# Shunt Active Power Filters in Three-Phase, Three-Wire Systems: A Topical Review

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## Abstract

**:**

## 1. Introduction

## 2. Power Circuit Configurations

#### 2.1. Two-Level Topologies

#### 2.2. Multilevel Topologies

#### 2.3. New Power Semiconductor Devices

## 3. Objectives of Active Power Filtering

- Unity power factor (UPF):

- Zero current distortion (ZCD):

- Reactive power compensation: when the reactive component of the fundamental load current is compensated, the supply current is distorted, but its fundamental is in phase with the voltage. Unity displacement power factor is obtained.
- Compensation of current harmonics only.

- Filtering of all harmonics: when a sinusoidal supply current is obtained but out of phase with respect to the voltage.
- Selective filtering of certain harmonics: when the resulting supply current is no longer sinusoidal and its zero crossings are out of phase with respect to the voltage.

## 4. Reference Current Generation

_{F}) in the point of common coupling (PCC). For this, there is the possibility of direct control of the inverter output current or indirect control of this current through the supply current upstream of the PCC (i

_{s}). Thus, depending on the type of control adopted, direct or indirect, one of the two currents constitutes the input of the current control block.

_{DCp}), and its waveform is a sinusoid of unity magnitude in phase with the supply voltage, provided by the voltage template generation block.

#### 4.1. Reference Current Generation for the Direct Control

_{Ftp}), which is prescribed to be obtained on the inverter AC-side, is the sum of the component i

_{Fp}(generated according to the compensation objective and a chosen calculation method based on measured load currents and supply voltages) and component i

_{Fup}(the active current required to cover the power losses and maintain the DC voltage at its prescribed value) [108].

#### 4.1.1. Time-Domain Methods

_{F}) in terms of an instantaneous active power (p) and an instantaneous reactive power (q), expressed in turn in terms of the components of the voltage vectors (v

_{α}and v

_{β}) and load currents (i

_{L}

_{α}and i

_{L}

_{β}) in the stationary orthogonal coordinate system (α-β). The components of p and q to be compensated (p

_{F}and q

_{F}) are extracted, and, according to them, the currents to be compensated in the stationary reference frame (α-β) are calculated, which are then transformed into the three-phase system (a, b, and c) (Figure 8). It is one of the methods with the most implementations in the SAPF control since the 1980s, when the first form of the p-q theory was proposed [147]. There are many implementations for three-phase, three-wire systems operating under sinusoidal voltage conditions, corresponding to the original theory [7,8,20,32,39,73,101,102,148,149,150,151,152,153,154]. Extended applicability of the method was also considered for operation under nonsinusoidal voltage conditions [108,146,155,156,157,158] and multilevel SAPFs [58,111]. In [159], a novel harmonic extraction method named “virtual input signal-based instantaneous power theory” is introduced to improve the performance under unbalanced conditions.

_{Ld}and i

_{Lq}) in the rotating coordinate frame aligned with the voltage vector. The angle required for the transformation is calculated only according to the components of the voltage vector in the stationary reference frame (α-β) and its modulus. Then, the active component of the fundamental harmonic is the DC component I

_{Ld}of the current i

_{Ld}and is obtained with an LPF. The components of the current desired to be drawn from the power supply after compensation in the rotating (d-q) reference frame are required to be I

_{Ld}and zero. Finally, the transition of the currents to the three-phase system follows (Figure 10). There are several implementations of the id-iq methods [165,166,167,168,169].

_{ka}) was defined as a function of an equivalent conductance (G), expressed as a collective active power (P

_{Σ}) and a collective effective voltage value (║v

_{Σ}║) [181]. The non-active currents to be compensated for on each phase are then expressed as the difference between the active currents and the load-distorted currents. Thus, the method only allows the total compensation of all inactive currents [146,153,157,182,183]. The simple algorithm is highlighted in Figure 12. As the excessive delay of the LPFs affects the SAPF dynamic response, the use of a generalized moving average filter having characteristics of short delay and flexible construction according to the characteristics of load current is proposed in [184]. A modified algorithm when the supply voltage is distorted is based on the estimation of the current reference that guarantees an optimal power exchange [185]. The impact on the FBD method when power supply voltage drops asymmetrically is analyzed in [186], and an improved reactive power and harmonic current detecting method based on voltage sequence decomposition is introduced.

