O.W. Andersen
USER’S MANUAL FLD6
LAPLACIAN ELECTROSTATIC FIELDS
MACHINE REQUIREMENTS
IBM PC compatible personal computer, 386/486 with math coprocessor, Pentium or equivalent, 1.44 Mb 3 1/2" diskette drive and at least 4 Mb RAM. The program runs under MS-DOS.
VGA display.
Plotting can be done in color or black and white on a large variety of printers and plotters, on letter size (A4) and larger paper formats. Plots can also be incorporated into documents by a word processor, such as Word or WordPerfect.
PROGRAM INSTALLATION
The program is supplied either on diskettes or transmitted on the Internet, together with installation instructions. It is installed in two directories, \FLD6 and \GRAPHICS, usually in unit C. Directory GRAPHICS is common for several programs, and does not need to be installed if it is already present.
In directory GRAPHICS a program INST will be executed. Questions will be asked on the screen about the display, and instructions will be given about modifications of AUTOEXEC.BAT.
About 61 Mb must be available on the harddisk for temporary storage after the program is installed, if the full capacity of the program is to be utilized.
If the user wants to make or modify a post processor, the Watcom Fortran compiler should be present in directory \WATCOM.
DOS extender DOS4GW.EXE can be removed from directories FLD6 and GRAPHICS and put into another directory, which is included in the PATH command in AUTOEXEC.BAT.
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RUNNING THE DEMO INPUT
An input file DEMO.INP is in directory FLD6. To run the program with this input, enter:
RUN DEMO.INP
After a few seconds, a field plot with 19 equipotential lines is displayed on the screen. The tic-marks show the positions of horizontal and vertical grid lines. Electrodes are red, and insulation is green.
Now use the cursor (arrow) keys to frame a smaller portion of the field plot, preferably in the area of the highest field strength. Strike ENTER, and a blowup plot is displayed on the screen. A new ENTER brings control back to DOS.
To transfer the plots to the printer using shareware PRINTGL, enter commands:
PLOT for the overall plot
BPLOT for the blowup
If you have a 6 or 4 pen plotter, it is usually connected to a serial communication port COM1-4. The pens should be 0.3 mm.
Pen 1: Black - Frame, text and area excluded from the calculations
Pen 2: Red - Electrodes
Pen 3: Blue - Insulation
Pen 4: Green - Equipotential lines
Plotting is done with the commands:
PLOTA4 (PLOTA in the US)
BPLOTA4 (BPLOTA in the US)
For plotting with a word processor, see page 22. Other commands are:
PLOTA3 (PLOTB in the US)
BPLOTA3 (BPLOTB in the US)
PLOTPRN for overall plot on a dot matrix printer
BPLOTPRN for blowup plot on a dot matrix printer
PLOTLAS for overall plot on a laser printer in HP-GL/2 mode.
BPLOTLAS for blowup plot on a laser printer in HP-GL/2 mode.
Output from the program is stored in file OUTPUT. To display it on the screen, enter:
COPYSCR OUTPUTfor direct display with paging, or
EDIT OUTPUTwith the use of the DOS editor.
Printing of the output can be done from Windows (see page 22), or directly with the command:
COPYPRN OUTPUT
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To display and print the input file, enter:
COPYSCR DEMO.INP
COPYPRN DEMO.INP
The output file contains detailed information about node potentials and field strengths in the triangles between the grid lines:
Horizontal lines 8 and 10
Vertical lines 1 and 4
This was requested in the input. Additional detailed information can be provided in file OUTPUT by entering the command
DETAILS
and answering the prompts. As a suggestion, in response to the prompts, answer:
Horizontal lines 5 and 7
Vertical lines 1 and 4
File OUTPUT can now be displayed and printed, as before.
To display the finite element grid on the screen, enter:
GRIDSCR
The grid can now be plotted, but to make it possible also to plot a blowup of the grid, frame a smaller portion of it with the cursor keys, as before.
It is seldom necessary to plot the grid. When it is done, the quality will be better if pens 2 and 3 are replaced with two black 0.7 mm pens. Overall and blowup plots are then made with the same commands as before.
