Input Power Factor Compensation Strategy for Zero CMV-SVM Method in Matrix Converters

The space vector modulation (SVM) method using only rotating vectors is very effective to suppress the common-mode voltage (CMV) for matrix converters (MCs). However, the effect of the input filter on the input power factor (IPF) has not been fully investigated when using this method. This study investigated the effect of the input filter on the displacement angle and proposes an IPF compensation strategy for the zero CMV-SVM method in MCs. The proposed strategy analyzes the duty cycles of rotating vectors under the IPF-compensation condition. Through this analysis, the proposed strategy adjusts the zero vector by using a set of three counterclockwise-rotating vectors or three clockwise-rotating vectors to make all the duty cycles non-negative, ensuring that the zero CMV-SVM method can be applied to compensate the IPF for the MCs. This study also determines the condition to achieve unity IPF for the main power source and the maximum allowable IPF if the above condition is not met. Finally, experimental results are provided to validate the theoretical study.


I. INTRODUCTION
In recent years, matrix converters (MCs) with bidirectional power flow capabilities have received considerable attention. In comparison to traditional back-to-back converters, MCs offer more compact and reliable operation owing to the absence of bulky electrolytic capacitors [1], as shown in Figure 1. Therefore, MCs have garnered significant research interest in industry, particularly the aircraft, electric-vehicle, and wind-generation industries [2]- [4]. However, MCs have not been widely applied in practice owing to several issues affecting input-filter design, bidirectional-switch technology, commutation techniques, and the common-mode voltage (CMV) [5]. Among these problems, the CMV between the motor neutral point and power supply ground is the main source of motor winding failure and bearing damage [6]- [8].
The associate editor coordinating the review of this manuscript and approving it for publication was Snehal Gawande. Furthermore, it also causes noise and electromagnetic interference problems, affecting surrounding electronic equipment [9].
Several modulation methods have been presented to effectively reduce the CMV for MCs. Among them, space vector modulation (SVM) is currently the most widely used technique owing to its advantageous features such as harmonic performance, flexibility to optimize the switching pattern, and achieving the highest modulation ratio [5], [10]. Two types of SVM methods are based on replacing the MC zero vectors with active vectors [11] or rotating the vectors [12] to reduce the CMV peak value to 42%. In [13], two lower-input line-to-line voltages are used to synthesize the desired outputvoltage vector to mitigate the CMV peak value with a lower total harmonic distortion of the output voltage and a reduction in switching loss. However, the proposed method has the disadvantage of a low voltage-transfer ratio (VTR) of less than 0.5. Guan et al. presented a modulation SVM method to reduce not only the peak value but also the RMS of the CM by using all valid switching states, including rotating-vector states [14]. Nguyen and Lee proposed an effective modulation scheme, including an SVM method using only rotating vectors and a modified four-step commutation technique, to achieve zero CMV for MCs [15]. More recently, Lei et al. suggested a simpler SVM method to accomplish zero CMV by adopting only three clockwise rotating vectors or counterclockwise rotating vectors [16]. However, the performance of the MC when using this method is reduced significantly because the rotating vectors used are very far from the reference output-voltage vector. Among the aforementioned techniques, the modulation scheme in [15] is the most effective solution for eliminating CMV in MCs, from the perspective of the output voltage quality.
Although zero CMV-SVM methods have been realized, there are still some issues to be resolved. Compensating the input power factor (IPF), affected by the input filter, is one of the most important issues to be handled. In practice, an LC filter is connected at the input of the MC to eliminate high-frequency harmonics of the input current and smooth it to satisfy EMI requirements [17]. However, the input filter produces a displacement angle between the source phase voltage and current [18]. This displacement angle will significantly degrade the IPF of the power source, especially at low VTRs, which may lead to severe power-factor penalties [19]. Therefore, it is important to consider the IPF compensation problem along with CMV reduction.
Fortunately, a previous study [19] briefly presented a method to compensate IPF for MCs in the zero CMV-SVM method. However, it did not fully investigate all the dutycycle cases. In addition, the method has not been experimentally verified. To address these issues, this article analyzes all duty cycles under IPF compensation. In the case of negative duty cycles, they will be adjusted to be zero duty cycles so that all duty cycles are positive. This article also determines the maximum IPF that the main power source can achieve according to the VTR. Finally, experiments are carried out to validate the proposed strategy.
Load displacement angle at output frequency, Output angular frequency

