Characterising Non-Intentional Supraharmonic Emissions from Inverters in Power Grids: Review and Challenges

Abstract

Supraharmonic emissions, referred to as voltage/current waveform distortions in the 2–150 kHz range, have been identified as an emerging power quality concern. With the increased number of non-linear devices connected to the power grid, such as photovoltaic inverter systems, supraharmonic disturbances are expected to increase. Despite being a source of supraharmonic emissions, power electronic equipment has become a ubiquitous technology due to recent advancements. Similarly, researchers around the world have started studying these emissions; however, complete systematic knowledge concerning supraharmonic emissions is yet to be achieved. This paper uniquely delves into characterising emissions using existing knowledge, significantly improving the understanding of their complex micro-level interactions and highlighting emerging challenges. The paper presents a comprehensive summary integrating existing studies on supraharmonic emissions in five key areas: emissions, propagation and attenuation, measurement techniques, modelling and simulation, and mitigation.

1. Introduction

Conventional power quality (PQ) studies have concentrated on voltage and current waveform distortions in the frequency range of 0–2 kHz; however, special attention has been paid to conducted emissions above 2 kHz over the past decade [1]. Waveform distortions in the 2–150 kHz frequency range are referred to as ‘supraharmonic emissions’ or ‘high-frequency harmonic emissions’; these emissions are categorised as intentional or non-intentional emissions [2]. Intentional emissions originate from any device or system designed to operate within the supraharmonic frequency range, where they are a planned and necessary part of its functionality (e.g., power line communication; PLC) that involves superimposing a high-frequency voltage signal onto a fundamental frequency voltage for communication purposes. Non-intentional emissions are generated as an unintended consequence of the operation, and mainly originate from power electronic (PE) devices due to their non-linear voltage–current characteristics [3]. Although PE interfaces are identified as a source of superharmonic, they have become a ubiquitous technology in almost every industry due to their high efficiency and flexibility. PE interfaces play a critical role in the energy industry, converting, controlling and conditioning electrical energy in an efficient way [4].

Distributed energy resources (DERs) are being connected to the grid in increasing numbers, and this trend is predicted to continue over the coming years, supporting the net-zero energy transition [5]. Regardless of the DER connection voltage level, every solar photovoltaic (PV) and wind renewable energy integration system equipped with a PE interface between the renewable energy source (RES) and the electricity supply network that is capable of introducing supraharmonic emissions in low-, medium- and high-voltage networks [6,7,8]. Figure 1 depicts the total renewable energy capacities and additions of different RES technologies in 2023. Among all technologies developed to achieve renewable energy targets, solar PV and wind are the most promising energy integration systems. In 2023 alone, solar PV and wind power capacity additions have increased by 34% and 13%, respectively. This is equivalent to 524 GW out of 536 GW of the total renewable energy additions in the year 2023. Other renewable power corresponds to geothermal power and heat, bioenergy and solar thermal heating.

Based on the signal type, in either time or frequency domains, supraharmonic emissions fall under three categories, namely, narrowband, broadband and recurrent oscillations [9,10]. Despite recurrent oscillations in the time domain, whether the emission is narrowband or broadband is determined based on the concentration of spectral components in the frequency domain. This frequency spectrum relies on parameters such as the signal measurement window, signal analysis window, and grouping method of frequency components, i.e., a 200 Hz grouping method might show a broadband signal while the 2 kHz grouping method shows a narrowband signal for a particular time domain signal. Electromagnetic compatibility (EMC) filters amplify the recurrent oscillations, and the same signal can be identified as either narrowband or broadband in the frequency domain [9]. The classification of supraharmonic emissions is depicted in Figure 2 with each signal type identified as follows:

• Narrowband signals: identified as individual frequencies in the frequency domain, mainly due to PLC.
• Broadband signals: identified as a spectrum of adjacent frequency components in the frequency domain, mainly due to individual end-user equipment with active power-factor correction (APFC).
• Recurrent oscillations: typically identified in every 10 ms in the time domain, mainly due to PE converters around the current zero-crossing.

Several PQ issues have been reported due to supraharmonic emissions, including audible noise, cable termination failures, tripping of residual current devices, flicker, and the disruption of PLCs [11,12]. A key difficulty in managing supraharmonic emissions is the lack of normative measurement methods to enable characterisation and enable further analysis [13]. As such, a rigorous and standardised measurement technique is required for evaluating EMC levels at frequencies above 2 kHz. Figure 3 depicts a summary of existing regulations that define the measurement/summation techniques to be used for waveform distortion across various frequency ranges.

