- Email: [email protected]
Investigation of polymer composites interfacing pressurized airflow
Electric Power Systems Research 77 (2007) 1118–1123
Investigation of polymer composites interfacing pressurized airflow I.A. Metwally ∗ Department of Electrical & Computer Engineering, College of Engineering, Sultan Qaboos University, P.O. 33, Al-Khod, Muscat 123, Oman Received 6 March 2006; accepted 17 September 2006 Available online 24 October 2006
Abstract This paper aims to characterize the polymer composites interfacing flowing air as a simulation of those used in large forced-gas cooled rotating machines and modern power transformers. Many factors have been investigated in order to show their effects on the current–voltage (I–V) characteristics. The results reveal that the air conditions play an important role in the I–V characteristics of polymer/flowing air/polymer gaps. The conduction current of such gaps increases with the increases in air-flow rate and temperature but it decreases with the increase in air pressure; especially at high temperature. It is also found that there is no significant effect of the combined-crossed ac magnetic field on the conduction current. Phenomenological explanations of the air–polymer–metal interfaces are introduced in the core of physicochemical reactions and injection processes. In addition, derivation of the dependence of volume charge density inside the test section on flow velocity is introduced, which interprets the trend of the experimental results. © 2006 Elsevier B.V. All rights reserved. Keywords: Polymer composites; Pressurized airflow; Conduction current; Space charge density; Combined-crossed ac magnetic field
1. Introduction Generally, large forced-gas cooled rotating electric machines incorporate different gas flow schemes depending on their ratings. Turbogenerators up to 50 MW adopt forced air-cooled in single- or double-ventilation system. Also, large capacity transformers with nonflammable coolant such as perfluorocarbon and the insulation composed of the coolant and SF6 gas have been recently developed with ratings up to 275 kV and 250 MVA [1]. For such complex arrangements, the forced coolant (air, hydrogen or SF6 ) is in direct contact with the solid insulation. Due to the increased demand of electrical power, the trend of the capacity and voltage ratings of electric machines and converters increases with reliable design. Polymers are often the best and most economic electrical insulating construction materials [2]. However, widespread applications of polymers, polymer composites and polymer coatings in many fields are the result of recent advances in modern technologies. Such composites are frequently used in the field of insulation of electric machines to overcome the drawbacks of an individual polymer [2]. In this
∗
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paper important factors are investigated to show their effects on the I–V characteristics of polymer/flowing air/polymer gaps under HVdc to simulate the dc machines, converters, and the dc potential building up inside HVac machines. 2. Experimental apparatus Fig. 1 shows the test rig arrangement. A controlled reciprocating air-compressor is used to compress the air in a 375 l main reservoir. An aluminum coaxial cylinder system (CCS) (axial length/outer diameter/inner diameter are 264/24/22 mm and 240/50/46 mm for the inner and outer cylinders, respectively) is used as the active part in the cycle; where both cylinders are fixed coaxially. Table 1 gives the details of the commercial solid insulating materials used. Two similar sheets of these insulating composites are fixed as a single layer on both the inner surface of the outer cylinder and the outer surface of the inner cylinder, where each one has 210 mm axial length. The conduction current (I) is measured from the inner aluminum cylinder via KeithleyTM 610 C electrometer. The pressure (P) and temperature (T) at the inlet of the CCS are also monitored. Calibrated rotameter and relative-humidity meters are also used to measure the mass-flow rate (Q), and relative humidity (RH), respectively. In order to discharge the polymer in the CCS after the application
I.A. Metwally / Electric Power Systems Research 77 (2007) 1118–1123
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Fig. 1. Test rig arrangement.
Table 1 Details of the polymer composites Number
Nominal thickness (m)
1 2 3 4
200 220 200 200
± ± ± ±
15% 15% 15% 15%
Film thickness (m)
Insulation class
Dielectric strength (kV) minimum
100 100 25 25
F F, ≤180 ◦ C C, ≤200 ◦ C C, ≤200 ◦ C
≥10 ≥12 ≥8 ≥7
of the dc voltage, a HVac of 5 kV (rms) is applied between tests to produce high concentration of bipolar ions, and hence neutralizing any concentration of monopolar surface charge. An axial ac magnetic field (H) was orthogonally applied to the existing radial dc electric field (E) via using a coaxial solenoid. Repeatability is checked by conducting all the experimental runs three times. All the samples used (1, 2, 3 and 4) are commercial polymer composites, and they, respectively, consist of PET (polyester) non-woven + PET film + PET non-woven with resin impregnation on both sides, Nomex (aramide paper) + PET film + Nomex, calendered Nomex + Kapton (polyimide) film + calendered Nomex, and fine glass fabric + Kapton film + fine glass fabric.
