12.4. Steady-State Current Conduction Analysis

Steady-state current conduction analysis determines the current density and electric potential (voltage) distribution caused by direct current (DC) or potential drop. You can apply two types of loads in this analysis: voltage and electric current. Refer to Electromagnetics in the Mechanical APDL Theory Reference for more information.

A steady-state current conduction analysis is assumed to be linear. That is, the electric current is proportional to the applied voltage.

The procedure for doing a steady-state current conduction analysis consists of three main steps:

The next few topics discuss what you must do to perform these steps.

12.4.1. Building the Model

To build the model, you start by specifying the jobname and a title for your analysis, using the following commands or GUI paths:

Command(s): /FILNAME, /TITLE
GUI: Utility Menu> File> Change Jobname
Utility Menu> File> Change Title

If you are using the GUI, the next step is to set preferences for an electric analysis: Main Menu> Preferences> Electromagnetics> Electric

You must set the preference to Electric to ensure that the elements needed for your analysis will be available. (The GUI filters element types based on the preference you choose.)

Once you have set the Electric preference, use the preprocessor (PREP7) to define the element types, the material properties, and the model geometry. These tasks are common to most analyses. The Modeling and Meshing Guide explains them in detail.

You can use the following types of elements in a steady-state current conduction analysis:

Table 12.9: Elements Used in a Steady-State Analysis

ElementDimens.Type
LINK68 3DTwo node thermal /electric line
PLANE230 2DEight node electric quadrilateral
SOLID5 3DEight node structural/thermal/magnetic/electric hexahedral
SOLID98 3DTen node structural/thermal/magnetic/electric tetrahedral
SOLID231 3DTwenty node electric hexahedral
SOLID232 3DTen node electric tetrahedral
SHELL157 3DFour node thermal/electric shell
MATRIX50 3DSuperelement

You must specify electric resistivity values RSVX, RSVY, and RSVZ using the MP command. These properties may be constant or temperature dependent.

12.4.2. Applying Loads and Obtaining a Solution

In this step, you define the analysis type and options, apply loads to the model, specify load step options, and initiate the finite element solution. The next few topics explain how to perform the following tasks:

12.4.2.1. Entering the SOLUTION Processor

To enter the SOLUTION processor, use either of the following:

Command(s): /SOLU
GUI: Main Menu> Solution

12.4.2.2. Defining Analysis Type

To specify the analysis type, do either of the following:

  • In the GUI, choose menu path Main Menu> Solution> Analysis Type> New Analysis and choose a Steady-state analysis.

  • If this is a new analysis, issue the command ANTYPE,STATIC,NEW.

  • If you want to restart a previous analysis (for example, to specify additional loads), issue the command ANTYPE,STATIC,REST. You can restart an analysis only if you previously completed a steady-state analysis, and the files Jobname.emat, Jobname.esav, and Jobname.db from the previous run are available.

12.4.2.3. Defining Analysis Options

Next, you define which solver you want to use. You can use the sparse solver (default), the Jacobi Conjugate Gradient (JCG) solver, the Incomplete Cholesky Conjugate Gradient (ICCG) solver, or the Preconditioned Conjugate Gradient solver (PCG).

To select an equation solver, use either of the following:

Command(s): EQSLV
GUI: Main Menu> Solution> Analysis Type> Analysis Options

12.4.2.4. Applying Loads

You can apply loads to a steady-state analysis either on the solid model (keypoints, lines, and areas) or on the finite element model (nodes and elements). You can specify several types of loads:

12.4.2.4.1. Current

Electric currents (AMPS) are concentrated nodal loads that you usually specify at model boundaries (the label AMPS is just a load label; it does not indicate the units of measurement). A positive value of current indicates current flowing into the node. For a uniform current density distribution, couple the appropriate nodes in the VOLT degree of freedom, and apply the full current at one of the nodes.

To apply current, use one of the following:

Command(s): F
GUI: Main Menu> Solution> Define Loads> Apply> Electric> Excitation> Current

12.4.2.4.2. Voltage (VOLT)

Voltages are DOF constraints that you usually specify at model boundaries to apply a known voltage. A typical approach specifies a zero voltage at one end of the conductor (the "ground" end) and a desired voltage at the other end.

To apply voltage, use the following command or GUI path:

Command(s): D
GUI: Main Menu> Solution> Define Loads> Apply> Electric> Boundary> Voltage

You can also apply current and voltage loads using the independent current and voltage source options of CIRCU124. For more information, refer to Electric Circuit Analysis.

