A New Concentration Detection System for SF 6 /N 2 Mixture Gas in Extra/Ultra High Voltage Power Transmission Systems

TL;DR: In this paper, the authors developed a new detection system for the first time to detect the gas concentrations of the SF6/N2 mixture in extra/ultra-high voltage power transmission systems.

Abstract: This paper develops a new detection system, for the first time, to detect the gas concentrations of the SF6/N2 mixture in extra/ultra-high voltage power transmission systems. The concentrations of SF6 and N2 are calculated from the thermal conductivity function of the mixture gas. The main contribution of this work is that a specially-designed thermostatic chamber with adaptive temperature controller is developed to ensure constant pressure of the gas flowed through the thermal conductivity sensor. Another contribution is the combination of multiple sensors (e.g. humidity and electrochemical sensors), which enables the detector to address the penetration effects of H2O and O2 in the SF6/N2 mixture. Experimental evaluation results using the prototype demonstrated that satisfactory accuracy (±1% of the measurement error) has been achieved for the concentration detection of the SF6/N2 mixture under variable operation conditions. Compared with existing detection techniques, the proposed detector not only can detect the SF6/N2 concentration by taking the air infiltration effect into account, but also reduce the cost.

Summary

1.1.1 Defining our Terms

• The authors begin by defining all the terms in the title of the thesis.
• A surface is K3 if it is nonsingular, simply-connected and has trivial canonical bundle.

1.1.2 The Picard Lattice

• The Picard Group Pic(S) is the group of isomorphism classes of line bundles on S. For K3 surfaces, this is equivalent to the group of linear equivalence classes of divisors (linear combinations of curves) on the surface.
• One way to distinguish K3 surfaces is to examine sublattices of H2(S, Z).
• So computing Pic(S) is essentially computing which 2-cycles are represented by algebraic curves.
• In general, it is a difficult and interesting problem to compute Pic(S) for a random surface.

1.1.3 Fibrations

• It happens that most of the surfaces the authors will examine in this thesis have elliptic fibrations.
• The authors often refer to irreducible fibres and components of reducible fibre as ‘vertical’ curves.
• A multisection, or n-section, intersects each general fibre at n points.
• In Figure 1.1, Pic(S) is roughly the group of different kinds of curves on the surface.
• While I have just defined Pic(S) for nonsingular surfaces, the theory extends to surfaces with A−D − E singularities as well.

1.1.4 Resolving Singularities

• One way that the authors obtain reducible fibres is from desingularizing a surface.
• The intuitive way to desingularize an object, e.g. for a cusp or node, is to embed the object into a larger-dimensional ambient space so one can “untwist” it in some sense.
• In particular, the authors examine an open subset U around a singular point x = xi, and consequently U × Pn−1.

1.1.5 Objects of Study

• Here, the authors examine all families of K3 surfaces which occur as Gorenstein hypersurfaces in weighted projective 4-space.
• The authors restrict their attention to a hyperplane of the weighted projective space, i.e. a 3-fold, so their hypersurface is of a three-fold, which is a surface.

1.2 History of the Problem

• In 1974, V.I. Arnold listed 14 surface singularities (called “exceptional unimodal critical points”).
• A. Gabrielov calculated the homology of the Milnor Lattice of vanishing cycles for each of these surface singularities.
• Pinkham, Dolgachev, and Nikulin explained this “strange duality” in the late 1970s, using the theory of K3 surfaces.
• Now, Calabi-Yau threefolds are the three-dimensional analogue of K3 surfaces; both have canonical class equivalent to 0.
• The quick answer to this is that many do, but not all.

1.3.1 Mirror Symmetry for Threefolds

• Before the authors answer the main question, they need to discuss the definition of mirror families.
• The authors will begin by thinking about Calabi-Yau threefolds for a moment.
• In the original definition of mirror symmetry, one of the properties that determines when threefolds X and X ′ are mirrors is the following relationship between the Hodge numbers: h1,1(X) = h2,1(X ′), h1,1(X ′) = h2,1(X).
• This property is equivalent to rotating the Hodge Diamond 90◦ counterclockwise and getting the same values back; in other words, the authors are setting the rank of Pic(X), which is h1,1, equal to the dimension of the moduli space (the tangent space to the space of deformations), which is h2,1.

1.3.2 Facts About K3 Surfaces

• Let us examine the Hodge Diamond for K3 surfaces.
• The Hodge Diamond is invariant under rotation 90◦ counterclockwise.
• In particular, both Pic(S) and the tangent space to the space of deformations lie within H1,1, which suggests that the authors will want to look at its structure when defining their analogous mirror symmetry.

