Development of a DC-Side Direct Current Controlled Active Ripple Filter for Eliminating the Double-Line-Frequency Current Ripple in a Single-Phase DC / AC Conversion System †

: The objective of this paper is to propose an active ripple ﬁlter (ARF) using the patented DC-side direct current control for eliminating the double-line-frequency current ripple in a single-phase DC / AC conversion system. The proposed ARF and its control strategies can not only prolong the usage life of the DC energy source but also improve the DC / AC system performance. At ﬁrst, the phenomena of double-line-frequency current ripple and the operation principle of the ARF are illustrated. Then, steady-state analysis, small-signal model, and control loop design of the ARF architecture are derived. The proposed control system includes: (1) a DC current control loop to provide the excellent ripple eliminating performance on the output of the DC energy source; (2) a voltage control loop for the high-side DC-bus voltage of the ARF to achieve good steady-state and transient-state responses; (3) a voltage feedforward loop for the low-side voltage of the ARF to cancel the voltage ﬂuctuation caused by the instability of the DC energy source. Finally, the feasibility of the proposed concept can be veriﬁed by the system simulation, and the experimental results show that the nearly zero double-line-frequency current ripple on the DC-side in a single-phase DC / AC conversion system can be achieved. feedforward control loop. The e ﬃ cacy of the proposed method is veriﬁed experimentally under steady-state conditions. The results show that the proposed ARF and its control strategies o ﬀ ers many advantages, such as a fast dynamic response, simple implementation, a nearly zero-steady state error, and the elimination of the double-line-frequency current ripple in a single-phase DC / AC conversion system above 90%.


Introduction
In recent years, the green energy conversion technologies for distributed generation system have become major industrial developments in the global trend of energy conservation and carbon reduction. Single-phase DC-AC power converters are generally used to supply AC loads in such applications [1][2][3][4][5]. The power generated by DC/AC conversion technologies according to user demands, and is then provided for stand-alone AC loads [6][7][8] or fed into the utility grid [9].
In a single-phase DC/AC conversion system, the DC input or AC output of the power converter would generate double-line-frequency instantaneous power in addition to the average power. Assuming that all the components of the converter are ideal, according to the law of conservation of energy, the instantaneous power at the DC input must be equal to that at the AC output. In this study, an ARF using the DC-side direct current control for eliminating the double-linefrequency current ripple in a single-phase DC/AC conversion system would be proposed. Compared with the other conventional control diagrams as shown in Figure 1b-d, the DC-side direct current control strategy is relatively simple to implement. The current command and feedback signals are  According to the different current measurement locations of the ARF as shown in Figure 1a, the conventional control diagram of the ARF can be classified into (1) the input current sensing point of the ARF, as shown in Figure 1b; and (2) the input current sensing point of the single-phase DC/AC power conversion system, as shown in Figure 1c,d. For locating the input current sensing point of the ARF, the proportional-resonant (PR) controller and the proportional-integral (PI) controller are cascade interconnection to achieve the zero steady-state error for tracking AC reference. For locating the input current sensing point of the single-phase DC/AC power conversion system, it requires the low pass filter (Figure 1c) or bandpass filter (Figure 1d) to filter the DC component of the input current of the single-phase DC/AC power conversion system. In summary, the ARF must provide AC current, which is difficult to control, and the above-mentioned methods cause the design process of system controller as well as its parameters more complicated and difficult indeed.
In this study, an ARF using the DC-side direct current control for eliminating the double-line-frequency current ripple in a single-phase DC/AC conversion system would be proposed. Compared with the other conventional control diagrams as shown in Figure 1b-d, the DC-side direct current control strategy is relatively simple to implement. The current command and feedback signals are DC values, hence the nearly zero-steady state error can be fulfilled easily. The steady-state analysis, small-signal model and control loop design of the proposed ARF architecture are derived. Figure 2 illustrates a single-phase DC/AC conversion system, and characteristic waveforms of the system for the power flows without and with the ARF are presented in Figure 3. Integration of the ARF into a single-phase DC/AC conversion system [26].

