**1. Introduction**

Exclusively, for commercial and household applications, a single-phase active power filter has emerged as a very promising converter technology for enhancing power quality. The deterioration of power quality has become the most significant issue in modern society. The presence of harmonics in the commercial and domestic applications causes equipment heating, malfunctioning of electrical and electronics equipment, and transformer heating. Compared with traditional passive filters, the active power filter has promising features in power semiconductor device losses, power quality, structural simplicity, power regulation ability, and expanding flexibility. According to filter connection, the active power filter is classified into shunt, series, series shunt, and hybrid. Due to their small size, low cost, ability to adjust both current harmonics and reactive power, and improved efficiency, SAPF are mostly employed in medium- and low-power installations. The voltage source inverter and passive energy storage devices, such as filter inductance and DC-link capacitor, make up the basic construction of the shunt active power filter.

The primary control goal of SAPF is to adjust for harmonics and reactive power produced by the Nonlinear Load (NLL). During the harmonic compensation procedure, current control is one part and reference harmonic current extraction is the other part.

**Citation:** Aljafari, B.; Rameshkumar, K.; Indragandhi, V.; Ramachandran, S. A Novel Single-Phase Shunt Active Power Filter with a Cost Function Based Model Predictive Current Control Technique. *Energies* **2022**, *15*, 4531. https://doi.org/10.3390/ en15134531

Academic Editors: Tek Tjing Lie and Enrique Romero-Cadaval

Received: 16 May 2022 Accepted: 20 June 2022 Published: 21 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Several approaches have been presented to determine the compensation current, such as DC-link capacitor voltage control, PQ theory, and DQ theory [1–6]. The author in [6] used a DC-link capacitor voltage management approach that did not require sophisticated calculations and was simple to apply. Various current control strategies, such as hysteresis control [7,8], double-band hysteresis current control [9], and the predictive PWM control technique [10], were advocated, and their quality was appraised in many research publications that can be found in the literature. Over the last decade, many researchers have focused on power converters using model predictive control due to its simplicity, rapid transient response, easy inclusion of constraints, and nonlinearities [11,12]. To reduce the algorithm complexity and shaping, traditional MPC approaches rely on one sample forward prediction. Long prediction horizons were proposed by the authors in [13] in order to enhance power converter performance control. The two-sample-ahead predictive control approach for an NPC inverter with an output LC filter was suggested, experimentally tested, and proven in [14].

The main issue in using the MPC approach is determining the way in which the weighting factors affect future system operations in order to produce the lowest feasible error in the controlled variables [11]. The approach of selecting appropriate weighting factors is another non-trivial multi-objective optimization issue [15]. Thus, MPCC is one of the most interesting techniques for SAPF application to achieve a good dynamic performance [16–19]. The authors in [16] used an MPCC method to a single-phase shunt active power filter for harmonics and reactive power compensation. In [17], the author proposed an MPC based on three-phase SAPFs to avoid using the weighting factor to compensate the unbalanced current and current harmonic components produced by singlephase nonlinear loads. The DC-link voltage during load fluctuations was measured using a multi-objective predictive control approach applied to a single-phase three-level neutralpoint-clamped (NPC)-based active power filter (APF) for harmonic compensation and self-support in [18]. In [19], the author suggested a modified U-cell five-level inverter (MPUC5) for a single-phase Active Power Filter (APF) using a Model Predictive Control (MPC) technique. Authors in [20] proposed a PV-based dual-stage, multi-functional gridconnected inverter. This approach offers better efficiency and more stability under load changing conditions.

The majority of work reported in the literature focuses on the dynamic performance of SAPF and THD of the source current. The lowering of power converter switching frequency is still a study area in the realm of FCS-MPC-based SAPFs [20].

This manuscript presents a novel current control technique based on the cost functionbased MPCC of a single-phase SAPF. The novelty of this manuscript is the use of a weighting factor in the cost function, which reduces the switching frequency and enhances the reactive power in the utility and removes harmonic currents in the PCC. The outcomes were compared with various traditional current control methods, and it was found that it effectively tracked references with reduced switching frequency. Complete simulations were conducted using the MATLAB/Simulink environment, and real-time analysis was performed using a single-phase SAPF prototype with the Cyclone-IV EP4CE30F484 FPGA control board to confirm the efficacy of the suggested method control approach. The main aims and contributions of this manuscript are as follows.

