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Essay: Modelling And Simulation Of Direct Torque

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Modelling And Simulation Of Direct Torque

Abstract’ This paper presents a direct torque control (DTC) of Permanent Magnet Synchronous Motor (PMSM) Drive using Artificial Neural Network (ANN) for low torque ripples. Conventional PMSM drive produces high ripple in electromagnetic torque which is not directly controlled. High torque ripple causes vibrations to the motor which may lead to component loss, bearing failure. The main drawback with the conventional Permanent Magnet Synchronous Motor (PMSM) Drive is high torque ripples and the speed of PMSM drive which reduces under transient and dynamic state of operating condition. This drawback is reduced by using proposed control technique. In this proposed control technique the PI controller is regulating the speed of the PMSM drive and the ANN is reducing the torque ripples. Complete simulation of the conventional PMSM drive is done in MATLAB Simulink.
Keywords’ Artificial Neural Network (ANN); Permanent magnet Synchronous motor drive (PMSM); Space Vector Modulation(SVM); Direct Torque Control (DTC); MATLAB Simulink.
Introduction
In last few years permanent magnet synchronous motor (PMSM) has acquired more and more application because of its properties such as small volume, light weight, high efficiency, small inertia, rotor without heat problem, etc. Direct Torque Control (DTC) is a new control method after vector control. It abandons decoupling thought of vector control, and uses the stator flux linkage directly to control the flux linkage and the torque of motor. Thus the dynamic response of the system is very fast. The DTC control strategy is applied for PMSM in order to improve the torque characteristics of the motor, which currently has caused the extensive attention of people [11].

The SVM technology looks the inverter and motor as a whole, by different switch modes of inverter to produce vary-frequency supply power for PMSM to ensure the stator flux is a circle. Different switching status corresponds to a different space voltage vector. The three-phase voltage vectors are seen as three independent components for SVM technology, it needs three modulators to adjust three phase voltages at the same time. The three-phase voltage space vectors synthesize a space vector which rotates as the power angular frequency ‘ for SVPWM technology, so only one Modulator is needed [1,2].
The artificial neural networks (ANN) are best suited for solving the problems that are nonlinear in nature. In ANN we use parallel processing methods to solve some real-world problems where it is difficult to define a conventional algorithms. The ability of ANN to learn large classes of nonlinear functions is well known [5]. It can be trained to emulate the unknown nonlinear plant dynamics by presenting a suitable set of input/ output patterns generated by the plant [5].

Permanent Magnet Synchronous Motor Drives
Permanent magnet synchronous motor (PMSM) have been a popular choice for transportation systems, including hybrid and plug-in hybrid vehicles, aerospace, and military applications. With growing electrification in hybrid vehicles, a significant need for reliability and fault-tolerant operation has been seen in addition to high power density and high efficiencies. This is particularly the case for mission-critical applications in aerospace and military applications, where the failure of a position or current sensor during operation can lead to catastrophic failure of the entire system. Several fault detection and fault-tolerant methods based on position/current estimation have been reported in the past decades. In this paper, a novel concept of universal sensors using search coils is proposed, to give the PMSM’s drive system a ‘+1’ fault tolerance [[6,7,10,11].

A two-phase PMSM
A two phase PMSM shown in fig. 1 and the windings are displaced in space by 90 degrees electrical and the rotor windings at an angle ??r from the stator d-axis winding. It is assumed that the q-axis leads the d-axis to a counter clockwise direction of rotation of the rotor. A pair of poles is assumed for this figure, but it is applicable with slight modification for any number of pairs of poles. Note that ??r is the electrical rotor position at any instant obtained by multiplying the mechanical rotor position by pairs of electrical poles.The d- and q-axes stator voltages are derived as the sum of the resistive voltage drops and the derivative of the flux linkages in the respective windings [12]
Direct Torque Control and modeling of PMSM
In the DTC of PMSM, the electromagnetic torque can be controlled by keeping the amplitude of the stator flux linkage constant and controlling the load angle by applying a proper stator voltage vector. By considering the saliencies, the actual flux and torque values are calculated first based on the proposed PMSM model, and in the hysteresis comparators, the calculated torque/flux are compared with the torque/flux references. Proper stator voltage vectors are selected form the outputs of the comparator based on the optimal voltage vector switching logic so as to minimize the errors between the reference and actual values of torque and flux [3,4].

