12.5. Harmonic Quasistatic Electric Analysis

A harmonic electric analysis determines the effects of alternating current (AC), charge or voltage excitation in electric devices. In this analysis, the time-harmonic electric and magnetic fields are uncoupled, and the electromagnetic field can be treated as quasistatic. Eddy currents are considered to be negligible, and the electric field is derived from the electric scalar potential. Capacitive effects and displacement current are taken into account. Refer to Electromagnetics in the Mechanical APDL Theory Reference for more information.

You can use this analysis to determine the voltage, electric field, electric flux density, and electric current density distributions in an electric device as a function of frequency in response to time-harmonic loading.

The procedure for doing a harmonic quasistatic analysis consists of three main steps:

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

12.5.1. Building the Model

To build the model, you first specify a jobname and a title for your analysis as described in Steady-State Current Conduction Analysis. If you are using the GUI, set preferences for an electric analysis and then use the preprocessor (PREP7) to define the element types, the material properties, and the model geometry.

To perform a current-based harmonic quasistatic analysis, you can use the following types of elements:

Table 12.12: Elements Used in a Current-Based Harmonic Analysis [1]

ElementDimens.Type
PLANE230 2DEight node electric quadrilateral
SOLID231 3DTwenty node electric hexahedral
SOLID232 3DTen node electric tetrahedral


  1. The reaction solution is current.

To perform a charge-based harmonic quasistatic analysis, you can use the following types of elements:

Table 12.13: Elements Used in a Charge-Based Harmonic Analysis [1]

ElementDimens.Type
PLANE121 3DEight node electrostatic quadrilateral
SOLID122 3DTwenty node electrostatic hexahedral
SOLID123 3DTen node electrostatic tetrahedral


  1. The reaction solution is charge.

The default system of units is MKS. In the MKS system of units, free-space permittivity is set to 8.85e-12 Farads/meter. To specify your own system of units and free-space permittivity use one of the following:

Command(s): EMUNIT
GUI: Main Menu>Preprocessor>Material props>Electromag Units

To model resistive and capacitive effects, a harmonic electric analysis requires the specification of electrical resistivity and electric permittivity, respectively. Define electrical resistivity values as RSVX, RSVY, and RSVZ on the MP command. Define relative electric permittivity values as PERX, PERY, and PERZ on the MP command.

You can specify losses by defining electrical resistivity (RSVX, RSVY, RSVZ) or a loss tangent (LSST) on the MP command. Resistivity and loss tangent effects are additive.

These properties may be constant or temperature dependent.

12.5.2. 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:

12.5.2.1. Entering the SOLUTION Processor

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

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

12.5.2.2. Defining the 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 Harmonic analysis.

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

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

12.5.2.3. Defining Analysis Options

Next, you define which solution method and which solver you want to use. Harmonic electric analyses require the full solution method. To select a solution method, use one of the following:

Command(s): HROPT,FULL
GUI: Main Menu> Solution> Analysis Type> New Analysis> Harmonic

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 one of the following:

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

To specify the frequency range, use any of the following:

Command(s): HARFRQ
GUI: Main Menu> Preprocessor> Loads> Load Step opts> Time/Frequency
Main Menu> Solution> Loads> Load Step opts> Time/Frequency

To specify the number of harmonic solutions within the load step, use either of the following:

Command(s): NSUBST
GUI: Main Menu> Preprocessor> Loads> Load Step Opts> Time/Frequenc> Freq & and Substps
Main Menu> Solution> Load Step Opts> Time/Frequenc> Freq & Substps

When specifying multiple substeps within a load step, you need to indicate whether the loads are to be ramped or stepped. The KBC command is used for this purpose: KBC,0 indicates ramped loads (default), and KBC,1 indicates stepped loads.

Command(s): KBC
GUI: Main Menu> Solution> Load Step Opts> Time/Frequenc> Time and Substps (or Time & Time Step)
Main Menu> Solution> Load Step Opts> Time/Frequenc> Time and Substps (or Time & Time Step)

To specify results data for the printed output file (Jobname.out), use one of the following:

Command(s): OUTPR
GUI: Main Menu> Preprocessor> Loads> Load Step Opts> Output Ctrls> Solu Printout
Main Menu> Solution> Load Step Opts> Output Ctrls> Solu Printout

You can also control the solution items sent to the results file (Jobname.rth). By default, the program writes only the last substep of each load step to the results file. If you want all substeps (that is, the solution at all time substeps) on the results file, use one of the following to specify a frequency or ALL or 1.

Command(s): OUTRES
GUI: Main Menu> Preprocessor> Loads> Load Step Opts> Output Ctrls> DB/Results File
Main Menu> Solution> Loads> Load Step Opts> Output Ctrls> DB/Results File

12.5.2.4. Applying Loads

You can apply loads in a harmonic analysis either on the solid model (keypoints, lines, and areas) or on the finite element model (nodes and elements). The type of loads you can specify depends on the element type chosen for a harmonic analysis.

