Comparison of Direct and Indirect Control Strategies Applied to Active Power Filter Prototypes

Abstract

The proliferation of power converters in modern energy production systems has led to increased harmonic content due to the commutation of active switching devices. This increase in harmonics contributes to lower system efficiency, reduced power factor, and consequently, a higher reactive power requirement. To address these issues, this paper presents both simulation and experimental results of various control strategies implemented on Parallel Voltage Source Inverters (PVSI) for harmonic mitigation. The proposed control strategies are categorized into direct and indirect control methods. The direct control techniques implemented include the instantaneous power method (PQ), the synchronous algorithm (DQ), the maximum principle method (MAX), the algorithm based on synchronization of current with the voltage positive-sequence component (SEC-POZ), and two methods employing the separating polluting components approach using a band-stop filter and a low-pass filter. The main innovation in these active power filter (APF) control strategies, compared to traditional or existing technologies, is the real-time digital implementation on high-speed platforms, specifically FPGAs. Unlike slower microcontroller-based systems with limited processing capabilities, FPGA-based implementations allow parallel processing and high-speed computation, enabling the execution of complex control algorithms with minimal latency. Additionally, the enhanced reference current generation achieved through the seven applied methods provides precise harmonic compensation under highly distorted and nonlinear load conditions. Another key advancement is the integration with Smart Grid functionalities, allowing IoT connectivity and remote diagnostics, which enhances system monitoring and operational flexibility. Following validation on an experimental test bench, these algorithms were implemented and tested on industrial APF prototypes powered by a standardized three-phase network supply. All control strategies demonstrated an effective reduction in total harmonic distortion (THD) and improvement in power factor. Experimental findings were used to provide recommendations for choosing the most effective control solution, focusing on minimizing THD and enhancing system performance.

1. Introduction

With the continuous development of modern electrical power supply systems, static power converters have become essential components. While they offer significant benefits, particularly in load control, they also introduce notable drawbacks. The switching actions of power semiconductor devices within these converters generate reactive power demand and distort the voltage and current waveforms in the supply system.

Active power filters (APFs), which are themselves based on static power converters, are classified according to their control mode (current-controlled mode [1,2,3,4] or voltage-controlled mode [5,6,7,8]) and their connection configuration (series [9,10,11], parallel [12,13,14], or hybrid [15,16]). APFs are widely used to compensate for power quality issues such as harmonic distortion, reactive power, and voltage variations caused by nonlinear loads [9,12,17,18,19]. A notable approach introduced in [14] determines the required compensation current by sensing the load current and subsequently adjusting it based solely on the line currents [11,20,21]. Another system proposed in [21] provides instantaneous reactive compensation and harmonic suppression without using voltage sensors, though it requires more complex hardware for generating the reference currents.

A current-controlled parallel APF (i^*_F) ensures that the supply current (i_s) remains sinusoidal regardless of the nonlinear load current (i_L), as illustrated in Figure 1. This topology also performs power-factor correction by maintaining an almost zero phase shift between the supply voltage and the grid-absorbed current, independent of the load-induced phase displacement at the user terminals.

The current-controlled parallel active filter can only act on downstream disturbances and is unable to reduce disturbances in the rest of the electrical network. From an economic point of view, there are solutions to reduce odd harmonics by connecting the power transformers or installing passive filters, with resonant circuits, combined with active current filters for a sinusoidal shape of the current in the power supply. According to power quality standards, the level of harmonic distortion must be limited [22,23].

Several methods can be employed to limit harmonic distortion in power systems. One approach is to install an LC filter in the rectifier’s DC-link, which helps maintain continuous current flow and reduce distortion. Harmonics can also be mitigated by increasing the short-circuit power of the supply system through reduced source impedance. Proper configuration of loads can enable mutual cancellation of harmonic components, while selecting appropriate transformer connection schemes—such as delta–wye arrangements—can further suppress specific harmonic orders. For high-power applications, using rectifiers with a higher pulse number significantly decreases the harmonic content. Active front-end rectifiers and inverters with integrated filtering elements also contribute to improved current quality by shaping or smoothing input waveforms. Finally, active power filters can dynamically inject compensating currents to counteract harmonics generated by nonlinear loads.

Many control strategies, such as the instantaneous reactive power theory originally developed by Akagi et al. [24], the d-q theory in a synchronous reference system [16], the synchronous detection method [25], and the band-stop filter method [26,27], are used in the development of three-phase APFs [28]. To improve the dynamic and steady state performances of the active power filter (APF), and taking advantage of advances in microelectronic technology, online APF control can be implemented using advanced algorithms, such as proportional-integral (PI) controllers [29,30,31], variable structure control [32,33,34], and intelligent control techniques, including fuzzy logic and neural network controllers [35]. With these improvements, APFs can provide fast corrective actions, even with dynamically changing nonlinear loads.

In summary, various control strategies exist for active power filters, each with its own advantages and disadvantages [36,37,38]. The best choice depends on the specific application requirements and the desired performance characteristics [39,40,41,42,43,44,45,46,47,48,49].

At the level of load current harmonic distortion, the following effects may occur in the power grid (

Table 1. Effects caused by load current distortions.

	Intermittent Effects	Steady State Effects
Load current ($I_{Load}$)	Malfunction of protective relays and circuit breakers; Increased voltage distortions due to resonance.	Increased power losses in the transmission, power distribution, and consumer chains. Low accuracy of measuring instruments and measurements. Voltage distortion is inversely proportional to the ratio $I_{Load}/I_{SC}$.

):

Compared to passive power filters, active filters can dynamically compensate the power grid independently of the system’s impedance, thereby avoiding resonance. They are also capable of continuously adjusting the reactive power, regardless of the grid frequency. Active power filters implement advanced algorithms, such as the Fast Fourier Transform (FFT), which computes the Discrete Fourier Transform (DFT) in the frequency domain, or the Park and Clarke transforms in the time domain. In contrast, the indirect control compensation process relies solely on the detection of line currents, differing from other conventional methods (Table 2) that require measurement of harmonics or reactive power components of the load.

In a three-phase circuit, power filters—whether passive, active, or hybrid—are connected at the common coupling point (PCC) of the system. The command-and-control circuit integrates measurement circuits, microcontrollers, and voltage source inverter (VSI) drivers.

In the case of a parallel-type active power filter, as shown in Figure 1, the reference current ($i_F^{*}$) is generated by a voltage source converter and is determined according to the applied control algorithms.

In Figure 2, the comparative configurations of the direct (a) and indirect (b) control systems are presented. In the case of indirect control (Figure 2b), fewer current transducers are required, as the measurement of the polluting load current is not necessary. The system uses the load current ($i_L$), the mains voltage ($V_s$), and the DC-link voltage ($V_{DC}$) as input signals (Figure 2a,b). Based on the reference currents delivered by the active filter, the corresponding gate signals are sent to the IGBT three-phase power bridge.

In a three-phase circuit, active power filters—whether passive, active, or hybrid—are connected at the point of common connection (PCC) (Figure 2). The objective of this paper is to synthesize the practical results of the implemented control strategies on the shunt active power filter prototypes [29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Based on the experimental results, the most effective compensation solution will be recommended for industrial applications [41]. The primary objectives of the implemented APFs are to maintain a constant DC-link voltage, ensure that the current supplied from the power grid is sinusoidal, and guarantee that the supplied current is in phase with the grid voltage.

