine generator systems with DFIG [15] reported the efficiency of a 5 MW DFIG to be just 50% near the cut-in speed. This is primarily due to the predominance of constant magnetizing current, in spite of low winding currents. An approach to determine the optimal rotor voltage for extracting maximum power at any wind velocity ensuring steady state stability of the generator was discussed in [16]. Different methods to improve efficiency and power factor of induction motor are presented in [17–21]. One of the techniques for extending the speed range of induction generator included pole changeable [5,22,23] stator winding. The stator is wound for two windings with different pairs of poles [5]. At lower speeds the

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Nomenclature

v s is ir Ps, Qs Rs , Rr Lls, Llr

stator voltage space vector stator current space vector rotor current space vector stator active and reactive powers stator and rotor phase winding resistances referred to stator stator and rotor phase winding inductances

winding with the higher pole pairs was used and at rated and higher speeds the winding with lower pole pairs was used. While this arrangement increases the efficiency at lower speeds, it is suitable only for constant speed wind turbines and moreover the size of machine is large to accommodate twin pole pair arrangement. In [24] a pole changing method for DFIG with cyclo-converter on rotor side was presented. Although the speed range is extended, the effects of this on power output and efficiency were not addressed and the complexity in implementation of cyclo-converter is extensive. Variable speed generators with full rating converters [25] can operate in full speed range i.e. down to cut in speed. However, the cost of the power converters is very high. In an offshore application [26], the DFIG was operated at rated V/f through an HVDC link and the power converters on rotor side are rated for 5% of machine rating. Using this scheme the efficiency of the system at lower wind speeds was improved. But the disadvantage of the scheme is that the number of converters required for control is higher. In another study [27], the induction generator was operated in doubly fed mode at nominal speeds and as a singly fed induction generator at lower speeds. Though the lower speed efficiency is improved, issues such as the basis for switching over from one mode to another, the ratings of the power converters employed, and MPPT, have not been discussed. Extending the speed range with limited rating converters while maintaining the efficiency of the generator has not received adequate attention so far. The main disadvantage with DFIG is that it requires higher rated power converters at lower speeds. Hence, with fractional rated converters the operating speed range of DFIG is limited to 70–130% around synchronous speed. In the present work a strategy is proposed for an efficient extended low speed operation, extracting the maximum power with fractional rated converters, thereby significantly reducing the size and cost of the converters. At lower speeds the mechanical power available is less. Therefore, a MPPT algorithm is proposed in which the total copper loss is minimized while the tracking maximum power from the wind turbine by switching operation to the SSC mode. The method involves determining the optimum value of the slip for a rotor speed. Further, from the optimum slip the rotor voltage and frequency are determined. At normal and high speeds (say 0.7– 1.3 p.u. of synchronous speed), the Wound Rotor Induction Machine (WRIM) is operated in doubly fed (DFIG) mode (Fig. 1a). The Rotor Side Converter (RSC) is controlled to extract the maximum power from the wind and the Grid Side Converter (GSC) is used to maintain the dc link voltage. At lower speeds (below 0.7 p.u.), the stator is short circuited (Fig. 1b) while the rotor is connected to grid through the converters to transfer the power from RSC to the grid through GSC. The RSC is operated to extract the maximum power from the wind while keeping the rotor voltage within limits (30% of stator nominal voltage) and the GSC is used to maintain the dc link voltage constant. This paper is organized as follows. In Section ‘Wind turbine characteristics’ the concept of maximum power tracking is explained. Theoretical analysis for two modes of operation viz.,

Lm

xs xm Pm

vw s

magnetizing inductance angular frequency of stator voltage angular speed of rotor (electrical) mechanical power wind velocity slip

the DFIG mode and the SSC mode and the respective control strategies are discussed in Section ‘Steady state model’. Section ‘Results and discussion’ describes the simulation and experimental results.

Wind turbine characteristics The output power from the wind turbine [13] is expressed as

Pm ¼ 0:5pqC p R2 V 3w

ð1Þ

where q is air density, Cp is the power coefficient, R is the radius of wind turbine. Optimum tip speed ratio and optimum power [13] for the wind are given by

kopt ¼

xopt R

ð2Þ

Vw

and Popt ¼ K opt x3opt where K opt ¼

ð3Þ

0:5pqC pmax R5 k3opt

xopt is the rotor speed at which turbine power for certain wind speed is maximum and Cpmax is the maximum power coefficient. The dynamic equation of wind turbine is expressed as dxm 1 ¼ ½T m  T L  Bxm  J dt

ð4Þ

where J is the turbine inertia, B is the friction coefficient, Tm is torque developed by the turbine, TL is the torque due to load and xm is the rotor speed.

