1 Introduction

With the rapid development of the electric power grid, many new and costly pieces of equipment are installed in the power system network. To achieve a reliable and uninterrupted power supply, the equipment must be healthy. However, the equipment is constantly exposed to lightning impulse voltages. Lightning is a natural phenomenon. The protective devices (exp- lightning arresters) are connected to power equipment to bypass lightning impulses. However, the protective devices may not work correctly against the lightning strokes due to their intermittent properties [1, 2]. So, the power equipment installed in the power system network should have the proper insulation strength to withstand the lightning impulse voltage.

According to IS-2071-1 [3] and IEC 60,060-1 [4], standard lightning impulse (SLI) voltage is a unidirectional voltage with no appreciable oscillation. It increases quickly to the peak value and decreases much slowly to zero. The standard waveshape of lightning impulse was first mentioned by IEC in 1962 [5]. The standard waveshape can be defined as (1.2 × 50) μs wave. It signifies that the time to reach the peak value of the waveshape is 1.2 μs, whereas the time to reach half of the peak value is 50 μs. In Fig. 1, the waveshape of (1.2 × 50) μs has been depicted. In Fig. 1, “t1” indicates the time to attain the peak value from the origin, whereas “t2” denotes the time to reach half of the peak value from the origin, respectively. It is pertinent to mention here that the permissible deviation in a SLI wave is less than ± 3% of the peak value, ± 30% of the front time, and ± 20% of the tail time. A lightning impulse voltage waveform (LIVW) is called a full lightning impulse voltage waveshape when no puncture or flashover occurs. The front time of lightning impulses must be limited up to 20 μs [3, 4]. Lightning impulse could be from a range of kHz to MHz. So, there is a rapid increment in stress within a short time duration, affecting the insulation system of power equipment. Therefore, power equipment are tested by keeping in mind that they have to withstand standard lightning impulse (SLI), and similarly, their insulation has been designed. However, in real life, the non-standard lightning impulse waveforms (NSLIW) are present in natural lightning impulse [6,7,8,9,10,11,12,13]. So, for a longer life span, reliable operation, and uninterrupted power supply, the insulation system of power equipment must be designed, considering NSLIW. Hence, the identification and characteristics of the non-standard lightning impulses voltage waveforms (NSLIVW) must be appropriately known.

Fig. 1
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The waveshape of lightning impulse voltage waveform [3]

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This review article presents a comprehensive study on the generation, classification, and the effects of non-standard lightning impulses over the electrical insulation throughout the past century. The paper is structured as follows: Categorization of NSLIW is described in section-2, while section-2 is subcategorized into two parts. In the first part (A), classification based on the length of the impulse waveform is shown, and the second part (B) illustrates the variation based on the nature of the impulse waveform. Variable parameters of NSLI depending on the nature of the impulse waveform are presented in section-3. Section-4 consists of the practical generation circuit of NSLI. It is subdivided into two sections. The generation circuit of (A, B, C-1, and D) waveforms is discussed in the first subsection, and the generation circuit of the rest two waveforms (C-2 and E) are described in the second subsection. The state-of-the-art study on the NSLIVW is analyzed in section-5. In section-6, the effect of NSLIVW on the insulation of HV equipment is discussed, and afterward, conclusions and references will end the article.

2 Categorization of non-standard lightning impulse waveforms

Lightning impulse waveform differs from these expected values [3, 4], then it is considered NSLIW. Previous research [6,7,8,9,10,11,12,13] shows that the waveshape of natural lightning impulse waves differs quite a bit from the SLIW [(1.2 × 50) μs]. Depending upon a variable tail time (length of wave tail time) and the nature of waveforms, NSLIW may be classified mainly into two sections.

2.1 Classification based on the tail time

An impulse waveform is called a “short-tail lightning impulse” if the tail time of the waveform is less than the standard value (50 μs), whereas the impulse waveform is known as “long-tail lightning impulse” when the tail time of the waveform is greater than the standard value (50 μs). Over the last few decades, researchers have been interested in short- and long-tail lightning impulses. In Table 1, the synopsis of the previous research based on impulse waveform variable tail time has been presented. The effect of variable tail time on different insulation systems (air, oil, cable, etc.) has also been mentioned in Table 1.

Table 1 Details study on short- and long-tail lightning impulse
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2.2 Classification based on the nature of lightning impulse waveform

According to several types of research, the nature of lightning impulse waveform in transmission lines and cable systems may differ from standard lightning impulse (SLI). The nature or waveshape of the lightning impulse waveform depends on the design and layout of the substation, the arrangement of equipment, and various states of switches [7, 11, 39,40,41,42]. Depending on the experimental investigation, Okabe et al. in [39,40,41,42] described five types of NSLIW as follows:

  1. i.

