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

Abstract

The extensive use of renewable energy systems with grid-connected inverters (GCIs) causes harmonic injection. Similarly, the imbalance in energy demand and supply causes frequency fluctuations. As a result of the increased harmonics and frequency fluctuations, the accuracy of power measurement using conventional methods continues to decline. Precision in power measurement is an essential factor for the billing and management of power supply and demand. Moreover, it is challenging to build a supply plan for the power demand and to manage the billing for the power consumption. To solve these problems, this paper proposes a novel method based on Lock-in Amplifier (LIA) and Lock-in Amplifier Frequency-Locked Loop (LIA-FLL) to measure the power with high precision and accuracy. The proposed method first tracks the variations in the input signal frequency using LIA-FLL and generates the updated reference signals for LIA. After that, the LIA is used to extract the accurate amplitude of each frequency component. The proposed method results in accurate and precise measurement, even with harmonics and frequency fluctuations. The validity of the proposed method is verified by comparing the power measurement results with the classical method, FFT, and ZERA COM3003 (a commercially available power measurement reference instrument).

1. Introduction

The rise in world population causes a rapid increase in energy demand and global warming. International stakeholders try to improve the environmental conditions around the world with the help of agreements and policies like the Paris Climate Agreement. In the power sector, to meet the increase in energy demand, the use of renewable systems with grid-connected inverters (GCIs) increases with every passing year [1,2,3,4,5,6,7,8]. However, the energy demand and supply imbalance and the use of GCIs cause harmonic injection and frequency fluctuations in the grid [9,10,11,12,13,14,15]. As a result, the accuracy of power measurement with conventional methods is gradually decreasing, which results in civil complaints due to wrong billing and adversely affects the prediction and management of power demand [16,17,18,19].

The conventional power measurement method is mainly divided into two types, a mechanical (induction type) power measurement method and an electronic power measurement method. First, the mechanical power measurement method offers straightforward design, efficient operation, and superior durability. However, the fixed coil overheats and affects the disk’s mechanical inertia when the voltage and current waveforms have harmonics or when the frequency is changed. As a result, the accuracy of power measurement reduces [20,21]. Consequently, the mechanical power measurement method is not preferred for the system with harmonics [21,22]. The second method is an electronic measurement, compensating for the disadvantages of the mechanical power measurement method. The electronic power measurement method is subdivided into analog and digital methods. With the development of technology, the analog method using an operational amplifier circuit is replaced by the digital method. In the digital method, the voltage and current waveforms are sampled and processed digitally in the microcontroller unit (MCU) to calculate power [16,23,24]. However, the non-sinusoidal grid conditions, harmonics, and frequency fluctuations combined to cause an error in zero-crossing detection even in the digital power measurement method. Therefore, there still be a reasonable measurement error in power [25]. Budeanu and Fryze introduced the classical definition of non-sinusoidal AC power. Budeanu concluded that there is a power distortion, causing the sum of the squares of real and active power to be less than that of the apparent power. Budeanu’s reactive power definition directly extends the definition under sinusoidal conditions. Later on, Fryze introduced his definition of reactive power based on the decomposition of supply current into active and reactive current components. Both these definitions are extended by many authors to clear the misconceptions and limitations [26,27,28]. Another digital method of measuring power is Fast Fourier Transform (FFT). This method calculates power separately for each frequency component after extracting the voltage and current for each component. If the input signal has noise or multiple harmonics, FFT can extract accurate results for each component. However, this method has limitations like spectral leakage, picket-fencing effect, and resolution. In input frequency fluctuation, these limitations cause reduced accuracy in power measurement. To solve this problem, a large amount of data is required, resulting in a problem of long computation time [24].

Lock-in Amplifier based power measurement is another method used to extract phase and amplitude information for specific frequency components from input signals having harmonics. It shows higher accuracy than that FFT. However, if the input signal frequency fluctuates, the lock-in amplifier shows an error in extracted information. To solve this problem few methods based on FFT have been proposed recently to track the frequency of lock-in amplifiers. However, the amplitude extraction results of these methods are not much accurate due to the limitation of FFT [29,30].

• 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.

Therefore, a better power measurement method than the traditional ones is needed for precise power measurement under harmonics and frequency fluctuations [25].

