Carrier-Based Discontinuous PWM Method for Five-Leg Inverter

This paper proposes a rotation carrier-based discontinuous pulse width modulation (CB-DPWM) method for the five-leg inverter (FLI). The FLI based on two-level topology consists of 10 switching devices for driving dual motors. Therefore, two switching devices can be reduced to compare the configuration using two three-leg inverters for driving dual motors. The proposed pulse width modulation (PWM) method is based on the reference signals which are used in existing carrier-based continuous pulse width modulation (CB-CPWM) method for FLI. In the proposed rotation CB-DPWM method, one of five-leg is periodically clamped to <inline-formula> <tex-math notation="LaTeX">$V_{dc}$ </tex-math></inline-formula><italic>/2</italic> or − <inline-formula> <tex-math notation="LaTeX">$V_{dc}$ </tex-math></inline-formula><italic>/2</italic> by adding the offset voltage to the reference voltages of the existing CB-CPWM method. The five reference voltages for all legs are considered to calculate the offset voltage of the proposed rotation CB-DPWM method. Consequently, since the proposed rotation CB-DPWM method has less switching than the existing CB-CPWM, the switching loss can be reduced and it results in the efficiency improvement. Simulation and experimental results confirm the effectiveness and feasibility of the proposed method.


I. INTRODUCTION
The dual motor drive systems (DMDSs) are widely used in many industrial fields such as propulsion system, ventilation system, textile, paper manufacturing, conveyer system and so on, and they have proved to be reliable and inexpensive. Generally, each motor of DMDSs requires a three phase voltage source inverter (VSI) for driving them independently, and two inverters share a common DC-link input voltage; therefore, a total of twelve switches are required. Recently, DMDSs have been researched for saving space and cost, and reducing power losses. Reducing the number of switching devices is desirable; therefore, many research results have shown simplified configurations for DMDSs. For example, a reducedswitch-count inverter [1]- [3], a nine-switch inverter [4]- [7], a mono inverter [8]- [10], a five-leg inverter [11]- [26], and so on.
The five-leg inverter (FLI) has a simple structure among several topologies, and is widely used to independently drive The associate editor coordinating the review of this manuscript and approving it for publication was Zhilei Yao . two induction motors. One phase of each three phase motor is connected to the same leg of FLI. The remaining phases of each three phase motor are connected to the remaining legs one by one as shown in Fig. 1. Therefore, FLI can save two switching devices compared with the dual three-leg inverter system. Mostly the reference voltages of the common leg for two induction motors are individual, as a result, the conventional PWM method cannot be applied directly for FLI because the common leg does not satisfy the control requirements of two induction motors. In order to overcome this drawback, however, many studies have suggested PWM methods for FLI such as the carrier-based sinusoidal PWM (CB-SPWM) and the carrier-based space vector PWM (CB-SVPWM).
There are several control methods for driving dual motors using FLI [11]- [26]. The similarity of these control methods is that the sum of the output voltages supplied to the dual motors is limited to the DC-link voltage. In addition, the switching devices of the common leg must withstand up to twice the current of the other leg. In this case, the different switching devices should be used for the 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/ FIGURE 1. Five-leg inverter system with two induction motors.
common, or the capacity of the FLI should be used only 50%. Reference [24] has been studied to overcome this drawback. This advanced speed control method is suitable for maintaining constant speed regardless of any load conditions. Furthermore, the maximum value of common leg current is always smaller than that of the other leg due to the angle controller which keeps the current phase difference of two induction motors connected to the common leg to 180 degrees. Therefore, it is not necessary to increase the switching device rating characteristic of common leg. The advanced control method can be effectively used in many industrial fields such as air conditioning system in railway or vehicle, dual cement kiln drive, conveyor belts and so on [38]- [40]. In this case, the FLI driving two motors independently can be used most efficiently when the two motors operate at the same speed, and the electrical phase difference between the two motors is controlled to 180 degrees. Therefore, the advanced control is applied as the control method of this paper. This paper proposes a rotation carrier based discontinuous PWM (CB-DPWM) method to increase the system efficiency. The CB-DPWM method has been well-known for the switching loss reduction of switching device. The CB-DPWM method leads the switching devices operation in only two of three legs. The discontinuous modulation section without switching can be set up to 120 degrees of the fundamental period of the reference voltage in three-leg inverter [27]- [37]. However, the PWM methods introduced in many papers related to FLI are typical continuous modulation schemes in which all switching devices always operates. Especially, [36] and [37] introduce various DPWM methods applied to FLI. Both papers implement various DPWM methods