2011 IEEE Applied Power Electronics Colloquium (IAPEC)
Direct Torque Control of Induction Machines Utilizing 3-level Cascaded H-Bridge Multilevel Inverter and Fuzzy Logic A. Mortezaei1, N. A. Azli2, N. R. N. Idris, S. Mahmoodi and N. M. Nordin
Power Electronics and Drive Research Group (PEDG), Energy Research Alliance Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia
[email protected] [email protected] Abstract—This paper proposes the use of a 3-level Cascaded HBridge Multilevel Inverter (CHMI) topology which results in further torque ripple minimization compared to the 2-level inverter-based Direct Torque Control (DTC). This is due to the increase in the inverter switching voltage vectors that allows minimization of the torque error. This in turn can reduce the Total Harmonic Distortion (THD) of the output voltage and current as well. This paper also presents two different control methods in selecting the appropriate output voltage vector for reducing the torque and flux error to zero. The first is based on the conventional DTC scheme using a pair of hysteresis comparators and look-up table to select the output voltage vector for controlling the torque and flux. The second is based on a new fuzzy logic controller (FLC) with Sugeno as its inference method to select the output voltage vector by replacing the hysteresis comparators and look-up table in the conventional DTC scheme. The latter has solved the problem of variable switching frequency which is the main characteristic of the former. By using FLC DTC not only the flux ripples reduce significantly but also the THD of the phase current decreases since a more sinusoidal current waveform is achieved. The simulation results have proven that by using the 3-level CHMI, torque ripple reduction is obtained compared to the 2-level inverter-based DTC while fuzzy DTC shows reduction in the stator flux ripples and the THD of the phase current.
I.
INTRODUCTION
II.
Direct Torque Control (DTC) has first been proposed by Takahashi in 1986. The basic of this high performance induction motor drive is limit cycle control and both fast torque response and efficiency operation are provided [1]. In DTC strategy the control of torque and speed are directly based on the electromagnetic state of the motor [2]. The main features of DTC are decoupled control of torque and flux, absence of mechanical transducers, very simple control scheme with low computational time, reduced parameter sensitivity and current regulator, PWM pulse generation as well as PI control of flux and torque and co-ordinate transformation are not required [3][4]. It only needs to know the stator resistance and terminal quantities (v and i) in order to perform the torque and stator flux estimations. The first industrial, speed-sensorless DTC induction motor drive has been introduced by ABB in 1996. This simple control scheme
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has gained popularity over the years and it is expected that they will soon replace the vector control drives commonly found in industrial applications [5]. It is well known that by using the multilevel inverter topology, the number of inverter states increases which results in having more inverter switching voltage space vectors to regulate instantaneously the electromagnetic torque and stator flux magnitudes in DTC strategy. Multilevel inverter also generates low dv/dt leading to low electromagnetic interference (EMI) and winding insulation stress which is desirable for high power and voltage applications [6]. By applying the 3-level cascaded H-bridge inverter, the number of effective switching voltage vectors is increased to nineteen including four different groups of voltage vectors. These different voltage vectors are available to be used to minimize the torque ripples of the induction machine. Two different control methods are introduced to control the torque and flux in a 3-level CHMI-based DTC. The first is based on the conventional DTC scheme using a pair of hysteresis comparator and look-up table while the second is based on an FL DTC scheme using Sugeno as its inference method to select the output voltage vector for minimizing the torque and flux error to zero. 3-LEVEL CASCADED H-BRIDGE MULTILEVEL INVERTER TOPOLOGY Fig. 1 shows the schematic diagram of a 3-level CHMI. The CHMI is composed of three phases, of which in each phase the H-bridge inverter is fed by an independent DC source. Fig. 2 shows the voltage space vector diagram of the 3-level CHMI. It has 19 effective voltage vectors which is divided into 4 different groups according to their magnitudes as follows: (V0), (V1, V4, V7, V10, V13, V16), (V3, V6, V9, V12, V15, V18), (V2, V5, V8, V11, V14, V17). Note that a 2-level inverter is only capable of producing 7 effective voltage vectors.
