COMPATIBILITY OF INSULATING MATERIALS IN INSULATING SYSTEM THE PHYSICS AND ENGINEERING Arijit Basuray NEO TELE-TRONIX PVT. LTD.(NTPL), Kolkata email:
[email protected] [email protected] Abstract: Compatibility of Insulating material in an insulation system always draws attention to high voltage engineers and designer of electrical machines and components. The compatibility is best understood when we understand the basic physical phenomenon related to this. Since the problem of compatibility is principally due to dielectric mismatch of different insulating materials and the electric field applied to the insulating system a designer or a practicing electrical engineer should have a clear idea of these parameters. Here the author tried to describe the whole thing in a quantum mechanical and field theoretic approach in a lucid way. Starting with an introduction to the basics of dielectrics and electrical field author tried to explain how the quantum and thermo dynamical state of composite insulating material within the bulk as well as in the interfaces between solid liquid or gaseous dielectric respond to the applied electric field with a brief account of electric conduction and breakdown in solid dielectric. Author described some practical insulating system and discussed the phenomenon of partial discharge related to incompatibility in insulation system. Keywords:
capacitors, switchgears, cables, high frequency transformers for power electronics and many other electrical applications. Attributes those make proper design of Insulation system difficult are but not limited to • Electric field distribution, • Parameters related to the insulation material (Quantum mechanical thermodynamical & Dielectric), • Interfaces between different dielectric materials, • Nature of voltage ie, Direct alternating and impulse voltage, • Change in field due to discharge development. Within this short span of the paper we cannot discuss in details on all these, rather our objectives are to approach gradually to different aspects of designing of Insulation system. Interface the basics: To start with, let us consider a simple configuration of interface of two different insulating materials confined between two electrodes parallel to each other.
Dielectric, Interface, Insulation, Conduction, Polaron, Electric field, Cast Resin, Partial Discharge. Introduction: For the last few decades we witnessed a lot of changes in the field of insulating materials. Synthetic polymeric insulation are gradually taking large share and electrical insulation system (EIS) in present scenario are playing an ever more important role in the manufacture of transformers, motors,
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Fig. 1 We know D = εE ……………………(1) where E= Electric Field ε= absolute permittivity
D= Displacement vector
1 V d d1 ⎛ ε 2 ⎞ ⎜⎜ − 1⎟⎟ + 1 d ⎝ ε1 ⎠ ……………..………………………… (4) =
ε 1 E1 = D1 = D2 = D = ε 2 E2 Basic assumption here is that D1 and D2 are equal considering that the conductivity of the insulating materials is regulated under AC field and hence no free charges are built up at the interface between the two layers.
∴ ε 1 E1 = ε 2 E 2 or
E1 ε 2 = E2 ε1 ……………………………… (2)
ε orE2 = 1 .E1 ε2
Now let the voltage applied across the electrodes be V, then
V = E1 d 1 + E 2 d 2 = E1 d 1 +
ε1 E1 d 2 ε2
=
Since ε 2 > ε 1 ,
Partially replacement of the gas with solid dielectric material does not improve the dielectric strength of oil or gas insulated system as the stress within the gas will then be even more than the original system.
⎞ ⎟⎟ ⎠
V deff ……………………………… (3)
Let us look at some practical situation where interfaces of dielectrics of different permittivity are obvious. Conductor
Where effective value of d is ⎛ε ⎞ deff = d 1 + d 2 ⎜⎜ 1 ⎟⎟ ⎝ε2 ⎠
+ + + + + + + + Layered Film Insulation
ε E Similarly E 2 d 2 + 2 2 d1 = V ε1 Or E 2 =
V d2 +
ε2 d1 ε1
ε1 < 1 hence deff < d ε2
layer with higher permittivity is increased.
V ⎛ε d 1 + d 2 ⎜⎜ 1 ⎝ ε2
The effective gap distance may be written as ⎛ε ⎞ deff = d 1 + d 2 ⎜⎜ 1 ⎟⎟. ⎝ε2 ⎠
d , ε 1 , ε 2 being constant for V 1 the field stress E 1 will always increase if the thickness of
Or
E1 =
The above equation reveals some essential effect. If the dielectric materials say gas of permittivity ε 1 between two electrodes is partially replaced by a material of higher permittivity under uniform electric field the effective gap of the gas decreases according to equation (3).
