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O.W. Andersen
USER’S MANUAL, ACCAN
AC CIRCUIT ANALYSIS
PROGRAM INSTALLATION
ACCAN is transmitted as a zip-file. It is extracted and installed in any directory (folder). The program can
also be installed on a memory stick and run from there.
RUNNING THE DEMO INPUT
N2
B3
Nx = Node x
Bx = Branch x
B4
B5
B6
N1
Fig. 1
Here all the Command Prompt commands and file names will be in capital letters. However, they are case
insensitive, and small letters can also be used.
To run the program with an input file DEMO.INP, enter:
RUN DEMO.INP
After about a second, the calculations are completed.
Output from ACCAN is stored in file OUTPUT. To display it on the screen, enter:
FILE OUTPUT
Batch command FILE starts the standard Windows program NOTEPAD. It will be used here for viewing,
editing and printing text files. The first time it is invoked, it should be set to Courier New size 8, word
wrap, and to no top and bottom extra text when printing. The window should always be maximized.
For the three parallel layer reactor, special input has been made to draw the connection diagram on the
screen, with indication directly on the diagram of calculated node voltages and branch currents. How this
is done, will be explained later. The input is in file DEMO.PLT. Enter command:
CONN DEMO.PLT
-2-
The graph that appears on the screen has been drawn on a Visual Basic Form. If the picture appears to be
cropped or too small, adjust the file SIZESCR.FIL. At the same time a bitmap picture file
PLOTFILE.BMP has been produced. Close the form and enter command:
PLOT
The graph now reappears in a standard Windows program. If it is desired to print it, crop the picture file
first to remove empty space and save it. Microsoft Office Picture Manager or Microsoft Paint can be used
for that. 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.
INPUT
The demo input file can be viewed with the command:
FILE DEMO.INP
What the numbers mean can be found on the input sheets. 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
-3-
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 sheets 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.
PROGRAM DESCRIPTION
ACCAN is suitable for load flow calculations, short circuit calculations, and for other types of ac circuit
analysis, also those involving mutual reactances (such as the reactor on Fig. 1). There are no restrictions on
how the circuits are connected.
The classical load flow solution methods consider only voltages to be the primary variables. This gives a
minimum of unknowns in the equations, and helps in being able to solve large problems. However, it
reduces the flexibility in the specification of the problems.
-4-
In ACCAN, both node voltages and branch currents are considered as primary variables. In load flow
calculations, generators are represented as voltage or current sources, and loads either as impedances or
current sources. Values of current in the current sources depend upon how the problem is formulated, and
only rough estimates may be known initially. Therefore, an iterative solution is often required.
Adjustments are made by the program on the basis of results from previous iterations.
At each iteration a complex coefficient matrix is set up relating the variables to each other on the basis of
node and branch equations. The matrix equation is solved directly by Gaussian elimination, immediately
yielding values of all the variables.
A slack bus generator is modelled as a simple voltage source with a fixed specified voltage. Other
generators can be modelled as current sources in a variety of ways. Active and reactive power can be
specified in the generator itself, or into or out of a relevant transmission line. The reactive power can also
be adjusted automatically by the program within specified limits, to give a specified voltage either at the
generator bus, or in an adjacent node.
Loads can be fixed impedances or current sources. Active and reactive power can be specified,
independent of voltage.
Shunt reactors and capacitors can also be modeled as current sources. The program can determine the
reactive power within specified limits to give a specified voltage at the reactor or capacitor bus.
Transmission lines can be either simple impedances or -equivalents, specified in per unit or absolute
values. Tap changing transformers can have the tap setting determined by the program, to give an
approximate specified voltage at a relevant node.
From a given set of input data, transmission lines can be disconnected simply by changing a code.
Systematic input data modification can be made by a small subroutine.
Normal output includes node voltages, branch currents, active and reactive power into and out of branches,
and deviations from specified voltages and power. Sums of active and reactive power are given for
generation, load, transmission lines and shunt reactors and capacitors.
A post processor permits graphical output in the form of a complete or partial connection diagram, with the
results of the calculation written in. All the user must do is to make up a small input file with plotting
instructions for each branch and node, or in the case of a load flow calculation, for each bus and
transmission line. An input program is available for this purpose.
If the connection diagram is large, calculation results may be hard or impossible to read on the graphical
output after the necessary reduction in scale. The diagram should then be broken up into several smaller
partial diagrams.
The program is limited to 500 variables (node voltages and branch currents), which in a load flow problem
corresponds to about 100-140 busses.
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 1
Numerical data are entered with the first digit in columns 1,11,21 etc., as indicated. Decimal point is optional.
The calculations are often made in per unit. This is always true in load flow calculations. Otherwise absolute values can be used,
provided the numbers stay within the limits of the formatted output.
