Classical Direct Torque Control for Switched Reluctance Motor Drive

Abstract

The modern electrical machines require higher efficiency in concern with pollution of the environment. Industries are focusing on bringing out new avenues in controlling the electric motors to adjust the speed and torque without compromising. The Direct Torque Control technique is suggested in this study. Slip control, which exploits a peculiar link between slip and torque, is the basic concept underlying this regulation. Direct torque control provides various benefits over field-oriented control, including reduced sensitivity to machine parameters, easy assembly, and quick dynamic torque response. As the voltage space vector is chosen in response to the inaccuracy in the flux linkage and torque, a current controller is unnecessary in this design. Low torque ripple, reduced noise, and reduced mechanical vibration are all attainable through proper torque management in the switching reluctance motor.

1. Introduction

Because of its simple mechanical structure, low cost, efficiency, The Switched Reluctance Motor (SRM) has the potential to become one of the most widely used low-cost electromechanical energy converters due to its advantageous torque/speed characteristic and very minimal requirement for maintenance. However, this drive’s non-uniform torque output characteristics and doubly salient construction mean it generates more noise and torque ripples, limiting its usefulness. As a result, various methods have been developed for reducing torque ripple in switching reluctance motors. Several torque control techniques are studied with the goal of enhancing the drive’s efficiency through reduced torque ripple and faster response times.

The early 1980s saw the development of Direct Torque Control for use with AC drives. In 2012, Yong Chang Zhang, et al., proposed a new direct torque control for three-level inverter supplied AC drives [1]. By adjusting the state voltage vectors in relation to the torque and flux errors, we are able to exert direct control over the torque. Direct torque control for a switching reluctance motor was developed by Moron et al. using the lyapunov function [2]. In order to precisely control the torque applied to a switching reluctance motor, Sahoo et al. presented a lyapunov function [3]. It was proposed by Yong Chang Zhang et al. in 2012 that a sensorless drive for a three-level inverter-fed induction motor could benefit from enhanced direct torque control [1]. A low-ripple torque control at high speeds was implemented by Jin Ye et al. for switching reluctance motor drives [4].

Improvements in switching reluctance motor performance were studied by Qingguo Sun et al., who looked into the role of direct torque control and torque sharing function [5]. Conventional direct torque control of the four-phase switching reluctance motor was created by Srinivas Pratapgiri and Prasad Polaki Venkata Narsimha in 2012 [6]. As the bandwidth of the hysteresis controller is restricted in this control, the decrease of torque ripple is minimal at best. For switching reluctance motors, proposed a method of shared control of current and flux linkage [7]. For switching reluctance motors, Jipun and Luk achieved sensorless direct torque control [8]. This article discusses a machine with a shorter flux path and modifies the electrical and mechanical phases so that they both add up to 45 degrees. When it comes to the direct torque management of a switching reluctance motor, Bosra et al. proposed a four-level converter [9].

Due to the odd number of phases, there is a paucity of material on direct torque control with four phase SRM. Compared to field orientation control, the DTC’s many benefits include reduced reliance on machine parameters, a quicker dynamic torque response, and a more straightforward design. Any current controller is unnecessary for the DTC as the voltage space vectors are chosen in response to flux linkage and torque faults. Direct torque control, or DTC, is a method whereby a motor’s torque and speed are adjusted in response to changes in the motor’s electromagnetic field.

2. Control strategy

When the converter switches, the motor’s flux and torque are directly controlled, making direct torque control an optimal AC variable frequency control concept. Figure 1 depicts the rudimentary DTC block diagram. Based on the estimated flux and torque and the reference flux and torque, the stator voltage and resistance may be calculated. Based on the output levels of this hysteresis comparator, the error is sent to the hysteresis comparator, and the switching table is used to determine the voltage vector that will be supplied to the voltage source inverter in order to obtain the reference torque. Direct torque control for a four-phase switching reluctance motor is outlined, together with its underlying principles, the specific steps involved, and the means for putting it into practise [10].

Figure 1.

Block diagram of classical DTC.

Because of their unique four-phase, eight-by-six-polar configuration, synchronous motors cannot be controlled using the same direct torque technique as inductance motors. SRM employs the reluctance principle for producing torque, with each phase functioning separately and sequentially. Torque is generated in either a positive or negative direction depending on the magnitude of the change in stator flux amplitude in relation to the rotor’s location. We call the former “flux acceleration” and the latter “flux deceleration,” respectively, when the value is positive or negative. Therefore, the following constitutes a definition of a novel approach to SRM regulation [11].