_{Lp}) and the instantaneous reactive component (i

_{Lq}), expressed as a function of the instantaneous active power of the load (p

_{L}) and the vector of instantaneous reactive power (

**q**

_{L}=

**v**

_{s}×

**i**

_{L}). Thus, to compensate both the harmonics and the reactive power of the load, the reference current imposed at the SAPF output has the following two components [146,187,188] (Figure 13):

_{L}

_{~}is the oscillatory component of the instantaneous active power of the load. There are different implementations of this method in the literature [146,187]. There are also implementations of applying FBD theory in the control of SAPF even under nonideal voltage conditions and unbalanced load [188,189,190,191].

_{p}) and inactive (i

_{q}) components of the current as a function of a reference voltage u

_{p}(t), which depends on the compensation objective. Thus, the reference voltage determines the waveforms of the currents absorbed from the power supply after compensation and can be either the supply voltage if a unity power factor is desired or the fundamental of the supply voltage if a sinusoidal current is desired after compensation [146,192,193]. In the expression of the active component of the current, the active power P(t) and the rms value of the reference voltage U

_{p}(t) are used, which are calculated over a previous time interval T

_{c}. There is research on the influence of this time interval, depending on the compensation objective [146,193,194]. Implementations based on GINAP theory in the control of a three-phase SAPF show outstanding results [150,183,191,195,196,197,198,199,200], including dynamic response [201]. Critical analysis of the compensation results using the p-q, FBD, and GINAP methods showed that the GINAP method leads to very good performance even under conditions of a non-sinusoidal supply voltage and non-periodic load currents [194,202].

#### 4.1.2. Frequency-Domain Methods

_{a}—related to the transmission of active power); reactive (i

_{r}—related to the reciprocating flow of energy); unbalanced (i

_{u}related to the load imbalance); and the load-generated component (i

_{g}—related to load nonlinearity or its parameters’ time-variance). The first three components of the current are included in the fundamental harmonic and can be expressed in terms of the equivalent admittance (Y

_{e}

_{1}= G

_{e}

_{1}+ jB

_{e}

_{1}) and the unbalanced admittance (A

_{1}) [225,226,227,228]. Figure 14 illustrates the principle of calculating the reference current by the CPC method under sinusoidal voltage conditions [146,229]. The CPC method has been successfully used to calculate the reference current in three-phase SAPFs [229,230,231,232,233,234,235].

