# Design and Implementation of a GaN-Based Three-Phase Active Power Filter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Gallium Nitride (GaN) High Electron-Mobility Transistor (HEMT) and Its Driving Requirements

_{GS}and turned off with zero or negative V

_{GS}. Generally, the turn-on threshold and highest allowed driving voltages of a GaN HEMT are much smaller than those of conventional Si-based switches. As a result, the careful design of driving circuit is necessary in order to avoid fault turn-on and high overshoot. Common suggestions include providing separate turn-on and turn-off driving paths, achieving minimized overlapping between driving and power loops, using Miller clamp and negative voltage sources to ensure reliable turn-offs, etc. [13].

## 3. Mathematical Modeling and Control Algorithms of GaN-Based Active Power Filter (APF)

#### 3.1. GaN-Based Three-Phase Active Power Filter

_{rms}, grid frequency = 60 Hz, rated power = 2 kVA, DC link voltage = 200 V, switching frequency = 50–100 kHz, DC voltage sensing factor = 0.012, AC current sensing factor = 0.05, AC voltage sensing factor = 0.0062, and DC voltage variation limit = 1%.

#### 3.2. Design of Direct Current (DC) Capacitor and Filter Inductors

_{dc}and I

_{dc}represent DC voltage and current, respectively, which can both be separated into their respective DC components (${\overline{V}}_{dc}$ and ${\overline{I}}_{dc}$) and AC components (${\tilde{V}}_{dc}$ and ${\tilde{I}}_{dc}$). In order to simplify the analysis, we make three assumptions: the conversion efficiency of the three-phase inverter is 100%, ${\tilde{V}}_{dc}$ is considered zero, and ${\overline{I}}_{dc}$ is considered zero because ${\tilde{I}}_{dc}$ is generally far larger than ${\overline{I}}_{dc}$. As a result, we obtain the following:

_{dc}represents DC link capacitance. Then, we obtain the voltage variation of the DC link capacitor:

_{sw}represents the switching frequency. It should be noted that if an electrolytic capacitor were used for this APF design case, a higher capacitor specification will be required.

_{sh}represents inductance value, and i

_{sh}represents inductor current. According to the relationship between voltage and current on an inductor, (5) can be expressed as follows.

_{sh}represents shunt inductor current ripple, D represents duty cycle, T

_{sw}represents switching period, and V

_{grid}represents grid voltage. The duty cycle can be expressed the following:

_{a}represents modulation factor and equals modulation signal divided by triangular wave amplitude (v

_{con}/v

_{tri}). Then, we get output AC voltage:

#### 3.3. Mathematical Modeling and Controller’s Design for GaN-Based Shunt APF

#### 3.3.1. Mathematical Modeling

_{sh_a}, i

_{sh_b}, and i

_{sh_c}represent three-phase inductor currents, v

_{AN}, v

_{BN}, and v

_{CN}represent switching point voltages, V

_{grid_a}, V

_{grid_b}, and V

_{grid_c}represent three-phase grid voltages, and v

_{nN}represents the voltage between the grid ground and the inverter ground. Also, the three-phase three-wire system satisfies the following condition:

_{nN}can be expressed as the following:

_{cona}, v

_{conb}, and v

_{conc}are compared with v

_{tri}respectively to trigger the switches of all three switching legs. The output voltages of the switching legs can be expressed as follows:

_{dc}/2V

_{tri}= K

_{pwm}yield the following:

#### 3.3.2. Design of Current Controllers

_{s}and k

_{v}represent AC current and voltage-sensing factors, respectively. Under ideal feed-forward conditions, the transfer function of current loop (d-axis or q-axis) is as follows:

_{Hi}) is as follows:

_{Gi1}) is as follows:

_{P}and k

_{I}are 16.0633 and 2.5232956, respectively. Figure 4 shows the Bode plot of the controller and plant, where the designed phase margin is 58 degrees.

#### 3.3.3. Design of DC Link Voltage Controller

_{m}and I

_{m}represent the maximum voltage and current under dq axes, respectively. According to trigonometric functions, Equation (34) can be simplified as follows:

_{dc}represents the conversion factor from AC side to DC side. According to Equations (38) and (39), we can obtain the transfer function of DC side voltage:

_{vd}and k

_{s}represent the sensing factors of DC voltage and AC current, respectively. Therefore, the transfer function of the DC voltage loop is as follows:

_{Hdc}) can be calculated as follows:

_{Gv1}) is as follows:

_{P}and k

_{I}are 0.5286 and 0.0001329397, respectively. Figure 7 shows the Bode plot of the controller and plant, where phase margin is 67 degrees.