Principle of Double-Line-Frequency Instantaneous Power
(a) (b) Figure 3. Key waveforms to illustrate the operating principles for double-line-frequency components of a single-phase DC/AC conversion system [26]: (a) without the ARF and (b) with the ARF.
The key waveforms without the ARF are shown in Figure 3a. In this figure, the instantaneous output voltage, output current, and output power of the single-phase DC/AC conversion system are The key waveforms without the ARF are shown in Figure 3a. In this figure, the instantaneous output voltage, output current, and output power of the single-phase DC/AC conversion system are expressed as v OUT , INV , i OUT,INV , and p OUT,INV , respectively, as follows: According to the conservation of energy and the assumption that the energy dissipation of the system can be neglected, the output power of the energy source p S can be expressed as follows: where P S is the average power and p R refers to the double-line-frequency ripple power generated by the product of v OUT,INV and i OUT,INV . Assuming that the energy source provides pure DC voltage (i.e., v S ≈ V S ), and the output current of the energy source can be derived as follows: where I S and i R refer to the DC current and the AC (ripple) current provided by the energy source, respectively.
Energies 2020, 13, x FOR PEER REVIEW 4 of 16 Figure 2. Integration of the ARF into a single-phase DC/AC conversion system [26].
(a) (b) Figure 3. Key waveforms to illustrate the operating principles for double-line-frequency components of a single-phase DC/AC conversion system [26]: (a) without the ARF and (b) with the ARF.
The key waveforms without the ARF are shown in Figure 3a. In this figure, the instantaneous output voltage, output current, and output power of the single-phase DC/AC conversion system are expressed as vOUT,INV, iOUT,INV, and pOUT,INV, respectively, as follows: According to the conservation of energy and the assumption that the energy dissipation of the system can be neglected, the output power of the energy source pS can be expressed as follows: where PS is the average power and pR refers to the double-line-frequency ripple power generated by the product of vOUT,INV and iOUT,INV.
Assuming that the energy source provides pure DC voltage (i.e., vS ≈ VS), and the output current of the energy source can be derived as follows: According to (7), the double-line-frequency ripple power generated by the single-phase DC/AC conversion system was completely reflected on the current provided by the energy source. As a result, the current ripple would suffer the performance of the energy source and substantially reduce its service life [27][28][29][30]. Figure 3b illustrates the key waveforms of the single-phase DC/AC conversion system after the integration of the ARF. In this figure, i IN,INV and i ARF are respectively defined as the input current of the single-phase DC/AC conversion system and the compensating current provided by the ARF. It can be seen from Figure 2, i IN,INV can be directly expressed as follows: The double-line-frequency ripple components of were provided by the ARF, as shown in (9):

Operating Principles of the ARF
The ARF must possess the ability of bidirectional power flow to provide double-line-frequency current ripple and thus yield a pure DC current of the energy source. As shown in Figure 4, the circuit architecture of the ARF is a bidirectional buck-boost converter. The polarities of the output current of the ARF can be divided into the boost and buck modes. When the polarity of the output current is positive, the ARF operates in a buck mode. By contrast, when the polarity of the output current is negative, the ARF operates in a boost mode.
The assumptions are made in analyzing the ARF: (1) the ARF operates in continuous conduction mode (CCM); (2) the drive signals for active switches Q 1 and Q 2 of the ARF are respectively defined as d 1 and d 2 ; (3) the DC-bus voltage v DC,ARF could be approximated as a constant value, i.e., v DC,ARF ≈ V DC,ARF ; (4) all voltages and currents in the ARF are periodic in steady-state condition; for simplicity, it is assumed that all the components of the ARF in Figure 4 are idealized.

Operating Principles of the ARF
The ARF must possess the ability of bidirectional power flow to provide double-line-frequency current ripple and thus yield a pure DC current of the energy source. As shown in Figure 4, the circuit architecture of the ARF is a bidirectional buck-boost converter. The polarities of the output current of the ARF can be divided into the boost and buck modes. When the polarity of the output current is positive, the ARF operates in a buck mode. By contrast, when the polarity of the output current is negative, the ARF operates in a boost mode.
The assumptions are made in analyzing the ARF: (1) the ARF operates in continuous conduction mode (CCM); (2) the drive signals for active switches Q1 and Q2 of the ARF are respectively defined as d1 and d2; (3) the DC-bus voltage vDC,ARF could be approximated as a constant value, i.e., vDC,ARF ≈ VDC,ARF; (4) all voltages and currents in the ARF are periodic in steady-state condition; for simplicity, it is assumed that all the components of the ARF in Figure 4 are idealized.  Figure 5a illustrates the circuit architecture of the ARF operated in the buck mode. When Q1 was turned off and Q2 was turned on, the relation between current iARF and voltage of inductor LARF can be calculated using the equation as follows:  Figure 5a illustrates the circuit architecture of the ARF operated in the buck mode. When Q 1 was turned off and Q 2 was turned on, the relation between current i ARF and voltage of inductor L ARF can be calculated using the equation as follows:

Buck Mode
when Q 1 was turned on and Q 2 was turned off, the relation between current i ARF and voltage of inductor L ARF can be calculated using the equation as follows: According to the volt-second balance principle of the inductor L ARF , the voltage conversion ratio between the low-voltage and high-voltage sides of the ARF can be derived as follows: Figure 5b illustrates the circuit architecture of the ARF operated in the boost mode. When Q 1 was turned off and Q 2 was turned on, the relation between current i ARF and voltage of inductor L ARF can be calculated using the equation as follows:

Boost Mode
Energies 2020, 13, 4772 6 of 16 when Q 1 was turned on and Q 2 was turned off, the relation between current i ARF and voltage of inductor L ARF can be calculated using the equation as follows: Likewise, according to the volt-second balance principle of inductor L ARF , the result of (12) was also applicable to the boost mode due to the ARF has the bidirectional power flow characteristic. If the drive signals of switches Q 1 and Q 2 are assumed to be complementary (i.e., d 1 = 1 -d 2 ), then the voltage conversion ratio of the ARF can be simplified as follows: Figure 5b illustrates the circuit architecture of the ARF operated in the boost mode. When Q1 was turned off and Q2 was turned on, the relation between current iARF and voltage of inductor LARF can be calculated using the equation as follows:

Boost Mode
when Q1 was turned on and Q2 was turned off, the relation between current iARF and voltage of inductor LARF can be calculated using the equation as follows: Likewise, according to the volt-second balance principle of inductor LARF, the result of (12) was also applicable to the boost mode due to the ARF has the bidirectional power flow characteristic. If the drive signals of switches Q1 and Q2 are assumed to be complementary (i.e., d1 = 1 -d2), then the voltage conversion ratio of the ARF can be simplified as follows: (a) (b)   Figure 6 illustrates the developed control system for the ARF. At first, it can be seen that the DC-bus voltage (v DC,ARF ) is sensed and compared with the voltage reference to produce an error signal. Second, the voltage controller receives the error signal to produce the average power reference signal, p s,ref , which is divided by the feedforward compensation signal (i.e., energy source voltage, v S ) to generate the current reference, i S,ref . In the inner current control loop, the energy source current (i S ) is sensed and compared with the current reference to generate the modulated signal (v con ) of the pulse width modulation (PWM) generator.

Control Strategy of the ARF
It is noted that the ARF must provide AC current (i.e. ripple current), which is difficult to control. In this study, the current reference and the sensed signals are all DC value, hence the nearly zero-steady state error can be fulfilled easily. In other words, this study proposes a method of indirectly regulating the output AC current of the ARF by directly controlling the input DC current of the energy source. According to Figure 7, the controller design of the outer voltage loop and inner current loop of the ARF was illustrated as follows.
Energies 2020, 13, 4772 7 of 16 bus voltage (vDC,ARF) is sensed and compared with the voltage reference to produce an error signal. Second, the voltage controller receives the error signal to produce the average power reference signal, ps,ref, which is divided by the feedforward compensation signal (i.e., energy source voltage, vS) to generate the current reference, iS,ref. In the inner current control loop, the energy source current (iS) is sensed and compared with the current reference to generate the modulated signal (vcon) of the pulse width modulation (PWM) generator. It is noted that the ARF must provide AC current (i.e. ripple current), which is difficult to control. In this study, the current reference and the sensed signals are all DC value, hence the nearly zerosteady state error can be fulfilled easily. In other words, this study proposes a method of indirectly regulating the output AC current of the ARF by directly controlling the input DC current of the energy source. According to Figure 7, the controller design of the outer voltage loop and inner current loop of the ARF was illustrated as follows.

Designing the Controller of the Current Loop
Considering the buck mode operation, the inductor voltage in one switching period can be expressed as follows: Perturbation was introduced into the inductor current and the drive signal d2 of Q2, and d1 = 1−d2. This study assumed that vS and vDC,ARF operated in a stable DC status. Thus, (16) can be rewritten as follows:   The bode plot of the response frequency of the current loop after receiving compensation from the controller is also illustrated in Figure 8. According to the figure, the zero crossover frequency (i.e., closed-loop bandwidth) was 3 kHz, and the phase margin was 60°. In other words, the closed-loop control enabled the ARF to attain sufficient response and stability.