Recently, researchers have devoted significant effort to developing systematic knowledge on supraharmonic emissions from equipment connected to electricity supply networks. Understanding the harmonic behaviour of multiple gird-tied inverters against the background voltage is studied in [16,17]. Appliances and equipment that have been evaluated include solar PV inverters [18,19,20,21], wind farms [22], LED lamps [23] and electric vehicle (EV) chargers [24]. Current waveforms of four supraharmonic sources—PV inverter (2.5 kW), EV, LED and televisions—were analysed in [25] to identify high-frequency emissions. The study emphasises that time-frequency (hybrid) analysis is important for fully understanding supraharmonic emissions in addition to time domain and frequency domain analysis. Supraharmonic reduction by spreading the spectrum of the emission in a randomised manner is discussed in [26]. Similarly, the authors of [27] investigated supraharmonic emissions from rolling mill converters and proposed a mitigation strategy under a random carrier frequency PWM method.

Through a comprehensive examination of diverse methodologies presented by researchers around the world, readers are able to identify existing power quality challenges in power grids. Existing review papers have made valuable contributions for understanding this supraharmonic emission phenomenon, including those on supraharmonic emission sources [28,29,30,31], measurement methods and standards [28,29,30,32,33,34], effects [29,30,33], mitigation techniques [29,31,33], and modelling and simulation [30]. Significant attention is paid to intentional and non-intentional sources, measurement and potential mitigation. However, only limited attention is paid to analysis and characterisation. Developing a comprehensive overview of the field of supraharmonic emissions related to inverters is limited, with existing papers covering all areas. This review offers a timely and critical synthesis of the literature on supraharmonic emissions from inverters, specifically highlighting the emerging challenges and opportunities in five key areas: emissions, propagation and attenuation, measurement techniques, modelling and simulation, and mitigation. While previous systematic reviews have focused on providing general overviews, this review uniquely delves into characterising these emissions using advanced methods, such as phase angle representation, and improving understanding of the complex interactions that occur at the micro-level.

The authors’ other research identifying and characterising different types of supraharmonic phenomena associated with solar PV inverters is presented, addressing some of the challenges identified in this study. Section 2 provides an overview of supraharmonic emissions associated with PE interfaces of RESs. Supraharmonic propagation and attenuation characteristics are discussed in Section 3. Section 4 covers the three existing measurement techniques defined by standardisation bodies, identifying alternative measurement techniques in the literature. Section 5 provides an overview of supraharmonic modelling and simulation approaches used in supraharmonic analysis. Mitigation techniques are provided in Section 6. Section 7 provides a summary of supraharmonic emissions associated with PE converters.

2. Emissions

The sources of high-frequency emissions are not restricted to RESs. Any device with a PE interface, such as street lamps, emits non-intentional emissions with different devices exhibiting different frequency spectra. A list of supraharmonic sources and general high-frequency ranges is provided in [6] as follows:

• Industrial size converters (9–150 kHz)
• Street lamps (up to 20 kHz)
• EV chargers (15–100 kHz)
• PV inverters (4–20 kHz)
• Household devices (2–150 kHz)
• PLC (9–95 kHz)

2.1. Switching Frequency Emissions

Switching frequency emissions are a predominant type of supraharmonic emission phenomenon, generated by the high-frequency switching of PE devices. These emissions are intrinsic to the operation of devices like voltage source converters (VSCs) and pulse-width modulated (PWM) converters.

The voltage/current waveforms at the output of a PE converter consist of supraharmonic emissions, the primary emission of which has been studied extensively [25,35,36]. The frequency spectrum of the voltage produced by PV inverters is dependent on several factors, including the frequency modulation index, the PWM switching technique (unipolar or bipolar), the use of multi-level PWM, three-phase or single-phase design, the amplitude modulation index, phase shifting, and dead zones [36,37]. Thus, the output voltage of a PV inverter is generally not periodic and does not follow a simple Fourier series. However, the harmonic spectrum of these waveforms follows the first type of Bessel function and can be written as (1) [38,39].

$$\begin{array}{cc}\hfill V_{inv}\left(t\right)& ={\displaystyle \frac{M{V}_{dc}}{2}}sin\left(\omega t\right)\hfill \\ \hfill & +{\displaystyle \frac{2V_{dc}}{\pi }}\left[\sum _{m=1,3,..}^{+\infty }\sum _{n=0,\pm 2,\pm 4,..}^{\pm \infty }{\displaystyle \frac{4J_n(mM\pi /2)}{3m}}sin\left({\displaystyle \frac{m\pi }{2}}\right)si{n}^2\left({\displaystyle \frac{n\pi }{3}}\right)cos(m{\omega }_{sw}t+n\omega t)\right]\hfill \\ \hfill & +{\displaystyle \frac{2V_{dc}}{\pi }}\left[\sum _{m=2,4,..}^{+\infty }\sum _{\pm 1,\pm 3,..}^{\pm \infty }{\displaystyle \frac{4J_n(mM\pi /2)}{3m}}cos\left({\displaystyle \frac{m\pi }{2}}\right)si{n}^2\left({\displaystyle \frac{n\pi }{3}}\right)sin(m{\omega }_{sw}t+n\omega t)\right],\hfill \end{array}$$

(1)

where M is the modulation index (amplitude ratio between the modulation wave and the carrier wave), $V_{inv}$ is the inverter output terminal voltage, $V_{dc}$ is the DC link voltage, ${\omega }_{sw}$ is the switching frequency, and $J_n$ is the first type of Bessel function. M is crucial for employing PWM techniques, which are used to mitigate EMI by distributing the emission energy over a wider frequency range and thus lowering the peak emission levels at specific frequencies [40].