1.3.3 Definition of Mirror Symmetry for K3 Surfaces

• To define Mirror Symmetry, the authors will analyze H2. Pic(S), the group of linear equivalence classes of Cartier divisors, injects into H2(S, Z) for K3 surfaces [BPV, p.241].
• Thus, there is no torsion in the image of Pic(S) in H2(S, Z), so the authors may consider Pic(S) as a lattice, and call it the Picard lattice.

1.4 Calculating ρ(S)

• In 1979, M. Reid classified and listed all families of weighted projective Gorenstein K3-hypersurfaces, but he never published this list.
• The degree of the generic surface is the weight of a variable times its degree in the equation.
• Because c is just the multiplication in R, it is an isomorphism because R0 is generated by 1.
• It is clear that these are independent by examining their intersections with each other.

1.5 Somewhat of an Aside: Lattices

• This section summarizes general background on lattices.
• The authors define a lattice as a pair (L, b) where L is a finite-rank free Z-module and b is a Z-valued nondegenerate symmetric bilinear form.
• The discriminant of a lattice is the determinant of the matrix of the associated bilinear form.

1.5.1 The Kodaira Classification of Fibres

• Later the authors will be searching for elliptic fibrations of their K3 surfaces.
• Good references for proof of this classification are [BPV] and [Miranda].
• On the graphs, each vertex represents a curve and each edge represents an intersection between two curves.
• A label on a vertex corresponds to the multiplicity of that curve in the fibre.
• Some of these fibres will never occur on their 95 surfaces; K3 surfaces do not have multiple fibres [BPV], so the authors will never see an mIn.

1.5.2 Dynkin Diagrams

• The graphs in Table 1.2 are the extended Dynkin diagrams.
• There are also “plain” Dynkin diagrams, some of which are presented in Table 1.3; a good reference for these is [Humphreys].
• Entry aij = 1 if curves i and j intersect (if there’s an edge between vertices i and j) and aij = 0 if curves i and j do not intersect (if there is no edge between vertices i and j).
• Set the diagonal entries aii = −2 because that is the self-intersection of each curve.
• The incidence matrix is symmetric and nondegenerate, and so represents the bilinear form for a lattice associated to each Dynkin Diagram.

Classification of the Forms

• The authors will define three classes of forms on GL: w p,k, uk, vk.
• A quadratic residue is denoted (a p ) and this notation is called the Jacobi-Legendre symbol.
• For 2 = 1 the authors choose a to be the smallest positive even number with a quadratic residue; for 2 = −1 they choose a to be the smallest positive even number without a quadratic residue.

Notions of Isomorphism

• 5.3.3 Theorem (i) Every nontrivial, nondegenerate irreducible quadratic form on a finite abelian group is isomorphic to one of uk, vk, w p,k. (ii) Every nondegenerate quadratic form on a finite abelian group is isomorphic to an orthogonal direct sum of uk, vk, w p,k. (iii) This representation of a quadratic form is not unique.
• Of course, there are also isomorphism relations which arise from these relations.

Orthogonality and Mirrors

• There are three contexts in which the authors use orthogonality.
• The authors determine −q(M) by multiplying the value of q on each element of GM by −1, and then determining what form this set of values corresponds to.
• In practice.

1.6 Computing Desingularization Graphs

• Generally, the authors use the toric description of each hypersurface to desingularize it, and use this desingularization to find an elliptic fibration.
• When the computer desingularizes the hypersurface, it outputs a graph which depicts each component of a resolved singularity and each face as a vertex, and intersections between them as edges.
• The authors now have a lattice, of the same rank as Pic(S), generated by curves on the surface, and which is certainly a sublattice of Pic(S).
• I will describe the process by which the authors obtain the desingularization graph.

1.6.1 The Toric Description

• The field of toric varieties is a way to use combinatorial language to describe algebraic varieties.
• Usually a toric variety is described by polyhedral cones or polytopes in Zn, where each lattice point in the object corresponds to a monomial in the coordinate ring of an affine piece (in the gluing sense) of the algebraic variety.
• Excellent references for basic information on toric varieties are [Fulton] and [Danilov].

Our Objects

• All of the 95 hypersurfaces are Gorenstein, i.e. they have the property that deg(S) = s; this comes from the adjunction formula in weighted projective space (see [Dolg3]).
• The authors wish to take the convex hull of all integral points of this rational polytope in order to view the associated hypersurface as a toric variety.
• 22 First, however, notice that the condition ∑ qixi = s means that the rational polytope lies in a hyperplane of R4.
• After transforming the rational polytope to R3, keeping the internal lattice fixed, the authors take the convex hull of all integral points, hereafter referred to as the Newton polytope.
• Many of the combinatorial features of the polytope correspond to geometric aspects of the hypersurface.

