Breakdown Characteristics of Oil-Pressboard Insulation under AC-DC ...

energies Article

Breakdown Characteristics of Oil-Pressboard Insulation under AC-DC Combined Voltage and Its Mathematical Model Qingguo Chen 1,2, *, Jinfeng Zhang 1,2, * 1 2

*

ID

, Minghe Chi 1,2, * and Chong Guo 2

Key Laboratory of Engineering Dielectrics and Its Application, Ministry of Education, Harbin University of Science and Technology, 52 Xuefu Road, Harbin 150080, China The School of Electrical and Electronics Engineering, Harbin University of Science and Technology, 52 Xuefu Road, Harbin 150080, China; [email protected] Correspondence: [email protected] (Q.C.); [email protected] (J.Z.); [email protected] (M.C.); Tel.: +86-451-8639-1601(Q.C.); +86-451-8639-1627 (J.Z.); +86-451-8639-1625 (M.C.)

Received: 3 May 2018; Accepted: 17 May 2018; Published: 22 May 2018

Abstract: An AC-DC combined voltage is applied to the oil-pressboard insulation near the valve side during the operation of a converter transformer. To study the breakdown characteristics of an oil-pressboard insulation under such voltages, a typical plate electrode structure was employed in the laboratory to conduct a breakdown test on the oil-pressboard insulation. The electrical field distribution and the DC contents of the transformer oil and the pressboard in composite insulation under the AC-DC combined voltage were simulated by their dielectric parameters. The breakdown strength of the transformer oil decreases with the increase in the DC content of the applied voltage, whereas that of the pressboard increases. For the oil-pressboard insulation, the breakdown voltage increases first and then decreases. The electric field strength decreases in the transformer oil with the increase in the DC content, whereas it increases in the pressboard. And the DC contents of the transformer and the pressboard in composite insulation were different from that of the applied voltage. Finally, based on the above results, a mathematical model was proposed to describe the breakdown characteristics of the oil-pressboard insulation under the AC-DC combined voltage; the theoretical and experimental results were in good agreement. Keywords: oil-pressboard insulation; AC-DC combined voltage; mathematical model; breakdown characteristics

1. Introduction The converter transformer is one of the most important pieces of equipment in high-voltage direct current (HVDC) power transmission projects, as it is used for AC-DC voltage conversion. The reliable operation of the converter transformer is a prerequisite for the stability of the entire system [1,2]. Compared to the conventional AC transformers, the converter transformer can withstand not only the AC voltage, lightning impulse voltage, and operating overvoltage, but also AC-DC combined voltage, polarity reversal voltage, and other complex conditions [3–5]. The electric field distribution in the oil-pressboard insulation under an AC-DC combined electric field is more complicated than that under an AC electric field alone. Moreover, the breakdown strengths of the oil and pressboard are affected by the DC content, thus complicating the insulation design of converter transformers [6–8]. The breakdown voltage of a composite dielectric is mainly affected by the electric field distribution and breakdown strength of the dielectric [9,10]. The electric field distribution in oil-pressboard insulations has been extensively studied, mostly based on the resistance-capacitance model, under AC-DC combined voltage and polarity-reversed voltage [11–13]. In an experimental study, Li et al. Energies 2018, 11, 1319; doi:10.3390/en11051319

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used a plate electrode to study the effect of thickness on the breakdown strength of a pressboard under AC-DC combined voltage. The results showed that the breakdown strength of the pressboard increased with the increase in the thickness under both DC voltage and AC-DC combined voltage, whereas it decreased under the AC voltage [14–16]. Rajan et al. used the parallel plate, rod-plate, and ball-plate type electrodes to study the breakdown voltage of a multi-layer impregnated pressboard under AC-DC combined voltage and concluded that the breakdown voltage under AC-DC combined voltage was higher than that under DC voltage but lower than that under AC voltage. Moreover, the effect of electric field distortion on the DC breakdown voltage was not obvious, whereas that on the AC breakdown voltage was obvious [17,18]. Li et al. studied the effect of DC voltage superimposed with a high-frequency AC voltage (50–600 Hz) on the breakdown strength of a pressboard and concluded that the space charge accumulated in the sample increased with the increase in the frequency, thereby decreasing the breakdown strength of the pressboard [19]. Chi et al. studied the effect of oil flow on the breakdown characteristics of an oil-pressboard insulation under AC-DC combined voltage. The results showed that the breakdown voltage of the oil-pressboard insulation increased first and then decreased with the increase in the DC content, and the breakdown voltage decreased with the increase in the flow rate [20]. In summary, the breakdown characteristics of oil-pressboard insulations have been studied preliminarily; however, the mathematical expression and mechanism of breakdown characteristics have not been reported in detail. In this paper, a typical plate electrode structure was used to study the breakdown characteristics of an oil-pressboard insulation. The mathematical expression for the electric field distribution was obtained using the dielectric parameters of the oil and pressboard. Based on this, a mathematic model for the breakdown characteristics of the oil-pressboard insulation was established to explain the effect of AC-DC combined voltage on the breakdown characteristics of the oil-pressboard insulation. 2. Experimental Method 2.1. Sample Preparation and Test Model A pressboard with a thickness of 0.25 mm and with dimensions of 10 cm × 10 cm was used for the test. The pressboard was dried under vacuum and immersed in transformer oil placed in a vacuum container. Karamay 45# transformer oil was used for the oil-pressboard insulation. The oil was filtered using an oil filter to remove impurities such as moisture and gas. Table 1 lists the dielectric parameters and moisture contents of the pressboard and transformer oil at room temperature [21]. Table 1. Dielectric parameters and moisture content of pressboard and transformer oil. Parameters