    “A-waveform” or “single-pulse waveform”: As the name suggests, the wave consists of a single pulse. The waveshape of the A-waveform is totally different from rest of the non-standard impulse waveforms. It neither has any steeper wavefront nor is oscillatory in nature. In Fig. 2, waveshape of A-waveform has been presented. [11, 39, 41, 42].

  2. ii.

    “B-waveform” or “Pulse-in wavefront waveform”: This type of waveform may be described with an abrupt growth in the wavefront region and a flat wave tail region. In Fig. 3, the waveshape of the B-waveform has been shown. The B-waveform occurrence depends upon the length between the surge arrester and the gas-insulated switchgear (GIS) terminal [7, 11, 42].

  3. iii.

    C-waveform: This type of waveform is defined as the “damped-oscillation waveform (single-frequency oscillation waveform).” There are many resonance points present in a substation because of various series and parallel equipment. C-waveform is generated when the oscillations between the substation’s incoming bushing and the GIS end become commanding. The “C-waveform” is also known as “C1-waveform.” If restriking happens within the substation, a higher-frequency surge with a damped-oscillation waveform is created. It is also recognized as “C2-waveform.” In C2-waveform, two different high frequencies can be observed [11, 39, 40]. “C1-waveform” and “C2-waveform” are shown in Figs. 4 and 5, respectively.

  4. iv.

    “D-waveform” or “Rising-oscillation waveform”: In this type of waveform, the magnitude of second peak is greater than the first peak and the magnitude reduces thereafter [11, 39, 41]. This type of waveform is generated because of the superposition of delayed surges, which appears due to frequent reflections between flashover points and bushings. In Fig. 6, a graphical representation of “D-waveform” has been illustrated.

  5. v.

    “E-waveform” or “double-frequency oscillation waveform”: This damped oscillating impulse waveform is generated due to superposition of two crucial frequencies. The reciprocating impulses on GIS primary bus and shorter branches are of comparatively low frequencies and high frequencies, respectively. The superposition of these two different frequency impulse waveforms generates the “double-frequency oscillation waveform” or “E-waveform.” E-waveform is shown in Fig. 7 [39].

Fig. 2
figure 2

The waveshape of single-pulse or A-waveform [39]

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Fig. 3
figure 3

The waveshape of pulse-in or B-waveform [42]

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Fig. 4
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C-1 waveform [39]

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Fig. 5
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C-2 waveform [39]

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Fig. 6
figure 6

The waveform of rising-oscillation or D-waveform [39]

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Fig. 7
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Waveshape of double frequency oscillation or E waveform [39]

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The characteristics of the non-standard lightning impulse waveforms would be appropriately identified by knowing the parameters of the NSLIWs. These parameters, i.e., rise-time, tail time, damping time constants, frequency ranges, and peak voltage magnitudes of first few peaks, are essential for identifying the characteristics of the NSLIWs. The details about those parameters are described in the next section.

3 Parameters of non-standard lightning impulse voltage waveform

In this section, the variable parameters of both standard and non-standard lightning impulse waveforms depending on voltage and time are illustrated in Table 2. These varying parameters of NSLIW were obtained by Okabe et al. [39] after the analysis of their experimental work. In Table 2, the rise-time for the first peak of the non-standard impulse waveform is specified as the “Tfront.” The wave tail time is denoted as “Ttail.” The damping time constant is represented as “τd.” Frequency is marked as “f.” A negative polarity voltage was implemented as the negative polarity voltage is observed to be much more stressful in the matter of insulation concerning the lightning surge period [39]. E1 and E2 are the voltages recognized as the first and second peaks of the impulse wave, respectively. For B-waveform, E2 is the voltage of the steady-state section of the impulse waveform, and the voltage magnitude of the third peak of the C-1 impulse waveform is noted as E3.

Table 2 Variables of test waveshapes [39]
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From this table it was observed that the impulse frequency was always in MHz range irrespective of the type of impulse waveform. The rise-time of the NSLIWs (A, B, C-1, and D) varied in the span of (0.2–1.2) μs, and for oscillating NSLIWs (C-2 and E), rise-time varied from (0.1886–1.176) μs. From the (E1/E2) ratio of the D-waveform, it was noticed that the voltage magnitude of the second peak is greater than the first peak, as it was stated in previous section. The generation of NSLIWs is necessary to know the effects of NSLIW on the electrical insulation and different test objectives. For that purpose, the generation circuit of NSLIW is essential. The generating circuits of NSLIW are discussed in the next section.

4 Generation of non-standard lightning impulse waveshape

The standard lightning impulses are practically generated with the help of an impulse voltage generator. The modifications are needed to the impulse voltage generator to generate non-standard lightning impulse voltage. In this section, the generation circuit is explained. The generation circuit for single-frequency NSLIW and double-frequency NSLIW are discussed in two subsections.