Based on the defined objectives, the shunt APF is designed around a control structure that includes a PLL loop to generate sinusoidal signals synchronized in frequency and phase with the phase voltages of the electrical power supply, an external loop for regulating the DC-link voltage, and three current regulation loops—one for each phase—implemented with a P-type (proportional) controller. The generated signals are fed into a hysteresis modulator to produce the control pulses for the three-phase active power filter. The voltage loop determines the amplitude of the current exchanged with the grid, while the current loops impose the sinusoidal reference currents. Using the hysteresis modulator, the control signals for the voltage source inverter within the APF simultaneously compensate for both the current harmonics in the grid and the reactive power.

From a constructive point of view, shunt active power filters (SAPFs) are composed of several key elements: a three-phase voltage inverter with pulse-width modulation (PWM) control; a real-time electronic computing system based on reconfigurable, high-speed FPGA-type digital circuits; voltage and current transducers; a general-purpose computer or PC for configuring the FPGA; a three-phase programmable AC voltage source; three-phase nonlinear electrical loads; and interface inductances between the voltage inverter and the point of common connection (PCC) between the source and the nonlinear loads.

Active power filters (APFs) are widely used to mitigate power quality issues such as harmonics, reactive power, and unbalanced loads. Despite significant advancements, existing control strategies for APFs exhibit several limitations. For example, traditional PI controllers in the synchronous reference frame (SRF) often respond slowly to sudden load changes or disturbances, resulting in reduced compensation accuracy during transient conditions. Additionally, methods based on the Fourier Transform or SRF may fail to detect harmonics accurately in non-stationary or distorted waveforms, leading to incomplete compensation and residual harmonic content.

Advanced control techniques can provide improved performance, but they often demand significant computational resources, which limit their real-time implementation, particularly in low-cost or embedded systems. Certain control schemes, such as PLL-based SRF methods, are sensitive to variations in system parameters, including grid frequency, voltage fluctuations, and load impedance, which can lead to reduced performance and compromised stability under changing grid conditions. Moreover, techniques like hysteresis control with variable switching frequency or complex coordinate transformations (dq0, αβ) complicate practical implementation, increasing the effort required for design, tuning, and maintenance. Additionally, some controllers achieve optimal performance only under balanced, linear load conditions, reducing their effectiveness in realistic industrial environments.

The consequence of these limitations is reduced effectiveness in realistic environments, such as industrial facilities with welding equipment or variable-speed drives. To address these challenges, adaptive control techniques can be employed to enhance the dynamic response and maintain performance under varying operating conditions. Additionally, advanced signal processing methods, such as wavelet transforms, empirical mode decomposition (EMD), or adaptive notch filters, can replace traditional FFT or SRF-based techniques to improve harmonic detection in non-stationary and distorted signals. The implementation of Digital Signal Processors (DSPs) or FPGAs allows for high-speed, parallel-processing control platforms, further enhancing system performance. Despite these advancements, challenges related to adaptability, detection accuracy, dynamic response, and implementation complexity remain. In conclusion, leveraging adaptive control, advanced signal processing, and hardware acceleration can effectively overcome these challenges, enabling more accurate and reliable compensation in active power filters.

In [50], based on the presented theory, the concept of a harmonic-free power system is introduced for both SAPF control modes: indirect and direct. Following these objectives, this paper presents the numerical and experimental results obtained on industrial active filter prototypes supplied from a standard voltage level. These results aim to facilitate technological transfer to industry [51]. The reference implementation is based on the experimental test bench of the parallel-type active filter [50]. The algorithms discussed in this paper have been previously tested and validated at low, non-standardized voltage levels [50]. In this study, however, active power filter solutions are implemented at a standard supply voltage. Based on the results from individually tested prototypes, comparative total harmonic distortion levels are presented, allowing the authors to recommend the most efficient harmonic compensator for the industrial oven load [41,42,43,51].

Figure 2. Block diagrams of the complete active power filter system, illustrating (a) the indirect control approach and (b) the direct control approach [51].

Figure 2. Block diagrams of the complete active power filter system, illustrating (a) the indirect control approach and (b) the direct control approach [51].

Table 2. Summary of the implementation procedures and key characteristics of the direct and indirect control algorithms employed in the active power filter system [52,53].

No.	Control Strategies of the APF Prototypes	Abbreviation of the Implemented Configuration
1	Developed on the principle of instantaneous powers (PQ)	FAP-0S
2	Developed on the principle of synchronous algorithm (DQ)	FAP-0US
3	Developed on the principle of maximum (MAX)	FAP-0IA
4	Developed on the principle of indirect control (CI)	FAP-0ET
5	Developed on the principle of synchronization of current with the voltage positive-sequence component (SEC-POZ)	FAP-0E
6	Developed on the low-pass filter separating polluting components method (LPF)	FAP-0SE
7	Developed on the band-stop (notch) filter separating polluting components method (BSF)	FAP-0D

Table 2. Summary of the implementation procedures and key characteristics of the direct and indirect control algorithms employed in the active power filter system [52,53].

No.	Control Strategies of the APF Prototypes	Abbreviation of the Implemented Configuration
1	Developed on the principle of instantaneous powers (PQ)	FAP-0S
2	Developed on the principle of synchronous algorithm (DQ)	FAP-0US
3	Developed on the principle of maximum (MAX)	FAP-0IA
4	Developed on the principle of indirect control (CI)	FAP-0ET
5	Developed on the principle of synchronization of current with the voltage positive-sequence component (SEC-POZ)	FAP-0E
6	Developed on the low-pass filter separating polluting components method (LPF)	FAP-0SE
7	Developed on the band-stop (notch) filter separating polluting components method (BSF)	FAP-0D

This paper aligns with the energy policies of Romania and the European Union by presenting research results obtained at Dunărea de Jos University of Galați. In the first part of the paper, the developed equipment, technical specifications of the industrial prototypes, and the control strategies implemented for each prototype are described, along with the corresponding mathematical models and experimental results. The numerical and experimental results presented in this article were obtained within the framework of the project “Knowledge transfer regarding increasing energy efficiency and intelligent power systems” (CRESC-INTEL), conducted under the Operational Program Competitiveness (POC). The project activities fall within the field of energy, aiming to improve energy efficiency through static conversion systems in industrial power networks and to develop industrial prototypes for subsequent production by partner enterprises.

The contributions of this paper are as follows [52,53]:

• The validation of shunt active power filter control strategies implemented on industrial prototypes.
• Demonstration of the applicability of both experimental and prototype systems across a wide range of electrical parameters.
• Implementation of power systems in real-time using versatile, reconfigurable electronic circuits based on FPGA technology.
• Comparative analysis of various active power filter control strategies under both direct and indirect operation modes.
• Identification of the most efficient compensation solution based on distortion analyses of the implemented control strategies on the industrial active power filter prototypes.

This paper is organized into six sections. The Introduction outlines the study’s objectives and provides a state-of-the-art review of active power filters, along with a discussion of the effects caused by load current distortions. Section 2, Materials and Methods, describes the control strategies used to improve power quality, each corresponding to a specific active power filter prototype; in total, seven control methods are examined. Section 3 presents the main technical data of the SAPF prototypes, while Section 4 introduces the block diagrams of the SAPF control systems, together with the implemented diagrams developed in Matlab/Simulink R2025b (The MathWorks, Inc., Natick, MA, USA) These models are used to derive the numerical values of the total harmonic distortion of the current (THDi). Section 5 reports the experimental results obtained from the SAPF prototypes and identifies the most effective control solution for harmonic compensation. Finally, Section 6 summarizes the key findings of the study, emphasizing the performance of the tested control strategies, the effectiveness of the SAPF prototypes, and the recommended solution for industrial applications.