Optionally, you can use other commands to apply loads to a steady-state analysis, and you also can specify output controls as load step options. For information about using these commands to apply loads and about the load step options available for steady-state analysis, see Alternative Analysis Options and Solution Methods.

12.4.2.5. Starting the Solution

In this step, you initiate the solution for all load steps using one of the following:

Command(s): SOLVE
GUI: Main Menu> Solution> Solve> Current LS

12.4.2.6. Finishing the Solution

To leave the SOLUTION processor, use either of the following:

Command(s): FINISH
GUI: Main Menu> Finish

12.4.3. Reviewing Results

The program writes results from a steady-state current conduction analysis to the results file, Jobname.rth (or to Jobname.rst if other degrees of freedom are available besides VOLT). Results include the data listed below:

Primary data: Nodal voltages (VOLT).

Derived data:

  • Nodal electric field (EFX, EFY, EFZ, EFSUM).

  • Nodal conduction current densities (JCX, JCY, JCZ, JCSUM). Supported only by PLANE230, SOLID231, and SOLID232.

  • Element conduction current densities (JSX, JSY, JSZ, JSSUM, JTX, JTY, JTZ, JTSUM).

  • Element Joule heat (JHEAT).

  • Nodal reaction currents.

You can review analysis results in POST1, the general postprocessor. To access the postprocessor, choose one of the following:

Command(s): /POST1
GUI: Main Menu> General Postproc

For a complete description of all postprocessing functions, see the Basic Analysis Guide.

12.4.3.1. Reviewing Results in POST1

To review results in POST1, the database must contain the same model for which the solution was calculated. Also, the results file (Jobname.rth or Jobname.rst) must be available.

To read results at the desired time point into the database, use either of the following:

Command(s): SET,,,,,TIME
GUI: Utility Menu> List> Results> Load Step Summary

If you specify a time value for which no results are available, the program performs linear interpolation to calculate the results at that time.

To identify the results data you want, use a combination of a label and a sequence number or component name.

You can now review the results by obtaining graphics displays and tabular listings. To obtain these, use the following:

Table 12.10: Reviewing Results

StepCommandsGUI Path
Produce contour displays. PLESOL, PLNSOL

Main Menu> General Postproc> Plot Results> Contour Plot> Element Solution

Main Menu> General Postproc> Plot Results> Contour Plot> Nodal Solu

Produce vector (arrow) displays. PLVECT

Main Menu> General Postproc> Plot Results> Vector Plot> Predefined

Main Menu> General Postproc> Plot Results> Vector Plot> User Defined

Produce tabular data listings. PRESOL, PRNSOL, PRRSOL

Main Menu> General Postproc> List Results> Element Solution

Main Menu> General Postproc> List Results> Nodal Solution

Main Menu> General Postproc> List Results> Reaction Solu


To gain access to certain element results data that are not otherwise directly accessible, you must use the following commands or menu paths after you have read the results into the database:

Table 12.11: ETABLE Results

StepCommandsGUI Path
Produce contour displays. ETABLE

Main Menu> General Postproc> Element Table> Define Table

Produce vector (arrow) displays. PLETAB

Main Menu> General Postproc> Plot Results> Contour Plot> Elem Table

Main Menu> General Postproc> Element Table> Plot Elem Table

Produce tabular data listings. PRETAB

Main Menu> General Postproc> List Results> Elem Table Data

Main Menu> General Postproc> Element Table> List Elem Table


POST1 performs many other postprocessing functions, including mapping results onto a path and load case combinations. For more information, see the Basic Analysis Guide manual.

12.4.4. Extracting Conductance from Multi-Conductor Systems

A key parameter from an electric solution is conductance. For multiple conductor systems, this involves extracting self and mutual conductance terms so that equivalent circuit lumped conductors can be defined for use in circuit simulators. The GMATRIX command macro has been developed to extract self and mutual conductance terms for multiple conductor systems.

See the Mechanical APDL Theory Reference for more details.

