Variable Carrier Phase-Shift Method for Integrated Contactless Field Excitation System of Electrically Excited Synchronous Motors

This article presents a novel contactless field excitation (CFE) system based on wireless power transfer (WPT), which utilizes the existing voltage source inverter (VSI) of the motor drive for electrically excited synchronous motors (EESMs). In conventional CFE systems, an extra high-frequency converter is required to excite the field winding. In this article, it is proposed to utilize existing voltage switching harmonics of the VSI for exciting the field winding while the low-frequency modulated component is used to drive the motor. In the proposed system, a novel variable carrier phase-shift method is developed to achieve constant input excitation voltage for the WPT part independently from the motor operation. In addition, a hybrid frequency detuning control method is introduced to adjust the field current. For experimental validation, a small-scale prototype with a 100-V dc-link and a 60-kHz switching frequency is established. It is observed that the field current could be kept almost constant at 5 A under different motor driving conditions operations regarding modulation index and fundamental frequency. Also, it is shown that the field current could be reduced by detuning the switching frequency. In brief, without an additional active converter and only with a software update, a cost-effective CFE system for EESMs can be easily implemented.


I. INTRODUCTION
T HE interest of the automotive industry is continuously increasing in electric vehicles (EVs) or hybrid EVs (HEVs) rather than internal combustion engine vehicles [1]. One of the critical parts of EVs and HEVs is the traction system, where permanent magnet synchronous motors are commonly preferred due to their high torque density [2]. However, high cost and limited supply of rare-Earth magnets such as Neodymium (Nd) and Samarium (Sm) encourage less-PM or no-PM motors such as electrically excited synchronous motors (EESMs) [3], [4], [5], [6]. EESMs can decrease the total cost and have flexible control thanks to their externally excited field windings [7], [8]. Moreover, they are more reliable as the demagnetization of PMs due to high temperature is not an issue in EESMs. However, power transfer to their rotating field windings is challenging. The most common method to excite field windings is to use slip rings with conductor rings and carbon brushes. Although slip rings are a mature and cost-effective technology, they require periodic maintenance due to the wear of the brushes [9]. Another method is to use brushless exciters that are, in fact, synchronous generators (SGs) with rotating rectifiers. However, this method is not applicable for variable speed drives such as in EVs [10]. Alternative to these methods, contactless field excitation (CFE) systems based on wireless power transfer (WPT) are proposed, as shown in Fig. 1(a) [11], [12], [13], [14], [15]. They have no physical contact between the rotating and stationary frames, eliminating the maintenance issue. However, extra high-frequency converter increases the cost and complexity.
The VSI of the motor drive generates a low-frequency modulated voltage with high-frequency switching harmonics. This low-frequency modulated voltage controls the speed and torque of the motor, whereas the motor windings filter out the highfrequency voltage harmonics thanks to high phase inductances. In this article, it is proposed that these high-frequency voltage harmonics of the existing motor drive can be utilized to energize the field winding while the low-frequency modulated voltage can still be used to drive the motor. The proposed system is shown in Fig. 1(b).
Motor drives use modulation techniques such as sinusoidal pulsewidth modulation (SPWM) or space-vector pulse width modulation. Yet, these modulation techniques affect the content of the high-frequency switching harmonics in addition to controlling the low-frequency modulated voltage. Therefore, an independent control algorithm for the high-frequency switching harmonic components is required. In this study, a novel variable carrier phase-shift method (VCPSM) is proposed to achieve independent field current control while driving the motor. The main advantage of the proposed method is that it can be applied in conventional motor drives by just updating the software, so the system can be easily implemented without extra cost.
The rest of the article is organized as follows. Section II presents the system structure and defines the problem. Section III proposes the VCPSM and control strategy of the field current. Section IV gives the WPT system's design stage regarding the proposed method's restriction. Sections V and VI present the experimental results and discussion, respectively. Finally, Section VII concludes this article.