surface of the chemisorbed reactants, (4) desorption of the product, and (5) diffusion of products away from the surface. Usually, the diffusion steps in (1) and (5) are very fast and are rarely rate determining [3]. Second, consider a polymer, having a relative permittivity εr , directly contacts with a metal. Assuming a continuous distribution of trap levels in the bandgap of the polymer, where Dv is the trap density per unit energy per volume. Such trapping sites exit in semicrystalline polymers at the interfaces between the amorphous and crystalline phases [4]. Hence, the total surface charge density ρs at the interface is given by [2] ρs =
εo εr Dv (φm − φp )
where φm and φp are the work function of the metal and polymer, respectively. Hence, for a given electrode material, Eq. (1) indicates that ρs increases with εr , but it decreases with φp . Third, when a polymer (p) brought in direct contact with an energized metal (M), modification and reduction of the potential barrier occurs. Hence, both electrons and holes can be injected into the polymer, depending on its energy levels [2]. Such processes can be represented by the following ionic equation at the cathode (e.g.) as M− + p → M + p −
3. Phenomenological explanations of air–polymer–metal interfaces First, heterogeneous physicochemical reactions at polymer–air interface have the following five consecutive of steps [3]: (1) diffusion of reactants to the surface, (2) adsorption of the reactants on the surface, (3) reaction at the
(1)
(2)
Localized surface states of polymers are those not forming extended bandlike states. They can be envisioned associated with at least the following on a molecular level [2]: (1) surface states induced by strain or chemical reactions and (2) surface dipole states. In the absence of the above mentioned surface states, the injection processes for holes and electrons can be represented
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by [2] φp − (φm + Ei ) ≤ 0
(3)
φm − (Ea + Ei ) ≤ 0
(4)
where Et and Ea are the energy required to cross the potential barrier at the electrode–polymer interface and the electron affinity, respectively. 4. Dependence of space charge density on flow velocity
ρv (r, z) εo
(6)
∇ · J = 0
(7)
J = ρv (r, z)U
(8)
where ρv (r, z) is the space charge density, J the current density is the ion velocity vector. The latter for r1 ≤ r ≤ r2 vector, and U is defined by = u ar + v az = μEr a r + A(r − r1 ) az U
(9)
where a r and a z are the unit vectors in the r- and z-coordinates, respectively and A is the laminar velocity constant. Assuming the mobility of ions (μ) is constant and independent of their life time. In addition, the space charge is assumed to affect only the magnitude not the direction of the electric field [6]. The electric is related to space field in the presence of space charge (E) 1 ) by [6] charge-free field (E = λE 1 E
(10)
where λ is the field enhancement factor (scalar point function of E 1 | ≈ dV/dV1 . Where these the space coordinates) and λ = |E/ fields are as = −∇V ≈ − E
dV dr
and
1 = −∇V1 ≈ − E
dV1 dr
= ∇ · (λE 1) = E 1 · ∇λ = ∇ ·E
ρv (r, z) εo
(12)
or Eq. (12) can be reduced to dλ ρv (r, z) = dr εo E1r
(13)
From Eqs. (8) and (9) in Eq. (7), yields
The space charge density at any point (r, z) inside the CCS (of radii r1 and r2 ) was derived in [5] as τJg 1+n r − r1 1 − exp − z exp − (5) ρv (r, z) = δ 2Aτδ δ √ where δ = τD = the Debye length, τ = εo /σ = permittivity of free space/air conductivity, D is the ionic diffusion coefficient, n = r2 /r1 , and Jg is the generated charge density at the electrode surface. Also, it is presumed by the analysis of the electroaerodynamics phenomenon results solely from the interactions of unipolar charge injection from the surface of each electrode surface which in contact with air, and not by dissociation of impurities in the bulk. In the steady state, the system of equations describing the ionized field in the flowing air condition is, respectively, given by Poisson’s, continuity and current density equations as = ∇ ·E
