Sensorless based SVPWM-DTC of AFPMSM for electric vehicles

AFPMSM is lighter, has a higher power-to-weight ratio, is shorter in length, is less expensive, and has a higher efficiency than the radial flux motor. Then AFPMSM is more suitable for driving the EV than radial flux motor. The proposed technique in this paper is the sensorless-based SVPWM-DTC of AFPMSM to drive electric vehicles. Sensorless research becomes more important in this circumstance since the axial motor can be placed inside the vehicle tire due to its condensed size and shape similar to the tires. DTC provides less fluctuation for the driver during driving for safety and comfort. SVPWM is preferred for its high performance. When measuring speed using a sensorless estimator, sensor inaccuracy is minimized, and the AFPMS motor can be mounted inside the tire. The control system is tested using two EVs driving cycles, and the results promise high performance. NEDC and HWFET driving cycles are used to test the proposed control scheme in 100 times less than the actual driving cycles’ time to test the coherence of the sensorless estimator. The results demonstrate that the proposed technique is valid for real-time applications with high-performance, minimum torque fluctuations, and minimum transient and steady-state errors.

For safety and comfort, DTC ensures less fluctuation for the driver while driving. SVPWM is recommended because its higher PF, lower THD rate, and lower switching losses, high efficiency, and good performance are achieved. A sensorless estimator is used to decreased sensor inaccuracy while observing speed, and the motor can also be inserted inside the tire using the sensorless estimator. Single-stator single-rotor, single-stator doublerotor, and double-stator single-rotor structures are the structures that come closest to being acceptable for usage in-wheel. But, the single-rotor single-stator structure, particularly the surface-mounted structure, is the more suitable one due to its small thickness. The AFPMSM can be mounted in-wheel, as shown in Fig. 1. Two driving cycles were used to test the total control system, with promising results. The paper items are AFPMSM model, DTC, SVPWM, straight-line guided by the reference speed sensorless estimator, simulation and driving cycles of EV results, and conclusion.

Axial flux permanent magnet synchronous motor model
The AFPMSM is an advanced technology that can be used for multi-megawatt applications and is suitable for applications that required high torque with low speed like electric tractions. Axial flux motors use less material and can also deliver higher power density than that of radial flux motors, and this means the axial flux motors suitable for an EV 5 . The axial flux motors are better than the radial flux motors because the radial flux motors are heavier than axial flux motors, longer than axial motor length, and the axial flux motor efficacy is higher 6 .
The AFPMSM's dq0 reference frame equations under assumptions of neglected saturation effect, losses generated by hysteresis, eddy currents, and stray. The studied AFPMSM not containing a salient pole effect, so L d equal to L q , and Sinusoidal back-EMF is as follow 17-20 :  where L da is the D axis winding inductance , L qa is the Q axis winding inductance. * Torque equation: where n is the number of phases, ψ f is the flux of the field of rotor windings.
The torque can be controlled by changing i qa for L da = L qa

Direct torque control (DTC)
The speed of three-phase AC electric motors can be adjusted using DTC in variable-frequency drives. Voltage and current measurements on the electric motor can yield an approximation of the magnetic flux and torque 21,22 .
where T e is the electromagnetic torque , P is the pole − pairs number , ψ sa is the flux of the field of stator windings , i sa is the stator current vector.
w h e r e T l is the torque of load , ω r is the rotor angular velocity , B is the damping coefficient , Jis the inertia moment forAFPMSM.
The electromagnetic torque could be written in the form of where δ is the torque angle. For L d equal to L q and the torque equation will be: From this equation, it is clear that changing electromagnetic torque depends upon changing angle δ. Flux estimation equations are Eqs. (3) and (4) and the AFPMSM stator flux given by: The AFPMSM reference flux is calculated from the following equation 21,22 .
A trial-and-error approach is used to evaluate the gains of the PI controller and the constants listed in Table 1 23 .

Space vector pulse width modulation (SVPWM) inverter
PWM waveform generation, switching time calculation model, and sector selection are all part of the SVPWM model in MATLAB [24][25][26] . The switching frequency of pulse width is 20,000 Hz, the DC voltage is 250-V, and the reference speed is 300 rpm. * Reference voltage and angle * Conversion time in any sector where n is the sector from 1 to 6, 0 ≤ α ≤ 60 o

Straight-line guided by the reference speed sensorless estimator
The proposed straight-line guided by the reference speed sensorless estimator is consists of the AFPMSM reference model, sensorless estimator, and sensorless corrector, as shown in Fig. 2. ✓ Axial flux permanent magnet synchronous motor reference model is explained using Eqs. (1) to (6).