The latest overall plot on the screen (field plot or grid) can be brought back with the command:
PLOTSCR
The field plot is brought back with:
FIELDSCR
and the grid with:
GRIDSCR
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ENTERING NEW INPUT
Input file names can be chosen arbitrarily, as long as they follow DOS conventions. However, to make it easy to retrieve old files, it is suggested that names are of the type:
961112-1.LAB
The file name starts with the date when the input was run, as yymmdd (y=year, m=month, d=day). Then follows the run number on that date, if more than one run was made. The three letter extension indicates for whom the run was made.
New input is made up most easily by modifying old input. It can be done by copying the old file to the new file, and then modifying it with an editor. Or it can also be done interactively. Try this with DEMO.INP as the old file, by entering:
INPUT DEMO.INP 961112-1.LAB
or by using another name for the new file.
A prompt on the screen asks for a new identification. The old identification was:
CYLINDER OVER PLANE
As a suggestion, enter:
NEW IDENTIFICATION
or any other combination of letters, numbers and special symbols on the keyboard.
Then one number at a time from the old input appears on the screen, with an explanation of what it means. If the same number is to be used again in the new input, simply strike ENTER. Otherwise enter the new number, and then strike ENTER. This procedure is also explained on the screen.
When running INPUT for the first time, change perhaps only one or two numbers. It is not important that all the input is fully understood at this stage. It will be explained in more detail later. When finished, compare the two inputs after printing them out:
COPYPRN DEMO.INP (was done earlier)
COPYPRN 961112-1.LAB
When input is checked or changed with an editor, headings can be inserted in the input file with the command:
HEADINGS 961112-1.LAB (or with another file name)
Before using the file, the headings must be removed with the command:
CLEANUP 961112-1.LAB
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A plot of the contour lines will be shown on the screen, and obvious input errors may be caught, by giving the command:
CHECK 961112-1.LAB
Another command which does the same, and also modifies the input grid automatically, if necessary to satisfy program requirements, is:
CORRECT 961112-1.LAB
Modified input will replace the original input, in this case in file 961112-1.LAB. If desired, the original input can be retrieved from file \GRAPHICS\INP1.FIL.
Before modification of the grid with CORRECT, it should be reasonably close to being right, and the number of vertical and horizontal break lines should be less than the maximum 64 with a good margin. However, even so, there is no guarantee of a successful modification.
An interactive graphical input program can be used when the new input has the same geometry as an existing input file, and only the coordinates are different. Try it with the commands:
GRAPHINP DEMO.INP NEW.INP
GRAPHINP TRANSF.INP NEW.INP
AUXILIARY FILES
Auxiliary files have the extension FIL, and are created by the programs. Some of them are deleted after they have served their purpose, others are kept and will appear in the directories. It is not normally necessary to pay any attention to them. However, it is useful to know the functions of two of the files in directory GRAPHICS. They are FOR.FIL and BAS.FIL.
The proper FOR.FIL is needed to run:
DETAILS and other post processors
FIELDSCR (creates a new BAS.FIL)
GRIDSCR (creates a new BAS.FIL)
The proper BAS.FIL is needed to run all the other plotting commands.
Blowup plots are normally preceded by a blowup on the screen. If they are not, overall plots will be produced, with the scale entered interactively.
If plots are to made at a later stage for earlier runs, it is necessary to save BAS.FIL.
It may also be desirable sometimes to save the file OUTPUT, in case it should be reexamined or printed later.
Of course, as long as the input file is saved, everything else can be recreated anyway.
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PROGRAM DESCRIPTION
An early version of the program is described in the paper:
O.W. Andersen, "Laplacian Electrostatic Field Calculations by Finite Elements with Automatic Grid Generation", IEEE Transactions on Power Apparatus and Systems, vol. PAS-92, Sept./Oct. 1973, pp. 1485-1492.
Numerous improvements have been made since this paper was written. One of them is that the finite element equations are now solved directly by Gaussian elimination, instead of as previously by iteration. Iterative solution used to have significant advantages in terms of speed and storage requirements, but with newer computers, it is more important that Gaussian elimination is safer and more accurate.
The grid generation has also been vastly improved, to give the best possible grid under all circumstances with maximum numerical accuracy, and a minimum of restrictions on the input specifications.
