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O.W. Andersen USER’S MANUAL FLD6 LAPLACIAN ELECTROSTATIC FIELDS PROGRAM INSTALLATION FLD6 must be installed in directory (folder) \FLD6 on the same computer and in the same unit (usually C) as GRAPHICS. The program is supplied on the Internet as e-mail attachments together with installation instructions RUNNING THE DEMO INPUT Here all the Command Prompt commands, directories (folders) and file names will be in capital letters. However, they are case insensitive, and small letters can also be used. 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. It has been drawn on a Visual Basic Form. If the picture appears to be cropped, adjust the file \GRAPHICS\SIZESCR.FIL. At the same time a bitmap picture file PLOTFILE.BMP has been produced in directory GRAPHICS. Close the form and enter command: PLOT The plot now reappears in a standard Windows program. The tic-marks to the left and at the bottom show the positions of horizontal and vertical finite element grid lines. Electrodes are red, and insulation is green. If it is now desired to print the field plot, crop the picture file first to remove empty space and save it. Rather than printing it directly, it is recommended to transfer the picture file to Microsoft Word. Here it can easily be resized and comments added before printing. Output from FLD6 is stored in file OUTPUT in directory FLD6. To display it on the screen for subsequent printing, enter: FILE OUTPUT Batch command FILE is equivalent to the DOS command START NOTEPAD, where NOTEPAD is the standard Windows program used here for viewing, editing and printing files. The first time it is invoked, it should be set to Courier New size 9 text, word wrap, and to no top and bottom text when printing. The window should always be maximized. -2- To display and print the input file, enter: FILE DEMO.INP The output file contains detailed information about node potentials and field strengths in the triangles between the grid lines: Horizontal lines 48 and 49 Vertical lines 1 and 2 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 47 and 49 Vertical lines 1 and 3 File OUTPUT can now be displayed and printed, as before. To display the finite element grid on the screen, enter: GRID After the form is closed, the grid also reappears with the command: PLOT -3- INPUT The demo input file can be viewed with the command: FILE DEMO.INP What the numbers mean can be found on the input sheet, page 5. For an explanation of what else can be done with the input file, copy it first to a new file with the command: COPY DEMO.INP NEW.INP Introduce headings with the command: HEADINGS NEW.INP To see how the file now has been modified, enter: FILE NEW.INP The abbreviated headings on the input file also explain the numbers. With a little experience, that explanation suffices to enter new numbers and to make up new input files. Old input as similar as possible is first copied to a new input file. Then headings are introduced and the file changed. Numbers always start in columns 1, 11, 21 and so on. They can be entered with or without decimal point. Before the new file can be run, the headings must be removed. Do this first with: CLEANUP NEW.INP A file without headings can have headings introduced and be viewed at the same time with: HEADFILE NEW.INP Headings can also be removed and the file run at the same time with: CLEANRUN NEW.INP New input must be entered very carefully, following explanations on the input sheet and instructions elsewhere in this manual. Small mistakes like a comma instead of a decimal point or a number starting in the wrong column are not tolerated. Some mistakes are caught by the program and are explained on the output. Another way to catch mistakes is by giving a command such as: CHECK NEW.INP The input must here be without headings. A picture similar to a field plot, but without equipotential lines, will be displayed on the screen. Mistakes with the geometry can be caught this way. -4- Another command which does the same, and also modifies the input grid automatically, if necessary to satisfy program requirements, is: CORRECT NEW.INP Modified input will replace the original input, in this case in file NEW.INP. 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. 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 DETAILED INFORMATION 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 zero) *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 *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 *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. -6- SPECIFICATION OF INPUT LINE 1. The identification can consist of up to 80 characters, including blanks. Most combinations 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 -7- 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 11, and of the last point in column 21. 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. -8- 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 4). 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". INSTRUCTIONS FOR ENTRY OF COORDINATES 1. The position of the reference point (origin) should normally be at the bottom left corner. However, for axi-symmetric fields, true radii can be given as input. 