II. SYSTEM STRUCTURE AND PROBLEM DEFINITION
The proposed system aims for an integrated CFE system for EESMs of EVs. A two-level voltage source inverter (VSI) is the most common topology in commercial EV drives [16]. In the past, discrete IGBTs or module IGBTs have been used with their switching frequencies around 20 kHz [17]. Since the WPT systems become bulky in this frequency range, the proposed integrated CFE system is not feasible. However, in recent years, wide-bandgap (WBG) semiconductors such as SiC MOSFETs or GaN HEMTs are becoming more popular in the automotive industry [18]. Thanks to their high switching frequencies up to 100 kHz, the passive components can be shrunk [19]. Similarly, a higher switching frequency reduces the size of the transmitter and receiver coils of the WPT system and makes the proposed integrated CFE system more feasible.
Several topologies, such as capacitive power transfer and inductive power transfer (IPT), can be used in CFE systems [15], [20], [21], [22], [23], [24], [25], [26], [27]. Reducing the size of the system is essential as the system should fit inside the motor. Therefore, the IPT system is chosen thanks to its wide range of frequency, power, and smaller size. In IPT systems, Tx and Rx coils are loosely coupled, resulting in inherently low power factors. Therefore, compensation circuits are generally used [28], [29], [30]. Series compensation is preferred in the Tx coil as a VSI is used in motor drives. Besides, the Rx side compensation is not used since achieving a lightweight and small volume on the rotating side is desired in the proposed system.
In the remaining parts of the article, a series-none (SN) topology is selected, and a 2-level 3-phase 3-wire (3Φ-3 W) VSI (driven by SPWM) is used, although the proposed system can be adapted to different converters, modulation techniques, or WPT systems.

A. Problem Definition
Conventional WPT systems have two wire inputs, and motor drives have three-wire outputs so that the WPT system can be connected between any two of three phases, as given in Fig. 2.
In this configuration (the WPT system will be connected between legs A and B), the excitation voltage of the WPT system (U i (t)) can be calculated as in where V DC is the dc-link voltage, and S A (t) and S B (t) are the switching function of leg A and leg B, which can be calculated by double Fourier series for SPWM, as presented in [31]. The generalized switching functions for leg A and leg B is shown in where m a is the modulation index, ω o is the angular frequency of the reference (fundamental) signal, θ o is the phase of the reference signal, J o is the zeroth order Bessel function, ω c is the angular frequency of the carrier (switching) signal, θ c is the phase of the carrier signal, and J k is the kth-order Bessel function. According to (2), the harmonic distribution of SPWM changes with modulation index, as shown in Fig. 3. Although several components exist, such as dc, fundamental, switching, and sideband harmonics, only the first switching harmonic and its sideband components (denoted by U f i (t)) dominate in the WPT system since the WPT system behaves like a bandpass filter characteristic, and its resonant frequency is tuned to near the switching frequency. Therefore, only U f i (t) can be used in the mathematical model. The first switching harmonic and its sideband components of the switching function can be calculated as in (3), (4), and (5) by taking (i = 1), (i = 1, k = −2), and (i = 1, k = 2) in (2), respectively where f o is the fundamental frequency, f s is the switching frequency, f s − 2f o is the lower sideband harmonic, and f s + 2f o is the higher sideband harmonic. After that, U f i can be calculated as in (6) shown at the bottom of this page, by subtracting the switching and its sideband harmonics of leg B from those of leg A In conventional SPWM, each phase uses the same carrier signals, which means that the carrier phase of leg A (φ c A ) and leg B (φ c B ) are equal. Hence, according to (6), the switching frequency disappears in U f i (t), and just only its sidebands exist. U i (t) and U f i (t) are plotted in Fig. 4 for different modulation indices. It is observed that U f i (t) increases with the modulation index, and zero voltage (zero excitation) occurs at some moments. These zero excitation instants create low-frequency power fluctuations that disrupt constant power transfer. Therefore, a control method is required to achieve a continuous/constant power transfer at the switching harmonic for the WPT system without disturbing the fundamental component. However, conventional control methods of the WPT system are not suitable for this.
A conventional method is to control the duty cycle but this also affects the fundamental component. Another method is frequency detuning control, but it cannot guarantee continuous power transfer since zero-voltage moments exist, indicated via red arrows in Fig. 4. The last method is to add a postregulation converter or use an active rectifier at the output of the WPT system. However, this increases the system's cost and complexity, and the problem of zero voltage moments still exists. In this article, a new control method, introducing variable carrier phase shift (CPS), is proposed to avoid zero-voltage moments and achieve continuous power transfer for changing modulation indices. The proposed method is similar to a dual-frequency power transfer system with a single converter [32], [33], [34], [35], [36]. In [33], a single-inverter-based dual-frequency WPT system is proposed using the programmed PWM method.
However, the programmed PWM method is computationally complex and requires switching angle calculations using offline algorithms, which is not feasible in dynamic systems such as our cases. In [34] and [35], multifrequencies are achieved by comparing superimposed sinusoidal reference signals with a high-frequency triangular carrier signal. However, in these methods, the switching frequency is higher than the operating frequencies of the WPT system, which increases the switching losses. In [36], multifrequency components are achieved by a multilevel inverter (MLI) with a switching frequency lower than its two-level alternatives. However, this system uses a higher number of switching components, which is actually the opposite of the main proposal. In [37], a CPS method is proposed to control the switching harmonic independently. The amount of the CPS is determined according to the modulation index. Since a constant CPS is applied until the modulation index changes, a low-frequency ripple exists there. The low-frequency fluctuation is shown in Fig. 5. Although the low-frequency fluctuation may be acceptable in rotating loads and can be reduced by increasing the output capacitance, it should be mitigated in the application of the field excitation system since it also creates a torque and speed ripple in the motor. In order to solve this problem, the VCPSM is proposed. This method calculates and updates the CPS for the switching interval rather than for the modulation.