II. CONVENTIONAL ZERO CMV-SVM METHOD
Using the symbols defined in Figure 1, let the three-phase source voltage be According to the space vector theory, three instantaneous source voltages can be represented by one vector v s , defined as follows: Similarly, space vectors-representing input voltages, output voltages, input currents, and output currents-are respectively defined as follows: Because the MC is supplied by a source voltage and the output load is inductive, the input phases should not be  short-circuited, and the output phases should not be opencircuited [10]. To satisfy these two constraints, there are only 27 valid switching states, corresponding to 27 space vectors, which are listed in Table 1. These switching states are classified into three groups, as follows: a) Eighteen switching states in Group I produce active vectors, with fixed directions and time-varying amplitudes of the output-voltage and input-current vectors. b) Three switching states in Group II produce zero vectors, including zero output-voltage and input-current vectors.
c) Six switching states in Group III produce rotating vectors, with fixed amplitudes and time-varying directions of the output-voltage and input-current vectors.
Among them, the six rotating vectors in group III produce zero CMV [14]- [16]. However, their angular positions always change along with the input voltage, so using these vectors is not simple. Nguyen and Lee, in [1] and [15], proposed a switching pattern using five rotating vectors within a sampling period to control MCs to have zero CMV. Among these five rotating vectors, four vectors act as active vectors to generate the desired output-voltage and input-current vectors, and one rotating vector acts as a zero vector to complete the sampling period. The four selected rotating vectors, which acts as active vectors, and their duty cycles are shown in Table 2 and equations (7)-(10): The duty cycle of the zero vector can be calculated as follows:    The zero vector can be executed using a set of three counterclockwise-rotating vectors (i.e., r 1 , r 3 , r 5 ) or clockwise-rotating (i.e., r 2 , r 4 , r 6 ) vectors with the same duty cycle: In the case of no compensation (δ i = 0), with the limits of α o andβ i in (11) and (12), respectively, only duty cycle d 3 can be negative. To ensure that the duty cycle d 3 of rotating vector r 3 is non-negative, the zero vector should be implemented using a set of three counterclockwise-rotating vectors, i.e., 0 = ( r 1 + r 3 + r 5 )/3. This means that, in addition to creating a main active vector as shown in (7)-(10), the rotating vectors r 1 , r 3 , and r 5 must execute an extra interval to create the zero vector, as follows: Therefore, in the conventional method, rotating vectors are finally selected as shown in Table 3, and their duty cycles are determined as follows: Substituting (7)   With the limits ofα o andβ i in (11) and (12), it is possible to prove that all duty cycles-d I , d II , d III , d IV , and d V -in (23)-(27) are non-negative.
All of these duty cycles must be less than 1, so the VTR in the conventional zero CMV-SVM method is limited as follows: q ≤ 1 2 (28)

III. PROPOSED IPF STRATEGY FOR ZERO CMV-SVM METHOD A. INPUT FILTER ANALYSIS
The input filter is a crucial component in a practical MC system, which is used to smooth the source current. However, it creates a displacement angle between current and voltage, leading to a low IPF. Therefore, it is important to study this displacement angle to improve the IPF. In MC systems, a second-order LC filter with a damping resistor is commonly used, as shown in Figure 4. From Figure 4, in the condition of R d ω s L f , the relationship between ( v i , i i ) and ( v s , i s )can be written as follows: Because the voltage drop at the input filter is very small in comparison to the source voltage, the input voltage of the MC and the source voltage are considered to be equal [19]: From (29) and (31), we can draw the vector diagram of input voltages and currents at the input filter, as shown in Figure 5. From Figure 5, it is possible to determine the displacement angle caused by the input filter as follows: In addition, based on the law of conservation of energy, we have the following: (33) is rewritten as follows: Combining (32) and (34), the displacement angle caused by the input filter can be determined by the MC parameters as follows: The following strategy will attempt to compensate the angle δ f in (35) as much as possible to achieve the maximum IPF of the power source.

B. PROPOSED IPF COMPENSATION STRATEGY
Since the vector v i is definite ( v i = v s ) and uncontrollable, the angle δ f in (35) can only be compensated by controlling the vector i i . Based on Figure 5, to compensate the angle δ f , the vector i i must be delayed by an angle δ i in comparison to v i , as shown in Figure 6. Therefore, the phase angle of the input current vector is determined as β i = α i −δ i . The patterns ofβ i are depicted in Figure 7 using the following limit: (36) VOLUME 8, 2020 Under this condition, from (7) to (10), duty cycles d 3 and d 4 may be negative: Therefore, it is clear that d 3 and d 4 cannot be negative at the same time. In light of this, the present paper proposes a strategy as follows: i) When d 4 > 0, the selected vectors and their duty cycles are the same as those in the conventional case.
ii) When d 4 < 0, to ensure that the duty cycle d 4 of the rotating vector r 4 is non-negative, the zero vector should be implemented by a set of three clockwise-rotating vectors, i.e., 0 = ( r 2 + r 4 + r 6 )/3. Therefore, in addition to creating the main active vector as shown in (7)-(10), the rotating vectors r 2 , r 4 , and r 6 must execute an extra interval to create the zero vector, as follows: The selected rotating vectors are shown in Table 4 and their duty cycles are calculated as follows: Substituting (7)-(10), (13), and (37)-(39) into (40)-(44), it is possible to obtain the following results: In the case of d 4 < 0, which implies thatβ i < 0, it is possible to prove that all duty cycles in (45)-(49) are positive, so the zero CMV-SVM method can be implemented in this case.
The limit of VTR in the zero CMV-SVM method with the compensated angle δ i is:

