Control of a Self-excited Squirrel Cage Induction ... - ScienceDirect

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ScienceDirect Energy Procedia 54 (2014) 35 – 46

4th International Conference on Advances in Energy Research 2013, ICAER 2013

Control of a self-excited squirrel cage induction machine based wind energy conversion system operating in both stand alone and grid connected modes Vikram Roy Chowdhurya, Dr. Debaprasad Kasthab* b

a Student

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India Professor Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India

Abstract This paper presents the controller design of a wind energy conversion system built around a self-excited squirrel cage induction machine that can be operated in both standalone and grid connected modes. The control scheme regulates the machine terminal voltage in the standalone mode and the grid side reactive power in the grid connected mode. Both a TCR type SVC and a VSI based STATCOM are employed as flexible reactive power sources. The overall control scheme has been developed and verified in MATLAB/SIMULINK platform. The power versus terminal voltage characteristics, the terminal voltage, system frequency and reactive power versus various load levels in different modes of operation are discussed. © 2014 Debaprasad Kastha. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selectionand andpeer-review peer-review under responsibility of Organizing Committee of ICAER Selection under responsibility of Organizing Committee of ICAER 2013 2013. Keywords: Wind turbine; Squirrel cage induction machine; Self excitation; SVC; STATCOM ;

1. Introduction Wind energy is considered to be one of the primary sources of renewable energy because it is abundant and pollution free. The progress made in semiconductor technology has helped immensely in designing efficient wind energy conversion systems used for power generation. However, the high initial cost of setting up a wind turbine and lack of proper wind potential hinders its extensive usage for power generation. As the quality of the electric power (voltage, frequency etc.) generated by such a system is dependent on the available wind speed to use the system most efficiently complex control strategy has to be developed. The challenges that one needs to overcome to design such a system is well known. For a self excited machine the terminal voltage and frequency varies to a great extent [1], [2]. As a remedy power compensators like SVC and STATCOM may be used for voltage control of such a system [3], [4]. SVC control and STATCOM control to operate them efficiently has been discussed in [4], [5],

* Corresponding author. Tel.: +91 - 3222 – 283058., E-mail address: [email protected]

1876-6102 © 2014 Debaprasad Kastha. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of Organizing Committee of ICAER 2013 doi:10.1016/j.egypro.2014.07.247

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Vikram Roy Chowdhury and Debaprasad Kastha / Energy Procedia 54 (2014) 35 – 46

[6]. Also pitch control of the wind turbine is employed to maintain the frequency of the generated voltage within the desired range [7], [8]. The papers mentioned above looks for a pitch control strategy only for cases when wind speed is higher than the rated value. But even with the rated wind speed if there is an outage in the grid continuous power to the local load cannot be supplied and it ends up in either shutting down of the turbine or the extra energy is dissipated in braking resistors. This paper develops an overall control strategy for a self excitation induction machine. Self excitation characteristics are derived from the machine equivalent circuit. The proposed method focuses mainly on keeping the terminal voltage and frequency at a desired value in the standalone mode and keeping the grid power factor unity in the grid connected mode operation. As mentioned above in the proposed control strategy the pitch controller is made such that even if there is some outage in the grid the local loads can be supplied satisfactorily maintaining its frequency and voltages within limits. In the proposed method, in place of two back to back converters only one fractionally rated power converter is used thereby, reducing the cost. Both the proposed controllers (using SVC and STATCOM) are verified in MATLAB/SIMULINK platform. The rest of the paper is organized as follows. Section II of the paper discusses the mathematical analysis of a self excited induction machine. Section III focuses mainly on the simulation models and control strategy development. Simulation results are presented in section-IV. Finally, conclusions are drawn in section-V. Nomenclature A ܸ௧ is the terminal voltage of the machine B ‫ܫ‬௦ ǡ ‫ܫ‬௥ are the stator and rotor currents respectively C ܴ௦ ǡ ܺ௟௦ ǡ ܴ௥ ǡ ܺ௟௥ are the stator and rotor resistance and reactance respectively D F and v are the per unit frequency and speed respectively E ܸௗ௖ is the dc bus voltage for the STATCOM

2. Mathematical Analysis Per phase steady state equivalent circuit of a self excited squirrel cage in term of per unit frequency is shown in Fig. 1 [1]. ܴ௦ ‫ܨ‬