From Eqs. (1), (3), and (4) the stator voltage equation in d-axis become
Taking ω e = Pω r then the current can be driven as: Again, by taking ω e = Pω r then the current can be driven as: The AFPMSM reference model stator current from Eqs. (26) and (28) is rewritten as the state variable as: where i d and i q are the reference direct and quadrature current respectively, ω e is the angular speed. ✓ Sensorless estimator Replacing the reference value with estimated value and obtaining (Eq. 31): where i d and i q are the estimated direct and quadrature current respectively, ω e is the angular speed. ✓ Sensorless corrector The error the reference and estimated currents is: Subtracting Eqs. (30) and (31), the error between the reference and the estimated currents is: The forward channel transfer function matrix is easily demonstrated to be a real matrix that is just positive. The electrical angular velocity adaptive law can then be determined using Popov hyper-stability theory by solving the Popov integral inequality 10 . The proposed sensorless speed can be estimated as Eq. (34) and the schematic diagram in Fig. 3. where ω in is the initial estimated speed without adjustment. The relation between the estimated speed and the multiplying of demand speed and the initial estimated speed is assumed to be seen as a straight-line equation as follow: where ω est andω d are the estimated speed and demand speed, respectively. Also, m is the slope of the straight-line.
At the ω d = 300rpm , the initial estimated speed without adjustment is found to be ω in = 10000rpm then, the slope is taken to be 10,000 to produce ω est = 300rpm.
The straight-line guided by the reference speed sensorless estimator is used to overcome changes in the drive's reference speed value by using the reference speed setting as a decision parameter.
Integrating the estimated speed as follows yields the rotor position:

Simulation and driving cycles of electric vehicle results
The control block diagram of the proposed control sensorless-based scheme of axial flux permanent magnet motor is shown in Fig. 4. The Axial flux motor parameters are listed in Table 2. Also, this control system is the direct torque control type, which shows the torque response to the reference torque, as shown in Fig. 8 for speeds 75, 150, 225, 300, and 200 m/s each for 2 sec. It also shows the flux response to the reference flux as in Fig. 9, while Figs. 10 and 11 show the current drawn by the motor at full torque as instantaneous and RMS values, respectively. In the following subsection, the AFPMSM with DTC will be subject to testing for driving vehicles using two test systems.  www.nature.com/scientificreports/ Light-duty vehicle type approval is based on the New European Driving Cycle (NEDC), which includes four repeats of a low-speed urban cycle and one highway drive with a 11,017-m distance, an 1180-s duration, and an average speed of 33.6 km/h. An example of NEDC Driving Cycle is shown in Fig. 12 27,28 .
Assume the EV tire diameter is 16 inch equal 16 × 2.54 = 40.64cm , then the radius is 40.64/2 = 20.32cm , the km h = 1000 2π×60×R tire = 1000 2π×60×20.32×10 −2 = 13.054rpm.        The straight-line guided by the reference speed sensorless estimator is tested to follow the reference NEDC speed cycle but with a time equal to 12 s instead of the standard time of the cycle, which is 1200 s. 12 s means the system response is faster than the actual NEDC by 100 times with high-performance and minimum transient and steady-state error, as shown in Fig. 13.
Environmental Protection Agency Highway Fuel Economy Test (HWFET) is modeled to drive cars by 16,503-m distance, 765-s duration, and 77.7 km/h average speed 28 . The straight-line guided by the reference speed sensorless estimator is tested to follow the reference HWFET speed cycle but with a time equal to 12 s instead of the standard time of the cycle, which is 1200 s. 12 s means the system response is faster than the actual NEDC by 100 times with high-performance and minimum transient and steady-state error, as shown in Fig. 14.

Conclusion
The AFPMSM is suitable to use inside the vehicle tire, especially with a sensorless speed estimator. This paper presents the application of straight-line guided by reference speed sensorless estimator-based PI-DTC using SVPWM to control the axial flux motor speed for driving EVs. DTC ensures that the driver's safety and comfort are not jeopardized during driving. With a lower switching loss, lower THD rate, and better power factor (PF), SVPWM is the preferred solution. A sensorless estimator is used to reduce sensor inaccuracy while monitoring speed, and by using the sensorless estimator, the motor can also be installed inside the tire. Two driving cycles are employed to test the control system, and the results show that it performs admirably. NEDC and HWFET driving cycles are used to test the system control by time less than 100 times the actual time to test the coherence Gear ratio = motor rated speed max. speed( km h ) × 13.054rpm   www.nature.com/scientificreports/ Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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