1.6.2 Desingularizing Hypersurfaces

• The desingularization of S is simplified because, as the authors show in this section, all singularities of S lie on the edges of the polytope.
• Almost all equations in the family of hypersurfaces are nondegenerate with respect to the Newton Polytope [Khovanskĭı, § 2].
• Whether this curve is singular or not is immaterial to whether there are singularities of S. Case 3 – Edges.
• To obtain the Newton polytope, the authors use the program Qhull from the Geometry Center.
• Qhull is designed to enumerate extremal points of a polytope, but it generally sacrifices accuracy for speed.

1.7 Forming Elliptic Fibrations

• An elliptic fibration is a regular map π : S → B from their surface S to some base curve B, such that the general fibre π−1(b) is an elliptic curve.
• Thus, we’ll be looking for subgraphs in the output of the Mathematica program which are isomorphic to graphs of fibres from Table 1.2 (very few of the curves in the graphs which the authors obtain from the surfaces have genus 1).
• The remaining aspect of forming fibrations is this: if the authors decompose the graph into subgraphs such that one of these subgraphs corresponds to an Extended Dynkin Diagram with a curve deleted, they may add that curve to complete the fibre.
• The only fibres which conform to these constraints are Ãn; each component is of multiplicity one.

1.7.1 The Mordell-Weil group of sections

• A section crosses each fibre once, so if the authors restrict all the sections to the generic fibre, they can consider the rational points they obtain as a group, 27 using the group law for elliptic curves.
• If the authors take the closure of these points to form sections again, they can see this group as formed by the sections themselves (not just the points).
• The authors call this the Mordell-Weil group of sections (or MW ); if there exists at least one singular fibre, then MW is a finitely-generated abelian group [Miranda, p. 69].

1.7.2 The Shioda-Tate Formula

• The Shioda-Tate formula is useful for analyzing possible elliptic fibrations.
• S → B b an elliptic fibration of a nonsingular model of S, and let ρ be the rank of Pic(S), also known as Let f.
• Most of the time the authors will find a fibration which shows that rk(MW ) = 0, i.e. MW is finite.
• Also, Pictors(S) is trivial because K3s are simply-connected.

1.8.1 “Obvious” Elliptic Fibrations

• An Elliptic Fibration with a Genus 1 Curve Figure 1.6 is number 65.
• The authors have a general fibre (curve 3) which intersects a section, and a 17-component reducible fibre.
• In order for disc(Pic(S)) to be an integer, the only possibility is that |MW |2 = 4, indicating that there are exactly two sections and that disc(Pic(S)) =.

An Example of an Elliptic Fibration with no Genus 1 Curve

• Again, the authors have not yet determined Pic(S) but they will see what to do soon.
• The authors have chosen to notice that they have two copies of Ẽ8; they view curve 3 as a 2-section and curve 10 as a section.

1.8.3 Intermediate Lattice Calculations

• This technique deals with the problems the authors had with numbers 65 and 52 above.
• Find all qL-isotropic subgroups of GL, also known as Step 1.
• The authors must also retain the original form on the first two copies of Z2 (w −1 2,1 ⊥ w12,1) because they weren’t involved in the calculation; they correspond to the zeros they suppressed above.
• In the example of number 26, the authors only computed qM for one of the three distinct qL-isotropic subgroups.
• The authors need to look on the graph for other fibrations which confirm that one of these choices is correct and that the others are not possible.

1.8.4 Methods for Fibrations Without Sections

• Sometimes we’ll only be able to find a fibration which has only multisections, and no sections.
• By definition, this is a non-Jacobian fibration.
• This completely determines Pic(S), though the authors do need the help of other techniques to complete the calculation.

1.8.6 Generalizations and Other Questions

• There are a few questions left unanswered by their calculations.
• The authors notice that not all families have mirrors on the list.
• Kreuzer and Skarke have done work which gives us an algorithm to find all 3- dimensional reflexive polytopes, and therefore all K3 surfaces which can be realized as toric hypersurfaces.
• The authors notice that there are some distinct families which have the same Pic(S).
• Miles Reid has a conjecture which does not explain this phenomenon, but perhaps will lead to some enlightenment.

2.1 Statement of the Conjecture

• Even though OS(1) is not necessarily locally free, it does correspond to some Weil divisor D. D is Q-Cartier, so the self-intersection of D is well-defined as D2 = (nD) 2 n2 , where n is the smallest multiple of D which is Cartier.
• The authors will calculate D2 more concretely: first notice that self-intersection changes by the degree of f when they pull back, so f ∗(D)2 = D2 · ∏ j qj.
• Denote by Apj the minimal resolution of each Apj . 2.1.0.3 Conjecture [Reid].

2.2 The M p, ι,k Lattices

• Then M p, ι,k is the lattice defined by the incidence matrix of the following graph: Begin with a central vertex c with self-intersection k.
• Note that there is no algorithm for computing the associated quadratic form (even for the Tp,q,r – see [Brieskorn]).

