Download II. Basic Concept

CS
Thermal Network Method
in the Design of Electric Power Equipment
Christoph Gramsch1, Andreas Blaszczyk2, Helmut Löbl1 and Steffen Grossmann1
1
Technical University Dresden, Institute of Electrical Power Systems and High Voltage Engineering,
01062 Dresden, Momsenstr. 10, Germany
2
ABB Corporate Research, 5405 Baden-Daettwil, Switzerland
1
{CGramsch, Loebl, Grossmann}@ieeh.et.tu-dresden.de , [email protected]
Abstract— The paper presents basic principles of the thermal
networks method. Modeling of network elements has been shown
for convection and radiation. A concept of hierarchical thermal
network models for complex geometries has been explained. An
example of the thermal network computation including
comparison with test results has been presented.
Keywords— thermal networks, thermal design, power devices
I.
INTRODUCTION
The Thermal Network Method (TNM) is based on a
substitution of an arbitrary 3D geometry by a circuit consisting
of thermal resistances, capacitances and heat sources. For such
a network the currents correspond to heat flow and the nodal
potentials to temperatures. Due to similarity of mathematical
formulations the electrical circuit programs can be used to
obtain a solution. The basic advantage of the thermal network
analysis is the fast computation time: steady state computations
of large models can be performed within a few seconds.
Therefore the TNM is very suitable for parameter studies and
become popular as a tool supporting the industrial design. A
drawback of TNM is the creation of the network, in particular
transition from the real geometry to a network based model.
This drawback can be mitigated by applying hierarchical
modelling approach and reusable library elements with readyto-use representations of the whole devices. In this paper we
describe such an approach and its application to real cases.
II.
numbers of Nusselt (Nu), Grasshof (Gr), Prandtl (Pr) and
Reynolds (Re). The following basic relationship can be used
 conv 
Nu  fluid
l ch
(2)
where  fluid is the thermal conductivity of fluid and lch the
characteristic length (e.g. the height of a vertical plate or the
diameter of a horizontal cylinder). The Nusselt number is
calculated for the natural convection with coefficients c1 and
n1:
Nu  c1 Gr Pr 1
n
(3)
while for the forced convection with coefficients c2 and n2:
Nu  c2 Ren2 .
(4)
The implemented convection resistances can be used for
the laminar and turbulent flow models in different fluids (air,
SF6, oil, H2O).
generated heat
P=I2R
LX
L
conduction
through insulation
conduction
along
conductor
BASIC CONCEPT
The basic concept of substituting the geometrical objects
by a thermal network model is shown for an example of a
coated conductor carrying electrical current I, Fig. 1. The
current generates temperature dependent power losses that are
conducted along the conductor (in copper) as well as through
the insulation layer and dissipated via convection and
radiation. A part of the generated heat can be stored in the
conductor material represented by the capacitance C (used for
the transient computations only). In this abstract we present
basic formulas for the calculation of the circuit elements
corresponding to convection and radiation.
The thermal resistance of convection can be expressed as
follows
R conv 
1
 conv A conv
(1)
with the convection coefficient  conv and the surface area
Aconv. The calculation of  conv is based on the similarity theory
[1,2,3], which requires evaluation of the characteristic
radiation
convection
R
S
C
Fig. 1. Thermal network model of a coated conductor
The radiation resistance is expressed in a similar way as (1):
R rad 
1
.
 rad A rad
(5)
The radiation coefficient  rad is based on the StefanBoltzmann-constant  , the emissivity  12 between the
radiating and absorbing surfaces and the absolute temperatures
T1 and T2 of both surfaces:
 rad 

12  T14  T24
T1  T2

(6)
CS
The value of  12 depends on emissivity of the emitting and
absorbing surfaces, their surface area and the viewing factor
between them. In case of a conductor located in a free space
the emissivity of the conductor outer surface can be used for
 12.
created model allows simulation of mass transfer phenomena
and has been used to study different ventilation solutions.
a)
8
7
Due to the temperature dependency of convection and
radiation resistances as well as power losses the network
problem is nonlinear. This kind of problems can be efficiently
solved using programs for analysis of electric circuits like
Spice or its commercial derivates (www.pspice.com).
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5
HIERARCHICAL APPROACH
The generation of a thermal network for a complex device
is a time consuming process. To make it easier and faster we
introduced a concept of hierarchical thermal networks. In
hierarchical approach we create networks consisting not only
of primitive elements representing physical phenomena like
resistors or sources but also models of whole components. For
example, the network scheme of a conductor shown in Fig. 1
consists of 5 thermal resistances, one capacitance and one
source. These elements can be wrapped together into a new
element representing the whole conductor with pins
corresponding to the heat conduction (L,LX), convection (C),
radiation (R) and the outer surface (S). The example in Fig. 2
shows application of the new “coated conductor” element
(denoted here as CN_gICYL1) in a network model
representing encapsulated conductor. In this model
additionally radiation, convection and eddy losses related to
enclosure walls as well as ventilation have been included. The
network from Fig. 2 can be again wrapped into a new
“encapsulated conductor” element and applied in higher
hierarchical levels.
For complex devices we use up to 5 hierarchical network
levels. The hierarchical approach allows a better management
of large models and reusability of components.
LX
L
3
2
1
b)
90
Temperature [°C]
III.
4
left
phase
75
mid
right phase
phase
Dotted lines =
measured temperatures
60
3
1
R
C
Fig. 2. Hierarchical thermal network with a coated conductor element
IV.
8
CONCLUSION
Thermal network method has been effectively applied to
thermal design of complex power devices like high and
medium voltage switchgear, transformers, bushings and
circuit-breakers. The hierarchical modeling approach allows
efficient handling of complex geometries. A good agreement
with experimental results can be achieved. The fast
computation times enable comprehensive parameter studies for
modeled devices.
EXAMPLE
An example of a complex power device is shown in Fig.
3a. Based on hierarchical thermal network approach we
computed steady state temperatures along the phase
conductors. The deviations between computations and tests are
for most measured points in the range of 3 K, see Fig. 3b. The
6
Fig. 3. Air insulated medium voltage switchgear arrangement: a) geometry
view b) comparison between measured and computed steady-state
temperatures
V.
S
Position
VI.
[1]
[2]
[3]
REFERENCES
J. P. Holman, “Heat Transfer,” McGraw-Hill Higher Education, 9th
edition, 2002
H. Böhme, “Mittelspannungstechnik,” Verlag Technik Berlin München,
2. Auflage, 2005
H. Löbl, “Basis of Thermal Networks,” (unpublished) Dresden
University of Technology, 1999.