Designing the Controller of the Current Loop
Considering the buck mode operation, the inductor voltage in one switching period can be expressed as follows: Energies 2020, 13, 4772 8 of 16 Perturbation was introduced into the inductor current and the drive signal d 2 of Q 2 , and d 1 = 1−d 2 . This study assumed that v S and v DC,ARF operated in a stable DC status. Thus, (16) can be rewritten as follows: when the converter was operated in the boost mode, the inductor voltage in one switching cycle can be expressed as: Perturbation was introduced into the inductor current and the drive signal d 1 of Q 1 . Similarly, v S and v DC,ARF were assumed to operate in a stable DC status.
Accordingly, (18) can be further expressed as: An observation of (17) and (19) indicated that the small-signal models derived in the buck and boost operational modes were the same. In addition, this study controlled the output current of the ARF indirectly by controlling the output current of the energy source to regulate the required current ripple provided by the ARF. Therefore, the derived small-signal model must undergo minor modifications. According to (8), the three branch currents of the input side of the ARF-integrated single-phase DC/AC conversion system were interrelated. This study assumed that the input current i IN,INV required by the single-phase DC/AC conversion system can be regarded as a definite value in consideration of small signals. In other words, perturbation in the current provided by the energy source would be directly reflected on the output current of the ARF.
Therefore, the introduction of perturbation into the two signals in (8) would result in the following equation:ĩ Substituting (17) or (19) into the equation, performing the Laplace transform, and deriving the transfer function of the small-signal model of the current loop is as follows: The equivalent circuit derived in the aforementioned process is illustrated in Figure 7. The parameters were V DC,ARF = 100 V and L ARF = 250 µH, and the open-loop gain of the current loop is expressed as (22).
where F m is the equivalent small-signal gain of pulse-width modulation, as follows where V tri is the peak value of the carrier wave of the PWM generator. According to Figure 7, the open-loop gain of the current loop was in a first-order integral form. Therefore, the controller only needed to be in a proportional-integral (PI) form to achieve satisfactory control. The form and parameters of the designed PI controller are presented as follows: After incorporating the compensation from the controller, the open-loop gain of the current loop is expressed as follows: The bode plot of the response frequency of the current loop after receiving compensation from the controller is also illustrated in Figure 8. According to the figure, the zero crossover frequency (i.e., closed-loop bandwidth) was 3 kHz, and the phase margin was 60 • . In other words, the closed-loop control enabled the ARF to attain sufficient response and stability. The bode plot of the response frequency of the current loop after receiving compensation from the controller is also illustrated in Figure 8. According to the figure, the zero crossover frequency (i.e., closed-loop bandwidth) was 3 kHz, and the phase margin was 60°. In other words, the closed-loop control enabled the ARF to attain sufficient response and stability.

Designing the Controller of the Voltage Loop
In practice, the capacitor voltage on the high-voltage side of the ARF also involved double-linefrequency components. Consequently, the compensation current command may be affected through feedback control, resulting in the failure to completely eliminate the double-line-frequency components at the output side of the single-phase DC/AC conversion system. To prevent this problem, the bandwidth of the voltage loop on the high-voltage side of the ARF must be substantially lower than the double-line-frequency to ensure that the current command remains unaffected.
According to Figure 9, the small-signal model of the voltage loop was derived as follows from the perspective of power, where pCH and iCH refer to the power and current of the capacitor energy storage on the high-voltage side of the ARF.

Designing the Controller of the Voltage Loop
In practice, the capacitor voltage on the high-voltage side of the ARF also involved double-line-frequency components. Consequently, the compensation current command may be affected through feedback control, resulting in the failure to completely eliminate the double-line-frequency components at the output side of the single-phase DC/AC conversion system. To prevent this problem, the bandwidth of the voltage loop on the high-voltage side of the ARF must be substantially lower than the double-line-frequency to ensure that the current command remains unaffected.
According to Figure 9, the small-signal model of the voltage loop was derived as follows from the perspective of power, where p CH and i CH refer to the power and current of the capacitor energy storage on the high-voltage side of the ARF.
Assuming the stable operation of v S and v DC,ARF , to consider (20) and substitute perturbation into i S and i CH . Thus, (27) can be rewritten as:ĩ Multiplying (28) by the capacitive resistance on the high-voltage side, to perform the Laplace transform, and then the transfer function of the small-signal model of the voltage loop can be expressed as follows: The parameters of the small-signal model of the voltage loop included v S = 36 V, V DC,ARF = 100 V, and C DC,ARF = 3400 µF. The open-loop gain of the voltage loop is as follows: Energies 2020, 13, 4772 10 of 16 Notice that (30), which includes the feedforward term of the S at denominator, which can eliminate fluctuation caused by v S . Similar to the current loop, the open-loop gain of the voltage loops was in a first-order integral form as well. Therefore, the PI form can be used on the controller. The parameters of the controller are expressed as follows: After incorporating the compensation from the controller, the open-loop gain of the voltage loop is presented as follows: Energies 2020, 13, x FOR PEER REVIEW 10 of 16 Figure 9. Small-signal equivalent circuit of the voltage loop. , Assuming the stable operation of vS and vDC,ARF, to consider (20) and substitute perturbation into iS and iCH. Thus, (27) can be rewritten as: Multiplying (28)  , The Notice that (30), which includes the feedforward term of the S at denominator, which can eliminate fluctuation caused by vS. Similar to the current loop, the open-loop gain of the voltage loops was in a first-order integral form as well. Therefore, the PI form can be used on the controller. The parameters of the controller are expressed as follows:

