Enhanced Dual-Spectrum Line Interpolated FFT with Four-Term Minimal Sidelobe Cosine Window for Real-Time Harmonic Estimation in Synchrophasor Smart-Grid Technology

Abstract

The proliferation of nonlinear loads and integration of renewable energy sources require attention for accurate harmonic estimation along with estimation of fundamental amplitude, phase, and frequency for protection, improving power quality, and managing power effectively in a smart distribution grid. There are currently different Windowed Interpolated Fast Fourier Transform (WIFFT) algorithms for harmonic voltage estimation, but estimation of current harmonics using WIFFT is not explored sufficiently. The existing WIFFT algorithms, when used for current harmonic estimation result in low accuracy due to spectral leakage and picket fence effect. On the other hand, Interpolated Discrete Fourier Transform (DFT) is used for synchrophasor quality metrics, but it is effective only when there are no harmonics and the fundamental frequency is constant. This paper proposes a unified solution, comprising of peak location index search (PLIS)-based Dual-Spectrum Line Interpolated Fast Fourier Transform (DSLIFFT) algorithm with 4-Term Minimal Sidelobe Cosine Window (4MSCW) for estimating both low-amplitude voltage or current harmonics and synchrophasor under variable frequency conditions for high-penetration renewable energy utility grids. The effectiveness of the proposed algorithm is validated by simulation studies and real-time experimentation using the National Instruments reconfigurable embedded system under nonlinear loading conditions.

1. Introduction

Accurate estimation of current and voltage harmonics, as well as real-time measurement of voltage space vectors, i.e., synchrophasors, are essential for power electronic based nonlinear loads and the integration of renewables in the modern distribution network. The methodology must be simple and allow fast computation for harmonics and synchrophasor, simultaneously, with retrofit computation capabilities. This paper contributes to advancing such a technology, in designing a suitable compensation and protection devices for the modern distribution network. Moreover, for the accuracy of the estimation method, as well as the requirements of international standards [1,2,3], it is important to have a fast, accurate, and easy-to-design compensation devices. The total harmonic distortion limits must be maintained at less than 5% as per the Institute of Electrical and Electronics Engineers (IEEE) standard 519-2014 [4].

Numerous signal processing methods have been adopted for the estimation of power system harmonics [5,6]. These methods are classified as non-parametric and parametric methods as reviewed in [5]. Parametric methods such as Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Multiple Signal Classification (MUSIC), Kalman Filter (KF), and Prony method require the prior information of the estimation signal for modeling; otherwise, it leads to erroneous results [5,6]. The computation time requirements of these methods are comparatively high. Moreover, they require appropriate load modeling [5,6]. To overcome these issues, non-parametric methods such as Fast Fourier Transform (FFT), Chirp Z-Transform (CZT), Wavelet Transform (WT), and Hilbert Hung Transform (HHT) are also evolved for harmonic estimation [5,6]. Given computational efficiency and simplicity, FFT is considered to be a highly suitable estimation method among all other parametric methods [6]. However, the FFT method has a limitation of spectral leakage and picket fence effect because of non-synchronous sampling due to variation in fundamental frequency [7]. To minimize the spectral leakage, window functions are adopted, and interpolation algorithms have been proposed to minimize the picket fence effect [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Thus, Windowed Interpolated FFT (WIFFT) algorithms have come into existence. However, due to fluctuating nature of harmonics caused by modern nonlinear loads and variations in fundamental frequency, there is no standard window and its associated interpolation algorithm for estimation of power system harmonics.

The accuracy of the harmonic estimation depends on the type of window and its corresponding interpolation algorithm. The window is selected based upon the narrowed main lobe, smaller sidelobe width, and rapid sidelobe roll of rate. The precise estimation of amplitude, frequency, and phase of the fundamental, as well as harmonics, depends on the window properties. Moreover, the minimization of spectral leakage is dependent on window length, window coefficients, and sampling frequency [6]. In [8,9] detailed discussion of windows and its properties are reported, especially for harmonic estimation. From the past two decades, various WIFFT algorithms using Hanning Window, Hamming Window, Blackman Window, Advanced Cosine Windows, Hanning Self-Convolution Window, Cosine Self-Convolution Window, Triangular Self-Convolution Window, Adaptive Kaiser Self-Convolution Window, Mutual Multiplication Window and Nuttal-Kaiser Window for harmonic analysis are reported in the literature [7,10,11,12,13,14,15,16,17,18,19,20,21,22]. Recently the Nuttall Window with triple-spectrum line interpolated FFT for analysis of harmonics was reported in [23]. However, a Dual-Spectrum Line Interpolated FFT (DSLIFFT) algorithm has been widely used for most of the above stated windows. Moreover, the DSLIFFT with the above windows is focused on voltage harmonics estimation. However, estimation of current harmonics is also important to explore as per the revised International Electro-technical Commission (IEC) 61000-4-30 standard [2] due to the exponential diffusion of nonlinear loads on the distribution network. Regarding current harmonics, the fundamental amplitude is lower. In this case, the DSLIFFT algorithm accuracy is low because of the identical harmonic spectral lines on different frequency bins. Moreover, the computation complexity is also another factor, which demands the enhancement of existing DSLIFFT for current harmonic estimation. Therefore, computational burden aspects can be quite interesting in big data analytics applications, where large amounts of data to uncover hidden patterns, correlations, and other insights [24]. However, the accurate estimation of the current harmonics is not explored sufficiently.