4.1 Generation of A, B, C-1, and D waveform:

The generation circuit of NSLIW (A, B, C-1, and D) is described here. Okabe et al. explained the NSLIWs generating circuit (A, B, C-1, and D) in [7, 42]. There the impulse voltage was generated with the help of an impulse voltage generator. The fundamental block diagram of the circuit elements used for the generation of NSLIWs is displayed in Fig. 8. The series–parallel combination of resistance (R), inductance (L), and capacitances (C) was connected through a sphere-gap. Then NSLIWs were generated by adequately controlling the series–parallel combination of RLC parameters. After the generation of NSLIW (A, B, C-1, and D), those were fed to the test objective. Here charging capacitance is denoted as CS and the inductance of the connecting wires is represented as L.

Fig. 8
figure 8

Schematic diagram of A, B, C-1, and D waveform generation [42]

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The fundamental of the working circuit has been described as follows: Across a series connected air gap the impulse voltage was generated. The LC oscillation was produced between the charging capacitance (CS) and test objective through inductance L. As a result, single-frequency oscillation impulse waveform (C-1) was produced. For the generation of the rising-oscillation (D) waveform, a lower value of resistance R2 was added to the C-1 waveshape generation circuit (as shown in Fig. 8). The circuit's time constant would be changed, and the oscillation will be increased. Hence, the voltage magnitude of the second peak will be more with respect to the first peak of the impulse voltage and D-waveform was generated.

It is essential to present (R3 + R4) to damp the oscillation of the C-1 waveform (in Fig. 8) for the generation of the B waveform. So, the oscillation ended within in one cycle only and steady-state took place in wave tail region. To generate an A waveform, the damping in the impulse wave tail region must be increased. It was done by decreasing the value of Rd. As a consequence, single-pulse waveform (A waveform) was produced. The charging capacitance (CS) primarily regulates the rise-time of NSLIW on the power supply end. The EMTP software is used to identify the specified circuit constants needed to generate the above four types of NSLIWs. To establish the reliability of the generated waveforms, these parameters of the generation circuit must be designed indeed.

4.2 Generation of C-2 and E waveform:

This section discussed the primary generation circuit for C-2 and E non-standard lightning waveforms. Okabe et al. had explained the generating circuit of NSLIWs (C-2 and E) [7,8,9, 39, 42,43,44,45,46,47,48,49,50,51,52,53,54]. Like in the previous section, test circuits were first created in EMTP. Evaluation, investigation, and generation of different voltage levels, gap between test electrode, settings of impulse generator, and circuit elements were done through EMTP. After that, the experimental setup was prepared. As explained in the previous section, the C-2 waveshape is developed fundamentally similar to the C-1 waveshape. The fundamental block diagram of the test circuit is illustrated in Fig. 9.

Fig. 9
figure 9

Schematic diagram of C-2 and E waveform generation [43]

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The experimental setup circuit was verified with a 300 kV single-phase supply. As the C-2 waveshape's frequency range is higher, one inductor was inserted after the series gap in the circuit. One high-valued resistor was added before the series gap to control the damping of the oscillating waves. For the generation of E-waveform, an inductance was put after the series gap to generate a high-frequency oscillation, and another inductance was placed before the series gap. A capacitance following the series gap to develop low-frequency oscillation. Hence, by the superposition of two high frequency oscillation, double-frequency oscillation waveform (E- waveform) was produced.

5 State-of-the-art study on non-standard lightning impulse voltage waveshape

Various researches have tried to illuminate different areas of non-standard lightning impulse waveform (NSLIW). In this paper, an attempt has been made to study and analyze the research outcomes (breakdown, limitations, etc.) of NSLIW.

A. R. Jones in 1954 [55] experimented with (1.5 × 40) µs LIW over standard insulation to check the precession of the integration method. It was discovered that the rod-gaps were much more superior to traditional solid insulation in terms of impulse flashover. Estimation of constants from the mathematical expressions was one of the biggest drawbacks of the integration method. In 1985, Shindo and Suzuki proposed an advanced model to recognize the predischarge current and computation of breakdown v-t characteristic [56]. The model was verified by using four types of LIs [(1.5 × 50) µs, (1.5 × 40) µs, (2.5 × 53) µs, and (2.4 × 9.6) µs] over rod–plane gap (0.25–5 m), rod–rod gaps (0.3–1.5 m) successfully. Li et al. in [57] experimented with two NSLIW [(0. 2 × 60) μs, (1. 25 × 60) μs] over the coaxial cylindrical gap and rod-sphere gaps in different dielectrics (exp- SF6 & air mix, N2, etc.). From the experiment, it was observed that 50% BDV of rod-sphere gap and coaxial cylindrical gap in the mixture of dry air, SF6 and N2 is inversely proportional to the sharpness of the wavefront region.