Simulation and Experimental Results
MATLAB © and PSIM © software were used to analyze and verify the feasibility of the proposed method. The specifications of the system are listed as follows: an input DC voltage of 36 V for the distributed energy source, an output AC voltage of 110 Vrms, and a rated power output of 500 W for single-phase DC/AC grid-connected operation [31]. The experimental platform was implemented, as shown in Figure 11. The parameters of circuit components and the specification of the experimental platform are listed in Tables 1 and 2, respectively.

Simulation and Experimental Results
MATLAB© and PSIM© software were used to analyze and verify the feasibility of the proposed method. The specifications of the system are listed as follows: an input DC voltage of 36 V for the distributed energy source, an output AC voltage of 110 Vrms, and a rated power output of 500 W for single-phase DC/AC grid-connected operation [31]. The experimental platform was implemented, Energies 2020, 13, 4772 11 of 16 as shown in Figure 11. The parameters of circuit components and the specification of the experimental platform are listed in Tables 1 and 2, respectively.

Simulation and Experimental Results
MATLAB © and PSIM © software were used to analyze and verify the feasibility of the proposed method. The specifications of the system are listed as follows: an input DC voltage of 36 V for the distributed energy source, an output AC voltage of 110 Vrms, and a rated power output of 500 W for single-phase DC/AC grid-connected operation [31]. The experimental platform was implemented, as shown in Figure 11. The parameters of circuit components and the specification of the experimental platform are listed in Tables 1 and 2, respectively. Figure 11. Experimental platform of a 500 W single-phase DC/AC conversion integrated with ARF.    The simulation and experimental results at 500 W before the ARF were integrated into the distributed energy source as shown in Figure 12a,b, respectively. The distributed energy source provides an average current of 13.85 A, the peak-to-peak value of the double-line-frequency current ripple is 24 A.
The only difference is that the peak value of the output current of the single-phase DC/AC conversion system are 6.3 A and 5.8 A, respectively. As shown in the results, the ripples strongly affect the service life of the DC energy source and reduces the operating efficiency of the power system.
Next, after integration of the ARF, the double-line-frequency current ripple is suppressed, the average current is 14 A and 14.25 A, the peak-to-peak value of the inductor current is 23 A and 22 A, the results are shown in Figure 13a,b, respectively. In this case, the life service of the distributed energy source not only increased, but the performance of the power system was also enhanced.
provides an average current of 13.85 A, the peak-to-peak value of the double-line-frequency current ripple is 24 A.
The only difference is that the peak value of the output current of the single-phase DC/AC conversion system are 6.3 A and 5.8 A, respectively. As shown in the results, the ripples strongly affect the service life of the DC energy source and reduces the operating efficiency of the power system. Next, after integration of the ARF, the double-line-frequency current ripple is suppressed, the average current is 14 A and 14.25 A, the peak-to-peak value of the inductor current is 23 A and 22 A, the results are shown in Figure 13a,b, respectively. In this case, the life service of the distributed energy source not only increased, but the performance of the power system was also enhanced.  Figure 14 shows the simulation and experimental results of the DC/AC output voltage and output current at 500 W when the ARF was integrated, respectively. In Figure 14a (simulation), the peak voltage of 155.7 V, the peak value of the output current is 6.25 A. In Figure 14b (experiments), the peak current of the output current is 5.8 A. Next, after integration of the ARF, the double-line-frequency current ripple is suppressed, the average current is 14 A and 14.25 A, the peak-to-peak value of the inductor current is 23 A and 22 A, the results are shown in Figure 13a,b, respectively. In this case, the life service of the distributed energy source not only increased, but the performance of the power system was also enhanced.  Figure 14 shows the simulation and experimental results of the DC/AC output voltage and output current at 500 W when the ARF was integrated, respectively. In Figure 14a (simulation), the peak voltage of 155.7 V, the peak value of the output current is 6.25 A. In Figure 14b (experiments), the peak current of the output current is 5.8 A.  