How to define spacecraft equivalent circuit?
This page describes how the spacecraft
equivalent is modelled in SPIS, and how the user inputs allow defining it.
Introduction
Spacecraft electrical behaviour can be modelled
by an electric circuit collecting and emitting currents from and to the plasma.
Some electric components of the equivalent circuit are just a way to mimic
materials (e.g. a dielectric coating is equivalent to a capacitor, possibly
with a resistor in parallel), while others are real physical devices (e.g. a
potential supply between SC ground and a Langmuir probe, a resistor between SC
and solar array grounds). Some components are also uniform over a subsystem of
spacecraft (a coated area), while others are unique. Both notions most often
coincide: uniform areas of coating equivalent to resistors and capacitors (we
can call them continuous components),
and a few real discrete devices (we can call them discrete components). The type and values of the continuous
components can be derived from the material properties (and dynamically from
particle flux for radiation induced conductivity), while the discrete
components have to be defined by user through extra data not deriving from
coating or any local data.
It was thus decided to have an automated
derivation of the continuous components from coating data, while the discrete
data have to be defined in an extra file. Of course another reason of that
choice is that defining a huge number of local values for continuous components
was not reasonable.
Continuous components
Continuous components are thus derived from the
user-defined material properties (mostly local fields).
Note also that they are affected by the switching on and off of conductivities
(volume, induced in
volume, and surface) through three global parameters. Their equivalent
circuit is the following:
Discrete components
Discrete components are not plugged on top of
coated surfaces, but between conductive parts of sub-systems, which may be considered
as a sub-system ground. The notion of electric (super) node was defined to
represent such local grounds (a piece of conductor indeed as the thick line on
the figure above). So, an electric super node can be the ground of SC
(predefined Id 0), a solar array ground, the box/ground of a system, the biased
part of a device�
Electric (super) nodes must first be defined.
This is done through the local field elecNodeId. The
(super) node Id is mapped by the code on each elementary surface of the mesh
from the definition by the user at group level. For each elementary mesh
surface coated by a dielectric an extra elementary node and extra capacitors
and resistors are automatically generated by the code (left hand side of the
figure above), while no extra node or component is added if uncoated or coated
by a conductive coating (right hand side of the figure above).
NB: node 0 is considered as spacecraft ground,
with the only real consequence that it always exists (other nodes only exist if
their Id appear somewhere on the spacecraft).
Discrete devices then have to be plugged
between the electric (super) nodes. They are defined by the user in a file of a
user-specified
name (default name is "circuit.txt"). The syntax of the circuit
file is described in the UI description page. It supports capacitors,
resistors, active bias and inductances (since SPIS v4.0). An example of global
circuit, including continuous and discrete components is given here:
Note that there is a special requirement if you
want to link more than two super nodes by voltage generators. This is a rare
situation, but it may be used to simply connect different nodes (0 bias). The
network of voltage generators between the connected nodes can be re-arranged
freely, provided correct voltages are computed. In the current status of the
solver the rule is that it should be rearranged so that all nodes are connected
to a common node (network in the shape of a star), with the node to all voltage
generator bearing the smallest number.
There is of course another constraint for such
a network of biases: no loop is allowed (whether the applied biases are
consistent with such a loop or not).
Spacecraft capacitance is defined as the ratio
of the total charge on an equipotential spacecraft to its potential: � Qsat = Csat Vsat.
It can be seen as "component"
capacitor plugged between the spacecraft at plasma ground located at infinity.
Electrodes are indeed the charges on top of spacecraft surfaces and in its
sheaths.
This capacitance value depends on plasma
conditions. In a code it can either be computed or user-defined. In SPIS it is
defined as the global parameter CSat.
For a non conductive non equipotential
spacecraft Csat may be
plugged from plasma ground to different parts of the spacecraft. By default Csat is spread over all
spacecraft local grounds in proportion to their respective areas Ai, as depicted in this
circuit:
This is representative of a sheath uniform all
over the spacecraft, resulting in local capacitance to be proportional to area.
In some cases the user may yet want to plug Csat to a specific part of
the spacecraft. It is possible to plug it to spacecraft ground only:
by defining a negative Csat (its absolute value is used by the code, of
course).
Be aware that the equations resulting from the
circuit above are singular: nodes 1 and 2 have no capacitive or other coupling
to any other node or ground. They are thus interpreted as having zero
capacitive coupling, which means that the smallest collected charge results in
an infinite potential (if circuit is integrated). In this case extra components
should thus be added in general (user-defined capacitors between nodes, biases,
etc.). This does not happen in the regular situation of a Csat spread over the whole spacecraft (CSat > 0).
Initialisations
At simulation start, potentials have to be
initialised (and capacitor charges consistently). They may then remain
unchanged or be modified if electric circuit integration is switched on (electricCircuitIntegrate
parameter).
There are 2 different types of initialisations:
-
the initPot local field
defines the potential on top of coatings
-
the definition of an active bias
between two super nodes initialises (but permanently!) the potential between
the nodes. Electric super nodes are first initialised to 0 potential. Then the
rule is that V Node1 Node2 deltaV forces node2 potential to
be node1 potential + deltaV.
For a coated surface the potential on top of the coating
("upper" capacitor electrode) is thus defined by initPot, while the
potential on ground below ("lower" capacitor electrode) is defined
the circuit definition (discrete device). For a conductive surface, the two
initialisations may collide: if an active potential is imposed to a conductive
node, the local values obtained from initPot are overridden by the potential
imposed by the bias defined in the circuit file.
A richer panel of initialisation capabilities
may be offered in future if needed (e.g. not-permanent non-zero initialisation
of super node grounds), but it was not found very useful now.