Download Step 5: Solve the circuit with ATP

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The Circuit: An ideal 120 Vrms, 60 Hz, single-phase voltage source drives a 200 W, pf
= 0.85, lagging load. The wiring between the source and load has resistance 0.50 Ω and
inductance 1 mH. A switchable power factor correction capacitor is connected across the
load to correct the load power factor to 0.95 lagging.
The Problem: Determine the equivalent series R and L that represent the load, assuming
that the load voltage is 120 Vrms. Build an ATPDRAW circuit with source, load,
capacitor, and probes. Use ATP to simulate 5 cycles before the capacitor is switched on,
and 5 cycles afterward. Use TOP to plot source voltage, source current, capacitor
voltage, and capacitor current.
(Note – my experience has shown that the manual naming of nodes is problematic and
should be avoided. Therefore, I suggest that you let ATPDRAW name the nodes, e.g.
XX0001, and then keep notes on the relationship between these names and your circuit
nodes.)
Solution
Step 1: Determine the series equivalent circuit for the load impedance
To find the series R and L for the load, begin by computing the reactive power drawn by
the load using
QP
1
pf 2
 1  200
1
0.85 2
 1  123.9VAr .
The complex power drawn by the load is
S
P
200
 cos 1 (pf ) 
 cos 1 (0.85)  23531.8o VA.
pf
0.85
(Note – a polar check of the complex number P + jQ confirms the above value for S).
Assuming that the load voltage has phase angle zero, the phasor current drawn by the
load is
~ ~ * ~ S* 235  31.8o
S  VI , I  ~ 
 1.958  31.8o Arms .
*
o
V
1200
(Note – the phase angle of the current is the negative of the power factor angle)
Using the series R, L load model,
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I 2rms R  P, R 
I 2rms X  Q, X 
P
200

I 2rms
Q

I 2rms
1.958 2
123.9
1.958
2
 52.2, and
 32.3, L 
X
32.3

 85.7mH .
 2(60)
(Note – my experience has shown that the resistance portion of the load model dominates
the response so that the inductance of the load can usually be ignored)
Step 2: Determine the capacitance of the power factor correction capacitor
The combined Q for the load and shunt capacitor is
QP
1
pf
2
 1  200
1
0.95 2
 1  65.7 VAr .
Thus, the capacitor must provide the difference between uncorrected and corrected VAr,
or 123.9 – 65.7 Var = 58.2 Var. C is found using
Q
2
Vrms
V2
120 2
1
1
1
, X  rms 
 247, X 
,C 

 10.74F.
X
Q
58.2
C
X 2(60)( 247)
Step 3: Avoid ATP numerical instability problems
ATP may have numerical instability problems if a voltage source is switched directly
onto an ideal capacitor. A similar problem occurs if a current source is switched on
through an ideal inductor. For these reasons, it is advisable to place a small resistor in
series with an ideal capacitor, and a large resistor in parallel with an ideal inductor.
“Small” means that the RC and L/R time constants are slightly larger than the ATP
integration time step. In our case, we will use an integration time step of one-thousandth
of a cycle of 60 Hz, or 16.67 ms/1000 = 16.67 s. Thus, the resistor in series with the
capacitor is selected using
RC  timestep , R 
timestep 16.67s

 1.59
C
10.74F
Therefore, R = 2 is a good choice.
Step 4: Build the ATPDRAW circuit
Execute ATPDraw.exe. Under “File,” select “New. The new file is automatically named
Noname.atp. With the cursor in the blank screen, right-click on your mouse to activate a
list of components. Build the circuit and save it. Under “View,” select “Refresh” to
refresh the screen. Alternately, press “r” on your keyboard.
The ATPDRAW circuit (named Starter.adp) is shown below. This image was saved in
ATPDRAW as metafile Starter.wmf by selecting “File” and then “Save metafile…” As
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you can see, sometimes the edges of the circuit are clipped in the metafile. In that case
you may consider the “Print Screen” option followed with paste and crop.
When you build your ATPDRAW file, be sure that that


