A Rotating Restart Method for Scalar (v/f) Controlled Synchronous Reluctance Machine Drives Using a Single DC-Link Current Sensor

This paper presents a rotating restart method for $v/f$ scalar controlled Synchronous Reluctance Machines (SynRMs) using a single DC-link current sensor. In such a case, the initial rotor position and speed are required to restart the machine due to the absence of a position sensor. The method proposes to inject three active voltage vectors in the stationary reference frame to induce the phase currents required for estimating the rotor position and speed. In addition, the phase current reconstruction method is proposed to reduce the distortion of the measured phase currents caused by adopting a single DC-link current sensor and to consequently enhance the rotor position estimation accuracy. With the proposed method, the appropriate voltage vector can be applied to the machine, thus minimizing the inrush current during the restart. Furthermore, the proposed method only requires the machine parameters on the nameplate, and it does not require any additional machine-specific tuning processes. This paper proposes a simple restart method suitable for scalar-controlled SynRM drives with a single DC-link current sensor. The effectiveness of the proposed restart scheme is validated through the simulation and experimental results.


I. INTRODUCTION
Industrial machines are typically started from the zero speed regardless of the control methods. However, in some cases, the machine is rotating before being fed by the inverter due to the momentary power interruptions or the delivered torque from the external load. If the voltage is applied from the zero frequency while the rotor is rotating, an overcurrent trip can occur due to both the voltage and the frequency mismatch. Especially, this is a serious problem in many applications with large shaft inertia because it may take several minutes for the machine to stop completely. In such cases, a flying restart would be a beneficial strategy to improve the productivity and time efficiency in industrial applications, as the machines can be started without waiting for them to reach the zero speed.
The associate editor coordinating the review of this manuscript and approving it for publication was Atif Iqbal .
Three-phase voltage source inverters have been widely used in variable frequency drive applications. In such systems, the motor current feedback signals are essential for the control systems, and two or three current sensors are usually required. However, the use of sensors generally increases the cost, volume, weight, and complexity. In low-cost drive systems, such as fans or pumps, the use of sensors should be minimized. Therefore, the control strategies of drive systems that use a single DC-link current sensor have been intensively investigated [1]- [5]. In addition, the use of a single DC-link current sensor removes the undesirable unbalance of the three-phase currents caused by the DC-offset and the gain sensitivity of the phase current sensors [3]. This work focuses on the inverter systems only using a single DC-link current sensor to drive AC machines.
Recently, SynRMs have been widely used in many industrial applications, as they offer higher power density and efficiency in comparison with induction machines (IMs), VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ and they also cost less than permanent magnet synchronous machines (PMSMs) [6], [7]. Moreover, SynRMs are controlled in v/f mode in many applications that do not require high dynamic performance, such as fans or pumps, so as to ensure easier commissioning by the endusers [8], [9].
The v/f scalar control only requires a few machine parameters, such as the machine rating and the V -f ratio. The goal of this work is to develop a restart method for scalar-controlled SynRMs that drive high inertia loads using a single DC-link current sensor. Various methods for estimating the machine speed have been proposed for IMs [10]- [17]. The proposed approach in [10]- [15] uses a frequency search method relying on the slip information because the stator current is minimized when the searching frequency reaches the rotor rotational speed. However, these methods are not suitable for SynRMs because the rotor current is not conducted in SynRMs. The approach in [16], [17] utilizes an adaptive flux observer and requires the DC current injection to estimate the rotor rotational speed. However, these methods require accurate machine parameter information and current controllers.
In the case of PMSMs, an approach in [18]- [22] was recently proposed for estimating the machine speed and position. These PMSM restart methods inject zero-voltage pulses to extract information about the rotor position from the current vector induced by the back electromotive force (EMF). However, this voltage injection method cannot be applied to restart SynRMs, as zero-voltage pulses do not induce the stator current. In SynRMs, if the current is not flowing through the stator winding, the back-EMF is not induced due to the absence of permanent magnets in the rotor even if the machine is rotating.