In 1988, M. Darveniza and A. E. Vlastos suggested to utilize the integration method to estimate the impulse strength of the NSLIW [58]. It was noted that by using this integration method, significant results were obtained irrespective of the class, type, and configurations of insulation. The results showed that the precision limits varied [(± 5) to (± 15)]%, depending on the gaseous insulation configurations. The same authors prescribed a theoretical concept with a generalized integration method to predict impulse v-t characteristics for NSLIW [59]. In 1989, Pigini et al. experimented the impulse breakdown for several gap distances (rod–rod gap, rod–plane gap) with a few NSLIWs [(1.6 × 50) µs, (1.6 × 18) µs, (0.7 × 25) µs, (0.5 × 50) µs, and (0.6 × 1750) µs] and suggested a new computation method for the calculation of v-t characteristics [60].

Task Force 15.09, led by P. Chowdhuri, compiled a bibliography on the NSLI voltages and reviewed the state of research in 1994 [61]. A comparative study has been done on the behavior of air gaps under transient voltages, generation, and measurements of fast-front impulse voltage waves. In the same year, Chowdhuri et al. experimented the critical BDV levels of different air gaps (rod–rod gap, rod–plane gap and sphere–sphere gap) with various NSLIWS [(0.025 × 0.5) µs, (0.025 × 25) µs, (0.12 × 25) µs, (0.12 × 50) µs, (1.2 × 25) µs, (1.2 × 50) µs, (10 × 50) µs, and (10 × 100) µs] [62]. From the experiment it was observed that the long- and short-time delays for breakdown occurred for fast-front and slow-front impulse waveforms, respectively. Chowdhuri et al. in 1997 performed breakdown tests of rod–rod gap with various NSLI [(1 × 4) µs and {(1.2 ⁓ 1.4) × (3.2 ⁓ 3.7)} µs]. One new model was proposed for the calculation of breakdown time. It was revealed that the breakdown voltage characteristics and the process of breakdown can be replicated by the proposed model [63].

Venkatesan et al. in 2002 had investigated the consecutive strategy for analyzing the impulse toughness of air under NSLI voltage. From the investigation it was observed that the effect on the non-uniform field distribution is sensitive to DE parameters, and an utterly consecutive strategy was established experimentally [6]. X. Q. Zhang experimentally analyzed the characteristics of corona under NSLI in the year 2006 [64]. In [64], a straightforward model was proposed to construct the q-u graph plots for different NSLIW (double exponential and damped oscillatory impulses) through a realistic approach.

In 2007, Ancajima et al. experimented on the reproduction of two medium voltage (MV) insulator’s v-t characteristics by applying an SLI (1.2 × 50) μs and a STLI (1.2 × 4) μs [65]. From experimental investigation, it was observed that the longest breakdown time of two MV insulators was 0.3 μs. In [66], Aniserowicz and Zielenkiewicz criticized the non-standard lightning protection devices. From the provided data and theory, it was revealed that the lightning preventers and early streamer emitters were overpriced as well as not so effective as the traditional lightning protection systems. In 2008, K. Bhuyan and S. Chatterjee studied the voltage and current response of power equipment under SLI (1.2 × 50) μs and NSLI (oscillatory waves) [67]. Yuvarajan et al. in [68] measured the breakdown strength of paper composite insulating material under AC, SLI, and NSLI voltage. It was noticed that the dielectric characteristic was compared at room and cryogenic temperature to show the supremacy of the solid insulating materials at liquid nitrogen. In the year 2008, Kadir et al. furnished a few previous research works on the NSLIW and utilized the PSCAD / EMTDC software to reveal the procedure of breakdown. It was observed that the instantaneous voltages were firmly relying on the span of leader and ailing relied on the crest voltage [69].

In 2010, Ancajima et al. presented the results obtained from the experiment performed with STLI [(1.2 × 4) μs] and SLIW [(1.2 × 50) μs] on two types of fiberglass core polytetrafluoroethylene (PTFE) covered insulators and focused on the v-t characteristics [30]. From the experimental results it was confirmed that the v-t characteristics of insulators may be accurately reproduced by Chowdhuri model [63]. In 2010, S. Venkatesan and S. Usa inspected the functioning of NSLI voltage over a short air gap using their newly suggested hyperbolical model [70]. C. P. Braz and A. Piantini in [71] revealed that the critical lightning impulse flashover voltage was always greater for negative polarity with respect to positive polarity after investigating the dielectric response of the distribution insulators for NSLIVs in 2011. In 2012 Braz et al. researched on the forecasting methods by observing the breakdown characteristics of 15 kV porcelain pin type insulators for different types of impulses [(1.2 × 4) µs, (1.2 × 10) µs, and [(1.2 × 50) µs] [72]. From the investigated results it was noticed that the DE Model may be used to forecast the behavior of MV insulators under standard and non-standard impulse voltages.

