Performance Analysis and Control of a Single-Phase Shunt Active Power Filter (SAPF) for Harmonic Mitigation in Non-Linear Loads
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Abstract
The proliferation of power electronic-based non-linear loads in modern distribution systems has introduced significant power quality challenges, primarily characterized by elevated Total Harmonic Distortion (THD) and poor power factor. This paper presents a rigorous performance analysis of a Single-Phase Shunt Active Power Filter (SAPF) designed for dynamic harmonic compensation and reactive power support. The proposed system utilizes a MOSFET-based H-bridge voltage source inverter (VSI) controlled via Instantaneous Power (PQ) Theory. To facilitate the application of PQ theory in a single-phase context, a transform-delay method is implemented to generate an orthogonal fictitious phase, enabling the calculation of instantaneous real and reactive power components. A proportional-integral (PI) controller maintains the DC link capacitor at a 700 V reference, while a Hysteresis Current Controller ensures precise tracking of the reference compensation current. Simulation results, conducted in MATLAB/Simulink, demonstrate that the SAPF effectively mitigates source current THD from an initial 46.65% to a minimum of 0.58%, significantly outperforming the limits established by the IEEE 519-2022 standard. The results validate the efficacy of the control architecture in restoring sinusoidal source current with an amplitude of 6.88 A under non-linear RL load conditions.
Keywords
Shunt Active Power Filter (SAPF), PQ Control Theory, Total Harmonic Distortion (THD), Power Quality, Hysteresis Current Control, Fast Fourier Transform (FFT).
I. Introduction
The strategic maintenance of power quality is a fundamental requirement for the operational stability and efficiency of modern electrical grids. As the grid evolves, the prevalence of non-linear loads—specifically bridge rectifiers coupled with inductive RL loads—has reached a critical mass. These loads draw non-sinusoidal currents, resulting in high harmonic content and significant reactive power consumption. Such distortions exacerbate system losses, induce thermal stress in distribution transformers, and can cause the malfunction of sensitive adjacent grid-connected equipment.
While passive filters have historically provided a low-cost solution for harmonic mitigation, they are inherently limited by fixed compensation characteristics, physical bulk, and the risk of resonance with the grid impedance. Consequently, the Shunt Active Power Filter (SAPF) has emerged as the preferred solution for real-time, dynamic compensation. This study investigates a single-phase SAPF utilizing a PQ-control-based H-bridge inverter to achieve real-time harmonic neutralization. The objective is to implement a robust control logic that extracts reference currents accurately, ensuring the source current remains purely sinusoidal regardless of load non-linearity. The following sections delineate the system's mathematical framework, the modeling environment, and a comprehensive analysis of the simulation results.
II. System Configuration and Methodology
The physical architecture of the SAPF is based on a shunt-connected Voltage Source Inverter (VSI) integrated at the Point of Common Coupling (PCC) between the AC source and the non-linear load.
A. System Components
The system hardware comprises the following primary elements:
• AC Voltage SourceA single-phase source with internal source inductance representing the grid impedance.
• Non-Linear LoadA diode bridge rectifier feeding an RL load, which serves as the source of non-sinusoidal current and reactive power demand.
• SAPF HardwareA MOSFET-based H-bridge inverter. A DC link capacitor serves as the energy storage element, providing the necessary DC bus voltage for the inverter’s switching operations.
• Coupling InductorAn inductor filter that interfaces the VSI with the PCC, smoothing the high-frequency switching ripples of the injected compensation current.
B. Operational Logic
The SAPF operates by continuously sensing the load current and source voltage. The control system calculates the instantaneous harmonic and reactive components required by the load. The inverter then generates a compensation current that is injected back into the PCC. This current is equal in magnitude but opposite in phase to the load's harmonic content, thereby neutralizing the distortion and ensuring the source provides only the fundamental active power.
