# A Novel Power Measurement Method Using Lock-In Amplifiers with a Frequency-Locked Loop

^{*}

## Abstract

**:**

## 1. Introduction

- Ref. [30] implemented the digital lock-in amplifier with an FFT phase-locked loop to automatically track the input signal’s frequency change. This article claimed an accuracy of less than 1%.
- Ref. [29] implemented a digital lock-in amplifier with a frequency-tracking algorithm based on the Discrete Fourier transform (DFT). This article claimed less than 0.1% accuracy for frequency tracking and voltage signal amplitude extraction. This accuracy is due to the limitation of the DFT, like spectral leakage and resolution.

## 2. Proposed Power Measurement Method Using LIAs with FLL

#### 2.1. Lock-In Amplifier (LIA)

#### 2.1.1. Phase Sensitive Detector (PSD)

#### 2.1.2. Low-Pass Filter (LPF)

_{2h}− f

_{1h}). To extract the fundamental component, the lowest frequency component (60 Hz) should be attenuated sufficiently. As a result, other higher-frequency components are eliminated as well. In this paper, ${\omega}_{c}\mathrm{and}k$ is selected as 5.3 Hz and 4, respectively. Equations (8) and (9) show the output of the LPF, where the residual AC ripples are removed. Only the desired frequency component at zero frequency remains, which leads to accurate measurements.

#### 2.1.3. Amplitude and Phase Extraction

#### 2.2. Lock-In Amplifier Frequency-Locked Loop (LIA-FLL)

#### 2.3. New Power Measurement Method Using LIA and LIA-FLL

_{T}). Figure 3 shows the block diagram of the proposed power measurement method using LIA and LIA-FLL.

## 3. Experimental Results and Discussion

#### 3.1. Experimental Setup and Configuration

#### 3.2. Frequency Tracking by Proposed LIA-FLL

#### 3.3. Comparison of the Power Measurement by the Proposed Algorithm and ZERA Instrument

#### 3.4. Power Measurement with FFT and Classical Method

#### 3.5. Power Consumption Measurement with LIA-FLL and Commercial Watt-Hour Meter

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of Lock-in Amplifier [37].

**Figure 2.**Block diagram of Lock-in Amplifier Frequency-Locked Loop [37].

**Figure 4.**Flow chart of the experimental procedure used for the power measurement by the proposed method.

**Figure 6.**LabVIEW results for frequency tracking with LIA-FLL: (

**a**) fundamental component (58 Hz, 60 Hz, and 62 Hz); (

**b**) 2nd harmonic (116 Hz, 120 Hz, and 124 Hz); (

**c**) 3rd harmonic (174 Hz, 180 Hz,186 Hz); (

**d**) 5th harmonic (290 Hz, 300 Hz, and 310 Hz); (

**e**) 7th harmonic (406 Hz, 420 Hz, and 434 Hz); (

**f**) 11th harmonic (638 Hz, 660 Hz, and 682 Hz).

**Figure 7.**Oscilloscope results for chroma power supply (60 Hz): (

**a**) voltage signal; (

**b**) current signal; (

**c**) FFT of the voltage signal; (

**d**) FFT of the current signal.

**Figure 9.**Percentage error for component-specific voltage, current, and power measured by LIA-FLL, taking ZERA as reference (58 Hz, 60 Hz, and 62 Hz).

**Figure 10.**Percentage error for component-specific voltage, current, and power measured by FFT, taking ZERA as reference (58 Hz, 60 Hz, and 62 Hz).

**Figure 11.**Percentage Error for Voltage, Current, and Power Measured by classical method taking ZERA as reference (58 Hz, 60 Hz, and 62 Hz).

**Figure 12.**Power consumption measurement results (initial and final readings): (

**a**) Watt-hour meter A; (

**b**) Watt-hour meter B.

**Figure 13.**The percentage error for power consumption was measured for the proposed method with LIA-FLL, Watt-hour meter A, and Watt-hour meter B.

