Direct Torque Control With Space Vector Modulation For Im Fed By Cascaded Multilevel Inverters

Direct Torque Control with Space Vector Modulation for Induction Motors Fed by Cascaded Multilevel Inverters Yi Wang, Heming Li, Xinchun Shi Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education North China Electric Power University 619 Yonghua North Street, Baoding , 071003, China [email protected] Abstract – Direct torque control (DTC) has achieved utilization on two-level inverters and three-level diode-clamped inverters, and it has high performance of speed control. But DTC hasn’t been utilized to cascaded multilevel inverters at present. In this paper, a novel space vector modulation (SVM) approach for cascaded multilevel inverters is presented firstly. Then by combining it with the DTC approach based on SVM, the approach of using DTC to cascaded multilevel inverters is presented. And it is verified by using a three-cell cascaded frequency control laboratory system. The proposed approach solves the issues that switching state table is difficult to generate and switching frequency is not fixed, which is arisen from using conventional DTC to cascaded multilevel inverters. It will be of benefit to the utilization of DTC on the speed control of induction motors fed by cascaded multilevel inverters.

I. INTRODUCTION Cascaded multilevel inverters have high power quality waveforms and easy to expend towards higher voltage operations compared with neutral point clamped (NPC) multilevel inverters. Variable frequency drives (VFDs) based on this topology have been widely used for energy-saving speed control applications, which do not need high precision of speed control, such as fun and pump motor drives. As the same time, the high performance of speed control is also required for high-voltage and large-capacity motor drive systems [1-2]. Direct torque control (DTC) provides fast and precise torque response, and has been widely used to two-level inverter drives in the past decade. However, for multilevel inverters DTC is only utilized to three-level NPC inverters at present [3-5]. In the classical DTC algorithm proposed by Takahashi and Depenbrock, the decoupling of nonlinear AC motor characteristics is achieved by the on-off operation of the hysteresis controller. However, the number of switching states of multilevel inverters is M3 (where M is the level number of multilevel inverters). For cascaded inverters the output voltage level number is generally over seven, so the look-up table of multilevel inverters that consist of so many switching states is very difficult to form. Fig.1 shows the space vector diagram of seven-level cascaded inverters. Hysteresis PWM controller can be replaced by space vector modulation (SVM) in DTC to make torque response smooth and switching frequency fixed. However, the SVM control of cascaded inverters requires complicated calculation algorithm, and this calculation is difficult to be finished by DSP in a very short

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sampling period of DTC. In this paper, based on Phase-Shifting Pulse Width Modulation (PSPWM) strategy of multilevel inverters and Space Vector Modulation Strategy (SVM) of two-level inverters, the scheme of Phase-Shifting Space Vector Modulation (PSSVM) for cascaded multilevel inverters is proposed. This strategy is easy to realize by the control system based on DSP and CPLD. Combining it with the classical DTC, a novel DTC scheme suitable for cascaded multilevel inverters is proposed. II. PHASE-SHIFTING SVM SCHEME Due to SVM scheme can synthesize arbitrary voltage vectors needed by the control strategy, SVM has become the most suitable modulation scheme for the speed control strategy with high dynamic performances such as vector control and direct torque control. According to the control demand of the drive system, the required voltage vector is synthesized by the actual existing voltage vectors which contain the zero vectors. The number of actual voltage vectors is decided by the switching states of a converter. For example, a seven-level converter has 343 switching states totally, and the whole space vectors distribution is shown in Fig.1. So the SVM control using so many vectors is very complex. Although some simplified control algorithms have been proposed recently, they are still too complicate to be realized for real-time control [6-7]. Therefore, SVM has been widely used in conventional two-level converters, but for multilevel converters, it is just applied to three-level diode clamped inverters [8], and is difficult to be extended to more level circuits.

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β

u

α

Fig. 1. Space vector diagram of seven-level inverters

At present, cascaded inverters usually adopt Triangular Carrier Phase-Shifting SPWM (PSPWM) strategy to generate multilevel PWM waveforms. Due to each power cell has the similar modulation scheme, it is simple to be realized and expanded to the more levels inverter. The proposed SVM control strategy in this paper also depends on this idea. Modulation scheme of one-cell cascaded inverters is proposed firstly. Then the phase-shifting SVM (PSSVM) that could make the cascaded cells generate multilevel waveforms is presented.

A LA

RA

LB

u=uL-uR

RB

where the vector uL and uR can be generated by the SVM strategy of traditional two-level inverters. In order to make the amplitude of the synthesized vector u to be the largest, the phase-difference of uL and uR should be 180o. The arm vectors synthesized principle is shown in Fig.3, and their voltage waveform synthesized principle is shown in Fig.4. Therefore, the SVM strategy of one-cell inverter is to decompose the desired generated vector to two vectors with same amplitude, and 180° phase difference, which can be generated by the two-level SVM strategy respectively.

