# Investigation and Development of the Brushless and Magnetless Wound Field Synchronous Motor Drive System for Electric Vehicle Application

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure and Principle of the Proposed WFSM Drive System

_{ef}to the field windings of the exciter stator, and then the induced AC currents I

_{exa}, I

_{exb}, and I

_{exc}in the armature windings of the exciter rotor flow to the rotating rectifier, and finally the AC current I

_{ex}is converted to DC current I

_{F}for the field excitation of WFSMs. For the coordination with I

_{F}, the currents I

_{A}, I

_{B}, and I

_{C}are regulated via a power converter and injected into armature windings to generate armature reaction magnetic potential. Therefore, under the joint action of exciting magnetic potential and armature reaction magnetic potential, the torque of WFSM is generated, and it drives the shaft of EVs.

## 3. System Analysis and Development

#### 3.1. Investigation and Analysis of the Main Motor

#### The Torque Characteristics of the Proposed WFSM

_{rms}. Additionally, when the armature current I

_{rms}remains constant, the torque T also increases with the exciting current. However, the torque T has little change with an increase in exciting current I

_{F}when the excitation current exceeds 50 A, and the relationship between the torque T and armature current I

_{rms}is approximate linearity. In fact, the proposed WFSM is designed under the rated working condition of exciting current at 60 A and armature current at 260 A. The nearly saturated core of the WFSM causes the linear characteristic of the relationship between torque T and armature current I

_{rms}.

#### 3.2. Analysis of the Exciter Characteristics

#### 3.2.1. The Principle of Single-Phase AC Excitation

_{ex}is the number of series turns per phase of exciter armature winding; K

_{ex}is the coefficient of armature winding; N

_{ef}is the number of series turns of exciting winding; and U

_{ef}is the exciting voltage.

_{ef}is the RMS of the exciting voltage, and f

_{1}is the frequency of the exciting voltage.

_{ef}and the turn ratio N

_{ex}/N

_{ef}can be increased to generate sufficient exciting current of the WFSM.

#### 3.2.2. The FEA Analysis of Single-Phase AC Excitation

_{ef}of the exciter and the field current I

_{F}of the WFSM under different exciting frequency I

_{F}and rotating speed are simulated, based on the 1/5 Maxwell model of the exciter, which is in series with the diode rectifier and the exciting winding of the WFSM, as shown in Figure 7.

_{ef}and I

_{F}changing with the exciting frequency f

_{1}under the condition of 0 r/min. With an increase in frequency f

_{1}, the exciting current I

_{F}increases, but due to the low impedance caused by the low frequency, the exciting current I

_{ef}of the exciter is very large and reaches thousands of amperes, which is far beyond the bear of the winding. When the frequency f

_{1}is more than 300 Hz, the exciting current I

_{ef}and I

_{F}decrease with an increase in frequency. Additionally, in Figure 10, when f

_{1}is more than 400 Hz, the input apparent power S

_{ef}and output exciting power P

_{ef}gradually decrease, and the energy conversion efficiency P

_{F}/P

_{f}is about 55%. Therefore, it is better for the exciting frequency f

_{1}to be at 400 Hz, considering the electric density of the exciting winding and the exciting power required by the WFSM.

_{ef}and the field current I changing with rotating speed at −60 °C and 180 °C. It is depicted that under the given temperature or field resistance RF, the exciting currents I

_{ef}and I

_{F}change inconspicuously with an increase in rotating speed, and basically remain constant, which is consistent with Equation (8). Even if the load resistance of the exciter increases by 2.36 times with a temperature increase from −60 °C to 180 °C, the changes in the exciting current I

_{ef}and I

_{F}are not obvious, which increase by less than 20%.

#### 3.3. Control Strategy of WFSM Drive System

#### 3.3.1. Approaches of Discrete Time Armature Current Regulator Design

_{d}, u

_{q}, i

_{d}, i

_{q}, R

_{s}, ω

_{e}, L

_{d}, L

_{q}, ψ

_{f}, and p denote the d–q axis stator voltage, the d–q axis stator current, the stator resistor, the motor electrical angular frequency, the d–q axis stator inductance, the flux linkage due to the field current, and the differential operator, respectively.

_{s}denotes the sampling period and the control computation and the PWM update delay is modeled as $1/z{e}^{j{\omega}_{e}{T}_{s}}$.