ܴ‫ܮ‬ ܸ‫ݐ‬ ‫ܨ‬

‫ܨ‬

݆ܺ௟௦ ‫ܫ‬௦

െ݆ܺܿ ‫ʹܨ‬

݆ܺ௅

݆ܺ௟௥ ‫ܫ‬௥ ܸ௚ ‫ܨ‬

݆ܺ௠

Fig .1: Equivalent circuit of a self excited induction machine

ܴ௥ᇱ ‫ܨ‬െ‫ݒ‬

37


The equations (1) - (4) describe the steady state performance of a self excited induction generator. These equations are used to obtain the operating characteristics of the machine by coding in MATLAB. ௏೟ ி

ൌ

௏೒

ி

௏೒ ி

ோ

൅ ‫ܫ‬௦ ቀ ிೞ ൅ ݆ܺ௟௦ ቁ

(1)

ோ

ೝ ൌ ‫ܫ‬௢ ሺ݆ܺ௠ ሻ ൅ ‫ܫ‬௥ ሺிି௩ ൅ ݆ܺ௟௥ ሻ

‫ܫ‬௅ ൌ ோ

(2)

௏೟

(3)

ಽ ା௝ி௑ಽ

ܲ௢ ൌ ͵‫ܫ‬௅ଶ ܴ௅

(4)

The steady state characteristics showing the terminal voltage and frequency versus active power output with the operating speed and terminal capacitance as parameters for an R-L load with a power factor of 0.8 lagging are shown below in Figs. 2 and 3 respectively. 1 pu speed in these Figs is 1500 rpm.

Fig. 2: Variation of terminal voltage with active power output

Fig 3: Variation of pu frequency (F) with active power output

From the figures above it is clear that to maintain constant voltage and frequency at the machine terminals of a self excited induction generator (i) the generator speed needs to be maintained fairly constant, (ii) controllable reactive power has to be provided at the machine terminal. In this work the generator speed is controlled by utilizing the turbine pitch control mechanism. Two types of reactive power compensators namely a TCR type SVC and a VSI type STATCOM are used in simulation. Controllers for these items and the simulation results are discussed next. 3. Simulation Models The wind turbine and the induction machine models available in simpower systems utility of MATLAB/SIMULINK platform are used for simulation. The parameters of the models are given in Table 1.

38

Vikram Roy Chowdhury and Debaprasad Kastha / Energy Procedia 54 (2014) 35 – 46 Table 1:Parameters of the Induction Machine Quantities

Values

Rated Voltage( L-L)

400 V

Rated Line Current

67.6 A

Number of poles

4

Stator resistance

0.191Ω

Stator leakage reactance Rotor resistance referred to

1.20mH 0.0812Ω

Stator Rotor reactance referred to

1.79mH

Stator Rated speed

1440 rpm

Rated H.P. of the machine

50.4

Operating frequency

50 Hz

The magnetization characteristic of the induction machine is shown in Fig. 4 ;

Fig. 4: Magnetization characteristics of the machine chosen

The overall frequency control scheme for standalone mode of operation is shown in Fig. 5. It has an outer frequency control loop followed by an inner speed control loop (shown in the dotted box in Fig. 5). The Frequency controller generates the speed reference through the action of a PI controller with anti wind-up. The speed controller which uses a PID controller for fast transient response as well as zero steady state error in turn gives a pitch angle command to the pitch angle controller of the turbine.

39


50

+

Proportional Controller -

Saturation +

Speed Ref

+

+

Integral Control

+

-

Actual Speed

Antiwindup PI

du/dt

-

f

+

X

Pitch angle command

+

Rate Limiter

Fig. 5: Block diagram for frequency and pitch control in stand-alone mode of operation

The control methodology for the machine terminal voltage with SVC and STATCOM type reactive power compensators is discussed next. The pitch control scheme is common for both these compensators.

Fig.6: The configuration of the SVC

Fig.7: The configuration of the STATCOM

The SVC used here is of FC-TCR type. This is switched such that the machine terminal voltage is kept within a specified limit. The self excitation capacitors of the machine act as the fixed capacitors (FC) of the SVC whereas the inductor is switched by the thyristors. An inverse cosine firing scheme is used for switching the SVC. In the control scheme the actual terminal voltage phasor value is compared with a reference and the error, after passing through a PI controller produces the control voltage for SVC firing.