Designs and analyzes a weighting factor-based MPCC technique to improve power quality.

To minimize the switching frequency of power switches and THD of the source current.

To assess the results using MATLAB/Simulink and verify them in real time using Cyclone-IV EP4CE30F484 FPGA technology.

The rest of this paper is organized as follows: Section 2.1 describes and models the single-phase SAPF; Section 2.2 elaborates on the weighting factor-based MPCC approach and Section 2.3 elaborates DC-link PI control scheme; Section 3 contains simulation outcomes; Section 4 provides hardware results where MPCC-based single-phase SAPF is also described; And, finally, the conclusions are presented in Section 5.

#### **2. A Modeling and Control Algorithm 2. A Modeling and Control Algorithm**  *2.1. Single-Phase SAPF Description and Modeling*

#### *2.1. Single-Phase SAPF Description and Modeling* The single-phase MPCC-based SAPF was designed to compensate for reactive power

*Energies* **2022**, *15*, 4531 3 of 17

described; And, finally, the conclusions are presented in Section 5.

The single-phase MPCC-based SAPF was designed to compensate for reactive power and current harmonics. Figure 1 illustrates how the single-phase SAPF comprises a singlephase VSI with four power switches and a DC side capacitor. While connected in parallel to the grid, the DC side capacitor supplies a DC voltage to the VSI and acts as an energy buffer. The SAPF is directly linked to the low-voltage grid via filter inductance (Lf) at the point of common coupling (PCC). This supplies a compensating current, which eliminates harmonics. The compensatory current is achieved via the use of DC-link capacitor voltage control method. and current harmonics. Figure 1 illustrates how the single-phase SAPF comprises a singlephase VSI with four power switches and a DC side capacitor. While connected in parallel to the grid, the DC side capacitor supplies a DC voltage to the VSI and acts as an energy buffer. The SAPF is directly linked to the low-voltage grid via filter inductance (Lf) at the point of common coupling (PCC). This supplies a compensating current, which eliminates harmonics. The compensatory current is achieved via the use of DC-link capacitor voltage control method.

The rest of this paper is organized as follows: Section 2.1 describes and models the single-phase SAPF; Section 2.2 elaborates on the weighting factor-based MPCC approach and Section 2.3 elaborates DC-link PI control scheme; Section 3 contains simulation outcomes; Section 4 provides hardware results where MPCC-based single-phase SAPF is also

**Figure 1.** Configuration of the single-phase shunt active power filter. **Figure 1.** Configuration of the single-phase shunt active power filter.

In both simulation and real-time analysis, a single-phase uncontrolled bridge rectifier with RL load was considered as the NLL. In both simulation and real-time analysis, a single-phase uncontrolled bridge rectifier with RL load was considered as the NLL.

Typical supply voltage and current may be expressed as Typical supply voltage and current may be expressed as

$$\mathbf{v}\_{\mathbf{s}}(\mathbf{t}) = \mathbf{V}\_{\mathbf{m}} \sin \omega \mathbf{t} \tag{1}$$

$$\dot{\mathbf{i}}\_{\mathbf{s}}(\mathbf{t}) = \dot{\mathbf{i}}\_{\mathbf{L}}(\mathbf{t}) - \dot{\mathbf{i}}\_{\mathbf{f}}(\mathbf{t}) \tag{2}$$

where V୫ —magnitude of supply voltage where V<sup>m</sup> —magnitude of supply voltage

A nonsinusoidal current is drawn when a nonlinear load is linked to a single-phase supply. This can be stated in the following way: A nonsinusoidal current is drawn when a nonlinear load is linked to a single-phase supply. This can be stated in the following way:

ஶ

$$\mathbf{i}\_{\mathcal{L}}(\mathbf{t}) = \sum\_{n=1}^{\infty} I\_{\mathbb{H}} \sin(\mathbf{n}\omega \mathbf{t} + \boldsymbol{\Theta}\_{\mathcal{n}})$$

$$\dot{\mathbf{i}}\_{\mathcal{L}}(\mathbf{t}) = \mathbf{I}\_{\mathcal{I}} \sin(\mathbf{n}\omega \mathbf{t} + \boldsymbol{\Theta}\_{\mathcal{I}}) \sum\_{n=2}^{\infty} I\_{\mathbb{H}} \sin(\mathbf{n}\omega \mathbf{t} + \boldsymbol{\Theta}\_{\mathcal{n}}) \tag{3}$$

where Iଵ & I୬—peak value of load current with fundamental and nth harmonic components, and θଵ& θ୬—phase angle of load current. where I<sup>1</sup> & In—peak value of load current with fundamental and nth harmonic components, and θ1& θn—phase angle of load current.

