Influence of Insulating Material Properties on Partial Discharges at DC Voltage

energies

Article Inﬂuence of Insulating Material Properties on Partial Discharges at DC Voltage

Marek Florkowski Department of Electrical and Power Engineering, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland; marek.ﬂ[email protected]

Received: 18 July 2020; Accepted: 19 August 2020; Published: 19 August 2020

Abstract: Understanding a partial discharge mechanism at direct current (DC) is an actual research topic that requires both modeling, simulations and measurements. This paper describes an influence of insulating material properties on partial discharges at DC voltage. Modifications of the traditional model reflecting the conditions of partial discharges (PD) inception and post discharge processes at DC voltage have been proposed. The aim was to show the partial discharge mechanisms and draw attention to the role of parameters of insulation materials adjacent to the cavity at DC voltage. The investigations were performed on two kinds of dielectric material used in power cables. Various combinations of specimens were designed to reveal the effect of the material resistivity on the PD activity. Key observations referred to the impact of the void adjacent material resistance on the partial discharge inception voltage threshold at DC voltage. The modified PD model was applied to analyze both inception and post discharge recovery stage. The role of dielectric properties of material adjacent to the void was investigated, highlighting its impact during static inception stage and in charging stage. Despite many simplifications introduced in the model, measurement results have confirmed the role of the dielectric material surrounding the void on partial discharge dynamics. The average time interval between PD pulses revealed a systematic relationship with respect to the applied voltage and specimen resistivity. This value can be considered in the future research for diagnostic indicator at DC voltage.

Keywords: partial discharges; DC voltage; high voltage insulation; diagnostics

1. Introduction The use of DC voltage in high voltage transmission systems is currently undergoing a renaissance. In fact, this applies to all voltage levels. On one side it refers to the highest voltage level and future HVDC (high voltage direct current) grids, not only peer-to-peer but also meshed ones. On the other side, enhancements in power electronics technologies have resulted in a broad interest in DC, also at medium and low voltage levels. Today DC systems are regularly observed in applications such as traction, e-mobility or solar converters and are more and more analyzed in power distribution solutions. The above elements imply interest in a design of reliable insulation of high voltage power equipment. Phenomena occurring in insulation in a strong electric ﬁeld result in aging and include ionization processes in the dielectric materials. The DC insulation is a crucial element of high voltage power equipment, such as cables, transformer bushings, converter transformers—especially the valve winding, capacitors, including DC capacitors in HVDC modules; wall bushings [1–4]. The problem of the reliability of electrical power devices refers—in both AC and DC systems—to the possibility of assessing the condition of the insulation systems under the action of operational stresses. One of the most reliable quality indicators of high voltage insulation systems is the measurement of partial discharges (PD). Partial discharges occur in high voltage, technical insulation systems causing deterioration and often during long term exposure are leading to a breakdown. The character of

Energies 2020, 13, 4305; doi:10.3390/en13174305 www.mdpi.com/journal/energies Energies 2020, 13, 4305 2 of 17 partial discharges in electrical insulation is dependent on the applied voltage waveform, resulting in different times, magnitudes and intensities of discharges for direct, alternating or impulse voltages. The mechanism of partial discharges is slightly different at AC and DC voltages. Many research studies over the last century have been dedicated to understanding that topic, however the majority was related to an alternating voltage. This paper is focused on the partial discharges occurring at DC voltage and the influence of material resistivity, impacting the PD dynamics. The presented research aimed at developing assumptions for future diagnostic methods for assessing the state of insulation subjected to DC voltage. This experiments were carried out in laboratory tests using model specimens, containing partial discharge sources from distinct insulation materials. Insulation materials with different electrical parameters, in particular electrical resistivity, were used to assess the impact on the parameters of PD pulse sets recorded in the detection system. Investigations were performed on two materials used for power cable insulation, i.e., electrotechnical cellulose and polyethylene. The influence of those materials on the PD pulse repetition rate was discussed. Modifications of the traditional model reflecting the conditions of PD inception and post discharge processes at DC voltage have been proposed, as it is well known there is a difference in PD mechanism under AC and DC voltage. The first one is determined by material electrical permittivity, whereas the latter one by electrical resistivity. The first model of partial discharge mechanism, so-called “a-b-c” model, was introduced by Gemant and Philipphoff [5] almost a century ago. Originally, they investigated power losses in mass impregnated power cables caused by discharges in the cavities. This approach was further modified by Whitehead and Kreuger in the 1950s [6]. In this model the external detectable charge, commonly called apparent charge, is smaller than the real charge related to the place of discharge, which cannot be measured directly. The IEC60270 standard [7] is based on this concept. Some researchers [8–10] challenge this concept arguing that instead of capacitance determined by a void shape, the radius of discharge channel should be assumed. However, from the general perspective apart from the (a-b-c) capacitive model, in 80 ties of last century Pedersen [9] has introduce a dipole model based on electric field theory and dielectric flux density, which has been further elaborated by Lemke [8,10]. They criticized the network-based capacitive model, which was not fully reflecting the physics of gas discharges. In their concept the cavity is not discharged via a spark gap but rather charged due to the creation of charge carriers as a consequence of ionization processes in the gas filled cavity. Instantly after the discharge event, the charges of both polarities are deposited on the anode and cathode side of the void wall and a dipole moment is established, which induces charges on the electrodes (induced charge model). In this way a space charge field, often denoted as Eq (Poisson electric field), opposes the electrostatic field caused by the applied external test voltage (Laplacian electric field). In this approach, the current caused by the charge carriers in the void is moving through the solid dielectric column and results in a statement that the external charge detectable at the terminals of the test object must be equal to the internal charge, which is in contrast to the apparent charge concept. Another doubt of the “a-b-c” model based on capacitances questions the fact that there are no real “capacitor electrodes”, especially associated with a conventional capacitance. On the other side, it should be underlined that the “a-b-c” model has been very successfully used in PD modeling, simulations and theoretical considerations over many decades [11–15]. It can be concluded, analyzing both capacitive and dipole models, that external charge detectable at the terminals of a specimen or real power equipment is a quantity reflecting the PD severity or at least is proportional to the PD causing deterioration. An unprecedented contribution to PD modeling was brought by Lutz Niemeyer at the beginning of 1990s, introducing a new approach that in many variations triggered PD-related simulation over the last three decades [16,17]. An important extension was the introduction of finite element modeling to PD simulations [18–20]. Thus, the third model used in this classification in partial discharge research is related to plasma physics. This model considers the plasma dynamics of the discharge and has been used for modeling dielectric barrier discharges. A well-established approach is to use drift diffusion equations that describe the dynamics of electrons, as well as positive and negative ions [21–26]. In Energies 2020, 13, 4305 3 of 17 Energies 2020, 13, x FOR PEER REVIEW 3 of 18 thatpositive model, and reflected negative and ions quantitatively [21–26]. In describedthat model are, reflected such processes and quantitatively as impact ionization, described attachment, are such recombination,processes as impact diffusion ionization, and drift attachment, of charges. The recombination, coupled approach diffusion of fluid and equations drift of charges. and Poisson The equationcoupled approach allow to obtain of fluid temporal equations evolution and Poisson of charge equation and electric allow fieldto obtain distribution temporal within evolution the void of duringcharge and the dischargeelectric field development distribution [27 within]. the void during the discharge development [27]. In the above context, in this paperpaper the influenceinfluence of materialmaterial resistivity on partial discharges at DC voltage in cavities are studied using a modifiedmodified “a-b-c”“a-b-c” model.model. The analysis was focused on two aspects, i.e.,i.e., static PD inception condition and post discharge recovery stage. The important novelty is to drawdraw attentionattention to the rolerole ofof materialmaterial resistanceresistance adjacentadjacent to the inclusioninclusion and interplayinterplay in the conditions for PD inception,inception, as well as post PD void charging. As an indicator indicator,, the evolution of an average interval between the PD pulses in predefinedpredefined measurementmeasurement timetime waswas observed.observed.