#### 3.3.4. Load Current Compensation Signals of APF

_{Ld}and i

_{Lq}represent dq-axis load currents, ${\overline{i}}_{Ld}$ and ${\overline{i}}_{Lq}$ represent dq-axis load currents with the fundamental frequency, and ${\tilde{i}}_{Ld}$ and ${\tilde{i}}_{Lq}$ represent the dq-axis components that require compensation. In order to obtain the compensation signals of the active current (q axis) i

_{Lq}

^{*}, i

_{Lq}is firstly filtered with an LPF and then subtracted from q-axis current feedback signal (i

_{Lq}), while the compensation signals of the reactive current (d axis) i

_{L}

_{d}

^{*}equals the whole d-axis current feedback signal (i

_{Ld}), as shown in Figure 8.

#### 3.4. Complete System of GaN-Based Shunt APF

## 4. Simulation Study and Results

#### 4.1. Simulation Scenario

_{0}–t

_{1}), the shunt APF, connected to a three-phase power grid with the line to line voltage of 110 V, 60 Hz, adjusts the DC link voltage to 200 V and the compensation function is not activated; at t

_{1}, compensation is activated to achieve a set of balanced grid currents, zero distortion, and unit power factor (PF), as shown in Figure 12. Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17 show the corresponding simulation results, and Table 2 shows root-mean-square (RMS) currents and total harmonic distortion (THD) data before and after compensation.

## 5. Hardware Implementation and Test Results

_{0}to t

_{2}. Figure 20 shows the DC link voltage and the output three-phase currents of the shunt APF from t

_{0}to t

_{2}. The related waveforms of grid phase-a voltage and three-phase currents and the fast Fourier transform (FFT) of the grid phase-a current before the before and after the APF is activated are shown in Figure 21 and Figure 22, respectively. As can be seen in Figure 22, after the APF is activated the unbalanced and distorted currents have been well compensated and the current is in phase with the grid voltage achieving the control objective of unity power factor. To demonstrate the performance of the designed controllers, Figure 23 shows the command and feedback signals of DC link voltage and the PI controller output signals. The dq-axis current commands and feedback signals are shown in Figure 24. To provide a set of quantitative results, Table 4 shows the measured RMS currents and calculated THD data before and after compensation. In the stage of hardware construction and tests, the system efficiencies at different switching frequencies are also explored. The arrangement of the test scenario and the detailed results are presented in the next section.

## 6. Discussion

#### 6.1. The Analysis of System Efficiency

_{dc}and measuring the corresponding P

_{ac}, the efficiency at a specific power level and switching frequency can be readily calculated. In this paper, three switching frequencies, i.e., 50, 80, and 100 kHz were tested. The calculated results are graphically shown in Figure 26. As can be seen in Figure 26, the maximum efficiency appears at about 50% of the rated load and it is found that when the switching frequency increases the efficiency decreases. This is mainly due to the increase in switching losses.

#### 6.2. The Thermographic Analysis of the System

#### 6.3. Related Technical Issues

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Equivalent circuits of the voltage control loop: (

**a**) equivalent circuit under synchronous reference frame; (

**b**) equivalent circuit on direct current (DC) side.

**Figure 9.**The circuit configuration of gallium nitride (GaN)-based shunt APF system and the block diagram of the control scheme.

**Figure 13.**The grid-side phase-a voltage and three-phase currents/DC link voltage/shunt APF three-phase currents (t

_{0}–t

_{2}).

**Figure 14.**Before t

_{1}: the grid phase-a voltage and three-phase currents/the fast Fourier transform (FFT) waveform of the grid phase-a current.

**Figure 15.**After t

_{1}: the grid phase-a voltage and three-phase currents/FFT waveform of the grid phase-a current.

**Figure 18.**(

**a**) Photo of GaN-based three-phase APF hardware; (

**b**) schematic of the hardware test and system.

**Figure 21.**Before t

_{1}: the grid phase-a voltage and three-phase currents and the fast Fourier transform (FFT) waveform of the grid phase-a current.

**Figure 22.**After t

_{1}: the grid phase-a voltage and three-phase currents and FFT waveform of the grid phase-a current.

**Figure 23.**The command and feedback signals of DC link voltage and the proportional-integral (PI) controller output signal (t

_{0}–t

_{2}).