The existing work in the literature on supraharmonic emission caused by high-frequency switching is summarised in

Table 1. Existing work on characterising PWM-based spectral components.

Ref.	Analysis	Contributions	Limitations
[35]	High-frequency harmonics amplification and resonance in modular multilevel converters connected to long cables.	Established mathematical model for converter-long cable-load system. Discussed high-frequency amplification and resonance frequency calculation that aligns with field test results.	Resonant frequency solved using SciPy tools.
[36]	Factors influencing supraharmonic emissions including sampling methods, carrier phase shifting, dead zones and PWM control strategies.	Provides variation of supraharmonic emissions associated with VSR against various factors through mathematical modelling and simulation analysis.	Only analyses single-phase half-bridge voltage source rectifier (VSR) converter, where generalisation of results to other types of converters is not addressed.
[41]	Characterisation of switching frequency emissions with variations in magnitude and frequency. Resonance due to interactions between devices.	Examined supraharmonic emission from various household devices. Studied interactions between multiple devices and the grid.	The quantification of supraharmonic emission through measurements should consider multiple analysis types, i.e., time domain, frequency domain, time-frequency.
[42]	Switching frequency emissions from grid-connected inverters (GCIs) around the switching frequency and its multiples.	Supraharmonic emissions of single-phase GCIs are strongly dependent on the DC-link voltage and the coupling inductor. Mathematical analyses of GCI parameters on emissions are verified using an actual setup and simulation study.	Generalisation of MATLAB/Simulink (Version R2021b) model due to potential discrepancies or modelling assumptions.
[43]	Supraharmonic emissions from grid-connected photovoltaic systems.	Examines emissions from a three-phase grid-connected PV system. Assesses combined supraharmonic effects on grid connection distortion.	Supraharmonic characteristics depend on the converter type rather than environmental conditions, requiring a more rigorous treatment of the performance of PV systems.
[44]	Supraharmonic distortion impacts power loss and heating, which result in the ageing of dielectric materials and medium voltage (MV) cable failures.	Analysis of supraharmonic distortion effects on power networks and derivation of limits for supraharmonics compared to harmonics.	Accurate measurement of supraharmonic emissions in MV networks is yet to be achieved.

.

2.2. Challenges

Some of the challenges identified in the reviewed literature in relation to understanding supraharmonic emissions are as follows:

• Understanding other types of emission phenomena associated with PE converters in addition to switching frequency emissions.
• Generalisation of supraharmonic characteristics for similar types of devices, different types of devices, and interactions between neighbouring PE converters.
• Is it acceptable/sufficiently accurate to focus only on primary emissions (disregarding secondary emissions) for high-frequency emissions studies? If so, is it valid for the full range (2–150 kHz) or any specific frequency range depending on the emission characteristics?
• Development of systematic knowledge on diversity between the emission spectra from individual devices, diversity in the time of use of equipment, and cancellation of emission in the complex plane.

3. Propagation and Attenuation

Several studies have been performed to understand supraharmonic propagation in low-voltage (LV) networks. A generalised expression for the voltage at a particular frequency is provided in [30], which can be used for propagation studies of supraharmonic emissions. The voltage at frequency f at a bus r is expressed in (2), where $Z_{rs}\left(f\right)$ is the transfer impedance from bus s to bus r and $I_s\left(f\right)$ is the current flowing to bus s. All parameters in this expression are complex numbers and rapidly changing with time. The transfer impedance between neighbouring devices is influenced by the number of devices and variable load conditions.

$$U_r\left(f\right)=\sum _{s=1}^N{Z}_{rs}\left(f\right)·I_s\left(f\right).$$

(2)

This expression does not address non-linear phenomena, and there is no definitive knowledge on how these will impact propagation in the superharmonic range.

3.1. Primary and Secondary Emission

To understand supraharmonic emissions and their propagation characteristics within and from installation, two driving forces are identified, termed “primary emission” and “secondary emission” [34]. Primary emission is the part of the supraharmonic emission at the device terminals driven by the sources within the device (driven by current), whereas secondary emission is the part of the supraharmonic emission driven by the sources outside of the device (driven by voltage). The authors of [30] have provided a simplified network model used to represent these emissions as depicted in Figure 4, where:

• I represents the total supraharmonic emission.
• $I_N$ and $Z_N$ represent the Norton equivalent of internal emission and impedance, respectively.
• $E_g$ and $Z_g$ represent the Thevenin equivalent of background voltage and grid impedance, respectively.