In the year 2013 Lopes et al. experimented on pin and post type insulators with various types of LIVWs [(0.5 × 5) μs, (0.5 × 10) μs, (0.5 × 20) μs, (0.5 × 50) μs, (1.2 × 5) μs, (1.2 × 10) μs, (1.2 × 20) μs, (1.2 × 50) μs, (3 × 10) μs, (2.9 × 16.1) μs, (4.5 × 16.1) μs, (5 × 20) μs, (5 × 50) μs, and (10 × 50) μs] [73]. From the experiment it was observed that the positive polarity up-down test was good enough to identify the smallest critical flashover voltage. In all trial states for checked insulators, it was noticed that the lightning withstand voltage rises for impulses with fast-front time. In [74], I. A. Metwally has identified that the phase angle sensitivity of Rogowski coil rises with the rise in the coil ending resistance, followed by deformation of the impulse waveform.

K. Bhuyan and S. Chatterjee in 2015 investigated the response of SLI and NSLIVWs on surge arresters [75]. From the results, it was found that NSLIs can develop higher voltage stress and cause a significant threat to the surge arresters. In 2015, G. Krithika and S. Usa have experimented with air insulation by utilizing the suggested advanced DE model [76]. A few types of LIVs [(1.2 × 50) μs, (1.2 × 44) μs, (1.2 × 55) μs, (0.8 × 50) μs, steep fronted overvoltage (0.58 × 50) μs and very fast transient overvoltage (VFTO) (0.09 × 50) μs] have been applied during the experiment. From the experimental results it was observed that the suggested DE model precisely forecasted the v-t characteristics of different insulation for various impulse overvoltages. In 2016, M. Shigihara and A. Piantini analyzed the critical flashover overvoltage [77]. The v-t characteristics curve of a standard 24 kV porcelain pin-type insulator was obtained for five LIVWs (1.2 × 4 μs, 1.2 × 10 μs, 1.2 × 50 μs, 3 × 10 μs, and 7.5 × 30 μs), of both polarities. Bhattacharyya et al., in 2016, through their investigation on the electric stress on an MV cable termination, showed that the highest electric stress due to different applied impulse voltage waveforms was detected at the earthed screen and the implanted diverter interface. It was found that the electric stress was higher for standard and non-standard chopped impulse waveforms. For all the impulse voltage waveforms, expanding the deflector angle could make the more uniform potential distribution at the interface [78]. In the year 2016, Huang and Zhang constructed an experimental system for the computation and comparison of the corona charge–voltage (q-u) curves under NSLIW (damped oscillation and double exponential impulses) [79]. Lopes et al. in [80] examined the critical flashover voltages and v-t characteristics curve for a few different LIVWs [(0.5 × 5) μs, (0.5 × 20) μs, (1.2 × 10) μs, (1.2 × 50) μs, (3 × 16) μs, (5 × 50) μs]. It was found that the negative polarity impulse is riskier for cut-out fuses (15–25) kV.

In 2018, Shigihara et al. modified a Marx impulse generator by varying the circuit parameters to generate the four selected NSLIWs [(1.2 × 4) μs, (1.2 × 10) μs, (3 × 10) μs, and (7.5 × 30) μs] and the SLI (1.2 × 50) μs [81]. The crucial dissimilarities were observed after comparing the four NSLIs with respect to SLI. In 2019, Jana et al. analyzed the numerical computation of non-standard lightning impulse energy storage system using impulse generator [1]. It was found that a single-stage two-level spark generator circuit with multi-level inverter integrated with supercapacitor was designed to simulate real-time non-standard lightning energy storing system. Mahmood et al. in 2019 utilized a risk-based insulation coordination technique to analyze the application of various lightning protection schemes of medium-voltage overhead lines [82]. Faria et al. in 2020 attempted to compare the withstand tests of MV switches and cut-out fuses with six LIVWs of both polarities [(0.5 × 5) µs, (0.5 × 20) µs, (1.2 × 10) µs, (1.2 × 50) µs, (3 × 16) µs, and (5 × 50) µs] [10]. From the results it was obtained that the negative polarity impulses are more harmful with respect to positive polarity. In [83], Liang et al. proposed a new non-intrusive technique to evaluate transient electric field distribution. It was observed that in time domain, the measured and calculated electric fields are absolutely same for impulse voltages. In 2021, H. M. Wickert and T. B. Marchesan suggested a new multiresolution wavelet analysis-based technique to simulate NSLIW for impulse tests in laboratories [84]. Various changes (magnitude, rise-time, and cut-off instant) were suggested on standard lightning impulse test to generate NSLIW. In 2022 Jana et al. proposed an impulse island controller to extricate and control the high voltage non-standard lightning impulse for storing in a supercapacitor [2].

The literature on the effect of non-standard lightning over the insulation of high voltage equipment is discussed in the next section.

6 The effect of non-standard lightning surge voltage waveform over the insulation of high voltage equipment

According to literature survey, it was found that several researches have been performed on the effect of non-standard lightning impulse (NSLI) on the insulation of HV equipment. A brief overview of the research outcome has been presented below.