III. PROPOSED VCPSM AND FIELD CURRENT REGULATION
The VCPSM aims to achieve a constant switching harmonic during each switching interval. In this section, first, a mathematical model is developed for SPWM. Then, the selection of the magnitude of the switching component is discussed. Finally, the regulation strategy of the field current is presented. Fig. 6 shows the SPWM technique with reference, carrier, and PWM signals, where different carrier signals (implying that

A. Mathematical Modelling
The duty cycle of each phase (D A , D B , D C ) follows its corresponding reference signal, as given in (7). In other words, square waves with varying duty cycles are generated within a switching interval. The duty cycles depend on the reference signals, as given in (7), and the phases of the square waves change with the phases of the carrier signals, as can be observed in Fig. 6. The first switching harmonic components of each calculated using the Fourier series, as given in Then, the normalized magnitude of the switching component for the phase-to-phase connection (S AB (t) f s ) can be calculated as in (9). Therefore, the magnitude of the switching harmonic (Ŝ AB fs ) can be calculated in the phasor domain as in (10) by taking the difference between two phasors Consequently, the magnitude of the switching component can be adjusted by introducing a phase shift between the carrier signals, and the required CPS value (φ CPS ) to keepŜ AB fs constant at the desired value can be calculated using (9), and found as given in However, it should be considered that the amount of CPS is restricted between 0 • and 180 • , which gives the minimum and maximumŜ AB fs . Besides, D A and D B are not independent variables, and they follow the reference signals. Therefore, the reachableŜ AB fs is restricted and changes regarding the parameters of D A , D B , and φ CPS . For these reasons, the selection ofŜ AB fs that is independent of the modulation index is challenging.

B. Selection ofŜ AB fs
According to phasor calculation in (10), the maximum and minimum values ofŜ AB fs should be complied by triangle inequality, as given in Hence, these maximum and minimum values change according to modulation indices, as shown in Fig. 7. The aim is to achieve a constantŜ AB fs for any motor operation. However, it is observed that the range of the allowedŜ AB fs is reduced by increasing the modulation index, and it may not guarantee a constant value for a higher modulation index. The allowedŜ AB fs values are plotted along modulation indices in Fig. 8.
The allowed range of the WPT system is inversely proportional to the range of the motor drive control. For example, S AB fs can be controlled between 0.30 and 0.60 for the modulation index below 0.6. Therefore, if a higherŜ AB fs is desired, the modulation index of the motor drive should be restricted to a lower value, which also decreases the dc-link utilization. However, the selection ofŜ AB fs , dc-link voltage, and modulation index are related to the system requirements. In this study, as a proof of concept, theŜ AB fs limit is selected at 0.44, where the  motor operation should be restricted to a maximum modulation index of 0.8.