#### 4.1.3. Soft-Computing Methods

#### 4.2. Reference Current Generation for the Indirect Control

## 5. Current Control Techniques

## 6. Modulation Strategies

#### 6.1. Sinusoidal PWM

#### 6.2. Space Vector PWM

## 7. DC-Voltage Control

## 8. Direct Power Control

## 9. Renewable Energy Sources Integration with SAPF

#### 9.1. PV Integrated SAPF

#### 9.2. Wind Energy Integrated SAPF

#### 9.3. Fuel-Cell-Integrated SAPF

#### 9.4. Hybrid Renewable Energy Sources Integration with SAPF

## 10. Optimizing the Sizing and Placement of SAPF

## 11. Trends and Future Developments

## 12. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ACO | Ant Colony Optimization |

ADALINE | Adaptive Linear Neurons |

ANF | Adaptive Notch Filter |

ANFIS | Adaptive Neuro Fuzzy Inference System |

ANN | Artificial Neural Network |

ANPC | Active Neutral Point Clamped |

APF | Active Power Filter |

BFO | Bacterial Foraging Optimization |

CHB | Cascaded H-Bridge |

CPC | Currents’ Physical Components |

CPT | Conservative Power Theory |

CSA | Cuckoo Search Algorithm |

CSD | Current Synchronous Detection |

CSI | Current Source Inverter |

DC | Direct Current |

DFT | Discrete Fourier Transform |

DPC | Direct Power Control |

DTC | Direct Torque Control |

DWT | Discrete Wavelet Transform |

EV | Electric Vehicle |

FBD | Fryze–Buchholz–Depenbrock |

FC | Flying Capacitor |

FED | Fundamental Element Detection |

FFT | Fast Fourier Transform |

FIR | Finite Impulse Response |

FRC | Fast Repetitive Control |

GA | Genetic Algorithm |

GaN | Gallium Nitride |

GINAP | Generalized Instantaneous Non-Active Power |

GIRP | Generalized Instantaneous Reactive Power |

GTO | Gate Turn-Off Thyristor |

GWO | Grey Wolf Optimizer |

HPF | High-Pass Filter |

IDWT | Inverse Discrete Wavelet Transform |

IGBT | Insulated-Gate Bipolar Transistor |

IFT | Inverse Discrete Fourier Transform |

IUWPT | Inverse Undecimated Wavelet Packet Transform |

IWPT | Inverse Wavelet Packet Transform |

LESO | Linear Extended State Observer |

LMS | Least Mean Square |

LPF | Low-Pass Filter |

LWT | Lifting Wavelet Transform |

MOSFET | Metal Oxide Semiconductor Field-Effect Transistor |

MPC | Model Predictive Control |

MPM | Matrix Pencil Method |

MPPT | Maximum Power Point Tracking |

MRF-PLL | Multiple Reference Frame-Based PLL |

NPC | Neutral-Point Diode Clamped |

PCC | Point of Common Coupling |

PI | Proportional-Integral |

PLL | Phase-Locked Loop |

PR | Proportional-Resonant |

PSO | Particle Swarm Optimization |

PSO-GWO | Particle Swarm Optimization-Grey Wolf Optimization |

PV | Photovoltaic |

PWM | Pulse Width Modulation |

RB–IGBT | Reverse Blocking-Insulated Gate Bipolar Transistor |

RDFT | Recursive Discrete Fourier Transform |

RES | Renewable Energy Source |

SAPF | Shunt Active Power Filter |

SDFT | Sliding Discrete Fourier Transform |

SGF | Savitzky–Golay Filter |

SiC | Silicon Carbide |

SMC | Sliding Mode Control |

SOGI | Second Order Generalized Integrator |

SPLL | Software Phase Lock Loop |

SPWM | Sinusoidal Pulse Width Modulation |

SRF | Synchronous Reference Frame |

SVM | Support Vector Machine |

SVPWM | Space Vector Pulse Width Modulation |

TTA | Transformation Algorithm |

UPF | Unity Power Factor |

UWPT | Undecimated Wavelet Packet Transform |

VSI | Voltage Source Inverter |

WB-LPF | Wavelet-Based Low Pass Filter |

ZCD | Zero Current Distortion |

ZSI | Z-Source Inverter |

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**Figure 1.**Types of static converters used in the structure of SAPF: (

**a**) voltage source inverter and (

**b**) current source inverter.

**Figure 3.**The three topologies of the most used three-phase, three-wire, three-level SAPFs: (

**a**) NPC, (

**b**) FC, and (

**c**) CHB.

**Figure 15.**Structure of the control system in the case of indirect current control, performed only based on the output of the DC-voltage controller.

**Figure 16.**Structure of the control system in the case of indirect current control using a reference component resulting from the measured load current and the supply voltage.

**Figure 18.**Adaptive band current hysteresis control loop structure in case of indirect current control.

Criterion | VSI | CSI |
---|---|---|

DC-energy storage | VSI uses a DC capacitor. The electrolytic capacitor is of low weight and economical but has a limited lifetime. | CSI uses a DC inductor. The inductor is heavy and bulky, high-cost, and provides more loss, but its lifetime is not limited. |