Nodes and branches are numbered. Start with the nodes. Node 1 receives the reference potential zero. In a one line diagram of a
three phase system. it represents the neutral. Each separate circuit (without electrical connection) must have a node with the
number one. When all the nodes are numbered, continue with the branches. The first branch receives the number of the last node
plus one. The last branch number is the same as the total number of variables, which are node potentials and branch currents. Each
branch contains only one component (impedance, voltage source, current source), and terminates at two nodes. Positive power flow
is from the first to the second node. Each tap changing of off ratio transformer introduces one extra node.
IDENTIFICATION (line 1):
No commas and max. 80 characters, including blanks
NUMBER OF MUTUAL REACTANCES ( 500, usually 0)
LAST NODE NUMBER
LAST BRANCH NUMBER
MAX. NUMBER OF ITERATIONS (  20, 1 if direct solution)
MAX. CHANGE OF VOLTAGE BETWEEN ITERATIONS (  0.0001 pu)
RELAXATION FACTOR (  1)
FREQUENCY
BASE 3-PHASE POWER, MVA
Col.
1
11
21
31
41
51
*1 61
*2 71
Data
Line
2
*1 Only required  0 if needed to convert input data to per unit or ohms.
*2 It is recommended to make the base MVA 1, 10, 100 or 1000.
Mutual reactances between branches (not required in load flow calculations)
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
FIRST BRANCH NUMBER
1
SECOND BRANCH NUMBER
11
MUTUAL REACTANCE (can be negative) 21
Input sheets 3 to 8 are not normally filled out. They only serve as a source of information about the data that are to be entered on
input sheet 2.
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 2
Column
1
11
21
31
41
51
61
71
1
11
21
31
Branch Code
See instructions on input sheets 3 to 8
New line
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It is not necessary to enter branch numbers in ascending order.
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 3
Generation
Slack bus, specified U
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, specified
ANGLE OF U, degrees, specified (usually 0)
Voltage source with specified U and P
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, specified
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, specified
Specified U, P, Q-MIN, Q-MAX
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, specified
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, specified
REACTIVE POWER Q, initial
Q-MIN, specified
Q-MAX, specified
Specified P, Q
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, initial
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, specified
REACTIVE POWER Q, specified
Specified U, Q-MIN, Q-MAX, active power interchange
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, specified
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, initial
REACTIVE POWER Q, initial
Q-MIN, specified
Q-MAX, specified
ACTIVE POWER INTERCHANGE
INTO = 1, OUT OF = 2
BRANCH NUMBER (transmission line or cable)
Specified Q, active power interchange
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, initial
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, initial
REACTIVE POWER Q, specified
ACTIVE POWER INTERCHANGE
INTO = 1, OUT OF = 2
BRANCH NUMBER (transmission line or cable)
Col.
1
11
21
31
41
Data
Line
2
bus
U
1
11
21
31
41
51
1
11
21
* 31
41
51
61
71
1
3
node 1
12
U
bus
I
1
11
21
13
node 1
31
41
51
61
1
11
21
* 31
41
51
61
71
1
11
21
31
14
U
bus
I
1
11
21
15
31
41
51
61
71
1
11
* The specified voltage is conditional on the reactive power staying within specified limits.
node 1
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 4
Generation, cont.
Specified P, reactive power interchange
BRANCH NUMBER
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, initial
ANGLE OF U, degrees, initial (often 0)
ACTIVE POWER P, specified
REACTIVE POWER Q, initial
REACTIVE POWER INTERCHANGE
INTO = 1, OUT OF = 2
BRANCH NUMBER (transmission line or cable)
Specified P, Q-MIN, Q-MAX, U in adjacent node
BRANCH NUMBER, GENERATOR
CODE
BUS, NODE NUMBER
ABS. VALUE OF U, adjacent node, specified
IN ADJACENT NODE NUMBER
ABS. VALUE OF U, GENERATOR BUS, initial
ANGLE OF U, GENERATOR BUS, DEGREES, initial
ACTIVE POWER P, specified
REACTIVE POWER Q, initial
Q-MIN, specified
Q-MAX, specified
Specified U in adjacent node, U = U0 + coeff. * ABS(I)
BRANCH NUMBER, GENERATOR (with current I)
CODE
BUS, NODE NUMBER
ADJACENT NODE NUMBER
ABS. VALUE OF CONSTANT VOLTAGE U0
ANGLE OF U0, DEGREES (often zero)
COEFFICIENT (can be negative)
U-LIM (upper or lower limit)
Col.