C. Field Current Regulation
In the proposed method, the power of the WPT system is not directly controlled, but it only guarantees to keep the input excitation voltage at a constant value. Therefore, a control strategy for the field current should be developed. Several conventional methods are used in WPT systems, such as duty cycle control and postregulation converter (or active rectifier). The duty cycle control is unsuitable for cooperating with the proposed method since it also changes the fundamental component. A postregulation converter could be used but it is not preferred as it increases the cost and complexity of the system. Alternatively, the frequency detuning method that controls the gain of the WPT system can be used, which does not require extra hardware and is simple to implement, so it is preferred in the proposed system. Accordingly, the overall control block diagram of the hybrid control strategy consisting of frequency detuning and VCPSMs is presented in Fig. 9.
A conventional PI controller can be used to regulate the current and speed of the motor. The proposed VCPSM algorithm calculates the carrier phases based on the duty cycles generated by this conventional PI controller. An additional PI controller regulates the field current by varying the switching frequency. Consequently, duty cycles, carrier phases, and switching frequency are used as input parameters for SPWM, and a VSI, governed by this SPWM, generates voltage waveforms to drive the motor.

IV. DESIGN OF THE SN-WPT SYSTEM
This section will first analyze the SN compensated WPT system and then present the system's design steps as a guideline.

A. Analysis of the SN-WPT System
The analysis of the SN-WPT system is similar to that of the LLC converter [38]. The circuit diagram of the SN-WPT system is shown in Fig. 10(a). The first harmonic approximation (FHA) can be used to analyze this system, as illustrated in Fig. 10(b).
In this system, the Tx-side capacitance (C TX ) is used to compensate for the leakage inductance, which is termed as L R . Therefore, the output voltage (U o ) depends on the transformer turns ratio (n) and input voltage (U i ) at the resonant frequency as given in Besides, the resonant frequency (f r ) is determined by the compensation capacitance, which is presented in Moreover, the transformer modeling parameters of leakage inductance (L R ), mutual inductance (L M ), turns ratio (n) are calculated as given in The system quality factor (Q) should be high enough to make the FHA valid. Q depends on the Rx-side self-inductance (L RX ) and load resistance (R RX ), which can be calculated as in (18). Besides, for higher quality factors, the system gain decreases sharply when the operation frequency moves away from the resonant frequency

B. Design Steps
The design procedure starts with determining input/output voltage and power ratings. The VCPSM generates the input voltage, which can be calculated as in The field winding ratings specify the output voltage and the load resistance in the transformer model. The reflected (load) resistance (R Rx ) and voltage (U o ) values are calculated as in where R F is the resistance of the field winding and U F is the applied voltage of the field winding. Later on, it is required to select the quality factor, which determines the frequency control bandwidth. In the literature, Q is selected between 2 and 10 as a rule of thumb [39], [40]. After that, L Rx is calculated by (18), where the resonant frequency is selected close to the switching frequency of the motor drive. Besides, it is needed to select the coupling coefficient, which can be practically achieved up to 0.8. Then, L Tx can be calculated as in Finally, the compensation capacitance can be calculated as given in (23). The gain at the resonant frequency does not directly depend on the capacitance value, but it just shifts the resonant frequency as shown in Fig. 11. Upon calculations above, the designed parameters of the SN-WPT system are shown in Table I C V. EXPERIMENTAL VALIDATION An experimental setup consisting of a 3Φ-3 W GaN-based inverter and an SN-compensated WPT-based CFE system is established, as shown in Fig. 12. Table I presents the WPT system parameters achieved in the experimental setup. They are slightly different from the designed parameters due to the manufacturing tolerances. First, the proposed method is tested to validate  the mathematical model. Second, the field excitation system is tested under several operating conditions of the fundamental frequency, modulation index, and switching frequency. Finally, the proposed CFE system is concurrently operated with the EESM.