Further FFT is also used for synchrophasor estimation [25]. In [26], application of space-vector interpolated Discrete Fourier Transform (DFT) method is presented for synchrophasor estimation. However, estimation under harmonic conditions is not reported. Moreover, WIFFT algorithm application for harmonic and synchrophasor estimation simultaneously under unstable fundamental frequency is not explored enough. As per the IEEE Standard C37.118.1a-2014 Phasor Measuring Units (PMUs) are classified as P-class and M-class for fast and accurate estimation of phasors under different abnormal conditions [27]. Recently reduced leakage synchrophasor estimation using Hilbert transform plus the interpolated DFT has been reported in [28]. However, the research is still in progress for developing the unified algorithm for P- and M-class PMUs regarding accuracy and simplicity.

Therefore, during the estimation of current harmonics and synchrophasor, the following issues need to be addressed. WIFFT is a simple and easy-to-implement method for harmonic voltage estimation; however, selection of the suitable window function and improvement of existing DSLIFFT for estimating the current harmonics accurately are essential. On the other hand, the improvement of synchrophasor estimation accuracy under variable frequency and harmonic conditions also need to be addressed. To address the above issues, in this article, a Peak Location Index Search (PLIS)-based DSLIFFT algorithm using 4-Term Minimal Sidelobe Cosine Window (4MSCW) is proposed as a generic approach to harmonics estimation (voltages or current) and synchrophasor at the same time under variable frequency operation. Because of the reasonable main lobe, lower sidelobe level and fast sidelobe roll of the rate the 4MSCW proposed in [14] has been adopted for PLIS-based DSLIFFT estimation process.

The Real-Time (RT) implementation of the proposed PLIS-based DSLIFFT algorithm using 4MSCW algorithm and its current harmonic and synchrophasor estimation accuracy with real-world nonlinear loads has been presented in this article.

The major contributions in this paper are as follows

• A PLIS-based DSLIFFT algorithm is presented for simplifying the estimation process and improving the estimation accuracy of low-amplitude voltage or current harmonic signal parameters as well as synchrophasors at a time with a 4MSCW.
• The application of 4MSCW for current harmonic and synchrophasor estimation at a time has been explored.
• The proposed algorithm is implemented and tested in RT with real-world nonlinear loads.

2. Materials and Methods

The 4MSCW functions and its corresponding PLIS-based DSLIFFT algorithm proposed in this article for harmonic and synchrophasor estimation are summarized in the following sections.

2.1. 4MSCW Function Overview

Numerous window functions are reported in the literature for harmonic spectral estimation, but there is a compromise in accuracy because of the window properties, such as main lobe, sidelobe widths, and sidelobe roll-off rates [8,9]. However, Cosine Windows (CWs) such as Hanning, Hamming, and Blackman are the most common window functions adopted in harmonic spectral analysis. Moreover, various CWs are reported in the literature for harmonic estimation [7,8,9,10,11,12,13,14,15,16,18,19,21,22,23]. Apart from another family of windows, CWs are well considered for harmonic estimation.

The basic discrete Cos^αx window function is expressed as follows:

$$w\left(n\right)=co{s}^{\alpha }\left(\frac{\pi n}{N}\right), 0\le \left|n\right|\le \frac{N}{2}$$

(1)

By changing the “α” value, different forms of CWs are developed. Here α takes integer values, and N is fixed to 2^k, where k is a natural number. Based upon the window function given in Equation (1) various advanced CWs are derived for harmonic estimation [7,8,9,10,11,12,13,14,15,16,18,19,21,22,23]. Given the main lobe, sidelobe, and sidelobe roll of rate requirements a 4MSCW is adopted for harmonic and synchrophasor estimation, a PLIS-based DSLIFFT algorithm has been developed to improve its accuracy matching with the RT signal analysis. The main objective of this algorithm is to estimate the spectral amplitude and phase of the harmonic current signals accurately. The discrete-time 4MSCW with length N and order H is expressed as:

$$w_{4MSCW}\left(n\right)={\displaystyle \sum }_{h=0}^{H-1}{\left(-1\right)}^h{a}_{h}cos\left(\frac{2\pi hn}{N}\right) forn=0,1,\dots ,N-1$$

(2)

where n represents the sample index, N represents the total number of samples, h denotes the fundamental and harmonic numbers and a_h represents the window coefficients. The CWs are developed based upon the H and a_h values to meet the computation requirements of the interpolation technique. The coefficients of a_h must comply with the following conditions.

$${\displaystyle \sum }_{h=0}^{H-1}{\left(-1\right)}^h{a}_h=0,{\displaystyle \sum }_{h=0}^{H-1}{a}_h=1$$

(3)