The high-frequency signal injection method can be used as an alternative method to estimate the rotor rotational speed and position [23]- [29], and it can accurately estimate the rotor position and speed even when the speed is near zero. However, this method requires the complex signal demodulation process to extract the rotor position information and the machine-specific tuning to maintain the constant bandwidth of the state filter or the observer. Therefore, it would sacrifice the simplicity of scalar control and increase the complexity of the restart algorithm. The method in [30] injects v 1 active voltage pulses to induce the stator current, and the rotor position angle and speed are extracted from the induced stator current. This method only requires information on the motor nameplate and the three-phase currents that are measured by the phase current sensors in the inverter. However, if the inverter system only uses a single DC-link current sensor to measure the machine current, the three-phase currents cannot be simultaneously measured with one active voltage vector during a single switching period. Therefore, the method in [30] is not applicable for inverter systems that only use a single DC-link current sensor. A restart method for SynRM drive systems that only uses a single DC-link current sensor was proposed in [31]; however, this method has a significant  position estimation error because of the used current sampling method.
This paper presents a restart method that injects three active voltage vectors to measure three-phase currents by using a single DC-link current sensor. The paper also proposes a current reconstruction algorithm to reduce the distortion of the phase currents measured by the DC-link current sensor and to consequently enhance the accuracy of the rotor position and speed estimation. The detailed implementation method is provided, and the simulation and experimental results are presented to verify the performance of the proposed approach.

II. SCALAR CONTROL FOR SynRM DRIVE
From Fig. 1, the equation describing the electrical dynamics of SynRM machines in the rotor reference frame can be represented as follows [29]: where p is the derivative operator, r s is the stator winding resistance, v r d and v r q are the d-q axis stator input voltages in the synchronous reference frame, i r d and i r q are the d-q axis stator currents in the rotor reference frame, L d and L q are the d-q axis stator inductances, and ω r is the rotor's electrical speed.
In the v/f control, the γ -δ axis synchronous reference frame is generally used for the control, where the δ-axis is aligned with the stator voltage vector. Only the amplitude and the frequency of the voltage vector are controlled without the information of the rotor position; therefore, the v/f control can easily be implemented compared to the vector control. Fig. 2 shows the phasor diagram of the stator voltage and current vectors in the γ -δ and d-q synchronous reference frames. The magnitude of the voltage command V s in the v/f control is determined to maintain the constant stator flux linkage λ s so as to have the same torque capability in all operating ranges [8], [9]. E s is the voltage induced by the stator flux linkage. The stator command voltage can be instantaneously calculated as [9]: where ω 0 is the speed command, V rated is the rated voltage, ω rated is the rated speed, I s is the magnitude of the current vector, and ϕ is the power factor. The magnitude of the current vector can be calculated from the three-phase currents measured by the DC-link current sensor [1]- [5]. In (2), the stator resistance voltage drop is compensated to maintain a constant flux. Also, the term I s cosϕ can be instantaneously calculated as: where θ v is the position angle of the stator voltage vector in the stationary reference frame. The open-loop v/f control of SynRM easily loses synchronization under load disturbances, as the synchronous motor is inherently unstable due to the absence of damper windings [8], [9]. Therefore, the v/f control for SynRMs requires a stabilizing feedback loop to ensure stable operation. Fig. 3 shows the conventional v/f control method with a stabilizing loop [9]. The frequency modulation signal ω e is generated in the stabilizing loop to tolerate the load disturbance. In the stabilizing loop, the calculated input power passes through the high-pass filter to extract the power perturbation P e . The proportional gain k p is properly selected to place the system poles in the stable region [9].

III. PROPOSED RESTART METHOD
This work aims to develop a restart algorithm suitable for scalar controlled SynRM drives using a single DC-link current sensor. The initial rotor position and speed are required to restart the motor in the free-running state. This section describes how the proposed method estimates the rotor position and speed during the free running of the rotor.