GMATRIX works with the following elements:

12.4.4.1. Ground Conductances and Lumped Conductances

Finite element simulation can readily compute and extract a "Ground" conductance matrix of conductance values that relate the current on one conductor with the conductor's voltage drop (to ground). Figure 12.1: Three Conductor System illustrates a three-conductor system (one conductor is ground). The following two equations relate currents on electrodes 1 and 2, I1 and I2, with the voltage drops for the electrodes, V1 and V2:

Figure 12.1: Three Conductor System

Three Conductor System

where Gg represents a matrix of conductances referred to as "ground conductances". These ground conductances do not represent lumped conductances typically used in a circuit simulator because they do not relate the conductances between conductors. However, the GMATRIX command macro can convert the ground conductance matrix to a lumped conductance matrix which is suitable for use in circuit simulators. Figure 12.2: Lumped Conductor Equivalence of Three Conductor System illustrates the lumped conductances between the conductors. The following two equations then relate the currents with the voltage drops:

In the equations above, conductance is in Siemens (1/Ω).

Figure 12.2: Lumped Conductor Equivalence of Three Conductor System

Lumped Conductor Equivalence of Three Conductor System

where Gl represents a matrix of conductances referred to as "lumped conductances".

12.4.4.2. Procedure

The GMATRIX command macro will perform multiple simulations and extract both the ground conductance matrix values and the lumped conductance matrix values. To prepare for GMATRIX, you must group the conductor nodes into node components. Do not apply any loads to the model (voltages, current, etc.). The component name applied to the conductor nodes must contain a common prefix, followed by a numerical suffix progressing from 1 to the highest numbered conductor in the system. The last numbered conductor in the system must be the ground conductor (the conductor whose potential is assumed to be zero). The procedure for using GMATRIX is as follows:

  1. Build and mesh the solid model with electric elements. Conductors are assumed to be perfect conductors and hence do not require a finite element mesh within the conductor domain. Only the surrounding conductive regions require a mesh. The resulting nodes on the boundary of the conductors represent the nodes that will be grouped into node components.

  2. Select the nodes on the surface of the each conductor and group them into node components:

    Command(s): CM
    GUI: Utility Menu> Select> Comp/Assembly> Create Component

    Share a command prefix for the component names, and use a numerical value sequencing from 1 to the highest numbered conductor. For example, in Figure 12.2: Lumped Conductor Equivalence of Three Conductor System, three node components would be defined for each set of conductor nodes. Using a prefix "cond", the node component names would be "cond1", "cond2", and "cond3". The last component, "cond3", would be the nodes representing the ground.

  3. Enter the SOLUTION processor:

    Command(s): SOLU
    GUI: Main Menu> Solution
  4. Select an equation solver (sparse or ICCG solver recommended):

    Command(s): EQSLV
    GUI: Main Menu> Solution> Analysis Type> Analysis Options
  5. Invoke the GMATRIX macro:

    Command(s): GMATRIX
    GUI: Main Menu> General Postproc> Elec&Mag Calc> Component Based> Self/Mutual conductance

    The GMATRIX command macro requires the following input:

    • A symmetry factor (SYMFAC). If there is no symmetry in the model, the symmetry factor is 1 (default). If you wish to model only a portion of the model by taking advantage of symmetry, use the symmetry factor as a multiplier to obtain the correct conductance.

    • The node component prefix name (Condname). This is the prefix of the node component names used to define the conductor node components. In the above example, the prefix name is "cond". The command macro requires that you put single quotes around the prefix name when entering the character string. Thus, the input for this example would be 'cond'. In the GUI, the single quotes are automatically handled by the program.

    • The number of conductor node components (NUMCOND). Insert the total number of conductor node components. In the above example, you would use "3".

    • Enter a name for the stored matrix of conductance values (Matrixname). The command macro stores the computed ground and lumped matrix values in a 3D array vector where the "i" and "j" columns represent the conductor indices, the "k" column indicates ground (k = 1) or lumped (k = 2) terms. The default name is GMATRIX. For example, the command macro stores the ground terms in GMATRIX(i,j,1) and the lumped terms in GMATRIX(i,j,2). The command macro also creates a text file containing the matrix values and stores it in a file with the stored matrix name and a .TXT extension.

Do not apply inhomogeneous loads before using the GMATRIX command. Inhomogeneous loads are those created by:

  • Degree of freedom commands (D, DA, etc.) specifying nonzero degree of freedom values on nodes or solid model entities

  • Force commands (F, BF, BFE, BFA, etc.) specifying nonzero force values on nodes, elements, or solid model entities

  • Any CE command with a nonzero constant term

GMATRIX executes a series of solutions to compute self and mutual conductance between conductors. The solutions, which are stored in the results file, are available for postprocessing, if desired. At the end of the execution, the command macro presents a summary table.