Steady state model Steady state models of WRIM are developed for predicting the performance in DFIG mode and SSC mode. In both DFIG and SSC modes the RSC is used to extract maximum power from the wind. Steady state analysis – DFIG mode of operation Fig. 1a shows the schematic diagram of DFIG. Tracking maximum power from the wind and controlling of stator side active and reactive power is carried out via RSC. Power factor at the grid is maintained through the GSC. Fig. 2a shows the per-phase equivalent circuit of DFIG referred to stator. The equations governing steady state operation are given by

V s  Rs Is ¼ jxs us

ð5Þ

V r  Rr Ir ¼ jsxs ur

ð6Þ

where us ¼ Lls Is þ Lm Im

ð7Þ

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GRID

GRID

DFIG

GSC

DFIG

GSC

RSC

(a)

RSC

(b)

Fig. 1. Schematic diagram for WRIM in (a) DFIG mode and (b) SSC mode.

Llr

Lls

is Rs

i fe vs

Rr / s i r

is

im Lm

R fe

vr s

(a)

Rs s

Llr

Lls

i fe

im

R fe

Lm

Rr i r

vr

(b)

Fig. 2. Steady state equivalent circuit diagrams (a) for DFIG mode and (b) for SSC mode.

and ur ¼ Lm Im þ Llr Ir :

ð8Þ

Is þ Ir ¼ Ife þ Im

ð9Þ

Rfe Ife ¼ jxs Lm Im

start Initialize turbine paramerters, grid voltage, frequency and machine paramerters

ð10Þ ⁄

The reactive power reference (Qs ) is set to zero to obtain unity power factor at the stator. Hence,

P Is ¼ pffiffiffis 3V s

ð11Þ

Stator, rotor and iron losses are given by

Assume wind speed =1m/s Compute optimum power and rotor speed at which speed is maximum (3 & 2) Compute stator current (11), magnetizing current (5) & (7), core loss current (10), rotor current (9) Compute rotor voltage using (6) & (8)

Pcus ¼ 3I2s Rs

ð12Þ

Pcur ¼ 3I2r Rr

ð13Þ

Compute rotor real and reactive power (15) & (16), losses (12-14), efficiency (17) Increment wind speed

and Pfe ¼ 3I2fe Rfe :

ð14Þ Wind speed > 12 m/s

Rotor active and reactive powers are given by

Pr ¼ 3RefV r Ir g

ð15Þ

and Q r ¼ 3ImfV r Ir g:

ð16Þ

The efficiency of DFIG is defined as the ratio of sum of stator active and rotor active powers to mechanical power

g¼

Ps þ Pr P mech

ð17Þ

Fig. 3 shows the flow chart for the predetermination of performance in DFIG mode to track the maximum power from the wind. The performance in DFIG mode is predetermined for wind speeds from 1 m/s to 12 m/s.

No

Yes stop Fig. 3. Flow chart for predetermination of performance in DFIG mode.

Steady state analysis – SSC mode Fig. 1b shows the block diagram of WRIM in SSC mode. At low speeds, the stator of induction generator is short circuited and the turbine power is transmitted to the grid through the converters on the rotor side (Fig. 1b). Fig. 2b shows the equivalent circuit of induction machine referred to the rotor in SSC mode. In this context, RSC is used to obtain the maximum power from the wind

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turbine and GSC is used to maintain dc link voltage constant and unity power factor at the grid. From the equivalent circuit (Fig. 2b) the steady state performance can be determined. Stator current is given by

the wind turbine is the maximum. To find the desired slip, the maximum magnitude of rotor voltage |Vr| is fixed in (29). Further, (29) is rearranged as follows:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sP m Is ¼  3Rs ð1  sÞ

where the constants a11–a15 are defined in the appendix. Possible roots for the 4th order Eq. (30) can be written as

ð18Þ

The voltage across magnetizing branch is expressed as

  I s Rs E¼ þ jxr Lls Is s

ð19Þ

Magnetizing and core loss current are given by

Im ¼

E jxr Lm

and Ife ¼

ð20Þ

E : Rfe

ð21Þ

Rotor current and voltage are given by

Ir ¼ Im  Is þ Ife

ð22Þ

V r ¼ Ir ðRr þ jxr Llr Þ þ E:

