A New Switching Technique for Direct Torque Control of Induction ...

A New Switching Technique for Direct Torque Control of Induction Motor using Four-Switch Three-Phase Inverter with DC – Link Voltage Imbalance Hong Hee Lee*, Phan Quoc Dzung**, Le Minh Phuong** , Nguyen Xuan Bac** *NARC, Ulsan University, Korea **Faculty of Electrical & Electronic Engineering, HCMC University of Technology, Ho Chi Minh City, Vietnam [email protected]; [email protected] ; [email protected] Abstract—This paper presents a new switching technique for Direct Torque Control of Induction Motor using Four-Switch Three Phase Inverter (DTC-FSTPI-IM) for low power applications with DC – link voltage imbalance. The new control algorithm and modified switching table are based using a realtime compensation SVPWM technique when generating switching control signal in consideration of unbalanced DC-link voltages by direct calculation of switching times based on four basic space vectors in FSTPI. By using reasonable mathematical transform, Direct Torque Control technique for FSTPI under DC-link voltage imbalance have been solved, which is based on the establishment of basic space vectors and modulation technique in similarity with six-switch three-phase inverters. This approach has a very important sense to solve hard problems for FSTPI under DC-link voltage imbalance. The validity of new proposed technique is verified by simulation and experimental results using Matlab/Simulink and DSpace 1104. Keyword: Direct Torque Control, Optimal Switching Table, Four-Switch Three-Phase Inverter (FSTPI), Six-Switch Three-Phase Inverter (SSTPI), DC-link ripple, DC – link voltage imbalance.

One of main differences between Four-Switch Three-Phase Inverter (FSTPI) and Six-Switch Three-Phase Inverter (SSTPI) is an using of two DC capacities. Because of this, the voltages of capacities are imbalance in its charge and defuse process. The second source of imbalance is a low output frequencies where unequal loading of the split link occurs for extended period [4]. To solve the mentioned above problem it could be used same ways, one of this is to increase the capacitance of DClink capacitors. However, this solution would add considerable cost and size. This paper presents a new effective method using real-time compensation DTC technique when generating switching control signal in consideration of unbalanced DC-link voltages by direct calculation of switching times based on four basic space vectors in FSTPI using the principle of similarity. Beside that, in this paper a modified switching table and a new control algorithm are presented . II. VOLTAGE SPACE- VECTOR ANALYSIS FOR FSTPI AND THE

I. INTRODUCTION Nowadays, a few research efforts have been directed to develop power converters with reduced losses and cost for driving induction motors. Hence, a reduced number of inverter switches is a promising solution. Among them the four switch three phase inverter (FSTPI) (fig.1) was introduced with four IGBT switches instead of six in a conventional three phase inverters (SSTPI) [1-9]. Recently, several scientific researches have been done for Four-Switch Three-Phase Inverters (FSTPI) with the target for reducing the cost of electric drives. Several inverter schemes with reduced number of switches have been proposed [1-5]. To obtain the simple, effective performances, the fast control of torque and flux in a DTC system for FSTPI-IM has been proposed [6]. DTC method for SSTPI-IM has been improved in some researches [7-13], while the torque and speed ripples are reduced. In order to reduce the speed (torque) ripple, the space vector modulation (SVM) can be increased by mixing highfrequency dither signals with modified modulator [8-12].

PRINCIPLE OF SIMILARITY

According to the scheme in fig.1 the switching status is represented by binary variables S1 to S4, which are set to “1” when the switch is closed and “0” when open. In addition the switches in one inverter branch are controlled complementary

Fig. 1.

DTC schema for FSTPI-Induction Motor.

