Power Control of Doubly Fed Induction Machine using a Rotor Side Matrix Converter

K. Spiteri, C.Spiteri Staines, M.Apap Dept. of Ind. Electrical Power Conversion

University of Malta, Msida, MSD 2080 Cyril.spiteri-staines@um.edu.mt, Maurice.apap@um.edu.mt

Abstract—This paper presents the control of a doubly fed induction machine (DFIM) via a matrix converter applied to the machine’s rotor side. The experimental set-up shall be used to show its viability for wind energy applications. Stator Field Oriented control of the machine was implemented for active and reactive power control. The effects of rotor side current harmonics, on the control scheme were analysed. The paper also presents experimental results for active and reactive power control for the variable speed DFIM including operation at zero Stator Reactive power.

I. INTRODUCTION Wind power is widely recognised as a viable source of

energy to aid conventional power generation. Variable speed driven turbines provide a means to continuously capture the maximum wind energy available such that maximum power operation is achieved under all conditions. Doubly-fed induction generators are considered to be a good alternative where a restricted variable speed generation system is needed [4]. The main advantage of the doubly-fed scheme over the singly-fed scheme is that the power converter required for the control of the machine can have a substantially reduced Volt-Ampere rating. The converter is installed on the rotor side and usually consists of two back-to-back voltage source inverters which allow bidirectional power flow. In this paper a matrix converter is proposed [1]-[3] since it is inherently bidirectional and can achieve four quadrant operation without requiring the need for any bulky and costly energy storage components. Further, the control schemes are simpler than those needed by the two stage power converters as both input current and output target voltages are modulated within the same algorithm.

Considering the above, together with its robustness and reliability, the matrix converter has been considered for the control of the DFIM. The practical difficulties and constraints encountered in such system integration are studied. The analysis employs a standard stator flux orientation (SFO)

vector control algorithm whilst space vector modulation (SVM) was used for the control of the matrix converter switches.

Figure 1. Wind Energy Conversion System Using DFIM & Matrix

Converter

II. CONTROL OF THE DFIM

A. DFIM Model The dynamic equations of the DFIM in the dq- frame are

given by:

( )

dq

dq

dqdq SeS

SSS jdt

diRv Ψ+

Ψ+= ω (1)

( )dq

dq

dqdq RslR

RRR jdt

diRv Ψ+

Ψ+= ω (2)

ROSSS iLiL +=Ψ (3)

SORRR iLiL +=Ψ (4)

where OSS LlL += and ORR LlL += are defined as the

stator and rotor self inductances respectively and Sl , Rl are the leakage inductances. A stator to rotor turns ratio of

1=srN has been assumed, and OL is the mutual/magnetising inductance.

B. Control of the DFIM Both SFO and Stator Voltage Orientation (SVO) methods

have been investigated in literature [6]-[9]. For the control of the DFIM presented in this work, the SFO scheme shown in Fig.2 was adopted.

Figure 2. Stator Flux Oriented Control

For the SFO scheme of Fig. 2: aligning the synchronous frame to the stator flux SΨ , SSd

Ψ=Ψ , 0=ΨqS ;

neglecting the per phase stator resistance SR and assuming

steady state grid supply ( ( ) 0=Ψdt

d S , no voltage dip, frequency swell, etc), equations (1) to (4) yield:

0=Ψ−=qd SeSv ω ,

dq SeSv Ψ= ω (5)

Since 0=

dSv , the q-component is given by: SS vvq

= .

The stator voltages and rotor currents are known quantities for the case of the DFIM rotor fed from a matrix converter, thus the rotor flux components can be written as:

ddd SS

ORRR L

LiL Ψ+=Ψ δ (6)

S

RORRR L

iLiL q

qq

2

−=Ψ (7)

Where ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

RS

O

LLL2

1δ is defined as the leakage

coefficient.

The rotor dynamic equations can be written as:

q

d

dd RslRR

RRRR iLdt

diLiRv ωδδ −+= (8)

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ψ+++=

S

SORRsl

RRRRR L

LiL

dt

diLiRv d

d

q

qqδωδ (9)

The torque equation is given by:

dq SRS

Oe i

LLp Ψ⎟

⎠⎞

⎜⎝⎛=Τ

23 (10)

and the d-axis stator current is give by:

S

ROSS L

iLi d

d

−Ψ= (11)

Fig. 3 shows a schematic block diagram for the DFIM control. The reference rotor current *

dRi and *qRi are obtained

from an imposed stator reactive current and machine torque respectively.