=
Gaseous Dielectric Oil/ Solid polymeric Insulation
+ + + + + + + +
(a) : Winding layers of Transformer
V ⎛ d2
ε 2 ⎜⎜
⎝ε2
+
d1 ⎞ ⎟ ε 1 ⎟⎠
V 1 d ε 2 ⎛ d1 d − d1 ⎞ ⎜ + ⎟ d ⎜⎝ ε 1 ε 2 ⎟⎠ V 1 = d 1 ⎛ d 1ε 2 + dε 1 − d 1ε 1 ⎞ ⎜ ⎟⎟ d ⎜⎝ ε1 ⎠ =
(b) : Motor winding within the core slot Fig. 2
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Mixed Dielectric:
We get
Now we will discuss about the mixed dielectric in dispersed mixture, a very know form of which is “Filled cast resin”. Primarily we can consider the Electric Field averaged over volumes which are large compared with the scale of the in homogeneities. The mixture is considered to be homogeneous and isotropic medium with respect to such an average field and so may be characterised by an effective permittivity εm. If Em and Dm be the field and Displacement vector averaged in this way we can write by definition
Dm = εmEm ………………………………. (5) If all the components of the mixture are isotropic and have little differences in their
permittivity it is possible to calculate εm in general form which is correct as far as terms of the second order in these differences. If We consider local field as E = Em + δE , the local ε
m
permittivity
as
ε
m
+ δε
where
( v )∫ ε dv …………………………..
= 1
(6)
obtained by averaging over the volume( v), We can write
Dm = (εm + δε)(Em + δE) ....……………. (7)
Since by definition mean value of δε and
ε mix = ε1 + 3cε1 (ε 2 − ε1 ) /(ε 2 + 2ε1 )
where c is the volume concentration of the emulsion. We must remember that the particles are in an external field which equals the mean field E . But in reality for a Resin Filler mixture the concentration of Filler is not small for many reason and are not perfectly spherical about which we will discuss in the latter part. Now if the mixture is heterogeneous the things become more complicated and in reality the dielectric substances what we use in Insulation system are heterogeneous and disordered. To evaluate a close effective permittivity extensive tensor based mathematical model then may be followed. Great physicist like Maxwell, Rayleigh, Wagner, Fröhlich, Landau and Lifshitz have proposed different models. It is hard or even impossible to describe this in a short span, rather in few words. We can hardly peep into the situation. Let us consider that inhomogeneous dielectric mixture fill the space between two parallel plate electrodes, then we can write.
ε eff = C C where C and Co are capacitance o in the presence and absence of any matter between the plates respectably. Considering the gap as small and neglecting any fringing effect because of the in-homogeneities, the charge density α on the plates will vary from one point to another.
δE are zero, we can write Dm = εmEm + δεδE
and in the zero order approximation εm
=ε .
First non zero correction term will be of the second order in δε as we see from equation (7). To get the exact derivation of permittivity of the mixture, making of further approximation is required where we assume……………… i)
Emulsion has an arbitrary difference between the permittivity ε 1 of the medium and ε 2 of the disperse phase.
ii)
Only a small concentration of the l particles exists in the emulsion and are assumed to be spherical.
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(a) : In-homogeneous structure of Insulation
Conduction under field:
(b) : Filter particle in Polymer composite Fig. 3 It is interesting to note that while discussing the field distribution for parallel dielectric slab we considered that there is no horizontal direction of field and hence flow. But at high field because of inhomogeneity we cannot consider this valid every where in the material. This is well manifested by the treeing phenomenon under repetitive application of high field described under. The progressive breakdown path is purely fractal in nature. Though it is extremely difficult to provide a realistic mathematical model yet here I am tempted to indicate a correlation of type of fractal growth with order, nature of the in homogeneity of the dielectric and Electric field.
From quantum mechanical considerations it is well understood that the intrinsic breakdown voltage for a pure solid dielectric should be very high as the band gap between valance band and conduction band is very high but in reality it is very difficult to get a pure dielectric without an impurity, vacant lattice positions, interstetials etc. on the normal lattice field. The conductivity of dielectric may be either ionic or electronic or both. It may be of extreme difficulty to separate these component experimentally, particularly at high electric field. The basic theoretical expression for all electrical conductivity is α =
∑n e μ i i
i
…………………. (8)
i
ni → density of carriers of the ith species ei → charge
μi → mobilities Taking thermodynamical consideration and results obtained from experiment one can write σ = σ 0 exp (− φ / K 0 T ) ……………………(9), σ and φ are obtained by experiment and T the absolute temperature.
At low field the conductivity can be described as (a) Trap controlled band conduction – This is due to excitation of electrons into the non localised levels of the conduction states or from non-localised levels of the valance states resulting in electron or hole current.
(a) : Treeing in Progress
Long back H Fröhlich proposed a model for amorphous dielectric which can be used to calculate the temperature dependence of trap controlled band conduction.
(b) : Treeing Fig. 4
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Fig. 5 In the energy level diagram (Fig.5), it is seen that D levels lies below the conduction level(C) by an amount of
2W >> ΔV
as, σ = c(1− c )
e2 R K0T
p where
p Transition probability between
Considering the electrons in C, S & D level being sufficiently numerous and in thermal equilibrium amongst themselves at a temperature say Teq where KoTeq
