# Electrical Analysis

An electrical analysis involves calculation of electric potential in structures subject to electrical loads.

The basic finite element equation to be solved for structures experiencing electrical loads can be expressed as:(1) ${K}_{C}\phi =f$ Where,
${K}_{C}$
Electrical conduction matrix
$\phi$
Electric potential
$f$
Electric current

This is the equilibrium equation of electric currents and is solved for the unknown electric potential.

## Electrical Analysis in OptiStruct

A standalone electrical analysis case in OptiStruct can be categorized into the following types:
Steady-State Electrical Conduction (SSEC)
The loading (current or enforced voltage) is time independent.
SSEC is used for Joule heating calculations, to generate Joule heating for further steady heat transfer analysis.
Example:
SUBCASE 1
ANALYSIS ELEC
SPC = 1
LOAD = 2
TEMP(MAT) = 4
Multi Steady Electrical Conduction (MSEC)
The loading (current or enforced voltage) is time dependent.
MSEC is mainly used to generate Joule heating for further transient heat transfer analysis.
Example:
SUBCASE 1
ANALYSIS ELEC
SPC = 1
DLOAD = 3
TEMP(MAT) = 4

## Coupled Electrical Analysis

Electrical analysis can be coupled with heat transfer analysis.

With coupled electrical analysis, the Joule heating from electrical analysis can be passed for further heat transfer analysis (for example, defrosting of a car windshield). Coupling can be 1-way or 2-way.
• Steady-State (linear/nonlinear) Heat Transfer analysis can only be coupled with SSEC.
• Transient (linear/nonlinear) Heat Transfer analysis can only be coupled with MSEC.
Note: Transient (linear/nonlinear) Heat Transfer analysis can still call an SSEC subcase via a DLOAD (that refers to a TLOAD, referencing a SSEC subcase). This is not a coupling and the solution from SSEC is used as a loading, like QVOL, in this case.

For an example use case, if the electrical load is constant and the electrical material is temperature independent, this method can greatly reduce computational time. Without this method, the solution must be computed at each time-step.

### 1-Way Coupling

1-way coupling is sufficient when electrical material is temperature independent. Since the material property is constant, the electrical subcase can be solved once. Some examples are:
Example 1: Steady-State Heat Transfer Analysis Calls SSEC as Loading
Subcase 101
ANALYSIS ELEC
SPC = 20
LOAD = 22
Subcase 102
ANALYSIS HEAT
SPC  = 21
JOULE = 101
LOAD = 25
Example 2: SSEC Uses Steady-State Heat Transfer Analysis to Update Material
SUBCASE 101
ANALYSIS ELEC
SPC = 20
LOAD = 22
TEMP(MAT) = 102
SUBCASE 102
ANALYSIS HEAT
SPC  = 21
LOAD = 25
Note: At this time, MSEC cannot be used a standalone subcase. It cannot use transient heat transfer subcase to update material.

### 2-Way Coupling

2-way coupling is required/used when electrical material is temperature dependent. Some examples are:
SSEC Uses Steady-State Heat Transfer to Update Material
Joule heating from SSEC is applied to steady-state heat transfer analysis.
SUBCASE 101
ANALYSIS ELEC
SPC = 20
LOAD = 22
TEMP(MAT) = 102
SUBCASE 102
ANALYSIS HEAT
SPC  = 21
JOULE = 101
LOAD = 25
MSEC Uses Transient Heat Transfer Analysis to Update Material
Joule heating from MSEC is applied to transient heat transfer analysis.
SUBCASE 101
ANALYSIS ELEC
SPC = 20
DLOAD = 23
TEMP(MAT) = 102
SUBCASE 102
ANALYSIS HEAT
SPC  = 21
JOULE = 101
DLOAD = 24 $This DLOAD cannot refer TLOAD of TYPE = JOULE TSTEP = 9 Examples for 1-way and 2-way coupling can be extended to nonlinear steady-state heat transfer subcases. ## Input A summary of the relevant input file entries in an electrical analysis. The relevant Subcase Information Entries are: Table 1. Subcase Information Entries Entry Purpose ANALYSIS = ELEC Defines an electrical analysis subcase JOULE References an electrical analysis subcase from a heat transfer subcase in a coupled thermo-electrical analysis The relevant Bulk Data Entries are: Table 2. Bulk Data Entries Entry Purpose SPC, SPCD Potential CURRENT Nodal current CDENST4 Current density MAT1EC Isotropic electrical material MAT2EC Anisotropic electrical material MATT1EC, MATT2EC Temperature dependent material PGAPEC Electrical resistance properties for gap elements PCONTEC Contact Electric Coefficient (CEC) for CONTACT element The TLOAD entry supports Joule loss density excitation (TYPE = J, JO, JOU, or JOUL). EXCITEID refers to the ID of a steady-state electrical subcase from which the Joule loss density can be applied to a transient heat transfer subcase. ## Analogy The following table summarizes the analogy of some electrical analysis entries with the existing thermal/structural analysis. Table 3. Analogy for Electrical Analysis Type Electrical Analysis Thermal Analysis Structural Analysis Result output Electrical potential Temperature Displacement Electrical field Temperature Gradient Strain Loads and boundary conditions CURRENT FORCE CDENST4 QBDY1 PLOAD4 SPC (Electrical potential) SPC (Temperature) SPC (Displacement) SPCD (Electrical potential) SPCD (Temperature) SPCD (Displacement) Material MAT1EC MAT4 MAT1 MAT2EC MAT5 MAT9 MATT1EC MATT4 MATT1 MATT2EC MATT5 MATT9 ## Problem Setup Example of an electrical analysis setup. The following input file snippet shows an example of an electrical analysis setup:$ *************************************************************
$EXAMPLE TO DEMONSTRATE AN ELECTRICAL ANALYSIS SETUP$ *************************************************************
OLOAD     = 11
VOLTAGE   = 11
GPCURRENT = 11
ELECMAT   = 22
ELECFIELD = 22
HEAT      = 22
CURRDEN   = 22

SUBCASE        1
LABEL HEAT
ANALYSIS HEAT
IC =        1
JOULE =     2
TSTEP =     9
DLOAD =     28
SPC   =     12
NLPARM =    6

SUBCASE        2
LABEL ELEC
ANALYSIS ELEC
DLOAD   =   3
SPC     =  10
TEMP(MAT) = 1.

BEGIN BULK
...

## Example

A visual example of modeling Joule heating in a Busbar system.

Busbars are commonly used in many applications to provide power to various electronic boxes.

The model consists is an electrical system with five circuits. The circuits are separated from each other using a thin di-electric layer.

An initial temperature of 20 degrees Celsius is applied to all the bodies.

Point currents are specified using the CURRENT Bulk Data Entry at the terminals, while 0V voltage is applied using SPC.
The temperature distribution on the model is:
The electric potential on the model is:

## Output

Supported output requests for electrical analysis.

Currently, results are only available in .h3d format in a separate *_elecht.h3d file.

The supported output requests are:
Table 4. Supported Output Requests for Electrical Analysis
Result Purpose Details
VOLTAGE Voltage Available by default
HEAT Joule loss density Available by default
CURRDEN Current density Available by default
ELECFIELD Electric field
ELECMAT Conductivity and resistivity
GPCURRENT Gap current
OLOAD Applied nodal current

A current balance summary table is available in the .out file for steady-state electrical conduction analysis. This is similar to the SPCFORCE output table and consists of total applied current and SPC current.

This table is currently unavailable for MSEC analysis.