Pressboard

Transformer Oil

Moisture content Resistivity Relative permittivity

0.43% 4.93 × 1014 Ω·m 3.22

6.3 mg/kg 1.15 × 1013 Ω·m 2.08

The main insulation of a large converter transformer is the barrel type structure, but its radius of curvature is large, so it is closer to a plate electrode in a small range. Hence, a plate electrode with an axisymmetric cylindrical structure is used to study the breakdown characteristics of the oil-pressboard insulation under AC-DC combined voltage, as shown in Figure 1.

Energies 2018, 11, 1319 Energies 2018, 11, x FOR PEER REVIEW Energies 2018, 11, x FOR PEER REVIEW

3 of 13 3 of 13 3 of 13 d=25mm d=25mm

High voltage electrode High voltage electrode

h1=15mm h1=15mm d1=0.25mm d1=0.25mm

d2=0.5mm d2=0.5mm

Transformer oil Transformer oil h2=15mm h2=15mm

Pressboard Pressboard

r=3mm r=3mm Ground electrode Ground electrode

Figure 1. 1. Test model. model. Figure Figure 1.Test Test model.

2.2. Test Test System 2.2. 2.2. TestSystem System The test system, system, comprising aa DC voltage power supply, an an AC voltage voltage power supply, a voltage The Thetest test system,comprising comprising aDC DCvoltage voltagepower powersupply, supply, anAC AC voltagepower powersupply, supply,aavoltage voltage divider, aa protective protective resistor(R (R2,, 30 30 kΩ/150 kV), a coupling capacitance capacitance (C3,, 0.01 0.01 μF/80 kV), filter divider, 2 2, 30kΩ/150 divider, a protectiveresistor resistor (R kΩ/150 kV), kV), aacoupling coupling capacitance(C (C3 3, 0.01µF/80 μF/80 kV), kV),filter filter capacitor (C 0, 0.5 μF/80 kV), voltage regulators, and high-voltage silicon stacks (D1, D2, 2 A/250 kV), capacitor (C , 0.5 µF/80 kV), voltage regulators, and high-voltage silicon stacks (D , D , 2 A/250 1 1, D 2 2, 2 A/250 kV), capacitor (C0 0, 0.5 μF/80 kV), voltage regulators, and high-voltage silicon stacks (D kV), can generate generate AC-DC AC-DC combined combined voltage, voltage, as as shown shown in in Figure Figure 2. 2. The rated power, output voltage voltage range can The rated power, output can generate AC-DC combined voltage, as shown in Figure 2. The rated power, output voltagerange range and rated rated frequency of of the voltage voltage regulators (T (T0, T1, T2) are V and 50 Hz, respectively. and are15 15kVA, kVA, 0–220 0–220 and ratedfrequency frequency ofthe the voltageregulators regulators (T0 0, ,TT11,, TT22)) are 15 kVA, 0–220 V V and and 50 50 Hz, Hz, respectively. respectively. The rated power, rated input/output voltage, rated output current and rated frequency of high The rated power, rated input/output voltage, rated output current and rated frequency of high The rated power, rated input/output voltage, rated output current and rated frequency voltage of high voltage test transformer (T 3, T4) are 15 kVA, 0.22/150 kV, 0.1 A and 50 Hz, respectively. The DC test transformer (T3 , T4 ) are 0.1 A kV, and 0.1 50 Hz, respectively. The DC content of voltage test transformer (T315 , TkVA, 4) are0.22/150 15 kVA, kV, 0.22/150 A and 50 Hz, respectively. The DC content of the AC-DCvoltage combined can be adjusted using regulators the voltageTregulators T1 and T2, and the AC-DC combined canvoltage be adjusted the voltage and T2 , and 1regulators content of the AC-DC combined voltage can using be adjusted using the voltage T1 the andvoltage T2, and the voltagecan amplitude can be adjusted using regulator the voltage amplitude be adjusted the voltage T0regulator .regulatorTT00. . the voltage amplitude canusing be adjusted using the voltage