The current SAPF compensation is then stated as The current SAPF compensation is then stated as

$$\mathbf{i}\_{\mathbf{f}}(\mathbf{t}) = \mathbf{i}\_{\mathbf{L}}(\mathbf{t}) - \mathbf{i}\_{\mathbf{s}}(\mathbf{t}) \tag{4}$$

The total instantaneous supply current, including losses after compensation, are then be stated as

i

$$\mathbf{I\_s^\*(t) = I\_{sp} \sin \omega t} \tag{5}$$

where Isp—peak value of supply current. The supply current's peak value and phase angle must be established. The amplitude of the supply current is then computed using a standard proportional integral (PI) controller to evaluate the DC-link voltage error.

#### *2.2. Model Predictive Current Control Algorithm 2.2. Model Predictive Current Control Algorithm*

be stated as

*Energies* **2022**, *15*, 4531 4 of 17

The block diagram of the proposed cost function-based MPCC algorithm in a single phase SAPF is shown in Figure 2. The two perditions are mainly used to improve the control performances [12]. With two-step prediction, the number of calculations and computational burdens are reduced, which is suitable for higher-power applications. It also improves load current control for various references and load circumstances [13]. The block diagram of the proposed cost function-based MPCC algorithm in a single phase SAPF is shown in Figure 2. The two perditions are mainly used to improve the control performances [12]. With two-step prediction, the number of calculations and computational burdens are reduced, which is suitable for higher-power applications. It also improves load current control for various references and load circumstances [13].

where Iୱ୮—peak value of supply current. The supply current's peak value and phase angle must be established. The amplitude of the supply current is then computed using a standard proportional integral (PI) controller to evaluate the DC-link voltage error.

The total instantaneous supply current, including losses after compensation, are then

∗(t) = Iୱ୮ sin ωt (5)

iୱ

**Figure 2.** Model predictive current control algorithm and DC-link capacitor voltage regulationbased reference current extraction of single-phase SAPF. **Figure 2.** Model predictive current control algorithm and DC-link capacitor voltage regulation-based reference current extraction of single-phase SAPF.

The vector equation models of the SAPF filter current dynamics are expressed as The vector equation models of the SAPF filter current dynamics are expressed as

$$V\_o = V\_i - R\_{eq}i\_o - L\_{eq}\frac{di\_o}{dt} \tag{6}$$

Single-phase SAPF system equivalent resistance and inductance *Req Leq* , , which may alternatively be written as Single-phase SAPF system equivalent resistance and inductance *Req*, *Leq*, which may alternatively be written as

$$\mathcal{R}\_{eq} = \mathcal{R}\_f$$

and and

$$L\_{eq} = L\_s + L\_f$$

*Leq* = *Ls* + *L <sup>f</sup>* To estimate the filter current at the instant of k + 1 with a sample period Ts, the first-To estimate the filter current at the instant of k + 1 with a sample period Ts, the first-order approximation of the derivative is used.

$$\frac{di\_o}{dt} = \frac{i\_f(k+1) - i\_f(k)}{T\_S} \tag{7}$$

*S T dt* Then, 4 possible predicted filter current values of the single-phase VSI related to the inverter output voltage V<sup>i</sup> can be attained from (6) and (7) as

$$i\_{f, \, pre}(k+1) = \frac{T\_s}{L\_{eq}}(V\_i(k) - V\_s(k)) + \left(1 - \frac{R\_{eq}T\_s}{L\_{eq}}\right)i\_f(k) \tag{8}$$

where *T<sup>s</sup>* is the sampling time, *i <sup>f</sup>* , *pre* and *i f* , are the predicted filter currents at the next and present states, respectively. For one-step prediction (N = 1), the four switching states are used to predict the SAPF filter current, as presented in Figure 3a.

inverter output voltage Vi can be attained from (6) and (7) as

are used to predict the SAPF filter current, as presented in Figure 3a.

,(+1) <sup>=</sup> ௦

**Figure 3.** (**a**) Control variable of one-step prediction horizon, (**b**) control variable of two-step prediction horizon. **Figure 3.** (**a**) Control variable of one-step prediction horizon, (**b**) control variable of two-step prediction horizon.