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The principle of the conventional DTC is to minimize the torque and flux errors to zero by using two hysteresis comparators. The hysteresis comparators are fundamental to the DTC scheme because they are responsible of both determining the appropriate voltage vector selection and the period of the voltage vector selected. It has been mentioned that a 3-level CHMI has 19 effective voltage vectors that can be chosen to minimize the error of torque and flux. To take the most advantages of using the 3level CHMI due to the increased number of space vectors, the following strategies are applied: Fig. 1. 3-level CHMI
1. Dividing the stator flux plan into twelve sectors of 30° degrees, starting with the first sector situated between -30° and 0°. By increasing the number of sectors to twelve, a more accurate selection of the inverter switching voltage vectors to minimize the error of the torque and flux to zero can be obtained, resulting in improvement of the responses of the flux and torque [6]. 2. Applying a 7-level hysteresis comparator to control the torque. Increasing the levels of torque hysteresis controller means defining more levels of error. This allows the controller to differentiate between small and large torque errors. This means that the voltage vectors chosen for large errors that happen during start up or due to a step change in torque or flux responses are different from those that are chosen during smaller errors or at steady state. Fig. 4 shows the torque and flux hysteresis comparator of a 3-level CHMI based-conventional DTC. It can be seen that a 2-level hysteresis comparator is applied to control the flux and a 7-level hysteresis comparator is applied to control the torque. The output of the flux hysteresis comparator which is the flux error status has 2 values of 0 and 1 and the output of the torque hysteresis comparator which is the torque error status has 7 integer values starting from -3 to 3. The optimum selection of the switching voltage vectors in all sectors of the stator flux plane in the 3-level CHMI based conventional DTC can be tabulated in the so-called optimum switching voltage vector selection table given by Table I. The table is used to select the voltage vectors depending on flux error, torque error and the stator flux orientation. The terms (TES), (FES), and (SEC) are equivalent to stator flux error status, torque error status and the sectors respectively. When the flux error status is 0 the flux decreases and when it is 1 the flux increases. When the torque error status has the value of between 3 to 1, the torque increases; 3 has the highest value of increase while 1 has the lowest value of increase. When the torque error status is 0 the torque maintains and when it has the value of -3 to -1, the torque decreases; -3 has the highest value of decrease and -1 has the lowest value of decrease.
Fig. 2. Voltage space vector diagram of the 3-level CHMI
Fig. 3. 2-level inverter-based conventional DTC scheme
III.
3-LEVEL CHMI-BASED CONVENTIONAL DTC
The basic configuration of the conventional DTC drive presented by Takahashi is as shown in Fig. 3. It composed of a 2-level Voltage Source Inverter (VSI), torque and flux estimators, voltage vector selector and two hysteresis comparators [1].
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reduce significantly but the Total Harmonic Distortion (THD) of the phase current also decreases since a more sinusoidal current waveform is achieved. The control scheme using the FLC is shown in Fig. 5.
Fig.4. Torque and flux hysteresis comparator of a 3-level CHMI TABLE I VOLTAGE VECTOR SELECTION TABLE Fig. 5. DTC scheme based on FLC
IV.
3-LEVEL CHMI-BASED FL DTC
The application of FLC using Mamdani as the inference method to select the output voltage vector has already been investigated in DTC [7][6]. However an FLC using Sugeno as the inference method for selecting the output voltage vector is introduced in this paper which has resulted in the solving of the problem of variable switching frequency in conventional DTC due to the replacement of the hysteresis comparators and look-up table. By using FL DTC not only the flux ripples
There are 3 inputs and 1 output variables for the FLC. The inputs variables are the error of the stator flux, the error of the torque and the angle of the stator flux. The membership functions for the torque error, stator flux error and stator flux position are as shown in Fig. 6. The linguistic terms used for the error of stator flux and torque membership functions correspond to the stator flux and torque error status of Fig. 4 and Table I. The universe of discourse of the stator flux position has been divided into 12 Fuzzy sets (S1 to S12) corresponding to the sectors in Table I. The output variable is discrete and includes 19 membership functions having the linguistic terms of (0, 1, 2 … 18) corresponding to 19 effective inverter switching voltage vectors of the 3-level CHMI (V0 - V18) of Fig. 2. It means that, for example, when the output of the FLC is 10, the inverter switching voltage vector V10 is selected for application to the inverter. The total number of rules is 168. The inference method used is Sugeno's procedure based on prod-probor decision and the Wtaver method is used for defuzzification. With this method, each value of the stator flux and toque errors and the angle of stator flux are located in a specific membership function. The control output obtained is one of the membership functions of the output variable fed to the inverter. The controller rules are based on Table I. In the description of the membership functions the correspondence between the linguistic terms and the labels utilized in Table I has been explained. The control rules for this controller are presented utilizing the 3 input and 2 output variables. The ith rule Ri is written as: Ri: if the flux error is Ai, the torque error is Bi and the flux position is Ci while the inverter switching vector is Ni.
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ripples of the flux as well as the percent THD of the phase current have reduced and a sinusoidal phase current has been achieved due to solving of the variable switching frequency problem created by the hysteresis controller. TORQUE RESPONSE
12 10
Torque(N-m)
8 6 4 2 0 -2 0
0.05
0.1 Time(s)
0.15
0.2
STATOR FLUX RESPONSE 1
Fig. 6. Membership functions for the input variables of the FLC
Nominal power, Nominal voltage (line-line) Nominal frequency Nominal speed Number of poles Stator resistance and inductance Rotor resistance and inductance Mutual inductance Reference torque Reference flux Step time
4 KW 400 V 50 Hz 50 Hz 1430 RPM 4 1.405Ω 0.005839H 1.395Ω 0.005839H 0.1722 H 10 Nm 1 Wb 0.01s
0.8 0.6 0.4 0.2 0 0
0.05
0.1 Time(S)
0.15
0.2
PHASE CURRENT 10
5
SIMULATION RESULTS
A total of 3 systems; 2-level inverter-based conventional DTC (2LC-DTC), 3-level CHMI-based conventional DTC (3LC-DTC), and 3-level CHMI-based FL DTC (3LF-DTC), have been simulated using MATLAB/Simulink to evaluate their performances. A l0 µs sample time has been set for all simulations conducted. Table II shows the induction motor parameters and reference values of torque and stator flux. The simulation carried out is the system response to a torque and stator flux step from 0 to the reference values for both magnitudes. Fig. 7 shows the simulation results of conventional DTC of an induction motor using a 2-level inverter. Fig. 8 shows the simulation results of conventional DTC of an induction motor using a 3-level CHMI while Fig. 9 illustrates the simulation results of FL DTC of an induction motor using a 3-level CHMI. By comparing the simulation results of (2LC-DTC) with (3LC-DTC), it is observed that the torque ripples reduce significantly in the latter. By comparing the simulation results of (3LC-DTC) with (3LF-DTC), it is seen that in the latter the
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Current(A)
V.