T1 T1

T3 T3

C3 C3

R2 R2 sample sample

AC power supply AC power supply

T0 T0 AC AC 220V 220V

DC power supply DC power supply T2 T4 T2 T4

D2 D2

D1 D1

R1 R1

voltage divider voltage divider RH RH

CH CH

RL RL

CL CL

C1 C1

C0 C0

Figure 2. Test system. Figure2.2.Test Testsystem. system. Figure

Figure 3 shows the waveform of the AC-DC combined voltage. The DC content of the voltage is Figure 3 shows the waveform of the AC-DC combined voltage. The DC content of the voltage is expressed Figureas3 follows: shows the waveform of the AC-DC combined voltage. The DC content of the voltage is expressed as follows: expressed as follows: U  = UUdcdc  100% (1) +U dc  η = =U ac dc ×100% 100% (1) (1) Udc UacU+ ac +U dc whereUUacacisisthe the peak of AC the AC voltage component, Uaverage dc is the average the DC voltage where peak of the component, and Udcand is the the DC of voltage where Uac is the peak of thevoltage AC voltage component, and Udc is theofaverage of the component. DC voltage component. The nomenclature sectionthe including the symbols and used parameters in this paper are The nomenclature section including symbols and used parameters in this paper are in component. The nomenclature section including the symbols and used parameters in thisshown paper are shown in Table 2. Table 2. in Table 2. shown

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Voltage(kV) Voltage(kV)

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Uac Uac Udc Udc

0

Time(s)

0

Time(s)

Figure voltage. Figure3.3.Waveform Waveformof ofAC-DC AC-DC combined combined voltage. Figure 3. Waveform of AC-DC combined voltage. Table Table2.2.Nomenclature Nomenclature section. Table 2. Nomenclature Symbols Parameters section. Unit Symbols Parameters Unit ε r Relative permittivity Symbols Parameters Unit εr Relative permittivity ρ Resistivity Ω·m εr Relative permittivity ρ Resistivity d Thickness m Ω ·m ρ Resistivity Ω·m d Thickness m C Capacitance F d Thickness m C Capacitance F R Resistance Ω Capacitance F R CE Resistance Ω Electric field strengths kV/mm R Resistance Ω kV/mm E Electric field strengths kV/mm Eb Breakdown strength Electric field strengths Eb E Breakdown strength kV/mm kV/mm U Voltage V Breakdown strength kV/mm V U Eb Voltage η DC content U Voltage V η DC content η DC content -

3. Test Results 3. Test Results 3. Test Results Figure 4 shows the breakdown strength of the transformer oil under AC-DC combined voltage 4 shows the breakdown strength of the oil under AC-DCwith combined voltage at Figure room temperature. The breakdown strength of transformer the transformer decreases the increase in at Figure 4 shows the breakdown strength of the transformer oil oil under AC-DC combined voltage room temperature. The breakdown strength of the transformer oil decreases with the increase in theroom DC temperature. content. TheThe breakdown transformer oil oildecreases under pure voltage in isthe at breakdownstrength strengthofof the the transformer with DC the increase DCthe content. The breakdown strength of the transformer oil under pure DC voltage is approximately approximately 66.5% under pure AC voltage, probably due tooil impurities such as moisture DC content. Thethat breakdown strength of the transformer under pure DC voltageand is 66.5% that under pure AC voltage, probably due to impurities such as moisture and gas. With gas. With the increase in the DC content of the applied voltage, the impurities more easily polarize, approximately 66.5% that under pure AC voltage, probably due to impurities such as moisture andthe increase in the content of electrodes the the impurities more easily polarize, andpolarize, they align and With they align between tovoltage, form discharge channel. gas. theDC increase inthe the DCapplied content of theaapplied voltage, the impurities more easily between thealign electrodes tothe form a discharge channel. and they between electrodes to form a discharge channel. 50

strength(kV/mm) Breakdown strength(kV/mm) Breakdown

50 45

45 40

40 35

35

0

Test data Fitting curve Test data Fitting curve 20 40

80

100

0

20 DC content 40 of applied60voltage(%)80

100

30

30 25 25

60

DCofcontent of applied Figure 4. Breakdown strength transformer oilvoltage(%) under AC-DC combined voltage.

Figure 4. Breakdown strength of transformer oil under AC-DC combined voltage. Figure 4. Breakdown strength of transformer oil under AC-DC combined voltage.