(one switch on, another switch off), therefore: S1+S4 = 1 S3+S2 = 1 (1) Phase to common point voltage depends on the turning off signal for the switch: Va 0 = 0; Vb 0 = S1V1 + (S1 − 1) ⋅ V2 ; (2) Vc 0 = S3V2 + (S3 − 1) ⋅ V1; V V (3) V1 = dc − ε .Vdc ; V2 = dc + ε .Vdc 2 2 Where : V1, V2 voltage across the dc-link capacitors; V1+V2=Vdc ε the imbalance factor ; − 1 ≤ ε ≤ 1 2 2 Combinations of switching S1-S4 form 4 general space vectors G G V1 → V4 (fig. 2; Table I), components αβ of the voltage vectors are gained from abc voltages by using Clark’s transformation: 1 1 ⎤ ⎡V ⎤ ⎡ a ⎡Vα ⎤ 2 ⎢ 1 − 2 − 2 ⎥ ⎢ ⎥ ⎥ ⎢Vb ⎥ ⎢V ⎥ = ⎢ 3 3⎥ ⎣ β ⎦ 3 ⎢0 − ⎢V ⎥ 2 2 ⎦⎥ ⎣ c ⎦ ⎣⎢

(4)

Where Va, Vb, Vc : phase voltages on the load (Y connection), defined by: 1 1 1 (5) Va = − (Vb 0 + Vc 0 ) ; Vb = (2Vb 0 − Vc 0 ) ; Vc = (2Vc 0 − Vb 0 ) 3

3

3

Voltage imbalance in the DC link causes the space vector G G G G origin to shift along the V1 / V3 axis, with V1 and V3 no longer being equal in magnitude, as described in Table 1. G In order to form the required voltage space vector Vref , we can use 3 or 4 vectors in one sampling interval Ts. For three phase induction motors, the stator flux linkage vector can be represented as follows [2,4,9]: G G (6) Ψ = ∫ V (t )dt

In case the motor is fed from a FSTPI inverter the flux linkage vector is: G G G (7) Ψ = t n ⋅ Vn + Ψ0 where n = 1..4 ; tn : duration of Vn. If the switching algorithms can ensure the best approximation by minimizing the discrepancy between vector

Fig. 2.

Voltage space vectors in the plan αβ (*)

If PWM output voltages are synthesized without considering the non-ideal DC link conditions then unbalanced stator voltages will result, which causes large current variations and the deviation of real flux-linkage vector [4, 7]. To simulate 6 non-zero vectors in SSTPI, in this proposed G G method, we use the effective vectors V1' ...V6' , when the length of the basic generated vector is equal the length of the shortest G G vector from V1 , V3 (Fig. 3, 4). Furthermore, when V1=V2, the same equations as in the case of balanced DC-link voltages are achieved [9]. These modified vectors are formed as follows:

G G G G G v1' = av1 ; v 2' = bv1 + cv 2 ; G G G G G v3' = cv 2 + dv3 ; v 4' = ev3 ; G G G G G G v5' = dv3 + cv 4 ; v6' = cv 4 + bv1

Where coefficients a, b, c, d, e are defined as follows: G G - Case 1: DC-link voltage V1 < V2 ( V1 > V3 ) (Fig.3) a =

V1 V 12 ;b = V2 V 2 ⋅ (V 1 + V 2

)

;c =

V1 ; V1 + V 2

(9)

V2 d = ;e = 1 V1 + V 2

G G - Case 2: DC-link voltage V1 > V2 ( V1 < V3 ) (Fig.4)

V1 V2 ;c = ; V1 + V 2 V1 + V 2

G G* loci Ψ and Ψ , the stator voltage performance will be

a = 1; b =

optimized. This approach is used successfully for FSTPI in case of the balance in DC link voltage [9].

V 22 d = V 1 ⋅ (V 1 + V 2

TABLE I.

(8)

(10)

V2 ;e = ) V1

COMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS

S1 0

S3 0

1

0

1

1

0

1

G V

Vα

Vβ

2V2 3 V2 − V1 3 2V1 − 3 V2 − V1 3

0

G V1

V1 + V2

G V2

3

−

0

G V3

V1 + V2

G V4

3

Fig. 3. Proposed SVPWM method in case of V1 < V2

Fig. 4.