• The stator flux linkage vector of the motor is kept within amplitude hysteresis bands.

• During the stator flux vector acceleration or deceleration, the torque can be controlled.

The control goal is accomplished by varying the voltage vector and speeding up or slowing down the stator flux vector in relation to the rotor rotation [12]. The magnitude of the torque is also a function of the instantaneous current, which is different from the way things are handled with traditional control. It is also shown that the stator current in this drive control system exhibits a first order delay with respect to the variation in stator flux. In this way, it is safe to assume that the current remains stable even if the flux is sped up or slowed down under control [13]. This permits the control method to regulate torque solely with respect to the value of the flux acceleration and deceleration, and independently of the current change. This is similar to the traditional control scheme, which assumes that the rotor flux remains unchanged despite variations in the stator flux and modifies the motor’s torque via regulation of the stator flux acceleration [14].

3. Impact of voltage vectors

The Direct Torque Control loop has a torque hysteresis controller with three levels (1, 0, and −1) and a flux hysteresis controller with two levels (1 & −1). The SR motor has a distinctive pole structure, hence the voltage space vector for each phase is said to be perpendicular to the pole’s central axis. Keep in mind that the physical winding topology of the motor has not been altered from its standard setting.

Each motor phase can be in one of three voltage states, determined on the drive’s circuit topology configuration. A zero-voltage loop arises and is defined as the condition “0” when current is flowing with one device off (V1 or V2). Similar to how the condition is described as “−1” when both devices (V1&V2) are switched off and “1” when both devices (V1&V2) are turned on, the motor phase experiences a negative voltage when both are off and a positive value when both are on. Table 1 displays the three voltage states that can exist in a four-phase SRM drive, which is a result of the switching function.

Switching stage of power converter	Terminal voltage of winding	Switching function S
V1 and V2 both on	Positive Voltage	1
VI and V2 one On and the other Off	Zero Voltage	0
Vl and V2 both Off	Negative voltage	−1

Table 1.

Switching function table.

As a result, there are (mn, where m represents no of voltage states and n represents no of phases) 81 distinct permutations, as opposed to just two for the classical DTC of the AC motor. Figure 2 depicts the eight alternative spatial locations of switching voltage vectors for defining the voltage states, which are defined in the same way as in the standard direct torque control algorithm but with equal amplitude voltage vectors that are separated by radians. The mathematical model of IM has typically been analysed using the dq coordinate system. Within a two-axis rotating reference frame, the abc to dq0 transformation determines the direct axis, quadratic axis, and zero sequence qualities of a three-phase sinusoidal signal. The park transformation is a standard tool for modelling three-phase electric machines. Because the stator and rotor values can be referred to a stationary or rotating reference frame, time-varying inductances can be eliminated.

Figure 2.

Spatial location of switching voltage vectors.

Each stator winding’s flux linkage is assumed to be at the magnetic pole’s centreline for the sake of convenience. Figure 3 shows the stable α-β coordinate as a result. In Eqs. (1) to (4), and Ψ_α and Ψ_β stand for the two-flux linkage that flows in the two equivalent rotors, generating the same flux as the stator ψ₁, ψ₂, ψ₃ and ψ₄ currents (1.4).

Figure 3.

Composition flux linkage vector of switched reluctance motor.

$$\mathrm{\Psi \alpha }=\frac{1}{\sqrt{2}}\left[\mathrm{\psi }1+\mathrm{\psi }2cos45-\mathrm{\psi }4cos45\right]$$E1

$$\mathrm{\Psi \beta }=\frac{1}{\sqrt{2}}\left[\mathrm{\psi }3+\mathrm{\psi }2sin45+\mathrm{\psi }4sin45\right]$$E2

$$\mathrm{\Psi s}=\sqrt{{\mathrm{\Psi \alpha }}^2+{\mathrm{\Psi \beta }}^2}$$E3

$$\mathrm{\delta }=\text{arct}\left({\mathrm{\Psi }}_{\mathrm{\beta }/}{\mathrm{\Psi }}_{\mathrm{\alpha }}\right)$$E4

where, Ψ_s is instantaneous composition flux linkage, is spatial position angle of composition flux linkage.