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Figure 5 shows the breakdown strength of the pressboard under AC-DC combined voltage at 5 showsThe the breakdown under AC-DC combined voltage roomFigure temperature. breakdownstrength strengthofofthe thepressboard pressboard increases with the increase in at theroom DC temperature. The breakdown strength of the pressboard increases with the increase in the DC content content of the applied voltage, and the breakdown strength under pure AC voltage is only of the applied voltage, breakdown strength under AC voltagepressboard is only approximately 31.6% approximately 31.6% and that the under pure DC voltage. Thepure oil-immersed is composed of that under pure DC voltage. The oil-immersed pressboard is composed of cellulose, with transformer cellulose, with transformer oil gap between the cellulose. The electric field in the transformer oil oil gap between the cellulose. electric fieldbecause in the transformer increases with the decrease in increases with the decrease in The the DC content of its lower oil permittivity compared to that of the DC content because its lower permittivity compared thateasily of thelead pressboard. And its lower the pressboard. And its of lower breakdown strength, whichtocan to the transformer oil breakdown strength, which can easily lead to the transformer oil breakdown. Once the breakdown breakdown. Once the breakdown occurs in the oil gap, it will initiate the breakdown of the entire occurs in the oil gap, it will initiate the breakdown of the entire pressboard. pressboard.

Breakdown strength(kV/mm)

240 Experimental data Fitting curve

200

160

120

80

40

0

20

40

60

80

100

DC content of applied voltage(%)

Figure Figure 5. 5. Breakdown Breakdown strength strength of of pressboard pressboard under under AC-DC AC-DC combined combined voltage. voltage.

The fitted expressions can be derived through exponential fitting. Table 3 lists the fitted The fitted expressions can be derived through exponential fitting. Table 3 lists the fitted expressions and the correlation coefficients for the breakdown strength of the transformer oil and expressions and the correlation coefficients for the breakdown strength of the transformer oil pressboard. and pressboard. Table 3. Fitted Expressions for Breakdown Strength. Table 3. Fitted Expressions for Breakdown Strength. Medium Fitted Expression Correlation Coefficient Transformer oil Ebo = 48.24 − 0.65 × exp(3.22 × η) 0.98 Medium Fitted Expression Correlation Coefficient Pressboard Ebp = −18.39 + 86.45 × exp(1.04 × η) 0.97 Transformer oil Ebo = 48.24 − 0.65 × exp(3.22 × η) 0.98 Ebp = −18.39 + 86.45 × exp(1.04 × η) Pressboard 0.97

Figure 6 shows the breakdown voltage of the oil-pressboard insulation under AC-DC combined voltage at room temperature. The breakdown voltage of the oil-pressboard insulation increases first Figure 6 shows the breakdown voltage of the oil-pressboard insulation under AC-DC combined and then decreases with the increase in the DC content. The breakdown voltage reaches its peak at a voltage at room temperature. The breakdown voltage of the oil-pressboard insulation increases first DC content of 68%. and then decreases with the increase in the DC content. The breakdown voltage reaches its peak at a DC content of 68%. 80

Breakdown voltage(kV)

70 60 50 40 30 20 10 0

0

20

40

60

80


100

Pressboard

Ebp = −18.39 + 86.45 × exp(1.04 × η)

0.97

Figure 6 shows the breakdown voltage of the oil-pressboard insulation under AC-DC combined voltage at room temperature. The breakdown voltage of the oil-pressboard insulation increases first and then decreases at 13 a Energies 2018, 11, 1319 with the increase in the DC content. The breakdown voltage reaches its peak6 of DC content of 68%. 80

Breakdown voltage(kV)

70 60 50 40 30 20 10 0


0

20

40

60

80

100

6 of 13


Figure Figure6.6.Breakdown Breakdownvoltage voltageof ofoil-pressboard oil-pressboardinsulation insulationunder underAC-DC AC-DCcombined combinedvoltage. voltage.

4.4.Mathematical MathematicalModel Modelof ofBreakdown Breakdownof ofOil-Pressboard Oil-PressboardInsulation Insulation 4.1. 4.1.Simplified SimplifiedModel Model To To study study the theeffect effectof ofDC DCcontent contenton onthe theelectric electricfield fielddistribution distributionin inthe theoil-pressboard oil-pressboardinsulation insulation more directly, the oil-pressboard insulation model, shown in Figure 1, is simplified to a physical more directly, the oil-pressboard insulation model, shown in Figure 1, is simplified to a physical model model of the oil-pressboard insulation, asinshown 1 and 2, and d1 of the oil-pressboard insulation, as shown Figurein7. Figure Eo and 7. EpE, oε1and andEεp2, , ερ11and and ερ22, ,ρand d1 ρand d2 are and d2 are the electric-field strengths, relativeresistivity, permittivity, resistivity, ofand the the electric-field strengths, relative permittivity, and thicknesses the thicknesses transformer of oil and transformer and pressboard, respectively. pressboard, oil respectively.