40


Fig. 8: Control voltage generation for firing the SVC for standalone mode

For the STATCOM the well known space vector based decoupled control theory is employed. First all the inverter equations are written in the voltage oriented frame of reference and then the control logic is implemented as discussed next. Equations of inverter in the voltage oriented frame of reference are: ௘ ܸௗ௦ூ‫ כ‬ൌ ‫ܫ‬ௗ௦ ܴ௦ ൅ ‫ܮ‬ ௘ ܸ௤௦ூ‫ כ‬ൌ ‫ܫ‬௤௦ ܴ௦ ൅ ‫ܮ‬

೐ ௗூ೏ೞ

௘ ௘ െ ߱௘ ‫ܫܮ‬௤௦ ൅ ܸௗ௦

(5)

௘ ൅ ߱௘ ‫ܫܮ‬ௗ௦ ൅ ܸ௤௦௘

(6)

ௗ௧ ೐ ௗூ೜ೞ

ௗ௧

In the above equations the d axis of the synchronously rotating reference frame is latched to the machine terminal voltage space vector. Therefore, ௘ ܸௗ௦ ൌ ܸ௦௘

(7)

&

ܸ௤௦௘ ൌ Ͳ

(8)

Now active power and reactive power are given respectively by; ଷ

௘ ௘ ௘ ‫ܫ‬ௗ௦ ൅ ܸ௤௦௘ ‫ܫ‬௤௦ ሻ P = ሺܸௗ௦ ଶ ଷ

௘ ௘ ௘ Q = ሺܸௗ௦ ‫ܫ‬௤௦ െ ܸ௤௦௘ ‫ܫ‬ௗ௦ ሻ ଶ

(9) (10)

Using equations (7) and (8) in equations (9) and (10) we have ଷ

௘ ܲ ൌ ܸ௦௘ ‫ܫ‬ௗ௦ ଶ

ଷ

௘ ܳ ൌ ଶ ܸ௦௘ ‫ܫ‬௤௦

(11) (12)

d-axis controllers From the above equations it can be concluded that the d axis current of the inverter actually controls the active power of the inverter. For the configuration of the inverter shown in the Fig. 7 the d axis component of the inverter current is used to control the dc bus capacitor voltage in such a way that it can be maintained at a fixed value. Therefore, there will be no net active power supplied/absorbed by the inverter other than some losses that it has to take from the terminals of the machine. Block diagrams of the d-axis controllers are shown in Fig. 9 below. In this controller a reference voltage for the dc bus (enough to control the terminal voltage and VAR) is compared with

41


the actual dc bus voltage and the error is processed through a PI controller to generate the inverter d-axis current command. Subsequently, the d-axis current controller generates the inverter d-axis voltage command in such a way that the actual d axis current of the inverter follows the reference. The switching frequency of the inverter is 1 kHz. The inner current control loop bandwidth is set to one tenth of the switching frequency and the outer voltage loop bandwidth is made one tenth of the inner loop bandwidth 900

+

PI with Anti windup

-

-1

Idref

+

PI with Anti windup

-

Vd1

Id

Vdc

+ -+

Vdsi*

Vs

weLIq

Fig. 9: d-axis controller for the STATCOM q-axis controllers The q axis component of the inverter current controls the reactive power transfer to/from the inverter This current component is used to control the machine terminal voltage in standalone mode of operation and the exchange of net VAR of the system with the grid in the grid connected mode of operation. Block diagrams of the q-axis controllers are shown in Fig. 10 below. The controller structure is similar to the d-axis controller except a cross coupling term is included in current controller.

280

+

-

PI with Anti Wind Up

-1

Vt

+ Iqref

0

+

-

PI with Anti Wind Up

-

PI With Anti Wind Up

Iq

Vq1

-1

Grid VAR Vqsi*

+ +

weLId

Fig. 10: q-axis controller for the STATCOM

4. Simulation Results The steady state and transient response of all the controlled variables depicted in Figs. 9 and 10 are shown in Fig. 11(a,b,c and d) below. For this figure the generator was working in the standalone mode of operation. The speed of operation was 1500 rpm and the load connected was 8 KW at 0.8 pf lagging.

42


Reference Vdc* and actual Vdc

Reference Id* and actual Id

950

50 Reference Actual

930

30

920

20

910 900 890 880

10 0 -10 -20

870

-30

860

-40

850 46.9 46.92 46.94 46.96 46.98 47 47.02 47.04 47.06 47.08 ---------------->Time(secs)

-50 46.95 46.96 46.97 46.98 46.99 47 47.01 47.02 47.03 47.04 47.05 ---------------->Time(secs)

47.1

Fig. 11(a): DC bus voltage

Fig. 11(b): d-axis current Reference Vt* and actual Vt

Reference Iq* and actual Iq

320

80 Reference Actual

75

Reference Actual

310 300 ---------------->Vterminal(volts)

70 ---------------->Iq(ampere)

Reference Actual

40

---------------->Id(ampere)

---------------->Vdc(volts)

940

65 60 55 50 45

290 280 270 260 250

40

240

35

230

30 46.95 46.96 46.97 46.98 46.99 47 47.01 47.02 47.03 47.04 47.05 ---------------->Time(secs)