2. Partial Discharges at DC Voltage It is knownknown thatthat progressiveprogressive highhigh voltagevoltage insulationinsulation deterioration c causedaused by PD in gas-filledgas-filled cavities (voids) is one ofof thethe majormajor factorsfactors limitinglimiting thethe lifetimelifetime ofof powerpower equipment.equipment. The quantity characterizing partial discharges in insulation systems at direct voltage is the number of impulses of discharges registered registered in in the th detectione detection circuit circuit at the at predefined the predefined time period time period or the time or the interval time between interval successivebetween successive PD pulses. PD The pulses. conditions The conditions for initiating for initiating discharges discharges in defects in defects the structure in the ofstructure insulation of systemsinsulation are systems determined—similarly are determined— tosimilarly alternating to voltage—by alternating voltage the value—by of the the electric value of field the strength electric necessaryfield strength for ionizationnecessary infor the ionization gas source in ofthe discharges. gas sourceAt of steady-statedischarges. At of DCsteady voltage,-state the of DC distribution voltage, ofthe the distribution electric field of the strength electric in thefield insulated strength systemin the insulated is a resistive system distribution. is a resistive The distribution. above fact is The the basisabove for fact the is analysisthe basis of for the the discharge analysis mechanismof the discharge at direct mechanism voltage, at including: direct voltage, including:

. conditionsconditions of of initiating initiating discharges discharges in gas inclusions in solid dielectrics, and . thethe impact impact of of the the properties properties of of insulation insulation materials materials on on the the quantities quantities characterizing characterizing this phenomenon.this phenomenon.

The main inﬂuenceinfluence on the PD dynamics at DC has material resistivity, unlike its permittivity at AC. To analyzeanalyze thethe static inception conditions at DC, the adopted “a “a-b-c”-b-c” model is applied applied [5,28 [5,28––3232].]. The investigations were performed on a model specimen reﬂectingreflecting oneone of the most typical defects in high voltage insulation. In a a model model shown shown in in Figure Figure 11,, the resistors represent thethe material properties. In fact, relationships of those resistors are crucial for partial discharge inception voltage (PDIV, Uinc) In fact, relationships of those resistors are crucial for partial discharge inception voltage (PDIV, Uinc) calculationscalculations at DC.

Figure 1. Equivalent circuit for partial discharge ( (PD)PD) modeling at direct current (DC).(DC).

In the equivalent circuit (Figure2), the source of the discharges represents the capacitance Cc In the equivalent circuit (Figure 2), the source of the discharges represents the capacitance Cc 16 and the resistance Rc. The air resistivity is very high, 1016 Ω m at temperature 20 ◦C[33], hence in and the resistance Rc. The air resistivity is very high, 10 Ω··m at temperature 20 °C [33], hence in reality the resistance Rc, representing the gaseous void, is much higher than the resistance of solid dielectric, which is represented by Ra2 and R’a2. The indexed resistances Ra and Rb reflect the part of a

Energies 2020, 13, 4305 4 of 17

reality the resistance Rc, representing the gaseous void, is much higher than the resistance of solid dielectric, which is represented by Ra2 and R’a2. The indexed resistances Ra and Rb reflect the part of a homogeneous dielectric, free from discharges. In this representation (Figure2a), the branch resistance Ra has been split according to the cavity profile, i.e., Ra2, R’a2 being parallel to the cavity (marked in red) and Ra1, R’a1, Ra3, R’a3 mimicking remaining parts. It is important to notice that usually the resistance Rc is much bigger than Ra2, R’a2, which are bypassing the resistance representing the gaseous void. The voltage build-up Uc required for PD inception corresponds to the voltage drop on resistance RA resultant from the combination of components Ra2 and R’a2. This is actually a very important novelty in modeling partial discharges occurrence at DC voltage. This effect is highlighted in Figure2a, indicating the twofold effect of resistance RA. At DC voltage two distinctive stages representing PD mechanism can be distinguished:

(a) inception stage, when PD will occur, assuming fulﬁllment of all conditions, (b) charging stage, when post-discharge recovery occurs.

It is shown in this paper that the void material properties, such as resistivity, both volume and surface, are crucial in proper modeling of above mentioned stages. The first one is influencing the inception phase, whereas the latter one impacting the charging time. Discharge stages in an air-filled cavity illustrate the simplified equivalent circuits:

inception stage (Figure2b) will occur when voltage drop on the equivalent resistance RA reaches the PD inception voltage Uinc, charging stage (Figure2c): charge ﬂow through volume resistance R0 and RA, including eﬀects of void walls represented by surface resistance of RA, will result in recovery voltage Uc build-up on the capacitance CC.

(a) Static inception stage Inception stage in this paper is analyzed mainly with respect to the required static inception electric field strength, i.e., other conditions such as availability of starting electron/time lag, residual charges and memory effects, dielectric surface condition or space charge are not considered [34–38]. The main novelty introduced in this paper in this aspect is related to the influence of the void adjacent resistivity on the inception conditions. Usually the void (gaseous) resistivity is taken to the calculations of the resistive potential distribution. However, it should be noticed that usually very high resistivity of a gaseous cavity is bypassed by the adjacent solid dielectric layer and its resistance as graphically illustrated in Figure2a. The static voltage drop Uc0 on the cavity results from the relationship between resistances RA representing resistance adjacent to the void (assuming Ra2, R’a2 << Rc) and resultant resistance R0 being combination of components Ra1, R’a1, Ra3, R’a3, Rb, R’b:

RA Uc0 = UDC (1) R0 + RA

(b) Charging stage Immediately after the discharge event, the voltage recovery process is starting, leading to charging of the void capacitance with a time constant resulting from the residual level according to resistance division. The next PD will occur when the inception voltage level Uinc is reached. In this process both volume dielectric resistivity and void wall surface resistivity are involved. The voltage waveform across the void represented by capacitance Cc is described by:

t τ Uc = Uc (Uc Uext)(e− DC ) (2) 0 − 0 − where τDC—voltage recovery time constant, Uext—PD extinction voltage. Energies 2020, 13, 4305 5 of 17

While crossing the threshold level, of the PDIV (Uinc) the consecutive discharge is triggered. The theoretical time tp elapsing between consecutive PD pulses is equal to [29]: ! Uc0 Uinc tp = τDC ln − (3) − · Uc Uext 0 − Energies 2020, 13, x FOR PEER REVIEW 5 of 18 where Uinc—PD inception voltage.