U

Transformer oil

Eo ρ1  d1

Pressboard

Ep ρ2 2 d2

Figure Figure7.7.Physical Physicalmodel modelof ofoil-pressboard oil-pressboardinsulation. insulation.

Figure 8 shows the equivalent circuit model of the oil-pressboard insulation, where U is the Figure 8 shows the equivalent circuit model of the oil-pressboard insulation, where U is the applied voltage, U1 and U2, C1 and C2, and R1 and R2 are the equivalent voltages, capacitances, and applied voltage, U1 and U2 , C1 and C2 , and R1 and R2 are the equivalent voltages, capacitances, resistances of the transformer oil and pressboard, respectively [15]. and resistances of the transformer oil and pressboard, respectively [15].

U1

C1

R1

U2

C2

R2

U

Figure 7. Physical model of oil-pressboard insulation.

Figure 8 shows the equivalent circuit model of the oil-pressboard insulation, where U is the applied voltage, U1 and U2, C1 and C2, and R1 and R2 are the equivalent voltages, capacitances, and Energies 2018, 11, 7 of 13 resistances of 1319 the transformer oil and pressboard, respectively [15].

U1

C1

R1

U2

C2

R2

U

Figure 8. Equivalent circuit of oil-pressboard insulation. Figure 8. Equivalent circuit of oil-pressboard insulation.

4.2. Mathematical Expression of Electric Field Distribution 4.2. Mathematical Expression of Electric Field Distribution The AC electric field component of the AC-DC combined electric field is distributed by the The AC electric field component of the AC-DC combined electric field is distributed by the capacitances of the transformer oil and pressboard. The DC electric field component of the AC-DC capacitances of the transformer oil and pressboard. The DC electric field component of the AC-DC combined electric field is distributed by the capacitance when the voltage is just applied but it is combined electric field is distributed by the capacitance when the voltage is just applied but it is distributed by the resistance in the steady state. To simplify the analysis, the analysis is focused on distributed by the resistance in the steady state. To simplify the analysis, the analysis is focused on the electric field distribution in the steady state, and the electric field in the medium is assumed to the electric field distribution in the steady state, and the electric field in the medium is assumed to be be uniform. Because of the superposition of the electric field, the electric field strength (Eo ) in the uniform. Because of the superposition of the electric field, the electric field strength (Eo) in the transformer oil and the electric field strength (Ep ) in the pressboard can be obtained using E = U/d, as follows: ( ρ Eo = ρ d +1ρ d Udc + ε d ε+2 ε d Uac sin(ωt) 2 2 2 1 1 1 1 2 (2) ρ E p = ρ d +2ρ d Udc + ε d ε+1 ε d Uac sin(ωt) 1 1

2 2

2 1

1 2

The following equations are obtained by substituting Equation (1) into Equation (2): (

where A =

ρ1 ρ1 d1 + ρ2 d2 ,

B=

Eo = AηU + (1 − η ) BU sin(ωt) E p = CηU + (1 − η ) DU sin(ωt)

ε2 ε 2 d1 + ε 1 d2 ,

C=

ρ2 ρ1 d1 + ρ2 d2

and D =

(3)

ε1 ε 2 d1 + ε 1 d2 .

As shown in Equation (3), Eo and Ep are mainly affected by the parameters of A and C when η is high, whereas they are mainly affected by the parameters of B and D when η is low. This indicates that the electric field distribution is significantly affected by the resistivity when the DC content is high and by the relative permittivity when the DC content is low. The breakdown of insulating material is mainly affected by the maximum value of the voltage waveform. Hence, the peak voltage (i.e., sin(wt) = 1) is chosen to analyze the electric field distribution in the oil-pressboard insulation, which can be obtained using Equation (3), as follows: (

Eo = BU + ( A − B)ηU E p = DU + (C − D )ηU

(4)