In 1973, Caldwell and Darveniza experimentally and analytically attempted to forecast the behavior of insulation when stressed by NSLIWs [85]. From the results it was observed that for positive polarity, the deviation between the experimental and analytical data was lesser with respect to negative polarity. T. Suzuki and K. Miyake in 1977 identified that the streamers and leaders have the major influences on the time of breakdown [86]. The experiments were performed with two NSLIVWs [(3 × 12) µs and (2.5 × 53) µs] over rod–plane gaps [(1–5 m) and (2 m & 3 m)] and rod–rod gaps [(2–5 m)]. In 1998, Koto et al. compared nine NSLIWs [{Waveform-A: A1: (0.20 × 0.26) µs; A2: (0.28 × 0.29) µs; A3: (0.60 × 1.15) µs}, {Waveform-B: B1: [(0.26 × 0.71) µs; E2/E1: 0.82]; B2: [(0.76 × 1.34) µs; E2 / E1: 0.73]; B3: [(0.98 × 5.00) µs; E2/E1: 0.88]} and {Waveform-C: C1: [(0.20 × 0.28) µs; E2/E1: 0.80; E3/E1: 0.66], C2: [(0.32 × 0.28) µs; E2/E1: 0.90; E3/E1: 0.82]; C3: [(0.52 × 0.57) µs; E2/E1: 0.82; E3/E1: 0.68]}] with SLIW (1.2 × 50 µs). From the research it was found that the flashover voltage of shorter wavefront was higher with respect to the minimum flashover voltage of SLIW [40].

Okabe et al. in [87] inspected about the dielectric characteristics (oil gaps and insulation between turns and models of insulation between sections) of oil-filled transformers under NSLIVs. It was observed that the BDV under oscillatory impulse voltages was higher in comparison with the SLIVs in the frequency span of (400 kHz–1 MHz). In [41], the authors have analyzed the insulation properties in SF6 gas with SLI [(1.2 × 50) µs] and a few NSLIWs [{Waveform-A: A1: (0.60 × 1.15) µs; A2: (0.85 × 1.65) µs; A3: (0.28 × 0.29) µs; A4: (0.20 × 0.26) µs}, {Waveform-B: B1: [(0.76 × 1.34) µs; E2/E1: 0.73]; B2: [(0.84 × 2.56) µs; E2/E1: 0.81]; B3: [(0.98 × 5.00) µs; E2/E1: 0.88]; B4: [(0.26 × 0.71) µs; E2/E1: 0.82]} and {Waveform-C: C1: [(0.32 × 0.28) µs; E3/E1: 0.90; (1.7 MHz)]; C2: [(0.52 × 0.57) µs; E3/E1: 0.82; (0.9 MHz)]; C3: [(1.2 × 1.40) µs; E3/E1: 0.75; (0.4 MHz)]; C4: [(0.20 × 0.28) µs; E3/E1: 0.82; (2.3 MHz)]}]. From the results it was found that the insulation does not face serious issues while encountering the shorter fronted impulse waveform. In [88], the authors have showed that mean BDV of turn-to-turn model is 1.5 times higher for NSLIVW with respect to SLIVW. Then the authors inspected on the generation of single-frequency and double-frequency oscillatory waveforms and the attributes of insulation under NSLIWs [49]. From the test results it was recognized that insulation properties (Vmin) were (15–24) % and (6–13) % higher for single-frequency oscillatory and double-frequency oscillatory waveforms, respectively, with respect to SLIW.

Usa et al. had shown to have sustainable success for unidirectional oscillating voltages while measuring the insulation strength for NSLWs using the modified DE method in 2002 [89]. In [90], Rokunohe et al. have inspected the properties of SF6 gas breakdown by changing the polarity of five pulse-type (A-waveform) NSLIWs [A1: (0.20 × 0.26) µs; A2-1: [(0.28 × 0.29)] µs; A2-2: [(0.27 × 0.28)] µs; A2-3: [(0.23 × 0.22)] µs; A3: (0.6 × 2.0) µs]. It was observed that the minimum breakdown voltage (BDV) (Vmin) is 10% more for NSLIWs with respect to SLI (LVmin). S. Okabe and S. Yuasa had investigated the evaluation method for NSLIW (A–D) of (oil gap, insulation between turns, and insulation between sections) oil-filled transformer in the year 2003. It was found that NSLIWs may be converted to SLIW, and crest value was reduced [91]. In [42], the authors have developed an experimental circuit to generate NSLIWs (A-D) and achieved almost similar waveforms as obtained by using EMTP. It was noticed that the breakdown voltage for gas insulated switchgear in NSLIW was (15–25) % higher than SLIW. In the same year, same group of authors inspected about properties of SF6 gas breakdown by applying eight NSLIWs [waveform-A: (For Gas Gap): A1: (0.20 × 0.26) µs, A2: [(0.28–0.28) × (0.22–0.29)] µs, A3: (0.32 × 0.58) µs, A4: (0.60 × 1.15) µs, A5: (0.85 × 1.65) µs; (For Spacer): A6: (0.30 × 0.34) µs, A7: (0.60 × 1.50) µs, A8: (0.91 × 1.84) µs]. It was observed that the experimental Vmin for SF6 gas under NSLIWs is more than LVmin of SLI [92].