where r is the distance measured along ion trajectory line (flux 1 = 0, and line) of the space charge. In the steady state ∇ · E Poisson’s equation yields
(11)
E1r
d d (μλρv (r, z)) + (vρv (r, z)) = 0 dr dz
(14)
Assuming a uniform axial flow velocity distribution dv/dz = 0 which is unaffected by the presence of the electric field. Hence, the dependence of space charge density on axial flow velocity in the presence of space charge is given by ε0 E1r μλ dμ 1+n ρv (r, z) = v (15) −λ − μ δ dr 2AτδE1r Eq. (15) interprets the increase in the conduction current with increasing mass-flow rate “flow velocity” (as shown in Figs. 4 and 6), where the space charge density decreases with flow velocity. 5. Experimental results The carrier injection from an electrode into the polymer bulk causes the variation of the current density as a function of temperature (T) and electric field (E) as [2] √ − β E φ m J = AT 2 exp − (16) kT where A is a constant independent of E, φm , the work function of the cathode, β a constant depends on the high frequency relative permittivity,√and k the Boltzmann constant. Plots of log (J) as a function of E show reasonable straight lines as given in Fig. 2 for all samples at T = 22 ◦ C. This test is done for the polymer composites alone between two parallel plates. From Figs. 3–6, the tests are done using the CCS. Fig. 3(a) shows that there is no dependence of the current (I) on air pressure (P) for different voltage levels and at 20 ◦ C, while raising the temperature to 50 ◦ C shows a decrease of the current when increasing air pressure. This is due to the fact that the mean free path is directly proportional to temperature and inversely to the gas pressure [7]. Fig. 4 indicates that negative voltage application to the outer cylinder of the CCS gives higher current. This is attributed to the increased electron emission when the outer cylinder is negatively charged. The higher the air flow rate, the higher is the current for both polarities, √ see Eq. (15). A linear relationship is observed for the I − Vdc curves up √ to Vdc = 2.5. For further increase in the applied dc voltage, a knee appears due to the fact that the space charge decreases slightly.
I.A. Metwally / Electric Power Systems Research 77 (2007) 1118–1123
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Fig. 2. J–E curves of the test samples at T = 22 ◦ C.
Fig. 4. I–V curves for sample 1 at RH = 20 ± 0.5%, r = 22 ◦ C and P = 300 kPa.
Fig. 5 illustrates that the current increases with temperature for all samples used. This is because of the field-dependent lowering of the potential barrier for thermionic injection. This trend can be also explained by Eq. (16). From the comparison between Figs. 2 and 5, it is obviously seen that the
flowing air conditions significantly affect the resultant conduction current in such gaps. In addition, this is because of space charge or a different mechanism of charge generation due to physicochemical reactions at flowing air/polymer interfaces, trap density, and injection process as given in Section 3. Fig. 6 shows the dependence of the current on the massflow rate (Q). It can be seen that for all samples, the current increases with mass-flow rate. This trend can be explained by Eq. (15). The increase in air-flow rate reduces the space charges and hence their field is reduced. This leads to the enhancement of the original field [8–11]. However, such charges lead to an opposing field; hence the resultant field is reduced. Therefore, it is expected that higher degradation rates of such polymer occur inside the machines at narrow ducts. Other results have shown that the application of the axial ac magnetic field (H) orthogonal to the existing radial dc electric field (E) via using a coaxial solenoid has no significant effect on the conduction current between the cylindrical electrodes.
Fig. 3. Dependence of I on P for sample 1 at Q = 2 g/s, RH = 19 ± 0.5%. (a) T = 20 ◦ C; (b) T = 50 ◦ C.
Fig. 5. I–V curves at Q = 2.62 g/s and P = 300 kPa.