Expressions for primary and secondary emissions are derived and represented in (3) and (4). The differentiation of these two forces from field measurements where both primary emissions and secondary emissions are present is not a simple task [6]. The combination of both primary and secondary emissions is yet to be completely distinguished.

$$I_1={\displaystyle \frac{Z_N}{Z_N+Z_g}}·I_N,$$

(3)

$$I_2={\displaystyle \frac{1}{Z_N+Z_g}}·E_g.$$

(4)

3.2. Propagation Between Devices Within Installation

The propagation between devices within an installation is directly influenced by the impedance seen by the supraharmonic source and the devices within the installation. The work presented in [45] concludes that when the number of devices with supraharmonic emissions increases within an installation, the total supraharmonic emissions flowing into the electricity network decrease. In general, supraharmonic emissions tend to flow within devices rather than propagate to the grid, and the number of supraharmonic emitting devices connected within the installation changes emission characteristics [46,47].

The study presented in [48] concludes that line impedance is a significant influence factor on supraharmonic propagation in industrial networks where most of the supraharmonic currents tend to flow within the installation. Particularly, propagation of supraharmonic emissions by wind power plant is presented in [8]. However, the work presented in [49,50] shows that RES can be identified as dominating supraharmonic sources in MV and LV networks as their emissions propagate over a distance of several kilometres in electrical networks.

A simple model to investigate the supraharmonic emissions of an installation with N number of devices is provided in [10]. The total emission is inversely proportional to the square root of the number of devices. It is suggested that the emissions partially cancel each other out due to the phase angle diversity of individual supraharmonics. However, some studies indicate that this is due to the low impedance path within the installation introduced by EMC filters. The authors of [49] propose a method to determine the partial contributions of supraharmonic emissions to the common supraharmonic distortion at a node; however, the study does not consider the non-linear transfer characteristics of the instrumentation transformer used to measure supraharmonic emissions in the MV network.

3.3. Propagation in an LV Network

The authors of [51] have examined the propagation of supraharmonic emissions in an LV network using a cascade of two-port network representation, which is shown in Figure 5. The main advantage of the two-port model is that the derivation of ABCD parameters can be obtained with a limited number of measurements.

• $V_s$ and $I_s$ represent sending end voltage and current, respectively.
• $V_r$ and $I_r$ represent receiving end voltage and current, respectively.
• Z and Y represent impedance and admittance, respectively.

$$\left[\begin{array}{c}{V}_s\\ I_s\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{V}_r\\ I_r\end{array}\right]$$

(5)

where,

A	= $1+YZ/2$
B	= Z
C	= $Y(1+YZ/4)$
D	= $1+YZ/2$

The existing work in the literature that aims to understand supraharmonic propagation is summarised in

Table 2. Existing work on supraharmonic propagation.

Ref.	Analysis	Contributions	Limitations
[51]	Dependence of propagation on the impedance of the grid and connected devices.	Presents a method for analysing supraharmonic propagation using a stochastic approach, which allows for a better understanding of the impact of LV loads in both strong and weak grid conditions.	Further investigation of the relationship between grid impedance and supraharmonic propagation is needed.
[8,52]	Propagation from wind power plants and photovoltaic systems.	Highlights the negative consequences of increased supraharmonics in power systems, including malfunction and failure of control circuits and protection devices, as well as insulation failures in cables and overheating of critical components like capacitor banks and transformers.	The impact of the multiple inverter system has not been provided. Generalisation of results due to variations in inverter technology and settings.
[46]	Propagation in low-voltage networks and interactions with nearby devices.	Propagation of supraharmonics towards the grid can vary, which is influenced by the number and type of connected devices and their impedance relative to the grid.	Does not address the long-term effects of supraharmonic emissions on the performance and reliability of various household devices
[53]	Propagation and attenuation by examining how supraharmonic currents behave in a low-voltage grid.	The study analyses the interaction between devices, specifically observing phenomena such as “frequency beating” and intermodulation, which can lead to the tripping of residual current devices, to better understand their impact on the grid.	Limited exploration of the broader implications of “frequency beating” and intermodulation interactions on the stability and reliability of the low-voltage grid.
[54,55]	Supraharmonic propagation in transformers.	Supraharmonic distortions can propagate through transformers, indicating that some components of the distortions propagate more easily, likely due to resonances. Distributed capacitances and leakage inductance affect the transfer characteristics.	Further investigation is required in this area to understand how transformers behave with increasing supraharmonics content from sources.

.

3.4. Challenges

Some of the challenges identified in relation to understanding supraharmonic propagation and attenuation are as follows:

• How can the difference between primary and secondary emissions be distinguished in high-frequency emission studies?
• What is the explanation for two different harmonic spectra observed in the current measurement at the terminal of an individual device and the summated current? Is it due to emission characteristics or a low impedance path created by the front-end filters of devices? Is this identified throughout the complete high-frequency range (2–150 kHz)?
• The accuracy of the two-port network model needs to be assessed in a more simplified way by measuring supraharmonic emissions at both ends of a radial cable.
• Accurate measurement of supraharmonic emissions in MV/HV networks to quantify the propagation where direct measurement options are unavailable.