220 46.9 46.92 46.94 46.96 46.98 47 47.02 47.04 47.06 47.08 47.1 ---------------->Time(secs)

Fig. 11(c): q-axis current

Fig. 11(d): Terminal voltage

In the above figure all control variables follow their respective references showing proper working of the controllers. It is to be noted that dc bus voltage controller generates a non-zero d axis current reference to account for the losses in the system. Transient performance of the system : For all the figures above a resistive load of 1 kW was switched on to the machine terminal at t=47 secs while the system was operating in the standalone mode at 1500 RPM and initially supplying a load of 8 kW at 0.8 lagging power factor. In all the figures above as the load is switched at the mentioned time the changes in the control variables are clearly visible from the above graphs.

43


Grid voltage and grid current with SVC connected

Grid voltage and current before and after the connection of STATCOM

300

300

Current Voltage

200

---------------->Vgrid(volts),Igrid(ampere)

---------------->Vgrid(volts),Igrid(ampere)

Voltage Current

100

0

-100

-200

-300 94.9

94.95

95

95.05 95.1 95.15 ---------------->Time(secs)

95.2

95.25

200

100

0

-100

-200

-300 34.2 34.22 34.24 34.26 34.28 34.3 34.32 34.34 34.36 34.38 ---------------->Time(secs)

Fig. 12(a): Grid voltage and current with STATCOM Switched at t=95 seconds

34.4

Fig. 12(b): Grid voltage and current with SVC

On the other hand, as seen from Fig. 12(a) and (b), when an SVC is used for VAR control the grid side displacement factor cannot be maintained at unity for similar operating condition as in Fig. 12(a) . Also the grid current has significant harmonic distortion. With the STATCOM the VAR control results are much better. As soon as the load is switched on the terminal voltage dips a little. The DC bus voltage or the machine current don’t change appreciably. The frequency dips by about 1 Hz when the load is switched on before coming back to its original reference within 0.01 sec. This is shown in the next figure. Actual frequency and its reference 55 Reference frequency Actual frequency

54

---------------->Frequency(Hz)

53 52 51 50 49 48 47 46 45 46.5

46.6

46.7

46.8 46.9 47 ---------------->Time(secs)

47.1

47.2

47.3

Fig. 13: Actual frequency and its reference during load switching at t=47 seconds

As the wind speed suddenly changes the machine speed also changes and the machine starts to take lagging VAR from the grid in the grid connected mode of operation. However, as seen in Fig. 14 the VAR controller for the grid connected mode of operation brings the power factor of the grid back to unity within a short time.

44


KVAR(Reference and Actual) 2 Reference Actual

---------------->Reactive Power(KVAR)

1.5 1 0.5 0 -0.5 -1 -1.5 -2 94.5

95

95.5 ---------------->Time(secs)

96

96.5

Fig. 14: Actual VAR and its reference as wind speed suddenly changes from 8m/s to 9m/s

Next we focus on the using space vector modulation over normal sine pulse width modulation so that we can have the same operation with a lower dc bus voltage, thereby reducing the dc bus capacitance requirement. The above simulation is carried out again implementing SVM technique and the same results are obtained. But the corresponding dc bus voltage required is approximately 15% lower than that of sine PWM as shown from the next graph. Reference Vdc* and actual Vdc with SVM 800 790

Reference Actual

---------------->Vdc(volts)

780 770 760 750 740 730 720 710 700 49

49.02 49.04 49.06 49.08 49.1 49.12 49.14 49.16 49.18 ---------------->Time(secs)

49.2

Fig. 15: DC bus voltage requirement with SVM technique implemented

From the above figure it is clearly visible that the DC bus voltage requirement is around 15% lesser than sine PWM. So if this technique is implemented we can have smaller dc bus capacitance. The only problem is this method is a computational intensive method and to avoid this we go for a carrier based SVM. The corresponding equations for carrier based SVM is given by; ‫כ‬ ܸ௔ǡ௕ǡ௖ ൅

‫כ‬ ௏೘೔೏

ଶ

‫כ‬ ൌ ܸ஺ǡ஻ǡ஼

(13)

The above equation means that if we have three sinusoidal waveforms then at any instant if we add the middle value

45


with them we will get the required waveform needed to perform SVM technique. The above equation is validated by a simulation result as shown below; Normal SPWM modulating signals