The spectral window corresponding to the 4MSCW derived from Equation (1) by using the Discrete-Time Fourier transform (DTFT) is written as follows

$$\begin{gathered} W_{4MSCW}\left(n\right)={\displaystyle \sum }_{h=0}^{H-1}\frac{a_h}{2}\left[e^{\frac{-j\pi \left(n-h\right)\left(N-1\right)}{N}}\frac{\sin (\left(n-h\right)\pi }{\sin \left(\frac{\left(n-h\right)\pi }{N}\right)} \\ +e^{\frac{-j\pi \left(n+h\right)\left(N-1\right)}{N}}\frac{\sin (\left(n+h\right)\pi }{\sin \left(\frac{\left(n+h\right)\pi }{N}\right)}\right] \\ forn=0,1,\dots ,N-1 \end{gathered}$$

(4)

Concerning the 4MSCW properties regarding the main lobe width between zero crossing, it must fulfill the following condition to get the |W_MSCW (n)| values as zeros.

$$\{\begin{array}{c}n\pm h=d\\ n\pm h\ne dN\end{array}ford=0,\pm 1,\pm 2,\dots ,+\infty$$

(5)

The adopted 4MSCW functions of type-1 and type-2 coefficients and properties adopted from [14] are tabulated in

Table 1. 4MSCW Coefficients and Properties.

Window Type	Window Coefficients				Main Lobe Width	Peak Sidelobe Level (dB)	Sidelobe Roll-off Rate (dB/oct)
	a0	a1	a2	a3
4MSCW type-1	0.355768	0.487396	0.144232	0.012604	4Hπ/N	−93	18
4MSCW type-2	0.3125	0.46875	0.1875	0.03125	4Hπ/N	−61	42

.

2.2. Mathematical Formulation of PLIS-Based DSLIFFT

The mathematical formulation of the harmonic signal is represented as:

$$x\left(n{T}_s\right)=x\left(t\right)={\sum }_{h=1}^H{A}_h\sin (2\pi f_{h}n{T}_s+{\phi }_h)\mathrm{where}n=0,1,\dots N-1$$

(6)

where the amplitude, frequency, and phase are denoted as A_h, f_h and φ_h, respectively. The sampling time of the signal is represented as T_s. Due to the unstable nature of the fundamental frequency, the sampling is non-synchronous, which leads to spectral leakage. To suppress the spectral leakage effect, the sampled signal is weighted by the window function. The FFT of the windowed sample signal under non-synchronous sampling is represented as:

$$X\left(k\right)={\displaystyle \sum }_{h=1}^H\frac{A_h}{2j}\left[e^{j{\phi }_h}{W}_{4MSCW}\left(k-k_h\right)-e^{j{\phi }_h}{W}_{4MSCW}\left(k+k_h\right)\right]$$

(7)

where k = 0, 1 … (N – 1), W_MSCW indicates the FFT of the 4MSCW function, k_h denotes the division factor of signal frequency and the frequency resolution, which is expressed as:

$$k_h=\frac{f_{h}N}{f_s}=l_h+{\xi }_h$$

(8)

where l_h is an integer value and ξ_h (0 ≤ ξ_h ≤ 1) is the fractional part. The negative frequency part is ignored in Equation (8). The sampling frequency used for computation is represented as f_s. The l_h and ξ_h are computed by PLIS-based DSLIFFT algorithm as described in the next section.

2.3. PLIS-Based DSLIFFT Algorithm

The detailed flowchart of the proposed PLIS-based DSLIFFT algorithm is depicted in Figure 1. The input current harmonic signal is sampled and weighted by the adopted 4MSCW after that the spectrum is computed. To compute the fundamental and harmonic peaks, PLIS method is proposed. In this method, a threshold factor (τ) is defined to ignore the estimation of peak locations of all the frequency bins. By defining the threshold factor, the peak location indexes are identified for the dominant harmonic frequency bins. Initially, the harmonic index is defined as I, and the threshold factor is considered to be 0.1% of the fundamental amplitude. The threshold factor is calculated from the relation between the fundamental and the considerable lowest harmonic amplitude which will contribute to the total harmonic distortion (THD). The importance of the threshold factor is to identify the significant harmonic peak value corresponding to the lower order harmonics. The threshold factor of 0.1% in PLIS method is based on the considerable dominant harmonic peak value concerning its fundamental amplitude. Usually, the least harmonic amplitudes which will impact the signal quality in the current signal will be 0.1% of the fundamental amplitude based on the knowledge of different nonlinear load current harmonic data. Therefore, threshold factor is considered to be 0.1%, to obtain the harmonic peak amplitudes. Afterward, DSLIFFT correction is applied to estimate the amplitude, phase, and frequency of the fundamental as well as all other harmonic orders. This procedure effectively decreases the computation process. However, the peak search process in the conventional DSLIFFT algorithm reported in the literature [11,12,13,14,15,16,17,18,20,21,22,23] will check for the entire frequency bin peak locations, which in turn increases the computation burden.

The main objective of the PLIS method is to identify the fundamental as well as adjacent harmonic spectral lines accurately.

2.4. Overview of DSLIFFT

After obtaining the locations of the spectral lines, an interpolation method is applied to estimate the amplitude, phase, and frequency of the harmonic signal. The conventional DSLIFFT algorithm presented in the literature [11,12,13,14,15,16,17,18,19,20,21,22] is improved by using the PLIS method. The spectral line location of the h^th harmonic component can be obtained from the PLIS method. The ξ_h can be estimated from the interpolation method from which amplitude, phase, and frequency of h^th harmonic can be accurately computed. The pictorial representation of the PLIS-based DSLIFFT using 4MSCW is illustrated in Figure 2.