2. The grid lines are horizontal and vertical, and the drawing should be oriented accordingly. For axi- symmetric problems, the axis of symmetry must be in the vertical direction (the same as the y- direction in flat, two dimensional problems), with the axis to the left. 3. On input line 11 only x(r)-coordinates are entered, on line 20 only y(z)-coordinates. 4. Contour lines can be open or closed curves. Single points can also be entered. For closed curves, the last point must have the same coordinates as the first. Only for closed curves, relative permittivity can be given different from zero. Whether the curves are entered in a clockwise or counter-clockwise direction is unimportant. 5. When points are supposed to have the same coordinates, or a point is supposed to be on a line segment belonging to another contour line, a maximum error of 0.01 mm is permitted, to allow for slight inaccuracies. 6. When the same line segment is entered twice, the grid is only fitted to the line segment the first time. Therefore, whenever electrodes have line segments in common with other contour lines, the electrodes should be entered first, to make sure that all the points on the electrodes receive the proper potential and code. -9- 7. A maximum of 150 points is permitted per contour line, for a maximum of 500 lines, but the total number of points must not exceed 1500. If more than 150 points are required for a contour line, it must be divided up into two or more parts. 8. The points should not be closer to each other than necessary, and with a spacing at least equal to the mesh size in that region (except when the points coincide). 9. If a contour line is put in outside of the section boundary, the program will move it to the section boundary. 10. When part of a contour line follows a section boundary, this part must be entered first, and points inside of the boundary must be further away from it than half a mesh size. This avoids problems that otherwise might arise due to grid points being unavailable on the boundary when this part of the line is fitted. 11. If a portion of the section is to be excluded from the calculations, a closed curve around this portion is specified with code=1. Permittivity and potential should be given as zero. Equipotential lines will enter at right angles. 12. In program FLD6, conducting media with floating potentials can be entered only as closed curves (conducting bodies). If in fact it is an open line (a surface), it must be approximated as a thin body. Conducting bodies are treated as dielectric materials with a high fictitious permittivity, such as 9000. For conducting surfaces, more accurate solutions are obtained by using program FLD7, Complex Potential Electric Fields (see separate instructions). A high fictitious surface conductivity is specified, such as 9000 1/Gohm. 13. Problems have sometimes arisen when three lines meet in a point at sharp angles, as shown in the figure. In such a case, the middle line must not be entered last, because grid points may then no longer be available for the line fitting. 14. An insulated electrode is entered with the outer contour first, with specifications for the insulation, and then the inner contour, with specifications for the electrode. 15. An electrode could have a shape as shown in the figure, an open line connected to a closed curve. In such a case, the 1 2 3 two parts should be specified as two separate contour lines. Only then the points within the area 2-3-4-5-2 will be recognized 5 4 as being inside a closed curve, and will receive fixed potentials. If only one contour line is used to describe the electrode, the program will still work if point 2 is put in twice, also as an intermediate point between points 1 and 3. But the program running time will be longer than necessary, and the field strengths inside of the electrode might not come out exactly zero, because of numerical errors. Intermediate points are only put in automatically by the program when they come from other contour lines, as in the example in the section "Preprogrammed Shapes". - 10 - ERROR MESSAGES The program aborts and prints out one or more of the following error messages, if it is necessary to modify the input. 1. The number of horizontal or vertical grid lines is more than 300. 2. The number of nodes in the grid is more than 60000. 3. There are more than 500 contour lines. 4. The contour line is described by more than 150 points. 5. The total number of points exceeds 1500. 6. The permittivity is given different from zero, and the last point on the contour line is not equal to the first. 7. The line fitting was interrupted for line segment - near -. (Coordinates define the line segment and the point where the line fitting got stuck.) 8. This point is too close to the preceding point -. (The point is defined by its coordinates.) 9. The program has moved node no. - from one line to another line which is too close. (The node is defined by its number and its coordinates.) 10. The area came out negative or zero for triangle with -. (The triangle is defined by its node numbers and coordinates.) Change line sequence or move grid lines. 