III. Control Strategy and Mathematical Modeling
The core of the SAPF performance lies in the precision of the reference current extraction. This study adapts the traditionally three-phase PQ control theory for a single-phase application.
A. Fictitious Phase Generation via Transform Delay
To apply PQ theory, an orthogonal two-phase system is required. In this single-phase implementation, the measured source voltage and load current are treated as the -axis components.
The -axis components are generated using a transform-delay block that produces a 90° phase shift:
where represents the fundamental period of the AC waveform.
This method produces a virtual orthogonal system suitable for instantaneous power computation.
B. Instantaneous Power Theory (PQ)
Using the orthogonal components, the instantaneous real power and reactive power are calculated as:
The instantaneous real power contains two components:
where
A low-pass filter (LPF) is used to extract the DC component .
C. DC Link Voltage Regulation
Maintaining the DC link voltage at 700 V is critical for the operation of the VSI.
The PI controller is defined as:
where
= proportional gain = integral gain.
The loss power compensates inverter switching losses and stabilizes the DC link voltage.
D. Reference Current Extraction
The final power reference becomes
The reference current is derived as
The actual filter current is then compared with .
A Hysteresis Current Controller produces the switching pulses for the H-bridge MOSFET inverter.
IV. Simulation Model and Parameters
The proposed SAPF control architecture was implemented using MATLAB/Simulink.
A. Technical Parameters
Parameter | Value |
Source Voltage (RMS) | 230 V |
System Frequency | 50 / 60 Hz |
DC Link Voltage Reference | 700 V |
Load Type | Bridge Rectifier + RL Load |
Source Current Amplitude | 6.88 A |
PI Controller Gains | Optimized for stability |
Modulation Method | Hysteresis Current Control |
B. Measurement Points
The following signals were monitored in the simulation:
• Source Voltage• Load Current• Compensation Current• Source Current• DC Link Voltage
These measurement points enable performance comparison before and after SAPF compensation.
V. Results and Discussion
A. Waveform Analysis
Before compensation, the load current exhibits a highly distorted waveform typical of diode bridge rectifiers. This distortion propagates directly to the source current.
Once the SAPF is activated, the source current transitions to a clean sinusoidal waveform with an amplitude of 6.88 A.
The DC link capacitor voltage stabilizes at 700 V, confirming effective PI controller operation.
B. Harmonic Performance (THD Analysis)
The harmonic mitigation performance is summarized in Table 2.
Table 2
Source Current THD Comparison
Condition | Source Current THD (%) |
Uncompensated System | 46.65 |
Compensated (FFT Max Frequency) | 2.45 |
Compensated (Fundamental Frequency FFT) | 0.58 |
C. Harmonic Order Analysis
The dominant harmonic components were significantly suppressed.
Harmonic Order | Magnitude |
0.5 % | |
0.0 % | |
0.06 % |
The suppression of the third harmonic is particularly important in single-phase rectifier systems.
D. Critical Assessment
The reduction in THD from 46.65% to 0.58% represents a substantial improvement beyond the IEEE 519-2022 limit of 5%.
The SAPF eliminates harmonic currents at the PCC, ensuring that the source only supplies fundamental active power. This reduces system losses, improves power factor, and enhances the operational reliability of the electrical distribution network.
VI. Conclusion and Future Scope
This work presented the design and performance evaluation of a single-phase Shunt Active Power Filter based on PQ control theory. A transform-delay method was employed to create orthogonal signals required for instantaneous power calculation. Simulation results demonstrated that the proposed SAPF significantly reduces harmonic distortion and maintains the DC link voltage stability.
The system successfully reduced source current THD to 0.58%, thereby satisfying IEEE power quality standards.
Future work may explore the integration of renewable energy sources within the DC link and the implementation of advanced control strategies such as Fuzzy Logic Control or Model Predictive Control (MPC) to further improve transient performance under dynamic loading conditions.
VII. YouTube Video
VIII. Purchase link of the Model
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