ð23Þ

Efficiency of WRIM in SSC mode is

g¼

ð24Þ

Pmech

It is evident from (18) and (22) that the stator and rotor copper losses are dependent on slip for a particular mechanical power and rotor speed. Hence, to obtain the optimum slip, a loss minimization algorithm is proposed. The total copper loss in generator is the sum of stator and rotor copper losses (neglecting iron losses). Hence, the total copper loss is chosen as the objective function.

f ðsÞ ¼ Ploss ¼

þ

3I2r Rr

ð25Þ

Rotor angular frequency is expressed as

xr ¼

xm

ð26Þ

1s

Differentiating the total copper loss function f(s) with respect to slip ‘s’ gives

df ðsÞ ¼ ða1 þ a2 Þs2 þ 2a3 s  a3 dðsÞ

ð27Þ

where a1, a2 and a3 are functions of the machine parameters and are defined in appendix. For the loss to be minimum, the right hand side of (27) should be zero. This is true when

s1;2 ¼

2a3 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2a3 Þ2  4ða1 þ a2 Þða3 Þ

ð28Þ

2ða1 þ a2 Þ

Since the induction machine is operating in generator mode, only a negative real value for the slip is valid. Considering the magnitude of rotor voltage (23), we get

jV r j2 ¼

h

Pm 3

3Rs sð1  sÞ

2

ða6 s2 þ a7 s þ a8 Þ þ ða9 s2 þ a10 s þ a9 Þ

ð30Þ

s1;2 ¼

a12 1  a18  2 4a11

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a17 4a218  2a16 þ a18

ð31Þ

s3;4 ¼

a12 1 þ a18  2 4a11

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a17 4a218  2a16  a18

ð32Þ

where constants a16–a18 are given in the appendix. Since the machine is in generating mode, only a negative real root is valid. Hence, with this negative real value of slip, rotor frequency is computed. Further, the flow chart for maximizing the efficiency of machine in SSC mode is illustrated in Fig. 4. Also, the rotor voltage is restricted to maximum of 0.3 p.u., corresponding to the limited rating of the RSC. Using the reference rotor voltage, modulation index is computed. The modulation index is multiplied with three phase unit vectors of frequency xr to obtain the reference sine wave signals for Sinusoidal Pulse width Modulation (SPWM). Gate pulses for RSC are generated using SPWM. Results and discussion

Pr

3I2s Rs

a11 s4 þ a12 s3 þ a13 s2 þ a14 s þ a15 ¼ 0

2

i

ð29Þ

The magnitude of optimum rotor voltage can be obtained by solving (29). Since the voltage rating of RSC is 30% of rotor voltage, the maximum rotor voltage is limited to 30% of the nominal value and slip is adjusted accordingly such that the power extracted from

Computer simulations are carried out to investigate the performance of the proposed control strategy. Two cases are considered. In the first case, simulation results (using Matlab/Simulink) are presented for a 250 kW machine while in the second case, both simulation and test results are presented for a 2.3 kW laboratory machine. Case study-1: A 250 kW wind turbine Based on the analysis presented in Section ‘Wind turbine characteristics’, the computer simulations are carried out to investigate the performance in DFIG mode and SSC mode for a wind turbine. The parameters of wind turbine are given in appendix. The performance of the generator in DFIG mode and SSC mode are shown in Figs. 5–7. 230 V and 370 A are considered as base values for voltages and currents respectively. Fig. 5a illustrates that the power fed to grid in SSC mode is slightly higher than that in DFIG mode at lower speeds. In the DFIG mode, the necessary rotor voltage, being proportional to slip, decreases as the speed approaches the synchronous speed (Fig. 5b). However, in the SSC mode, the required rotor voltage increases with speed due to increasing mechanical power input. However, in this mode, the rotor voltage is intentionally not allowed to rise beyond 0.3 p.u. corresponding to the limited rating of power converters (Fig. 5b) through converter control. Thus, by design, the injected rotor voltage vs. speed curve has a maximum permissible value in accordance with the power converter rating. The point ‘Y’ marks the threshold speed at which the rotor voltage limit is reached. The variations of stator and rotor currents with rotor speed are shown in Fig. 5c and d respectively. While the trends in stator current reflect the increasing mechanical power (Fig. 5c), the trends in rotor current and the magnetizing current indicate the combined effect of increasing mechanical power and the driving voltage(s). At lower speeds, with nominal levels of driving voltages in the doubly fed mode, the magnetizing current and the rotor current are greater in the DFIG mode and the same are lower in the SSC mode due to low applied voltage of the rotor. However, due to the increasing mechanical power and the cap on the injected rotor