Figure 3. SFO Control Scheme for DFIM

C. Stator Flux Angle Calculation

The Flux angle used for orientation (Fig. 3) is calculated from the equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛

ΨΨ

= −

α

βθS

SeSFO

1tan (12)

In the experimental implementation, the integral required for the flux calculation was achieved via a digital low-pass filter with a cut-off frequency of 1 1. −srad . A high-pass filter of cut-off frequency of 0.31 1. −srad was used to eliminate the dc component.

III. EXPERIMENTAL SET-UP

The DFIG system was set-up by coupling the induction machine to a commercial four quadrant dc drive which was to act both as a prime mover and a load unit. A matrix converter was designed, built and installed on the rotor side of the DFIG. The machine parameters are found in the appendix (Table II).

The matrix converter for the rotor side control was constructed using nine Semikron SK60GM123 insulated gate bi-polar transistor (IGBT) modules. An FPGA based interface card was used for the data acquisition of the voltage and current sensors and the encoder. The FPGA also provided protection against over-voltages, over-currents and included a watchdog circuitry. The control platform for the DFIM and matrix converter control was a C6713 DSP. Data transfer and ‘on line’ reference changes were carried out between the DSP and a PC via the DSP board’s host port interface (HPI).

A. Current Control Loop Operation The discretised PI controller performance was tested

separately using the de-energised DFIM rotor side as a passive RL load. The machine stator was short-circuited allowing testing of the machine dynamics under similar conditions to those experienced during normal drive operation (controlled rotor currents and stator grid-connected). With this set-up the response to a step demand in both

dRi and qRi currents were recorded as shown in Fig. 4.

From the measured rise time '' rt , delay time '' dt and peak overshoot, it can be shown that the PI controller’s performance corresponds to a damping factor of 5.0=ζ

and a bandwidth of Hzfn 15= .

IV. ROTOR CURRENT HARMONICS

When operating the DFIM at rated supply voltage with current demands *

dRi and *qRi set at A4 and A3 respectively

(at a slip of 25%), the rotor currents shown in Fig. 5 are obtained. Fig. 6 shows the rotor current spectrum where the fundamental frequency and other frequencies of relatively large amplitude can be observed.

These current harmonics are due to the machine winding

harmonics in the induced rotor voltage and are mainly attributed to :

a. Non-sinusoidal distributed stator and/or rotor windings (placed in slots).

b. Variations in machine reluctance during rotational movement due to the presence of stator and rotor slots.

Figure 4. Testing of current contollers: D and q- rotor currents for a step demand of 4A and 3A respectively.

Considering that these harmonics will increase in

amplitude as the relative rotational speeds increase, they might ultimately deteriorate the system performance under certain conditions if they are not taken into consideration [6],[11]. Table I summaries what is documented on DFIM in literature [11] as concerns the machine winding harmonics The harmonics observed in Fig 6. are in agreement with this table.

TABLE I. ROTOR HARMONICS [11]

Harmonic Frequency

slipgrid fnfm )56()6( −−

slipgrid fnfm )56()6( −+

slipgrid fnfm )16()6( −−

slipgrid fnfm )16()6( +− For, n = 1,2,3… and m = 1,2,3…

The rotor current harmonic spectrum obtained in Fig.6

shows that the most prominent harmonics are: a. the ( )slipGrid ff ±6 , ( )slipGrid ff 236 − and,

b. the slipf5 and the slipf7

Figure 5. Rotor Currents (steady state current waveforms)

Figure 6. Harmonic Spectrum of Rotor Current (current spectra for Fig. 5)

The harmonics in (a) are due to the machine’s windings and magnetic eccentricity as explained above, whilst the harmonics in (b) are due to the matrix converter switching and commutation. Fig. 6 shows also other harmonics at ( )RGrid ff + which could be caused either by an unbalanced stator/rotor winding or an unbalanced supply voltage.