2. Materials and Methods

The industrial prototypes share the same constructive structure as the FAP-0L [50], allowing them to be powered either from a programmable three-phase alternating voltage source or autonomously from the alternating voltage at the common connection point (PCC). To validate the control operation of both the experimental system (FAP-0L) and all prototypes at standardized voltage levels, seven control strategies have been implemented (Table 2):

• Indirect control (CI): This strategy does not require the active power filter to have knowledge of the harmonics of the load currents or the reactive power components [54,55,56,57,58].
• Positive-Sequence Current Synchronization Control (SEC-POS, FAP-0E): This control strategy operates by synchronizing the source current with the positive-sequence component of the source voltage, ensuring a balanced current that remains in phase with the voltage [59,60,61,62].
• Polluting Component Separation Control—Band-Stop Filter (BSF, FAP-0SE): In this strategy, the load currents are processed through a band-stop filter designed to remove the fundamental frequency, resulting in reference currents that correspond to the harmonic components for all three phases [63,64,65,66,67,68,69,70,71,72].
• Maximum Principle Control (MAX, FAP-0IA): This strategy filters the distorted load current to extract its fundamental component. The alternating current generated by the active filter is made to follow the reference signal obtained from the current reference generator. In this method, the distorted load current passes through a band-pass filter tuned to the fundamental frequency (50 Hz), which introduces zero gain attenuation and a 180° phase shift. As a result, the filter output equals the fundamental component of the load current but is phase-shifted by 180°. By adding the load current to this phase-shifted fundamental component, the reference current waveform required to compensate only for the harmonic distortion is obtained. Additionally, to provide the reactive power demanded by the load, the signal from the band-pass filter is synchronized with the corresponding source phase voltage. Consequently, the active filter current leads its voltage, supplying the required reactive power while absorbing the real power needed to maintain constant DC-link voltage and compensate for switching losses [73,74,75,76].
• Instantaneous Power Control (PQ, FAP-0S): This method compensates for harmonic currents in both balanced and unbalanced voltage conditions by using the instantaneous power theory. The control algorithm calculates the instantaneous active and reactive powers of the load and determines the appropriate compensating currents that the active filter must inject. By doing so, the harmonic and reactive power components are effectively mitigated, ensuring that the supply current remains as close as possible to a sinusoidal waveform and in phase with the source voltage [9,77,78,79,80,81].
• Synchronous Reference Frame Control (DQ, FAP-0US): This method uses the synchronous DQ reference frame to extract the harmonic components of the load current. By transforming the three-phase load currents into the rotating DQ frame, the harmonic and reactive components can be separated from the fundamental active component. The active power filter then injects the compensating currents to cancel out these distortions, ensuring that the supply current remains sinusoidal and in phase with the source voltage. This approach is effective for both balanced and unbalanced loads, providing precise harmonic mitigation in dynamic conditions [82,83,84,85,86,87,88].
• Control based on Separation of Polluting Components—Low-Pass Filter (LPF, FAP-0D): This method employs a low-pass filter to extract the fundamental component of the load current, isolating it from the harmonic (polluting) components. The active power filter then injects currents that compensate for the harmonics, ensuring that the supply current remains sinusoidal and in phase with the grid voltage. This approach is particularly useful for effectively reducing harmonic distortion while maintaining the reactive power requirements of the load [89,90,91].

One of the key features of SAPFs is the reduction of harmonic content. Consequently, the direct control strategies (methods 1–3 and 5–7 from Table 2) require measurement of the highly polluting load currents. In contrast, the indirect control (method 4) does not measure the load currents directly; instead, the reference currents for the SAPF are obtained through indirect estimation or calculation based on specific power theories or system measurements [50].

3. Main Technical Data of the SAPF Prototypes

In this section, the technical datasheets of the implemented active power strategies on the various industrial prototypes are outlined.

Table 3. The main technical data of the PQ prototype.

Rated Voltage		400 V ±10% [V]
Rated frequency		50 [Hz]
Rated current		125 [A]
Phase numbers		3 Phase + PE
Degree of protection		IP21
Cooling		Forced cooling
Compliance standards		EN 61000-6-2 [92], EN 61000-6-4 [93], EN 50178 [94]
Control method		LabVIEW FPGA, principle of instantaneous powers (PQ)
Communication interface		ETHERNET; RS 232; RS 485; CAN; USB.
Harmonic range		1–50 (50–2500 Hz/50 Hz)
Dimensions (L × W × H) mm		1020 × 370 × 1170
Main circuit fuses		Yinrong RT18L-125 100 A
Auxiliary circuit fuses		Schrack AM417506 C16/1N
Climatic conditions	Ambient temperature	Relative humidity	Atmospheric pressure
Operational	5–40 °C	5–85%	86–106 kPA
Storage	−25–55 °C	5–95%	86–106 kPA
Transport	−25–70 °C	95%	70–106 kPA

summarizes the key technical specifications of the active power filter prototype implemented using the instantaneous power (PQ) control method.

In Figure 3, the physical PQ prototype is presented.

The main technical data of the DQ prototype is like the PQ prototype (Table 1).

In Figure 4, an overview of the physical DQ prototype is presented.

The main technical specification of the MAX prototype differs primarily from the previously mentioned prototypes in terms of its rated current, which is 150 A. An overview of the physical MAX prototype is shown in Figure 5.

In Figure 6, an overview of the physical indirect control prototype is presented.

The main technical specifications of the indirect control prototype are similar to those of the PQ prototype (Table 1), with the primary difference being a nominal current of 200 A. An overview of the physical SEC-POZ control-based prototype is shown in Figure 7.

For the band-stop (notch) filter separating polluting components control-based prototype, the rated current is 125 A. An overview of the physical notch control-based prototype is presented in Figure 8.

In Figure 9, an overview of the physical low-pass filter separating polluting components control-based prototype is presented.

For the low-pass filter separating polluting components control-based prototype, the rated current is 25 A.

4. Numerical Results

The numerical results obtained are presented separately for the indirect control and direct control methods. This section presents the dynamic models of the power supply systems, which include the power supply, the nonlinear load consisting of a six-pulse bridge uncontrolled rectifier, and the static power equipment for the active elimination of harmonics from the national power grid, namely the active power filter (Figure 1), with a control structure based on the methods presented in Table 2 (Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9) [42,43,44,45,46,47,48,49,52,53].

4.1. Indirect Control

Indirect control refers to a strategy in which the reference currents for the active power filter (APF) are not directly measured from the load currents but are obtained through indirect estimation or calculation based on certain power theories or system measurements. In APF applications, the indirect control method is primarily used to generate the reference compensating currents that the APF must inject into the system to cancel harmonics and reactive power components. The main advantages of indirect control include the elimination of direct harmonic extraction from the load current, which simplifies signal processing, improves robustness against measurement noise, eases implementation in real-time control and provides effective operation with instantaneous power theories that provide direct insight into the power components. In Figure 10, the basic block diagram of the indirect control strategy for the active power filter is presented.

In Figure 11, an overview of the indirect control implementation in MATLAB–Simulink is presented. By using this indirect control approach within MATLAB–Simulink, a total harmonic distortion of the supply current (THDi) of 3.17% was achieved, as shown in Figure 12.