The electric field in oil and pressboard calculated by Equation (3) varies with time, while the result of Equation (4) calculation is its maximum value. Using Equation (4), the electric field distribution in the oil-pressboard insulation with different DC contents is simulated under a voltage of 10 kV. Figure 9 shows the simulation results. As shown in Figure 9, the electric field strength of the transformer oil decreases with the increase in the DC content, whereas that of the pressboard increases. As listed in Table 1, ρ1 = 0.023ρ2 , ε1 = 0.646ε2 , and d1 = 2d2 , which makes A = 0.088 mm−1 , B = 1.51 mm−1 , C = 3.82 mm−1 and D = 0.98 mm−1 . Hence, A − B < 0 and C − D > 0 in Equation (4). Thus, Eo decreases and Ep increases with the increase

that the electric field distribution is significantly affected by the resistivity when the DC content is high and by the relative permittivity when the DC content is low. The breakdown of insulating material is mainly affected by the maximum value of the voltage waveform. Hence, the peak voltage (i.e., sin(wt) = 1) is chosen to analyze the electric field distribution in the oil-pressboard insulation, Energies 2018, 11, 1319 8 of 13 which can be obtained using Equation (3), as follows:

 Eo = BU + ( A − B)U

in the DC content when the peak voltage is the same. The DC contents of the transformer oil (η o ) and (4) + (C − D)U  E p =DU(4), pressboard (η p ) can be obtained using Equation shown as follows:

The electric field in oil and pressboard calculated ( Aη by Equation (3) varies with time, while the ηo = Aη + B(value. 1− η ) result of Equation (4) calculation is its maximum Using Equation (4), the electric field (5) Cη = Cηdifferent distribution in the oil-pressboard insulationη pwith DC contents is simulated under a voltage + D (1− η ) of 10 kV. Figure 9 shows the simulation results.

Electric field strength(kV/mm)

40 35 30 25 20 Transformer oil Impregnated pressboard

15 10


8 of 13

5

in the DC content when the peak voltage is the same. The DC contents of the transformer oil (ηo) and 0 pressboard (ηp) can be obtained using as follows: 80 0 20 Equation40(4), shown60 100 DCcontent of applied voltage (%) A

o =

A +strengths B (1- ) of transformer oil and pressboard.  Figure 9. Simulation field Figure 9. Simulation results results of of the the electric electric field strengths of transformer oil and pressboard. (5) 

C  = p C + of D (the 1- )transformer oil decreases with the increase As shown in Figure 9, the electric field strength Figure 10 shows the DC contents of the transformer oil and pressboard of the oil-pressboard in the DC content, whereas that of the pressboard increases. As listed in Table 1, ρ1 = 0.023ρ2, ε1 = 10different shows theDC DCcontents contents of of the transformer oil andThe pressboard of the of oil-pressboard insulationFigure under applied voltage. DC contents the transformer 0.646ε2, and d1 = 2d2, which makes A = 0.088 mm−1, B = 1.51 mm−1, C = 3.82 mm−1 and D = 0.98 mm−1. insulation under different DC contents of the applied voltage. The DC contents of the transformer oil DC oil and pressboard are the same as that of the applied voltage when the applied voltage is pure Hence, Apressboard − B < 0 and C the − Dsame > 0 inasEquation (4). Thus,voltage Eo decreases andapplied Ep increases with the DC increase and are that of the applied when the voltage is pure voltage or pure AC voltage. In other cases, the DC content of the transformer oil is lower than that or pure AC voltage. In other cases, the DC content of the transformer oil is lower than that of of thevoltage applied voltage, whereas the DC content of the pressboard is higher than that of the applied the applied voltage, whereas the DC content of the pressboard is higher than that of the applied voltage. As the resistivity of the pressboard is significantly greater than that of the transformer oil, voltage. As the resistivity of the pressboard is significantly greater than that of the transformer oil, the DC voltage component of the applied voltage is mainly applied to the pressboard. As a result, the DC voltage component of the applied voltage is mainly applied to the pressboard. As a result, the the DC of the thepressboard pressboardincreases increases of transformer the transformer oil decreases. DCcontent content of andand thatthat of the oil decreases. 100

DC content of medium(%)

ηo ηp

80

η

60

40

20

0

0

20

40

60

80

100

DC content of applied voltage (%) Figure 10. DC contents of transformer oil and pressboard.

Figure 10. DC contents of transformer oil and pressboard.

As ηo and ηp are different from η, the ηo and ηp corresponding to the breakdown strength are different from the η corresponding to the breakdown strength. By substituting Equation (5) into the fitting expression of the breakdown strength, listed in Table 3, the breakdown strengths of the transformer oil and pressboard of the composite insulation (Ebo′ and Ebp′) corresponding to the DC content of the applied voltage can be obtained as follows:

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As η o and η p are different from η, the η o and η p corresponding to the breakdown strength are different from the η corresponding to the breakdown strength. By substituting Equation (5) into the fitting expression of the breakdown strength, listed in Table 3, the breakdown strengths of the transformer oil and pressboard of the composite insulation (Ebo 0 and Ebp 0 ) corresponding to the DC content of the applied voltage can be obtained as follows: (