2.2.1 Questions of Isomorphism

• The authors can only answer this question for “∼=” in the sense of graph theory, not of lattice theory.
• The key is to notice that two different M p, ι,k graphs can be isomorphic only if the authors can move the central vertex from one spot c to another c′.
• Then, if there are more than three branches, the authors cannot move c in any way such that the branches from c′ form As.
• Finally, the authors have the same problem if more than one branch from c is forked.
• The authors prove the isomorphism relations with pictures; figure 2.1 proves the third relation.

2.2.2 Signature of M p, ι,k

• In [Brieskorn, §1.9] the author calculates the signature of the Tp,q,r lattices from the formula for the discriminant.
• Given this information, the authors can produce the matrix via another Mathematica procedure .
• The following table lists p, ι, k, and the discriminant.

The Detailed Calculations

• The sections are numbered identically to the numbering of the weight-vectors in [Yonemura].
• There is a paper [Mir-Mor] by Miranda and Morrison, which helps us determine when a lattice is unique, in cases where ρ ≥ 3 but Nikulin’s criteria do not apply.
• Of course, if this number is 1, the lattice is unique.
• 69 – We are unable to check the existence of the mirror lattice because the authors know of no existing lattice of any rank with this form.
• A fibration has good rank if it satisfies the Shioda-Tate formula with rk(MW ) = 0.

4.1 Moduli Spaces of Vector Bundles

• The authors can now talk about various moduli spaces of vector bundles with v(E) = v.
• The authors will see that if they can satisfy the hypotheses of [Mukai2, Proposition 6.4], they can use it to obtain such a map.

4.2 Construction of Vector Bundles

• The authors aim to show that they can construct a vector bundle from a minimal index multisection, so that J(S) will be isomorphic to MH(d, F, 0).
• Another way to view the Jacobian fibration is as a compactification of the relative Picard variety Pic◦S/P1 [Enriques I].

4.3.1 Proof that α is well-defined

• Not every vector bundle E has a cycle ξ associated to it.
• For the many requirements E must satisfy, see [Tyurin, § 2].
• B(E) is the variety of cycles associated to a bundle E.

4.3.3 Proof that α is an isomorphism of varieties

• Mukai often claims that his results hold for ρ > 11.
• Reading his papers carefully reveals that this is because he is only certain that TS embeds primitively into H2 for ρ > 11.

Tables of Forms and Values

• The authors list the forms and their values for every form used in this thesis.
• The authors will only analyze those with u and v as components.

CanonicalClass[dualverts_] :=

• First the authors load in the packages required, also known as Explanation of the code.
• The authors move the dual polytope far into the all-positive orthant so that VertexEnumeration will work correctly.
• The dual’s vertices also correspond to positive normal vectors to the bounding hyperplanes of the polytope, and VE uses this information to produce information on the original polytope.
• The authors use this information to compute with the formula KX = O(S(ai − 1) ∗ Fi), where the ai are defined by ai = minj < ni, vj >, the ni are the negative normal vectors to the faces, and the vj are the vertices.

SingGraph[dualverts_,LIP_,filename_].

• This command, given the vertices for the dual polytope (positive normal vectors to the faces of the polytope) and a filename, writes a description of the graph obtained by desingularizing the polytope.
• One can view the results of SingGraph by loading the Combinatorica package and using the command ShowLabeledGraph[ReadGraph["filename"]].
• The few lines of code (through the definition of the list ni) serve the purpose of correlating the enumeration of their list of the faces to the enumeration of the VertexEnumeration and KFaceList process.
• Now the authors define two functions (singtype and singnumber) which tell us the type and multiplicity of singularity for each edge.
• To do this, the authors dot LIP with the normal vector to the plane of the face.

Figures

Fig. 4. Oxygen sensor conditioning circuit.

Fig. 5. Mechanical structure of the thermostatic chamber.

Fig. 6. Cloud picture around the TCS208F ambient temperature.

Fig. 7. The prototype of the proposed SF6/N2 concentration detector.

Fig. 8. The experimental tests using the proposed SF6/N2 concentration detection prototype.

Fig. 10. The detection results under extreme temperature conditions: (upper left) SF6, (upper right) N2, (lower left) H2O, and (lower right) O2.

Fig. 9. The concentration detection results: (upper left) SF6, (upper right) N2, (lower left) H2O, and (lower right) O2.

Fig. 1. The overall design of the SF6/N2 concentration detection system.

Fig. 3. The equivalent diagram of temperature control circuit in Fig. 2.

Fig. 2. The temperature control circuit of the thermal conductivity sensor.