Indirect control involves evaluating signals from the network, such as the supply voltage or fundamental components, to estimate the current behavior and generate a control signal that ensures proper harmonic compensation, without directly measuring the polluting current. The algorithm relies on information obtained from the analysis of the network voltage and current through various estimation and calculation techniques to produce the compensating current that eliminates harmonics. By using this approach, an accurate compensation solution can be achieved without directly intervening in the load current. In Figure 10, the basic block diagram of the indirect control for the active power filter is presented, while Figure 11 shows the MATLAB–Simulink implementation of this control strategy. Using this simulation setup, a total harmonic distortion of the supply current (THDi) of 3.17% was obtained, as depicted in Figure 12.

4.2. Direct Control of Active Power Filters

In the direct control category, six methods are employed for regulating the operation of the SAPF.

4.2.1. Instantaneous Power (PQ)-Based Control

The instantaneous power theory, also known as the PQ theory, was proposed by Akagi [24] in the 1980s and has become a widely used method for the control of shunt active power filters, particularly in three-phase systems. This theory is highly effective for real-time harmonic extraction, operation under non-sinusoidal conditions, and simultaneous compensation of harmonics, reactive power, and unbalanced loads. The PQ theory calculates instantaneous active power (P) and instantaneous imaginary/reactive power (Q) in the stationary α–β reference frame, obtained via the Clarke transformation, and uses these values to generate a compensation current that cancels unwanted non-fundamental components.

Real-time implementations of harmonic elimination based on this theory have been reported in [95], while its application to unbalanced loads and unsymmetrical power supplies is discussed in [96]. In typical power systems, voltage and current waveforms can be distorted by harmonics, causing problems such as overheating, voltage fluctuations, and interference with other equipment. The PQ theory allows the separation of instantaneous active power, related to actual energy transfer, from instantaneous reactive power, related to energy temporarily stored and returned by reactive components. This separation enables dynamic, instantaneous compensation of harmonics and adapts effectively to changing load conditions.

However, inaccurate calculation of harmonic components may occur if the voltage waveform is distorted, which can lead to suboptimal compensation. In this study, the PQ control method, based on sinusoidal source current control, was implemented on one of the prototypes [81]. In Figure 13, the basic block diagram of the instantaneous power-based control for the active power filter is presented.

The PQ control method was implemented in MATLAB–Simulink to simulate the active power filter operation. Using this implementation, a total harmonic distortion of the current (THDi) of 3.64% was obtained, as shown in Figure 14. This result demonstrates the effectiveness of the instantaneous power theory in compensating for harmonic components and improving the quality of the supply current.

The current control system is implemented in the fixed reference frame (a, b, c). The reference current generation is performed according to the Akagi method [24]. The control logic is based on calculating the active and reactive power of the load, which determines the phase and magnitude of the current that the active power filter must inject into the system. The filter’s current references are computed as shown in Figure 11. In this process, the three-phase source voltages and the three-phase load currents are transformed into the (α,β) stationary reference frame using the direct Clarke transform. Figure 15 presents the MATLAB–Simulink implementation of the PQ control algorithm.

4.2.2. Synchronous Algorithm (DQ)-Based Control

Synchronous Algorithm (DQ)-Based Control: This control strategy is highly effective for dynamic and precise harmonic compensation. The DQ control provides fast dynamic response, accurate harmonic extraction, reactive power compensation, and grid synchronization (via PLL). The algorithm [82,83,84,85,86,87,88] is based on transforming the three-phase voltages and currents (a, b, c) into a synchronous d-q coordinate system, which allows the separation of active and reactive current components and facilitates precise control of the compensating current as dc quantities. The synchronous DQ algorithm (Park transform) converts load currents into DC quantities synchronized with the supply voltage, mapping nonlinear three-phase signals into a rotating reference frame aligned with the fundamental frequency (50 Hz). This transformation enables precise separation of the active (real) and reactive (imaginary) components, making the control more efficient. Operating synchronously with the grid ensures that the filter current is correctly aligned with the fundamental voltage. The DQ algorithm [97] also enables fast and accurate harmonic current compensation, reducing voltage distortion and improving the power factor with high performance. However, it requires complex calculations, potentially additional hardware for real-time implementation, and may need modifications to handle variable or unbalanced load conditions effectively.

In Figure 16, the basic block diagram of the synchronous algorithm (DQ) based control of the active power filter is presented.

By implementing DQ control in MATLAB–Simulink, a total harmonic distortion of the current (THDi) of 3.40% was obtained (Figure 17), demonstrating its effectiveness in harmonic compensation and reactive power management compared to other strategies.

In Figure 18, the MATLAB–Simulink implementation of the synchronous algorithm (DQ) control is shown, illustrating the transformation of three-phase voltages and currents into the d-q reference frame and the generation of the corresponding compensating currents for the active power filter.

4.2.3. Maximum Principle (MAX)-Based Control

The APF controller continuously monitors the load current waveform and employs maximum value detection to track the peak instantaneous current. By identifying when and where the current deviates from an ideal sinusoidal shape, the controller estimates the harmonic distortion. This comparison between the actual load current and the ideal sinusoidal reference allows the APF to generate an appropriate compensating current, effectively reducing harmonics and maintaining a more sinusoidal current flow in the power system. The MAX Detection Method offers a simple and effective approach for harmonic compensation in active power filters. It is easy to implement, requiring less computational effort, and provides a fast, real-time response by detecting the maximum harmonic values directly in the time domain, without the need for FFT or other frequency domain analyses. Additionally, it is relatively robust to waveform distortions and frequency fluctuations. However, the method has some limitations: it is sensitive to noise, such as spikes, which can affect peak detection; it is generally less accurate than advanced techniques like DQ or PQ theory; and it may struggle with unbalanced loads, where the fundamental current is not tracked precisely. Overall, the MAX method is well-suited for low-cost or simple APF applications requiring fast, time domain compensation, but may be less effective in complex or high-precision scenarios. The MAX control method is particularly suitable for low-cost APF designs, single-phase APFs, and real-time control applications where DSP resources are limited. It operates by extracting the fundamental component from the distorted load current using a band-pass filter (BPF) tuned to the network frequency (50 Hz). The primary objective is to accurately identify the fundamental component corresponding to the ideal current and generate the corresponding compensating signal. The BPF is centered at 50 Hz, with 0 dB attenuation at this frequency to preserve the fundamental component, and introduces a 180° phase shift. This phase inversion is critical, as it produces an inverted reference signal used to compensate for harmonics and reactive power. The algorithm monitors the maximum amplitude of the extracted fundamental component, and when this peak is reached, the exact phase of the fundamental signal is determined. This phase information is then used to align the compensating signal generated by the active power filter.

In Figure 19, the basic block diagram of the maximum principle (MAX)-based control of the active power filter is presented.

The distorted load current is measured and passed through a band-pass filter tuned to 50 Hz, which extracts the fundamental component. At the filter output, the signal is phase-inverted, introducing a 180° phase shift at the central frequency [73,74,75,76]. The reactive power demanded by the load is supplied by synchronizing this phase-inverted signal with the network voltage. Harmonic compensation is achieved by adding the extracted fundamental component, obtained via the maximum method, to the load current. A key advantage of this approach is that the compensating current is derived directly from the load current, without requiring any reference frame transformations.

Implementation of the maximum principle (MAX) control in MATLAB–Simulink resulted in a total harmonic distortion of the current (THDi) of 4.32% (Figure 20).