(a)

(b) (c)

FigureFigure 2. (a ) 2. PD (a model) PD model at DC at reﬂecting DC reflecting the role the of role material of material resistivity resistivity adjacent adjacent to the tovoid, the (b void,) equivalent (b) equivalent circuit of inception stage, RA—resistance adjacent to the void (combination of components circuit of inception stage, RA—resistance adjacent to the void (combination of components Ra2, R’a2), Ra2, R’a2), R0—resultant resistance from combination of components Ra1, R’a1, Ra3, R’a3, Rb, R’b, (c) R0—resultant resistance from combination of components Ra1, R’a1, Ra3, R’a3, Rb, R’b,(c) equivalent equivalent circuit of charging stage, UDC—terminal voltage on a specimen. circuit of charging stage, UDC—terminal voltage on a specimen.

In a simplified form, assuming Uext = 0, tp can be expressed as:

푈푖푛푐 푡푝 = −휏퐷퐶 ∙ 푙푛 (1 − ) (4) 푈푐0

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In a simpliﬁed form, assuming Uext = 0, tp can be expressed as: ! Uinc tp = τDC ln 1 (4) − · − Uc0

Denoting the ratio of cavity voltage to PD inception voltage n = Uc0 , the above equation has the Uinc form: 1 tp = τ ln 1 (5) − DC· − n The time constant in the above conﬁgurations equals to:

R0RA τDC = Cc (6) R0 + RA

Thus, for example, for Uinc = 0.9Uc0 the approximate time between the PD pulses is:

R0RA tp = 2.3τDC =2.3 Cc (7) R0 + RA

As was mentioned above, the simplified calculation does not take into account statistical effects, such as time lag or memory effects, however it provides good proximity. The PD electric field strength in gaseous void, denoted as Ep, should be similar for AC and DC according to Paschen’s formula at a given pressure. The electric field inception level in the air void depends strongly on the cavity thickness. For small cavities (a—cavity thickness in cm) the approximate electric breakdown strength in air at normal pressure can be expressed by an empirical formula [39]:

7 Ep = 23 + [kV/cm] (8) √a

Common value of electric ﬁeld withstand Ep for few millimeters interspaced cavity at normal pressure is 3 kV/mm, whereas for submillimeter distance it goes up to 5 kV/mm, and further to 9 kV/mm for tiny voids 0.01 mm thick.

3. Experimental Setup, Instrumentation and Specimens The investigations presented in this paper were performed on the model flat, round cavity (diameter D, thickness d2) embedded in the homogenous insulating material, being a source of discharges. Two glass plates, on upper and bottom side, applied pressure to the void in order to achieve mechanical stability. Such a specimen consists of five layers, i.e., two glass plates with thickness d0 each, layer containing void (thickness d2) and two flakes making the top and bottom side of the cavity with thickness d1 each. The geometrical representation of the specimen is illustrated in Figure3 and corresponds to the model shown in Figure1. Assuming the dielectric relative permittivity ε and resistivity of the dielectric layers ρ:

εg, ρg of the glass plate (layer 0), ε1, ρ1 of the top/bottom cavity ﬂake (layer 1), ε2, ρ2 of the layer containing void (layer 2), and the above mentioned geometry, the approximate partial discharge inception voltage (PDIV) thresholds on the specimen terminals can be estimated, both for AC (Uinc_AC) and DC (Uinc_DC) cases. The equation reﬂects the AC case taking into account material permittivity and thickness of the insulating layer (assuming relative permittivity of air equal one): ! 2d0 2d1 Uinc_AC = + + d2 Ep (9) εg ε1 · Energies 2020, 13, x FOR PEER REVIEW 6 of 18

푈 Denoting the ratio of cavity voltage to PD inception voltage 푛 = 푐0 , the above equation has 푈푖푛푐 the form: 1 푡 = −휏 ∙ 푙푛 (1 − ) (5) 푝 퐷퐶 푛 The time constant in the above configurations equals to:

푅0푅퐴 휏퐷퐶 = 퐶푐 (6) 푅0 + 푅퐴

Thus, for example, for Uinc = 0.9Uc0 the approximate time between the PD pulses is:

푅0푅퐴 푡푝 = 2.3휏퐷퐶 =2.3 퐶푐 (7) 푅0+푅퐴 As was mentioned above, the simplified calculation does not take into account statistical effects, such as time lag or memory effects, however it provides good proximity. The PD electric field strength in gaseous void, denoted as Ep, should be similar for AC and DC according to Paschen’s formula at a given pressure. The electric field inception level in the air void depends strongly on the cavity thickness. For small cavities (a—cavity thickness in cm) the approximate electric breakdown strength in air at normal pressure can be expressed by an empirical formula [39]: 7 퐸푝 = 23 + [kV/cm] √a (8)

EnergiesCommon2020, 13, 4305value of electric field withstand Ep for few millimeters interspaced cavity at normal7 of 17 pressure is 3 kV/mm, whereas for submillimeter distance it goes up to 5 kV/mm, and further to 9 kV/mm for tiny voids 0.01 mm thick. For DC case, material resistivity and layer thickness is considered:

Energies3. Experimental 2020, 13, x FOR Setup PEER REVIEW, Instrumentation and Specimens ! 7 of 18 2ρg 2ρ1 U = d + d + d Ep (10) The investigations presented inc in_ DC this paperρ 0 wereρ performed1 2 · on the model flat, round cavity Assuming the dielectric relative permittivity2 ε and resistivity2 of the dielectric layers ρ: (diameter D, thickness d2) embedded in the homogenous insulating material, being a source of At DC voltage, insulating material conductivity reveals strong temperature dependence, which is . discharges.εg, ρg of the Two glass glass plate plates, (layer on 0), upper and bottom side, applied pressure to the void in order to not considered in this paper. Hence, the temperature has strong effect at DC voltage on electric field . achieveε1, ρ1 of mechanical the top/bottom stability. cavity Such flake a (layer specimen 1), consists of five layers, i.e., two glass plates with distribution and related charging stage with recovery voltage build-up, including influence on PD . thicknessε2, ρ2 of d the0 each, layer layer containing containing void void (layer (thickness 2), d2) and two flakes making the top and bottom side ofdynamics the cavity [40 with]. The thickness measurements d1 each. presented The geometrical in this paper representation were performed of the atspecimen room temperature. is illustrated The in and the above mentioned geometry, the approximate partial discharge inception voltage (PDIV) Figureelectrode 3 and configuration corresponds presented to the model in Figure shown4 ensures in Figure a uniform 1. electric field in a cavity space. Both thresholdselectrodes on have the aspecimen diameter terminals 40 mm. can be estimated, both for AC (Uinc_AC) and DC (Uinc_DC) cases. The equation reflects the AC case taking into account material permittivity and thickness of the insulating layer (assuming relative permittivity of air equal one):