In this paper, a novel power measurement method using a Lock-in Amplifier (LIA) and Lock-in Amplifier Frequency-Locked Loop (LIA-FLL) is proposed for single-phase systems. The proposed novel LIA-FLL tracks the frequency of the input signal using LIA-FLL. It updates the frequency of LIA reference signals continuously to keep it the same as the frequency of the input signal. The LIA uses the updated reference signals to extract the voltage and current for each component, followed by the power calculation for each component individually. The proposed method exhibits superior precision in signal extraction as compared to FFT [31,32,33,34,35,36,37]. To verify the efficiency of the proposed method, power measurement is performed under the condition of 25% total harmonic distortion (THD). The results are compared with the power measured through ZERA COM 3003, a power measurement reference device.

2. Proposed Power Measurement Method Using LIAs with FLL

The proposed power measurement is based on LIA, which extracts the accurate amplitude of desired frequency component and LIA-FLL, which tracks any variation in the frequency of the input signal.

2.1. Lock-In Amplifier (LIA)

The LIA has three segments, as shown in Figure 1, Phase Sensitive Detector (PSD), Low-Pass Filter (LPF), and Amplitude and Phase Extraction.

2.1.1. Phase Sensitive Detector (PSD)

In PSD, the input signal is multiplied by the reference signals (sine and cosine), and the frequency of the reference signals is the same as the frequency component to be extracted. Equation (1) shows the input current signal of ‘n’ harmonics.

$$I_{sig}=I_{amp}\left(\begin{array}{c}\sin \left({\omega }_{f}t+{\theta }_f\right)+\\ m_2\sin \left(2{\omega }_{f}t+2{\theta }_f\right)+\\ \cdots \\ m_n\sin \left(n{\omega }_{f}t+n{\theta }_f\right)\end{array}\right),$$

(1)

where ‘$I_{amp}$’ is the peak amplitude of the fundamental component, ‘$m_n$’ is the amplitude ratio of the nth harmonic, and ‘${\omega }_f$’ and ‘${\theta }_f$’ is the frequency and phase information of the fundamental component, respectively.

Reference signals to be multiplied with the input signal are defined in Equation (2).

$$\begin{gathered} I_{\sin \_ref}=\sin \left(k{\omega }_{ref}t+k{\theta }_{ref}\right), \\ {I}_{\cos \_ref}=\cos \left(k{\omega }_{ref}t+k{\theta }_{ref}\right), \end{gathered}$$

(2)

where ‘$k$’ defines the order of the reference signal selected according to the harmonic component to be extracted. The ‘${\omega }_{ref}$’ and ‘${\theta }_{ref}$’ is the frequency and phase of the reference signal, respectively. Both reference signals have unity amplitude, and the phase difference between them is 90°.

The PSD output is the product of the input current signal with reference signals, represented in Equation (3).

$$\begin{gathered} I_x=I_{sig}\times \sin \left(k{\omega }_{ref}t+k{\theta }_{ref}\right), \\ {I}_y=I_{sig}\times \cos \left(k{\omega }_{ref}t+k{\theta }_{ref}\right), \end{gathered}$$

(3)

Equation (4) shows the trigonometric identity that the product of two sinusoids can be represented as the sum of two sinusoids.

$$\begin{gathered} \sin \left(a\right)\cos \left(b\right)=\frac{1}{2}\left\{\sin \left(a-b\right)+\sin \left(a+b\right)\right\}, \\ \sin \left(a\right)\sin \left(b\right)=\frac{1}{2}\left\{\cos \left(a-b\right)-\cos \left(a+b\right)\right\}, \end{gathered}$$

(4)

Equation (3) is further expanded using the trigonometric identity shown in Equation (4). The signal represented in Equations (5) and (6) contains desired frequency components shifted to zero frequency (DC), and other harmonics are shifted to non-zero frequencies.

$$I_x=\frac{I_{amp}}{2}\left[{\displaystyle \sum }_{\begin{array}{c}n=1,2,3,\cdots \\ k=1,2,3,\cdots \end{array}}{m}_n\left\{\begin{array}{c}\cos \left(\begin{array}{c}\left(k{\omega }_{ref}-n{\omega }_f\right)t\\ +\left(k{\theta }_{ref}-n{\theta }_f\right)\end{array}\right)\\ -\cos \left(\begin{array}{c}\left(k{\omega }_{ref}+n{\omega }_f\right)t\\ +\left(k{\theta }_{ref}-n{\theta }_f\right)\end{array}\right)\end{array}\right\}\right],$$