In Figure 21, the MATLAB–Simulink implementation of the maximum principle (MAX) control is shown.

4.2.4. Principle of Current Synchronization with the Voltage Positive-Sequence Component (SEC-POZ) Based Control

Controlling active power filters (APFs) based on current synchronization with the positive-sequence component of the voltage is a robust and selective method and is particularly effective in unbalanced and distorted power systems. This approach ensures that the compensation current injected by the APF remains synchronized with the positive-sequence component of the grid voltage, representing the balanced and clean portion of the voltage waveform.

The SEC-POZ method is based on extracting the positive-sequence component of the supply voltage using symmetrical component analysis. It generates a reference current that is in phase with this component, ensuring active power flow while the APF injects only the non-active current components, including harmonics, as well as positive-, negative-, and zero-sequence components. Consequently, the source supplies only the positive-sequence active power. This approach is particularly effective in weak or distorted grids, nonlinear and unbalanced loads, and distributed generation systems. The main objectives of the control are to maintain a unity power factor, ensure balanced sinusoidal currents drawn from the supply, eliminate harmonic, reactive, and unbalanced components from the load current, and preserve synchronization with the positive-sequence voltage.

The advantages of the SEC-POZ method include its ability to operate under unbalanced and distorted voltage conditions, ensure that only active power is drawn from the source, provide perfectly sinusoidal and balanced source currents, and maintain resilience against grid disturbances. The main challenges include the critical requirement for accurate positive-sequence extraction—especially under distorted voltage conditions—which demands a robust PLL with adequate filtering, as well as a slightly increased computational burden resulting from the required transformations and sequence separation.

In Figure 22, the basic block diagram of the active power filter control that is based on current synchronization with the voltage positive-sequence component (SEC-POZ) is presented.

In a system with unbalanced loads and non-sinusoidal supply voltages, the positive-sequence component is responsible for generating the magnetic field corresponding to the normal operation of electrical machines [38,67,70]. The SEC-POZ method aims to balance the power supply currents, reduce harmonics, and maintain them in phase with the positive-sequence component of the supply voltage. This approach ensures a minimum zero-sequence current, correct phasing of the positive-sequence supply current with the corresponding voltage, and consequently eliminates harmonic distortions, maintains a balanced load current, achieves unity power factor, and improves overall efficiency. The fundamental component of the supply voltage is extracted using a band-pass filter. Through symmetrical component transformation (Fortescue), the positive-sequence voltage is obtained. By measuring the load currents, the average instantaneous power is calculated and integrated over a period of the supply voltage to determine the load’s active power. Based on this, the maximum value of the positive-sequence reference current is derived. The sinusoidal reference current waveform is then generated as shown in the block diagram of Figure 22, and the filter reference currents are obtained by comparing them with the corresponding load currents.

By implementing the maximum principle (MAX) control in MATLAB–Simulink, a THDi value of 4.24% was obtained (Figure 23). In Figure 24, the MATLAB–Simulink implementation of the voltage positive-sequence component (SEC-POZ) control is presented.

4.2.5. Band-Stop Filter (Notch Filter)-Based Control

A band-stop filter (also known as a notch filter) is designed to remove a specific range of frequencies, and in this case, the fundamental frequency (50/60 Hz). For a band-stop filter centered at 50 Hz (or 60 Hz), the fundamental frequency is blocked while the harmonics are allowed to pass through. The active power filter (APF) is then controlled to inject the same harmonic quantities in opposite phase, effectively canceling them and ensuring that only the fundamental current is drawn from the source, resulting in a cleaner power system.

The advantages of this control method include a simple control strategy, no need for complex transformations (such as dq0), and the possibility to tune it to remove specific harmonics using multiple band-stop filters. However, some drawbacks exist: filtering may introduce delays that affect dynamic response, the band-stop filter must be carefully designed to isolate the fundamental frequency accurately, and the method is less suitable for real-time control of rapidly changing loads without optimization.

The elimination of the fundamental frequency from the load current is achieved using the notch filter, which extracts the harmonic components and ensures a sinusoidal waveform for the load currents. Synchronization of the APF current references is performed using the supply voltages. In Figure 25, the basic block diagram of the band-stop filter (notch filter) method for separating polluting components is presented.

By implementing the band-stop (notch) filter method for separating polluting components in MATLAB–Simulink, a THDi value of 5.06% was obtained (Figure 26).

Figure 27 shows the MATLAB–Simulink implementation of the notch (band-stop) filter.

4.2.6. Direct Control: Low-Pass Filter (LPF)-Based Control

In Figure 28, a basic block diagram of the low-pass filter control method is presented.

A low-pass filter (LPF) in active power filters (APFs) passes low-frequency components while attenuating high-frequency harmonics. Within APFs, the LPF is typically employed to extract the fundamental component from a distorted current or voltage signal, thereby enabling accurate harmonic compensation and effective reactive power control. The LPF-based control method is a simple and practical approach for eliminating unwanted current components, such as harmonics and reactive power, from the load current. Its main advantages include simplicity (no complex mathematical transformations), direct operation in the ABC reference frame, real-time capability, and flexibility for integration with other control methods. However, the method also has limitations: it cannot distinguish between reactive and harmonic currents, performs poorly under unbalanced loads (no symmetrical component analysis), requires careful tuning to avoid performance degradation, and provides no phase information to guarantee a unity power factor by itself. LPF-based control is typically applied in small- to medium-scale shunt APFs, industrial loads with known harmonic content, as a pre-filter within PQ or DQ methods, and in applications where simplicity is preferred over selectivity.

The control algorithm based on the separation of polluting components using a low-pass filter (LPF) is an effective technique for three-phase active power filters, aimed at eliminating high-frequency harmonics and improving electrical power quality. The LPF allows signals below a specific cutoff frequency to pass while attenuating higher-frequency components, such as harmonics, that are undesirable in the power system.

The low-pass filter (LPF) is highly effective in removing high-order harmonics, which are considered polluting components of the current signal. By attenuating these unwanted harmonics and preserving the fundamental frequency, the LPF helps restore a nearly ideal sinusoidal waveform, improving power quality, protecting equipment, and reducing energy losses. Harmonics can cause overheating, power loss, and potential damage to transformers, generators, and other sensitive electrical devices. The LPF is simple to implement and provides a straightforward solution for eliminating harmonics in three-phase power systems, focusing only on the polluting frequencies without affecting the fundamental signal. However, some limitations exist: low-amplitude frequency components that are useful may be inadvertently filtered out; rapid load variations can delay the filter’s response, requiring frequent adjustments; and significant deviations in grid frequency (50 Hz or 60 Hz) can compromise performance, sometimes necessitating an adaptive filter for optimal operation.

By implementing the low-pass filter (LPF) method for separating polluting components in MATLAB–Simulink, a total harmonic distortion of the supply current (THDi) of 3.56% was obtained (Figure 29).

In summary, multiple control strategies are available for active power filters, each offering distinct advantages and limitations. The optimal choice depends on the specific application requirements, system conditions, and the desired performance in terms of harmonic compensation, reactive power control, and dynamic response.

5. Experimental Results

The high-speed cRIO-9039 FPGA-based calculation platform was employed for algorithm implementation. The nonlinear load consisted of a 5 kW oven connected to the PCC through a three-phase rectifier power bridge. A switching frequency of 15 kHz was used, while the current and voltage signals were acquired at a 52 kHz sampling rate. All experimental results were obtained using a FLUKE 437 Series II Power Quality and Energy Analyzer, set at 400 Hz.