The frequency spectrum expression is written as [11,12,13,14,15,16,17,18,19,20,21,22]:

$$X\left({\xi }_h\right)=\frac{A_h}{2j}\left[e^{j{\phi }_h}{W}_{4MSCW}\left({\xi }_h-k_h\right)\right]\mathrm{for}{\mathsf{\xi }}_h=0,1,\dots \dots N-1$$

(9)

The two amplitude spectral lines represents the h^th harmonic is considered to be l_h1 and l_h2 (where l_h1 = I l_h2 = I + 1, l_h1 < k_h < l_h2). The peak locations of the harmonic amplitudes are obtained from PLIS method.

Let y₁ = |X(I)| and y₂ = |X (I + 1)|, then y₁ and y₂ are written as follows:

$$y_1=\left|X\left(I\right)\right|=\left|A_h\right|·\left|W_{4MSCW}(2\pi \left(I-k_h\right)/N\right|$$

(10)

$$y_2=\left|X\left(I+1\right)\right|=\left|A_h\right|·\left|W_{4MSCW}(2\pi \left(\left(I+1\right)-k_h\right)/N\right|$$

(11)

The least-square curve fitting is used to find the spectral amplitudes. The resultant expression of an independent variable α is expressed as

$$\alpha =k_h-l_{h1}-0.5 for-0.5\le \alpha \le 0.5$$

(12)

The y₁ and y₂ are expressed as

$$y_1=\left|X\left(I\right)\right|=\left|A_h\right|·\left|W_{4MSCW}(2\pi \left(-\alpha +0.5\right)/N\right|$$

(13)

$$y_2=\left|X\left(I+1\right)\right|=\left|A_h\right|·\left|W_{4MSCW}(2\pi \left(-\alpha +0.5\right)/N\right|$$

(14)

To compute the harmonic parameters, a symmetrical coefficient β which is a function of α is considered, where the β expression regarding α can be written as

$$\beta =g\left(\alpha \right)=\frac{\left(y_2-y_1\right)}{\left(y_2+y_1\right)}$$

(15)

From Equations (13) and (14), $\beta$ can be expressed as

$$\beta =g\left(\alpha \right)=\frac{\left|W_{4MSCW}\left(2\pi \left(-\alpha +0.5\right)/N\right)\right|-\left|W_{4MSCW}\left(2\pi \left(-\alpha -0.5\right)/N\right)\right|}{\left|W_{4MSCW}\left(2\pi \left(-\alpha +0.5\right)/N\right)\right|+\left|W_{4MSCW}\left(2\pi \left(-\alpha -0.5\right)/N\right)\right|}$$

(16)

Based on the window order, the α expression concerning β is derived from least-square curve fitting technique. The relation between α and β is derived as follows using the polynomial approximations.

$$\alpha ={\alpha }_0\beta +{\alpha }_1{\beta }^2+{\alpha }_2{\beta }^3+{\alpha }_3{\beta }^4+{\alpha }_4{\beta }^5$$

(17)

The polynomial coefficients of 4MSCW type-1 and type-2 coefficients are tabulated in

Table 2. 4MSCW Polynomial Coefficients.

Window Type	a0	a1	a2	a3	a4
4MSCW type-1	2.6645	-	0.2806	-	0.1313
4MSCW type-2	3.5	-	-	-	-

.

After calculating the α value, the amplitude, frequency and phase values are calculated based upon the following interpolated formulas

$$k_h=\alpha +I+0.5$$

(18)

$$A_h=\frac{2y_1}{\left|W_{MSCW}\left(2\pi \left(I-k_h\right)\right)/N\right|}$$

(19)

$$f_h=\frac{k_h{f}_s}{N}$$

(20)

$${\phi }_h=\arg \left(X\left(I\right)\right)-\arg \left[W_{MSCW}\left(\frac{2\pi \left(I-k_{h }\right)}{N}\right)\right]+\frac{\pi }{2}$$

(21)

The main enhancement in this interpolation algorithm is a PLIS method, which is used to determine the amplitude of dominant harmonic frequency peak locations, instead of searching the amplitudes of all the frequency bins peak locations. Then interpolation is applied to estimate the amplitude, phase, and frequency of the fundamental as well as harmonic components, where the fundamental component estimation is useful for synchrophasor processing. The proposed algorithm is developed in RT using Laboratory Virtual Instrument Engineering Workbench (LabVIEW) programmed National Instruments (NI) compact Reconfigurable Input/output system (cRIO) system described in [29].

3. Simulation Results

This section demonstrates the simulation results of the proposed PLIS-based DSLIFFT using 4MSCW. Initially, the proposed algorithm simulated in a LabVIEW environment with a programmed harmonic test signal. The amplitudes and the corresponding phases of the programmed harmonic signal for fundamental frequency values of 49.5 Hz and 50.5 Hz are depicted in

Table 3. Simulated harmonic test signal information.