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shown a linear relation between the current density and the square root of the applied electric field. • Higher degradation rates of polymer composites in contact with flowing gas can occur at high flow rate and temperature, and/or at low pressure. • The dependency of the current and the current density versus the applied voltage on the temperature and the gas flow rate has been correlated to the derived formula. • There is no significant effect of the combined-crossed E- and H-fields on conduction current. Acknowledgments The author wishes to acknowledge his indebtedness to both August Krempel Soehne GmbH & Co. (Germany) for providing the insulating samples, and Prof. Markus Zahn (Laboratory for Electromagnetic and Electronic Systems, MIT, USA) for his valuable discussions. References [1] K. Hiraishi, et al., Development and practical operation of perfluorocarbon immersed 275 kV transformers with SF6 gas insulation, IEEE Trans. PWRD 10 (2) (1995) 880–888. [2] D.A. Seanor, Electrical Properties of Polymers, Academic Press Inc., New York, USA, 1982. [3] G.W. Castellan, Physical Chemistry, third ed., Addison-Wesley Publishing Company Inc., Massachusetts, USA, 1983, Chapter 34. [4] M. Ieda, Electrical conduction and carrier traps in polymeric materials, IEEE Trans. Elect. Insul. 19 (2) (1984) 162–178. [5] I.A. Metwally, Flow electrification of transformer oil: effects of mixed fields, IEEE Trans. Dielect. Elect. Insul. 5 (4) (1998) 518–526. [6] M. Abdel-Salam, et al., Monopolar corona on bundle conductors, IEEE Trans. Power Appl. Syst. 101 (10) (1982) 4079–4089. [7] E. Kuffel, W.S. Zaengl, High Voltage Engineering: Fundamentals, First ed., Pergamon Press, 1984. [8] I.A. Metwally, A.A. A-Rahim, Flow electrification phenomenon in forced air-cooled rotating electric machines, IEEE Trans. Dielect. Elect. Insul. 5 (6) (1998) 966–971. [9] H. Janssen, J.M. Seifert, H.C. Karner, Interfacial phenomena in composite high voltage insulation, IEEE Trans. Dielect. Elect. Insul. 6 (5) (1999) 651–659. [10] G. Chen, Y. Tanaka, T. Takada, L. Zhong, Effect of polyethylene interface on space charge formation, IEEE Trans. Dielect. Elect. Insul. 11 (1) (2004) 113–121. [11] A.A.O. Tay, Y. Ma, T. Nakamura, S.H. Ong, A numerical and experimental study of delamination of polymer–metal interfaces in plastic packages at solder reflow temperatures, in: The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, ITHERM ’04, vol. 2, 1–4 June 2004, pp. 245–252. Fig. 6. I–V curves at RH = 21 ± 0.5%; T = 22 ◦ C and P = 300 kPa. (a) Sample 2; (b) sample 3; (c) sample 4.
6. Conclusions • A derived formula for the dependence of space charge density on air/gas flow velocity is introduced. • Nomex and PET based composites give lower current density than that of the glass-fiber based one, where all samples have
Ibrahim A. Metwally (IEEE M’93–SM’04) was born in 1963. He received the B. Eng. degree in electrical engineering (Hons.), the M. Eng. degree in high-voltage engineering, and the Ph.D. degree in high-voltage engineering from Mansoura University (MU), Mansoura, Egypt, in 1986, 1990, and 1994, respectively. The Ph.D. degree was received in collaboration with Cardiff University, Cardiff, UK. He is currently a Full Professor with the Department of Electrical Engineering, MU. He has been seconded to the Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, Muscat, Oman, as an Associate Professor since August 2002. From 2000 to 2002 and in the summers of 2003, 2004 and 2006, he joined
I.A. Metwally / Electric Power Systems Research 77 (2007) 1118–1123 the University of the Federal Armed Forces, Munich, Germany, as a Visiting Professor. His areas of research include oil- and gas-flow electrification in both electric power apparatus and pipelines, measurements of fast impulse voltages and currents, line insulators and zinc-oxide surge arresters, coronas on overhead transmission lines, impulse voltage characterization and modeling of electrical machines, particle-initiated breakdown in gas-insulated switchgear (GIS) and gas-insulated transmission lines (GITL), power quality, stray-current corrosion in the oil industry, and hazards of lightning strikes to buildings, overhead power lines, and aircrafts. Prof. Metwally is a Fellow of the Alexander von Humboldt (AvH) Foundation, Bonn, Germany, a Senior Member in the Institute of
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Electrical and Electronics Engineers (IEEE) and a Member of the International Electrotechnical Commission (IEC). He has published 90 papers, where about half of them in highly reputed international journals. He was awarded both the First Rank of the State Prize in Engineering Sciences in 1998 and 2004, and the Late Prof. Dr.-Ing. M. Khalifa’s Prize in Electrical Engineering in 1999 and 2005 from the Egyptian Academy of Scientific Research and Technology. His biographical profile was published in Who’s Who in Science and Engineering in 2001. (Mansoura University, P.O. Box 17, Mansoura 35516, Egypt. Tel.: +4989 60043940 or +2050 2244105 Ext. 1259/1411, fax: +2050 2244690, E-mail addresses: [email protected] or [email protected].)