1
11
21
Data
Line
16
U
31
bus
41
51
61
71
1
11
I
node 1
1
11
21
*1 31
41
51
61
71
1
11
21
1
11
21
31
41
*2 51
61
71
17
adjacent node
low impedance
bus
I
node 1
adjacent node
18
Load
Specified impedance
BRANCH NUMBER
1
CODE
11
21
BUS, NODE NUMBER
21
RESISTANCE
31
REACTANCE (negative if capacitive)
41
ACTIVE = 1, DISCONNECTED = 0
51
Specified impedance in ohms per phase, to be converted to per unit by the program
BRANCH NUMBER
1
CODE
11
22
BUS, NODE NUMBER
21
RESISTANCE
31
REACTANCE (negative if capacitive)
41
BASE LINE VOLTAGE, KV
51
ACTIVE = 1, DISCONNECTED = 0
61
bus
I
node 1
bus
node 1
*1: The specified voltage is conditional on the reactive power staying within specified limits.
*2: If the source is overloaded with angle of U0 equal to zero, the load can often be reduced by shifting the phase angle a few
degrees. A minimum load will occur for a certain angle. In a purely inductive circuit, the angle is negative. If the source is still
overloaded, the voltage must be reduced. In an M-G set, the phase angle of U0 is adjusted with the motor excitation.
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 5
Load, cont.
Specified P, Q (independent of voltage)
Col.
Data
Line
BRANCH NUMBER
1
CODE
11
23
BUS, NODE NUMBER
21
ABS. VALUE OF U, INITIAL
31
ANGLE OF U, degrees, initial (often 0)
41
ACTIVE POWER P, specified
51
REACTIVE POWER Q, specified (neg. if capacitive)
61
Specified series resistance, inductance and capacitance, to be converted to ohms by the program.
BRANCH NUMBER
1
CODE
11
24
BUS, NODE NUMBER
21
RESISTANCE
31
INDUCTANCE, mH
41
CAPACITANCE, F
51
ACTIVE = 1, DISCONNECTED = 0
61
Specified series impedance
BRANCH NUMBER
1
CODE
11
25
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
RESISTANCE
41
REACTANCE (negative if capacitive)
51
ACTIVE = 1, DISCONNECTED = 0
61
Specified P and Q in series impedance
BRANCH NUMBER
1
CODE
11
26
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
ABS. VALUE OF U, INITIAL (difference between nodes)
41
ANGLE OF U, degrees, initial (often 0)
51
ACTIVE POWER P, specified
61
REACTIVE POWER Q, specified (negative if capacitive)
71
bus
I
node 1
bus
node 1
first node
last node
first node
I
last node
Shunt reactors/capacitors
Specified reactance
BRANCH NUMBER
1
CODE
11
31
BUS, NODE NUMBER
21
REACTANCE (negative if capacitive)
31
ACTIVE = 1, DISCONNECTED = 0
41
Specified reactance in ohms per phase, to be converted to per unit by the program.
BRANCH NUMBER
1
CODE
11
32
BUS, NODE NUMBER
21
REACTANCE (negative if capacitive)
31
BASE LINE VOLTAGE, KV
41
ACTIVE = 1, DISCONNECTED = 0
51
Specified U, Q-MIN, Q-MAX
BRANCH NUMBER
1
CODE
11
33
BUS, NODE NUMBER
21
ABS. VALUE OF U, specified
* 31
ANGLE OF U, degrees, initial (often 0)
41
REACTIVE POWER Q, initial
51
Q-MAX, specified
61
ACTIVE=1, DISCONNECTED=0
71
* The specified voltage is conditional on the reactive power staying within specified limits.
bus
node 1
bus
I
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 6
Transmission (lines, cables, transformers)
Specified series impedance
Col.
Data
Line
BRANCH NUMBER
1
CODE
11
41
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
RESISTANCE
41
first node
REACTANCE (negative if capacitive)
51
ACTIVE = 1, DISCONNECTED = 0
61
Specified series impedance in ohms per phase, to be converted to per unit by the program.
BRANCH NUMBER
1
CODE
11
42
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
last node
RESISTANCE
41
REACTANCE (negative if capacitive)
51
BASE LINE VOLTAGE, KV
61
ACTIVE = 1, DISCONNECTED = 0
71
-equivalent with three branches
BRANCH NUMBER, SERIES IMPEDANCE
1
CODE
11
43
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
SERIES RESISTANCE ) often including
41
SERIES REACTANCE ) transformer impedance
51
first node
CAPACITIVE SHUNT ADMITTANCE Y
61
FIRST BRANCH NUMBER WITH SHUNT ADMITTANCE Y/2 71
LAST BRANCH NUMBER WITH SHUNT ADMITTANCE Y/2
1
ACTIVE = 1, DISCONNECTED = 0
11
-equivalent with three branches, ohms and μF per phase to be converted to per unit by the program.