2푑0 2푑1 푈푖푛푐_퐴퐶 = ( + + 푑2) ∙ 퐸푝 (9) 휀푔 휀1 For DC case, material resistivity and layer thickness is considered:

2휌푔 2휌1 푈푖푛푐_퐷퐶 = ( 푑0 + 푑1 + 푑2) ∙ 퐸푝 (10) 휌2 휌2 At DC voltage, insulating material conductivity reveals strong temperature dependence, which is not considered in this paper. Hence, the temperature has strong effect at DC voltage on electric field distribution and related charging stage with recovery voltage build-up, including influence on PD dynamics [40]. The measurements presented in this paper were performed at room temperature.

The electrode configuration presented in Figure 4 ensures a uniform electric field in a cavity space. Figure 3. DielectricDielectric layered layered specimen specimen and notation, ε——dielectricdielectric relative permittivity, ρ —electric—electric Both electrodes have a diameter 40 mm. resistivity, d—thickness,—thickness, DD—void—void diameterdiameter (explanation(explanation inin text).text).

FigureFigure 4. S 4.pecimenSpecimen with with electrodes. electrodes.

TheThe specimen specimen dimensions dimensions are are summarized summarized in inTable Table 1.1 .

TableTable 1. 1.SpecimenSpecimen dimensions. dimensions.

DD d d0 d1 dd21 d2 DimensionDimension [mm] [mm] 6 6 2 2 0.5 0.9 0.5 0.9

TheThe experiments experiments presented in in this this paper paper were were performed performed on insulating on insulating paper (PK) paper and cross-linked(PK) and crosspolyethylene-linked polyethylene (XLPE). The (XLPE). electrical The properties electrical of properties the specimens, of the speciﬁcally specimens, the specifically permittivity the and permittivityresistivity, and are shownresistivity, in Table are 2shown. in Table 2.

Table 2. Electrical properties of materials in specimens.

Glass PK XLPE Surface resistivity [Ω] 8.01010 2.01012 21013 Volume resistivity [Ω·m] 1.11011 4.61013 61014 Relative dielectric permittivity 7.9 2.8 2.4

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Table 2. Electrical properties of materials in specimens.

Glass PK XLPE Surface resistivity [Ω] 8.0 1010 2.0 1012 2 1013 · · · Volume resistivity [Ω m] 1.1 1011 4.6 1013 6 1014 · · · · Relative dielectric 7.9 2.8 2.4 permittivity

Energies 2020, 13, x FOR PEER REVIEW 8 of 18 In order to investigate the inﬂuence of insulating material resistivity on PD inception and recovery stage,In the order following to investigate four specimens the influence were compared: of insulating material resistivity on PD inception and recovery stage, the following four specimens were compared: PK—(1): specimen made of insulating paper (PK—layer 1 and layer 2), . PKXLPE—(2):—(1): specim specimenen made made of insulating of polyethylene paper (XLPE—layer(PK—layer 1 and 1 and layer layer 2),2), . XLPEXLPE-PK-XLPE—(3):—(2): specimen made void of layer polyethy 2 madelene of (XLPE PK and—layer top/bottom 1 and layer layers 2), 1 made of cross-linked . XLPEpolyethylene-PK-XLPE (XLPE),—(3): void layer 2 made of PK and top/bottom layers 1 made of cross-linked polyethylene (XLPE), PK-XLPE-PK—(4): void layer 2 made of XLPE and top/bottom layers 1 made of insulating paper . PK-XLPE-PK—(4): void layer 2 made of XLPE and top/bottom layers 1 made of insulating (PK). paper (PK). The geometry of the specimens was kept constant for all above conﬁgurations. In all those cases The geometry of the specimens was kept constant for all above configurations. In all those cases layer 0 refers to glass plate. The graphical representation of specimens is shown in Figure5. layer 0 refers to glass plate. The graphical representation of specimens is shown in Figure 5.

Figure 5. Graphical representation of specimen configurations: (a) insulating paper (PK), (b) Figure 5. Graphical representation of specimen configurations: (a) insulating paper (PK), (b) polyethylene (XPLE), (c) top/bottom insulating paper, void layer XLPE, (d) top/bottom XLPE, void polyethylene (XPLE), (c) top/bottom insulating paper, void layer XLPE, (d) top/bottom XLPE, void layer PK. layer PK. The PD measurements, both at AC and DC voltage, were performed in a setup shown in Figure6. PartialThe discharges PD measurements, were recorded both at using AC and a wideband DC voltage, detection were performed system ICM in+ a, setup connected shown to in a controlFigure 6.unit Partial via GPIB discharges bus. The were measurements recorded using at DCa wideband voltage weredetection carried system out inICM+, time connected mode, within to a definedcontrol unittime via interval GPIB (up bus. to The 600 smeasurements in this paper). at Both DC high voltage voltage were AC carried and DC out signals in time were mode, provided within by defined an HV timeamplifier interval (TREK (up 20to/ 20B)600 s controlled in this paper). by a programmableBoth high voltage waveform AC and generator DC signals AFG were 3102C. provided The voltage by an HV amplifier (TREK 20/20B) controlled by a programmable waveform generator AFG 3102C. The reference signal was obtained from a HV resistive divider (R1,R2). The PD signal was captured using a voltage reference signal was obtained from a HV resistive divider (R1, R2). The PD signal was measuring impedance Zm, connected in series with a coupling capacitor Ck = 100 pF, then filtered and capturedpre-amplified using in a signalmeasuring conditioning impedance unit Z SCU.m, connected The AC inmeasurements series with a coupling were recorded capacitor within Ck = 60 100 s inpF, a thenphase-resolved filtered and mode pre resulting-amplified in D( in ϕ signal, q, n) pattern conditioning acquisition unit (8 SCU.8 16 The bit), whereasAC measurements in DC mode, were the · · recordedPD pulse w distributionithin 60 s in in a time phase was-resolved obtained. mode In the resulting latter case, in D( especiallyφ, q, n) pattern the evolution acquisition of time (8 × interval 8 × 16 bit),between whereas pulses in was DC investigated, mode, the PD in a pulse voltage distribution range from in inception time was up obtained. to 20 kV In DC. the In latter both cases, case, especiallyPDIV was the detected. evolution of time interval between pulses was investigated, in a voltage range from inception up to 20 kV DC. In both cases, PDIV was detected.

Figure 6. Measuring set-up for PD acquisition at AC and DC voltage: R1, R2—resistive divider,

Ck—coupling capacitor, Zm—coupling impedance, SCU—signal conditioning unit and preamplifier.