Investigation of polymer composites interfacing pressurized airflow I.A. Metwally ∗ Department of Electrical & Computer Engineering, College of Engineering, Sultan Qaboos University, P.O. 33, Al-Khod, Muscat 123, Oman Received 6 March 2006; accepted 17 September 2006 Available online 24 October 2006
Abstract This paper aims to characterize the polymer composites interfacing flowing air as a simulation of those used in large forced-gas cooled rotating machines and modern power transformers. Many factors have been investigated in order to show their effects on the current–voltage (I–V) characteristics. The results reveal that the air conditions play an important role in the I–V characteristics of polymer/flowing air/polymer gaps. The conduction current of such gaps increases with the increases in air-flow rate and temperature but it decreases with the increase in air pressure; especially at high temperature. It is also found that there is no significant effect of the combined-crossed ac magnetic field on the conduction current. Phenomenological explanations of the air–polymer–metal interfaces are introduced in the core of physicochemical reactions and injection processes. In addition, derivation of the dependence of volume charge density inside the test section on flow velocity is introduced, which interprets the trend of the experimental results. © 2006 Elsevier B.V. All rights reserved. Keywords: Polymer composites; Pressurized airflow; Conduction current; Space charge density; Combined-crossed ac magnetic field
1. Introduction Generally, large forced-gas cooled rotating electric machines incorporate different gas flow schemes depending on their ratings. Turbogenerators up to 50 MW adopt forced air-cooled in single- or double-ventilation system. Also, large capacity transformers with nonflammable coolant such as perfluorocarbon and the insulation composed of the coolant and SF6 gas have been recently developed with ratings up to 275 kV and 250 MVA [1]. For such complex arrangements, the forced coolant (air, hydrogen or SF6 ) is in direct contact with the solid insulation. Due to the increased demand of electrical power, the trend of the capacity and voltage ratings of electric machines and converters increases with reliable design. Polymers are often the best and most economic electrical insulating construction materials [2]. However, widespread applications of polymers, polymer composites and polymer coatings in many fields are the result of recent advances in modern technologies. Such composites are frequently used in the field of insulation of electric machines to overcome the drawbacks of an individual polymer [2]. In this
∗
Tel.: +968 24142532; fax: +968 24413454. E-mail address: [email protected].
0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.09.008
paper important factors are investigated to show their effects on the I–V characteristics of polymer/flowing air/polymer gaps under HVdc to simulate the dc machines, converters, and the dc potential building up inside HVac machines. 2. Experimental apparatus Fig. 1 shows the test rig arrangement. A controlled reciprocating air-compressor is used to compress the air in a 375 l main reservoir. An aluminum coaxial cylinder system (CCS) (axial length/outer diameter/inner diameter are 264/24/22 mm and 240/50/46 mm for the inner and outer cylinders, respectively) is used as the active part in the cycle; where both cylinders are fixed coaxially. Table 1 gives the details of the commercial solid insulating materials used. Two similar sheets of these insulating composites are fixed as a single layer on both the inner surface of the outer cylinder and the outer surface of the inner cylinder, where each one has 210 mm axial length. The conduction current (I) is measured from the inner aluminum cylinder via KeithleyTM 610 C electrometer. The pressure (P) and temperature (T) at the inlet of the CCS are also monitored. Calibrated rotameter and relative-humidity meters are also used to measure the mass-flow rate (Q), and relative humidity (RH), respectively. In order to discharge the polymer in the CCS after the application
I.A. Metwally / Electric Power Systems Research 77 (2007) 1118–1123
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Fig. 1. Test rig arrangement.
Table 1 Details of the polymer composites Number
Nominal thickness (m)
1 2 3 4
200 220 200 200
± ± ± ±
15% 15% 15% 15%
Film thickness (m)
Insulation class
Dielectric strength (kV) minimum
100 100 25 25
F F, ≤180 ◦ C C, ≤200 ◦ C C, ≤200 ◦ C
≥10 ≥12 ≥8 ≥7
of the dc voltage, a HVac of 5 kV (rms) is applied between tests to produce high concentration of bipolar ions, and hence neutralizing any concentration of monopolar surface charge. An axial ac magnetic field (H) was orthogonally applied to the existing radial dc electric field (E) via using a coaxial solenoid. Repeatability is checked by conducting all the experimental runs three times. All the samples used (1, 2, 3 and 4) are commercial polymer composites, and they, respectively, consist of PET (polyester) non-woven + PET film + PET non-woven with resin impregnation on both sides, Nomex (aramide paper) + PET film + Nomex, calendered Nomex + Kapton (polyimide) film + calendered Nomex, and fine glass fabric + Kapton film + fine glass fabric.