Parameters	Harmonic Orders (Fundamental Frequency = 49.5 Hz and 50.5 Hz)
	1	3	5	7	9	11	13	15	17
Amplitude (A)	2.5	0.4	0.35	0.3	0.25	0.2	0.2	0.15	0.2
Phase (deg)	40	115	−30	110	−20	100	−10	−90	0
Frequency (Hz)	49.5	148.5	247.5	346.5	445.5	544.5	643.5	742.5	841.5
	50.5	151.5	252.5	353.5	454.5	555.5	656.5	757.5	858.5

. The signal frequencies are considered as 49.5 Hz and 50.5 Hz to justify the estimation accuracy under non-synchronous sampling frequency, the input signal is analyzed by using PLIS-based DSLIFFT with 4MSCW. The proposed PLIS-based DSLIFFT using 4MSCW results are compared with the conventional DSLIFFT algorithm reported in [11,12,13,14,15,16,17,18,19,20,21,22] using 4MSCW. The simulated benchmark signal waveform representation is depicted in Figure 3.

The amplitude estimation of the benchmark harmonic test signal and its error comparison for 4MSCW type-1 and type-2 with fundamental frequency values of 49.5 Hz and 50.5 Hz are tabulated in

Table 4. Amplitude estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Amplitude (A) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Amplitude (A) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Amplitude Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	2.4824	2.4899	0.7028	0.4020
3	0.3753	0.3857	6.1643	3.5653
5	0.3375	0.3211	3.5652	8.2501
7	0.2998	0.2918	0.0502	2.7204
9	0.2448	0.2496	2.0958	0.1525
11	0.1831	0.1985	8.4625	0.7695
13	0.1967	0.1910	1.6485	4.5175
15	0.1498	0.1395	0.1524	6.9757
17	0.1916	0.1960	4.2013	1.9859

,

Table 5. Amplitude estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Amplitude (A) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Amplitude (A) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Amplitude Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	2.4866	2.4998	0.5361	0.0071
3	0.3811	0.3999	4.7318	0.0035
5	0.3405	0.3498	2.7285	0.0371
7	0.2999	0.2988	0.0384	0.4133
9	0.2460	0.2497	1.6013	0.1162
11	0.1870	0.1988	6.5141	0.5870
13	0.1975	0.1999	1.2588	0.0111
15	0.1498	0.1496	0.1162	0.2658
17	0.1936	0.1970	3.2176	1.5171

,

Table 6. Amplitude estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Amplitude (A) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Amplitude (A) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Amplitude Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	2.3930	2.4977	4.2795	0.0931
3	0.3999	0.3967	0.0266	0.8342
5	0.3393	0.3455	3.0453	1.2898
7	0.2829	0.2874	5.7078	4.1883
9	0.2494	0.2483	0.2479	0.6866
11	0.1960	0.1890	2.0134	5.5007
13	0.1854	0.1995	7.3230	0.2709
15	0.1490	0.1395	0.6867	6.9756
17	0.1976	0.1999	1.1892	0.0447

and

Table 7. Amplitude estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Amplitude (A) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Amplitude (A) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Amplitude Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	2.4181	2.4982	3.2777	0.0709
3	0.3999	0.3975	0.0210	0.6367
5	0.3418	0.3466	2.3292	0.9845
7	0.2869	0.2904	4.3793	3.2077
9	0.2495	0.2487	0.1888	0.5237
11	0.1969	0.1916	1.5380	4.2192
13	0.1887	0.1996	5.6291	0.2065
15	0.1492	0.1420	0.5237	5.3599
17	0.1982	0.1999	0.9077	0.0341

. Correspondingly the fundamental and harmonic frequencies and phase estimation values are depicted in

Table 8. Frequency estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Frequency (Hz) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Frequency (Hz) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Frequency Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	49.5000346	49.50003683	−7.4406 × 10−05	−6.9938 × 10−05
3	148.5000878	148.5000365	−2.4595 × 10−05	−5.9110 × 10−05
5	247.5000069	247.5001234	−4.9840 × 10−05	−2.7740 × 10−06
7	346.5000111	346.5000139	−4.0007 × 10−06	−3.2111 × 10−06
9	445.5000269	445.4999988	2.7295 × 10−07	−6.0283 × 10−06
11	544.5000422	544.5002823	−5.1850 × 10−5	−7.7484 × 10−06
13	643.5000888	643.5000947	−1.4715 × 10−05	−1.3799 × 10−05
15	742.5000096	742.5000303	−4.0779 × 10−06	−1.2987 × 10−06
17	841.5000116	841.5000183	−2.1798 × 10−06	−1.3728 × 10−06

,

Table 9. Frequency estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Frequency (Hz) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Frequency (Hz) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Frequency Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	49.5000000	49.5000000	−3.1142 × 10−08	−5.7960 × 10−10
3	148.5000001	148.5000000	−6.7450 × 10−08	−5.1360 × 10−09
5	247.5000000	247.5000000	8.5180 × 10−09	−9.5515 × 10−10
7	346.4999999	346.5000000	4.0677 × 10−08	1.1977 × 10−10
9	445.4999999	445.5000000	2.9231 × 10−08	−4.1347 × 10−10
11	544.4999998	544.5000000	2.8381 × 10-08	−4.7089 × 10-10
13	643.5000001	643.5000000	−9.5225 × 10−09	−1.1344 × 10−10
15	742.4999999	742.5000000	7.0338 × 10−09	−4.9105 × 10−10
17	841.5000000	841.5000000	−1.5468 × 10−09	1.6209 × 10−10