Energies 2020, 13, x FOR PEER REVIEW 8 of 18

In order to investigate the influence of insulating material resistivity on PD inception and recovery stage, the following four specimens were compared: . PK—(1): specimen made of insulating paper (PK—layer 1 and layer 2), . XLPE—(2): specimen made of polyethylene (XLPE—layer 1 and layer 2), . XLPE-PK-XLPE—(3): void layer 2 made of PK and top/bottom layers 1 made of cross-linked polyethylene (XLPE), . PK-XLPE-PK—(4): void layer 2 made of XLPE and top/bottom layers 1 made of insulating paper (PK). The geometry of the specimens was kept constant for all above configurations. In all those cases layer 0 refers to glass plate. The graphical representation of specimens is shown in Figure 5.

Figure 5. Graphical representation of specimen configurations: (a) insulating paper (PK), (b) polyethylene (XPLE), (c) top/bottom insulating paper, void layer XLPE, (d) top/bottom XLPE, void layer PK.

The PD measurements, both at AC and DC voltage, were performed in a setup shown in Figure 6. Partial discharges were recorded using a wideband detection system ICM+, connected to a control unit via GPIB bus. The measurements at DC voltage were carried out in time mode, within defined time interval (up to 600 s in this paper). Both high voltage AC and DC signals were provided by an HV amplifier (TREK 20/20B) controlled by a programmable waveform generator AFG 3102C. The voltage reference signal was obtained from a HV resistive divider (R1, R2). The PD signal was captured using a measuring impedance Zm, connected in series with a coupling capacitor Ck = 100 pF, then filtered and pre-amplified in signal conditioning unit SCU. The AC measurements were recorded within 60 s in a phase-resolved mode resulting in D(φ, q, n) pattern acquisition (8 × 8 × 16 bit), whereas in DC mode, the PD pulse distribution in time was obtained. In the latter case,

Energiesespecially2020, the13, 4305 evolution of time interval between pulses was investigated, in a voltage range9 from of 17 inception up to 20 kV DC. In both cases, PDIV was detected.

Figure 6. R R Figure 6. MeasuringMeasuring set-up set-up for for PD PD acquisition acquisition at at AC AC and and DC DC voltage: voltage: R11,, R22—resistive—resistive divider, C —coupling capacitor, Z —coupling impedance, SCU—signal conditioning unit and preampliﬁer. Ckk—coupling capacitor, Zmm—coupling impedance, SCU—signal conditioning unit and preamplifier. 4. Experimental Results The experiments have been performed on two types of specimens representing high voltage cable insulation. First one denoted as (PK) represents the insulating paper, while the second one (XLPE) represents the cross linked polyethylene. Both specimens contained the same size of the embedded void shown in Figure4. For reference, ﬁrst the partial discharges were measured at AC voltage and then the sequence at DC voltage was recorded. The partial discharge inception voltage thresholds (PDIV) obtained both from calculations (Equations (9) and (10)) and measurements are shown in Table3. For calculations, the dimensions (Table1), as well as the electrical permittivity and resistivity (Table2) were used. The notation PK-XLPE-PK used in this paper means: void layer material XLPE and top/bottom layers PK. The only symbol PK or XLPE denotes the whole specimen made from the homogenous insulating material.

Table 3. Partial discharge terminal inception voltage calculated and measured at AC and DC voltage.

PDIV AC [kV] PK XLPE PK-XLPE-PK XLPE-PK-XLPE calculated 9.3 9.1 8.8 9.1 detected 9.5 9.4 9.2 9.7 PDIV DC [kV] calculated 11.5 10.5 9.0 11.0 detected 14.0 12.0 13.0 12.0

The four specimens having the same geometry but diﬀerent compositions of insulating materials reveal slightly diﬀerent PD inception voltages. In AC case, determined mainly by materials permittivity the spread is less visible, than in DC case forced by materials resistivity, where deviations between materials are more pronounced. In AC measurement, the lowest value was detected for PK-XLPE-PK specimen 9.2 kV and the highest one for XLPE-PK-XLPE 9.7 kV. The PDIVAC for PK specimen was 9.5 kV and 9.4 kV for XLPE. Generally, no large scatter between PD inception voltage levels was observed at AC voltage. The PD phase-resolved patterns obtained at PD inception at AC voltage for all specimens are shown in Figure7. All patterns reveal similar character in terms of phase range, number of discharges and statistical distribution of discharges, since at AC voltage all specimens are very similar. Energies 2020, 13, 4305 10 of 17 Energies 2020, 13, x FOR PEER REVIEW 10 of 18

FigureFigure 7. 7. PartialPartial dischargesdischarges patterns at AC in inceptionception voltage voltage for for specimens: specimens: (a ()a PK,) PK, (b ()b XLPE,) XLPE, (c) ( c) PK-XLPE-PK,PK-XLPE-PK, (d(d)) XLPE-PK-XLPE.XLPE-PK-XLPE.

SinceSince there there isis nono referencereference pointpoint in time at DC voltage voltage (unlike (unlike voltage voltage zero zero crossing crossing at at AC), AC), the the PDPD patterns patterns showshow thethe dischargedischarge pulse peak value value and and a a time time stamp, stamp, in in the the assumed assumed recording recording time. time. DiDifferentfferent values values of of thethe interinter PDPD pulsepulse time interval result result f fromrom the the impact impact of of the the insulation insulation resistivity resistivity onon recovery recovery voltagevoltage time constant ττDCDC. The. The PD PD patterns patterns recorded recorded for forall specimens all specimens at DC at voltage DC voltage 20 20kV kV are are shown shown in in Figure Figure 8,8 ,with with a a60 60 s szoomed zoomed view view (600 (600 s sfor for XLPE). XLPE). Among Among specimens, specimens, the the longest longest averageaverage timetime intervalinterval ttp_avgp_avg equalequal to to 20 20 s s is is for for (XLPE) (XLPE) (Figure (Figure 8b),8b), whereas whereas for for (PK) (PK) (Figure (Figure 8a)8a) it it is is muchmuch shorter—around shorter—around 4 4 s, s which, which clearly clearly indicates indicates the the e ffeffectect of of the the material material resistivity. resistivity. In In all all cases cases the voidthe void capacitance capacitance is the is the same. same. In In case case of of DC DC voltage, voltage, the the lowest lowest PDIV PDIV 9 kV9 kV was was also also calculated calculated for PK-XLPE-PKfor PK-XLPE specimen.-PK specimen. In this In casethis case the higher the higher resistivity resistivity of XLPE of XLPE with with respect respect to PK to leads PK leads to higher to higher voltage drop on the void than in reverse case, i.e., lower terminal inception UDC voltage. voltage drop on the void than in reverse case, i.e., lower terminal inception UDC voltage. It is worth noting the different approach in PDIV determination. In AC case it was assumed stable PD with at least two pulses per period, whereas in DC case the PDIV is much more tricky due to ultra-low repeatability compared to AC case. Thus, in this case it should be interpreted as a detection level. In practice, discharge measurements are usually made with the applied DC voltage equal to several times the inception voltage [41].