Proposed SVPWM method in case of V1 > V2

G To simulate zero vectors of SSTPI, we use the effective V0' :

G G G V0' ⋅ t z = V1 ⋅ t1 + V3 ⋅ t3

(11)

TABLE III.

METHOD

Δ Flux

Δ Torque

1 1 0 0

1 -1 1 -1

Where t1 and t3 are calculated by equations :

⎧et1 − at3 = 0; ⎨ ⎩t1 + t3 = t z

(12)

The Voltage Space-Vectors for FSTPI on the principle of similarity in case of the DC-link voltage balance is shown in Fig. 5. The Voltage Space-Vectors for conventional SSTPI is shown in Fig.6. The similarity between space vectors of FSTPI is presented in Table II. In order to reduce the torque and speed ripples by using the principle of similarity for voltage space vectors, optimum switching table in the proposed method is established similarly for the SSTPI switching table. The αβ plan is divided in to six sectors, and for each sector, the optimal space vector is chosen accordingly to the required torque and flux by using the effective vectors (equations 8, 11). III. NOVEL SWITCHING TECHNIQUE FOR DTC The objective of the DTC is to maintain the motor torque and stator flux within a defined band of tolerance by selecting the most convenient voltage space vector from the look-up table (switching table). In the case of the conventional switching table of DTC for FSTPI-IM, one of four active vectors is chosen (Table III) [6]. These vectors are synthesized using the basic space vectors with the duty cycle of 50% (switching period is Ts). The same way is done for effective zero space vector (Table IV).

Fig. 5. Voltage SpaceVectors for FSTPI on the principle of similarity in case of DC-link voltage balance

TABLE II.

Fig. 6.

Basic space vectors in SSTPI

COMPARISON BETWEEN SPACE VECTORS OF FSTPI AND SSTPI

Used voltage space vectors for SSTPI V1 V2 V3 V4 V5 V6 V0, V7

Used voltage space vectors for FSTPI (case balance) V23M V3 V43M V14M V1 V12M V0M

Used voltage space vectors for FSTPI (case imbalance) V ’1 V ’2 V ’3 V ’4 V ’5 V ’6 V’0M

CONVENTIONAL SWITCHING TABLE FOR DTC CONTROL

TABLE IV. Δφ (Flux)

1

-1

Sector 1 2400÷3300 V2 V1 V3 V4

Sector 2 -300 ÷ 600 V3 V2 V4 V1

Sector 3 600÷1500 V4 V3 V1 V2

Sector 4 1500÷2400 V1 V4 V2 V3

PROPOSED SWITCHING TABLE FOR DTC CONTROL METHOD Sector

ΔT (Torque)

1 -1 0 1 -1 0

I -30÷30

II 30÷90

III 90 ÷150

V’2 V’6 V13M V’3 V1 V13M

V’3 V’1 V13M V’4 V’6 V13M

V’4 V’2 V13M V ’5 V’1 V13M

TABLE V.

IV 150 ÷210

V ’5 V’3 V13M V’6 V’2 V13M

V 210 ÷270

VI 270 ÷330

V’6 V’4 V13M V’1 V’3 V13M

V’1 V ’5 V13M V’2 V’4 V13M

VECTOR DURATIONS FOR SECTOR I

Sector 1 Δ Flux=1; Δ Torque=1 tA_on = Ts*(1-(b-c+1)/2); tB_on = Ts; For V'6 Δ Flux=1; Δ Torque= -1 tA_on = Ts; tB_on = Ts*(1-(c-b+1)/2); For V0M=V13M Δ Flux=1; Δ Torque=0 tA_on = Ts-a*Ts/2; tB_on = Ts-e*Ts/2; For V'3 Δ Flux= -1; Δ Torque=1 tA_on=0; tB_on = Ts*(1-(c-d+1)/2); For %V'1 Δ Flux= -1; Δ Torque= -1 tA_on = Ts; tB_on = Ts; For V0M=V13M Δ Flux=1; Δ Torque=0 tA_on = Ts-a*Ts/2; tB_on = Ts-e*Ts/2; From higher outlines, vector durations in the proposed DTC method for each sector is calculated and shown in Table V (for sector 1). The flux and torque calculations remain the same. The stator flux is estimated as follows: For V'2