,

Table 10. Frequency estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Frequency (Hz) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Frequency (Hz) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Frequency Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	50.5000422	50.5000159	−8.3555 × 10−05	−3.14059 × 10−05
3	151.4999135	151.5000478	5.7095 × 10−05	−3.15744 × 10−05
5	252.5001140	252.5000150	−4.5132 × 10−05	−5.95614 × 10−06
7	353.4999881	353.5000803	3.3715 × 10−06	−2.27095 × 10−05
9	454.5000656	454.5000181	−1.4439 × 10−05	−3.98165 × 10−06
11	555.5001266	555.5001078	−2.2782 × 10−05	−1.93978 × 10−05
13	656.5000193	656.5000285	−2.9417 × 10−06	−4.34459 × 10−06
15	757.5000407	757.5001457	−5.3686 × 10−06	−1.923 × 10−05
17	858.5000624	858.5000213	−7.2647 × 10−06	−2.48504 × 10−06

,

Table 11. Frequency estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Frequency (Hz) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Frequency (Hz) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Frequency Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	50.5000001	50.5000000	−2.2646 × 10−07	−2.03743 × 10−09
3	151.4999994	151.5000000	3.6736 × 10−07	4.81584 × 10−09
5	252.5000000	252.5000000	1.9738 × 10−08	3.6238 × 10−10
7	353.4999999	353.5000000	2.0310 × 10−08	1.59258 × 10−10
9	454.5000001	454.5000000	−1.5487 × 10−08	1.36637 × 10−10
11	555.5000002	555.5000000	−3.2930 × 10−08	6.71479 × 10−11
13	656.5000001	656.5000000	−7.9165 × 10−09	−5.25211 × 10−10
15	757.5000000	757.5000000	−4.0858 × 10−09	−3.76255 × 10−11
17	858.5000000	858.5000000	3.9645 × 10−09	1.73331 × 10−10

,

Table 12. Phase estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Phase (deg) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Phase (deg) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Phase Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	39.9018	40.0345	0.2454	−0.0861
3	114.7082	115.1044	0.2537	−0.0908
5	−29.7853	−30.1692	0.7156	−0.5640
7	110.0253	109.9035	−0.0230	0.0877
9	−20.1676	−20.0241	−0.8382	−0.1207
11	100.3316	100.0481	−0.3316	−0.0481
13	−9.8551	−9.8817	1.4489	1.1826
15	−90.0466	−90.1555	−0.0517	−0.1728
17	−0.0024	−0.0008	0	0

,

Table 13. Phase estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 49.5 Hz.

Harmonic Order (h)	Phase (deg) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Phase (deg) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Phase Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	39.9033	40.0366	0.2418	−0.0914
3	114.7098	115.1098	0.2523	−0.0954
5	−29.7806	−30.1688	0.7312	−0.5625
7	110.0258	109.9043	−0.0234	0.0870
9	-20.1676	−20.0225	−0.8381	−0.1125
11	100.3420	100.0507	−0.3420	−0.0507
13	−9.8515	−9.8763	1.4849	1.2375
15	−90.0452	−90.1549	−0.0502	−0.1721
17	−0.0024	−0.0008	0	0

,

Table 14. Phase estimation comparison using 4MSCW type-1 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Phase (deg) Estimation Using 4MSCW Type-1 with DSLIFFT [12,13,14,15,16,17,18]	Phase (deg) Estimation Using 4MSCW Type-1 with Proposed PLIS-Based DSLIFFT	The Relative Error of Phase Estimation (%)
			4MSCW Type-1 with DSLIFFT	4MSCW Type-1 with Proposed PLIS-Based DSLIFFT
1	39.7577	39.9156	0.6057	0.2110
3	114.9842	115.0985	0.0138	−0.0856
5	−29.8017	−30.0666	0.6611	−0.2219
7	109.7212	110.1140	0.2535	−0.1036
9	−20.0598	−20.0490	−0.2990	−0.2448
11	100.1596	100.1303	−0.1596	−0.1303
13	−10.3180	−10.0318	−3.1795	−0.3177
15	−90.0972	−90.0900	−0.1080	−0.1000
17	0.0012	−0.0001	0	0

and

Table 15. Phase estimation comparison using 4MSCW type-2 with DSLIFFT and proposed PLIS-based DSLIFFT, when the fundamental frequency = 50.5 Hz.

Harmonic Order (h)	Phase (deg) Estimation Using 4MSCW Type-2 with DSLIFFT [12,13,14,15,16,17,18]	Phase (deg) Estimation Using 4MSCW Type-2 with Proposed PLIS-Based DSLIFFT	The Relative Error of Phase Estimation (%)
			4MSCW Type-2 with DSLIFFT	4MSCW Type-2 with Proposed PLIS-Based DSLIFFT
1	39.7593	39.9166	0.6018	0.2086
3	114.9810	115.1013	0.0165	−0.0881
5	−29.7975	−30.0656	0.6750	−0.2188
7	109.7209	110.1189	0.2537	−0.1081
9	−20.0574	−20.0478	−0.2869	−0.2391
11	100.1643	100.1369	−0.1643	−0.1369
13	−10.3173	−10.0300	−3.1726	−0.3000
15	−90.0958	−90.0980	−0.1065	−0.1089
17	0.0126	−0.0012	0	0

.

Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14 and Table 15 concern amplitude, frequency, and phase estimation results using 4MSCW of type-1 and type-2-based DSLIFFT algorithm and proposed PLIS-based DSLIFFT algorithm. In view of the simulated results, the PLIS-based DSLIFFT with4MSCW of type-2 has better accuracy than the 4MSCW of type-1. Moreover, it is evident that the accuracy of the 4MSCW of type-2 with proposed PLIS-based DSLIFFT algorithm with respect to the percentage relative errors of the fundamental amplitude, phase, and frequency are in the order of 10⁻³, 10⁻⁹, and 10⁻² and it exhibits better results than the 4MSCW of type-2 with conventional DSLIFFT algorithm with different harmonic amplitudes.

The percentage relative error variations of fundamental and harmonic amplitudes, frequencies and phases estimation to the harmonic orders with proposed PLIS-based DSLIFFT and conventional DSLIFFT using 4MSCW type-1 and type-2 at frequency values of 49.5 Hz and 50.5 Hz are depicted in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9. From the responses of Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, it is evident that the 4MSCW type-2 with proposed PLIS-based DSLIFFT algorithm exhibits more accurate estimation over the 4MSCW type-1 with the proposed algorithm as well as 4MSCW type-1 and type-2 with conventional DSLIFFT algorithm. Moreover, the fundamental amplitude, frequency, and phase estimation are more accurate in view of its lowest percentage relative error values under different fundamental frequencies.

The RT validation of the proposed PLIS-based DSLIFFT algorithm on estimating the real-world harmonic signals are presented in the next section.

4. RT Validation

The RT implementation of the proposed PLIS-based DSLIFFT using 4MSCW is discussed in this section. The detailed experimental setup and its drawing are depicted in Figure 10. Precise selection of sampling frequency and window size gives the accurate results in RT. For better accuracy and minimized errors, the sampling frequency is considered to be 3 kHz and the window size is 1024 as per the sampling theorem concepts. Moreover, the sampling frequency satisfies the Nyquist frequency requirement. Based on the sampling frequency and the window length the frequency resolution satisfies the measurement requirements as discussed in [6]. The RT process flowchart in RT estimation is shown in Figure 11.

The common real-world loads such as Compact Fluorescent Lamp (CFL), Triode for Alternating Current (TRIAC) controlled exhaust fan and Switched Mode Power Supply (SMPS) of the Personal Computer (PC) to serve different nonlinear loads are considered for estimation. NI-cRIO-based virtual instrumentation experimental setup is developed for harmonic and synchrophasor estimation. It is one of the potential RT estimation tools for the harmonic signal and synchrophasor as per the international standards [1,2,3]. The cRIO uses Field-Programmable Gate Array (FPGA) architecture for digital signal processing. The proposed PLIS-based DSLIFFT using 4MSCW has been deployed in the LabVIEW configured host computer and interfaced to the NI LabVIEW powered cRIO 9082 which is equipped with Intel Core-i7 dual core with a Central Processing Unit (CPU) frequency of 1.33GHz [29]. It consists of a reconfigurable embedded chassis with integrated intelligent real-time controller and data acquisition modules for signal acquisition. The real-world harmonic loads considered for RT harmonics and synchrophasor analysis are shown in

Table 16. Real-world nonlinear load data.

Type of Load	Ratings
Compact Fluorescent Lamp (CFL)	220–240 V, 50 Hz, 85 W
TRIAC controlled Exhaust Fan	220–240 V, 50 Hz, 20 W, 1750 rpm
SMPS of the PC	Input: 230 V AC, 50 Hz, Output: 12V DC, 0.3 A

.

The procedural steps to implement the PLIS-based DSLIFFT algorithm with 4MSCW in RT
Step 1	Sampling the real-world harmonic signal, here the harmonic signal is acquired from real-world nonlinear load using NI 9239 analog module [30].
Step 2	The acquired signal is processed through the FPGA I/Os of NI-cRIO 9082 system [29], then convert the sampled signal into a weighted signal using 4MSCW and compute the weighted signal FFT.
Step 3	The NI-cRIO 9082 system is interfaced to the host computer, where the proposed PLIS-based DSLIFFT algorithm using 4MSCW method is implemented in LabVIEW virtual instrumentation environment.
Step 4	Use the PLIS-based DSLIFFT algorithm using 4MSCW of type-2 to find out the fundamental as well as harmonic spectral amplitudes accurately.
Step 5	Display the results.

The nonlinear loads (CFL+SMPS of the PC) current waveform acquired by using NI-cRIO is depicted in Figure 12, where the switch 1 and switch 2 of the nonlinear loads are in ON position and switch 3 of the exhaust fan is in OFF position. The NI-cRIO is a Heterogeneous computing platform, where the signal acquisition is done by using FPGA configured input channels and computation is performed on the RT processor.