Energies 2020, 13, 4305 11 of 17 Energies 2020, 13, x FOR PEER REVIEW 11 of 18

FigureFigure 8. 8. PartialPartial discharges discharges patterns patterns at 2020 kV DC voltage for specimens: (a (a) ) PK, PK, (b (b) ) XLPE, XLPE, (c ()c ) PK-XLPE-PK,PK-XLPE-PK, (d ()d XLPE-PK-XLPE.) XLPE-PK-XLPE. 5. Discussion It is worth noting the different approach in PDIV determination. In AC case it was assumed stableTheoretically, PD with at theleast PD two inception pulses per voltage period at DC, whereas voltage in should DC case reveal the PDIV similar is valuesmuch more for homogenous tricky due specimensto ultra-low with repeatability the same geometry. compared It isto to AC some case. extent Thus material-independent, in this case it should and be mainly interpreted influenced as a bydetection the proportion level. In of practice, the layers’ discharge thickness. measurements However, the are PD usually pulse made repetition with ratethe isapplied heavily DC influenced voltage byequal material to several resistivity times and the capacitance inception voltage of the void.[41]. It was shown that the static PD inception voltage is determined by the resistivity of dielectric material adjacent to the wall void and is not influenced by the5. gasDiscussion resistivity, to be usually few orders of magnitude higher. This is of course one of the inception conditionTheoretically, apart from the starting PD inception electron voltage availability at DC and voltage avalanche should multiplication reveal similar fulfillment. values for homogenousThe apparent specimens capacitance withC c theof a same gaseous geometry. (air filled, It ε is= to1) some cavity extent (D = 6 material mm, d2 =-independent0.9 mm) equals and to: mainly influenced by the proportion of the layers’ thickness. However, the PD pulse repetition rate D 2 is heavily influenced by material resistivity andπ capacitance2 of the void. It was shown that the static PD inception voltage is determined byCc the= εεresistivity0 =of 0.3dielectricpF material adjacent to the wall void(11) d2 and is not influenced by the gas resistivity, to be usually few orders of magnitude higher. This is of wherecourseε one= 8.85 of 10 the12 inceptionF m 1. condition apart from the starting electron availability and avalanche 0 · − · − multiplicationThe term apparent fulfillment. is used since cavity is not representing a real capacitor [8,9,27]. The calculated resistanceThe ofapparent layer number capacitance one C forc of both a gaseous PK and (air XLPE filled, specimen, ε = 1) cavity based (D = on6 mm, measured d2 = 0.9 resistivitymm) equals of 12 14 bothto: materials, equals to 4.6 10 Ω and 0.7 10 Ω, respectively. Hence, the roughly estimated time tp · · between PD pulses yields 6 s for PK and 80 s for XLPE.퐷 2 휋 ( ) The comparison of the average time tp versus2 applied voltage in a range from 14 kV to( 2011) kV 퐶푐 = 휀휀0 = 0.3 푝퐹 for different specimen configurations is shown in푑 Figure2 9. In each case, with increasing voltage, the intervalwhere ε between0 = 8.85  PD10−12 pulses F·m−1. decreases. The relationship tp(U) follows an exponential course for all measuredThe configurations. term apparent is used since cavity is not representing a real capacitor [8,9,27]. The calculated resistance of layer number one for both PK and XLPE specimen, based on measured resistivity of both materials, equals to 4.6  1012 Ω and 0.7 1014 Ω, respectively. Hence, the roughly estimated time tp between PD pulses yields 6 s for PK and 80 s for XLPE.

Energies 2020, 13, x FOR PEER REVIEW 12 of 18

The comparison of the average time tp versus applied voltage in a range from 14 kV to 20 kV for different specimen configurations is shown in Figure 9. In each case, with increasing voltage, the interval between PD pulses decreases. The relationship tp(U) follows an exponential course for all Energies 2020, 13, 4305 12 of 17 measured configurations.

FigureFigure 9. TheThe relationship of time tp betweebetweenn consecutive PD pulses versus applied DCDC voltagevoltage UUDCDC forfor various various specimen specimen configurations. conﬁgurations.

TheThe measurement measurement results results have have been been shown shown in in semi semi logarithmic logarithmic plot plot and and the the trend trend lines lines approximatedapproximated by by exponential functions, are yielding following relationships between time ttpp (in(in seconds)seconds) and and applied applied voltage voltage U (in(in kV): kV):

p  55 −0.48U0.48U XLPEXLPEt pt(U(U))= = 2.82.81010 ee− (12(12)) · p  6 −0.64U PK t (U) = 1 106 e 0.64U (13) PK tp(U) = 1 10 e− (13) · XLPE-PK-XLPE tp(U) = 1.5105 e−0.61U (14) 5 0.61U XLPE-PK-XLPE tp(U) = 1.5 10 e− (14) · PK-XLPE-PK tp(U) = 8103 e−0.47U (15) 3 0.47U PK-XLPE-PK tp(U) = 8 10 e− (15) Specimens (1) and (2) represent a homogeneous · insulating medium in terms of resistivity, whereasSpecimens specimens (1) and (3) (2)and represent (4) a heterogeneous a homogeneous one, insulating in which mediumthe resistivity in terms can of represent resistivity, different whereas surfacespecimens conditions (3) and of (4) the a heterogeneous source of discharges, one, in e.g. which, degraded the resistivity due to canaging represent processes. diff Accordingerent surface to theconditions formula of (7) the— sourcetp(τDC), of while discharges, increasing e.g.,degraded material due resistivity to aging the processes. time interval According will increase.to the formula In a heterogeneous(7)—tp(τDC), while dielectric, increasing apart material from the resistivity effect of theresistivity time interval (plots will(3) and increase. (4) in InFigure a heterogeneous 9), one can presumedielectric, the apart influence from the of etheffect surface of resistivity conditions (plots in (3) the and source (4) in of Figure discharges9), one canon the presume value theof inception influence andof the extinction surface conditions voltages. Non in the-homogeneous source of discharges void surfaces on the valuecan be of also inception related and to modeling extinction of voltages. aging andNon-homogeneous erosion processes. void surfaces can be also related to modeling of aging and erosion processes. The longest tp time, due to higher material resistivity of XLPE comparing with PK, is observed for homogeneous XLPE specimen. While replacing in this specimen the cavity layer by PK material, the curve has moved down, reflecting the influence of the cavity wall material indicated in a model in Figure2c. The lower surface resistivity of PK with respect to XLPE results in bypassing the void capacitance during charging period and recovery voltage build-up. Considering PK specimen, the Energies 2020, 13, x FOR PEER REVIEW 13 of 18