Carrier based SVM modulating signals 1

1 0.8 0.6

0.6

---------------->Modulating Signals

---------------->Modulating Signals

0.8

0.4 0.2 0 -0.2 -0.4 -0.6

0.4 0.2 0 -0.2 -0.4 -0.6

-0.8

-0.8

-1 0

0.005

0.01

0.015

0.02 0.025 0.03 0.035 ---------------->Time(secs)

0.04

0.045

Fig. 16(a): Normal SPWM modulating signals

0.05

-1

0

0.005

0.01

0.015

0.02 0.025 0.03 0.035 ---------------->Time(secs)

0.04 0.045

0.05

Fig. 16(b): Carrier based SVM modulating signals

Also next the grid transient is reported i.e. if while in grid is connected suddenly if it is needed to open the system from the grid what will be the transients in terminal voltage of the machine is reported next. The corresponding transient due to sudden grid outage is shown below; RMS value of terminal voltage during grid opening transient Vref Vactual

---------------->Terminal voltage

250

200

150

100

50

0 65

65.5

66

66.5 67 67.5 ---------------->Time(secs)

68

68.5

69

Fig. 17: Transient in machine terminal voltage due to sudden grid outage

From the above figure it is clear that when the grid is suddenly out and the machine operation is again returning to standalone mode there is a dip in the terminal voltage and a transient and this takes appreciable time in seconds to settle to its desired value. The reason for this is the slow response of pitch controller due to mechanical constraints of the wind turbine blades i.e. to say for the wind turbine chosen we have pitch control slew rate to be ±12º/sec. So the response is slower compared to voltage. As soon as the grid is disconnected the speed of the machine increased as only local load is present then. As it is clear from self-excited induction machine characteristics above that for a particular load to have a certain voltage at machine terminals we must have a particular speed. So as soon as the speed is increased the capacitive load line shifts away from the machine magnetization characteristics and so the flux can’t be maintained thereby machine terminal voltage falls. This can be attributed as a limitation of the above scheme and future works can be done in wind turbine blade design so that more flexible blades can be made so that a slew rate of much higher than the present value can be imposed on it without mechanical damage. 5. Conclusion

46


The paper presents a simple control technique for a self excited squirrel cage induction generator based wind power conversion system. The machine terminal frequency is kept within prescribed limits by controlling the turbine blade pitch angle. Only one power electronic converter i.e. a STATCOM or a SVC is used to control the machine terminal voltage in the stand alone mode and the machine terminal power factor in the grid connected mode of operation. The overall control strategy of the STATCOM is more complex compared to the SVC. But the performance of the system is far superior compared to what can be achieved with the passive filter SVC. In comparison to a normal back to back converter system normally used for wind power generation using squirrel cage induction machines the proposed scheme uses only one fractionally rated inverter to control the machine terminal voltage/power factor. This is expected to save capital investment towards the system as well as cut down on the losses. References [1] S.S. Murthy, O.P. Maw and A.K. Tandon, "Analysis of self-excited induction generators", Proceedings of IEE, Vol. 129, Part C, No. 6, pp.260265, November 1982. [2] N.H. Malik and S.E. Hague, "Steady state analysis and performance of an isolated self-excited induction generator", IEEE Transactions on Energy Conversion, Vol. EC- 1, No. 3, pp.134-139, September 1986. [3] T.J.E. Miller, “Reactive Power Control in Electrical System” , John Wiley & Sons. Inc, 1982. [4] Narain G. Hingorani, Laszlo Gyugyi, “Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems” IEEE press 1999, Chapters 1-6. [5] K. M. Abbott and J. D. Wheeler, “Simulation and Control of Thyristor Drives”, IEEE Transactions on Industrial Electronics and control instrumentation, vol. IECI-25, No. 2, MAY 1978, pp. 130-137 [6] S. Hazra and P.S. Sensarma “Self-excitation and control of an induction generator in a stand-alone wind energy conversion system”, IET Renewable Power Generation, vol. 4 issue. 4 Jan 2010 pp. 383-393. [7] Samir Hazra, Subhashish Bhattacharya , “Short Time Power Smoothing of a Low Power Wave Energy System” IECON 2012-38th annual conference on IEEE industrial electronics society 25-28 Oct 2012, pp. 5846-5851 [8] Chowdhury M.M. ; Haque M.E. ; Gargoom, A. ;Negnevitsky, M. “A direct drive grid connected wind energy system with STATCOM and supercapacitor energy storage” Power System Technology POWERCON- IEEE International Conference, Oct 30-Nov 2 2012 pages 1-6 [9] Dr. Parthasarathi Sensarma , “Analysis and development of a distribution STATCOM for power quality compensation”; PhD thesis, Department of Electrical Engineering IISc Bangalore, Bangalore 560012, July 2000.