C. MAXIMUM COMPENSABLE ANGLE AND MAXIMUM IPF
Even though the proposed IPF compensation strategy attempts to compensate the angle δ f in (35) as much as possible to achieve the maximum IPF of the power source, it is not always possible to compensate all values of δ f to achieve unity IPF. This section covers the conditions for the MC to achieve unity IPF, and the maximum allowable IPF value when unity cannot be reached.

1) CONDITION TO ACHIEVE UNITY IPF
According to [20], the relationship between δ s , δ i and δ f is: To obtain the unity IPF (δ s = 0), from (35) and (51), the compensated angle δ i must be: Let the quality factor Q be defined as From (50), (52), and (53), the condition for MC to achieve unity IPF using the zero CM-SVM method is:    From (54), it is possible to derive the following condition:   From (55), we can finally determine the condition to achieve unity IPF for MCs as follows:

2) MAXIMUM ALLOWABLE IPF
When the condition in (56) is not satisfied, the MC cannot achieve unity IPF, and it is necessary to determine the maximum allowable IPF. In this case, from (50) and (51), we have the following relationship: (57) VOLUME 8, 2020   To achieve the maximum allowable IPF, the compensated angle must be maximized, thus: cos δ i = 2q. Therefore, it is possible to calculate: From (57) and (58), it is possible to calculate: Finally, the maximum allowable IPF can be determined as follows:

IV. EXPERIMENTAL RESULTS
To verify the proposed theoretical study, experiments for the proposed IPF strategy are carried out using a threephase power supply, LC filter, and a three-phase symmetrical passive RL load with the parameters shown in Table 5. The switching frequency is 10 kHz. The MC was built using 18 insulated-gate bipolar transistors (IRG4PF50WD). Main control was implemented using fixed-point digital signal processors (TMS320F2812). A complex programmable logic device (EPM7128SLC84-15) was used for four-step commutation.
With the parameters in Table 5, condition (56) to achieve unity IPF for MCs, in this case, will be:  Figures 8 and 9 show the MC input and output waveforms when using the zero CMV-SVM method without compensation at q = 0.4. In this case, the IPF achieved is 0.84. The CMV is almost zero, other than a small amount of noise owing to the commutation process [1], as shown in Figure 10.
Subsequently, the maximum compensated angle is applied to the zero CMV-SVM method; the MC input and output waveforms are shown in Figures 11 and 12, respectively. As can be seen, q = 0.4 meets the condition in (61), so the MC can achieve unity IPF in this case. The proposed IPF compensation strategy does not affect the results of the CMV, and it can be seen that the CMV is nearly zero in Figure 13.
When the MC operates at a low voltage transfer ratio, i.e., q = 0.2, the IPF is only 0.37, as shown in Figures 14 and 15. Since q = 0.2 does not satisfy the condition in (61), the MC cannot achieve unity IPF. Therefore, after applying the maximum compensated angle, the MC only achieves a maximum IPF of 0.97, as shown in Figures 17 and 18. It is clear that this value is in good agreement with the theoretical predictions in (60). Because the zero CMV modulation method is used, the CMV is always almost zero, as shown in Figures 16 and 19, for both uncompensated and compensated cases.
The IPF results in other cases of VTR, within the range of 0 to 0.5, are shown in Figures 20 and 21 without compensation and the proposed IPF compensation strategy, respectively. It can be seen from Figures 20 and 21 that experimental results are in good agreement with the proposed theoretical results.

V. CONCLUSION
This article has presented an IPF compensation strategy for the zero CMV-SVM method. The proposed strategy investigated the displacement angle caused by the input filter and its effect on the value of duty cycles upon compensation. The proposed strategy decides which rotating vectors are synthesized into zero vectors, thereby making all duty cycles non-negative, allowing the zero CMV-SVM method to be applied. This article also specifies when the main power source can achieve unity IPF and the maximum allowable IPF according to the VTR. Experimental results confirmed that the MC's IPF is in good agreement with the proposed theoretical results.