The longest tp time, due to higher material resistivity of XLPE comparing with PK, is observed for homogeneous XLPE specimen. While replacing in this specimen the cavity layer by PK material, the curve has moved down, reflecting the influence of the cavity wall material indicated in a model Energies 2020, 13, 4305 13 of 17 in Figure 2c. The lower surface resistivity of PK with respect to XLPE results in bypassing the void capacitance during charging period and recovery voltage build-up. Considering PK specimen, the replacementreplacement ofof thethe middlemiddle voidvoid layerlayer byby XLPEXLPE resultsresults inin slightlyslightly lowerlower DCDC inceptioninception voltage,voltage, i.e.,i.e., 11.511.5 kVkV forfor PKPK vs.vs. 9.09.0 kVkV forfor PK-XLPE-PK,PK-XLPE-PK, thusthus higherhigher repetitionrepetition ofof PDPD pulsepulse in in thethe latter latter case. case. AsAs was was mentioned mentioned before, before, for smallfor small cavities cavities the PD the inception PD inception voltage voltagethreshold threshol stronglyd depends strongly ondepends cavity thickness.on cavity thickness. The simulation The simulation presented inpresented Figure 10 in is Figure highlighting 10 is highlighting this effect for this two effect cavities: for two (1) withcavities: thickness (1) with 1.3 thickness mm (red line)1.3 mm and (red (2) withline) and thickness (2) with 2.3 thickness mm (blue 2.3 line). mm Since (blue the line). void Since capacitance the void incapacitance the second in casethe second is half case of the is hal thinnerf of the one thinner (Cc1 = one2C (cC2),c1 = the 2C correspondingc2), the corresponding time constants time constants have relationshiphave relationshipτ1 > ττ21. > However,τ2. However, taking taking into into account account the the eff effectect of of thickness thickness dependent dependent electric electric fieldfield strength,strength, thethe breakdownbreakdown electricelectric fieldfield inin thethe firstfirst casecase willwill bebe 4.24.2 kVkV/mm/mm whichwhich correspondscorresponds toto thethe inceptioninception voltagevoltageU Uincinc1 = 5.55.5 kV, kV, whereas in the second case for electric fieldfield 3.73.7 kVkV/mm/mm thethe inceptioninception voltagevoltage is is UUincinc2 = 8.68.6 kV. kV. This interplay impacts the occurrence occurrence of of PD PD pulses pulses (Figure (Figure 10 10b)b) and and as as visualizedvisualized inin FigureFigure 10 10aa forforτ τ11 >> τ2,, results in tp22 >> tpt1p. 1.

FigureFigure 10.10. InﬂuenceInfluence ofof cavitycavity thicknessthickness (1.3(1.3 mm—red,mm—red, 2.32.3 mm—blue)mm—blue) onon recoveryrecovery voltagevoltage buildbuild upup and time tp between consecutive PD pulses, (a) cavity charging voltage, (b) PD pulses (Uext = 2.5 kV). and time tp between consecutive PD pulses, (a) cavity charging voltage, (b) PD pulses (Uext = 2.5 kV). The eﬀect is even more predominant rising the PD extinction voltage from 2.5 kV (Figure 10a) to The effect is even more predominant rising the PD extinction voltage from 2.5 kV (Figure 10a) 4 kV in Figure 11. The void surface conductivity strongly depends in polymeric materials on the PD to 4 kV in Figure 11. The void surface conductivity strongly depends in polymeric materials on the dynamics, hence surface erosion, aging is leading to greater material surface conductivity, thus lower PD dynamics, hence surface erosion, aging is leading to greater material surface conductivity, thus PD extension voltage. lower PD extension voltage. The voltage drop ∆U on void capacitance Cc due to partial discharge equals to: The voltage drop ∆U on void capacitance Cc due to partial discharge equals to:

∆∆U푈==U푈inc −U푈ext ((16)16) 푖푛푐− 푒푥푡 TheThe extinction extinction voltage voltage represents represents the the charge chargeQ neutralization Q neutralization conditions conditions in the discharge in the discharge source: source:

Q = ∆U Cc (17) 푄 = ∆푈·∙ 퐶푐 (17)

ExtinctionExtinction voltagevoltageU Uextext cancan assumeassume certaincertain valuevalue ((UUextext , 0) depending on the surfacesurface dischargingdischarging dynamicsdynamics in in the the discharge discharge source. source. Depending Depending on the on extinction the extinction voltage voltage level, the level, void the charging void charging voltage canvoltage assume can waveformsassume waveforms shown in shown Figures in 10 Figures and 11 .10 Additionally, and 11. Additionally, in case of thein case train of of the PD train pulses of thePD memorypulses the eff memoryect of charges effect accumulatedof charges accumulated on the void on surface the void [34 ,sur36]face should [34,36 be] considered,should be considered, due to an alternating effect of the resultant electric field distribution inside the void. Not neutralized surface charges also influence time lag, throughout starting electron availability. Since this paper is focused on Energies 2020, 13, x FOR PEER REVIEW 14 of 18

Energiesdue to2020 an, 13 alternating, 4305 effect of the resultant electric field distribution inside the void.14 of Not 17 neutralized surface charges also influence time lag, throughout starting electron availability. Since this paper is focused on highlighting the influence of dielectric material properties on PD modeling highlightingand basic processes, the inﬂuence those of effect dielectrics were material not considered. properties on PD modeling and basic processes, those eﬀects were not considered.

Figure 11. Inﬂuence of cavity thickness (1.3 mm—red, 2.3 mm—blue) on recovery voltage build up Figure 11. Influence of cavity thickness (1.3 mm—red, 2.3 mm—blue) on recovery voltage build up and time tp between consecutive PD pulses, (a) cavity charging voltage, (b) PD pulses (Uext = 4 kV). and time tp between consecutive PD pulses, (a) cavity charging voltage, (b) PD pulses (Uext = 4 kV).

The time interval tp between consecutive PD pulses depends on: The time interval tp between consecutive PD pulses depends on: volume resistivity ρ of the solid dielectric, and the higher the resistivity value, the longer the . volume resistivity ρ of the solid dielectric, and the higher the resistivity value, the longer the time interval, time interval, thickness of the solid dielectric, . thickness of the solid dielectric, capacitance Cc representing the gaseous inclusion, including its thickness and surface. The void . capacitance Cc representing the gaseous inclusion, including its thickness and surface. The void thickness has inﬂuence on the PD inception voltage. While increasing cavity thickness within thickness has influence on the PD inception voltage. While increasing cavity thickness within certain range, the inception voltage Uinc will decrease, resulting in the reduction of the time certain range, the inception voltage Uinc will decrease, resulting in the reduction of the time interval tp. interval tp. extinction voltage U . . extinction voltage Uext.