RC

β II

u2

(1)

LC

N Fig. 2. Structure of one-cell cascaded inverter

A. PSSVM of One-cell Cascaded Inverter The structure of a one-cell cascaded inverter is shown in Fig.2. It has six bridge arms, and these arms can be divided into two groups, which are the left arm group LA, LB, LC and the right arm group RA, RB, RC. The voltage vector of left arm uL(uLA, uLB, uLC) and the voltage vector of right arm uR(uRA, uRB, uRC) can be generated when the two arm groups voltages are controlled respectively, and the H-bridge voltage vector u(uAN, uBN, uCN) can be calculated from the following equation

C

B

u6

III

I

uL u3

u

u4 uR

IV

u1

α

VI u5

V

Fig. 3. Relationship between arm vectors and synthesized vector uLA

uRA

0

0.005

0.01

0.015

t/s

0

0.005

0.01

0.015

t/s

0

0.005

0.01

0.015

t/s

uAN

Fig. 4. Output voltage waveform of H-bridge with SVM

B. PSSVM of N-cell Cascaded Multilevel Inverter A

C

B

The structure of N-cell cascaded inverters is shown in Fig.5. The output voltage vector of the inverter u can be decomposed to 2N arm vectors (N left arm vectors and N right arm vectors ), and it is given by the equation u=uL1+uL2+…+uLi+…+uLN-uR1-uR2-…-uRi…-uRN

(2)

where uLi and uRi are the left and right arm vectors of the ith H-bridge cell, and they have the same amplitude and opposite phase. Assuming the sampling period of SVM control is Ts. The effecting time of left arm (or right arm) vector of each cell is same, i.e. Ts, but their phases are different. If four-part modulation strategy is adopted, the phase-shifting time of different H-bridge vectors is Ts/N, and if seven-part modulation strategy is adopted, it becomes Ts/2N. Therefore, there are phase differences between the H-bridge vectors. The H-bridge vector synthesized principle is shown in Fig.6, and their voltage waveform synthesized principle is shown in Fig.7.

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A1

B1

C1

Ai

Bi

Ci

AN

BN

CN N

Fig. 5. Structure of N-cell cascaded inverter

uLi = uRi ≈

β II

u2

u

u6

III I uL1,2,3

u3

u4

uR1,2,3 IV

α

VI u1

u5

V

Fig. 6. Phase-shifting and synthesizing theory of three-cell cascaded inverter vectors u1

u2

0

0.005

0.01

0.015

0.005

0.01

0.015

t/s

0

0.005

0.01

0.015

t/s

0

0.005

0.01

0.015

t/s

III. DTC BASED ON PHASE-SHIFTING SVM

u3

uAN

Fig. 7. Waveform synthesizing theory of a three-cell cascaded inverter

The sampling period Ts is commonly very short, so the phase differences can be neglected when calculating the vectors amplitudes. Then the amplitude of every vector is about 1/2N of that of the synthesized vector, and it can be calculated by

ω r∗ ωr −

Te∗

PI

Te − ΔΨ s

Ψ s∗

Ψs

ΔTe

(3)

The above generation of the 2N vectors are all based on SVM strategy of traditional two-level circuits, just on time sequence aspect, every cell vector has fixed time difference Ts/N or Ts/2N. Therefore, only the calculation of the two basic vectors of the left and right arms needs to be completed by DSP, and the driving signals of six arms of one-cell cascaded inverters are generated correspondingly. Driving signals of other cells can be obtained by corresponding delay when distributing the driving signals of each cell by CPLD or FPGA. Compared with two-level SVM, this strategy does not increase the calculation work of DSP. So it is easy to be realized in real-time control. The waveform composing theory of three-cell cascaded inverter is shown in Fig.7.

t/s

0

1 u 2N

The main issues of traditional DTC are the large torque ripples and unfixed switching frequency. In order to solve these problems, SVM is adopted to DTC technique. The combination of SVM and DTC avoids the look-up table for selecting vectors which is difficult to form in cascaded inverters, and fix the switching frequency so that the multilevel waveform can be synthesized. Furthermore the demand of sampling period of traditional DTC is very strict, and usually it is 25us, which is too short to complete the PWM calculation for multilevel inverters. After SVM is adopted, the sampling time can also be prolonged for the zero vectors are added in every period. In this paper, the proposed novel DTC strategy is combined by Phase-Shifting SVM (PSSVM) and the classical DTC, and accordingly DTC is extended to the cascaded inverter. By PSSVM-DTC the speed control performance of high-voltage motors is improved, and the harmonic content of output voltage and current is reduced largely, and the torque ripple can also be further lighten.