5.1. Indirect Control [53]

As has been specified previously, the rated current of the indirect-based control prototype is 200 [A].

a.

Experimental Results Without the APF Connected

Figure 30 and Figure 31 show, respectively, the voltage and current waveforms when the nonlinear load is supplied without the active power filter connected.

At the moment the nonlinear load is connected, the total harmonic distortion of the power supply phase voltage is THDu = 1.1% (Figure 32).

The total harmonic distortion of the supply current at the moment of nonlinear load connection is THDi = 28.9% (Figure 33).

b.

Experimental Results with the APF Connected

By connecting the active power filter at the PCC, the following experimental results were obtained. At the moment of nonlinear load connection, the waveform of the power supply phase voltage is shown in Figure 34.

The total harmonic distortion (THDu) of the power supply phase voltage with the active power filter connected is significantly reduced compared to the uncompensated case, demonstrating the effectiveness of the APF in mitigating voltage distortions.

By connecting the SAPF at the PCC, Figure 35 illustrates the resulting voltage and current waveforms of the power supply, showing improved sinusoidality of the current and reduced harmonics in the voltage due to the active compensation provided by the filter.

By connecting the SAPF at the PCC, the total harmonic distortion of the supply voltage at the moment of nonlinear load connection is reduced to THDu = 0.3% (Figure 36), demonstrating the effective harmonic compensation provided by the active power filter.

The total harmonic distortion for the power supply phase current with SAPF in case of nonlinear load connection is THDi = 4.3% (Figure 37).

Following the connection of the active power filter at the PCC,

Table 4. Harmonic influence of the active power filter on the indirect-based control prototype.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	4.3

presents the comparative experimental results of total harmonic distortion (THD) for both the power supply phase voltage and current, highlighting the effectiveness of each implemented control strategy.

After connecting the active power filter at the point of common coupling (PCC), a significant reduction in total harmonic distortion for both the phase voltage and current was observed:

• THDu (phase voltage) decreased from 1.1% to 0.3%
• THDi (phase current) decreased from 28.9% to 4.3%

Figure 38 illustrates a comparative view of the harmonic distortions before and after SAPF connection, clearly showing the improvement in power quality for both voltage and current.

5.2. Direct Control

5.2.1. PQ Control

The experimental results without the APF connection remain the same as in the indirect control case. Therefore, only the results with the SAPF connected at the PCC are presented.

Upon connecting the active power filter, the following observations were made: at the moment the nonlinear load is energized, Figure 39 shows the waveform of the power supply phase voltage with the SAPF in operation.

Voltage waveforms from the power supply with an active power filter connection show a significant improvement in quality compared to the case without APF. The waveform becomes more sinusoidal, with reduced distortion, as the SAPF compensates for harmonics and reactive power introduced by the nonlinear load. This is reflected in the measured total harmonic distortion (THDu), which drops substantially.

Current waveforms from the power supply with the SAPF connection (Figure 40) illustrate an improvement in the THD parameter. The active power filter effectively reduces harmonic distortion in the current drawn by the nonlinear load, while also maintaining a nearly sinusoidal supply voltage. The current waveform is reshaped close to its fundamental component, and the voltage waveform shows minimal distortion, demonstrating the SAPF’s capability to mitigate harmonics, compensate reactive power, and improve overall power quality.

The total harmonic distortion (THDu) of the supply voltage at the moment of nonlinear load connection is 1.1% (Figure 41), indicating that before any compensation by the active power filter, the voltage waveform is already fairly clean, with only minor distortion introduced by the nonlinear load.

The total harmonic distortion (THDi) of the supply current at the moment of nonlinear load connection is 5.7% (Figure 42), showing that the nonlinear load introduces noticeable harmonic content into the current, even though the voltage distortion remains relatively low.

After connecting the active power filter (APF) to the point of common coupling (PCC),

Table 5. Harmonic influence of the active power filter on the studied PQ-based control.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	5.7

presents the comparative experimental results of total harmonic distortion (THD) for both the supply phase voltage and current. These results highlight the effectiveness of the APF in reducing harmonic content, improving power quality, and ensuring cleaner and more sinusoidal currents and voltages in the system.

At the same time, a significant reduction in total harmonic distortion is observed:

• Phase voltage THDu: reduced from 1.1% to 0.3%
• Phase current THDi: reduced from 28.9% to 5.7%

This demonstrates the APF’s effectiveness in mitigating both voltage and current harmonics, thereby improving overall power quality (Figure 43).

5.2.2. DQ Control

By connecting the active power filter at the PCC, the following experimental results are obtained. At the moment of nonlinear load connection, in Figure 44, the waveform of the power supply phase voltage is presented.

By SAPF connection at the PCC, in Figure 45, the three-phase load current waveforms are shown.

The total harmonic distortion of the supply voltage at the moment of nonlinear load connection is THDu = 1.1% (Figure 46).

The total harmonic distortion of the supply current at the moment of nonlinear load connection is THDi = 7% (Figure 47).

Following the connection of the active power filter in the PCC, in

Table 6. Harmonic influence of the active power filter on the studied DQ-based control.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	7

, the comparative total harmonic distortion experimental results for both power supply phase voltage and current are presented.

After connecting the active power filter at the common coupling point, a significant reduction in the total harmonic distortions level for both the phase current and the supply voltage can be observed:

-

TDH_U—from 1.1% to 0.3%,

-

TDH_I—from 28.9% to 7%.

In Figure 48, the harmonic distortion comparisons in both cases, without SAPF and with SAPF, are shown.

5.2.3. Principle of Maximum (MAX) Control Method

By connecting the active power filter at the PCC, the following experimental results are obtained. At the moment of nonlinear load connection, in Figure 49, the waveform of the power supply phase voltage is presented.

By connecting the SAPF at the PCC, Figure 50 presents the resulting voltage and current waveforms of the power supply.

By SAPF connection at the PCC, the total harmonic distortion level of the supply voltage at the moment of nonlinear load connection is decreased to THDu = 0.3% (Figure 51).

The total harmonic distortion for the power supply phase current with SAPF in case of a nonlinear load connection is THDi = 6.9% (Figure 52).

Following the connection of the active power filter in the PCC, in

Table 7. Harmonic influence of the active power filter on the MAX-based control.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	6.9

, the comparative total harmonic distortion experimental results for both power supply phase voltage and current are presented.

After connecting the active power filter at the common coupling point, a significant reduction in total harmonic distortion is observed for both the phase voltage and current:

-

THDu decreases from 1.1% to 0.3%,

-

THDi decreases from 28.9% to 6.9%.

In Figure 53, the harmonic distortion comparisons in both cases, without SAPF and with SAPF, are shown.

The comparison of harmonic distortion shows a marked improvement when the SAPF is connected. Without the SAPF, the total harmonic distortion of the phase voltage (THDu) is 1.1% and of the current (THDi) is 28.9%. With the SAPF in operation, these values drop to 0.3% and 6.9%, respectively.

5.2.4. Synchronization of Current with the Voltage Positive-Sequence Component, SEC-POS

By connecting the active power filter at the PCC, the following experimental results are obtained. At the moment of nonlinear load connection, in Figure 54, the waveform of the power supply phase voltage is presented.

By SAPF connection at the PCC, in Figure 55, both the voltage and current waveforms of the power supply are shown.