A. APPLYING ACTIVE VOLTAGE PULSES
The proposed method basically excites the machine with v 1 , v 3 , and v 5 voltage vector pulses to measure the resulting stator current. In Fig. 4, v 1 , v 3 , and v 5 voltage vectors are applied in sequence at times t 1 , t 2 , and t 3 , respectively, and this voltage injection process is continuously repeated while estimating the rotor position and speed of the motor in the free-running state. When applying active voltage vector pulses to a machine, the pulse time (t pulse ) of the applied voltages is assumed to be much shorter than the stator time constants (τ d = L d /r s , τ q = L q /r s ). Thus, the stator resistance r s can be neglected, and the induced current by the applied voltage pulse can be expressed by simplifying (1) as: The active voltage vectors applied to excite the machine can be expressed in the synchronous rotor reference frame as: Here, V dc is the DC-link voltage of the voltage source inverter (VSI), θ r is the actual electric rotor angle, and n is the number of the applied voltage vectors (n = 1, 3, 5). When the voltage vector v 1 is injected to the machine, the d-q axis voltage can be expressed as: Since the machine is driving a high inertia load, the rotor speed ω r can be assumed constant. Thus, the d-q axis current in the rotor reference frame that is driven by the voltage VOLUME 8, 2020 vector v 1 can be obtained by solving (4) through the Laplace transform: where t pulse is the applied pulse time of the voltage v 1 . The initial state of the d-q axis currents is zero because the machine is in the free-running state. Since t pulse is short enough, cos(ω r t pulse ) and sin(ω r t pulse ) can be considered, respectively, as 1 and ω r t pulse . Then, the d-q axis current of (7) can then be simplified as: From (8), the induced current in the proposed method does not depend on the rotor speed. The d-q axis current can be transformed using the inverse Park's transformation to threephase currents in the stationary reference frame as: The three-phase currents in (9) consist of two terms. The first term is the DC-offset current, and the second term is the oscillated portion with respect to the rotor position. The rotor position can be estimated by extracting the AC term from the induced stator current. Also, it can be noted that the frequency of the AC current is two times faster than the rotor electrical frequency.

B. ROTOR POSITION AND SPEED ESTIMATION
This work focuses on developing the restart method by only using a DC-link current sensor without using phase current sensors. In such a case, the three-phase currents cannot be simultaneously measured while estimating the rotor position and speed. Thus, v 1 , v 3 , and v 5 voltage pulses are applied in sequence to measure the three-phase currents as shown in Fig. 5. When an active voltage v 1 is applied to the machine at t 1 , the phase a current is measured by the DC-link current sensor [1]- [5]. Then, the measured phase a current is held until the next v 1 voltage is applied at t 4 . Similarly, the phase b and c currents are respectively measured when the v 3 and the v 5 voltage pulses are applied. t sw is the switching period   of the inverter. The active voltage pulses are injected every two switching periods to induce the current from zero. This is because the initial state of the stator current is zero when deriving the induced current in (7)- (9). This method can also use v 2 , v 4 , and v 6 voltage vector pulses to measure the threephase currents. For example, when v 2 voltage pulse is applied, the DC-link current in the inverter is equal to the negative value of phase c current. Fig. 6 shows the simulation results of the three-phase currents in the estimation mode when the v 1 , v 3 , and v 5 voltage vectors are applied to the machine in consecutive order. The machine parameters used for the simulation are listed in Table 1. The rotor speed in the simulation is 1,800 rpm, and the applied voltage pulse duty cycle is 50%. The figure on the top shows the actual discontinuous three-phase currents induced by the voltage pulses, the second waveforms show the sampled three-phase currents that are updated at the end of each applied voltage pulse as shown in Fig. 5, and the bottom one shows the actual rotor position. The sampled three-phase currents have a negative sequence although v 1 , v 3 , and v 5 are applied in a positive sequence. The resulting three-phase currents by the v 1 , v 3 , and v 5 voltage vector pulses are expressed as: where i a , i b , and i c are the induced currents at t 1 , t 2 , and t 3 , respectively. As previously mentioned, the controller holds each sampled phase current value until the next instant of applying the same voltage vector. The three-phase currents measured at t 1 , t 2 , and t 3 are used to estimate the rotor position in every switching period. Before estimating the rotor position, the DC-offset terms in (10) should be removed from the measured three-phase currents. The DC-offset current can be obtained by averaging the three-phase currents for several periods of the machine fundamental frequency. Then, the AC current terms (i a_AC , i b_AC , and i c_AC ) are calculated by subtracting the DC-offset