Full text

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1

Abstract—This paper develops a new detection system, for the
first time, to detect the gas concentrations of the SF
6
/N
2
mixture in
extra/ultra-high voltage power transmission systems. The
concentrations of SF
6
and N
2
are calculated from the thermal
conductivity function of the mixture gas. The main contribution of
this work is that a specially-designed thermostatic chamber with
adaptive temperature controller is developed to ensure constant
pressure of the gas flowed through the thermal conductivity
sensor. Another contribution is the combination of multiple
sensors (e.g. humidity and electrochemical sensors), which enables
the detector to address the penetration effects of H
2
O and O
2
in
the SF
6
/N
2
mixture. Experimental evaluation results using the
prototype demonstrated that satisfactory accuracy (±1% of the
measurement error) has been achieved for the concentration
detection of the SF
6
/N
2
mixture under variable operation
conditions. Compared with existing detection techniques, the
proposed detector not only can detect the SF
6
/N
2
concentration by
taking the air infiltration effect into account, but also reduce the
cost.
Index Terms—SF
6
/N
2
, gas mixture, microfluidic thermal
conductivity sensor, constant temperature control, trace O
2
This project is support by the National Science Foundation of China (NSFC)
(No. 51505265, 51505475 and U1610109), UOW VC Postdoctoral Fellowship,
the National Research Foundation of South Africa (grant numbers:
IFR160118156967 and RDYR160404161474) and Tertiary Education Support
Programme (TESP), ESKOM, South Africa.
Baojun Qu is with the Province-Ministry Joint Key Laboratory of EFEAR,
Hebei University of Technology, Tianjin 300130, China. (e-mail:
529435754@qq.com).
Dr. Qingxin Yang is a full professor at Tianjin Key Laboratory of AEEET,
Tianjin Polytechnic University, Tianjin 300387, China (e-mail:
yangqingxin@tjpu.edu.cn).
Dr. Yongjian Li is a full professor at the Province-Ministry Joint Key
Laboratory of EFEAR, Hebei University of Technology, Tianjin 300130,
China. (e-mail: liyongjian@hebut.edu.cn).
Dr. Reza Malekian is with the Department of Electrical, Electronic and
Computer Engineering, University of Pretoria, Pretoria 0002, South Africa
(e-mail: reza.malekian@ieee.org).
Dr. Zhixiong Li is with the School of Mechatronic Engineering, China
University of Mining and Technology, Xuzhou 221116, China; School of
Mechanical, Materials, Mechatronic and Biomedical Engineering, University
of Wollongong, Wollongong, NSW 2522, Australia (Corresponding author,
e-mail: zhixiong.li@ieee.org).
I. INTRODUCTION
wing to outstanding insulating characteristics and
arc-quenching capacity, the Sulfur hexafluoride (SF
6
) gas
has been widely used in extra/ultra-high voltage power
transmission systems [1-5]. Usually, SF
6
gas is pressurized [6]
in the electrical equipment to improve its capacitance and
insulation performance because the heat capacity and dielectric
strength increase with the pressure increase of SF
6
. However,
with the increase of the gas pressure, the liquefaction
temperature of SF
6
will increase accordingly. Under the
pressure of 0.22 MPa (i.e., 275 kV level), its liquefaction
temperature is -40℃, whereas under 0.6 MPa (i.e., 500 kV
level), the liquefaction temperature increases to -25℃ [7]. In
cold regions, the liquefaction of the SF
6
gas will cause the
decrease of the SF
6
pressure inside the electrical equipment,
resulting in degradation of insulation performance [8]. In
addition, SF
6
gas is very costly and sensitive to non-uniform
electric field [9]. The contribution of greenhouse effect of SF
6
is 23,900 times of CO
2
[10, 11]. More importantly, SF6 has
been included in the gas list by the Kyoto Protocol (1997),
whose emissions should be limited [12]. Hence, it is crucial to
develop alternatives to SF
6
in electrical equipment [13, 14].
Currently, the development of environmental-friendly
replacement of SF
6
is a hot topic, aiming to improve the
insulation properties and reduce greenhouse effect of the gas in
electrical equipment [15-18]. The mixture of SF
6
/N
2
is an
promising alternative to SF6 and has shown good potentials for
practical applications [19, 20]. For example, when the content
of SF
6
is 50% in the SF
6
/N
2
mixture in uniform electric field,
the electric strength of the mixed gas is almost 85% of the
strength of the pure SF
6
gas [17]. In addition, the cost of SF
6
/N
2
is much cheaper and the emission is much smaller than that of
SF
6
while the stability and safety levels of SF
6
/N
2
are much
higher than that of SF
6
. The liquefaction problem of SF6 is also
solved by the mixture of SF6/N2 (e.g., the liquefaction point of
60% SF6+40% N2 mixture is -42℃under 0.6 MPa). As a
result, the SF
6
/N
2
mixture gas is gradually replacing the SF
6
gas
in extra/ultra-high voltage transmission systems [21-23]. For
A New Concentration Detection System for
SF
6
/N
2
Mixture Gas in Extra/Ultra High Voltage
Power Transmission Systems
Baojun Qu, Qingxin Yang,Yongjian Li, Member, IEEE, Reza Malekian, Senior Member, IEEE,
Zhixiong Li, Member, IEEE
O