A. Input Excitation Voltage of the VSI
The voltage waveform between phase A and phase B is measured while SPWM is applied in different modulation indices. The normalized voltage waveform and its decomposition of the switching harmonic are shown in Fig. 13 for different modulation indices.
It is observed that a constant input excitation at a 0.44 normalized gain is achieved until the modulation index of 0.8. The value starts fluctuating in higher modulation indices, after which is named the uncontrollable region. However, there is also a small fluctuation in the controllable region, and it can be ignored since it is under 5% of 0.44.

B. WPT System
The WPT system is connected between phase A and phase B, like the previous test. The output of the WPT system is connected to the field of the EESM, but the phases of the EESM are not excited, which is equivalent to a stationary machine. First, the dc-link voltage and fundamental frequency are adjusted to 100 V and 100 Hz. The field current, Tx current, and input excitation voltage are measured for several modulation indices in the controllable region, as presented in Fig. 14. The mean currents of the field winding for the modulation index of 0, 0.25, 0.5, and 0.75 were measured at 4.83 A, 4.72 A, 4.95 A, and 4.93 A, respectively. Therefore, it is concluded that an almost constant field current can be achieved while changing the modulation index. These minor differences (maximum 5%) can be compensated by detuning the switching frequency, which will be discussed.
Second, the modulation index is kept at 0.6, and the fundamental frequency alters to 100 Hz from 200 Hz. The field current, Tx current, and input excitation voltage are given in Fig. 15. Accordingly, it is monitored that the field current is not affected by the fundamental frequency.
Finally, the modulation index and fundamental frequency are kept at 0.6 and 100 Hz. As presented in Fig. 16, the switching frequency is altered to 60 kHz from 62 kHz. In this case, the field current decreases from 5 A to 2.5 A. Hence, it is achieved that the field current could be regulated by the hybrid frequency detuning method.

C. Concurrent Operation of the CFE System and EESM
In this test, the phases of the EESM are also excited in addition to the field winding. The speed of EESM is increased from 52 to 101 r/min. The phase A current of the EESM and the field current are given in Fig. 17. As the speed of the motor increases, a slight difference in the field current has been observed, which is due to two main reasons. The first one is that the dead times are not involved in the mathematical model for ease of calculation. The second one is the additional voltage induced at the receiver coil by the mechanical rotation of the motor. Even though, experimentally, it has been observed that the deviation remains below 2%, both effects will be investigated in Section VI. This small error can also be compensated by detuning the switching frequency, as discussed before.

D. Effect of VCPSM on the Stator Current
The proposed VCPSM utilizes the magnitude of the first switching frequency for the field current control. Therefore, the proposed system generates higher effective voltage harmonics   than conventional SPWM, but the high phase inductance filters out these harmonics at the stator current. An exception would be motors with low inductance, such as air-cored machines, where the voltage harmonics may lead to increase current and torque ripples.
An RL load with an impedance equal to the stator winding is used in this test since the field windings could not be appropriately excited without the proposed method, causing an improper motor operation. The test is initialized using conventional  SPWM, which generates uncontrolled sideband and switching frequency. The field and stator currents measured as 2.5 A and 1.23 A RMS , also seen in Fig. 18. Then, the proposed method is employed. The field current achieved the desired magnitude of 4.55 A without a low-frequency ripple. Moreover, it is observed that the stator current remains constant throughout this test, as expected.

E. Dynamic Performance of the VCPSM
A step change in the reference of the field current (i.e., the output of the WPT system) is applied to evaluate the dynamic performance of the proposed method, as shown in Fig. 19. At t 1 , I F reference is changed, and I P H−A is deviated due to this change. At t 2 , I F is settled. At t 3 , the controller brings I P H−A to the previous value. Although the controller is not fully optimized, it is observed that the overshoot of the system is acceptable, and the steady-state error is negligible. Furthermore, a low-frequency fluctuation in the field current has been observed. This fluctuation develops independently of the proposed modulation method, and it stems from the magnetic field distortion phenomenon known as generated opposite magnetic field due to the stator current of the ac machine. This low-frequency fluctuation can be mitigated by a flux compensation control technique that adjusts the field winding excitation based on the load conditions (i.e., stator currents).