The waveforms of the power supply phase voltage and current at the point of common coupling (PCC) demonstrate the effect of the SAPF. With the SAPF connected, the current waveform becomes significantly smoother and closely sinusoidal, while the voltage waveform shows a marked reduction in harmonic distortion.

The total harmonic distortion of the supply voltage at the moment of nonlinear load connection is THDu = 0.2% (Figure 56).

The total harmonic distortion of the supply current at the moment of nonlinear load connection is THDi = 5.1% (Figure 57).

Following the connection of the active power filter in the PCC, in

Table 8. Harmonic influence of the active power filter on the studied SEC-POS power system.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.2
	THDI [%]	28.9	5.1

, the comparative total harmonic distortion experimental results for both power supply phase voltage and current are presented.

The connection of the active power filter at the common coupling point results in a marked improvement in power quality. The total harmonic distortion of the phase voltage (THDu) is reduced from 1.1% to 0.2%, while the total harmonic distortion of the current (THDi) drops from 28.9% to 5.1%.

Figure 58 illustrates the reduction in harmonic distortion achieved by the SAPF, comparing the cases without and with the filter connected.

5.2.5. Low-Pass Filter Separating Polluting Components Control Method

When the active power filter is connected at the PCC, significant improvements in power quality are observed. Figure 59 presents the waveform of the power supply phase voltage immediately after the nonlinear load is connected.

By connecting the SAPF at the PCC, Figure 60 shows the power supply phase voltage and current waveforms.

Figure 61 shows that at the moment of nonlinear load connection, the total harmonic distortion of the supply voltage is THDu = 1.1%.

The total harmonic distortion of the supply current at the moment of nonlinear load connection is THDi = 7% (Figure 62).

Following the connection of the active power filter in the PCC, in

Table 9. Harmonic influence of the active power filter on the studied power system.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	7

, the comparative total harmonic distortion experimental results for both power supply phase voltage and current are presented.

The connection of the active power filter at the common coupling point results in a marked improvement in power quality. The total harmonic distortion of the phase voltage (THDu) is reduced from 1.1% to 0.3%, while the total harmonic distortion of the current (THDi) drops from 28.9% to 7%.

Figure 63 illustrates the reduction in harmonic distortion achieved by the SAPF, comparing the system without the filter to the system with the filter connected.

5.2.6. Band-Stop (Notch) Filter Separating Polluting Components Control Method (Notch Control)

By connecting the active power filter at the PCC, the following experimental results were obtained. At the moment of nonlinear load connection, Figure 64 presents the waveform of the power supply phase voltage.

By SAPF connection at the PCC, in Figure 65, both the voltage and current waveforms of the power supply are shown.

The total harmonic distortion of the supply voltage at the moment of nonlinear load connection is THDu = 1.1% (Figure 66).

The total harmonic distortion of the supply current at the moment of nonlinear load connection is THDi = 5.6% (Figure 67).

Following the connection of the active power filter in the PCC, in

Table 10. Harmonic influence of the active power filter on the studied band-stop power system.

		Without Active Power Filter	With Active Power Filter
Voltage level test 230 Vac	THDU [%]	1.1	0.3
	THDI [%]	28.9	5.6

, the comparative total harmonic distortion experimental results for both power supply phase voltage and current are presented.

After connecting the active power filter (APF) to the point of common coupling, a significant reduction in total harmonic distortion (THD) is observed for both the supply voltage and phase current. Specifically, the voltage THD decreases from 1.1% to 0.3%, while the current THD drops from 28.9% to 5.6%, demonstrating the effectiveness of the APF in mitigating harmonic distortion and improving overall power quality. In Figure 68, the harmonic distortion comparisons in both cases, without SAPF and with SAPF, are shown. Figure 68 presents a comparison of harmonic distortion in both scenarios: without the SAPF and with the SAPF.

In

Table 11. THDu and THDi with SAPF connected at PCC.

No.	Control Strategies of the APF Prototypes	THDu [%]	THDi [%]
1	Developed on the principle of instantaneous powers (PQ)	0.3	5.7
2	Developed on the principle of synchronous algorithm (DQ)	0.3	7
3	Developed on the principle of maximum (MAX)	0.3	6.9
4	Developed on the principle of indirect control (CI)	0.3	4.3
5	Developed on the principle of synchronization of current with the voltage positive-sequence component (SEC-POZ)	0.2	5.1
6	Developed on the low-pass filter separating polluting components method (LPF)	0.3	7
7	Developed on the band-stop (notch) filter separating polluting components method (BSF)	0.3	5.6

, the comparative experimental results of harmonic distortions are shown.

In

Table 12. Active power filter comparative features of the control algorithms.

Control Type	Instantaneous Power Theory (p–q)	Synchronous Reference Frame (d–q)	Maximum Detection	Positive Sequence Synchronization	Low-Pass Filter-Based	Indirect Control	Notch Filter Based
Basic Principle	Power decomposition in α–β frame	Transformation to d–q rotating frame	Extracts maximum values of distorted current	Extracts fundamental positive-sequence	Filters harmonics using LPF	Uses a reference estimation + error correction	Filters specific frequency (50/60 Hz)
Domain	Time domain (α–β components)	Synchronous rotating frame	Time domain	Frequency domain (sequence components)	Time domain	Hybrid (model + feedback)	Frequency domain
Harmonic Compensation	High (for 3-phase 3-wire)	High (especially for unbalanced systems)	Moderate	Good (depends on extraction accuracy)	Moderate to High	Depends on controller	Excellent for targeted harmonics
Reactive Power Compensation	Yes	Yes	Not directly	Not directly	Not directly	Yes	Not directly
Reference Current Accuracy	High (if balanced)	Very High (even if unbalanced)	Moderate	High (with PLL)	Moderate	Moderate to High	Very High (for known freq.)
Computational Complexity	Moderate	High (due to transformations & PLL)		High (requires sequence extraction)	Low	Medium	Medium
Real-Time Capability	Good	Can be limited by PLL performance	Very Good	Dependent on synchronization speed	Very Good	Good	Good
Dynamic Response	Moderate	High (if PLL is fast)	Fast	Slower (due to sequence extraction)	Slower (depends on filter order)	Moderate	Moderate
Sensitivity to Grid Distortion	High	Lower (if proper synchronization)	High	Low	Moderate	Varies	Low
Implementation Difficulty	Moderate	Complex	Easy	Complex	Easy	Moderate	Moderate

Note: In Table 12, items highlighted in bold indicate the most important or critical characteristics for evaluating each control type. Bold text emphasizes the key strengths or limitations of the respective method, helping the reader quickly identify the most relevant performance aspects.

, comparative features between the active power filter algorithms are depicted.

The synthesis of the control algorithms implemented and tested in active power filter (APF) prototypes can be described from an implementation perspective.

1. The “Positive Sequence” algorithm (Figure 22) calculates the effective value of the consumer’s electrical power to determine the amplitude of the sinusoidal current that must be imposed on the phase power supply. In this case, the regulated current corresponds to the grid current, which is the sum of the APF current and the consumer current.

2. The “Positive Sequence with Band stop Filter” algorithm (Figure 25) determines the shape and amplitude of the current injected by the APF at PCC, starting from the shape and amplitude of the load current: a band stop filter is applied that eliminates the fundamental component (50 Hz) from the load current. The result is summed (with the sign changed to compensate for the nonlinear components of the load current) with the sinusoidal shape of the current necessary to maintain the DC-link energy at a constant value. In this method, the regulated current corresponds to the current injected by the APF. FOB introduces a phase shift of 180 degrees at the central frequency. Band-stop filters are created by combining low-pass and high-pass filters in parallel.