Stator Flux (Wb)
TABLE II MOTOR PARAMETERS AND REFERENCE VALUES
0
-5
-10
0.1
0.12
0.14 0.16 Time(s)
0.18
0.2
Fig. 7. Torque and stator flux responses and phase current of the 2-level inverter-based conventional DTC
12
10
10
8
8 Torque(N-m)
Torque(N-m)
TORQUE RESPONSE 12
6 4
6 4
2
2
0
0
-2 0
0.05
0.1 Time(s)
0.15
TORQUE RESPONSE
-2 0
0.2
0.05
0.15
0.2
STATOR FLUX RESPONSE
1
1
0.8
0.8
Stator Flux (Wb)
Stator Flux (Wb)
STATOR FLUX RESPONSE
0.1 Time(s)
0.6 0.4 0.2
0.6 0.4 0.2
0 0
0.05
0.1 Time(s)
0.15
0 0
0.2
0.05
PHASE CURRENT 10
0.1 Time(s)
0.15
0.2
PHASE CURRENT
8 6 4 Current(A)
Current(A)
5
0
-5
2 0 -2 -4 -6
-10
0.1
0.12
0.14 0.16 Time(s)
0.18
-8
0.2
Fig. 8. Torque and stator flux responses and phase current of the 3-level CHMI-based conventional DTC
0.1
0.12
0.14 0.16 Time(s)
0.18
0.2
Fig. 9. Torque and stator flux responses and phase current of the 3-level CHMI-based FL DTC
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VI.
VII.
CONCLUSION
DTC enables both quick torque response and efficient operation and has many advantages compared to Field Oriented Control (FOC), such as less machine parameter dependence, simpler implementation and quicker dynamic torque response It only needs to know the stator resistance and terminal quantities (v and i) in order to perform the stator flux and torque estimations. Although DTC is gaining popularity, there are a few drawbacks that need to be addressed. Variable switching frequency and high torque and flux ripples are two major problems, which draws full attention of most researchers. The simulation results have clearly shown that the 3-level CHMI-based DTC is capable of significantly reducing the torque ripples compared to the 2-level inverter-based DTC. The simulation results have also verified that utilizing the FLC that employs Sugeno as the inference method for selecting the output voltage vector instead of the hysteresis controller has resulted in the reduction of the flux ripples significantly as well as reduces the THD of the phase current by making it sinusoidal. .
REFERENCES
[1] I. Takahashi, T. Noguchi, (1986) “A new quick-response and high efficiency control strategy of an induction motor”, IEEE Trans. Ind. Appl., Vol. IA-22, No 5, pp. 820-827. [2] John R G Schofield, (1995) “Direct Torque Control DTC”, IEE, Savoy Place, London WC2R 0BL, UK. [3] L. Tang, L. Zhong, M. F. Rahman, Y. Hu, (2002) “An Investigation of a modified Direct Torque Control Strategy for flux and torque ripple reduction for Induction Machine drive system with fixed switching frequency”, 37th IAS Annual Meeting Ind. Appl. Conf. Rec., Vol. 1, pp. 104-111. [4] N. R. N. Idris, A. H. M. Yatim, (2000) “Reduced torque ripple and constant torque switching frequency strategy for Direct Torque Control of induction machine”, 15th IEEEApplied Power Electronics Conference and Exhibition 2000 (APEC 2000), Vol. 1, pp. 154-161. [5] P. Tiitinen and M. Surandra, (1996) “The next generation motor control method, DTC direct torque control”, Proceeding of the 1996 International Conference on Power Electronics Drives and Energy System for Industrial Growth, N. Delhi, India, Vol.1, pp. 37-43. 111 [6] del Toro, X., Calls, S., Jayne, M.G., Witting, P.A., Arias, A., Romeral, J.L., (2004) “Direct torque control of an induction motor using a three-level inverter and fuzzy logic”, IEEE Conf., Vol.2, pp. 923-927 [7] Mir, S. A.: Zinger. D. S.: Elbuluk. M. E. "Fuzzy Controller for Inverter Fed Induction Machines." IEEE Transactions ont Itndustrial Applications. vol. IA-21, no. 4. Jani/Feb 1993. pages 1009-1015.
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