Basic Electrical Simulator

Spreadsheet for Performing Complex Number, Sequence Component, and Other Basic Electric System Calculations

Disclaimer

Purpose of this Spreadsheet

Instructions, Notes

0

Revision Notes:Rev. 1.0; 10/14/02; Initial version, consisting of the following sheets: ComplexCalc, ABC012, Basic Faults, Other Calcs, Graphs, Intermediate Calcs.Rev. 1.1; 09/03; ABC012 sheet: gave explanation of xfmr theory, added mag * & / 1.732 calc, revised a few default field views. Rev. 2.0: 10/18/04; Added more per unit calcs on "Other Calcs" sheet. Added the blank "User's Calcs" sheet. Added "Z,ABC<>012" sheet. Renamed some sheets.

Doble Engineering Pvt Ltd, 305-SAKAR BUILDING, OLD PADRA ROAD, VADODARAPhone: (+91) (265) 555 77 15 - Fax:(+91) (265) 235 62 85 - Website: http://www.doble.com

ELECTRIC FORMULA CALCULATOR - KAMIN DAVE- DOBLE ENGINEERING PVT. LTD, 305 - SAKAR BUILDING, OLD PADRA ROAD, VADODARA

This spreadsheet presents basic calculations associated with electrical power. In developing this Tool Doble Engineering Pvt ltd has attempted to develop accurate calculation methods, but Doble Engineering Pvt ltd does not warrant that the Tool is free from bugs, errors, or other program limitations. Users are encouraged to consult with a Doble Engineering Pvt ltd representative to determine the accuracy of the data and results for the specific use or purpose of the user.By use of this Tool, the user agrees that Doble Engineering Pvt ltd disclaims all warranties of noninfringement of third party rights, quality, performance, merchantability, or fitness for a particular purpose. The user assumes the entire risk as to the quality and performance of the Tool. In no event will Doble Engineering Pvt ltd be liable for any indirect, special, or consequential damages. In the event of any litigation regarding this Tool, the user agrees that the venue shall be the State of Illinois.

This spreadsheet is intended to assist in the performance of various calculations associated with electric power flow. It is essentially a complex number and sequence components calculator and a shortcut to do a few other basic calculations.

=> See each sheet for instructions specific to that sheet.If the Excel Analysis ToolPak is installed and working properly, the cell to the left should contain "100+100i." If it says "#NAME?" or any other message, see the instructions above.

Spreadsheet for Performing Complex Number, Sequence Component, and Other Basic Electric System Calculations

Disclaimer

Purpose of this Spreadsheet

Instructions, Notes

Revision Notes:Rev. 1.0; 10/14/02; Initial version, consisting of the following sheets: ComplexCalc, ABC012, Basic Faults, Other Calcs, Graphs, Intermediate Calcs.Rev. 1.1; 09/03; ABC012 sheet: gave explanation of xfmr theory, added mag * & / 1.732 calc, revised a few default field views. Rev. 2.0: 10/18/04; Added more per unit calcs on "Other Calcs" sheet. Added the blank "User's Calcs" sheet. Added "Z,ABC<>012" sheet. Renamed some sheets.

, 305 - SAKAR BUILDING, OLD PADRA ROAD, VADODARA

This spreadsheet presents basic calculations associated with electrical power. In developing this Tool Doble Engineering Pvt ltd has attempted to develop accurate calculation methods, but Doble Engineering Pvt ltd does not warrant that the Tool is free from bugs, errors, or other program limitations. Users are encouraged to consult with a Doble Engineering Pvt ltd representative to determine the accuracy of the data and results for the specific use or purpose of the user.By use of this Tool, the user agrees that Doble Engineering Pvt ltd disclaims all warranties of noninfringement of third party rights, quality, performance, merchantability, or fitness for a particular purpose. The user assumes the entire risk as to the quality and performance of the Tool. In no event will Doble Engineering Pvt ltd be liable for any indirect, special, or consequential damages. In the event of any litigation regarding this Tool, the user agrees that the venue shall be the State of Illinois.

This spreadsheet is intended to assist in the performance of various calculations associated with electric power flow. It is essentially a complex number and sequence

If the Excel Analysis ToolPak is installed and working properly, the cell to the left should contain "100+100i." If it says "#NAME?" or any other message, see the

3 04/19/2023 document.xls

Basic Complex Number Calculator

Real Imaginary Rect<=>Polar Magnitude Degrees +/-, Conjugate, Clear Move/Copy Data:

Quantity 1 20.00000 15.00000 25.00000 36.870

Quantity 2 10.00000 18.00000 20.59126 60.945

Memory 1 10.00000 15.00000

Memory 2 20.00000 25.00000

Memory 3 30.00000 35.00000

Memory 4 40.00000 45.00000

Calculate:

Calc Results: Real Imaginary Magnitude Degrees Copy results to:

Q1 + Q2 20.00000 33.00000 38.58756 58.782

100+100i

User Notes:

Instructions/Notes:=> Click on red arrows to convert between rectangular and polar formats, and click on M1/2/3/4 and Q1/2 to copy data from field to field as indicated. Click on Q1<=>Q2 to exchange Q1 and Q2 data.=> After entering rectangular Q1 and Q2 data, click on the indicated function boxes to see the appropriate information in the "Calc Results" field.=> Almost all calculations are done on the "Intermediate Calcs" sheet and macros involving calculations are simply copying data from the Intermediate Calcs page.