BRANCH NUMBER, SERIES IMPEDANCE
1
CODE
11
44
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
SERIES RESISTANCE ) ohms, often including
41
last node
SERIES REACTANCE ) transformer impedance
51
F PER PHASE, FOR CALC. OF SHUNT ADMITTANCE Y
61
FIRST BRANCH NUMBER WITH SHUNT ADMITTANCE Y/2 71
LAST BRANCH NUMBER WITH SHUNT ADMITTANCE Y/2
1
BASE LINE VOLTAGE, KV
11
ACTIVE = 1, DISCONNECTED = 0
21
Specified series resistance, inductance and capacitance, to be converted to ohms by the program.
BRANCH NUMBER
1
CODE
11
45
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
RESISTANCE
41
INDUCTANCE, mH
51
CAPACITANCE, F
61
ACTIVE = 1, DISCONNECTED = 0
71
node 1
When included in per unit line impedance, per unit transformer impedance must be converted to the base MVA, specified on input
sheet 1. This implies that nameplate per unit impedance must be multiplied by (base MVA)/(nameplate MVA).
Ohms per phase is found by multiplying nameplate per unit impedance by (base line kV) /(nameplate MVA)
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 7
Tap changing or off ratio transformers, involving one additional node and two branches.
Specified U in per unit of voltage at first, non regulated node.
Col.
Data
BRANCH NUMBER, VOLTAGE SOURCE
1
CODE
11
51
FIRST NODE NUMBER (non regulated node)
21
LAST NODE NUMBER
31
BRANCH NUMBER, CURRENT SOURCE
41
U, SPECIFIED IN PU OF VOLTAGE AT FIRST NODE
51
ANGLE OF U WITH RESPECT TO VOLTAGE AT FIRST
NODE (degrees, specified, often 0)
61
Specified U in arbitrary node. U is in phase with the voltage at the first node.
BRANCH NUMBER, VOLTAGE SOURCE
1
CODE
11
52
FIRST NODE NUMBER
21
LAST NODE NUMBER
31
BRANCH NUMBER, CURRENT SOURCE
41
ABS. VALUE OF U, specified approximately
51
IN NODE NUMBER
61
U PER STEP, per unit of base line voltage
71
INITIAL STEP NUMBER, positive or negative
1
MAX. NUMBER OF STEPS, NEGATIVE DIRECTION
11
POSITIVE DIRECTION
21
Line
U
I
node 1
Zeros if
disconnected
AC CIRCUIT ANALYSIS
PROGRAM ACCAN
INPUT SHEET 8
Voltage sources
Specified U
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
ABS. VALUE OF U, specified
ANGLE OF U, degrees, specified
Linear function
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
U = COEFFICIENT
TIMES VALUE OF VARIABLE NO.
+ COEFFICIENT
TIMES VALUE OF VARIABLE NO.
Function, programmed by user (see user's manual)
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
Col.
1
11
21
31
41
51
1
11
21
31
41
51
61
71
1
11
21
31
Data
Line
1
9
First node
U
Last node
10
Current sources
Specified I
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
ABS. VALUE OF I, specified
ANGLE OF I, degrees, specified
Linear function
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
I = COEFFICIENT
TIMES VALUE OF VARIABLE NO.
+ COEFFICIENT
TIMES VALUE OF VARIABLE NO.
Function, programmed by user (see user's manual)
BRANCH NUMBER
CODE
FIRST NODE NUMBER
LAST NODE NUMBER
1
11
21
31
41
51
1
11
21
31
41
51
61
71
1
11
21
31
11
19
First node
I
Last node
20
- 13 -
BRANCH EQUATIONS
Impedance:
U1
I
r
x
U2
(x can be capacitive)
xm
Im
Fig. 2
U1 - U2 = (r+jx)I + jxmIm
The equation is used to determine either U1, U2 or I.
Voltage source:
U
U1
I
U2
Fig. 3
U2 - U1 = U
The equation is used to determine U1 or U2. I must be determined from a node equation (I = 0).
Current source:
I
U1
U2
Fig. 4
The branch current is set equal to that of the current source. U1 and U2 must be determined from other
branch equations.
If there are isolated nodes, they are given the voltage zero. Isolated and disconnected branches get zero
currents.
- 14 -
ASSIGNMENT OF NODE EQUATIONS FOR DETERMINATION OF BRANCH CURRENTS
A node equation is derived from the sum of the currents into the node equal to zero. It is used to determine
the current in one of the branches connected to the node.
Initially up to three branches can be assigned tentatively in array ASSIG(500,3). For node I, the branch
which is finally chosen will eventually end up in ASSIG(I,1). If it can be determined already at the outset
which branch will be used, the branch is assigned in a singular assignment. In multiple assignments, initial
preference is given to branches with only voltage sources, otherwise to the branches with the lowest
branch numbers.