4. Measurement/ Summation Techniques

The three methods stipulated in international regulations, i.e., IEC 61000-4-7 [56], IEC 61000-4-30 [57] and CISPR 16-1-1 [58], are based on frequency domain analysis. As per the Nyquist criterion, the maximum frequency of the frequency-domain ($f_{max}$) shall be half of the sampling frequency ($f_s$) used to measure the time-domain waveform [59]. The time-domain signal and the frequency spectrum after the discrete Fourier transformation (DFT) are illustrated in Figure 6. Despite the involvement of DFT in all three methods, there are a few differences in their measurement and analysis intervals [60]. The measurement interval is the time period across which the DFT is applied. The analysis interval is the minimum time window in which a measurement result must be produced in accordance with the international regulation.

Table 3. Comparison of measurement and analysis intervals defined in the three methods.

Method	Measurement Interval (${\mathit{t}}_{\mathit{m}}$) (ms)	Freq. Spectrum Resolution ($1/{\mathit{t}}_{\mathit{m}}$) (Hz)	Analysis Interval
IEC 61000-4-7	200	5	=$t_m$ (no gaps/overlap)
IEC 61000-4-30	0.5	2000	<$t_m$ (with gaps)
CISPR 16-1-1	20	50	>$t_m$ (with overlap)

provides a comparison of measurement and analysis intervals for the three measurement methods. A graphical representation of Table 3 is depicted in Figure 7.

4.1. IEC 61000-4-7

IEC 61000-4-7 is a standard that provides guidelines for measuring harmonic and interharmonic distortion in AC power systems. The standard differentiates between harmonics and interharmonics and considers measurements of components up to 9 kHz (above harmonic frequencies) using DFT.

Annex B (informative) of IEC 61000-4-7 defines the employment of a frequency analysis technique with a frequency resolution of 5 Hz and a 200 Hz band aggregation using 200 ms of signal to measure harmonic emissions up to 9 kHz. The method involves grouping spectral components according to the root sum squared (RSS) method with possible aggregations in time. It is well-established, widely used in power quality analyses, and provides detailed frequency and magnitude information for supraharmonic components.

One of the advantages of the IEC 61000-4-7 measurement methodology is that it is gapless and has a very good reproducibility. However, power system disturbances vary over time, and continuous measurement of the entire frequency range is essential for accurate assessment. Due to the fixed longer measurement interval (200 ms), this methodology may be less suitable for determining the characteristics of supraharmonic signals, which vary rapidly in frequency or magnitude. The method is also susceptible to spectral leakage and windowing effects, which impact the accuracy of measurements.

4.2. IEC 61000-4-30

IEC 61000-4-30 provides guidelines for the measurement of power quality parameters in AC power supply systems. The measurement methodology defined in IEC 61000-4-30 is specifically focused on the measurement of voltage, current, and power quality parameters, including harmonics and interharmonics, in the frequency range up to 9 kHz and supraharmonics in the frequency range from 9 kHz to 150 kHz. Annex B (informative) specifies the use of DFT with 0.5 ms intervals, 2 kHz frequency resolution, and aggregation into average and maximum values of the 32 measurement intervals present in every 10/12 cycles for measuring supraharmonics emissions. This method is designed to provide detailed frequency and magnitude information for supraharmonic components in the specified frequency range.

One of the key advantages of the IEC 61000-4-30 methodology is the focus on the measurement of supraharmonics in the higher frequency range, which is increasingly relevant due to the proliferation of modern electronic equipment that is a source of emissions in this frequency band. The method provides a standardised approach for assessing supraharmonic distortion in power systems.

However, the IEC 61000-4-30 methodology may have limitations in accurately estimating supraharmonic components with low magnitudes and in the presence of noise. The measurement interval is 8% of the total analysis interval, causing it to disregard the majority of the measured data. The methodology may also exhibit reduced robustness to noise and limitations in performance when compared to alternative measurement methodologies, particularly in the presence of time-varying signals.

4.3. CISPR 16

CISPR 16 is a standard used for the assessment of emissions from equipment under test (EUT) in laboratory conditions, particularly for EMC testing. The measurement methodology involves the use of a spectrum analyser with a tuneable filter and detector (peak and quasi-peak) to measure emissions in the frequency range 9 kHz to 30 MHz. As specified in the standard, a digital quasi-peak detector is used to create an RC circuit analogue behaviour and a critically damped meter.

Measurement and analysis intervals for a Gaussian window ($\alpha$ = 5.8) are used to ensure a −6 dB bandwidth of 200 Hz in [60]. Figure 7d depicts the same Gaussian window in which measurement interval is set as 20 ms with a 90% overlap. The schematic of the CISPR 16 measurement methodology is depicted in Figure 8.

Key aspects of the CISPR 16 method include:

1.