F. Effect of the VCPSM on the Efficiency
The losses of the motor drive were measured with and without the proposed method for the same modulation index and fundamental current, as presented in Table II. The input power increases when the proposed method is employed since the motor drive also excites the field winding. A minor increase in drive losses is observed. This increase causes the efficiency to decrease a little, but this efficiency decrease is negligible.

A. Effect of Mechanical Rotation of the Motor
The generalized formula of the induced voltage on the Rx coil (V RX-Induced (t)) is given in where L M (t) is the mutual inductance and I TX (t) is the transmitter current.
In an ideal case, the circular structure of the Tx and Rx coils creates a rotational symmetry, resulting in the derivative of the mutual inductance (L M ) being zero. In this case, we can only consider the ac excitation of the Tx coil. However, several nonidealities from manufacturing, such as asymmetry or axial misalignment of the coils, form a changing mutual inductance, which can be modeled as in where L M,DC is the average mutual inductance for a full rotation, ω m the mechanical angular frequency, andL M,AC and φ L M are the peak value and the phase of the fundamental fluctuation, respectively. Accordingly, two components of the induced voltage can be calculated as in whereÎ TX , ω s and φ I TX are the peak value, the electrical angular frequency, and the phase of the Tx current, respectively. As an example, the rotation speed of the motor in EVs can reach around 18 000 r/min, which equates to 300-Hz mechanical frequency. However, this effect can be neglected as the switching frequency is in the order of tens of kilohertz thanks to the WBG semiconductors. Moreover,L M,AC (t) is quite small compared to the L M (t) (maximum 5% of L M (t)). Considering all these, the impact of mechanical rotation on the field current is below 0.25% compared to the electrical excitation, even in the worst case scenario (500-Hz mechanical frequency, 10-kHz switching frequency, and mutual inductance fluctuation of 5%).

B. Effect of Dead Time
In practical terms, dead time is necessary to prevent short circuits or shoot-through currents that could damage the switches. Introducing dead time changes the effective duty cycle of the switches since the CPS is calculated as given in (11). Therefore, the changes in effective duty cycles influence the calculation of the required phase shift. However, the dead time is approximately between 0.5% and 2% of the switching interval. Consequently, since the dead time has little impact on the effective duty cycles, it can be ignored for ease of calculation.

C. Effect of the Switching Frequency
In the past, conventional inverters having Si-based semiconductors have allowed switching frequencies below 20 kHz [17] because the switching losses and thermal restrictions set the upper limit. Although the proposed method can be applied to Si-based inverters, this restricted switching frequency range makes the WPT system bulky since a lower switching frequency enlarges the Tx and Rx coils' size.
Fortunately nowadays, with the development of (WBG) devices such as GaN and SiC semiconductors, the switching frequency of the inverters has increased up to tens of kilohertz with thermally manageable switching losses [41], [42]. Eventually, by utilizing WBG semiconductors, a sweet spot in the switching frequency that makes the proposed method feasible can be found.

VII. CONCLUSION
This article proposes a novel WPT-based CFE system that can be integrated into conventional EESMs. Unlike traditional systems, the proposed method utilizes the existing motor drives and does not require extra converters on both the Tx and Rx sides, reducing the cost and complexity. This study also presents a novel VCPSM for independent control of the field and phase current while using conventional PWM methods. However, the proposed method does not control the field current to the full range. It only guarantees a constant excitation voltage for different modulation indices. Therefore, a hybrid control strategy consisting of the VCPSM and frequency detuning methods is also presented to regulate field current. A prototype with a three-phase GaN-based motor drive with 100-V dc-link and 60-kHz switching frequency was established to validate the proposed system. It was observed that the input excitation of the WPT system is kept constant at 44-V peak, which also means that the field current is kept almost constant at 5 A while changing the modulation index. Also, it was achieved that the field current was reduced from 5 to 2.5 A by detuning the switching frequency. Furthermore, it was experimentally observed that the proposed system has a negligible effect on the stator current and drive efficiency. Consequently, a cost-reduced CFE system for EESMs is achieved by only updating the control algorithm without using active converters.