**Figure 27.**Thermographic photos of the proposed GaN-based three-phase APF prototype: (

**a**) TPH3207 device switching at 50 kHz; (

**b**) TPH3207 device switching at 80 kHz; (

**c**) TPH3207 device switching at 100 kHz; (

**d**) DSP; (

**e**) communication interface; (

**f**) inductors; (

**g**) relay; (

**h**) signal processing integrated circuits (ICs).

Nonlinear Load | Linear Load | Unbalanced Load | ||||
---|---|---|---|---|---|---|

R_{L1} | L_{L1} | L_{L2} | R_{L2} | R_{L3}, R_{L4} | ||

50 Ω | 6 mH × 3 | 152 mH × 3 | ∞ Ω | 50 Ω |

Power Grid Currents and Unbalance Ratio (UR) | |||
---|---|---|---|

Item | Without APF(t_{0}–t_{1}) | With APF(t_{1}–t_{2}) | |

i_{grid_a} (A) | 2.9 | 2.84 | |

i_{grid_b} (A) | 3.42 | 2.87 | |

i_{grid_c} (A) | 3.87 | 2.89 | |

UR (%) | 14.91 | 0.94 | |

THD | |||

Item | Without APF(t_{0}–t_{1}) | With APF(t_{1}–t_{2}) | |

THD (i_{grid_a}) (%) | 19.18 | 3.91 | |

THD (i_{grid_b}) (%) | 15.56 | 3.94 | |

THD (i_{grid_c}) (%) | 13.89 | 3.94 |

**Table 3.**Devices in Figure 18a.

Number | Device | Value/Part Number |
---|---|---|

(1) | Microcontroller | TMS320F28335 |

(2) | Interface circuit of the microcontroller | N/A |

(3)–(5) | GaN HEMT pairs | TPH3207 |

(6) and (7) | DC link capacitors | 680 mF/450 V |

(8)–(10) | Filter inductors | 0.5 mH |

(11)–(13) | Filter capacitors | 10 μF/300 V |

Power Grid Currents and Unbalance Ratio (UR) | ||
---|---|---|

Item | Without APF (t_{0}–t_{1}) | With APF (t_{1}–t_{2}) |

i_{grid_a} (A) | 2.93 | 2.91 |

i_{grid_b} (A) | 3.43 | 2.94 |

i_{grid_c} (A) | 3.95 | 3.02 |

UR (%) | 14.83 | 2.13 |

THD | ||

Item | Without APF (t_{0}–t_{1}) | With APF (t_{1}–t_{2}) |

THD (i_{grid_a}) (%) | 20.23 | 4.15 |

THD (i_{grid_b}) (%) | 16.57 | 4.08 |

THD (i_{grid_c}) (%) | 15.48 | 4.05 |

Paper | Switching Device | Function | Power | Switching Frequency | Efficiency |
---|---|---|---|---|---|

[16] | IGBT | Motor drive | 8 kW | 20 kHz | 95.5% |

[17] | MOSFET | Motor drive | 1.5 kW | 15 kHz | 92% |

[18] | SiC | Electric vehicle | 8.8 kW | 50 kHz | 97% |

proposed | GaN | Active power filter | 2 kVA | 50 kHz | 97.2% |

80 kHz | 96.7% | ||||

100 kHz | 95.6% |

Sensed Object | Operating Temperature (°C) |
---|---|

TPH3207 @ 50kHz switching frequency | 40.9 |

TPH3207 @ 80kHz switching frequency | 46.7 |

TPH3207 @ 100kHz switching frequency | 51.4 |

DSP | 47.5 |

Communication interface | 46.5 |

Inductors | 30.4 |

Relays | 43.2 |

Signal processing integrated circuits (ICs) | 31.0 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Ma, C.-T.; Gu, Z.-H. Design and Implementation of a GaN-Based Three-Phase Active Power Filter. *Micromachines* **2020**, *11*, 134.
https://doi.org/10.3390/mi11020134

**AMA Style**

Ma C-T, Gu Z-H. Design and Implementation of a GaN-Based Three-Phase Active Power Filter. *Micromachines*. 2020; 11(2):134.
https://doi.org/10.3390/mi11020134

**Chicago/Turabian Style**

Ma, Chao-Tsung, and Zhen-Huang Gu. 2020. "Design and Implementation of a GaN-Based Three-Phase Active Power Filter" *Micromachines* 11, no. 2: 134.
https://doi.org/10.3390/mi11020134