11. Coordinates of grid density break lines are not in increasing order. - 11 - PREPROGRAMMED SHAPES Two preprogrammed shapes that can be entered in a simplified manner are used very frequently, circular arcs and rectangles with horizontal and vertical sides. The way they are entered will be explained by means of the example in the figure. mm electrode 50 30 25 =2 =3 10 electrode 0 30 45 65 95 110 The bottom electrode is specified only by its two end points. The intermediate points are put in automatically by the program. The region with = 2 includes a circular arc at the upper left corner. It is somewhat roughly drawn, but is supposed to have 5 points, between which straight line segments are drawn by the program. It can be specified as follows: 0030.0 0000.0 0065.0 0000.0 0065.0 0025.0 9000.0 0001.0 Codes 0005.0 0015.0 Number of points and radius 0045.0 0010.0 Coordinates of center (can be negative) 0090.0 0180.0 Starting angle and finish angle (degrees) 0030.0 0000.0 An x-coordinate 9000 mm is recognized by the program as a code, telling it that a preprogrammed shape of some kind follows. The value 1 in the corresponding y-position indicates that the shape is a circular arc. Angles are measured counter-clockwise from the horizontal, in the usual way. If the contour line progresses through the arc counter-clockwise, as in the example, the finish angle must be greater than the starting angle. Conversely, if the progression is clockwise, the finish angle must be smaller than the starting angle. The region with = 3 is a rectangle with horizontal and vertical sides, which can be specified as follows: 9000.0 0002.0 Codes 0065.0 0000.0 Coordinates of lower left corner 0095.0 0030.0 Coordinates of upper right corner - 12 - Right angle insulation barriers with sharp and rounded corners have also been preprogrammed, because of their use in insulation structures of large transformers and reactors. SHARP RIGHT ANGLE BARRIERS (4 possible orientations) X2, Y2 9000.0 0004.0 Codes X1 Y1 X2 Y2 T1 T2 Th’k = T2 Th’k = T1 X1, Y1 X1, Y1 X2, Y2 CURVED RIGHT ANGLE BARRIERS (4 possible orientations) The angles are similar to the ones shown above, except that the right angle corner is rounded. This makes T1=T2=T, and the specifications are: 9000.0 0005.0 Codes X1 Y1 X2 Y2 T R Thickness and inside radius of corner In the region of the rounded corner, it is important that the grid is sufficiently dense. It will usually be satisfactory to have the line spacing no more than T or (outside radius)/5, whichever is smaller. 7 contour line points are generated along the inside radius, 8 along the outside radius. - 13 - POST PROCESSING After the main program has been run, the run identification and all the essential calculated and input information are in file \GRAPHICS\FOR.FIL, and can be retrieved for further processing. This includes all the potentials and node and contour line coordinates. Three post processors are supplied with the program, both in source code and in executable versions. One of them is called DETAILS, and has been described earlier on page 2. Another one draws a graph on the printer, plotter or screen of field strengths along or perpendicular to a specified line, and is started with the command: GRAPH If an open contour line is drawn only for the purpose of calculating field strengths along it, permittivity, potential and code should all be given as zero. Points along it must be specified wherever it crosses or touches other contour lines. The third post processor is for analysis of breakdown stresses in oil and creepage stresses along transformer board in oil. Curves are drawn for stress distribution, and comparisons can be made directly with permissible limits. It is based on a method proposed by the Swiss insulation manufacturer Weidmann and is started with the command: WEIDMANN It is recommended to have printed output available before running GRAPH and WEIDMANN, in order to answer the questions on the screen. Coordinates must be given accurately, down to the last digit. The Fortran source code for all post processors is in file PPROC.FOR. It contains numerous comment lines, and new post processors can be added by the user, if desired. - 14 - POLARITY REVERSAL When a dc voltage is applied to an insulation structure, at first there will be a capacitive distribution of potentials. The distribution can be found by running FLD6 in the normal way, with permittivities specified for the different materials. After considerable time, in the order of minutes or even hours, the charges throughout the structure will have reached an equilibrium state, and the potential distribution will be resistive. It can be found by running FLD6 with permittivities replaced by conductivities. If now the polarity of the dc voltage is reversed, this involves a sudden change equal to twice the original voltage. Since again considerable time will elapse before the charges reach their new equilibrium state, at first there will be a capacitive distribution due to the step voltage, superimposed on the resistive distribution before the change. If Vac is the potential at a point in the insulation calculated for capacitive distribution, and Vdc is the potential calculated at the same point for resistive distribution, immediately after the polarity reversal, the potential will be (or with opposite signs): Vpr = 2Vac - Vdc The highest and lowest potentials are no longer necessarily at the electrodes, and