2
example, the insulation performance of SF
6
/N
2
has already
been evaluated in a real world 550 kV power transmission
system by the New Northeast Electric Company [22]. For
another example, in more than 200 km of GIL (gas-insulated
transmission line) installed by Alstom Grid, the SF6/N2 mixture
has been considered in insulation design [13].
However, in practice H
2
O and O
2
may penetrate into the
SF
6
/N
2
mixture during its service life, resulting in insulation
performance degradation. For instance, the seal device may
deteriorate after some usage time and H
2
O and O
2
in the air may
penetrate through the seal into the SF
6
/N
2
mixture. It is crucial
to detect the concentration of H
2
O and O
2
in practice while an
effective detection system is not developed in literature. Most
of existing systems are developed for SF
6
detection [24].
Generally, there are thermal conductivity sensor based [25],
Infrared sensor based [26], ultrasonic sensor based [27], and
photo-acoustic sensor based [2, 28] SF
6
gas detection systems.
Huang et al. [22] used the thermal conductivity sensor to detect
the SF
6
concentration in electrical equipment. Wang et al. [26]
combined the infrared and electrochemical SO2 sensors to
detect the SF6 decomposition. Stone [27] used the ultrasonic
sensor for partial discharge diagnostics in electrical equipment.
Sherstov et al. [28] adopted the photo-acoustic sensor for SF
6
detection. However, to the best of our knowledge, the detection
of SF
6
/N
2
mixture considering the H
2
O and O
2
elements has not
been found yet in literature [29-31].
In order to address the aforementioned issue, this paper aims
to develop a new detection system for concentration detection
of SF
6
/N
2
mixture considering the H
2
O and O
2
penetration
effect in extra/ultra-high voltage power transmission systems.
The working principle and detailed hardware construction were
described in this paper. Particularly, the humidity and
micro-oxygen sensors were integrated into the detection system
to detect the H
2
O and O
2
concentration in the SF
6
/N
2
mixture. A
temperature control circuit and specially-designed thermal
conductivity room were developed to make accurate detection
results of the SF
6
and N
2
concentrations. The
contribution/novelty of this work include
1) the developed system is applicable and effective to
detecting SF
6
/N
2
mixture with H
2
O and O
2
penetration
effect;
2) for the first time, a prototype of the proposed detection
system is developed.
Experimental tests under regular and extreme operating
conditions were conducted to evaluate the performance of the
prototype on SF
6
/N
2
concentration detection.
II. THE PROPOSED DETECTION SYSTEM
A. System Design Principle
Fig. 1 depicts the overall design of the SF
6
/N
2
concentration
detection system, which is mainly consisted of one thermostatic
chamber temperature detection and control module, one signal
detection and conditioning module, one moisture detection
module, one oxygen detection and conditioning module, and
one flow monitoring and conditioning module. The thermal
detection module is installed in the thermal conduction
chamber to ensure the consistency of the heat detection. The
micro-thermal conductivity sensor TCS208F is used and its
output is recorded by the signal detection and conditioning
module. The moisture detection module adopts DMT242J
sensor to detect H
2
O in the gas mixture and the oxygen
detection and conditioning module measures the concentration
of trace O
2
. The flow monitoring and conditioning module
adopts the mass flow meter to measure the gas flow rate.
PC Touch Screen
TCP/IP
RS232
Human Interface
CPU Microprocesso (STM32)
Temperature
PWM
output
A/D Collection
P
O
W
E
R
M
O
D
U
L
E
Flash
Storage
DI/DO
Temperature
Control in Thermal
Conductivity
Room
Signal Detection
and Conditioning
Module
Oxygen
Detection and
Conditioning
Module
Flow
Detection and
Conditioning
Module
AWM
4330
Sensor
Three-
way
valve
Electroch-
mical
Sensor
PT100
Thermal
Resistor
PT100
Thermal
Resistor
Heating
rod
TCS208F
Sensor
Moisture
Detection
Module
DMT242J
Sensor
Fig. 1. The overall design of the SF
6
/N
2
concentration detection system.
B. Detection Principle of SF
6
/N
2
Mixture
Based on MEMS structure, the microfluidic thermal
conductivity sensor (TCS208F) integrates metal thin-film
thermosensitive elements, and in each element there are four
resistors (R
m1
, R
m2
, R
t1
and R
t2
). R
m1
and R
m2
are used to heat the
film and measure the film temperature. R
t1
and R
t2
are used to
detect the ambient temperature and perform temperature
compensation. Neglecting the effect of thermal convection and
thermal radiation in the TCS208F sensor, the operation power
of the film can be expressed as
2
m m m
2
m m m
(1 )
[1 ( )]
P I R T
I R T T T