Parameter | Measurement |
---|---|

Voltage | 220.121 |

Current | 4.5249 |

Power | 996.03 |

Parameter | Voltage | Current |
---|---|---|

Fundamental Wave | 100% | 100% |

2nd Harmonic | 10.09% | 10.08% |

3rd Harmonic | 10.99% | 10.96% |

5th Harmonic | 11.11% | 11.08% |

7th Harmonic | 11.14% | 11.10% |

11th Harmonic | 11.21% | 11.16% |

THD | 24.41% | 24.33% |

Parameter | ZERA | |
---|---|---|

Voltage [V] | Fundamental Wave | 213.8697 |

2nd Harmonic | 21.5794 | |

3rd Harmonic | 23.5042 | |

5th Harmonic | 23.7609 | |

7th Harmonic | 23.8250 | |

11th Harmonic | 23.9748 | |

Current [A] | Fundamental Wave | 4.3959 |

2nd Harmonic | 0.4431 | |

3rd Harmonic | 0.4818 | |

5th Harmonic | 0.4870 | |

7th Harmonic | 0.4879 | |

11th Harmonic | 0.4905 | |

Power [W] | Fundamental Wave | 940.1676 |

2nd Harmonic | 9.5634 | |

3rd Harmonic | 11.3243 | |

5th Harmonic | 11.5733 | |

7th Harmonic | 11.6255 | |

11th Harmonic | 11.7618 | |

P_{T} | Total Power | 996.0162 |

Parameter | Proposed LIA-FLL | |
---|---|---|

Voltage [V] | Fundamental Wave | 213.8611 |

2nd Harmonic | 21.5789 | |

3rd Harmonic | 23.5026 | |

5th Harmonic | 23.7599 | |

7th Harmonic | 23.8239 | |

11th Harmonic | 23.9736 | |

Current [A] | Fundamental Wave | 4.3960 |

2nd Harmonic | 0.4431 | |

3rd Harmonic | 0.4818 | |

5th Harmonic | 0.4870 | |

7th Harmonic | 0.4879 | |

11th Harmonic | 0.4906 | |

Power [W] | Fundamental Wave | 940.1430 |

2nd Harmonic | 9.5633 | |

3rd Harmonic | 11.3236 | |

5th Harmonic | 11.5730 | |

7th Harmonic | 11.6247 | |

11th Harmonic | 11.7614 | |

P_{T} | Total Power | 995.9894 |

Parameter | FFT | |
---|---|---|

Voltage [V] | Fundamental Wave | 213.8394 |

2nd Harmonic | 21.5410 | |

3rd Harmonic | 23.4410 | |

5th Harmonic | 23.7023 | |

7th Harmonic | 23.7186 | |

11th Harmonic | 23.8180 | |

Current [A] | Fundamental Wave | 4.3948 |

2nd Harmonic | 0.4414 | |

3rd Harmonic | 0.4805 | |

5th Harmonic | 0.4850 | |

7th Harmonic | 0.4868 | |

11th Harmonic | 0.4902 | |

Power [W] | Fundamental Wave | 939.7826 |

2nd Harmonic | 9.5094 | |

3rd Harmonic | 11.2650 | |

5th Harmonic | 11.4961 | |

7th Harmonic | 11.5481 | |

11th Harmonic | 11.6771 | |

P_{T} | Total Power | 995.2785 |

Parameter | Classical Method |
---|---|

Voltage [V] | 219.9010 |

Current [A] | 4.5204 |

Power [W] | 994.0581 |

**Table 7.**A comparison between LIA-FLL, Watt-hour meter A, and Watt-hour Meter B, based on measured power consumption taking ZERA COM3003 as a reference.

Method | Power Consumption | %Error |
---|---|---|

ZERA | 498.000 Wh | - |

Proposed LIA-FLL | 498.013 Wh | 0.0027% |

Commercial Watt-Hour Meter A | 500.000 Wh | 0.4015% |

Commercial Watt-Hour Meter B | 500.000 Wh | 0.4015% |

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**MDPI and ACS Style**

Rehman, A.; Cho, K.; Choi, W.
A Novel Power Measurement Method Using Lock-In Amplifiers with a Frequency-Locked Loop. *Electronics* **2023**, *12*, 2219.
https://doi.org/10.3390/electronics12102219

**AMA Style**

Rehman A, Cho K, Choi W.
A Novel Power Measurement Method Using Lock-In Amplifiers with a Frequency-Locked Loop. *Electronics*. 2023; 12(10):2219.
https://doi.org/10.3390/electronics12102219

**Chicago/Turabian Style**

Rehman, Abdur, Kangcheoul Cho, and Woojin Choi.
2023. "A Novel Power Measurement Method Using Lock-In Amplifiers with a Frequency-Locked Loop" *Electronics* 12, no. 10: 2219.
https://doi.org/10.3390/electronics12102219