The following assumptions are made to derive the dynamic model:
The stator windings are balanced with sinusoidally distributed magnetomotive force (mmf).
The inductance versus rotor position is sinusoidal.
The saturation and parameter changes are neglected.
Schematic diagram of voltage source inverter is shown in Fig. 2. The eight possible voltage space vectors which include six active voltage vectors (V1-V6) & two zero voltage vectors (V7 & V8) as shown in Fig. 3. These eight vectors are the combination of three switching modes Na, Nb and Nc. When the upper switches are ON, then the switching value is ‘p’ and when the lower switches are ON, then the switching value is ‘n’.

(V_(s,k) ) ??=2/3 V_dc [N_a+aN_b+a^2 N_c] (1)

Where Vdc is the dc link voltage of inverter, a=ej2??/3

Schematic diagram of voltage source inverter.
The equation of stator output phase voltages is following

[‘(V_a^s@V_b^s@V_c^s )]=V_dc/3 [‘(2&-1&-1@-1&2&-1@-1&-1&2)][‘(N_a@N_b@N_c )] (2)

Eight voltage vector switching configuration
The equations of conversion from V_a^s,V_b^s and V_c^s to V_ds^s and V_qs^s are following equations (3), and (4).

V_ds^s=2/3 N_a-1/3 N_b-1/3 N_c (3)

V_qs^s=-1/’3 N_b+1/’3 N_c (4)

The representation of the behavior of PMSM drive using DTC is described in the stator stationary reference frame by following equations

V_ds^s=R_s i_ds^s+d/dt ‘_ds^s (5)

V_qs^s=R_s i_qs^s+d/dt ‘_qs^s (6)
The stator winding flux linkages can be written as the sum of the flux linkagesdue to their own excitation and mutual flux linkages resulting from other winding current and magnet sources. The q and d stator flux linkages are written as
‘_qs=L_qq i_qs+L_qd i_ds ‘+"’" ‘_af ‘sin’??_r (7)
‘_ds=L_qq i_qs+L_qd i_ds ‘+"’" ‘_af ‘cos’??_r (8)
Where ??r is the instantaneous rotor position. The windings are balanced and therefore their resistances are equal and denoted as Rs = Rq = Rd. The d and q stator voltages can then be written in terms of the flux linkages and resistive voltage drops as
V_qs=R_s i_qs+’i_qs PL_qq+L’_qq ‘Pi’_qs+L_qd Pi_ds+i_ds PL_qd ‘+"’" ‘_af P’sin’??_r (9)
V_ds=R_s i_ds+’i_qs PL_qd+L’_qd ‘Pi’_qs+L_dd Pi_ds+i_ds PL_dd ‘+"’" ‘_af P’cos’??_r (10)

Lqq and Ldd are the self-inductances of the q- and d-axes windings, respectively. The mutual inductances between any two windings are denoted by L with two subscripts where the first subscript denotes the winding at which the emf is measured due to the current in the other winding indicated by the second subscript. The symmetry of the q- and d-axes windings ensures that Lqd and Ldq are equal.
The third term exists because of saliency, i.e., when Lq’Ld. In surface mount magnet machines, the inductances are equal and, therefore, L2 is zero and the third term in the above equation vanishes. Also disappearing in the matrix’s second term are the position-dependent terms, resulting in a simple expression for surface mounted magnet machines in stator reference frames. It is then given by

[‘(V_qs@V_ds )]=R_s [‘(i_qs@i_ds )]+[‘(L_1&0@0&L_2 )] d’dt [‘(i_qs@i_ds )]+’_af ‘_r [‘(‘cos’_??r@’sin’_??r )] (11)

The instantaneous electromagnetic torque

T_e=3/2 P/2 [‘_af+(L_d-L_(q)) i_dr ] i_qr (12)

The voltage vectors are randomly chosen from a hexagon when a hysteresis controller is used. That hexagon contains seven possibilities (Fig. 4). v1 through v6 correspond to the six active switching state vectors, whereas v1 and v8 both correspond to the zero voltage vector. The corresponding phase voltages which is a function of the DC-bus voltage Vdc are listed in Table I (T1, T2 and T3 are the switching devices).