TheThe lastlast factor,factor, whichwhich isis thethe extinctionextinction voltagevoltageU Uextext, isis directlydirectly relatedrelated toto thethe statestate ofof thethe surfacesurface betweenbetween whichwhich thethe dischargedischarge developsdevelops (walls(walls ofof aa cavity).cavity). ThisThis statestate determines,determines, inin thethe mostmost generalgeneral terms,terms, thethe valuevalue ofof itsits surfacesurface resistivity,resistivity, whichwhich inin gasgas inclusioninclusion hashas anan impactimpact onon thethe accumulationaccumulation ofof chargescharges onon itsits surface.surface. TheThe degreedegree ofof dischargedischarge concentrationconcentration onon thisthis surfacesurface beforebefore subsequentsubsequent dischargesdischarges maymay vary.vary. IncompleteIncomplete neutralizationneutralization ofof gasgas inclusioninclusion surfacesurface meansmeans thatthat therethere isis residualresidual potentialpotential after after the the discharge discharge event, event, denoted denoted as extinction as extinction voltage. voltage. The random The random nature of nature both inception of both voltageinceptionUinc voltageand extinction Uinc and voltageextinctionUext voltageleads toUext statistical leads to analysis statistical of analysis the set of of impulses the set of of impulses discharges, of anddischarges, thus the and time thus intervals the timetp between intervals recorded tp between impulses. recorded Assuming impulses. the probability Assuming distribution the probability (e.g., normaldistribution distribution) (e.g., normal of the U distribution)inc and Uext voltage of the values,Uinc and the U partialext voltage discharge values, mechanism the partial at DC discharge voltage canmechanism be illustrated at DC by voltage a combination can be illustrated of time intervals by a combinationtp and applied of time high intervals voltage t values.p and applied The above high analysisvoltage ofvalues. the impact The above of various analysis factors of the on theimpact value of ofvarious the time factors interval on tthep between value of pulses the time refers interval to the elementstp between in pulses the equivalent refers to circuit the elements of the insulation in the equivalent system with circuit the sourceof the ofinsulation discharges system in the with form the of gas-filledsource of inclusion. discharges An in additional the form factor of gas of fluctuations,-filled inclusion. mentioned An additional above, in the factor theoretical of fluctuations, model of dischargesmentioned mayabove, be thein the “field theoretical effect”, asmodel a result of discharges of the accumulation may be the of discharge“field effect charges”, as a on result boundary of the surfacesaccumulation in the sourcesof discharge of discharges charges and on interaction boundary with surfaces charges in in the the sources solid dielectric. of discharges This e ff andect applies in particular to dielectrics with polar structures from the group of synthetic polymers. Energies 2020, 13, x FOR PEER REVIEW 15 of 18

Energies 2020, 13, 4305 15 of 17 interaction with charges in the solid dielectric. This effect applies in particular to dielectrics with polar structures from the group of synthetic polymers. InIn a a stationary stationary model, the time interval ttp is constant. constant. The The average average ttpp timetime obtained obtained from from measurementsmeasurements results results from from the the stochastically stochastically modified modiﬁed inter inter-PD-PD pulse intervals. In In the the exemplary exemplary casecase presented presented below, below, the the implemented implemented variability variability o off inception inception and and extinction extinction threshold threshold levels levels is is basedbased on on normal normal Gaussian Gaussian distribution distribution with assumed standard deviations σσincinc andand σext.. The The graphical graphical illustrationillustration of of a a stochastic stochastic PD PD model model at at DC DC voltage voltage is is shown shown in in Figure Figure 1212..

FigureFigure 12. 12. VariabilityVariability of of tp ttimep time in ina stoc a stochastichastic PD PDmodel model at DC at DCvoltage, voltage, variable variable inception inception Uci andUci

extinctionand extinction Uce voltageUce voltage levels levels according according to normal to normal distribution distribution with withstandard standard deviation deviation σinc andσinc σandext, respectively.σext, respectively.

TheThe analysis analysis of of the the mechanism mechanism of of partial partial discharges discharges in in insulation insulation s systemsystems at at DC DC voltage voltage leads leads toto the the determination determination of of the the quantity quantity that that can can be be used used as as an an indicator indicator of of the the state state of of insulation insulation due due to to thethe destructive destructive processes processes occurring occurring in in it it under under the the action action of of partial partial discharges. discharges. In In this this analysis analysis based based onon discharge discharge modelin modeling,g, the the term term “ “insulationinsulation state state”” refers refers to to the the surface surface transformation transformation processes processes in in gasgas inclusion, inclusion, known known as as erosion erosion processes. processes. The The occurrence occurrence of of these these processes processes can can be be evaluated evaluated in in longlong-term-term laboratory agingaging tests.tests. TheThe diagnosticdiagnostic indicator indicator of of the the insulation insulation system system condition condition due due to theto theeffect effect of partial of partial discharges discharges in it may in it be may the numberbe the number of pulses of in pulses the detection in the detection circuit in the circuit predefined in the predefinedtime period, time resulting period, from resulting the time from interval the time between interval successive between pulses.successive pulses. 6. Conclusions 6. Conclusions This paper reports the influence of insulating material properties on partial discharges at DC This paper reports the influence of insulating material properties on partial discharges at DC voltage. The investigations were performed on two kinds of dielectric material used in power cables. voltage. The investigations were performed on two kinds of dielectric material used in power Various combinations of specimens were designed to reveal the effect of the material resistivity on the cables. Various combinations of specimens were designed to reveal the effect of the material PD activity. The modified PD model was applied to analyze both inception and post discharge recovery resistivity on the PD activity. The modified PD model was applied to analyze both inception and stage. The role of dielectric properties of material adjacent to the void was investigated, highlighting post discharge recovery stage. The role of dielectric properties of material adjacent to the void was its impact during static inception stage and in charging stage. In the latter one, both volume resistivity investigated, highlighting its impact during static inception stage and in charging stage. In the latter and surface resistivity of cavity walls are involved. The void adjacent material properties play a key one, both volume resistivity and surface resistivity of cavity walls are involved. The void adjacent role setting the inception voltage threshold at DC voltage. The interplay between the gaseous void material properties play a key role setting the inception voltage threshold at DC voltage. The resistivity and the solid dielectric resistivity was highlighted, which is especially important for proper interplay between the gaseous void resistivity and the solid dielectric resistivity was highlighted, modeling and simulations of partial discharges at DC voltage.

Energies 2020, 13, 4305 16 of 17

Despite many simpliﬁcations introduced in the model, measurement results have conﬁrmed the role of the dielectric material surrounding the void on partial discharge dynamics. The average time interval between PD pulses revealed systematic relationship with respect to the applied voltage and specimen properties. Variability of this time signature in a stochastic PD model at DC voltage was shown with respect to the stochastic changes of both partial discharge inception and extinction voltage levels according to normal distribution. The longest average time between consecutive PD pulses, due to higher material resistivity of XLPE comparing with PK, is observed for homogeneous XLPE specimen. This value can be considered in the future research for diagnostic indicator at DC voltage.

Funding: This research received no external funding. Conﬂicts of Interest: The author declares no conﬂict of interest.

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