Coordinate decomposition concept yields composition flow linkage height that is 1.4% greater than energy conservation approach, as seen in the aforementioned formulae. As a result, that SRM will spend a lot of time operating at the magnetic saturation point. While steady error is still ensured, motor efficiency drops dramatically towards magnetic saturation. Using the α-β vector block, we can determine which part of the plane the flow vector occupies. Sector of the plane in which the flow vector lies is one of eight, with each sector separated from the others by 45 degrees. If the stator flux linkage is in the kth region, increasing the flux with the switching vectors U k+1 and U k−1, or decreasing it with U k+3 and U k−3, is possible. Switching vectors U k +1 and U k +3 can be used to enhance the torque, whereas U k−1 and U k−3 can be used to decrease it. Table 2 illustrates the converter’s voltage switching vector selection. There are eight “active” voltage vectors labelled U1 through U8 and two “null” vectors labelled U0 and U9.

Hysteresis controller		Voltage vector selection
Φ	T	S (1)	S (2)	S (3)	S (4)	S (5)	S (6)	S (7)	S (8)
1	1	U2	U3	U4	U5	U6	U7	U8	U1
	0	U0	U9	U0	U9	U0	U9	U0	U9
	−1	U7	U8	U1	U2	U3	U4	U5	U6
0	1	U3	U4	U5	U6	U7	U8	U1	U2
	0	U0	U9	U0	U9	U0	U9	U0	U9
	−1	U6	U7	U8	U1	U2	U3	U4	U5

Table 2.

Switching voltage vector for converter.

3.1 Classical direct torque control results

The aforementioned technique is used to model the direct torque control scheme implemented in a MATLAB/Simulink simulation of a four-phase switching reluctance motor drive. One torque hysteresis controller with three levels and another flux hysteresis controller with two levels are used to create the simulation model. With reference to equations 1.2–1.4, the, α, β flux transformation is performed. The phase count and rotor-position angle inform the design of the flux sector. The voltage switching vectors form the basis for the lookup table. In the virtual experiment, a 4-phase motor is used. Each zone’s switching vector is chosen from the vector table based on the output signals from the two-hysteresis comparator, which are in turn determined by the position sensor. The stator flux hysteresis band in this control approach is set to 0.01Wb, and the torque hysteresis band is set to 0.3Nm; both values are held within these bounds throughout all simulations. Within 50 milliseconds, the motor will have reached the desired speed, having drawn a starting current that was capped by the converter’s components’ maximum ratings. The tests are performed at a constant stator flux of 0.3Wb under a wide range of load torques.

Using a proportional integral controller with kp and ki set to 0.10 and 0.01 respectively, the speed error is transformed into the reference torque. The simulation was run to examine how well the hysteresis controller worked under varying speeds and loads. The 1.5 kilowatt, 3800 revolution per minute, 4 Newton-meter reluctance drive is put through its paces with a dc voltage of 120 volts. It has been decided that 10mH will be the aligned Inductance and 49mH will be the unaligned Inductance. We’ve decided on a value of 0.008kg.m.m for the moment of inertia and 0.01N.m.s for the coefficient of friction. Below are examples of switching reluctance motor drive performance under a variety of load and speed scenarios.

4. Performance at rated load condition

When first activated, the switching reluctance drive is subjected to the rated load torque and speed. In Figure 4, we see the current and torque response in this situation. The phase current and total torque time scale variation is assumed to be 0.71–0.76 seconds for simplicity in interpreting the responses. It can be seen from the curve that the rated condition yields a maximum current of 8A.

Figure 4.

Current and torque response of the motor at rated load condition.

The hysteresis controller minimises torque inaccuracy by choosing the best switching vector, which in turn minimises torque ripple as depicted in the image. Using the following Equation, one can get both the total torque production and the torque ripple in percentage terms (5).

$${\mathrm{T}}_{\text{ripple}}={\left[\left({\mathrm{T}}_{\max }-{\mathrm{T}}_{\min }\right)/{\mathrm{T}}_{\mathrm{avg}}\right]}^{\ast }100\%$$E5

The figure is further enlarged to specify the variation of the torque ripple accurately at rated torque over a wide range of speed and is shown in Figure 5.

Figure 5.

Torque ripple waveforms at rated torque (a) Rated speed (b) Half rated speed (c) 10% of rated speed.