Figure 14 shows the simulation and experimental results of the DC/AC output voltage and output current at 500 W when the ARF was integrated, respectively. In Figure 14a (simulation), the peak voltage of 155.7 V, the peak value of the output current is 6.25 A. In Figure 14b (experiments), the peak current of the output current is 5.8 A. To add a soft-start circuit made the output of the system start up smoothly, the current remained stable, the output voltage increased to 100 V smoothly without overshot, and the soft-start time was about 0.55 s. The results are shown in Figure 15a To add a soft-start circuit made the output of the system start up smoothly, the current remained stable, the output voltage increased to 100 V smoothly without overshot, and the soft-start time was about 0.55 s. The results are shown in Figure 15a,b, respectively. To add a soft-start circuit made the output of the system start up smoothly, the current remained stable, the output voltage increased to 100 V smoothly without overshot, and the soft-start time was about 0.55 s. The results are shown in Figure 15a,b, respectively. As seen in Figures 12 to 15, the simulation coincided with experimental results to validate the proposed method. These results correspond with the calculations in the steady-state analysis as well. Figure 16a illustrates spectrum of the input current at 120 Hz before the integration of ARF and Figure  16b verifies the double-line-frequency current ripple of the input side is significantly reduced By observing Figure 17, in the full load case, the peak-to-peak current ripple is 24 A, which is 175% of the average value. When ripple suppression was enabled, the peak-to-peak current ripple reduced to 2 A, which was 14% of the average value. Therefore, it can be proved that energy source As seen in Figures 12-15, the simulation coincided with experimental results to validate the proposed method. These results correspond with the calculations in the steady-state analysis as well. Figure 16a illustrates spectrum of the input current at 120 Hz before the integration of ARF and Figure 16b verifies the double-line-frequency current ripple of the input side is significantly reduced. To add a soft-start circuit made the output of the system start up smoothly, the current remained stable, the output voltage increased to 100 V smoothly without overshot, and the soft-start time was about 0.55 s. The results are shown in Figure 15a,b, respectively. As seen in Figures 12 to 15, the simulation coincided with experimental results to validate the proposed method. These results correspond with the calculations in the steady-state analysis as well. Figure 16a illustrates spectrum of the input current at 120 Hz before the integration of ARF and Figure  16b verifies the double-line-frequency current ripple of the input side is significantly reduced By observing Figure 17, in the full load case, the peak-to-peak current ripple is 24 A, which is 175% of the average value. When ripple suppression was enabled, the peak-to-peak current ripple reduced to 2 A, which was 14% of the average value. Therefore, it can be proved that energy source By observing Figure 17, in the full load case, the peak-to-peak current ripple is 24 A, which is 175% of the average value. When ripple suppression was enabled, the peak-to-peak current ripple reduced to 2 A, which was 14% of the average value. Therefore, it can be proved that energy source was integrated with ARF and the double-line-frequency current ripple of the energy source could be significantly reduced. Figure 18 show that the highest conversion efficiency is about 97%.
Energies 2020, 13, x FOR PEER REVIEW 14 of 16 was integrated with ARF and the double-line-frequency current ripple of the energy source could be significantly reduced. Figure 18 show that the highest conversion efficiency is about 97%.    Finally, the comparison dataset for the system integrated with, and without the ARF, the actual efficiencies are measured by a WT310 power analyzer under different loads, as listed in Table 3.  Finally, the comparison dataset for the system integrated with, and without the ARF, the actual efficiencies are measured by a WT310 power analyzer under different loads, as listed in Table 3.

Conclusions
In this paper, simulations and experiments were carried out to demonstrate that the proposed ARF and its DC-side direct current control system structure could be potentially applied to produce a zero-ripple input current single-phase DC/AC architecture (patented [32,33]). The proposed control system has a DC current control loop, a voltage control loop, and a voltage feedforward control loop. The efficacy of the proposed method is verified experimentally under steady-state conditions. The results show that the proposed ARF and its control strategies offers many advantages, such as a fast dynamic response, simple implementation, a nearly zero-steady state error, and the elimination of the double-line-frequency current ripple in a single-phase DC/AC conversion system above 90%.