Experimental tests were carried out to verify the origin of

the rotor current harmonics and their effect on the current controllers. It was determined that due to their high frequency, they lay outside the controller’s bandwidth and hence beyond its capability whatsoever [6]. For clarity, it was decided to show filtered rotor currents (filtered by a low pass filer of 80 Hz) for the waveforms presented in the following results section.

V. RESULTS

A. Power Control of DFIM

The stator active and reactive power are given by:

eSRS

OS q

iLLP ωΨ−= 3 (13)

⎟⎟⎠

⎞⎜⎜⎝

⎛−Ψ−=

dRS

SO

S

SSS i

LvL

LvQ 3 (14)

The above equations show that the active ( SP ) and

reactive ( SQ ) powers can be controlled by means of the rotor’s quadrature and direct current. Thus for power control the DFIM was operated under ‘current-mode’ control by means of the ‘torque’ current,

qRi and the ‘field’ current dRi .

The system’s operational speed was set by the speed controlled regenerative dc drive which was simulating a wind generation system. Figures 7 and 8 show the system’s stator power output during step demands of 3A and 4A in the rotor’s quadrature and direct currents respectively.

Figure 7. Stator Active and Reactive Power for step demand in

qRi of 3A.

Figure 8. Stator Active and Reactive Power for step demand in

dRi of 4A.

B. Variable Speed Operation of DFIM Figures 9 to 11 show varying speed operation of the DFIM from below synchronous to above synchronous speed whilst generating. The speed was varied from 1050 rpm to 1800 rpm (i.e slip varied from 0.3 to -0.2) by the speed controlled dc drive whilst maintaining constant rotor currents (

dRi and Rqi of 4A and 1.5 A respectively). Fig. 11 shows

the change in rotor power according to, SR sPP −= , when the slip changes sign at operation above synchronous speed.

Figure 9. Rotor Currents

dqRi controlled during Speed Transition.

Figure 10. Rotor Current Variation (for Fig. 9).

Figure 11. Rotor Power Transition for operation Below (0-4.5sec) and Above Synchronous Speed (4.5-8sec).

C. Stator Unity Power Factor Operation For correct operation, the DFIM’s stator flux is required to

remain constant throughout its operation. The machine magnetisation current required to maintain the stator flux can either be fed from the stator side or the rotor side or both together. For grid connected systems it is often desired to opt for zero reactive power. This can be achieved by setting

dRi equal to the machine magnetisation current, such that SQ in equation (14) is reduced to zero.

In Fig. 12, initially the stator flux is maintained by the

stator circuit, after 0.15s, the Stator VArs are reduced to zero by supplying the machine magnetisation current entirely by the rotor side. (Since the DFIM used requires a magnetisation current which is larger than the rotor winding rating, the supply voltage had to be reduced by 40%). Fig. 13 shows the stator side voltage and current where it can be observed that the stator current does a 180 degree phase change on reducing SQ to zero.

Figure 12. Stator Reactive Power reduced to zero whilst maintaining constant Stator Flux (Machine Magnetisation Current Stepped from Stator to Rotor Side).

Figure 13. Stator Phase Voltage, Stator Phase Current and Rotor Phase Current and for a step change in Stator Reactive Power to zero (corresponding to Fig. 12.)

VI. CONCLUSIONS The paper has presented the application of a matrix

converter to a DFIG wind energy system. The matrix converter was used for control of the rotor side of the induction machine to achieve Active and Reactive stator power control under varying speed operation. An analysis of the effects of the inherent rotor current harmonics on the current controllers was also discussed. Experimental results for P and Q control and operation at below and above synchronous speed operation are presented. Further it has been shown that zero stator reactive power is possible by supplying the machine’s magnetization current from the rotor circuit.

VII. APPENDIX

TABLE II. DFIM MOTOR PARAMETERS

Parameter Stator Rotor Power 1.5kW -

Phase voltage, current 220V, 4.5A 150V, 3.7A

Resistance 1.16Ω 1) 1.60Ω 1)

Frequency 50Hz -

Leakage Inductance 6.5mH 2) 6.5mH 2)

Mutual Inductance 117.1mH 2)

Turns ratio (stator to rotor) 1.32 1) from dc test, 2) referred to rotor

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