surface of the chemisorbed reactants, (4) desorption of the product, and (5) diffusion of products away from the surface. Usually, the diffusion steps in (1) and (5) are very fast and are rarely rate determining [3]. Second, consider a polymer, having a relative permittivity εr , directly contacts with a metal. Assuming a continuous distribution of trap levels in the bandgap of the polymer, where Dv is the trap density per unit energy per volume. Such trapping sites exit in semicrystalline polymers at the interfaces between the amorphous and crystalline phases [4]. Hence, the total surface charge density ρs at the interface is given by [2] ρs =
εo εr Dv (φm − φp )
where φm and φp are the work function of the metal and polymer, respectively. Hence, for a given electrode material, Eq. (1) indicates that ρs increases with εr , but it decreases with φp . Third, when a polymer (p) brought in direct contact with an energized metal (M), modification and reduction of the potential barrier occurs. Hence, both electrons and holes can be injected into the polymer, depending on its energy levels [2]. Such processes can be represented by the following ionic equation at the cathode (e.g.) as M− + p → M + p −
3. Phenomenological explanations of air–polymer–metal interfaces First, heterogeneous physicochemical reactions at polymer–air interface have the following five consecutive of steps [3]: (1) diffusion of reactants to the surface, (2) adsorption of the reactants on the surface, (3) reaction at the
(1)
(2)
Localized surface states of polymers are those not forming extended bandlike states. They can be envisioned associated with at least the following on a molecular level [2]: (1) surface states induced by strain or chemical reactions and (2) surface dipole states. In the absence of the above mentioned surface states, the injection processes for holes and electrons can be represented
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by [2] φp − (φm + Ei ) ≤ 0
(3)
φm − (Ea + Ei ) ≤ 0
(4)
where Et and Ea are the energy required to cross the potential barrier at the electrode–polymer interface and the electron affinity, respectively. 4. Dependence of space charge density on flow velocity
ρv (r, z) εo
(6)
∇ · J = 0
(7)
J = ρv (r, z)U
(8)
where ρv (r, z) is the space charge density, J the current density is the ion velocity vector. The latter for r1 ≤ r ≤ r2 vector, and U is defined by = u ar + v az = μEr a r + A(r − r1 ) az U
(9)
where a r and a z are the unit vectors in the r- and z-coordinates, respectively and A is the laminar velocity constant. Assuming the mobility of ions (μ) is constant and independent of their life time. In addition, the space charge is assumed to affect only the magnitude not the direction of the electric field [6]. The electric is related to space field in the presence of space charge (E) 1 ) by [6] charge-free field (E = λE 1 E
(10)
where λ is the field enhancement factor (scalar point function of E 1 | ≈ dV/dV1 . Where these the space coordinates) and λ = |E/ fields are as = −∇V ≈ − E
dV dr
and
1 = −∇V1 ≈ − E
dV1 dr
= ∇ · (λE 1) = E 1 · ∇λ = ∇ ·E
ρv (r, z) εo
(12)
or Eq. (12) can be reduced to dλ ρv (r, z) = dr εo E1r
(13)
From Eqs. (8) and (9) in Eq. (7), yields
The space charge density at any point (r, z) inside the CCS (of radii r1 and r2 ) was derived in [5] as τJg 1+n r − r1 1 − exp − z exp − (5) ρv (r, z) = δ 2Aτδ δ √ where δ = τD = the Debye length, τ = εo /σ = permittivity of free space/air conductivity, D is the ionic diffusion coefficient, n = r2 /r1 , and Jg is the generated charge density at the electrode surface. Also, it is presumed by the analysis of the electroaerodynamics phenomenon results solely from the interactions of unipolar charge injection from the surface of each electrode surface which in contact with air, and not by dissociation of impurities in the bulk. In the steady state, the system of equations describing the ionized field in the flowing air condition is, respectively, given by Poisson’s, continuity and current density equations as = ∇ ·E