   
     
.
(1)
where I
m
is the sensor current, R
m
(= R
m1
+ R
m2
) is the film
resistor, α is the temperature coefficient, T
m
is the operation
temperature, and T is the initial ambient temperature.
Because the sensor heat is completely absorbed by the gas,
the thermal equilibrium model in Eq. (1) can be simplified as

3
1m()P Q S T T

    
.
(2)
Where λ is the gas thermal conductivity and S is the contact area
between the film resistor and gas. The temperature difference
ΔT after thermal equilibrium is
1
m
2
mm
(1 )( )
S
T T T T
IR




     
.
(3)
In order to ensure that the microfluidic thermal conductivity
sensor works stably, a temperature control circuit is designed
for the thermal conductivity sensor (see Fig. 2). In Fig. 2, the
operational amplifier TLC2652 is used to amplify the micro
signals. R
t1
is controlled by the microcontroller to keep the
temperature as a constant.
1
t1 m1 m2
2
1m
2
( ) (1 )
R
(1 )
R
R R R T
R
R
T
R


     

   
.
(4)
where R
1
and R
2
are the resistors of the control circuit. Thus, the
thermal conductivity of the mixture gas can be calculated by
2
m t1
0
2
t1 m 1 2
2
U
RR
S R R R R R





  
.
(5)
where U
0
is the sensor voltage. Eq. (5) is the thermal
conductivity of SF
6
, N
2
and O
2
mixture.
IN-
C
XA
C
XB
IN+
V+
V-
CALMP
OUT
U
o
+10V
1
2
3
4
5
6
8
R
1
IN-
IN+
V+
V-
OUT
GND
1
2
3
4
5
7
8
TLC2652
U
1
U
2
C
1
CALMP
7
GND
TLC2652
R
m1
+R
m2
-8V
R
t1
IN4148
C
XA
C
XB
C
2
6
GND
R
2
C
3
C
4
C
5
C
6
C
7
C
8
-8V
Fig. 2. The temperature control circuit of the thermal conductivity sensor.
When the system reaches the thermal equilibrium, R
m
and R
t1
can be considered as constant values. As a result, a linear
relationship can be learnt between U
0
and

from Eq. (5). Let us
assume that the O
2
/H
2
O content infiltrated into the SF
6
/N
2
mixtures meets the requirements of IEC60480-2004 [32]. So
the chemical reactions in equilibrium condition can be
expressed as follows:
e + SF
6
→ SF
n
+ (6-n)F + e, n≤5
SF
2
+ O
2
→ SO
2
F
2
e + O
2
→ O + O + e
SF
5
+ O → SOF
4
+ F
Figure 3 depicts the equivalent diagram of the thermal
conductivity sensor at its thermal equilibrium condition. It is
used as a signal conditioning device to control the temperature
of the gas.
IN-
IN+
OUT
R
1
R
m1
+R
m2
R
t1
GND
R
2
Adjustable
current
Conditioning
circuit
Fig. 3. The equivalent diagram of temperature control circuit in Fig. 2.
In Fig. 3, the Wheatstone bridge can be fall into balance
condition through adjusting the resistances R
1
and R
2
after the
passing of SF
6
/N
2
mixture. The current determines the working
temperature of the sensor at this moment. When the measured
gas is passed through the sensor, the coefficient of thermal
conductance

will increase, resulting in the decrease of the
sensor temperature and the measured resistance R
m
. As a result,
the bridge is out of balance, and the unbalanced voltage is
amplified and sent to the regulation circuit, where the output of
the current source is adjusted so that the current is increased
with the decrease of the sensor temperature. By doing so, no
matter how the thermal conductivity

changes, the sensor
temperature can keep as a constant to prevent inaccurate
measurement or sensor damage due to overheating.
In order to determine the thermal conductivity of SF
6
/N
2
, it
needs to know the thermal conductivity of O
2
. In the gas
mixture of SF
6
, N
2
, H
2
O and O
2
, due to the absence of the
chemical reaction between the components, the thermal
conductivity is approximated by the arithmetic mean of the
thermal conductivity in Eq. (6).
1 1 2 2 3 3 4 4C C C C
    
   
(6)
Where

denotes the thermal conductivity of the gas mixture,

i
(i = 1, 2, 3, 4) respectively denotes the thermal conductivity of
SF
6
, N
2
and O
2
, and C
i
(i = 1, 2, 3, 4) is the volume percentage
of

i
. The sum of volume percentage parameters satisfies

Frequently asked questions

Q1. What are the contributions in "A new concentration detection system for sf6/n2 mixture gas in extra/ultra high voltage power transmission systems" ?