Laboratory setting: the methodology is primarily intended for use in a controlled laboratory environment for assessing emissions from individual EUT.

2.

Spectrum analyser: the methodology involves the use of a spectrum analyser equipped with a tuneable filter and detector to scan the frequency range sequentially over long measurement times.

3.

Peak and quasi-peak detection: the methodology utilises peak and quasi-peak detectors to assess emissions and their impact on radio transmission interference.

4.

Line impedance stabilisation network (LISN): the method may involve the use of an LISN to stabilise the line impedance in EMC testing that helps to ensure accurate and repeatable measurements of emissions from electronic devices [61,62].

Limitations and considerations associated with the CISPR 16 methodology, when considering application for electricity supply network measurements, include:

1.

Computational burden: implementing a digital instrument with the capability to measure the entire frequency range simultaneously may result in a high computational burden, particularly for evaluating the signal amplitude in each frequency band [13].

2.

Reproducibility: the tolerances of the methodology and the potential for different compliant implementations may raise concerns about the reproducibility of results, particularly for electricity supply network measurements [63].

3.

Relevance to power supply quality: while the methodology is useful for assessing emissions and their impact on radio transmission, questions have arisen regarding its relevance to assessing the quality of power supply in the electricity supply grid environments [64].

4.4. Alternative Methods

All three measurement methods mentioned in international regulations are considered non-parametric methods which involve DFT. However, attention has been drawn to parametric methods despite the higher computational burden requirement compared to non-parametric methods [65]. Alternative measurement methodologies have been developed and compared using synthetic signals or recorded power system waveforms in [60,66]. The authors of [67] proposed a method based on DFT analysis using a flat-top window, where the sliding measurement window is synchronised with the short-term fundamental period to reduce spectral leakage in measuring supraharmonic emissions.

Table 4. Existing work on alternative measurement methodologies.

Ref.	Measurement Method	Principle Operation	Advantages	Limitations
[65,68]	Matrix pencil method	Parametric estimation using singular value decomposition on data matrix.	Improved robustness to time-varying signals, high time resolution, effective noise reduction.	Primarily for lab emissions, lack of comprehensive knowledge on performance limits, complex and expensive.
[69]	Compressive sensing method	Reconstruction of sparse signals from fewer samples.	Reduced sampling rate, high frequency resolution, availability of various algorithms.	Relies on sparsity, computationally intensive, sensitive to noise.
[70,71,72]	Wavelet approach	Wavelet Packet Decomposition (WPD) for time-frequency analysis.	Robust against power frequency deviations, suitable for stationary and non-stationary signals	Coefficients affected by time deviation, choice of wavelet influences results.
[73,74]	Subsampling approach	Analogue filter banks to decompose harmonic spectrum with subsampling of sub-bands.	Reduced sampling rate requirements, reduced computational burden	Affected by analogue filter characteristics, requires frequency correction, analogue-to-digital converters may not be optimised for subsampling.
[13,61,75]	Quasi-peak (QP)-based methods	RM-A: Adaption of the IEC 61000-4-7 method for CISPR band A with a 20 ms measurement window. Light-QP: Alternative to the CISPR method, which uses the RM-A method to produce RMS values every 20 ms. Statistical QP: Statistical relationship between the RMS and QP values for CISPR Band A	Efficient QP estimation, lower computational burden than CISPR 16	Primarily focused on QP values.

summarises the existing work in the literature that develops alternative measurement techniques. Each method offers a unique approach with its own set of advantages and disadvantages concerning frequency and time resolution, noise immunity, computational complexity, and suitability for different applications. However, ongoing research and development efforts are focused on creating more standardised and precise digital approaches to address the growing need for reliable quasi-peak measurements in the supraharmonic frequency range.

4.5. Challenges

Some of the challenges identified in the reviewed literature in relation to supraharmonic measurement are as follows:

• Supraharmonic measurement requires high time resolution capability to capture high-frequency waveform distortion, which cannot be achieved with conventional measuring equipment. Therefore, a normative measurement technique is required for the design of measuring equipment, which in turn is the key to the recording and analysis of high-frequency emissions.
• Existing measurement techniques presented in standards provide indicative magnitude values, i.e., minimum, maximum, quasi-peak, RSS, for a group of supraharmonic emissions. Is there any possibility of defining a phase angle representation for a harmonic emissions band, allowing the identification of supraharmonic summation characteristics?
• Lack of reproducibility with IEC 61000-4-30/CISPR measurement techniques.
• No convention to differentiate narrowband and broadband signals in the frequency domain. A broadband signal in the IEC 61000-4-7 method (200 Hz resolution) may be identified as a narrowband signal in the IEC 61000-4-30 method (2 kHz resolution).

5. Modelling and Simulation

The control structure of a VSC is not a new topic and has been studied extensively [76,77,78,79,80]. Several studies have been undertaken with the aim of improving the control strategies related to PV inverter modelling.

The existing work in the literature on modelling approaches and simulation techniques is summarised in

Table 5. Existing work on modelling and simulation techniques.