using the space vector modulation (SVM) method and analyze the characteristics of various DPWM methods. In general, SVM method requires a lot of computation time to apply the micro-controller unit (MCU). SVM method has to select the switching vector corresponding to the reference voltage from the vector table and calculate the dwelling time for every control period. However, many studies have found modulation methods that can have the same effect as SVM method when an appropriate offset voltage is applied to the CB-SPWM method [41]- [43]. In addition, DPWMMAX, which clamps the reference voltage to 0.5V dc , and DPWMMIN, which clamps to −0.5V dc , increase conduction loss to one of the two switches in the half-bridge leg. It leads to thermal unbalance between legs. In [37], various DPWM methods were implemented and analyzed based on the space vector modulation method for a five phase induction motor. The shift of five-phase induction motor between each phase voltage is 72( = 2π/5) degrees. Among the various DPWM methods introduced in [37], DPWM1 method applies DPWMMAX and DPWMMIN alternately to the reference voltage every 36 degrees. However, DPWM1 method in [37] is not suitable for driving dual motor system using the advanced speed control method because the shift of five phase voltages is not fixed at 72 degrees. To overcome these drawbacks, this paper proposes a rotation CB-DPWM method. The proposed rotation CB-DPWM method simply implements the DPWM method using the carrier-based modulation method with the offset voltage. Using the proposed method, the computation time can be shorter than that of SVM method. In addition, the proposed rotation CB-DPWM method alternately applies the offset voltage for DPWM method every reference voltage period. Therefore, it is possible to increase the system efficiency and balance the loss of the switching devices. The simulation and experimental results are implemented to confirm the feasibility of the proposed method. Fig. 1 shows the main circuit of the FLI with the two induction motors. The FLI consists of five legs with ten switching devices, a DC-link source (V dc ), and two induction motors, respectively. The leg A and B are connected directly to phases a1 and b1 of the induction motor 1 (IM1), respectively. Similarly, the leg D and E are connected directly to phases a2 and b2 of the induction motor 2 (IM2), respectively. As a result, there is a common leg C, which is shared by both phase c1 of IM1 and phase c2 of IM2. It is possible to reduce the number of switching devices and simplify the circuit structure compared with conventional configuration consisting two three-leg inverters.

B. ADVANCED SPEED CONTROL METHOD
In general, when two induction motors connected to FLI are driven in synchronization, the maximum current of the common leg flows up to twice the other leg current. The maximum current (I c,peak ) of the common leg considering the load condition is expressed as where i c,m1 and i c,m2 are the C-phase current of two induction motors, and α represents the angle between i c,m1 and i c,m2 , respectively. As shown in (1), if α is to be zero, the magnitude of the common leg current is twice as large as that of other legs. To overcome this drawback, therefore, [24] proposes two control schemes.
1) The angle controller in [24] minimizes I c,peak of FLI by maintaining the rotor flux angle difference between two induction motors in reverse.
2) The slip controller in [24] maintains the same speed of both induction motors regardless of the load conditions. Fig. 2 shows the simplified control block diagram of the advanced speed controller proposed in [24]. T m1,load and T m2,load represent the load torque condition of each motor, ω r,m1 and ω r,m2 represent the speed of each motor, θ m1 and θ m2 represent the electrical angle of each motor, ω * r,m1 and ω * r,m2 represent the reference speed of each motor, I * dqen (n = 1, 2) represents the d-q axis reference current, I dqen (n = 1, 2) represents the d-q axis current, I * den,r (n = 1, 2) represents the d axis rated reference current, I * den,c (n = 1, 2) represents the output of the slip controller, and S x (x = a, b, c, d, e) represents the gate signal, respectively. First, the load torques of two induction motors are compared. Next, the induction motor with a larger load torque is driven by speed controller. At this time, the speed of the other induction motor is synchronized with the speed of the induction motor having a large load torque through the slip controller. In addition, the angle controller is used to maintain the rotor flux angle between two induction motors as 180 degrees to minimize the common leg current of FLI.

III. CB-PWM FOR FLI
The CB-PWM method for FLI has been continuously developed through many studies. Among existing CB-PWM methods for FLI, the double zero sequence (DZS) method used in this paper is the simplest method [11]- [13]. The DZS method uses two offset voltages called as the zero-sequence signals. Fig. 3 shows the modulation scheme using the DZS method. In general, the pole voltage of inverter is determined by the switching devices on-off state of each phase. The reference voltages (V * as,n , V * bs,n , and V * cs,n ) determine the switching devices on-off state of each phase in the CB-PWM method and can be expressed as where V n is the pole voltage amplitude and f n is the frequency of stator electrical speed for IM1 and IM2, respectively. V * as,n , V * bs,n , and V * cs,n are called as the reference voltage of CB-SPWM method.