(5)

$$I_y=\frac{I_{amp}}{2}\left[{\displaystyle \sum }_{\begin{array}{c}n=1,2,3,\cdots \\ k=1,2,3,\cdots \end{array}}{m}_n\left\{\begin{array}{c}\sin \left(\begin{array}{c}\left(k{\omega }_{ref}+n{\omega }_f\right)t\\ +\left(k{\theta }_{ref}+n{\theta }_f\right)\end{array}\right)\\ +\sin \left(\begin{array}{c}\left(k{\omega }_{ref}-n{\omega }_f\right)t\\ +\left(k{\theta }_{ref}-n{\theta }_f\right)\end{array}\right)\end{array}\right\}\right],$$

(6)

2.1.2. Low-Pass Filter (LPF)

The PSD output is given to the LPF to extract phase and amplitude information of the desired component by filtering out the DC component. The transfer function of the LPF is defined in Equation (7).

$$H_{LPF}\left(s\right)={\left(\frac{{\omega }_c}{s+{\omega }_c}\right)}^k,$$

(7)

where ‘${\omega }_c$’ and ‘k’ is the cut-off frequency and order of the LPF, respectively. The design of LPF is based on the lowest frequency component, which is 60 Hz (f_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.

$$I_d=\frac{I_{amp}}{2}\left[\cos \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right],$$

(8)

$$I_q=\frac{I_{amp}}{2}\left[\sin \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right],$$

(9)

2.1.3. Amplitude and Phase Extraction

In this section, the outputs of the LPF containing the DC component are used to extract the amplitude and phase of the specific frequency component.

The amplitude of the $n$th harmonic is calculated in Equation (10) by using Equations (8) and (9). Equation (10) is further simplified using Equation (11).

$$A_n=\sqrt{{\left(\frac{I_{am{p}_n}}{2}\right)}^2\left\{\begin{array}{c}{\left[\cos \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right]}^2\\ +{\left[\sin \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right]}^2\end{array}\right\}},$$

(10)

$${\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right)=1,$$

(11)

$$A_n=\left(\frac{I_{am{p}_n}}{2}\right),$$

(12)

The phase of $n$th harmonic is calculated by Equation (13), which can be further simplified by Equation (14). Thus, LIA extracts the accurate amplitude and phase information of voltage and current signals for each harmonic component.

$${\theta }_n={\tan }^{-1}\left\{\frac{\frac{I_{am{p}_n}}{2}\left[\sin \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right]}{\frac{I_{am{p}_n}}{2}\left[\cos \left(\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right)\right]}\right\},$$

(13)

$${\theta }_n=\left\{\left(k{\omega }_{ref}-n{\omega }_f\right)t+\left(k{\theta }_{ref}-n{\theta }_f\right)\right\},$$

(14)

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

The LIA-FLL has two segments, as shown in Figure 2, the LIA and FLL. The phase output of LIA is used by FLL to calculate the correct frequency of the input signal. The updated frequency from FLL is used to generate reference signals of LIA to extract the desired frequency component accurately. The LIA gives phase as an output. The FLL takes phase information as the input and calculates the derivative of phase (Δθ). The Δθ is amplified with a PI controller to give the change in frequency (Δf). This change in frequency is added to the desired frequency to get the accurate frequency of the input signal. The tracked frequency is used to calculate the phase shift needed to synchronize the phase of the input signal and reference signals. This new frequency is used to generate new reference signals using LIA. Figure 2 shows the block diagram of the proposed LIA-FLL.

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

This section describes the power calculation using the input voltage and current signals. The LIA-FLL tracks the variations in the input signal frequency and updates the LIA reference signals accordingly. The tracked frequency from the LIA-FLL is used to generate the reference signals with the same frequency and phase as the input signal. These updated reference signals and the input signal (voltage and current) are used by separate lock-in amplifiers for voltage and current to extract the accurate amplitude for each frequency component. These extracted voltage and current magnitudes are multiplied to calculate the power for each frequency component. The power calculated for n-components are added to get total power (P_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

This section describes the experimental setup and configuration used for power measurement. The programmable AC source (Chroma 61704) is configured with the voltage, frequency, and THD profile to supply power to the load. The supply voltage is configured as 220 V (rms single-phase), and the load used is a 1 kW (48 Ω) resistive load (single-phase). The harmonic profile of the AC source is configured for THD of 25% (Vf: 100%, Vh2: 11.1%, Vh3: 11.2%, Vh5: 11.2%, Vh7: 11.2%, and Vh11 11.2%). According to IEEE Std 519-2022, the THD limit is 8% for the system with less than 1 kV [38]. However, in these experiments, a higher THD is used to test the robustness of the proposed method. Figure 4 shows the flow chart of the experimental procedure. The voltage and current signals for the connected load are acquired using the voltage sensing circuit and the current probe, respectively. The voltage sensing circuit is implemented with an LV 25-P voltage sensor with a measurement range of 500 V DC/AC, and the current probe (Chauvin Arnoux, P011015105Z) is used with a measurement range of 10 A. The SFD-1515 (AC to DC converter) provides ±15 V biasing to the voltage sensor.