ASSIGNMENT OF BRANCH EQUATIONS FOR DETERMINATION
OF BRANCH CURRENTS AND NODE POTENTIALS
A branch equation can be used to determine the branch current, or the potential at one of its two nodes.
The branch number and the two node numbers are therefore often entered initially in array ASSIG(500,3).
For branch I, the variable which is finally chosen will eventually end up in ASSIG(I,1).
The potential at node 1 is the reference potential zero. Therefore, node 1 is never assigned. If it is possible
to determine at the outset that only one of the three variables can be used, it is assigned in a singular
assignment.
SINGULAR ASSIGNMENTS
If a branch B has a current source, an open switch or is short circuited, the branch equation for branch B
must be used to determine the current in branch B.
If a branch B with only a voltage source is connected to node Nx, and its other node is N1 with the
reference potential zero, then the node equation for node Nx must be used to determine the branch current
in branch B. The inverse singular assignment also applies, in that the branch equation for branch B must be
used to determine the node potential at node Nx.
If a node NxN1 has only one branch B connected to it without a current source, an open switch or a short
circuit, then the node equation for node Nx must be used to determine the branch current in branch B. Also
here the inverse singular assignment applies, in that the branch equation for branch B must be used to
determine the potential at node Nx.
- 15 -
FINAL ASSIGNMENTS
In the final assignments in ASSIG(I,1), all the variables should appear once, so that they can be determined
by an equal number of linear equations. The rearrangement of array ASSIG to accomplish this from the
initial tentative assignments where variables may be missing in ASSIG(I,1) and appear more than once, is
done with an algorithm which rotates variables between ASSIG(I,1), (I,2) and (I,3), eliminates variables,
and successively narrows down the choice. This algorithm has been refined to a point where it is very
reliable. Nevertheless, it is easy to conceive of haphazard node and branch numbering for some circuits,
which will make its task impossible. The numbering should be done in an orderly fashion, with node and
branch numbers progressing through the circuit in roughly the same way.
CURRENT AND VOLTAGE SOURCE DETERMINATION
Current, on the basis of active power P, reactive power Q and voltage U (* means complex conjugate):
P+jQ
I = ()*
U
If the voltage U is specified at the bus or in an adjacent node, and the reactive power Q is unspecified, a
new value of Q at iteration n is calculated from the values of U and Q at iterations n-1 and n-2 as:
U-Un-2
Qn = Qn-2 + R  (Qn-1 - Qn-2)
Un-1 - Un-2
U is the specified voltage, and R is the relaxation factor given on input sheet 1. Qn is set equal to the limit,
if one of the specified limits Q-MIN or Q-MAX is exceeded.
If the active generator power P is to be determined from a specified power interchange P i in a relevant
transmission line, the value of P is similarly:
Pi-Pi,n-2
Pn = Pn-2 + R  (Pn-1 - Pn-2)
Pi,n-1 - Pi,n-2
At the first iteration, initial values are always entered in Eq.(1). Later, U is taken from iteration n-1. At the
second iteration, it is not yet possible to use equations (2) and (3), so arbitrary, reasonable values must be
chosen.
In a tap changing transformer with code 52 the tap setting at the n-th iteration can be adjusted one step up
or down, depending on how the calculated voltage compares with the specified voltage. The limits must of
course be observed. The relaxation factor does not apply to this adjustment. The value of I in the current
source is determined so that the apparent power in the current source equals that of the voltage source.
- 16 -
PLOTTING OF CONNECTION DIAGRAMS
A post processor can be used to plot a complete or partial connection diagram with the results of the
calculation written in. This is done on the basis of a small input file with plotting instructions for each
branch and node, or in the case of a load flow calculation, for each bus and transmission line. Input file
DEMO.PLT for the parallel layer reactor in Fig. 1 is shown below. The parameters are explained later.
They always start in columns 10, 15, 20, 25 etc., and the name of a subroutine in capital letters starts in
column 1. The resulting graph is on the last page of the manual.
NODE
NODE
SOURCE
LR
LR
LR
5
5
5
40
70
100
20
65
20
20
20
20
100
100
5
40
70
100
20
65
65
65
65
65
0
2
3
4
5
6
1
-1
-1
-1
An input file STEV.PLT for a load flow graph is also shown. It is for example 10.1 on page 219 of W.D.
Stevenson: "Elements of Power System Analysis", second edition, McGraw-Hill 1962. The resulting graph
is also on the last page of the manual.
BUS
WHITE
BUS
RED
BUS
GREEN
BUS
BLUE
BUS
YELLOW
TRAN
TRAN
TRAN
TRAN
TRAN
TRAN
70
105
195
160
2
7
0
0
70
120
155
85
3
0
10
0
0
50
80
25
4
8
0
0
145
170
195
25
5
0
11
0
0
50
80
105
6
0
9
0
75
150
190
5
75
150
160
160
160
25
25
85
75
150
190
5
75
150
105
85
25
105
85
25
2
2
2
4
4
3
6
3
5
6
3
5
12
13
14
15
16
17
12
13
14
15
16
17
0
0
0
0
0
0
0
0
0
0
0
0
When subroutine BUS is called by an input line, it must be followed by a line with the name of the bus.