Then, 4 possible predicted filter current values of the single-phase VSI related to the

where ௦ is the sampling time, , and , are the predicted filter currents at the next and present states, respectively. For one-step prediction (N = 1), the four switching states

൫() − ௦()൯ + ቆ1 − ௦

ቇ () (8)

The four switching states are predicted at the sampling time (k + 2) for a two-step prediction horizon (N = 2) in Figure 3b. The four switching states are predicted at the sampling time (k + 2) for a two-step prediction horizon (N = 2) in Figure 3b.

To put it another way, the filter current may be extended to a two-step prediction horizon time as follows: To put it another way, the filter current may be extended to a two-step prediction horizon time as follows:

$$i\_{f, pre}(k+2) = \frac{T\_{\rm s}}{L\_{eq}}(V\_i(k+1) - V\_{\rm s}(k+1)) + \left(1 - \frac{R\_{\rm eq}T\_{\rm s}}{L\_{eq}}\right)i\_f(k+1) \tag{9}$$

As a result, at the sampling instant (k), the control approach identifies a switching state that lowers the cost function in the sampling instant (k + 2). Table 1 shows the valid single-phase SAPF switching states. As a result, at the sampling instant (k), the control approach identifies a switching state that lowers the cost function in the sampling instant (k + 2). Table 1 shows the valid single-phase SAPF switching states.

**Table 1.** Switching states of single-phase SAPF. **Table 1.** Switching states of single-phase SAPF.


The suggested approaches' primary control goals are to improve reference current The suggested approaches' primary control goals are to improve reference current tracking and minimize switching frequency. The cost function might be stated as [5]:

0 0 0

tracking and minimize switching frequency. The cost function might be stated as [5]:

$$\mathbf{g}\_1 = \left( i\_{f,ref}(k+2) - i\_{f,ref}(k+2) \right)^2 \tag{10}$$

$$\mathbf{g\_2} = \lambda\_{sw} \times \mathbf{n\_c} \tag{11}$$

where ௦௪ is weighting factor for switching frequency reduction of the VSI; when ௦௪ > 0, switching frequency minimization can be achieved. is the number of commutations of the power semiconductors in VSI. where *λsw* is weighting factor for switching frequency reduction of the VSI; when *λsw* > 0, switching frequency minimization can be achieved. *n<sup>c</sup>* is the number of commutations of the power semiconductors in VSI.

 can be expressed as follows: *n<sup>c</sup>* can be expressed as follows:

$$m\_{\mathcal{C}} = \sum\_{\mathbf{x} = a, b} |\mathcal{S}\_{\mathbf{x}}(k) - \mathcal{S}\_{\mathbf{x}\prime} opt(k)| \tag{12}$$

where *Sx*(*k*) is the predicted switching state and *Sx*, *opt*(*k*) is the optimal switching state in the previous sample.

Usually, *λsw* is obtained using repetitive simulations to achieve optimal results for the control objective. *λsw* is evaluated using the switching frequency *fsw* and source current Total Harmonic Distortion (THD).

The final cost function combining (10) and (11) is given as

$$\mathbf{g} = \mathbf{g}\_1 + \mathbf{g}\_2 \tag{13}$$

The first-term focuses on the current tracking and the second-term focuses on the reduction in switching frequency.

The switching frequency (*Fsw*) is determined by counting the number of switching changes (*nsw*) during a particular time interval *Tf* .

$$F\_{sw} = \frac{n\_{sw}}{T\_f}$$

So the overall cost function aims to reduce the switching frequency and THD as much as possible. The detailed cost function based MPCC is demonstrated in Modified MPCC Algorithm (Algorithm 1).

The DC-link voltage should be kept constant in SAPF applications, and the source current reference is determined using the DC-link capacitor voltage regulation technique to compensate for the harmonic and reactive power provided by the non-linear load.