from the measured three-phase currents as: i a_AC (t 1 ) = I mag cos 2θ r(t1) ; i b_AC (t 2 ) = I mag cos 2θ r(t2) + 2π 3 ; i c_AC (t 3 ) = I mag cos 2θ r(t3) − 2π 3 Here, I mag is the amplitude of the current, and it can be presented as V dc · t pulse /3·(1/L d − 1/L q ). With the Clarke transformation, the α-β axis currents i s α_AC and i s β_AC in the stationary reference frame can be obtained. As a result, the rotor position can be estimated by injecting the active voltage pulses as: where θ est is the estimated rotor angle, θ r is the actual rotor angle, and θ error is the error term of the estimated rotor angle. The estimated position angle inherently has an estimation error due to the way it samples and holds the motor current. This error increases with the increase in the rotor speed due to the limited samples of the current measurements. The current reconstruction method is introduced to reduce the error in the rotor position estimation. The difference in the instantaneous phase a current between the two sequential switching periods can be defined as: where θ I and ω I are the estimated angle and the estimated speed of the current vector in (11), respectively. As previously mentioned, the rotational speed ω I of the current vector is two times faster than the rotor electrical speed ω r . I mag is the phase current magnitude, and it can be calculated from the α-β axis currents i s α_AC and i s β_AC . Since t sw is short enough, cos(ω I t sw ) and sin(ω I t sw ) can be respectively considered as 1 and ω I t sw . Then, (13) can be simplified as: The phase a current is reconstructed using (14) with the estimated current angle, speed, and magnitude until the next v 1 voltage pulse is applied to the machine. In the same way, this reconstruction method can be applied to the phase b and c currents. The three-phase currents are only reconstructed with the following when each phase current is not updated with the DC-link current sensor.
where k indicates the current switching period and k-1 indicates the previous switching period. Fig. 7 shows the simulation results of the current vector angle estimation when the proposed current reconstruction method is used. The rotor speed in this simulation is 1,800 rpm. The top plot shows the sampled phase a current at every six switching periods as shown in Fig. 5. The ideal phase a current is also plotted to clearly demonstrate the distortion of the sampled phase current. The second plot shows the actual current vector position and the current vector position estimated from the sampled three-phase currents. The bottom plot shows the error of the estimated current vector position. In the left half region, the phase current is updated every six switching periods, and the current reconstruction method is not used. This phase current distortion causes a significant error in the estimation of the current vector position. The maximum estimation angle error of the current vector position is about 30 [deg.] at this speed, which may cause a restart failure due to the inrush current at the VOLUME 8, 2020  instant of restarting. In the right half region, the current reconstruction method is used. The phase current is updated every six switching periods with the current measured with the DC-link current sensor, and the phase current is reconstructed every switching period using (15). The distortion of the phase current is significantly reduced. As a result, the accuracy of the position estimation is enhanced. Fig. 8 shows the proposed block diagram for estimating the rotor position angle and the rotor speed while using the phase current reconstruction. The estimated rotor position angle passes through the PI type state filter to minimize the estimation error. The transfer function of the PI type state filter is as follows:θ est θ est = K p s + K I s 2 + K P s + K I (16) The gains are set to place all the closed-loop eigenvalues at 100 rad/s. The rotor speed can be estimated by the PI type state filter as shown in Fig. 9, and the additional low-pass filter (LPF) is used to reduce the ripple of the speed extracted from the state filter. The cutoff frequency of the LPF is selected as 10 Hz. The estimated speed, which passes through the LPF, is used to reconstruct the phase currents and restart the machine. The delay of position and speed estimation caused by the PI type state filter and the LPF is negligible because the rotor speed variation is almost constant, as the machine drives a high inertia load. Fig. 10 shows the proposed complete scheme for restarting the SynRM. In the normal operation mode, the machine is controlled with the v/f scalar control with the modulation frequency ω e to ensure stable operation in all the operating ranges [9]. The controller is set with the motor nameplate parameters, and the drive system only uses a single DC-link current sensor. When a restart is required, the rotor position and speed of the free-running motor are estimated with the three-phase current measured by the DC-link current sensor. The dotted block is the proposed part that was  shown in Fig. 8 for the rotor position and speed estimation. Fig. 11 shows the schematic of a 3-phase inverter with a single DC-link current sensor.