This name is plotted on the graph.
The plotting is done as explained on pages 1 and 2, where the parameter for the CONN batch command is
the name of the input file with the plotting instructions.
- 17 SUBROUTINES THAT CAN BE CALLED IN PLOTTING INPUT FILES
C
C
C
C
---------
SUBROUTINE NODE(X1,Y1,X2,Y2,IN)
DRAWS NODE AS HORIZONTAL LINE FOR Y1=Y2 OR VERTICAL LINE FOR X1=X2
BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE NODE POTENTIAL (CAN BE ZERO).
IF IN=0, THE SUBROUTINE SIMPLY DRAWS A HORIZONTAL OR VERTICAL LINE.
C
C
C
C
C
-----------
SUBROUTINE SOURCE(X1,Y1,X2,Y2,IN,IARR)
DRAWS SOURCE HORIZONTALLY FOR Y1=Y2 OR VERTICALLY FOR X1=X2
BETWEEN X1,Y1 AND X2,Y2.
IN IS THE BRANCH NUMBER (VARIABLE NOT DRAWN IF IN=0).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE VARIABLE.
C
C
C
C
C
C
C
---------------
SUBROUTINE LR(X1,Y1,X2,Y2,IN,IARR) OR RL(X1,Y1,X2,Y2,IN,IARR)
DRAWS INDUCTOR, RESISTOR AND ARROW HORIZONTALLY IF Y1=Y2,
VERTICALLY IF X1=X2, BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE CURRENT (IN AND IARR CAN BE ZERO).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE CURRENT.
THE LENGTH BETWEEN X1,Y1 AND X2,Y2 MUST BE >= 55 MM IF THE BRANCH
IS HORIZONTAL, 45 MM IF IT IS VERTICAL.
C
C
C
C
C
C
C
---------------
SUBROUTINE R(X1,Y1,X2,Y2,IN,IARR)
DRAWS RESISTOR AND ARROW HORIZONTALLY IF Y1=Y2,
VERTICALLY IF X1=X2, BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE CURRENT (IN AND IARR CAN BE ZERO).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE CURRENT.
THE LENGTH BETWEEN X1,Y1 AND X2,Y2 MUST BE >= 40 MM IF THE BRANCH
IS HORIZONTAL, 30 MM IF IT IS VERTICAL.
C
C
C
C
C
C
C
---------------
SUBROUTINE L(X1,Y1,X2,Y2,IN,IARR)
DRAWS INDUCTOR AND ARROW HORIZONTALLY IF Y1=Y2,
VERTICALLY IF X1=X2, BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE CURRENT (IN AND IARR CAN BE ZERO).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE CURRENT.
THE LENGTH BETWEEN X1,Y1 AND X2,Y2 MUST BE >= 40 MM IF THE BRANCH
IS HORIZONTAL, 30 MM IF IT IS VERTICAL.
C
C
C
C
C
C
C
---------------
SUBROUTINE C(X1,Y1,X2,Y2,IN,IARR)
DRAWS CAPACITOR AND ARROW HORIZONTALLY IF Y1=Y2,
VERTICALLY IF X1=X2, BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE CURRENT (IN AND IARR CAN BE ZERO).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE CURRENT.
THE LENGTH BETWEEN X1,Y1 AND X2,Y2 MUST BE >= 32 MM IF THE BRANCH
IS HORIZONTAL, 22 MM IF IT IS VERTICAL.
- 18 -
---------------
SUBROUTINE RC(X1,Y1,X2,Y2,IN,IARR) OR CR(X1,Y1,X2,Y2,IN,IARR)
DRAWS RESISTOR, CAPACITOR AND ARROW HORIZONTALLY IF Y1=Y2,
VERTICALLY IF X1=X2, BETWEEN X1,Y1 AND X2,Y2.
IN IS THE VARIABLE NUMBER FOR THE CURRENT (IN AND IARR CAN BE ZERO).
IARR=1 MEANS ARROW POINTING RIGHT OR UP, IARR=-1 LEFT OR DOWN.
IARR MUST CORRESPOND WITH THE POSITIVE DIRECTION OF THE CURRENT.
THE LENGTH BETWEEN X1,Y1 AND X2,Y2 MUST BE >= 47 MM IF THE BRANCH
IS HORIZONTAL, 37 MM IF IT IS VERTICAL.