The response curve (a) indicates that the torque achieves a minimum of 3.94 Nm and a maximum of 4.15 Nm, with an average of 4.0 Nm reached at 0.09 s. Torque is 5.2% of the total estimated force. According to the torque response curve(b), the specified torque is reached in 0.09 seconds, after which the output torque ranges between a maximum of 4.18 Nm and a minimum of 3.92Nm. An average torque value of 4.01Nm was measured. The percentage of torque ripple is 6.47 percent. In the torque response curve (c), the rated torque is reached in 0.09 s, following which the output torque ranges between a maximum of 4.2 Nm and a minimum of 3.9 Nm. Torque production (T_avg) is measured to be 4.05 Nm on average. Torque ripple is 7.4 percent, according to the calculations.

5. Performance at 75% of the rated load

At first, the SRM drive is stimulated at 75% load torque at a variety of rated speeds. Figure 6 displays the resulting current and torque response. According to the graph, the rated condition produces a maximum current of 6A.

Figure 6.

Phase current and torque response at 75% of the rated load with rated speed.

The suggested controller outperforms the alternative proposed controller in terms of torque response and current response under the aforementioned conditions. Figure 7 enlarges the torque response curve displayed in Figure 6 to show the precise fluctuation of torque under 75% of the rated load situation with respect to the extensive range of speed variation.

Figure 7.

Torque response at 75% of the rated load (a) Rated speed (b) half of rated speed (c) 10% of rated speed.

In 0.08 seconds, the output torque (T_out) reaches 75% of the specified torque, and from there it varies between a maximum of 3.13 Nm and a minimum of 2.98 Nm, as shown in the response curve (a). Generally speaking, 3.0Nm is the average torque production (T_avg) that was measured. Torque ripple is 5.0% as determined by the calculation.

Torque output (T_out) reaches 75% of rated torque in 0.08 seconds, as shown by the response curve (b), and then ranges between a maximum of 3.18 Nm and a minimum of 2.98 Nm. Torque production (T_avg) is measured to be 3.1 Nm on average. 6.4% is the percentage value derived for the torque ripple. Torque output (T_out) reaches 75% rated torque in 0.08 seconds, and after that, it ranges between a maximum of 3.12 Nm and a minimum of 2.90 Nm, as shown by the torque response curve (c). It has been determined that the average torque output (T_avg) is 3.05 Nm, and that the torque ripple is 7.2% of that value. The output torque (T_out) achieves 75% of rated torque in 0.08 s, as shown by the response curve (a), and then ranges between a maximum (T_max) of 3.13 Nm and a minimum (T_min) of 2.98 Nm.

Generally speaking, 3.0Nm is the average torque production (T_avg) that was measured. Torque ripple is 5.0% as determined by the calculation. Torque output (T_out) reaches 75% of rated torque in 0.08 seconds, as shown by the response curve (b), and then ranges between a maximum of 3.18 Nm and a minimum of 2.98 Nm. Torque production (T_avg) is measured to be 3.1 Nm on average. 6.4% is the percentage value derived for the torque ripple. Torque output (T_out) reaches 75% rated torque in 0.08 seconds, and after that, it ranges between a maximum of 3.12 Nm and a minimum of 2.90 Nm, as shown by the torque response curve (c). It has been determined that the average torque output (T_avg) is 3.05 Nm, and that the torque ripple is 7.2% of that value (Figure 8).

Figure 8.

Current and torque response at 50% of the load torque with rated speed.

In order to clearly demonstrate the fluctuation in torque under 50% of the rated load condition with respect to the different speed conditions, the above depicted torque response curve has been extended. Figure 9 demonstrates the observable range of values.

Figure 9.

Torque response at 50% of the rated load (a) Rated speed (b) half rated speed (c) 10% of rated speed.

In 0.08 seconds, the output torque (T_out) reaches 50% of its rated value, and from there it varies between a maximum (T_max) of 2.1 Nm and a minimum (T_min) of 2.0 Nm, as shown in the response curve (a). Torque production (T_avg) is calculated to be 2.02 Nm on average. 4.9% is the percentage value determined to be the torque ripple output. The torque output (T_out) reaches 50% of the specified torque in 0.08 s, and then it ranges between 2.11 Nm and 1.99 Nm (T_max and T_min, respectively) as shown in the torque response curve (b). Torque production (T_avg) was measured to be 2.0Nm on average. 6 percent is the calculated ripple percentage of torque. The torque output (T_out) reaches 50% of the specified torque in 0.08 seconds, as shown by the curve (c), and then ranges between a maximum (T_max) of 2.13 Nm and a minimum (T_min) of 1.99 Nm.