Ref.	Analysis	Contributions	Limitations
[81]	Modelling of Switching frequency emissions from single-phase power electronic converters (PECs).	A numerical case study of a fixed switching frequency converter is presented, demonstrating the application of different modelling approaches, i.e, time domain, frequency domain and hybrid models.	Lack of comprehensive validation procedures for the proposed models, suggesting that further research is required to establish robust methods for validating their accuracy and effectiveness.
[82]	Modelling of single-phase EV charger in Simulink environment	Assess cumulative emissions from single-phase EV chargers, extending the aggregation and diversity factors to the supra-harmonic range.	Further research is required to explore the effects of varying power levels among multiple EV chargers.
[83]	Modelling of multiple grid-connected VSC systems in MATLAB/Simulink environment.	Proposed model uses voltage sources connected in parallel with LCL filters to characterise switching frequency emissions at individual VSCs and the total supraharmonic current emission flowing into the grid.	Does not address potential mitigation strategies for reducing supraharmonic emissions in grid-connected systems.
[84]	Proposed a frequency-domain-based multiparameter model of PE devices.	Provides a methodology for defining accurate frequency-domain simulation models of PE devices through frequency-dependent multiparameter scanning, which allows for the assessment of harmonic contributions under various operating conditions and network impedances.	The accuracy of the simplified equivalent frequency-domain models compared to the EMT simulations in the time domain.
[85,86,87,88,89,90,91,92]	Improving solar PV inverter models	Adding a virtual admittance to the system via modification of the current control loop. Improvement of PV controller with a simplified dq controller, proposing not to obtain orthogonal current components. Application of virtual inertia by adjusting phase locked loop (PLL) parameters.	Accuracy of harmonic models for high-frequency harmonic analysis.

.

Challenges

Some of the challenges identified within the reviewed literature in relation to modelling and simulation are as follows:

• A complete understanding of emission characteristics is missing due to the lack of accurate harmonic models. Comprehensive models are only available from the inverter manufacturer. Thus, a generic simulation model is necessary for understanding supraharmonic characteristics.
• Models have been developed for harmonic analysis in the low-frequency range. However, the validity of these models in the high-frequency range is yet to be verified.
• For a multiple inverter system, it is assumed that each inverter operates at the same operating state. Thus, the linear summation is valid for low-frequency harmonic emissions. Do high-frequency emissions follow the same principle irrespective of the emission phenomena?

6. Mitigation

Due to the interferences caused by supraharmonic emissions, recent attention has focused on the provision of mitigation techniques. A number of studies have begun to develop mitigating techniques without compromising the operation of the equipment. Oversizing of the filter will increase the cost unnecessarily, and undersized filters will be ineffective. Ref. [4] provides three different methods of mitigation: (a) reduction of emissions (equipment or installation), (b) improvement of network performance or reduction of the transfer level in the network, (c) improvement of immunity (equipment or installation).

The most practical way of mitigating supraharmonic emissions is by placing harmonic filters between the equipment and the grid. The filters should be designed considering the spectral impedances, secondary emissions and the resonances [10]. The author of [93] provides the three major methodologies for limitation of harmonics, where suitability depends on the current and voltage involved, the nature of the load and the system parameters such as the short circuit level at the point of connection.

The existing work in the literature on supraharmonic mitigation techniques is summarised in

Table 6. Existing work on supraharmonic mitigation techniques.

Ref.	Analysis	Contributions	Limitations
[94]	Passive filters	Impact of passive filters installed close to the source of harmonic emitter to trap the harmonic currents at the source and reduce propagation to the grid.	Introducing the resonance phenomenon, interacting capacitors of the passive filters with network inductances.
[95]	Active filtering techniques	Injection of harmonic currents into the system that are equivalent to the harmonic currents caused by harmonic emitters, but of opposite polarity to restore the sinusoidal waveform. Different control methods deployed in active filters, i.e, fuzzy logic, neural network and model predictive.	Costly compared to conventional passive filters.
[25,26]	Random PWM generation	Supraharmonic reduction by spreading the spectrum of the emission in a randomised manner. Uses random-pulse position modulation, which is similar to conventional PWM control with constant switching frequency; however, the pulse is randomly positioned during the switching period. A pseudo-random carrier that randomly combines two triangular carriers (both of the same frequency and opposite in phase) is proposed to produce randomness. The randomly selected “low” or “high” carrier is used to generate pseudo-random frequency carrier waveforms to generate PWM.	Further research is required for a better understanding of the interactive coupling mechanism of supraharmonics among converters.
[96,97,98,99]	Multi-level converters	Reduction of supraharmonic emissions from PE converters with the proper technology. Multi-carrier based PWM uses several triangular carrier signals to reduce output voltage harmonic content. Phase Shifted PWM is the most commonly used technique in Flying Capacitor & Cascaded H Bridge converters, which enables a reduction in switching frequency components and improved THD. Level-shifted PWM is widely used in neutral point clamped converters, which leads to less distorted line voltages but high harmonic content in input current.	Traditional assessments have been made for line-commutated converters, while self-commutated converters can generate significantly higher frequencies. Relevant technology to be deployed with the understanding of the correct usage of the converter.