C. IMPLEMENTATION OF THE PROPOSED RESTART METHOD
The procedure for implementing the proposed restart method is explained in this section. First, the voltage vectors v 1 , v 3 , and v 5 are applied to the machine, which maintains its free-running state due to the high inertia load. The initial duty of the applied voltage is set to 50%. The magnitude of the phase current induced by the v 1 , v 3 , and v 5 voltage pulses is calculated using (8) as: where I s is the magnitude of the phase current vector. At this point, it should be noted that this current magnitude cannot be calculated before applying the voltage pulses because the d-q axis inductance is not generally listed on the motor nameplate. From (17), if the DC-link voltage is too high or the applied voltage pulse time is too long, an undesired overcurrent can take place. Therefore, a strategy for adjusting the pulse duty is proposed using the measured current magnitude and the machine current rating. If the magnitude of the phase current that is induced by the first voltage pulse exceeds the level of the rated current, the new pulse duty is calculated as: t pulse_new = I rated 10 I s t pulse (18) where I rated is the rated current and I s is the magnitude of the phase current caused by the first voltage pulse. The new pulse duty is then calculated to induce a much smaller current than the motor rated current. Then, the voltage pulses are applied again with the new pulse duty (t pulse_new ). Another concern is that the electromagnetic torque is generated by the applied voltage pulses during the estimation  of the rotor position and speed. The torque equation of the SynRM is given by [29]: where P is the machine pole number. The torque generated by the current induced by the v 1 voltage pulse is calculated by substituting (8) into (19) as: Similarly, when the v 3 and v 5 voltage pulses are applied, the magnitude of the generated torque is the same as in (20). This resulting torque is negligible if the voltage pulse time, which mainly depends on the switching period, is sufficiently short. In addition, the average torque generated for a single revolution is zero; therefore, it does not cause a high braking torque. Fig. 12 shows the simulation results when applying the voltage pulses to the machine in the estimation mode. The rotor speed in this simulation is 1,800 rpm, and the applied voltage pulse duty cycle is 50%. The top plot shows the actual three-phase currents, the second plot shows the torque generated by the induced current, and the bottom plot shows the actual rotor position while injecting the active voltage pulses. Next, the induced phase currents are averaged to calculate the DC-offset component, which is essential for extracting the three AC current terms (i abc_AC ). With the extracted AC current terms, the rotor position and speed are estimated.
The estimated position angle (θ est ) is aligned with the d-axis in the rotor reference frame. The angle should be compensated for the voltage to be applied to the q-axis so as to ensure a positive electric torque at the restart instant.
The compensated angle (θ comp ) is given by: By adding π/2 to θ est , the estimated angle can be aligned to the q-axis. The third term in (21) is to compensate for the current sampling delay (ω est t sw ) and the switching period delay (ω est t sw /2) [22], and t sw is the PWM switching period. When the stator voltage (V r q = V and V r d = 0) is applied to the q-axis, the resulting d-q axis current is calculated from (4) as: The d-q axis current in the rotor reference frame is always positive at the restart instant if the pulse time is short enough. Finally, the stator voltage is applied to restart the motor. The voltage magnitude is gradually increased from zero to avoid the inrush current, and the applied voltage frequency is fixed to the estimated rotor electrical speed. When the magnitude of the voltage reaches the rated v/f value, the increase is stopped.

IV. EXPERIMENTAL RESULTS
Experiments were conducted to validate the performance of the proposed restart method. In Fig. 13, the dynamo testbed consists of the tested SynRM and an induction motor as a load machine. The SynRM parameters are given in Table 1. The VSI used for driving the test motor includes both phase current sensors and a DC-link current sensor. However, a DC-link current sensor is only used to implement the proposed restart method. The phase current sensors are used for validating the proposed restart method by monitoring the actual current. The load motor is fed by another commercial VSI.