where r is the distance measured along ion trajectory line (flux 1 = 0, and line) of the space charge. In the steady state ∇ · E Poisson’s equation yields
(11)
E1r
d d (μλρv (r, z)) + (vρv (r, z)) = 0 dr dz
(14)
Assuming a uniform axial flow velocity distribution dv/dz = 0 which is unaffected by the presence of the electric field. Hence, the dependence of space charge density on axial flow velocity in the presence of space charge is given by ε0 E1r μλ dμ 1+n ρv (r, z) = v (15) −λ − μ δ dr 2AτδE1r Eq. (15) interprets the increase in the conduction current with increasing mass-flow rate “flow velocity” (as shown in Figs. 4 and 6), where the space charge density decreases with flow velocity. 5. Experimental results The carrier injection from an electrode into the polymer bulk causes the variation of the current density as a function of temperature (T) and electric field (E) as [2] √ − β E φ m J = AT 2 exp − (16) kT where A is a constant independent of E, φm , the work function of the cathode, β a constant depends on the high frequency relative permittivity,√and k the Boltzmann constant. Plots of log (J) as a function of E show reasonable straight lines as given in Fig. 2 for all samples at T = 22 ◦ C. This test is done for the polymer composites alone between two parallel plates. From Figs. 3–6, the tests are done using the CCS. Fig. 3(a) shows that there is no dependence of the current (I) on air pressure (P) for different voltage levels and at 20 ◦ C, while raising the temperature to 50 ◦ C shows a decrease of the current when increasing air pressure. This is due to the fact that the mean free path is directly proportional to temperature and inversely to the gas pressure [7]. Fig. 4 indicates that negative voltage application to the outer cylinder of the CCS gives higher current. This is attributed to the increased electron emission when the outer cylinder is negatively charged. The higher the air flow rate, the higher is the current for both polarities, √ see Eq. (15). A linear relationship is observed for the I − Vdc curves up √ to Vdc = 2.5. For further increase in the applied dc voltage, a knee appears due to the fact that the space charge decreases slightly.
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Fig. 2. J–E curves of the test samples at T = 22 ◦ C.
Fig. 4. I–V curves for sample 1 at RH = 20 ± 0.5%, r = 22 ◦ C and P = 300 kPa.
Fig. 5 illustrates that the current increases with temperature for all samples used. This is because of the field-dependent lowering of the potential barrier for thermionic injection. This trend can be also explained by Eq. (16). From the comparison between Figs. 2 and 5, it is obviously seen that the
flowing air conditions significantly affect the resultant conduction current in such gaps. In addition, this is because of space charge or a different mechanism of charge generation due to physicochemical reactions at flowing air/polymer interfaces, trap density, and injection process as given in Section 3. Fig. 6 shows the dependence of the current on the massflow rate (Q). It can be seen that for all samples, the current increases with mass-flow rate. This trend can be explained by Eq. (15). The increase in air-flow rate reduces the space charges and hence their field is reduced. This leads to the enhancement of the original field [8–11]. However, such charges lead to an opposing field; hence the resultant field is reduced. Therefore, it is expected that higher degradation rates of such polymer occur inside the machines at narrow ducts. Other results have shown that the application of the axial ac magnetic field (H) orthogonal to the existing radial dc electric field (E) via using a coaxial solenoid has no significant effect on the conduction current between the cylindrical electrodes.
Fig. 3. Dependence of I on P for sample 1 at Q = 2 g/s, RH = 19 ± 0.5%. (a) T = 20 ◦ C; (b) T = 50 ◦ C.
Fig. 5. I–V curves at Q = 2.62 g/s and P = 300 kPa.