4.1. Case 1: RT Harmonic Estimation of CFL and SMPS of the PC

The amplitude, phase, and frequency of the fundamental and harmonics estimated by the proposed laboratory RT experimental test bench (NI-cRIO) and the Tektronix Power Quality Analyzer (PQA) model PA4000 [31] are tabulated in

Table 17. Case 1: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Amplitude (A) Measured Using PQA (Tek-PA4000)	Amplitude (A) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	0.4977	0.4974	0.0698
3	0.2839	0.2821	0.6266
5	0.2154	0.2117	1.7319
7	0.1625	0.1570	3.3688
9	0.1333	0.1330	0.2404
11	0.1091	0.1091	0.0242
13	0.1076	0.1038	3.5233
15	0.1037	0.1018	1.8444
17	0.0880	0.0874	0.6956

,

Table 18. Case 1: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Frequency (Hz) Measured Using PQA (Tek-PA4000)	Frequency (Hz) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	49.95	49.95000000	1.5123 × 10−09
3	149.85	149.85000000	2.3758 × 10−10
5	249.75	249.75000000	8.1686 × 10−11
7	349.65	349.65000000	−8.0636 × 10−11
9	449.55	449.55000000	−6.2287 × 10−11
11	549.45	549.45000000	5.7149 × 10−11
13	649.35	649.35000000	−8.0238 × 10−11
15	749.25	749.25000000	6.0587 × 10−11
17	849.15	849.15000000	1.0753 × 10−10

and

Table 19. Case 1: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Phase (deg) Measured Using PQA (Tek-PA4000)	Phase (deg) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	17.983	17.9564	0.14780
3	−120.99	−119.9192	0.88502
5	110.49	110.3468	0.12959
7	−18.289	−18.4017	−0.61626
9	−140.37	−140.4560	−0.06124
11	98.337	98.4469	−0.11174
13	−13.938	−13.8060	0.94690
15	−139.16	−139.0005	0.11463
17	97.427	97.4327	−0.00589

. The Tektronix PA4000 is one of the standard instrument used for the voltage or current harmonic estimation. The PQA results and the 4MSCW type-2-based proposed PLIS-based DSLIFFT configured RT estimation system results are relatively identical and the proposed system exhibits better accuracy under the nonlinear loaded condition as per the requirement of international standards [1,2,3].

4.2. Case 2: RT Harmonic Estimation of TRIAC Controlled Exhaust Fan Load

The current drawn by the exhaust fan only when the CFL and SMPS of the PC loads are in OFF condition is shown in Figure 13. The RT system and the PQA estimation results of amplitude, frequency, and phase for exhaust fan case also depicted in

Table 20. Case 2: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Amplitude (A) Measured Using PQA (Tek-PA4000)	Amplitude (A) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	0.291	0.2907	0.0698
3	0.071	0.0709	0.0632
5	0.019	0.0186	1.7318

,

Table 21. Case 2: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Frequency (Hz) Measured Using PQA (Tek-PA4000)	Frequency (Hz) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	49.95	49.9500000	1.2913 × 10−09
3	149.85	149.8500000	−6.3863 × 10−10
5	249.75	249.7500000	−1.3610 × 10−09

and

Table 22. Case 2: Comparison of proposed PLIS-based DSLIFFT with type-2 4MSCW and Tektronix PQA.

Harmonic Order (h)	Phase (deg) Measured Using PQA (Tek-PA4000)	Phase (deg) Measured Using Proposed Algorithm with NI-cRIO	The Relative Error (%)
1	0	0.0001	0
3	158.90	158.88	0.0072
5	0	0.0008	0

. These results also exhibit the identical accuracy of the proposed algorithm in RT estimation of fundamental and harmonic components.

It is clear that the proposed PLIS-based DSLIFFT with 4MSCW of type-2 has improved characteristics when compared to the conventional DSLWIFFT for nonlinear load current harmonic estimation. The proposed PLIS-based DSLIFFT with 4MSCW of type-2 has improved accuracy and better online response in compliance with PQA measured data as per IEC 61000-4-30 [2], which recommends the measurement of current harmonics. Therefore, this paper addresses the issues of current harmonic estimation simultaneously with synchrophasors. The above loads are the most common nonlinear loads using in the residential, commercial, and industrial applications. There is a real need to compute these harmonics effectively for mitigation purpose. Moreover, the fundamental quantities estimation such as fundamental amplitude, phase, and frequency is used for synchrophasor applications. It is confirmed by both the simulation and RT results that proposed PLIS-based DSLIFFT with type-2 4MSCW has better accuracy. Furthermore, the accuracy of the fundamental quantities estimation under harmonic distortion condition is high, which is a benefit for the synchrophasor estimation in distorted conditions.

5. Conclusions

This paper proposed a PLIS-based DSLIFFT with 4MSCW for estimation of power system voltages or current harmonics and synchrophasor metrics with advanced efficiency and fast computation. It has better accuracy and precision under non-synchronous sampling, low amplitude, and fractional harmonic frequency when compared to previous solutions. Simulation and experimental results corroborate the effectiveness, using the techniques described in this paper for harmonic and synchrophasor estimation simultaneously under variable frequency conditions. Improved performance indices were examined with experimental results by considering real-world harmonic signals. The simulation and experimental results satisfy requirements of international standards such as IEC 61000-4-7, 4-30, and IEEE 1159-2009. Therefore, our proposed PLIS-based DSLIFFT with 4MSCW can estimate voltage or current harmonics, as well as compute voltage space-vector synchrophasor, even under distorted conditions and variable grid frequencies in real-time, ready to retrofit any power system or smart-grid installation.