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start Initialize turbine parameters, grid voltage, frequency and machine parameters Assume wind speed =1m/s Compute maximum mechanical power and corresponding rotor speed for a given wind speed Solve (27) for s and take negative value of s Compute stator current (18), magnetizing current (20), rotor current (22), and rotor voltage (23) No

If |Vr|< Vrlimit Yes

Solve (30) for s and take negative value of s Compute stator current (18), magnetizing current (20), rotor current (22), rotor voltage (23)

Compute rotor real and reactive power (15) & (16), losses (12-14), efficiency (24) Increment wind speed No

Wind speed > rated speed Yes stop

Fig. 4. Flow chart for predetermination of performance in SSC mode.

1.2

-0.8

rotor voltage (p.u.)

grid power (p.u.)

-1 - 0.1 - 0.05

-0.6

0 0.1

0.6

-0.4 -0.2

0.9

0.6 Rotor voltage limit Y

0.3

-0.093

DFIG SSC

0.6

0

DFIG SSC

0

0.5

1

0.72

0

0

1.5

0.5

speed (p.u.)

(a) 1.2

Magnetizing current

Rotor current DFIG SSC

0.8 0.6 0.4

DFIG SSC

DFIG SSC

1

current (p.u.)

stator current (p.u.)

1.5

(b)

1.2 1

1

speed (p.u.)

0.8 0.6 0.4

Y

Y

0.2

0.2 0

0

0.5

1

1.5

0

0

0.5

1

speed (p.u.)

speed (p.u.)

(c)

(d)

1.5

Fig. 5. Performance of WRIM in DFIG mode and SSC mode. (a) Grid active power vs. rotor speed, (b) rotor voltage vs. rotor speed, (c) stator current vs. rotor speed, and (d) magnetizing current and rotor current vs. rotor speed.

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V.R.R. Rudraraju et al. / Electrical Power and Energy Systems 70 (2015) 61–69

0.9

DFIG SSC

0.4

DFIG SSC

0.7 0.5

0.3

slip

rotor VA (p.u.)

0.5

0.2

0.3 0.1

Y

0.1

-0.1 -0.3

0 0

0.5

1

1.5

0

0.2

0.4

speed (p.u.)

0.6

0.8

1

1.2

1

1.2

1.4

speed (p.u.)

(a)

(b)

DFIG SSC

rotor copper losses

stator copper losses

0.06

0.04

0.02

DFIG SSC

0.04

0.02

0

0

0

0.2

0.4

0.6

0.8

1

1.2

0

1.4

0.2

speed (p.u.)

0.4

(c)

0.8

1 DFIG SSC

0.91

efficiency

0.8

0.1

0.6 0.4 0.2

DFIG SSC

0.6

0

0

0

0.2

0.4

1.4

(d)

0.2

total copper losses

0.6

speed (p.u.)

0.6

0.8

1

1.2

1.4

0

0.2

0.4

0.6

0.8

speed (p.u.)

speed (p.u.)

(e)

(f)

1

1.2

1.4

Fig. 6. Performance of WRIM in DFIG mode and SSC mode. (a) Rotor VA vs. rotor speed, (b) slip vs. rotor speed, (c) stator copper losses vs. speed, (d) rotor copper losses vs. speed, (e) total copper losses vs. speed, and (f) efficiency vs. rotor speed.

Is

Is

Vs

Vr

Vr Ir Im

Im

Ir

(a)

(b)

Fig. 7. Phasor diagram of machine at wind speed of 4 m/s. (a) DFIG mode and (b) SSC mode.

voltage, the rotor and stator currents increase with speed in the SSC mode. The low magnetizing current in the SSC mode is noticeable in Fig. 5d. In the DFIG mode, the rotor slip (Fig. 6b) has an inverse relationship with the rotor speed. However, in the SSC mode the converter

control process enforces an optimal rotor frequency (and thereby an optimal slip) at any rotor speed to track the maximum efficiency. As a result, the slip is held generally low through the speed range. In the DFIG mode, the rotor VA decreases with speed while it increases in the SSC mode (Fig. 6a). Stator, rotor and total copper

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DFIG DCM

ωr GSC

DC supply

Three phase thyristor controlled rectifier

Three phase supply

GRID

RSC

Vdc

Vs

Is

FPGA based controller

Ir

Fig. 8. Schematic diagram of experimental setup.