uq∗

PI

ud∗

PI

Cascaded Multilevel Inverter

PSSVM

θ Ψs

−

Flux & Torque Estimation Encoder Fig.8. System diagram of PSSVM-DTC

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M ~

Rs

L s'

is

u

us

After ascertain of the reference voltage vector, it can be synthesized by PSSVM algorithm, and the driving signals of every cell are generated correspondingly. IV. SIMULATION AND EXPERIMENTAL RESULTS

e ~

Fig. 9. Simplified circuit of the induction motor

The PSSVM-DTC system diagram is shown in Fig.8. The observation model of torque and flux is same as traditional DTC, so it will not be detailed in this paper. After the calculation of the flux error and torque error, as for how to decide the desired voltage vector by them, several effective strategies have been proposed [9]. In order to reduce the calculation work of DSP, the scheme of using PI controller to derive the voltage vector is adopted in this paper, and its principle is illustrated as follows. The simplified circuit of induction motors is shown in fig. 9. The stator flux can be estimated by t

Ψ s = ∫ (us − Rs is )dτ

For the DTC strategy of cascaded multilevel inverters proposed in this paper, simulations using MATLAB/Simulink and experiments based on a motor drive laboratory system fed by a three-cell cascaded inverter are completed. The simulation results are shown in Fig.10, and the experimental results are shown in Fig.11. The experimental system is designed according to the structure of high-voltage cascaded converters that have been widely produced, but the voltage and power level have been decreased, and it can drive the induction motor of 380V/2.2KW.

(4)

0

and the flux variety in the sample time is ΔΨ s = (us − Rs is )Ts

(5)

Ψ s ( n + 1) − Ψ s ( n) = u( n)Ts = (us (n) − Rs is )Ts

(6)

ΔΨ s = Ψ s (n + 1) − Ψ s ( n) ≈ udTs

(7)

uqTs = Ψ s (n + 1) sin(Δθ ) ≈ Ψ s (n + 1) ⋅ Δθ ≈ Ψ s* Δθ

(8)

From equations (7) and (8), ud and uq can be expressed as

uq =

Δθ * Ψ s = ωeΨ s* Ts

(9) (10)

The relationship of electric torque and flux is 3 p Te = (Ψ r × Ψ s ) 2 L's

1000 0

0

0.05

0.1

0.15 0.2 (a) Speed

0.25

0.3

0.35

t/s

0

0.05

0.1

0.15 0.2 (b) Torque

0.25

0.3

0.35

t/s

0

0.05

0.1

0.15 0.2 0.25 (c) Phase voltage

0.3

0.35

t/s

0

0.05

0.1

0.15 0.2 0.25 (d) Line voltage

0.3

0.35

t/s

0

0.05

0.1

0.3

0.35

t/s

Te/N·m 2 0

Then the following equation can be derived

ud = ΔΨ s / Ts

n/rpm

ua/V 300 -300

ul/V 600 -600

ia/A 1 -1

(11)

The equation (11) shows that the regulation of electric torque can be realized by changing the angle between stator flux and rotor flux under the condition of their amplitudes are constant. Due to the large inertia of rotor, its flux can’t be changed suddenly. Thus the electric torque can be regulated by changing the stator flux speed ωe. The equation (10) shows that ωe is decided by uq, so the electric torque can be regulated by uq. From the above analysis the following conclusion can be derived: the amplitude of stator flux is decided by ud, and the electric torque is decided by uq when the flux amplitude is constant. By adopting tow PI controller to regulate flux and electric torque respectively, the ud and ud can be derived.

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0.15 0.2 (e) Current

0.25

Ψβ/Wb 1

0

-1 -1

0 1 Ψα/Wb (f) Flux Fig. 10 Simulation waveforms of PSSVM-DTC for a three-cell cascaded inverter

V. CONCLUSION In this paper, Phase-shifting SVM strategy suitable for cascaded inverters is proposed, and a novel DTC control strategy based on it is also presented to improve the speed control performance of high-voltage motor drives. The complex look-up table for hysteresis control of multilevel inverters is avoided by the proposed DTC algorithm. The proposed PSSVM algorithm is based on the two-level SVM strategy, and only one-cell driving signals are needed to be calculated. Other driving signals can be obtained by a fixed time delay. So lots of repeat calculation is avoided. Therefore, the calculation work of DSP and the length of the sampling period of DTC are similar with the DTC with SVM of two-level inverters, and its industrial utilization will not be difficult. It provides an effective way to extend the high-performance control strategies of two-level converters into the cascaded multilevel converters.

(a) Voltage

V. REFERENCES

(b) Current

n/pu 1

[1]

0.5

[2]

0

0

1

2

3

4

t/s

[3]

(c) Speed

Ψβ/pu

[4]

1 0

[5]

-1 -2 -2

-1

0

1

Ψα/pu

(d) Flux

[6]

Te/pu 1 0.8

[7]

0.6 2.2

2.22

2.24 2.26 (e) Torque

2.28

t/s

[8]

Fig. 11 Experimental waveforms of PSSVM-DTC for a three-cell cascaded inverter

The experimental system includes nine power cells which using MOSFET of 500V/20A as the power device of main circuit, IR2130 as driving circuit, and TMS320-6713 DSP and XC95108 CPLD as the kernel of the control system. The sampling period TS=200us.

[9]

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