3. The algorithm “Maximum Method” (Figure 19 and Figure 21) determines the shape and amplitude of the grid current, taking into account the RMS value (Figure 21), the largest of the phase consumer currents. This value, scaled accordingly, is added to the current requirement to maintain a constant DC-link voltage from the inverter side. In this approach, the regulated current corresponds to the grid current, that is, the sum of the APF current and the consumer load current. Band-pass filters are constructed by combining a low-pass filter (LPF) in series with a high-pass filter (HPF). This type of filter was used in the MAX and SEC_POS methods.

4. The “PQ” algorithm (Figure 13, Figure 14 and Figure 15) determines the polluting components (Figure 15) of the load current, in order to impose the appropriate compensating current components by the SAPF (Figure 15). The classical time domain reference frame transform (Clarke/Park) is used to obtain the polluting components. In this control strategy, the regulated current corresponds to the APF current.

5. The “DQ” algorithm (Figure 16 and Figure 18) extracts the polluting components of the load current in order to generate the appropriate compensating components in the APF injected current. In this control strategy, the regulated current corresponds to the APF current.

6. The “Positive sequence, with low-pass filter” algorithm (Figure 28) identifies the polluting components of the load current in order to generate the corresponding compensating components in the APF injected current. The harmonic content of the load current is extracted using a low-pass filter that removes the 50 Hz fundamental component from the measured signal. In this control strategy, the regulated current corresponds directly to the APF current.

7. The “Indirect Control” algorithm (Figure 11) does not include a dedicated loop for identifying the linear or nonlinear characteristics of the load. Instead, it relies on regulating the DC-link stored energy of the inverter and using current transducers placed on the grid supply conductors, which measure the sum of the APF current and the nonlinear load current. In this approach, the regulated current corresponds to the grid current, that is, the combined current of the APF and the consumer load.

Indirect control is a particularly attractive strategy for active power filters (APFs) because it does not require direct measurement of the polluting current in the grid. This feature reduces the complexity of the measurement equipment and the associated implementation costs, making it a simpler and more cost-effective solution compared to direct control methods that typically require additional current sensors. Being less invasive, indirect control minimizes the impact on grid equipment and allows for easier integration of the APF without significantly affecting overall grid performance. The method is effective for improving power quality and harmonic compensation in three-phase networks, particularly in systems where energy efficiency and equipment protection are priorities. Although there are challenges related to the accuracy of estimation and the complexity of control algorithms, the advantages in cost reduction and flexibility make indirect control a practical and efficient approach. Future enhancements in modern APFs may involve low switching-loss and EMI-aware PWM techniques, such as space vector modulation (SVM), random PWM, or soft-switching methods. These improvements can further increase efficiency, reduce electromagnetic interference, and improve thermal management compared to basic fixed-frequency SPWM techniques.

The instantaneous power theory, often implemented as PQ control, provides a powerful framework for designing active harmonic filters. By extracting instantaneous active and reactive power, the APF can determine the appropriate compensating current to mitigate harmonic distortions in real time. This method is particularly effective under non-sinusoidal and unbalanced conditions, providing dynamic and instantaneous compensation. However, careful implementation is required due to the need for classical reference frame transformations (Clarke and Park), and incorrect application may reduce compensation effectiveness.

A more advanced approach is the synchronization of the APF current with the positive sequence component of the supply voltage, known as SEC-POS or positive-sequence control. This method focuses on the useful components of the voltage, ensuring that the APF injects only the compensating currents necessary to eliminate harmonics while maintaining a high power factor. While the method significantly improves power quality and balances the system currents, it is computationally complex and demands high-performance control equipment for accurate operation.

The maximum principle (MAX) control method derives the compensating current directly from the load current without requiring reference frame transformations. By doing so, it maximizes active current contribution and minimizes reactive current, effectively reducing harmonic distortion and improving the power factor. This method is particularly suited for systems with variable loads, allowing precise and dynamic compensation. However, the complexity of the algorithm and potential implementation costs are important considerations when selecting this method.

Experimental results, summarized in Table 11, indicate that indirect control achieved the lowest total harmonic distortion of the supply current (THDi) when supplying a nonlinear oven load via a rectifier. This highlights that, in certain practical scenarios, estimation-based indirect control can outperform more sophisticated direct control strategies in terms of harmonic mitigation. Overall, each control method has its own trade-offs between complexity, cost, and performance, and the choice depends on the specific requirements of the power system. Future improvements in APF technology, particularly the adoption of advanced PWM techniques, can enhance overall efficiency, reduce electromagnetic interference, and ensure better thermal management, thus optimizing the integration of APFs into modern electrical networks [98].

6. Conclusions

The proposed objectives have been implemented and validated on seven industrial active power filter (APF) prototypes. Following individual tests of these power filters, it was observed that applying indirect control yielded the lowest distortion of the supply current signals, achieving the minimum current total harmonic distortion (THD) factor at a 230 V phase-to-ground supply voltage.

Both the experimental system and the prototypes consist of interconnected programmable electronic components and equipment designed to reduce current harmonics and compensate for reactive power in electrical power supply networks. The experimental system, FAP-0L, allows testing of filters for any electrical network configuration, including 110 V, 220 V, and 230 V alternating voltage systems, and supports both 50 Hz and 60 Hz frequencies. The system operates within the limits of 0–330 V line-to-neutral or 0–570 V line-to-line voltage, a voltage frequency range of 30–100 Hz, and a maximum power of 30 kVA. The industrial APF prototypes were tested across a wide supply voltage range of 10–230 V AC at 50 Hz and are designed to operate nominally at 230 V AC and 50 Hz. All control strategies for the APFs are implemented on FPGA-based programmable digital circuits, configurable via a desktop computer, and capable of autonomous operation.

The APF control structure is composed of a phase-locked loop (PLL) that generates sinusoidal signals synchronized in frequency and phase with the supply network voltages, an outer loop for regulating the DC capacitor voltage, and three independent current regulation loops—one for each phase. Each current loop employs a proportional (P-type) regulator followed by a hysteresis modulator to generate the control pulses for the three-phase bridge of static switches. The voltage loop determines the amplitude of the current exchanged with the supply network, while the current loops impose the reference currents, calculated as the product of the amplitude and the reference sinusoidal signals. The hysteresis modulator allows the inverter control signals to simultaneously compensate for current harmonics, maintain the required DC capacitor voltage through pulse-width modulation, and provide reactive power compensation.

Overall, the use of indirect control proved to be the most effective solution for harmonic mitigation, achieving superior performance compared to other control strategies in reducing supply current distortion.

7. Patents

Marian, G.; Ionut, E.S.; Constantin, S.R.; Razvan, B. Unification of the Implementation and Testing of Control Algorithms for Three-Phase, Low-Voltage, Parallel-Type Active Power Filters, in Experimental Stand and in Prototypes, Active Power Filters. Patent 137988 A2, 25 August 2022.

Marian, G.; Ionut, E.S.; Constantin, S.R.; Razvan, B., Alexandru, D., Iulian G. Experimental system for implementing and testing parallel-type three-phase low-voltage active electronic power filters, has programmable three-phase electrical loads and some interface inductances provided between the voltage inverter and the common source-polluting load connection point. Patent RO137368-A2, 2021.