-1 Experimental

Simulated DFIG SSC

-1.2

Experimental

Simulated

DFIG SSC Proposed

grid power (p.u.)

mechanical power (p.u.)

-1.6

-0.8

-0.4

DFIG SSC Proposed

DFIG SSC

-0.8 -0.6 -0.4 -0.2 0

0 0

0.5 1 speed (p.u.)

0

1.5

0.5 1 speed (p.u.)

(a)

(b) 1.2

0.6 Experimental

Simulated

0.5

DFIG SSC Proposed

DFIG SSC

0.4

Experimental

Simulated

stator current (p.u.)

rotor voltage (p.u.)

1.5

0.3 0.2 0.1

1

DFIG SSC Proposed

DFIG SSC

0.8 0.6 0.4 0.2

6E-16 0

0.2

0.4

0.6

0.8

1

1.2

1.4 0

-0.1

0

0.5

1

speed (p.u.)

speed (p.u.)

(c)

(d)

1.5

Fig. 9. Performance in DFIG mode, SSC mode and proposed strategy. (a) Mechanical power vs. rotor speed, (b) grid active power vs. rotor speed, (c) rotor voltage vs. rotor speed, and (d) stator current vs. rotor speed.

loss in the DFIG mode and SSC mode are shown in Fig. 6c–e respectively. At lower speeds the total losses are greater in DFIG mode compared to those in SSC mode and hence the efficiency is higher in SSC mode (Fig. 6f). This is due to the reduction in magnetizing current in SSC mode as the rotor voltage is low. Fig. 7a and b show the phasor diagrams for the generator operation at a low wind speed of 4 m/s in DFIG mode and SSC mode respectively. These are drawn considering rotor voltage as the reference phasor. As can be noted, at the same mechanical power, the magnetizing current and rotor current are higher in DFIG mode compared to those in SSC mode.

Case study-2: A 2.3 kW laboratory prototype WRIM Simulations and experimentation are carried out on a 2.3 kW WRIM for verification of the speed range extension and efficiency improvement with the proposed scheme. Fig. 8 shows the schematic diagram of the experimental setup. The machine parameters are given in appendix. A 5-hp DC motor is used to emulate the wind turbine characteristics using armature control. The stator voltages, stator currents and rotor currents are sensed using LEM sensors. Altera cyclone II FPGA is used to generate firing pulses for RSC and GSC. The rotor power circuit consists of two power

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V.R.R. Rudraraju et al. / Electrical Power and Energy Systems 70 (2015) 61–69

0.5

1.4 Simulated DFIG SSC

rotor reactive power (p.u.)

rotor current (p.u.)

1.2

Experimental DFIG SSC Proposed

1 0.8 0.6 0.4 0.2 0

DFIG SSC

DFIG SSC Proposed

0.3 0.2 0.1 0

0

0.5

1

0

1.5

0.5

1

speed (p.u.)

speed (p.u.)

(a)

(b)

1.5

0.8

0.6 DFIG SSC Proposed

DFIG SSC

0.4

efficiency (p.u.)

0.5

Experimental

Simulated

Experimental

Simulated

rotor VA (p.u.)

Experimental

Simulated

0.4

0.3 0.2 0.1

DFIG SSC

DFIG SSC Proposed

0.6

0.4

0.2

6E-16 0

0.2

0.4

0.6

0.8

1

1.2

1.4

-0.1

0

speed (p.u.)

(c)

0

0.5

1

1.5

speed (p.u.)

(d)

Fig. 10. Performance of WRIM in DFIG mode, SSC mode and proposed strategy. (a) Rotor currents vs. rotor speed (b) rotor reactive power vs. rotor speed, (c) rotor VA vs. rotor speed, and (d) efficiency vs. rotor speed.

Table 1 Comparison of machine performance in DFIG mode and SSC mode.

converters (MD B6CI 800/415-30 F) of Semikron make. The RSC is operated at a switching frequency of 5 kHz. Power reference is set based on the rotor speed information. 240 V and 4.7 A are considered as base values for voltages and currents respectively. Fig. 9a shows the reference mechanical power [13] with speed. The mechanical power is proportional to the cube of wind speed. Markers indicate the experimental results. Power fed to the grid while tracking maximum power from the wind is shown in Fig. 9b. In DFIG mode the rotor voltage varies proportionally with the slip and in SSC mode the rotor voltage increases with speed (Fig. 9c). With the proposed strategy switching is made from SSC mode to DFIG mode at 0.7 p.u. speed. The stator current is shown in Fig. 9d. As the maximum rotor voltage is fixed at 30% of the nominal, the stator and rotor currents exceed the rated values at higher speeds in SSC mode. With the proposed strategy the stator and rotor currents are within limits.