To extend the linear region to 1.1547 times wider than the SPWM method [11], the offset voltage (V offset,n ) is used and calculated as v offset,n = − V max,n + V min,n 2 , (n = 1, 2).
where V max,n represents the maximum reference voltage and V min,n represents the minimum reference voltage, respectively. Using V offset,n , which is first zero-sequence signal of DZS, it is possible to obtain similar results with the third harmonic injection modulation scheme of three-leg inverter. This method is called CB-SVPWM. In the CB-SVPWM, the reference voltages (V * an,n , V * bn,n , and V * cn,n ) of each motor are expressed as (4) by adding the V offset,n to (2).
The six reference voltages calculated from (4) should be reduced to five corresponding to the number of inverter legs. The C-phase reference voltage, V * cn,2 , is added as an offset voltage to the A-and B-phase reference voltages of IM1, whereas the C-phase reference voltage, V * cn,1 , is added as an offset voltage to the A-and B-phase reference voltages of IM2. This offset voltage is a zero-sequence component and does not appear in the line-to-line voltage of each induction motors [11]. Therefore, the final reference voltages (V * as , V * bs , V * cs , V * ds , and V * es ) for FLI can be expressed as Therefore, the FLI operates with the continuous PWM in the linear region, as if both induction motors are driven by independent three-phase inverters. In addition, the available DC-link voltage depends on the magnitude of each reference voltage. For example, if the modulation index Fig.4 shows the process of generating the final reference voltages according to α. The final reference voltages for the FLI exist in the linear region. In addition, when the advanced speed control method is applied, the final reference voltages of FLI are shown in Fig. 4(a).

IV. PROPOSED ROTATION CB-DPWM FOR FLI
Generally, among the various voltage modulation methods, a CB-CPWM method in which all switching devices are switched at all times within a switching cycle is widely used. Recently, many studies on the inverter efficiency improvement have been conducted. Among several switching modulation methods, the DPWM method reduces switching loss by fixing the switch state to ON or OFF for a certain time. This paper proposes a CB-DPWM method for FLI that increases the inverter system efficiency. The proposed rotation CB-DPWM method is implemented by clamping one of five pole voltages of FLI to half of DC-link voltage using the offset voltage (V offset,DPWM ). Fig. 5 shows the voltage modulation block diagram of the proposed CB-DPWM method. The V offset,DPWM for proposed CB-DPWM method is calculated by using V * as , V * bs , V * cs , V * ds , and V * es of existing CB-SVPWM method. For five reference voltages of FLI, the offset voltage for the proposed CB-DPWM method should be selected so that the reference voltages limit the following: Therefore, the offset voltage limitation for the proposed CB-DPWM is expressed as Since FLI has five reference voltages unlike the three-leg voltage inverter, the maximum and minimum value (V max,FLI and V min,FLI ) of the five reference voltages are calculated instantaneously as Using (7) and (8), the V offset,DPWM for proposed CB-DPWM method of FLI is calculated as Fig. 6 shows the five reference voltages and the offset voltages of the FLI with the advanced speed control method. When the advanced speed control method is applied, the C-phase reference voltage cancels out because the phase difference of the output voltages supplied to the two induction motors is 180 degrees. In addition, the A-and D-phase reference voltage are symmetrical to each other, and B-and E-phase reference voltage are also symmetrical to each other. The offset voltage for the proposed CB-DPWM method is clamped to 0.5V dc or −0.5V dc , respectively, when the magnitude of each reference voltage is at its maximum or minimum. Therefore, two offset voltages for the proposed CB-DPWM are shown in (9). To apply the proposed CB-DPWM to FLI, only one of two offset voltages is used. In this case, however, one of the two switches in each leg is stressed. To address this drawback, this paper proposes the rotation CB-DPWM method as shown in Fig. 7. When the proposed rotation CB-DPWM method is applied to FLI, the final reference voltage is clamped to 0.5V dc at the maximum value among the five reference voltages during one period of the reference voltage, and in next period of the reference voltage, the final reference voltage is clamped to −0.5V dc at the minimum value among the five reference voltages. Therefore, V offset,DPWM is expressed as  Similarly, as shown in blue dashed line in Fig. 8, during a section where the V * ds is the largest in positive, V * ds is fixed at V dc /2 to keep the top switch of D-phase ON state. The reference voltage in the other section is changed to match the fundamental voltage. This operation is repeated based on one cycle of the reference voltage. Fig. 9 shows the five reference voltages of the proposed rotation CB-DPWM method in MI m1 = MI m2 = 0.35. Comparing Fig. 8 with Fig. 9, when the MI decreases, V offset,DPWM must be large because a large clamping voltage is required for the proposed rotation CB-DPWM method. As shown in Fig. 9, the proposed rotation CB-DPWM method can be applied to FLI even if the MI is decreased by using five reference voltages. Fig. 10 shows the reference voltages of the proposed rotation CB-DPWM method when the electrical angle between VOLUME 8, 2020 two induction motors is 90 degrees. Similarly, the proposed rotation CB-DPWM method can be implemented using V offset,DPWM with different electrical angles between the two induction motors. In this case, the proposed rotation CB-DPWM method can be applied to FLI, but the current value of C-phase increases as described previously.