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shown a linear relation between the current density and the square root of the applied electric field. • Higher degradation rates of polymer composites in contact with flowing gas can occur at high flow rate and temperature, and/or at low pressure. • The dependency of the current and the current density versus the applied voltage on the temperature and the gas flow rate has been correlated to the derived formula. • There is no significant effect of the combined-crossed E- and H-fields on conduction current. Acknowledgments The author wishes to acknowledge his indebtedness to both August Krempel Soehne GmbH & Co. (Germany) for providing the insulating samples, and Prof. Markus Zahn (Laboratory for Electromagnetic and Electronic Systems, MIT, USA) for his valuable discussions. References [1] K. Hiraishi, et al., Development and practical operation of perfluorocarbon immersed 275 kV transformers with SF6 gas insulation, IEEE Trans. PWRD 10 (2) (1995) 880–888. [2] D.A. Seanor, Electrical Properties of Polymers, Academic Press Inc., New York, USA, 1982. [3] G.W. Castellan, Physical Chemistry, third ed., Addison-Wesley Publishing Company Inc., Massachusetts, USA, 1983, Chapter 34. [4] M. Ieda, Electrical conduction and carrier traps in polymeric materials, IEEE Trans. Elect. Insul. 19 (2) (1984) 162–178. [5] I.A. Metwally, Flow electrification of transformer oil: effects of mixed fields, IEEE Trans. Dielect. Elect. Insul. 5 (4) (1998) 518–526. [6] M. Abdel-Salam, et al., Monopolar corona on bundle conductors, IEEE Trans. Power Appl. Syst. 101 (10) (1982) 4079–4089. [7] E. Kuffel, W.S. Zaengl, High Voltage Engineering: Fundamentals, First ed., Pergamon Press, 1984. [8] I.A. Metwally, A.A. A-Rahim, Flow electrification phenomenon in forced air-cooled rotating electric machines, IEEE Trans. Dielect. Elect. Insul. 5 (6) (1998) 966–971. [9] H. Janssen, J.M. Seifert, H.C. Karner, Interfacial phenomena in composite high voltage insulation, IEEE Trans. Dielect. Elect. Insul. 6 (5) (1999) 651–659. [10] G. Chen, Y. Tanaka, T. Takada, L. Zhong, Effect of polyethylene interface on space charge formation, IEEE Trans. Dielect. Elect. Insul. 11 (1) (2004) 113–121. [11] A.A.O. Tay, Y. Ma, T. Nakamura, S.H. Ong, A numerical and experimental study of delamination of polymer–metal interfaces in plastic packages at solder reflow temperatures, in: The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, ITHERM ’04, vol. 2, 1–4 June 2004, pp. 245–252. Fig. 6. I–V curves at RH = 21 ± 0.5%; T = 22 ◦ C and P = 300 kPa. (a) Sample 2; (b) sample 3; (c) sample 4.
6. Conclusions • A derived formula for the dependence of space charge density on air/gas flow velocity is introduced. • Nomex and PET based composites give lower current density than that of the glass-fiber based one, where all samples have
Ibrahim A. Metwally (IEEE M’93–SM’04) was born in 1963. He received the B. Eng. degree in electrical engineering (Hons.), the M. Eng. degree in high-voltage engineering, and the Ph.D. degree in high-voltage engineering from Mansoura University (MU), Mansoura, Egypt, in 1986, 1990, and 1994, respectively. The Ph.D. degree was received in collaboration with Cardiff University, Cardiff, UK. He is currently a Full Professor with the Department of Electrical Engineering, MU. He has been seconded to the Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, Muscat, Oman, as an Associate Professor since August 2002. From 2000 to 2002 and in the summers of 2003, 2004 and 2006, he joined
I.A. Metwally / Electric Power Systems Research 77 (2007) 1118–1123 the University of the Federal Armed Forces, Munich, Germany, as a Visiting Professor. His areas of research include oil- and gas-flow electrification in both electric power apparatus and pipelines, measurements of fast impulse voltages and currents, line insulators and zinc-oxide surge arresters, coronas on overhead transmission lines, impulse voltage characterization and modeling of electrical machines, particle-initiated breakdown in gas-insulated switchgear (GIS) and gas-insulated transmission lines (GITL), power quality, stray-current corrosion in the oil industry, and hazards of lightning strikes to buildings, overhead power lines, and aircrafts. Prof. Metwally is a Fellow of the Alexander von Humboldt (AvH) Foundation, Bonn, Germany, a Senior Member in the Institute of
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Electrical and Electronics Engineers (IEEE) and a Member of the International Electrotechnical Commission (IEC). He has published 90 papers, where about half of them in highly reputed international journals. He was awarded both the First Rank of the State Prize in Engineering Sciences in 1998 and 2004, and the Late Prof. Dr.-Ing. M. Khalifa’s Prize in Electrical Engineering in 1999 and 2005 from the Egyptian Academy of Scientific Research and Technology. His biographical profile was published in Who’s Who in Science and Engineering in 2001. (Mansoura University, P.O. Box 17, Mansoura 35516, Egypt. Tel.: +4989 60043940 or +2050 2244105 Ext. 1259/1411, fax: +2050 2244690, E-mail addresses: [email protected] or [email protected].)