Expanded features for multilevel structures | Yes | No |

Power ratings | Low/medium | Medium |

Control | Simple | Complex |

Speed of response | Fast | Medium |

Switching frequency | High | Low/medium |

Switching ripple in output currents | Higher | Lower |

Total power losses | Low | High |

Requirements for protection | Usual | Separate clamp circuit for overvoltage |

Efficiency when operating at light load conditions | Lower | Higher |

Technique | Strengths | Weaknesses |

Fixed hysteresis band control | Simple implementation; good stability; accurate current tracking; very fast transient response; and robustness to the load parameter variation | Variable switching frequency; increased switching losses; complicated filter design and selection of the DC-voltage value; and audio noises |

Adaptive hysteresis band control | Fixed switching frequency; reduced high-frequency components of the power supply current; reduced switching losses; and better dynamic response under transient load conditions | Increased complexity of the control structure |

Model predictive control | Easy inclusion of nonlinearities and constraints; minimizes the switching frequency in high-power inverters | Need of precise knowledge of the filter model; a lot of calculations are required |

Deadbeat predictive control | High dynamic performance; fast response; zero steady-state error; constant switching frequency; and high compatibility for digital implementation | Performance highly depends on the accuracy of the system model; inherent delay due to the calculations |

Sliding mode control | Strong robustness against parameter drift; system dynamics is unaffected by circuit parameters and only depend on the selected sliding surface; and reliable performance during transients | Chattering phenomenon in discrete implementation; need to choose a compromise between good transient and zero steady state performance |

Proportional-resonant control | Periodic error elimination; periodic disturbance rejection; small steady state tracking error; and good compromise between cost and performance | Compensation effect decreases when the grid frequency fluctuates; weaker performance for dynamic loads |

Repetitive control | Can be used to track the fundamental wave and multiple specific frequency harmonics; robust performance for periodic issues; and zero-steady-state error at all harmonic frequencies | Difficult to obtain a very fast response for fluctuating loads; difficult to guarantee system stability |

Multi-loop control | Good performance of the LCL-type SAPFs | Controller design is complicated considering delay effect; require of a large number of sensors |

Multiresonant control | Enable sinusoidal currents regardless of the distorted grid voltage harmonic content | The number of resulting controller gains to be tuned grows linearly with the number of frequencies to be dealt with; tuning procedures require good expert knowledge |

Fuzzy logic control | Does not depend on a specific mathematical model; suitable for the control of unknown and uncertain systems; easy implementation for nonlinear systems; fast response; constant switching frequency; insensitive to variations in parameters and operating points | Selective harmonic elimination is not suitable; slow control method |

**Table 3.**Switching table for DPC [259].

dp | dq | θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{5} | θ_{6} | θ_{7} | θ_{8} | θ_{9} | θ_{10} | θ_{11} | θ_{12} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 101 | 111 | 100 | 000 | 110 | 111 | 010 | 000 | 011 | 111 | 001 | 000 |

1 | 1 | 111 | 111 | 000 | 000 | 111 | 111 | 000 | 000 | 111 | 111 | 000 | 000 |

0 | 0 | 101 | 100 | 100 | 110 | 110 | 010 | 010 | 011 | 011 | 001 | 001 | 101 |

0 | 1 | 100 | 110 | 110 | 010 | 010 | 011 | 011 | 001 | 001 | 101 | 101 | 100 |

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**MDPI and ACS Style**

Popescu, M.; Bitoleanu, A.; Suru, C.V.; Linca, M.; Alboteanu, L.
Shunt Active Power Filters in Three-Phase, Three-Wire Systems: A Topical Review. *Energies* **2024**, *17*, 2867.
https://doi.org/10.3390/en17122867

**AMA Style**

Popescu M, Bitoleanu A, Suru CV, Linca M, Alboteanu L.
Shunt Active Power Filters in Three-Phase, Three-Wire Systems: A Topical Review. *Energies*. 2024; 17(12):2867.
https://doi.org/10.3390/en17122867

**Chicago/Turabian Style**

Popescu, Mihaela, Alexandru Bitoleanu, Constantin Vlad Suru, Mihaita Linca, and Laurentiu Alboteanu.
2024. "Shunt Active Power Filters in Three-Phase, Three-Wire Systems: A Topical Review" *Energies* 17, no. 12: 2867.
https://doi.org/10.3390/en17122867