Ebo 0 (η ) = Ebo (ηo ) Ebp 0 (η ) = Ebp η p

(6)

50

250

48

230

46

210

44

190

42

170

40

150

38

130

36

Ebo′

110

34

Ebp′

90

32

Breakdown field strength(kV/mm)

Breakdown strength(kV/mm)

Figure 11a,b show the breakdown strengths (Ebo 0 and Ebp 0 ) corresponding to the DC content of the applied voltage and the breakdown strengths (Ebo and Ebp ) corresponding to the DC content of the medium, respectively. Ebo 0 is greater than Ebo , and Ebp 0 is greater than Ebp when the DC content is the same. Figure 10 shows that η o is lower than η, whereas η p is higher than η. The test results show that Ebo decreases and Ebp increases with the increase in the DC content; therefore, Ebo (η o ) is greater than Ebo (η), and Ebp (η p ) is greater than Ebp (η). According to Equation (5), Ebo 0 (η) is greater than Ebo (η), and Ebp 0 (η) is greater than Ebp (η). Thus, the breakdown strength corresponding to the DC content of the applied voltage is greater than that corresponding to the DC content of the medium when the DC Energies 11, same. x FOR PEER REVIEW 9 of 13 content2018, is the

70

30

50 0

20

40

60

80

100


250

48

230

46

210

44

190

42

170

40

150

38

130

36

110

34

Ebo

90

32

Ebp

70

30



(a) 50

50 0

20

40

60

80

100

DC content of medium(%)

(b) Figure 11. Breakdown strengths of transformer oil and pressboard in composite insulation. Figure 11. Breakdown strengths of transformer oil and pressboard in composite insulation. (a) (a) Breakdown strength corresponding to the DC content of applied voltage; (b) Breakdown strength Breakdown strength corresponding to the DC content of applied voltage; (b) Breakdown strength corresponding to the DC content of medium. corresponding to the DC content of medium.

4.3. Mathematical Model of Breakdown Voltage of Oil-Pressboard Insulation The breakdown voltages (Uo-ca and Up-ca) of the oil-pressboard insulation are calculated on the basis of the breakdown strengths and electric field distributions of the transformer oil and pressboard of the composite insulation. They can be expressed as follows by substituting Equation (6) into Equation (4).

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4.3. Mathematical Model of Breakdown Voltage of Oil-Pressboard Insulation The breakdown voltages (Uo-ca and Up-ca ) of the oil-pressboard insulation are calculated on the basis of the breakdown strengths and electric field distributions of the transformer oil and pressboard of the composite insulation. They can be expressed as follows by substituting Equation (6) into Equation (4). The results calculated by substituting Equation (6) into Equation (4) is the minimum value of the results calculated by substituting Equation (6) into Equation (3):   Uo-ca =  U p-ca =

Ebo 0 (η ) B+( A− B)η Ebp 0 (η ) C +(C − D )η

(7)

When the oil-pressboard insulation breaks down, either the transformer oil or the pressboard breaks down first. The voltage will then be applied to the other medium completely, and the DC content of the other medium becomes the DC content of the applied voltage. When the applied voltage is higher than the breakdown voltage of the other medium, the composite insulation will break down. When the applied voltage is lower than the breakdown voltage of the other medium, the breakdown voltage of the composite insulation becomes the breakdown voltage of the other medium. Thus, the voltage calculated using Equation (7) must be compared with the breakdown voltages of the pure transformer oil and pure pressboard. Ubo and Ubp are the breakdown voltages of the pure transformer oil and pure pressboard, respectively, expressed as follows: (

Ubo = Ebo (η )d1 Ubp = Ebp (η )d2

(8)

The calculated breakdown voltage of the oil-pressboard insulation is Ub , which is related to Uo-ca , Up-ca , Ubo , and Ubp . The relationship between them can be expressed as follows: h i Ub = max min Uo-ca , U p-ca , Ubo , Ubp

(9)

Figure 12 shows the variations in Ub , Uo-ca , Up-ca , Ubo , and Ubp under different DC contents of the applied voltage. The green-solid line represents the calculated breakdown voltage of the oil-pressboard insulation. The figure shows that Uo-ca is lower than Up-ca when the DC content is low, whereas Uo-ca is greater than Up-ca when the DC content is high. This indicates that the transformer oil will break down first if the DC content is low, and the pressboard will break down first if the DC content is high. Ubo and Ubp are lower than Uo-ca and Up-ca under different DC contents. This indicates that the other medium will break down immediately after any one of the mediums in the composite insulation breaks down first. As shown in Figure 12, Ub is Uo-ca when the DC content is in the range of 0–59%, and it increases with the increase in the DC content. Ub is Up-ca when the DC content is in the range of 60–100%, and it decreases with the increase in the DC content. The above analysis shows that Uo-ca and Up-ca are affected by their breakdown strengths and electric field distributions; however, their variation rates with respect to the DC content are different. The breakdown strength and electric field strength of the transformer oil decrease with the increase in the DC content, but the former decreases slower than the latter. This increases Uo-ca with the increase in the DC content. The breakdown strength and electric field strength of the pressboard increase with the increase in the DC content, but the former increases slower than the latter. This decreases Up-ca with the increase in the DC content. Thus, the breakdown voltage of the oil-pressboard insulation increases first and then decreases with the increase in the DC content.