the voltage on the source is given as a peak value, i.e., 1202 = 169.7 V.
capacitances are specified in F, and inductances are specified in mH.
It is helpful to add legends to components to better document the circuit. Node names
can be displayed by right-clicking the node and selecting the display option.
The ATP Settings screen is shown below. Note that the integration time step is 16.67 s,
the total solution time is 16.67 ms, and Xopt and Copt are zero (indicating that inductors
and capacitors are specified in terms if mH and F, respectively.
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Step 5: Solve the circuit with ATP
First, direct ATPDRAW to make the ATP input file, and save it as Starter.atp in the main
ATP directory where the ATP program is located. Starter.atp is listed below. Ordinarily,
you need not examine this file. However, in case of errors, it is sometimes helpful for
debugging purposes, used in conjunction with the ATP Rule Book.
BEGIN NEW DATA CASE
C -------------------------------------------------------C Generated by ATPDRAW December, Sunday 7, 2003
C A Bonneville Power Administration program
C Programmed by H. K. Høidalen at SEfAS - NORWAY 1994-2001
C -------------------------------------------------------$PREFIX,C:\ATPDRAW\Usp\
$SUFFIX, .LIB
C dT >< Tmax >< Xopt >< Copt >
1.667E-5
.1667
500
1
1
1
1
0
0
1
0
C
1
2
3
4
5
6
7
8
C 345678901234567890123456789012345678901234567890123456789012345678901234567890
/BRANCH
C < n 1>< n 2><ref1><ref2>< R >< L >< C >
C < n 1>< n 2><ref1><ref2>< R >< A >< B ><Leng><><>0
XX0002XX0003
.5
1.
0
XX0007
52.2 85.7
0
C Damping resistor
XX0012XX0011
2.
0
C Power factor correction capacitor
XX0012
10.74
0
/SWITCH
C < n 1>< n 2>< Tclose ><Top/Tde ><
Ie
><Vf/CLOP >< type >
XX0001XX0002
MEASURING
1
XX0003XX0009
.0833
1.
0
XX0009XX0011
MEASURING
1
XX0003XX0007
MEASURING
1
/SOURCE
C < n 1><>< Ampl. >< Freq. ><Phase/T0><
A1
><
T1
>< TSTART >< TSTOP >
14XX0001 0
169.7
60.
-1.
1.
/INITIAL
/OUTPUT
XX0001XX0007XX0012
BLANK BRANCH
BLANK SWITCH
BLANK SOURCE
BLANK INITIAL
BLANK OUTPUT
BLANK PLOT
BEGIN NEW DATA CASE
BLANK
Next, after the ATP input file is created, run ATP by clicking the tpbig.exe icon in
the main ATP directory. ATP creates output file Starter.pl4.
Step 6: View output results with TOP
ATP and TOP use the ATPDRAW internally-generated node names. For reference
purposes, the source voltage and current probes are attached to node XX0001, the load
voltage and current probes are attached to node XX0007, the capacitor voltage probe is
attached to node XX0012, and the capacitor current probe is attached to node XX0009.
Execute TOP, and then using “File,” and “Open,” open file Starter.pl4. On the right of
the screen, select “All,” and then press “OK.” Under “Graph” and then “New Graph,”
select XX0001, XX0007, and XX0012 (i.e., the three voltage probes). To zoom in, under
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“Graph,” select “Scale.” Under X Axis, click off the Autoscale. Enter 70 for the
Minimum:”, and 100 for the Maximum:” (i.e., milliseconds). Under “File” and “Export,”
save the picture as Windows metafile “Starter.wmf.”
The three voltages are shown below (the individual graphs can be discerned on a color
screen).
S T A R T E R > X X 0 0 0 1 (T y p e 4 )
S T A R T E R >X X 0 0 0 1 (T yp e 4 )
300
S T A R T E R >X X 0 0 0 7 (T yp e 4 )
S T A R T E R >X X 0 0 1 2 (T yp e 4 )
V o lt a g e
(V )
200
100
0
-100
-200
70
80
90
100
T im e ( m s)
E le ctro te k C o n ce p ts®
T O P , T h e O u tp u t P ro ce sso r ®
The capacitor voltage (blue) is zero until the switching point. Source voltage (black) and
load voltage (red) are approximately equal and relatively unchanged before and after the
switching transient.
Similarly, the three currents plotted, saved as Windows metafiles, and are shown below:
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S T A R T E R > X X 0 0 0 1 -X X 0 0 0 2 (T y p e 8 )
S T A R T E R >X X 0 0 0 1 -X X 0 0 0 2 ( T yp e 8 )
S T A R T E R >X X 0 0 0 9 -X X 0 0 1 1 ( T yp e 8 )
(M a g )
20
M a g n it u d e
S T A R T E R >X X 0 0 0 3 -X X 0 0 0 7 ( T yp e 8 )
15
10
5
0
-5
-10
70
80
90
100
T im e ( m s)
E le ctro te k C o n ce p ts®
T O P , T h e O u tp u t P ro ce sso r ®
Load current is red, source current is black, and capacitor current is blue. The source and
load currents are equal before the capacitor is switched. Afterward, the load current is
unchanged, but the source current is slightly reduced and advanced, as is expected once
the power factor correction capacitor is added. The capacitor current leads the load
current by approximately 120 degrees.