LAPLACIAN ELECTROSTATIC FIELDS PROGRAM FLD6 INPUT SHEET
Numerical data are entered with the first digit in columns 1,11,21 etc., as indicated. (Does not apply to coordinate lines.) Decimal point is optional.
IDENTIFICATION (line 1): Max. 80 characters, including blanks
Col. Data Line
FLAT / AXI-SYMMETRIC FIELD (1 or 2) 1
MINIMUM RADIUS (zero if flat field) 11 2
SCALE, INPUT DRAWING (usually 1) 21
CAPACITANCE REQUIRED (0 or 1) 31
1 3
VERTICAL GRID 11 4
DENSITY BREAK LINES 21 5
(Remainder of lines must 31 6
be filled out with zeros. 41 7
Max. 300 grid lines and 51 8
60000 nodes.) 61 9
71 10
COORDINATE LINE(S) *1 11
1 12
HORIZONTAL GRID 11 13
DENSITY BREAK LINES 21 14
(Remainder of lines must 31 15
be filled out with zeros. 41 16
Max. 300 grid lines and 51 17
60000 nodes.) 61 18
71 19
COORDINATE LINE(S) *1 20
POTENTIALS AND FIELD STRENGTHS REQUIRED BETWEEN
FIRST HORIZONTAL LINE ) 1 21
LAST HORIZONTAL LINE ) zeros, if not 11 22
FIRST VERTICAL LINE ) required 21 23
LAST VERTICAL LINE ) 31
SCALE, FIELD PLOT (used only for printer or plotter, not on screen) 1
NUMBER OF EQUIPOTENTIAL LINES (19 gives 5% volts per line) 11 24
RELATIVE PERMITTIVITY, IF NOT GIVEN OTHERWISE 21
NUMBER OF CONTOUR LINES (max. 500) 31
For each contour line:
NUMBER OF POINTS (max. 150, 1500 total) *2 1 25
RELATIVE PERMITTIVITY (zero for electrodes) 11 27
POTENTIAL, VOLTS (zero, except at electrodes) 21 29
CODE (2 at electrodes, otherwise usually 0)*3 31
COORDINATE LINE(S) *1 26,28,30
NUMBER OF POINTS (max. 150, 1500 total) *2 1 31
RELATIVE PERMITTIVITY (zero for electrodes) 11 33
POTENTIAL, VOLTS (zero, except at electrodes) 21 35
CODE (2 at electrodes, otherwise usually 0)*3 31
COORDINATE LINE(S) *1 32,34,36
NUMBER OF POINTS (max. 150, 1500 total) *2 1 37
RELATIVE PERMITTIVITY (zero for electrodes) 11 39
POTENTIAL, VOLTS (zero, except at electrodes) 21 41
CODE (2 at electrodes, otherwise usually 0)*3 31
COORDINATE LINE(S) *1 38,40,42
*1: See separate description.
*2: Actually pairs of coordinates, codes, etc.
*3: Code 1 excludes an area from the calculations, with equipotential lines perpendicular.
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SPECIFICATION OF INPUT
LINE 1. The identification can consist of up to 80 characters, including blanks. It will appear on the first output sheet, and also on the field plot on the printer or plotter. Any combination of letters, numbers and special symbols on the keyboard can be used.
LINE 2. The drawing is always oriented with the x or r-axis horizontally, and with the y or z-axis vertically. The origin for input coordinates must be in a position where all the coordinates come out positive, and is often in the bottom left corner. For axi-symmetric fields, true radii are often given as input.
Axi-symmetric problems always have the z-axis to the left. The minimum radius is the true radius from the axis of symmetry. It will be equal to zero if the axis of symmetry is the left field boundary.
The scale of the input drawing (a smaller drawing has a smaller scale) should nearly always be specified as one. In any case, it should be between 0.1 and 10, for the output to contain a sufficient number of significant digits. If in fact the scale is outside of this range, it should be multiplied by an appropriate factor, for example 0.1 or 10, to make it come out right. The specified minimum radius (col. 11) and the output information must then also be modified accordingly.
LINES 3 TO 10. Line numbers are entered for vertical grid lines, where the grid density changes (grid density break lines). In the example in figures 3 and 4 of the IEEE paper, they are 1, 13 and 25.