Input : *i f* ), (*Vdc* ) Output : *Sa*, *S<sup>b</sup>* Step 1: At the instant (k + 1) based on (8), predict the filter current *i f* , *pre* Step 2: At the instant (k + 2) based on (9), predict the filter current *i f* , *pre* Step 3: Calculate *nc* for all switching states based on (12) Step 4: Evaluate the cost function (g) based on (13) Step 5: Choose the ideal switching state and apply to the SAPF. Return to Step 1

#### *2.3. DC-Link Capacitor Voltage Control PI Control Scheme*

The voltage of the DC-link capacitor is regulated using a traditional PI controller. To retain the DC-link capacitor voltage constant, compensate the total losses of the converter; to obtain the amplitude of source current reference, the PI control is used. The source current amplitude from the PI controller output is expressed as

The PI controller obtains the value of *k*, which can be stated as follows:

$$k = k\_p \left( V\_{dc,ref} - V\_{dc} \right) + k\_i \int V\_{dc,ref} - V\_{dc} \rangle dt \tag{14}$$

where *k<sup>p</sup>* and *k<sup>i</sup>* are the gain values of the PI controller, *Vdc*,*re f* is the DC-link voltage reference, and *Vdc* is the measured DC-link voltage.

The PLL is used to generate the sine waveform. The output of the PI controller is multiplied by the sine waveform to generate the source current reference.

$$i\_{s.ref} = k \times \mu = k \times \sin \omega t \tag{15}$$

The NLL current is then combined with the supply current reference to produce the filter reference current. Finally, the MPCC receives the filter reference current and actual filter current signals to generate SAPF gating signals. This PI controller employs optimal gain values (*kp*,*k<sup>i</sup>* ).

#### **3. Simulation Results**

To validate the suggested control strategy, simulations were run in the MATLAB/ Simulink program with the parameters listed in Table 2. A two-step prediction horizon with a sampling time of T<sup>s</sup> = 10 µs and cost function are indicated in Equation (4), where the switching frequency reduction term is considered. The execution times required for the one step and two-step prediction algorithms are 5 µs and 8 µs, respectively. With the developments in the microprocessor technology, it is easy to handle this higher computational requirement and also the easy inclusion of constraints and nonlinearities.


To validate the suggested control strategy, simulations were run in the MATLAB/Simulink program with the parameters listed in Table 2. A two-step prediction horizon with a sampling time of Ts = 10 μs and cost function are indicated in Equation (4), where the switching frequency reduction term is considered. The execution times required for the one step and two-step prediction algorithms are 5 μs and 8 μs, respectively. With the developments in the microprocessor technology, it is easy to handle this higher computational requirement and also the easy inclusion of constraints and nonlinearities.

**Table 2.** Major components of single-phase SAPF. **S. No Description Components Value** 

**Table 2.** Major components of single-phase SAPF.

**3. Simulation Results** 

*Energies* **2022**, *15*, 4531 7 of 17

#### *3.1. Performance Analysis with Resistive and Inductive (RL) Load Condition 3.1. Performance Analysis with Resistive and Inductive (RL) Load Condition*

The simulation results of the proposed control approach with resistive and inductive loads are shown in Figure 4. When the proposed algorithm-based SAPF was switched on at 0.1 s, with a power factor of one, the source current became sinusoidal. The simulation results of the proposed control approach with resistive and inductive loads are shown in Figure 4. When the proposed algorithm-based SAPF was switched on at 0.1 s, with a power factor of one, the source current became sinusoidal.

**Figure 4.** *Cont*.

**Source current THD &** 

**Figure 4.** (**a**) Single-phase SAPF switch on response (**b**) source, load, and filter currents. **Figure 4.** (**a**) Single-phase SAPF switch on response (**b**) source, load, and filter currents. Weighting factor ௦௪ in the control algorithm must be adjusted heuristically through

Weighting factor ௦௪ in the control algorithm must be adjusted heuristically through simulations. By varying ௦௪ from 0 to 0.35, the switching frequency was reduced from 15.071 to 7.284 kHz and the THD increased from 3.53 to 6.203%, as presented in Figure 5. The effect of ௦௪on the source current for different weight factors is presented in Figure 6. The THD level of the source current before filtering was 28.47%, and the matching har-Weighting factor *λsw* in the control algorithm must be adjusted heuristically through simulations. By varying *λsw* from 0 to 0.35, the switching frequency was reduced from 15.071 to 7.284 kHz and the THD increased from 3.53 to 6.203%, as presented in Figure 5. The effect of *λsw* on the source current for different weight factors is presented in Figure 6. The THD level of the source current before filtering was 28.47%, and the matching harmonic spectrum is given in Figure 6A. simulations. By varying ௦௪ from 0 to 0.35, the switching frequency was reduced from 15.071 to 7.284 kHz and the THD increased from 3.53 to 6.203%, as presented in Figure 5. The effect of ௦௪on the source current for different weight factors is presented in Figure 6. The THD level of the source current before filtering was 28.47%, and the matching harmonic spectrum is given in Figure 6A.