V. SIMULATION RESULTS
The simulation of FLI with proposed rotation CB-DPWM method was implemented by PSIM software to verify the operation of the proposed method. The simulation circuit is the same with Fig. 1 and the parameters of IM1 and IM2 are stated in Table 1. For the verification of the proposed DPWM method, the speed of two induction motors connected to FLI was controlled at 300rpm. In addition, the simulation was conducted under the same load conditions for simplicity. Fig. 11 shows the simulation results of the reference voltage (V * as , V * bs , V * cs , V * ds , and V * es ) with the CB-SVPWM (MI m1 = MI m2 = 0.577). As described in [24], since the angle control is applied in the advanced speed control, the phase difference between V * cs,1 and V * cs,2 is 180 degrees. Therefore, V * cs,1 and V * cs,2 cancel out each other, and V * cs is close to zero as shown in Fig. 11 and (5).   The proposed CB-DPWM method uses V max,FLI and V min,FLI from the five existing CB-SVPWM reference voltages to generate the offset voltage (V offset,DPWM ). In addition, two offset voltages are alternately added to the five reference voltages to balance the switching losses. Therefore, using the proposed rotation CB-DPWM method, four reference voltages except the C-phase reference voltage are repeatedly clamped to 0.5V dc or −0.5V dc every one period of the reference voltage. V * cs,DPWM is the same shape as V offset,DPWM as shown in Fig. 12. Fig. 13 and Fig. 14 show the simulation results of the pole voltages (V aN , V bN , V cN , V dN , and V eN ) and the phase currents with the existing CB-SVPWM method and the proposed CB-DPWM method. The pole voltage of the inverter depends on the switching operation of the switching device. As shown in Fig. 13, the pole voltages with the existing CB-SVPWM are continuous. However, the pole voltages with the proposed CB-DPWM method are discontinuous as shown in Fig. 14. In the discontinuous section, no switching loss occurs because the switching devices do not perform the switching operation. In addition, as the pole voltages of the proposed CB-DPWM method, only four of the five legs perform the switching operation. As a result, the amount of switching can be reduced by 20% compared to the existing CB-SVPWM method. Fig. 15 shows the simulation results of advanced speed control with the proposed rotation CB-DPWM method under the variable load condition at 300 rpm. The advanced speed control, introduced in [24], ensures that both motors are electrically symmetrical and maintain the same speed despite variation of load conditions. For example, the simulation results show that when T m1,load decreases, the reference q-axis synchronous frame current of IM2 (I * qe,m2 ) decreases by the angle controller, and the reference d-axis synchronous frame current of IM2 (I * de,m2 ) decreases by the slip controller. In addition, FLI always operates with the proposed rotation CB-DPWM as shown in Fig. 15(d). Through the simulation results, the advanced speed control method using the proposed rotation CB-DPWM method shows that the peak current of I c is smaller than that of the other phases in spite of variable load conditions.