ψ sα = ψ sα 0 + (vsα − isα ⋅ Rs ) ⋅ Ts ψ sβ = ψ sβ 0 + (vsβ − isβ ⋅ Rs ) ⋅ Ts

The estimated flux follows:

(13)

~ Ψ and flux angle sector are defined as

~ Ψs = ψ s2α + ψ s2β ; ⎛ ψ sβ ⎞ ⎟⎟ ⎝ ψ sα ⎠

θ i = arctan⎜⎜

The torque is estimated by the following formula:

(14)

~ 3P T = (ψ sα isβ −ψ sβ isα ) 2

(15)

Where: vs, is stator voltage and current vectors Rs stator resistance P number of pole pair T electromagnetic torque ψs stator flux vector sampling time Ts

Fig. 11. Rotor speed response (conventional method)

Fig. 12. Rotor speed response (proposed method)

Fig. 13. Stator Flux locus (conventional method )

Fig. 14. Stator Flux locus (proposed method )

IV. SIMULATION OF THE PROPOSED DTC METHOD FOR FSTPI-IM A Simulink/Matlab is used to validate the proposed DTC method for FSTPI-IM. The induction motor model for the simulation studies has the follows parameters: Type: Three-phase, squirrel-cage induction motor. 220V, 1HP, 1680r/min, Rs = 3.2 (Ω), Rr = 2.336 (Ω), Ls = 0.2965 (H), Lr = 0.2965 (H), Lm = 0.2931 (Ω), P = 2, Jm = 0.0034 (kgm2). The simulated DTC system driven by FSTPI uses a proposed switching table (Table 4). The torque controller has 3 levels: -1, 0, 1; The flux controller has 2 levels: -1, 1. The parameters used in simulation are given below: - Vdc = 300V - Torque hysteresis band = 10% - Flux hysteresis band = 1% - Reference flux λs* = 0.3 Wb. - Reference torque: T* = 5 Nm when 0 s ≤ t ≤ 0.1 s; T* = 8 Nm when 0.1 s ≤ t ≤ 0.2s; T* = 5 Nm when 0.2 s ≤ t ≤ 0.3 s; T* = -10 Nm when 0.3 s ≤ t ≤ 0.4s; T* = 5 Nm when 0.4 s ≤ t ≤ 0.5s. - Sample time : Ts = 5e-5 - Load torque TL = 5Nm at t = 0.1s. - Time of simulation t = 0.5s. 1. Case study 1: In case of the balanced DC-link voltage (Fig.7-14)

Fig. 7. Stator Flux response (conventional method )

Fig. 9. Torque response (conventional method )

2. Case study 2: In case of unbalanced DC-link voltage V1/V2=0.815 (Fig. 15-21)

Fig. 15. Stator Flux response (conventional method )

Fig. 16. Stator Flux response (proposed method )

Fig. 17. Torque response (conventional method)

Fig. 18. Torque response (proposed method)

Fig. 19. Stator Flux locus (conventional method)

Fig. 20. Stator Flux locus (proposed method)

Fig. 8. Stator Flux response (proposed method )

Fig. 10. Torque response (proposed method)

Simulation results demonstrate the performance of the proposed and conventional DTC method for FSTPI-IM under balanced DC link voltages, while the good responses of the flux, torque, and speed are obtained (fig. 7-14) with reduced torque ripples (fig. 10).