Rotor current is shown in Fig. 10a. Rotor reactive and apparent powers (Fig. 10b and c) increase with speed in SSC mode while they decrease with speed in DFIG mode. Fig. 10d shows the efficiency improvement in SSC mode at low speeds. The proposed strategy indicates that, both the efficiency and speed range are improved with the same fractional rated converters. Table 1 shows a comparison of the machine performance in DFIG mode and SSC mode. It is observed that the rotor voltage exceeds 0.3 p.u. for rotor speeds below 0.7 p.u. in the DFIG mode while in the SSC mode the maximum rotor voltage is limited to 30%. Also in SSC mode, the rotor VA rating does not exceed 0.3 p.u. for rotor speeds below 0.7 p.u. Further, through implicit slip control, efficiency is maintained high in the SSC mode at lower speeds (outlined by oval shape in Table 1). Thus the proposed strategy, illustrates that through adoption of mode change over from DFIG to the SSC mode, it is possible to extract maximum power

V.R.R. Rudraraju et al. / Electrical Power and Energy Systems 70 (2015) 61–69

from the wind turbine even at lower speeds without sacrificing efficiency and without violating the rating of the RSC. Conclusions The study demonstrates the detailed analysis and methodology for extended and efficient low speed operation of a DFIG with fractional rated power converters. Apart from the DFIG mode for the limited slip (or speed) range, the generator is operated in ‘SSC mode’ at lower speeds so as to maintain the efficiency while not exceeding the converter VA ratings. In DFIG mode, maximum power is extracted from the wind turbine while maintaining unity power factor at stator. An algorithm to minimize the total copper loss is proposed for SSC operation for obtaining maximum efficiency at low speeds. The efficacy of the proposed method is validated through simulations on machine and tests and simulations on a 2.3 kW laboratory induction machine. For a 250 kW generator, the range of improvement in efficiency is zero to 15%, while the low speed operation is extended from the typical 0.7 p.u. to 0.3 p.u. with moderate efficiencies using the same 0.3 p.u. rated power converters. Appendix A

Rs 2 Rr a25 Lls a þ a3 þ 1; a2 ¼ 2a3 ; a3 ¼ ; a4 ¼ 1 þ ; Rr 4 Rs Lm Rs a5 ¼ ; a ¼ a4 Rr ; a7 ¼ a4 Rr  Rs  a5 xm Llr ; xm Lm 6

a1 ¼

a8 ¼ Rs þ a5 xm Llr ; a9 ¼ a5 Rr ; a10 ¼ xm Lls þ a4 xm Llr þ 2a5 Rr ; a11 ¼ ða26 þ a29 ÞP m þ 3jV r j2 Rs ; a12 ¼ ð2a6 a7 þ 2a9 a10 ÞPm  3jV r j2 Rs ; a13 ¼ ða27 þ a210 þ 2a6 a8 þ 2a29 ÞPm þ 9jV r j2 Rs ; a14 ¼ ð2a7 a8 þ 2a10 a9 ÞPm  3jV r j2 Rs ; a15 ¼ ða28 þ a29 ÞPm ; a16 ¼

a18

8a11 a13  3a212 a3  4a11 a12 a13 þ 8a211 a14 ; a17 ¼ 12 ; 2 8a11 8a311

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u   3 a a221  4a320 t 21 þ 1 2a16 1 a20 ; ; a19 ¼ ¼ þ a19 þ 3 2 3a11 3 a19 a20 ¼ a213  3a12 a14 þ 12a11 a15 ;

a21 ¼ 2a313  9a12 a13 a14 þ 27a212 a15 þ 27a11 a214  72a11 a13 a15 :

Machine parameters Rated power Rs (X) Rr (X) Lls, Llr (H) Lm (H) Stator voltage (V) Stator current (A) Turns ratio

250 kW 20e3 20e3 0.2e3 4.2e3 400 370 1

2.3 kW 3.45 5.26 0.02487 0.28 415 4.7 1.92

69

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