the transformer oil decrease with the increase in the DC content, but the former decreases slower than the latter. This increases Uo-ca with the increase in the DC content. The breakdown strength and electric field strength of the pressboard increase with the increase in the DC content, but the former increases slower than the latter. This decreases Up-ca with the increase in the DC content. Thus, the breakdown voltage of the oil-pressboard insulation increases first and then decreases with the increase in the DC Energies 2018, 11, 1319 11 of 13 content. 150

Breakdown voltage（kV）

Uo-ca Up-ca

120

Ubo Ubp Ub

90

60

30

0

0

20

40

60

80

100

DC content of applied voltage (%) Figure thethe breakdown voltage of oil-pressboard insulation under different DC Figure 12. 12. Calculation Calculationof of breakdown voltage of oil-pressboard insulation under different contents. DC contents.

Figure 13 shows the test and calculation results of the breakdown voltage of the oil-pressboard Figure 13 shows the test and calculation results of the breakdown voltage of the oil-pressboard insulation. The trends in the test and calculation results are the same. The numerical difference is insulation. The trends the test and calculation results are the same. The numerical difference is Energies 2018, 11, x FOR PEERin REVIEW 11 of 13 insignificant (the correlation coefficient between them is 0.963). This shows that the mathematical insignificant (the correlation coefficient between them is 0.963). This shows that the mathematical model proposed proposed in in this this paper can well describe the breakdown characteristics characteristics of of an oil-pressboard model insulation under AC-DC combined voltage. 80

Breakdown voltage（kV）

70 60 50 40 30 20 Test results Calculation results

10 0

0

20

40

60

80

100

DC content of applied voltage(%) Figure Figure 13. 13. Comparison Comparison of of test test and and calculation calculation results results of of oil-pressboard oil-pressboard insulation insulation breakdown. breakdown.

5. 5. Conclusions Conclusions In study, aabreakdown breakdowntest testwas wasconducted conductedonon oil-pressboard insulation under ACIn this this study, anan oil-pressboard insulation under thethe AC-DC DC combined voltage. A mathematical expression for the electric field distribution was then combined voltage. A mathematical expression for the electric field distribution was then established to established to analyze the changes in the electric field distribution and DC content. Finally, a analyze the changes in the electric field distribution and DC content. Finally, a mathematic model for mathematic model for the oil-pressboard insulation breakdown was proposed. The following are the the oil-pressboard insulation breakdown was proposed. The following are the main conclusions of main conclusions of this study: this study: (1) With the increase in the DC content of the applied voltage, the breakdown strength of the transformer oil decreases, whereas that of the pressboard increases. Moreover, the breakdown voltage of the oil-pressboard insulation increases first and then decreases. (2) With the increase in the DC content of the applied voltage, the electric field strength of the transformer oil decreases, whereas that of the pressboard increases.

Energies 2018, 11, 1319

(1)

(2) (3)

(4)

(5)

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With the increase in the DC content of the applied voltage, the breakdown strength of the transformer oil decreases, whereas that of the pressboard increases. Moreover, the breakdown voltage of the oil-pressboard insulation increases first and then decreases. With the increase in the DC content of the applied voltage, the electric field strength of the transformer oil decreases, whereas that of the pressboard increases. Under AC-DC combined voltage, the DC content of the pressboard is higher than that of the applied voltage, whereas the DC content of the transformer is lower than that of the applied voltage. When the DC content is same, the breakdown strength corresponding to the DC contents of the transformer oil and pressboard of the composite insulation is lower than that corresponding to the DC content of the applied voltage. The breakdown voltage calculated by the proposed model is in good agreement with the experimental results.

Author Contributions: Q.C. and J.Z. conceived and designed the experiments; C.G. performed the experiments; J.Z. and M.C. analyzed the data; J.Z. wrote the paper. Funding: This research was funded by the Project Supported by the National Key Research and Development Program of China (No. 2017YFB0902704), the National Natural Science Foundation of China (No. 51677046) and the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (No. UNPYSCT-2016159). Conflicts of Interest: The authors declare no conflict of interest.

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