C
C
C
C
C
C
C
C
-----------------
SUBROUTINE BUS(XL,XC,XR,Y,IN,IG,IL,IR)
DRAWS BUS AS A HORIZONTAL LINE BETWEEN XL,Y AND XR,Y WITH
GENERATION ABOVE BETWEEN XC-9,Y AND XC+9,Y+22.5 AND
LOAD BELOW BETWEEN XC-9,Y-22.5 AND XC+9,Y.
VARIABLE NUMBERS ARE:
IN: NODE POTENTIAL
IG: GENERATOR CURRENT
IL: LOAD CURRENT
IR: CURRENT, SHUNT REACTOR OR CAPACITOR (ZERO IF NONE)
C
C
C
C
C
C
C
C
C
-------------------
SUBROUTINE TRAN(X1,Y1,X2,Y2,IF,IL,ITF,ITL,I1,I2)
DRAWS TRANSMISSION LINE AS A VERTICAL OR SLANTED LINE BETWEEN
X1,Y1 AND X2,Y2. MAX SLANT 30 DEGREES WITH VERTICAL.
VARIABLE NUMBERS ARE:
IF: VOLTAGE, FIRST BUS (AT X1,Y1)
IL: VOLTAGE, LAST BUS (AT X2,Y2)
ITF: CURRENT INTO LINE
ITL: CURRENT OUT OF LINE
I1: CURRENT, SHUNT REACTOR OR CAPACITOR AT X1,Y1 (ZERO IF NONE)
I2: CURRENT, SHUNT REACTOR OR CAPACITOR AT X2,Y2 (ZERO IF NONE)
-----------------------
SUBROUTINE TRAN2(X1,Y1,X2,Y2,IF,IL,ITF,ITL,I1,I2,I3,I4)
DRAWS TRANSMISSION LINE WITH TWO WINDING TRANSFORMER AS A
VERTICAL OR SLANTED LINE BETWEEN X1,Y1 AND X2,Y2.
VARIABLE NUMBERS ARE:
IF: VOLTAGE, FIRST BUS (AT X1,Y1)
IL: VOLTAGE, LAST BUS (AT X2,Y2)
ITF: CURRENT INTO LINE
ITL: CURRENT OUT OF LINE
I1: CURRENT, SHUNT REACTOR OR CAPACITOR AT X1,Y1 (ZERO IF NONE)
I2: CURRENT, SHUNT REACTOR OR CAPACITOR AT X2,Y2 (ZERO IF NONE)
I3: VOLTAGE BEFORE TRANSFORMER
I4: VOLTAGE AFTER TRANSFORMER
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
- 19 -
When subroutines BUS is called by an input line, it must be followed by a line of text. It serves as
identification.
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.
PROGRAM ACCAN
AC CIRCUIT ANALYSIS
THREE PARALLEL LAYER REACTOR
RELAXATION FACTOR 0.000
FREQUENCY
0.0
BASE 3-PHASE POWER, MVA
FIRST BRANCH NO.
4
4
5
BRANCH
3
4
5
6
CODE
11
21
21
21
ITERATION NO.
1
0.000
SECOND BRANCH NO.
5
6
6
NODE
1
2
2
2
MUTUAL REACTANCE
0.603900
0.523400
0.606100
OTHER INPUT DATA
2.000E+00 5.770E+02
2.950E-02 7.638E-01
2.720E-02 6.779E-01
2.920E-02 7.561E-01
0.000E+00
1.000E+00
1.000E+00
1.000E+00
MAX. CHANGE OF VOLTAGE
363.203400
GENERATION
LOAD
TRANSMISSION
SHUNT REACTORS/CAPACITORS
ACTIVE POWER
0.0000E+00
3.1767E+03
0.0000E+00
0.0000E+00
REACTIVE POWER
0.0000E+00
2.0954E+05
0.0000E+00
0.0000E+00
NODE NO.
1
2
VOLTAGE
ABS. VALUE
0.000000
363.203400
ANGLE, DEG.
0.0000
89.1315
REAL COMP.
0.000000
5.505490
IMAG. COMP.
0.000000
363.161682
BRANCH NO.
3
4
5
6
CURRENT
ABS. VALUE
577.000000
189.226135
194.202057
193.608704
ANGLE, DEG.
0.0000
0.4083
-0.9077
0.5114
REAL COMP.
577.000000
189.221329
194.177689
193.600998
IMAG. COMP.