the difference between them will normally be considerably higher than for the purely capacitive or resistive distribution, sometimes approaching twice the value. This, combined with a very uneven distribution across materials of different characteristics, can result in extremely high stresses in sometimes unexpected areas. Two input files PRAC.INP and PRDC.INP are supplied with the program. They are for ac and dc distribution respectively, for a very simple insulation structure. The only difference between them is that permittivities in PRAC.INP have been replaced by conductivities in PRDC.INP. If it is desired to study the capacitive and resistive distributions first, this can be done in the normal way with the commands: RUN PRAC.INP and RUN PRDC.INP To get the solution at polarity reversal, use the command: PR PRAC.INP PRDC.INP The program then solves the two cases in sequence, and superimposes the potentials from the two solutions in the proper way. The field plot and the program output will be for polarity reversal. One application of this is in transformers for HVDC transmission lines. The insulation structures are partly stressed by dc voltages, which change polarity during transitions between rectifier and inverter operation. - 15 - ANALYSIS OF BREAKDOWN AND CREEPAGE STRESSES IN OIL It was mentioned on page 14 that the program has a post processor called WEIDMANN. It is used for the analysis of breakdown stresses in oil and for creepage stresses along transformer board in oil. The method was developed by H. Weidmann AG, Switzerland. Creepage strength is a function of the length of the creepage path, and follows a hyperbolic function in a homogeneous field, similar to the breakdown strength of oil versus gap length. Creepage strength of transformer board in oil, approximately: kV/mm = 15 * mm-0.37 rms Breakdown strength of oil, approximately: kV/mm = 21.5 * mm-0.37 rms These curves are drawn by the post processor, and can be compared with actual stresses. The problem, however, is how to relate actual stresses to those in a homogeneous field. An example will explain the procedure. Fig. 1 shows a field plot for a 400 kV "Faltenbalg" terminal connection in a transformer, and Fig. 2 shows a bar graph of the creepage stress along the surface of the insulation. Post processor WEIDMANN analyses this stress, and draws the creepage stress distribution curve on Fig. 3. The criterion for a satisfactory design is that this curve is under the creepage stress limit curve with a sufficient margin. The kV/mm at a certain point on the stress distribution curve is the maximum average stress for the corresponding length. As an example, the stress at the 100 mm point is found by taking a length 100 mm as shown on Fig. 2, and moving it back and forth to a position where the average stress for this length is a maximum. This average stress is the 100 mm point on the stress distribution curve on Fig. 3. The first point on the stress distribution curve gives the maximum calculated stress along the creepage path, at a length equal to the corresponding length of the triangle side in the finite element calculation. The last point on the stress distribution curve gives the average stress along the whole length of the creepage path. The end points of a creepage path are points where either the stress changes direction, or where it goes down to zero and remains there for a considerable length. Analysis of breakdown stresses must be made for one oil gap at a time (between insulation barriers or electrodes). After RUN FALTENBG.INP (not in demo) Fig. 1 After GRAPH Contour line 17 Fig. 2 After WEIDMANN Actual/calculated field strengths 6300 Contour line 17 Fig. 3 - 19 - THE COMMAND PROMPT ENVIRONMENT The Command Prompt window should be maximized and the size adjusted to fill the screen after right clicking the top title bar. Cursor size small and letter size 12x16 pixels are recommended. If Command Prompt goes into full screen mode by an application, it can be brought back with Alt-Enter. Since many PC users are not familiar with Command Prompt, here are some hints and frequently used commands. The commands are examples and may be modified in obvious manners. Large and small letters are interchangeable. Commands given once on startup, perhaps in a STARTUP.BAT file: SET COPYCMD=/Y Deactivates warning on overwriting existing files. PATH=C:\SYSTEM;C:\QBASIC Specifies search paths for executable files. SUBST P: C:\DRIVEP Substitutes drive P for directory (or folder) C:\DRIVEP making P a virtual drive (or unit). Other commands: C: Moves to unit C or another unit. CD\ Changes to base directory. MD GRAPHICS Makes directory GRAPHICS. CD\GRAPHICS Changes directory to GRAPHICS, just below the base directory. COPY OLD.INP NEW.INP Copies old file OLD.INP to a new file NEW.INP. COPY /? Explains options available for command COPY. REN OLD.INP NEW.INP Renames OLD.INP as NEW.INP. DEL OLD.INP Deletes OLD.INP. DIR *.INP Lists all files in the directory with extension INP. DIR *.I?? Lists all files in the directory with three letter extension starting with I. START NOTEPAD OUTPUT Invokes Windows program NOTEPAD with file OUTPUT. START PLOTFILE.BMP Starts a standard Windows program to process the bitmap file. After RUN DEMO.INP After GRAPH