Generally speaking, we can say that the torque output (T_avg) is 2.02 Nm. Torque ripple is determined to be 6.9% of total output.

6. Performance at 25% of the rated load torque

In order to trigger the SRM dive, a 25% load torque is applied while the speed is varied. We evaluate the performance of the proposed controller by measuring and tabulating the torque and current responses. Figure 10 depicts this rated-speed torque and current response. This curve shows that at the rated condition, the maximum current is 2A.

Figure 10.

Current and torque profile for 25% of the load torque at rated speed.

The aforementioned torque response curve is simplified to clearly demonstrate the accurate fluctuation of torque under 25% of the rated load situation with respect to the broad range of speed variation. Figure 11 displays this variance.

Figure 11.

Torque profile for 25% of the load torque (a) Rated speed (b) half rated speed (c) 10% of rated speed.

It can be seen in the torque output profile (a) that the output torque (T_out) reaches 25% of the specified torque in 0.07 seconds, and then ranges between a maximum of 1.01 Nm and a minimum of 0.99Nm. The computed proportion of torque ripple output is 2.0%, and the average torque output (T_avg) is 1.00Nm.

Torque output (T_out) achieves 25% rated torque in 0.07 s, as shown by the torque response curve (b), and then ranges between a maximum of 1.015 Nm and a minimum of 0.99 Nm. To be precise, T_avg is 1.0Nm, which is the average torque production. According to the numbers, the torque ripple is 2.5%.

Torque output (T_out) achieves 25% rated torque in 0.07 s, as suggested by the response curve (c), and then ranges between a maximum of 1.02 Nm and a minimum of 0.99 Nm. Torque production (T_avg) averaged out to be 1.01 Nm. The percentage of torque output is 3.0%.

7. Performance under variable load condition

In the dynamic simulation, the speed was maintained at a constant rated condition throughout. There were two potential scenarios: It took 0.34 seconds to double the command torque T_com from the first case shown in Figure 12 to the second case whereas it took 0.65 seconds to halve the torque back down to 2 N.m from 4 N.m. According to the figure, the controller has excellent dynamic performance, with T_out increasing to 2 Nm in just 0.06s.

Figure 12.

Torque profile under external load variation.

The most significant drawback of the conventional direct torque control is its slow response to initial torque and flux changes. Changes between steady state and step-up states use the same vectors, making it impossible to differentiate between large and tiny errors in flux and torque. Both AI and conventional techniques of control over AI can alleviate these issues. To smooth out the driving torque at any rated speed and torque, the next few chapters will focus on such smart controllers.

8. Comparative study

An analysis is made on Neural Network Controller and the revealed observations are made; Table 3 shows the performance comparisons between different controllers.

Sl. no	Proposed controller based DTC	Rated speed in%	Torque ripple in % with respect to the % applied load torque				Computational time (sec)
			100	75	50	25
1	Hysteresis controller	100	6.0	5.0	4.9	2.0	Equal to run time
		50	6.48	6.4	6	2.5
		10	7.4	7.2	6.9	3.0
2	Fuzzy controller	100	4.7	4.0	3.5	1.5	4.34
		50	5.7	5.6	5.4	2.1
		10	6.6	6.2	5.9	2.4
3	Neural network controller	100	3.5	3.3	2.5	1.3	3.17
		50	4.4	3.98	3.5	1.8
		10	5.6	5.2	5.0	2.2

Table 3.

Performance comparison between different controllers.

9. Conclusion

The direct torque control technique is tested for switched reluctance motor, Direct torque Control technique is able to minimize the ripple content in the motor torque output at different operating conditions. the torque ripple is almost minimized in the range of about 1.5% to 2% for a fixed speed with variable torque. The settling time of the torque and the response time of the speed is also reduced, which in turn increases the efficiency of the machine. The major drawback with the proposed controller is the fixation of weights during the real time application which reduce the flexibility and adaptability of the system. This drawback or limitation can be overcome by using hybrid intelligent controller.