In 2004, Sathish et al. experimented with [(1.2 × 50) µs, (1.6 × 80) µs and (1.2 × 23) µs] impulses to estimate the v-t characteristics of various thicknesses OIP insulation [93]. It was found that the regression analysis was utilized to establish the developed mathematical model. Okabe et al. in [94] investigated the dielectric characteristics of (oil gap, insulation between turns, and insulation between sections) oil-filled transformers in the presence of NSLIWs. From the results it was revealed that the B-type waveform’s breakdown occurs in sharp wavefront section rather than wave tail region. In the year 2004, S. Okabe and S. Yuasa investigated the evaluation method of NSLIWs for SF6 gas and spacer insulation and showed that NSLIWs are converted into equivalent SLIWs. It was observed that due to significant attenuation, NSLIW is less harmful for insulation [95].

S. Venkatesan and S. USA, in 2005, experimentally found v–t characteristics for various gap distances using SLIW [(1.2 × 50) µs] by using the DE model [96]. It was found that the percentage error between the actual time of breakdown and estimated time is less than 10%. In the year 2005, Ancajima et al. experimented on the breakdown features of MV insulators by using STLI [(1.2 × 4) µs] and SLI [(1.2 × 50) µs] [97]. From the experiments, it was observed that the model suggested by Chowdhuri et al. [63] was superior in forecasting for LIs irrespective of their polarity, and the 50% BDV of SLI was (7–27) % less than STLI because of the higher insulation pressure of STLI.

In 2006, Yokoi et al. investigated the insulation attributes of CO2 gas for single-frequency oscillatory waveforms with several frequencies from 5.3 to 20 MHz and damping ratios [50]. From the investigation it was revealed that in the case of τd = 0.15 μs to 5.1 μs, the NSLIW’s Vmin were (8–36) % more than SLI’s Vmin in CO2. Kaneko et al. in the same year inspected the process of assessment for actual LI based on insulation features for the CO2 gas gap [98]. In [51], the authors have explained the insulation features of CO2 gas for single-frequency oscillatory waveforms with different frequencies (1.3 to 4.0 MHz). From the investigation it was observed that no significant changes were found in the v-t characteristics curve while changing the damping of the oscillation.

S. Venkatesan and S. USA in [99] have examined the impulse strength of transformer insulation with NSLIWs. From the investigation it was recognized that the functioning of insulation under unidirectional NSLIWs has been estimated with the help of v–t characteristics and the DE method. S. Okabe in [100] showed that for NSLIW (A and B-waveform), mean BDV of oil-immersed transformers were greater with respect to mean BDV under the SLIW. The authors in [101] showed that for NSLIW (C and D-waveform), the mean BDV of oil-immersed transformers were lesser for SLIW with respect to damped-oscillation waveform and rising oscillation waveform, respectively. In [52], S. Kaneko and S. Okabe have examined insulation characteristics of N2 gas for a non-standard lightning impulse waveform having different frequencies (2.7 MHz–20.0 MHz) and damping ratios. From the experiment it was found that the with respect to numerous frequencies, the lowest Vmin recognized were (9–20)% more than Vmin of SLI in N2 [52].

In 2008, S. Okabe and J. Takami examined an evaluation method of the oil-immersed transformer (oil gaps, insulation between turns, and insulation between sections) for NSLIWs [11]. It was observed that NSLIWs were usually less dangerous for winding insulation with respect to SLIWs. In [53], Okabe et al. obtained the dielectric breakdown v-t characteristics of the SF6 gas gap for various conditions. It was recognized that the dielectric breakdown voltage was (6–36)% higher for NSLIW with respect to SLI. For C-2 waveform, Vmin increased with the decrease of damping time constant (τd) while the frequency is kept constant. For E-waveform, Vmin remained same irrespective of frequencies when damping time constant (τd) is kept constant.

In [102], an attempt has been made by Mitra et al. to recognize the voltage stress on transformer winding insulation under various types of terminal excitation. They have optimized the design of insulation of HV transformer and established that severe stress on insulation occurs if terminal excitation frequency matches with any of winding’s inherent frequencies. As a result, it may lead to damage of transformer and transformer winding insulation [102]. In [103], Okabe et al. analyzed the K-factor technique by applying the insulation properties under an overshoot waveform in NSLIW.