.

Challenges

Some of the challenges identified within the reviewed literature in relation to harmonic mitigation are as follows:

• There are many PWM modulation techniques that have been developed to reduce switching frequency emissions in PE converters. However, a quantitative analysis of these reductions is yet to be performed.
• Lack of simulation models of PE converters makes it difficult to:

  1.

  Quantify the reduction of switching frequency emissions against PWM modulation technique.

  2.

  Introduce effective PWM modulation techniques to suppress switching frequency emissions.

7. Conclusions

This paper provides a comprehensive literature review on supraharmonic emissions from PE converters, highlighting the challenges in developing systematic knowledge. Five key areas—emissions, propagation and attenuation, measuring techniques, modelling and simulation, and mitigation—were considered to summarise the existing knowledge. There are three measurement methods available in the standards; however, no normative method has been accepted for field measurements. Further, conventional measuring instruments are only capable of measuring low-order harmonics, with high-frequency measurements requiring a significant additional computational burden depending on the measurement technique adopted. Thus, it is evident that a measurement standardisation framework for the supraharmonic frequency range is a pivotal requirement for assessing these emissions. This enables further research on standardisation work on imposing compliance limits for emissions in the supraharmonic range. With the advancements of PE interfaces, higher switching frequencies have been achieved, which has resulted in shifting resonance frequencies above 2 kHz. More research is needed in this direction to develop systematic knowledge on these two phenomena, preferably with high-frequency modelling techniques.

Substantial challenges remain in accurately measuring, comprehensively understanding, and effectively mitigating these high-frequency disturbances. The non-stationary nature of supraharmonics, the lack of standardised measurement techniques and emission limits, and the complexities of their propagation in modern electrical networks all contribute to the difficulties in understanding supraharmonic emissions. Further research work is required to develop existing systematic knowledge.

The development of accurate harmonic models of PE converters is challenging due to modelling complexities. According to the literature, the lack of accurate models makes it challenging to understand PE harmonic emission characteristics and provide mitigation techniques ensuring the reliable and sustainable integration of solar PV systems into the power grid.

A summary of the authors’ research work is presented in

Table 7. The authors’ other research work on characterising supraharmonic emissions from PV inverters.

Ref.	Analysis	Contributions
[100]	Understanding the harmonic behaviour of a grid-tied rooftop solar PV system based on measurements.	There are three harmonic current emission bands present within the frequency spectrum up to 20 kHz: 1. Low-frequency band in the 0–2 kHz range; 2. Broadband high-frequency band in the 2–5 kHz range due to the resonance introduced by the front-end filter of the inverter; 3. Narrowband high-frequency band near 16 kHz due to the switching frequency of the inverters considered. It has been identified that the inverter current comprises two components, called the circulation current component and the grid current component. General mathematical expressions for harmonic currents were derived for a system consisting of multiple inverters connected in parallel.
[101]	Proposes three methods to represent the phase angle for grouped supraharmonic emissions that assist in understanding their diversity.	Out of existing high-frequency harmonic measurement techniques, the IEC 61000-4-7 method, which provides phase angle information, is used to investigate the applicability of the summation law for high-frequency harmonic emissions. Results show that resonance emissions align in phase, allowing for simple addition. In contrast, switching frequency emissions are spread across the phase diagram, indicating phase diversity and cancellation.
[102]	Characterisation of harmonic resonance phenomenon of multi-parallel PV inverter systems	Presents the solar PV inverter modelling aspects considering the resonance impact, where a mathematical approach is presented to understand the resonant frequency variation within a system as the number of inverters changes. The characteristics were verified with the MATLAB/Simulink inverter model for both LCL and LC filter types.
[103]	Reduction of supraharmonic emissions in solar PV inverters via coordinated carrier waveform-based PWM technique	Developed a generic solar PV inverter model to characterise supraharmonic emissions corresponding to the switching frequency of PWM signals. The PV inverters were modelled using the most common voltage-oriented control under a synchronous reference frame in the MATLAB/Simulink software environment. The impact of carrier waveform phase shift has been evaluated as a technique for mitigating these switching-related emissions when multiple similar inverters are installed together, as in solar farms or larger commercial installations.

, assisting in characterising supraharmonic emissions while addressing some of the challenges identified in former sections. The time domain measurements were analysed using the measurement methodology specified in IEC 61000-4-7, which was extended for emissions above 9 kHz to maintain consistency. The contributions include identifying different types of phenomena associated with solar PV inverters, understanding/characterising emission phenomena from an identical inverter system, proposing phase angle representation methods to understand the phase angle diversity of supraharmonic emissions, and proposing switching frequency emission mitigation techniques that introduce new directions for future research.