Inverter voltage vectors
Inverter switching ststes and their corresponding voltage vectors
T1 T2 T3 Vk Va Vb Vc
0 0 0 V8 0 0 0
1 0 0 V1 2Vdc/3 -Vdc/3 -Vdc/3
1 1 0 V2 Vdc/3 Vdc/3 -2Vdc/3
0 1 0 V3 -Vdc/3 2Vdc/3 -Vdc/3
0 1 1 V4 -2Vdc/3 Vdc/3 Vdc/3
0 0 1 V5 -Vdc/3 -Vdc/3 2Vdc/3
1 0 1 V6 Vdc/3 -2Vdc/3 Vdc/3
1 1 1 V7 0 0 0

Conventional pmsm Drives Model
AC6 block of the SimPower Systems electric drives library models a permanent magnet (PM) synchronous motor drive with a braking chopper for a 100kW motor. It models a flux weakening vector control for a 100 kW, 12500 rpm, salient pole PMSM powered by a 288 Vdc source. The mechanical system is represented externally. That’s why the input of the motor is the speed and the output is the electromagnetic torque. Fig. 5 shows block diagram of conventional PMSM drive [13].

Block diagram of conventional permanent magnet synchronous motor (PMSM) drives.
proposed technique
Principles of Artificial Neural Networks
Artificial neural networks use a dense interconnection of computing nodes to approximate nonlinear functions. Each node constitutes a neuron and performs the multiplication of its input signals by constant weights, sums up the results and maps the sum to a nonlinear activation function g; the result is then transferred to its output. The neural network training is shown in fig. 7. A feed forward ANN is organized in layers: an input layer, one or more hidden layers and an output layer. A MLP consists of an input layer, several hidden layers, and an output layer. Node i, also called a neuron, in a MLP network is shown in Fig. 6. It includes a summer and a nonlinear activation function g [1,5,13].

A multilayer perceptron network with one hidden layer
The inputs xk, k = 1…K to the neuron are multiplied by weights wki and summed up together with the constant bias term ‘i. The resulting i n is the input to the activation function g. The activation function was originally chosen a sigmoid function [1,5,13].
y_i=g_i=g(‘_(i=1)^N”w_ji x_j ‘+’??_i ‘) (14)

Neural network training.

Neural Network architecture for DTC of a PMSM motor

Block Layer1 and Layer2

Open Simulation Block of Layer1 and Layer2

Simulation Results
The simulation results from the conventional and Proposed ANN based PMSM drives MATLAB models are obtained for 3hp PMSM drives where VSI input DC link voltage is 220V. The parameter values of PMSM drive are shown in Table II. The simulation results of conventional and proposed Artificial Neural Network (ANN) are shown in Fig. 11 and Fig. 12, respectively. By comparing the results of electromagnetic torque waveforms achieved through Conventional PMSM drive and Artificial neural network (ANN) based PMSM drive is peak-to-peak ripples of 120 ‘ 100 Nm (20 Nm) in Conventional PMSM drive and 110 ‘ 100 Nm (10 Nm) in Proposed ANN based PMSM drives as shown in Table III. Reduction in current has also been observed in the proposed ANN based PMSM motor drives.

(a)

(b)

(c)

(d)

(e)
Simulation results of conventional 3hp PMSM drives (a) Stator Current Ia, Ib and Ic (b) Voltage Vq and Vd (c) Electromagnetic torque (d) Speed (e) Mechanical Power

(a)

(b)

(c)

(d)

(e)
Simulation results of Proposed ANN based PMSM drives (a) Phase a Current (b) Phase b Emf (c) Electromagnetic torque (d) Speed (e) Mechanical Power.
PERMANENT MAGNET SYNCHRONOUS MOTOR DRIVE PARAMETER OF 3HP
Parameters Nominal values
Resistance (R) 0.008296??
Inductance (Ld) 0.17415845761mH
Inductance (Lq) 0.29268882377mH
Pole pair 4
Voltage (V) 288V
Speed 1250RPM