RTI Data

thongsoDCKDB

DS1104SLAVE Board PWM-Interrupt

1

Phi_s_beta

Step isa

Interrupt source

DS1104SLAVE_PWMINT

Phi_s_alf a

Timer Task Assignment2

M* Delta_Phi [-1,1]

Gain

Cpsi

Duty cy cle a Duty cy cle b

M

Mo men M

Duty cy cle c

Ct

dA_on

0

Phi_s

isb

PWM Stop

Delta_M [-1,0,1] Psi_alpha

0.9

isc

1

Phi_s*

fcn

Phi_s*

Gain1 Compare and Trigger

Moment Estimator

Psi_beta

dA S1

S1

dB S2

S2

In case of the DC link voltage imbalance, performance of the proposed method is better (fig.16,18,20,21) in comparison with the conventional one (fig.15,17,19).

Fig. 22.

Interface between Matlab/Simulink and Dspace 1104 Card for FSTPI-IM .

Phi

V2

V2

dB_on

Vsc

Vsb

fcn Vb

Pulse Generator

Flux Estimator Vsa

Phi_s_alfa

isc

V1

Voltage Sensor Ia

V1

Switching Table V2

Ib

Scope3

Vc

Phase Voltage Calculator

Ic

Current Sensor

Fig. 23.

V. EXPERIMENTAL RESULTS The experimental setup is carried out by a DSpace 1104 system with I/O card for real time control (Sample time: Ts = 5e-5). An interface board was build to receive the gate-drive signal, isolated them and connected to the four switches which were implemented using integrated IGBT 60A. The output from FSTPI was connected to a three phase induction motor (Fig.22). The induction motor has the follows parameters: Threephase, squirrel-cage induction motor 400V, Y connected, 2.2kW, 2280r/min., Rs = 3Ω; Rr= 1.96Ω; Ls= 0.3739H; Lr = 0.3739H; Lm = 0.3585H; P = 1; The DC link voltage was adjusted at V1=56.5V, V2=46.5V and the split capacitors are rated at 6800μF. The Hall-effect current sensors (isa,b,c) and voltage sensors (VDC1,2), which have been used to receive feedback signals, are LEM LA55-P and LV25-P respectively. The DTC system driven by FSTPI uses a proposed switching table (Table 4). The control algorithm is executed by Matlab/Simulink program (Fig.23) and it provides the duty cycles dAon and dBon for generating control signals. The parameters of the torque controller, the flux controller, torque hysteresis band, flux hysteresis band are the same as the simulated DTC system. Reference flux changes from ψs* = 0.42 to 0.9 Wb. Reference torque: T* = 2 Nm.

isb

Rotor speed response (proposed method) in case of unbalanced DC –link voltage

isa

Fig. 21.

Phi_s_beta

Va

V1

DTC Control Algorithm using Matlab Simulink with DSpace Card DS1104.

Fig. 24.

Fig. 25.

Phase-to DC neutral point voltage waveforms Va0 (K=10) for FSTPI (From Oscilloscope Tektronix TDS 2012).

Reference and estimated stator flux and stator Flux locus

[7]

[8]

[9]

[10]

[11] Fig. 26.

Stator current waveforms for FSTPI.

The experimental responses including steady-state phase to DC neutral point voltage, transient response of stator flux and stator currents are shown in Fig.24-26 correspondingly. VI. CONCLUSION A new switching technique for Direct Torque Control of Induction Motor using Four-Switch Three Phase Inverter (DTC-FSTPI-IM) for low power applications with DC – link voltage imbalance has been presented. The modified switching table in this method is based on the principle using real-time compensation DTC technique when generating switching control signal in consideration of unbalanced DClink voltages by direct calculation of switching times based on basic space vectors in FSTPI. The validity of new proposed technique is verified by simulation and experimental results using Matlab/Simulink and DSpace 1104. Simulation and experimental results demonstrate the good performance of the proposed DTC for FSTPI-IM, while the good responses of the voltage, stator flux and stator currents are obtained. ACKNOWLEDGMENT The authors gratefully acknowledge Vietnamese Ministry of Science and Technology (MOST) and NARC, Ulsan University for providing excellent supports and facilities. REFERENCE [1]

[2]

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[4]

[5] [6]

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