Table 12.14: Load Types

AnalysisElement TypesLoads
Current-Based Analysis PLANE230, SOLID231, SOLID232

Current

Voltage

Charge-Based Analysis PLANE121, SOLID122, SOLID123

Charge

Surface charge density

Volume charge density

Voltage


12.5.2.4.1. 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

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

12.5.2.4.2. Charge

Electric charges (CHRG) are concentrated nodal-force loads. To apply them, use the following command or GUI path:

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

12.5.2.4.3. 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 voltage loads using the independent voltage source option of CIRCU124. For more information, refer to Electric Circuit Analysis.

12.5.2.5. 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

12.5.2.6. Finishing the Solution

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

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

12.5.3. Reviewing Results

The program writes results from a harmonic electric analysis to the results file, Jobname.rth. Results include the data listed below:

Primary data: Nodal DOF (VOLT).

Derived data:


Note:  Some output quantities depend on the element type used in the analysis.


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

  • For a current-based analysis using electric elements, nodal conduction current densities (JCX, JCY, JCZ, JCSUM).

  • For a charge-based analysis using electrostatic elements, nodal electric flux densities (DX, DY, DZ, DSUM).

  • Element current densities (JSX, JSY, JSZ, JSSUM). This output item represents the total (that is, sum of conduction and displacement current densities). It can be used as a source for a subsequent magnetic analysis.

  • Element conduction current densities (or total measurable current density) (JTX, JTY, JTZ, JTSUM).

  • Element Joule heat generation rate per unit volume (JHEAT). This is a time-averaged value.

  • Element stored electric energy (SENE). This is a time-averaged value.

  • For a current-based analysis using electric elements, nodal reaction currents.

  • For a charge-based analysis using electrostatic elements, nodal reaction charges.

You can review analysis results in POST1, the general postprocessor, or in POST26, the time-history postprocessor. To access the general postprocessor, choose one of the following:

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

To access the time-history postprocessor, choose one of the following:

Command(s): /POST26
GUI: Main Menu> TimeHist Postproc

The following table summarizes the applicable labels for the /POST1 and /POST26 commands.

Table 12.15: Command Labels

Output QuantityLabelCommand(s)Analysis
Current-based [1]Charge-based [2]
Nodal DOFVOLT PRNSOL, PLNSOL, ETABLE, NSOL YY
Nodal electric fieldEF PRNSOL, PLNSOL, PRESOL, PLESOL, PRVECT, PLVECT, ETABLE, ESOL YY
Nodal conduction current densityJCY
Nodal electric flux densityDY
Element total current densityJS [3] PRESOL, PLESOL, PRVECT, PLVECT, ETABLE, ESOL YY
Element conduction current densityJT [3]YY
Element Joule heat generation rate per unit volume (time-averaged)JHEAT PRESOL, PLESOL, ETABLE, ESOL YY
Element stored electric energy (time-averaged)SENEYY
Nodal reaction currentAMPS RFORCE, PRRFOR, PRRSOL, PRESOL, PLESOL Y
Nodal reaction chargeCHRGY


  1. PLANE230, SOLID231, and SOLID232 are current-based.

  2. PLANE121, SOLID122, and SOLID123 are charge-based.

  3. Refer to Table 12.8: Current Densities in Low-Frequency Analyses for the meaning of this label.

For a complete description of all postprocessing functions, see The General Postprocessor (POST1) and The Time-History Postprocessor (POST26) in the Basic Analysis Guide.

12.5.3.1. 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) must be available.

The procedures for reviewing POST1 harmonic electric analysis results are identical to the procedures described in Steady-State Current Conduction Analysis with the following exception. Results from a harmonic electric analysis are complex and consist of real and imaginary components. Set KIMG=0 or KIMG=1 on the SET command to read the real or imaginary results respectively.

12.5.3.2. Reviewing Results in POST26

To review results in POST26, the time-history postprocessor, the database must contain the same model for which the solution was calculated, and the results file (Jobname.rth) must be available. If the model is not in the database, restore it using one of the following:

Command(s): RESUME
GUI: Utility Menu> File> Resume Jobname.db

Then use one of the following to read in the desired set of results.

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

POST26 works with tables of result item versus frequency, known as variables. Each variable is assigned a reference number, with variable number 1 reserved for frequency. Therefore the first things you need to do is define the variables using the following commands or GUI paths.

Table 12.16: Defining Variables

StepCommand GUI Path
Define primary data variables NSOL Main Menu> TimeHist Postpro> Define Variables
Define derived data variables ESOL Main Menu> TimeHist Postpro> Define Variables
Define reaction data variables. RFORCE Main Menu> TimeHist Postpro> Define Variables

Once you have defined these variables, you can graph or list them (versus time or any variable) using the following commands or GUI paths.

Table 12.17: Graphing and Listing Variables

StepCommand GUI Path
To graph variables. PLVAR Main Menu> TimeHist Postpro> Graph Variables
To list variables. PRVAR Main Menu> TimeHist Postpro> List Variables
To list only the extreme variables. EXTREM Main Menu> TimeHist Postpro> List Extremes

POST26 offers many other functions, such as performing math operations among variables, moving variables into array parameters, etc. For more information, see The Time-History Postprocessor (POST26) in the Basic Analysis Guide.

By reviewing the time-history results at strategic points throughout the model, you can identify the critical time points for further POST1 postprocessing.