_{s}is usually used to replace L

_{d}and L

_{q}for modeling:

_{plant}and G

_{op}is shown in Figure 15, where K = 0.35. After the compensation of the current regulator G

_{c}, the system has a sufficient gain margin and phase margin, and the low-frequency gain is also raised by the integrator. The performance of the current loop compensated by G

_{c}is satisfactory.

#### 3.3.2. Design of Excitation Current Coordination Control Strategy

_{s}applied to the WFSM armature through the inverter is as follows:

_{dc}:

_{s}can avoid being clamped by the DC bus voltage during high-speed operation, which is the key factor for the WFSM to realize constant power operation in a wider speed range. Therefore, the excitation current amplitude reference can be calculated by selecting the appropriate voltage vector amplitude, and the voltage vector amplitude can be kept constant through closed-loop control. The control block diagram is shown in Figure 14. In the low speed range, the excitation current will always maintain the upper limit to obtain the maximum torque per ampere. After entering the high speed range, the excitation current amplitude reference is calculated by the PI regulator. Note that its reference needs to be limited to avoid magnetic circuit saturation.

_{p}, K

_{r}, ω

_{o}, and ω

_{c}denote the proportional coefficient, the resonance coefficient, the resonant angular frequency, and the resonant bandwidth angular frequency. The transfer function in the s-domain is mapped to the z-domain through bilinear transformation:

_{s}is 0.25 ms. However, bilinear transformation is a type of nonlinear mapping. Mapping points in the left-hand plane of the s-domain to the unit circle of the z-domain will cause frequency distortion, which will increase with an increase in the T

_{s}, as shown in Figure 17. Therefore, the resonance frequency designed in the s-domain will shift after being transformed into the z-domain, which needs to be corrected.

_{c}is the correction coefficient.

_{PR}can be expressed as

_{c}can be expressed as

## 4. Experimental Verification

#### 4.1. AC Excitation Characteristics

_{ef}are applied to the rotating transformer, the corresponding excitation current I

_{ef}remains constant at different speeds and increases linearly with U

_{ef}.

#### 4.2. Torque under Different Armature Current

## 5. Conclusions

- The exciter excited by single-phase constant frequency current has the characteristics of current amplification and constant current source, and the amplification factor is almost independent of load and speed;
- The torque of the main motor is proportional to the armature current;
- The additional control DOF introduced by the field current is the key for WFSM to obtain high torque capability in the low speed region and to have a wider constant power region.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**The EMF of exciter armature winding under different rotor position angles. (

**a**) The angle between the phase A winding axis and the exciting winding axis is 0°; (

**b**) the angle between the phase A winding axis and the exciting winding axis is 30°; (

**c**) the angle between the phase A winding axis and the exciting winding axis is 60°; (

**d**) the angle between the phase A winding axis and the exciting winding axis is 90°.

**Figure 10.**The curve of input apparent power S

_{ef}, output power P

_{F}, and transformation efficiency changing with frequency.

**Figure 11.**The curve of I

_{ef}and I

_{F}changing with rotating speed under −60 °C and 180 °C: (

**a**) the curve of exciting current I

_{ef}; (

**b**) the curve of exciting current I

_{F}.

**Figure 13.**Vector diagrams of the 1st and 2nd quadrant operation: (

**a**) 1st quadrant operation; (

**b**) 2nd quadrant operation.

**Figure 16.**The bode diagram of parameters’ mismatch: (

**a**) resistance changes from 0.5R

_{s}to 3R

_{s}; (

**b**) inductance changes from 0.5L

_{s}to 2L

_{s}.

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**MDPI and ACS Style**

Li, Y.; Wang, Y.; Zhang, Z.; Li, J.
Investigation and Development of the Brushless and Magnetless Wound Field Synchronous Motor Drive System for Electric Vehicle Application. *World Electr. Veh. J.* **2023**, *14*, 81.
https://doi.org/10.3390/wevj14040081

**AMA Style**

Li Y, Wang Y, Zhang Z, Li J.
Investigation and Development of the Brushless and Magnetless Wound Field Synchronous Motor Drive System for Electric Vehicle Application. *World Electric Vehicle Journal*. 2023; 14(4):81.
https://doi.org/10.3390/wevj14040081

**Chicago/Turabian Style**

Li, Yanhui, Yiwei Wang, Zhuoran Zhang, and Jincai Li.
2023. "Investigation and Development of the Brushless and Magnetless Wound Field Synchronous Motor Drive System for Electric Vehicle Application" *World Electric Vehicle Journal* 14, no. 4: 81.
https://doi.org/10.3390/wevj14040081