The output analog signals from the voltage sensing circuit and the current probe are converted into digital signals using NI myDAQ. The analog-to-digital converter in the NI myDAQ operates with 16 bits and a 100 kHz sampling rate. The proposed method implemented by LabVIEW detects the frequency and calculates the power for each frequency component. Figure 5 shows the block diagram of the experimental setup used for the power measurement. Red and black line represents live and neutral wire, respectively.

The ZERA COM3003, a commercially available reference power measurement instrument, is also connected to compare the measurement results with those proposed.

3.2. Frequency Tracking by Proposed LIA-FLL

This section discusses the frequency tracking results obtained using LIA-FLL with the previously explained experimental setup. The experiment is performed for three input signal frequencies (58 Hz,60 Hz, and 62 Hz) with a 100 kHz sampling rate under 25% THD condition (Vf: 100%, Vh2: 10.09%, Vh3: 10.99%, Vh5: 11.11%, Vh7: 11.14%, Vh11: 11.21%). In this experiment, the frequency shift of ±2 Hz is selected according to the standard for frequency deviation of ±1.5 Hz defined by Korean Electric Power Corporation (KEPCO) [39]. However, a higher frequency deviation value is selected to test the robustness of the proposed method.

To achieve the frequency shift for the experiment, the programmable AC supply (Chroma 61704) is configured with voltage, frequency, and THD profiles of 220 Vrms, 60 Hz, and 25% THD respectively. The power is supplied to the resistive load, and the NI myDAQ converts the sensed voltage and current signal to the digital domain. The proposed LIA-FLL implemented using LabVIEW acquires voltage and current data from NI myDAQ, tracks the correct input frequency, and updates the LIA reference signals. Next, we changed the frequency setting of the Chroma to 62 Hz and again performed the same experiment. The same procedure was followed for 58 Hz as well. The frequency tracking results show that the proposed LIA-FLL takes 500 ms to lock the frequency initially and 150 ms to follow the further variations. Figure 6 shows the results for the proposed LIA-FLL. It shows that the proposed frequency tracking algorithm works effectively at different frequencies.

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

In this section, the power measurement results by the proposed method are shown, and the results will be discussed. The chroma power supply generates the system signals (voltage and current) with harmonics for defined voltage and frequency profiles of 220 V (rms single-phase) and 60 Hz, respectively. Figure 7 shows chroma’s output voltage and current signals when connected with a 48 Ω resistive load under 25% THD condition and the frequency spectrum for these voltage and current signals obtained using the oscilloscope.

As mentioned, the ZERA COM3003 is connected in parallel to compare the power measured with the proposed LIA-FLL. Figure 8,

Table 1. Instantaneous voltage, current and power measurement results by ZERA instrument display.

Parameter	Measurement
Voltage	220.121
Current	4.5249
Power	996.03

,

Table 2. THD Measurements by ZERA instrument.

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%

and

Table 3. Component-specific current, voltage, and power measurements by ZERA equipment.

	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
PT	Total Power	996.0162

show the power and THD measurements performed by ZERA with an input signal frequency of 60 Hz and 25% THD condition, respectively.

The proposed LIA-FLL is used for power measurement with the same testing condition of THD and system signal. The LabVIEW code based on LIA-FLL acquires voltage and current data from NI myDAQ. The LIA-FLL updated the LIA reference signals and accurately measured the voltage, current, and power for the fundamental and each harmonic component.

Table 4. Component-specific current, voltage, and power measurements by proposed LIA-FLL.

	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
PT	Total Power	995.9894

shows the results obtained for component-specific voltage, current, and power with LIA-FLL at 60 Hz.

The same power measurement experiment is performed using LIA-FLL by changing the input signal frequency to 58 Hz and 62 Hz to analyze the performance under the frequency variations. As mentioned earlier, the ZERA COM 3003 is connected to compare the accuracy of the power measurements by the proposed LIA-FLL. The measurement error for the proposed LIA-FLL with three different input frequencies (58 Hz, 60 Hz, and 62 Hz) is calculated by comparing the component-specific voltage, current, and power measured by ZERA COM 3003. The results from Figure 9 show the percentage error in total power measured by LIA-FLL, taking those by ZERA as a reference. Results show that the percentage error in power for the proposed method is less than the standard accuracy of ±0.02% (class 0.02).