Field strengths are assumed to be constant within each triangle in the numerical solution, and the grid should be fine enough for this to be true within acceptable accuracy, especially in critical regions. In any case, the grid lines must be close enough, so that contour line points are at least as far apart as the grid lines in the same region.
LINE(S) 11. One or more lines which contain x or r-coordinates of the grid density break lines are entered here. Up to 10 coordinates are entered on one line. Each coordinate consists of a five digit number with one digit after the decimal point. Then there is a blank before the next coordinate. When a coordinate is less than 1000 mm, it is entered with leading zeros. In the example, the coordinates are:
0000.0 0050.0 0120.0
LINES 12 TO 19. In the example, horizontal grid density break line numbers are 1, 9 and 39.
LINE(S) 20. y-coordinates in the example:
0000.0 0040.0 0100.0
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LINES 21 TO 23. The detailed output information increases the bulk of the output and the computing time significantly, and should therefore be limited to those areas where it is of real interest. The field strengths in triangles adjoining those with the highest calculated values will give valuable information about the accuracy of the results.
If only one area of detailed output is desired, lines 22 and 23 are filled out with zeros.
Detailed output information can also be requested after the program is run, with the command DETAILS (see earlier). DETAILS creates a new file OUTPUT, and destroys the earlier file.
LINE 24. The scale of the field plot is unimportant for the plot on the screen. It is used for the plot on the printer or plotter, but if the value is given too large, it is reduced automatically by the program. The plot is automatically tilted 90 degrees, if this permits a better utilization of the paper.
LINES 25. It is important that the contour lines are entered in a proper sequence, since the grid is fitted to line segments that are common for two or more lines only the first time they are entered. This usually means that electrodes should be entered first, so that they receive the proper potentials and codes throughout.
Along straight line boundaries, it is sometimes desirable to be able to specify a linear variation of potential. This can be done by using code 2.1, with the potential of the first point in column 31, and of the last point in column 41.
The number of points (col. 1, line 25) is used only to enable the program to read the input properly. It actually means the number of pairs of five digit numbers, entered in coordinate line format. This should be kept in mind when preprogrammed shapes (see separate instructions) are used to describe the contour lines.
COORDINATE LINES
A line can contain one, two, three, four or five pairs of coordinates, codes, etc. When more lines are needed because there are more than five pairs, only the last line can have fewer than five.
Each coordinate usually consists of a five digit number, with one digit after the decimal point. Then there is a blank before the next coordinate. The x or r-coordinate is entered first, then the y or z-coordinate. When a coordinate is less than 1000 mm, it is entered with leading zeros. Example:
0000.0 0100.0 0030.2 0400.5 0102.6 1206.8
x y x y x y
point 1 point 2 point 3
Other possibilities are:
123.45 Normally coordinates can be rounded to the nearest 1/10 mm.
1234.56 To be avoided, because no blank will separate the next number.
-123.4 Permissible as coordinate of center of circular arc.
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PREPARATION OF INPUT DRAWING
The preparation of the input drawing for transfer of coordinates should be done with great care.
1. A rectangular section is framed (by pencil), where the field is to be calculated.
2. If the boundary conditions make it desirable, estimated flux lines can be drawn in, deleting parts of the section from the calculations (Fig. 10 of the IEEE paper). This is rarely necessary.
3. Positions of grid density break lines (Fig. 3 of the IEEE paper), whose coordinates are to be entered on input lines 11 and 20, are marked on a horizontal and a vertical line on the drawing. The spacing between the lines can also be put in, and the line numbers which are to be entered on input lines 3-10 and 12-19. During this process it is important to make mesh sizes reasonably in accordance with the requirements in the various areas, with the finest meshes in the regions of the highest field strengths. It is also important to observe requirements 8 and 10 in the "Instructions for Entry of Coordinates". Grid lines must always be spaced at least as close to each other as the contour line points in the same region. If they are not, the situation may be remedied by running program CORRECT (see page 5).
4. Now all the points along electrodes, dielectric materials and estimated flux lines, which are to be entered, are marked on the drawing with their coordinates. This is done in accordance with "Instructions for Entry of Coordinates".