VI. EXPERIMENTAL RESULTS
The experiments have been implemented using the FLI systems for the performance verification of the proposed rotation CB-DPWM method. Fig. 16 shows the experimental set of FLI systems. The experimental set includes two induction motors, five switching device modules consisting of SKM50GB063D made by SEMIKRON, five gate drivers consisting of SKHI22BR made by SEMIKRON, two DC-link capacitors, a control board equipped with TMS320F285377D made by TI, a DC-link voltage sensor, six output current sensors, control board power supply, a DA board, two load inverter made by YASKAWA and two dynamic braking resistors. The experimental conditions were set the same as the simulation conditions in Table 1. In addition, the speed of the two induction motors connected to the FLI was controlled by the advanced speed control method at 300rpm, and the load torque of the two induction motors was set to 9Nm.   other, and the C-phase reference voltage of the FLI is close to zero due to the angle controller. However, if the load torque conditions of the two induction motors are different, the reference voltage of C-phase also appears in irregular sinusoidal waveform because the current flowing through the two induction motors is different, but it is not larger than the other phase reference voltage due to the angle controller. Fig. 18 shows the experimental results of five reference voltages (V * as,DPWM , V * bs,DPWM , V * cs,DPWM , V * ds,DPWM , and V * es,DPWM ) with proposed rotation CB-DPWM method. V offset,DWPM is calculated using the reference voltages of the existing CB-SVPWM method, and the reference voltages  of the proposed CB-DPWM method is generated by adding the offset voltage to the reference voltages of the existing CB-SVPWM method. In addition, the offset voltage can be used to clamp the reference voltages to 0.5V dc or −0.5V dc every one period of the reference voltage as shown in Fig. 18. Therefore, when V offset,DWPM is added to the V * xs (x = a, b, c, d, e), it is confirmed that the clamping section for the proposed DPWM operation occurs. Fig. 19 shows the experimental results of the pole voltages (V aN , V bN , V cN , V dN , and V eN ), the reference voltages, and the output currents when the proposed rotation CB-DPWM method is applied. As shown in Fig. 19, the pole voltages are discontinuous because the switching devices do not switch operation by the reference voltages. However, the C-phase switching devices always operate because the V * cs,DPWM always exists between −V dc /2 and V dc /2.    (θ m1 and θ m2 ) of two induction motors and the A-phase pole voltage (V aN ). As shown in Fig. 20, even if the proposed rotation CB-DPWM method is applied to FLI, the phase angle of IM1 and IM2 always differ by 180 degrees due to the angle controller, and it was confirmed that the C-phase current of FLI is close to zero because the I c,1 and I c,2 cancel out each other under the same load conditions. Fig. 21 shows the experimental results of the advanced speed control method [24] with the proposed rotation CB-DPWM method. The load condition can be changed by applying the DC signal to the load inverter manufactured by YASKAWA. Fig. 21(b) shows the experimental results when T m2,load is changed from 9Nm to 7Nm. As with the simulation results in Fig. 15, I * de,m2 and I * qe,m2 are decreased by the advanced control method. In this case, the phase difference of V * cs,1 and V * cs,2 is kept symmetrical by the angle controller. However, since the magnitudes of V * cs,1 and V * cs,2 are different from each other, it can be seen that the C-phase current increases slightly. In addition, the D-phase current of FLI connected to the A-phase of IM2 decreases because the load condition of IM2 decreases. Fig. 21(c) shows the experimental results when T m1,load is changed from 9Nm to 7Nm. In this case, the C-phase current of FLI converges to zero because the load conditions of the two induction motors are the same. Fig. 21(d) and (e) show the experimental results in the opposite situation of Fig. 21(a) and (b). From V aN as shown in Fig. 21, it is proved that the proposed rotation CB-DPWM method can be applied to the advanced speed control method [24] under the variable load condition. Fig. 22 and 23 show the experimental results of the pole voltages with the existing CB-SVPWM method and the proposed rotation CB-DPWM method. As with the simulation results, the switching losses in the proposed rotation  CB-DPWM method are reduced compared to the existing CB-SVPWM method because only eight of the ten switching devices operate in all switching intervals. Table 2 shows the efficiency of FLI with the existing CB-SVPWM method and the proposed rotation CB-DPWM method. The power analyzer for efficiency measurement is PX8000 made by YOKOGAWA. When the two induction motors were controlled at a constant speed, the system efficiency was measured by increasing or decreasing the load torque. As shown in Table 2, the system efficiency of FLI is always high when the proposed rotation CB-DPWM method is applied. The experimental results show that the proposed rotation CB-DPWM method is about 1.5% more efficient than the existing CB-SVPWM method when the V dc is 300V and the load torque with the maximum MI is 9Nm.

VII. CONCLUSION
In this paper, we propose a simple rotation CB-DPWM method using the offset voltage and increase the system efficiency of FLI. FLI has the advantage of being able to drive two induction motors independently by reducing the number of switching devices. By applying the proposed rotation CB-DPWM method which can reduce the number of switching device to FLI, it is possible to reduce switching loss and to balancing control of switching loss between two switches in a leg. The proposed rotation CB-DPWM method can be easily applied to hardware such as digital signal processor (DSP) because it uses the offset voltage simply calculated using the reference voltages of the existing CB-SVPWM. The experimental results show that the rotation CB-DPWM method proposed in this paper can increase the system efficiency of FLI. Therefore, by using the proposed rotation CB-DPWM method, the inverter can be made compact and it can contribute to the cost reduction of FLI. The simulation and experimental results confirm the feasibility and the effectiveness of the proposed rotation CB-DPWM method compared with the existing CB-SVPWM method.