3.4. Power Measurement with FFT and Classical Method

Fast Fourier Transform (FFT) is another method used for power measurement. This method calculates power separately for each frequency component after extracting the voltage and current for each component. For power measurement with this method, the LabVIEW code based on the FFT acquires data from NI myDAQ. First, the frequency resolution of 1.5 Hz is used to observe the effect of spectral leakage. Next, the LabVIEW code extracts the voltage and current for each frequency component. Then these extracted voltage and current values are used to calculate the component-specific power.

Table 5. Component-specific current, voltage, and power are measured by FFT.

	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
PT	Total Power	995.2785

shows the component-specific voltage, current, and power measurement results of the FFT method at 60 Hz.

To analyze the performance of the FFT method under frequency fluctuations, the same experiment is performed with two other input signal frequencies of 58 Hz and 62 Hz. The measurement error for the FFT method with three different input frequencies (58 Hz, 60 Hz, and 62 Hz) is calculated by comparing the component-specific voltage, current, and power measured by ZERA COM3003. Figure 10 shows the maximum percentage error for the FFT method is 0.115% which is higher than the proposed LIA-FLL. The FFT shows an increase in error as the frequency fluctuates due to the picket-fencing and spectral leakage effect at frequencies (58 Hz and 62 Hz).

The classical method (numerical integration) is another conventional method used for power measurement in digital electronics meters. This method multiplies discrete samples of rms voltage and rms current. This product is repeated for ‘n-samples’ where ‘n’ is the period sampling number of the digital signal. Then the summation result is divided by ‘n’. The period of the digital signal is kept fixed [16]. The testing conditions for the experiment with the classical method are the same, with 25% THD. The LabVIEW code based on the numerical integration algorithm acquires the digital signals for voltage and current from NI myDAQ and calculates the power.

Table 6. Voltage, current, and power are measured by the classical method.

Parameter	Classical Method
Voltage [V]	219.9010
Current [A]	4.5204
Power [W]	994.0581

shows the voltage, current, and power measured by the classical method under the 25% THD condition and the input signal frequency of 60 Hz.

To analyze the performance of the classical method under frequency fluctuations, the same experiment is performed with two other input signal frequencies of 58 Hz and 62 Hz. The measurement error for the classical method with three different input frequencies (58 Hz, 60 Hz, and 62 Hz) is calculated by comparing the component-specific voltage, current, and power measured by ZERA COM 3003. Figure 11 shows the percentage error for the classical method. The results show that the measurement error for the classical method is higher than that of the proposed LIA-FLL. The error increases as the frequency fluctuates because the digital signal ‘n’ period is fixed. In contrast, the input signal frequency is shifted, which means the digital signal does not fit into the digital window of n samples. This leads to an inaccurate measurement if the frequency of the input signal deviates.

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

The proposed LIA-FLL measures the thirty-minute power consumption under 25% THD condition. Two commercially available watt-hour meters and ZERA COM3003 are also used to measure the thirty-minute power consumption under the same testing conditions. Figure 12 shows the commercially available watt-hour meters A and B during the power consumption measurement.

The power consumption measurement results for the proposed LIA-FLL and commercially available watt-hour meters are compared with the power consumption measurement results for ZERA COM3003.

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%

shows the percentage error in measurement performed by each method.

The results show that the power consumption measurement with both commercial watt-hour meters shows an error of 0.401% compared to the results by ZERA COM3003. However, the measurement performed by the proposed LIA-FLL method shows an error of 0.0027%. Figure 13 shows the percentage error in power consumption for the proposed method with LIA-FLL, watt-hour meter A, and watt-hour meter B.

4. Conclusions

This article proposes a novel power measurement method based on the LIA with FLL to get accurate power measurements under non-sinusoidal grid conditions. The proposed LIA-FLL tracks the input signal frequency and updates the LIA reference signals. The LIA extracts the component-specific voltage and current from the input signal having harmonics and frequency fluctuations. The component-specific voltage and current result in accurate power and watt-hour measurement.

To verify the performance of the proposed method, the experiment is performed for three different input signal frequencies of 58 Hz, 60 Hz, and 62 Hz under the 25% THD condition. In addition, the measurement results of the proposed method are compared with the results for the conventional methods and the reference device ZERA COM3003. The comparison verifies that the proposed method shows an accuracy of ±0.0027% or less, which is better than the standard accuracy class 0.02, for power and watt-hour measurement even with an input signal having harmonics and frequency fluctuations.