Comparison between Conventional and ANN based PMSM Drives
S.No. Parameter Conventional Proposed ANN PMSM Motor Drives Remarks
1 Torque Ripples 20 Nm 10 Nm Reduced
2 Speed Same Same Same
3 Current Same Same Same
4 Voltage Same Same Same

Conclusion
From the control side, proposed techniques are used here for minimizing the torque ripples in PMSM drives. Control techniques can apply advanced methods here for minimizing torque pulsation, depending on the appropriate information of machine parameters. In order to suit any application where needed it is necessary to produce a PMSM drive with smooth operation. Proposed ANN technique reduce torque ripples associated to machine control and drives that could be minimized through different control techniques. Controller part of the drive system are responsible for suppression of the ripples, and the techniques that can be used entail a variety of arrangement of configurations. Some techniques require hardware modification or add-on stages, whereas other schemes are based on algorithm techniques. The effective solution mainly depends on the application limitation and applied controller despite the number of techniques that have been reported for minimizing pulsating torque production.
References
Baoping, C., Yonghong, L., Qiang, L., & Haifeng, Z. (2009, December). An Artificial Neural Network Based SVPWM Controller for PMSM Drive. In Computational Intelligence and Software Engineering, 2009. CiSE 2009. International Conference on (pp. 1-5). IEEE.
Qian Yang and Zhiqiang Kang, Minghui Zhang and Nannan Zhao ‘Study on Space Vector PWM Technology of PMSM Control System Based on dSPACE’, International Conference on Information and Automation Yinchuan, China, August 2013 pp 576-580.
Yan, Y., Zhu, J., Guo, Y., & Lu, H. (2006, October). Modeling and simulation of direct torque controlled PMSM drive system incorporating structural and saturation saliencies. In Industry Applications Conference, 2006. 41st IAS Annual Meeting. Conference Record of the 2006 IEEE (Vol. 1, pp. 76-83). IEEE.
Bian, C., Ren, S., & Ma, L. (2007, August). Study on direct torque control of super high-speed PMSM. In Automation and Logistics, 2007 IEEE International Conference on (pp. 2711-2715). IEEE.
Kumar, R., Gupta, R. A., & Bansal, A. K. (2007, June). Identification and control of PMSM using artificial neural network. In Industrial Electronics, 2007. ISIE 2007. IEEE International Symposium on (pp. 30-35). IEEE.
Kung, Y. S., Wang, M. S., & Huang, C. C. (2009, June). DSP-based adaptive fuzzy control for a sensorless PMSM drive. In Control and Decision Conference, 2009. CCDC’09. Chinese (pp. 2379-2384). IEEE.
Choi, H. H., Vu, N. T. T., & Jung, J. W. (2011). Digital implementation of an adaptive speed regulator for a PMSM. Power Electronics, IEEE Transactions on, 26(1), 3-8.
Lakshmi, G. Sree, S. Kamakshaiah, and Tulasi Ram Das. "Closed loop PI control of PMSM for hybrid electric vehicle using three level diode clamped inverter for optimal efficiency." In Energy Efficient Technologies for Sustainability (ICEETS), 2013 International Conference on, pp. 754-759. IEEE, 2013.
Hadef, M., M. R. Mekideche, and A. Djerdir. "Vector controlled permanent magnet synchronous motor (PMSM) drive with stator turn fault." In Electrical Machines (ICEM), 2010 XIX International Conference on, pp. 1-6. IEEE, 2010.
Da, Yao, Xiaodong Shi, and Mahesh Krishnamurthy. "A Novel Universal Sensor Concept for Survivable PMSM Drives." IEEE TRANSACTIONS ON POWER ELECTRONICS 28, no. 12 (2013).
Ming, Chen, Gao Hanying, and Song Hongming. "Simulation study on a DTC system of PMSM." In Strategic Technology (IFOST), 2011 6th International Forum on, vol. 1, pp. 564-569. IEEE, 2011.
S. Venna, S.Vattikonda, S. Mandarapu ‘Mathematical modelling and Simulation of Permanent Magment Synchronous Motor’, In International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, Issue 8, August 2013, pp 3720-3726.
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