This paper develops a new detection system, for the first time, to detect the gas concentrations of the SF6/N2 mixture in extra/ultra-high voltage power transmission systems. The main contribution of this work is that a specially-designed thermostatic chamber with adaptive temperature controller is developed to ensure constant pressure of the gas flowed through the thermal conductivity sensor. This journal article is available at Research Online: https: //ro. uow. edu. au/eispapers1/1309 

Q2. What are the future works in "A new concentration detection system for sf6/n2 mixture gas in extra/ultra high voltage power transmission systems" ?

In addition, future work will also compare the concentration detection performance of different sensors ( e. g., infrared sensor or ultrasonic sensor or photo-acoustic sensor ) using the sensor-array technique in the designed thermostatic chamber. 

Q3. What is the effect of thermal convection and radiation in the TCS208F?

Neglecting the effect of thermal convection andthermal radiation in the TCS208F sensor, the operation powerof the film can be expressed as2m m m2 m m m(1 )[1 ( )] 

Q4. What are the averaging errors for the gas elements?

The averaging repeated detection errorsfor all 10 samples were ±0.21%, ±0.09%, ±1.4% and ±1.3% forthe four gas elements, respectively. 

Q5. What is the reason why the prototype was made?

The detection results of the prototypedemonstrated that the measurement errors of SF6 and N2 were within ±0.05%, and their repeatability error was less than 1.0%. 

Q6. What is the temperature of the thermostatic chamber?

When the temperature of the thermostaticchamber is stabilized at the setting value, the gas mixture entersinto the thermostatic chamber. 

Q7. What is the thermal equilibrium model in Eq. 1?

Because the sensor heat is completely absorbed by the gas,the thermal equilibrium model in Eq. (1) can be simplified as1 m( )P Q S T T .(2)Where λ is the gas thermal conductivity and S is the contact areabetween the film resistor and gas. 

Q8. What is the coefficient of thermal conductivity of the mixture?

When the measuredgas is passed through the sensor, the coefficient of thermalconductance will increase, resulting in the decrease of thesensor temperature and the measured resistance Rm. 

Q9. What is the thermal conductivity of the gas mixture?

In the gas mixture of SF6, N2, H2O and O2, due to the absence of the chemical reaction between the components, the thermalconductivity is approximated by the arithmetic mean of thethermal conductivity in Eq. (6).1 1 2 2 3 3 4 4C C C C (6)Where denotes the thermal conductivity of the gas mixture, i (i = 1, 2, 3, 4) respectively denotes the thermal conductivity ofSF6, N2 and O2, and Ci (i = 1, 2, 3, 4) is the volume percentage of i. 

Q10. What is the effect of the unbalanced voltage?

As a result, the bridge is out of balance, and the unbalanced voltage isamplified and sent to the regulation circuit, where the output ofthe current source is adjusted so that the current is increasedwith the decrease of the sensor temperature. 

Q11. What is the mechanical structure of the inlet spiral pipeline?

The mechanical structure of the thermostatic chamber is shown in Fig. 5, where the inlet spiral pipeline functions as a buffer to stabilize the pressure of the gas flow. 

Q12. What is the detection accuracy of the prototype?

the detection performance of the prototype wasevaluated under extreme temperature conditions of the chamber, that is, high temperature (40℃±3℃) and low temperature (-10℃±3℃) conditions. 

Q13. What is the thermal conductivity of the SF6/N2 mixture?

By doing so, nomatter how the thermal conductivity changes, the sensortemperature can keep as a constant to prevent inaccuratemeasurement or sensor damage due to overheating. 

Q14. How can the authors calculate the vapour pressure in the gas?

So the vapour pressure Pw in the gas can be calculated byw wsP RH P (9)Then the absolute moisture amount can be calculated from Pw using the specific parameters of DMT242. 

Q15. What is the thermal conductivity of the wheatstone bridge?

In Fig. 3, the Wheatstone bridge can be fall into balancecondition through adjusting the resistances R1 and R2 after the passing of SF6/N2 mixture. 

Q16. Why is the thermal conductivity sensor based system more expensive than the infrared sensor?

Thanks to the specially-designed thermostatic chamberwith temperature control unit, the measured volumeconcentration (ppm) of the proposed detection system can beeasily converted into mass concentration (e.g., mg/m3) whilesome other sensor measurements (e.g., infrared sensor andultrasonic sensor) need to add pressure and temperaturemodules for the conversion, which may increase the cost andcomplexity of the detection system further. 

Q17. What is the maximum error of the detector?

According to theInternational ISO Standard 14040 [35], IEC60480-2004 [32]and National Standard of China, the maximum allowable errorof the detector for SF6, N2, H2O and O2 are respectively ±0.5%, ±0.5%, ±0.05% and ±0.05%. 

Q18. What was the temperature of the gas in the sample?

The concentration of each gas element in each sample was repeatedly measured for 8 times under the stableoperation condition of the detector, and the mean value of themeasurements was taken as the final measurement for eachsample.