0.000000
1.348558
-3.076461
1.727903
POWER INTO BRANCH
ACTIVE
REACTIVE
0.0000E+00 0.0000E+00
1.5315E+03 6.8711E+04
-4.8209E+01 7.0535E+04
1.6934E+03 7.0299E+04
POWER OUT
ACTIVE
3.1767E+03
0.0000E+00
0.0000E+00
0.0000E+00
OF BRANCH
REACTIVE
2.0954E+05
0.0000E+00
0.0000E+00
0.0000E+00
PROGRAM ACCAN
AC CIRCUIT ANALYSIS
STEVENSON EXAMPLE 10.1
RELAXATION FACTOR 1.000
FREQUENCY
0.0
BASE 3-PHASE POWER, MVA
BRANCH
7
8
9
10
11
12
13
14
15
16
17
CODE
2
12
23
23
23
41
41
41
41
41
41
ITERATION NO.
1
2
3
4
5
6
NODE
2
4
6
3
5
2
2
2
4
4
3
0.000
OTHER INPUT DATA
1.020E+00 0.000E+00
1.040E+00 0.000E+00
1.000E+00 0.000E+00
1.000E+00 0.000E+00
1.000E+00 0.000E+00
6.000E+00 5.000E-02
3.000E+00 1.000E-01
5.000E+00 1.500E-01
6.000E+00 5.000E-02
3.000E+00 5.000E-02
5.000E+00 1.000E-01
1.000E+00
6.000E-01
6.000E-01
4.000E-01
2.000E-01
4.000E-01
6.000E-01
2.000E-01
2.000E-01
4.000E-01
3.000E-01
2.000E-01
3.000E-01
1.000E-01
1.000E+00
1.000E+00
1.000E+00
1.000E+00
1.000E+00
1.000E+00
0.000E+00
1.000E+00
MAX. CHANGE OF VOLTAGE
1.024774
0.019740
0.016223
0.010769
0.000853
0.000073
THE SOLUTION CONVERGED TO THE SPECIFIED MAXIMUM CHANGE OF VOLTAGE
GENERATION
LOAD
TRANSMISSION
SHUNT REACTORS/CAPACITORS
ACTIVE POWER
1.6516E+00
1.6001E+00
5.1501E-02
0.0000E+00
REACTIVE POWER
8.0598E-01
5.9998E-01
2.0600E-01
0.0000E+00
NODE NO.
1
2
3
4
5
6
VOLTAGE
ABS. VALUE
0.000000
1.020000
0.954768
1.040025
0.923464
0.993123
ANGLE, DEG.
0.0000
0.0000
-3.9412
2.0010
-8.0075
-2.0726
REAL COMP.
0.000000
1.020000
0.952510
1.039391
0.914460
0.992473
IMAG. COMP.
0.000000
0.000000
-0.065625
0.036315
-0.128641
-0.035917
BRANCH NO.
7
8
9
10
11
12
13
14
15
16
17
CURRENT
ABS. VALUE
0.715537
1.065370
0.636874
0.702633
0.446473
0.219506
0.228312
0.269045
0.417804
0.649706
0.178539
ANGLE, DEG.
-26.7970
-23.4952
-20.5056
-30.5042
-22.0435
-23.4307
-31.7665
-25.3299
-18.9693
-26.4039
-17.0878
REAL COMP.
0.638695
0.977044
0.596521
0.605383
0.413836
0.201406
0.194111
0.243179
0.395115
0.581930
0.170657
IMAG. COMP.
-0.322586
-0.424734
-0.223097
-0.356657
-0.167566
-0.087284
-0.120197
-0.115105
-0.135812
-0.288922
-0.052461
POWER INTO BRANCH
ACTIVE
REACTIVE
0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00
6.0004E-01 1.9999E-01
6.0004E-01 2.9999E-01
3.9999E-01 9.9996E-02
2.0543E-01 8.9030E-02
1.9799E-01 1.2260E-01
2.4804E-01 1.1741E-01
4.0575E-01 1.5551E-01
5.9436E-01 3.2144E-01
1.6600E-01 3.8770E-02
DEVIATIONS FROM SPECIFIED VOLTAGE
NODE NO.
2
4
VOLTAGE DEVIATION
0.000000
0.000025
DEVIATIONS FROM SPECIFIED POWER
BRANCH NO.
8
9
10
11
DEVIATION, POWER INTO BRANCH
ACTIVE
REACTIVE
0.0000E+00
0.0000E+00
4.3491E-05 -7.7987E-06
3.8908E-05 -8.2119E-06
-7.8231E-06 -3.6502E-06
POWER OUT OF BRANCH
ACTIVE
REACTIVE
1.0655E-04
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
POWER OUT
ACTIVE
6.5147E-01
1.0001E+00
0.0000E+00
0.0000E+00
0.0000E+00
2.0303E-01
1.9278E-01
2.3718E-01
3.9702E-01
5.7325E-01
1.6281E-01
OF BRANCH
REACTIVE
3.2904E-01
4.7695E-01
0.0000E+00
0.0000E+00
0.0000E+00
7.9393E-02
1.0175E-01
7.3976E-02
1.2060E-01
2.3701E-01
2.6020E-02