K. Bhuyan and S. Chatterjee in [12] have simulated standard and NSLIW on power transformer. It was observed that the major and minor level impact occur on power transformer insulation due to SLIW and NSLIW, respectively. The high voltage stress was developed in between the winding and ground of transformer by SLIW due to its long-tail time. The higher voltage stress was observed at the middle of the winding due to chopped impulses. In [54], Wada et al. experimentally investigated the insulation attributes of N2 gas for NSLIs [Double (E-waveform) and Single (C2-waveforms] frequency oscillation waveforms) and assembled information for better designing of insulation. It was noticed that for the quasi-uniform electric fields, very severe damage may be caused by negative polarity of both the waveforms.

In [104] Wang et al. showed that the insulation between turns model could tolerate the excess oscillating NSLIWs with respect to SLIWs by investigating the breakdown properties of sphere-plate system and between turns insulation model. By using the hyperbolic model, G. Krithika and S. USA mathematically modeled the v-t characteristics in the same year [105]. The investigation recognized that the effect of oscillatory waves was more with respect to their equivalent lightning impulses, and the breakdown strength of oil impregnated paper (OIP) was inversely proportional to the frequency of oscillation [105]. Sankarganesh et al. in [106] tried to construct a technique to investigate the observation of the breakdown characteristics of a transformer winding insulation under NSLIV. From the results it was revealed that the BDV of transformer winding insulation was higher with respect to standard lightning impulse voltages (SLIVs) under oscillatory impulse voltages (400 kHz–1 MHz). Sarathi et al. showed that BDV of liquid N2 is higher for the negative polarity of unidirectional oscillatory impulse voltage (UOIV) (25 kHz–65 kHz) and oscillatory impulse voltages (OIVs) [107].

K. Bhuyan and S. Chatterjee in [13] investigated the electric stresses on transformer winding insulation for SLI and NSLIVs (0.8 × 2.8) µs. It was found that NSLIVWs build up HV stresses, which produces the highest threat to equipment's insulation. The peak value, steepness, and front and tail of impulse wave had an essential role in finding out the insulation's functioning [13]. In [108], the v–n characteristic of OIP insulation under impulse voltage with different waveforms was experimentally achieved by Sun et al. From the experimental results, it was observed that the OIP insulation displays superior insulating performance to resist continuous NSLIVW. The BDV of OIP insulation is depended on the wavefront time of the applied impulse waveform.

In [109], Wang et al. suggested that the BDV of paper insulation increased with the reduction in front time. In [110], Wang et al. researched on the breakdown characteristics for oil-paper insulation under LIWs with oscillations. From the experimental results it was revealed that the rise in BDV is inversely proportional to wavefront time. Oil-paper insulation could resist higher low frequency-oscillating LIWs with respect to SLIW [110]. In [111], Hua et al. inspected the v–n characteristics of polypropylene (PP) film and oil-impregnated paper (OIP) with various waveforms [(0.24 × 50) μs, (0.4 × 50) μs, (0.72 × 50) μs, (1.2 × 50) μs, (3.3 × 50) μs, (6 × 50) μs, (1.2 × 25) μs, (1.2 × 100) μs, (1.2 × 198) μs, and (1.2 × 500) μs], respectively. From the experimental study, it was found that the impulse voltage surviving capability of OIP PP film is proportional and inversely proportional to the time of the wavefront and time to wave tail, respectively. In [112] Zhou et al. analyzed the regulation of rise-time and overshoot of impulse voltage waveform for transformer having large entrance capacitance through simulation as well as experiments. The rise-time of the impulse waveform has been varied in the range of (2.04–2.16 μs). From the result, it was observed that the surge protective device performed much better while connected to the twisted line rather than attached with parallel or ring line [112].

In [113], Z. A. Mubarak and S. Usa experimentally demonstrated that the dielectric breakdown strength of OIP decreases under different waveshapes [17% for SLI, 2% for VFTO] as the paper insulation thickness rises from 0.25 to 0.75 mm. In [114], Florkowski et al. have compared the response of transformer winding under different impulse voltages. From the research work it was observed that the transformer generally has few resonant frequencies. The maximum value of overvoltage inside the transformer winding will be reached if the frequency of the oscillating NSLIW matches with the resonant frequency of transformer.

7 Conclusion and future scope

This paper involves a detailed and comprehensive study regarding the non-standard lightning impulse waveforms published over the last century. From the literature survey, it can be observed that the classified parameters of NSLIW are somehow different from standard lightning impulse. From this study, identification of non-standard lightning impulse voltage and the effects of different non-standard lightning impulse voltage waveforms on the high voltage equipment can be recognized. Therefore, this study will be beneficial for the researchers to get relevant information about the NSLIW. Further, with this information, the design of the electrical insulation may be modified to withstand the NSLIW. Moreover, the life expectancy of power equipment will be enhanced.

As a future scope, an experimental circuit for generating non-standard lightning impulse waveforms will be verified in laboratory. The generated non-standard lightning impulse waveforms will be applied to different types of insulation (like OIP, XLPE, silicon rubber insulator, etc.) to study the effect of NSLIW on electrical insulation.