**Figure 5.** Variation effect of weighting factor λ on the supply current THD and switching frequency. **Figure 5.** Variation effect of weighting factor λ on the supply current THD and switching frequency.

**Figure 5.** Variation effect of weighting factor λ on the supply current THD and switching frequency. **Weighing Factor** An acceptable value of ௦௪ for the validation testing would be 0.1 since, with weight factor ௦௪ = 0.1, the source current THD was determined to be 4.66% and the switching frequency was reduced from 15.071 to 12.866 kHz as shown in Figure 6B. An acceptable value of *λsw* for the validation testing would be 0.1 since, with weight factor *λsw* = 0.1, the source current THD was determined to be 4.66% and the switching frequency was reduced from 15.071 to 12.866 kHz as shown in Figure 6B.

frequency was reduced from 15.071 to 12.866 kHz as shown in Figure 6B.

An acceptable value of ௦௪ for the validation testing would be 0.1 since, with weight factor ௦௪ = 0.1, the source current THD was determined to be 4.66% and the switching

**Figure 6.** Simulation results of source current and harmonic spectrum: (**A**) source current (before compensation), (**B**) source current waveform (λ = 0), (**C**) source current waveform (λ = 0.05), (**D**) source current waveform (λ = 0.1). **Figure 6.** Simulation results of source current and harmonic spectrum: (**A**) source current (before compensation), (**B**) source current waveform (λ = 0), (**C**) source current waveform (λ = 0.05), (**D**) source current waveform (λ = 0.1). **Figure 6.** Simulation results of source current and harmonic spectrum: (**A**) source current (before compensation), (**B**) source current waveform (λ = 0), (**C**) source current waveform (λ = 0.05), (**D**) source current waveform (λ = 0.1).

#### *3.2. Performance Analysis with Resistive and Capacitive (RC) Load 3.2. Performance Analysis with Resistive and Capacitive (RC) Load 3.2. Performance Analysis with Resistive and Capacitive (RC) Load*

In this analysis, the SAPF system was analyzed with the RC load condition. The supply current THD before compensation was 35.36%. When SAPF was connected to the PCC In this analysis, the SAPF system was analyzed with the RC load condition. The supply current THD before compensation was 35.36%. When SAPF was connected to the PCC In this analysis, the SAPF system was analyzed with the RC load condition. The supply current THD before compensation was 35.36%. When SAPF was connected to the PCC at 0.05 s, the source current THD reduced from 35.36 to 3.97%.

at 0.05 s, the source current THD reduced from 35.36 to 3.97%. The comparative analysis of the proposed controller with a conventional MPCC is shown in Table 3. From the results, it can be observed that the proposed MPCC offers a at 0.05 s, the source current THD reduced from 35.36 to 3.97%. The comparative analysis of the proposed controller with a conventional MPCC is shown in Table 3. From the results, it can be observed that the proposed MPCC offers a The comparative analysis of the proposed controller with a conventional MPCC is shown in Table 3. From the results, it can be observed that the proposed MPCC offers a better performance in terms of reduced source current THD and switching frequency.

better performance in terms of reduced source current THD and switching frequency. **Table 3.** Summary of the simulation test results for weighting factor-based MPCC of single-phase better performance in terms of reduced source current THD and switching frequency. **Table 3.** Summary of the simulation test results for weighting factor-based MPCC of single-phase **Table 3.** Summary of the simulation test results for weighting factor-based MPCC of single-phase SAPF, including THD and switching frequency with RC load.


**FSW (kHz)** - 14.307 12.620

**FSW (kHz)** - 14.307 12.620

using four IGBT switches with protection and control circuits from Mitsubishi Intelligent Power Modules (IPMs). A diode bridge rectifier with a series resistor and an inductor was also included. Load variation was achieved by connecting and disconnecting parallel

using four IGBT switches with protection and control circuits from Mitsubishi Intelligent Power Modules (IPMs). A diode bridge rectifier with a series resistor and an inductor was also included. Load variation was achieved by connecting and disconnecting parallel

**4. Experimental Results** 

**4. Experimental Results** 