The experimental results in Fig. 14 demonstrate the effectiveness of the current reconstruction method in reducing the current distortion caused by using the DC-link current sensor in the estimation mode, thus enhancing the accuracy of rotor position estimation. An encoder sensor is used to only monitor the actual rotor position so as to validate the proposed current reconstruction method. In the left half region of the plot, the phase a current is updated with the DC-link current sensor when the v 1 voltage pulses are applied and the current reconstruction method is not enabled. The blue line is the AC current term calculated by subtracting the DC-offset from the measured phase a current. The yellow line is the actual rotor position angle θ act , and the purple line is the rotor angle θ est estimated using (11) and (12) with the AC current terms of the three-phase currents. From (12), the range of the estimated rotor angle is from −π/2 to π/2 because the output of the arctangent function is divided by 2. The estimated rotor angle has a significant error in comparison with the actual rotor position. In the right half region, the phase current is updated every six switching periods by the DC-link current sensor, and the phase current is reconstructed every switching period  using (15). The blue line shows the reconstructed phase a current. After enabling the proposed current reconstruction method, the phase current distortion is significantly reduced, and the accuracy of the rotor position estimation is enhanced. Fig. 15 shows the experimental results that validate the performance of the rotor speed estimation method when the rotor speed is reduced. First, the rotor was operating at 1,800 rpm. Next, the inverter was intentionally stopped, and the voltage pulses were applied to estimate the rotor position and speed. The blue line is the actual rotor speed, and the purple line is the estimated rotor speed. The results of this test show that the proposed method has a good performance in terms of speed estimation. Fig. 16 shows the experimental results of the proposed rotating restart method when the mechanical rotor speed is about 70 rpm, 400 rpm, and 1,600 rpm. The restart tests were implemented with the following steps. The motor was operating at the reference speeds 90 rpm, 450 rpm, and 1,800 rpm. The inverter driving the SynRM was intentionally stopped for 0.3 second in Fig. 16(a). Fig. 16(b) and (c) are the cases when the inverter was stopped for 1.5 seconds. The motor was decelerated due to the influence of friction. Then, the rotor position and speed were estimated by injecting the v 1 , v 3 , and v 5 voltage pulses, and the motor was again fed by the inverter. The estimation process of the position and speed lasts for 0.7 second in Fig. 16(a) and 1.0 seconds in Fig. 16(b) and (c), respectively. In Fig. 16, the rotor angle (yellow line) and the rotor speed (purple line) were estimated from the measured currents (green line). The blue line plots the applied stator voltage at the restart instant, and the command voltage is calculated from the rated v/f ratio. The magnitude of the applied stator voltage was gradually increased from zero to prevent the inrush current. The results of this test verify that the proposed method can successfully estimate the rotor position and speed and that a restart can be implemented without causing inrush currents. Fig. 17 shows the experimental results of the existing restart method presented in [31] for scalar controlled SynRM drives with a single DC-link current sensor. The test was conducted at the rotor speed 450 rpm. In contrast to the proposed method, the existing method does not include the phase current reconstruction algorithm. This method has a significant rotor position estimation error as shown in the left half region of Fig. 14. This causes larger current oscillations at the restart instant compared to the proposed method in Fig. 16(b).

V. CONCLUSION
This paper presents a restart method suitable for scalar v/f controlled SynRM drives with a single DC-link current sensor. This study proposes the three active voltage vector injection method to measure the three-phase currents with a DC-link current sensor in the estimation mode, and it presents the rotor position and speed estimation method from the induced phase currents. In addition, the proposed current reconstruction algorithm can reduce the distortion of the measured phase currents caused by using the single DC-link current sensor and enhance the accuracy of rotor position estimation.
The advantage of the proposed method is that the performance of the rotor speed and position estimation is not affected by the accuracy of the machine parameters because only the ratings listed on the nameplate are necessary for the proposed method. In addition, this method injects voltage pulses in the stationary reference frame and measures only the DC-link current. Then, the rotor position information can be extracted by averaging the measured current. Therefore, the proposed method is simpler than the conventional methods that require the complex signal demodulation process and the machine-specific tuning. The performance of the proposed method was verified by the experimental results.