If the Excel Analysis ToolPak is installed and working properly, the cell to the left should contain "100+100i." If it says "#NAME?" or any other message, or you see "#VALUE!" messages on this sheet, see the Instructions Sheet for details on enabling Excel's Analysis ToolPak.

Q1+Q2

M2

M2M1Q2

M2M1Q1

Q2Q1

Q2Q1

M1Q2Q1

Q1xQ2Q1-Q2

Q1<=>Q2

Q1/Q2 Q1^2 Sqrt Q1 1/Q1

Clear

Clear

Clear

Clear

+/- Conj.

+/- Conj.

Q1xQ2*

Clear

Q1 || Q2

Q2Q1Clear

Q2Q1Clear

M3

M3 M4

M4

M4M3

Calculations use data in RECTANGULAR FORMAT. If Polar data is entered, click on the Polar to Rect. Conv. button before clicking on a Calculate button.

►►◄◄

►►◄◄

R<P R>P


Basic Sequence Components Calculator and Converter

A-B-C Phase Quantities 0-1-2 Sequence Quantities

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees Copy data to; Misc. functions:A-N -1.1790 0.0000 8.4344 37.776 0 0.0000 0.0000 0.0000 0.000

Vl-n B-N 0.0000 0.0000 4.3748 -139.635 1 3.4777 2.5833 4.3322 36.606C-N 1.1790 0.0000 4.0689 -145.008 2 3.1890 2.5833 4.1041 39.010

A-B 10.0000 8.0000 12.8062 38.660 0 0.0000 0.0000 0.0000 0.000Vl-l B-C 0.0000 -0.5000 0.500 -90.000 1 2.9793 6.8868 7.5036 66.606

C-A -10.0000 -7.5000 12.500 -143.130 2 7.0207 1.1132 7.1084 9.010

A 0I B 1

C 2

A 0Mem 1 B 1

C 2A 0

Mem 2 B 1C 2

Voltage Xfmr Effects on V and I Current Xfmr Effects on I

Pri./Sec. ph./ph. voltage ratio: 1 CT ratio (N:1): 1

Pos.Seq. Phase shift; Pri.=>Sec. 30 for N:5 ratio, N= 5(Transformer Effects Use ABC-Rect. Data)

Secondary

Quantities Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees Copy to:A-N 0

Vl-n B-N 1C-N 2A-B 0

Vl-l B-C 1C-A 2A 0

I B 1C 2

100+100i

User Notes:

Notes / Instructions:=> The spreadsheet implements the classical phase to sequence and sequence to phase calculations (see cell H4 and O4 comments), along with polar/rectangular conversion.=> Green and yellow are user input fields. Yellow indicates a field used in the Transformer Effects calculations.=> Vca and Vll-Vo are not user inputs because: a) two Vl-l quantities define the third. Vca was selected as defined by equation. b) Vl-l has no ground reference and hence no Vo.=> Transformer effect calculations use ABC-Rectangular data in yellow fields.=> See notes in cell D28 for an explanation of the Voltage Xfmr Effects calculations.=> The spreadsheet accepts any voltage transformer phase shift, even one that is physically impossible. Use your good judgment when entering phase shifts.=> The calculations Mem1 = V x I* (= S) and Mem2 = I + Mem1 (= Isum, for differential applications) use ABC-Rectangular format data.=> CT secondary calculations for delta connections are for lines outside of the delta.


M2M1

M2M1

Vl-lVl-n

+/-

+/-

Clear

All Other Xfmr Config.

(Vo & Io blocked)

Wye-Gnd / Wye-Gnd

Wye Sec.no phase

shift

Delta A-C Sec.I1,I2@-/+30deg

Io blocked

M2M1

Clear Secondary Data

M2M1

M2M1

I

Vl-lVl-n ClearI

M2M1 +/-

Delta A-B Sec. I1,I2@+/-30deg

Io blocked

Vl-n

Vl-l

I

Convert

ConvertConvertConvert

ConvertConvertConvert

Convert Convert Convert Convert

Convert

Mem2 = I + Mem1 (using ABC-Rect. data)

Mem1 = Vln x I* (using ABC-Rect. data)

Clear

Clear

Clear

A-B-C Phase Quantities 0-1-2 Sequence Quantites

H4

Sequence / phase conversions: a = 1@120 a^2 = 1@240 Va = (V0 + V1 + V2) Vb = (V0 + a^2*V1 + a*V2) Vc = (V0 + a*V1 + a^2*V2) V0 = (1/3) (Van + Vbn + Vcn) V1 = (1/3) (Van + a*Vbn + a^2*Vcn) V2 = (1/3) (Van + a^2*Vbn + a*Vcn)

O4

Sequence / phase conversions: a = 1@120 a^2 = 1@240 Va = (V0 + V1 + V2) Vb = (V0 + a^2*V1 + a*V2) Vc = (V0 + a*V1 + a^2*V2) V0 = (1/3) (Van + Vbn + Vcn) V1 = (1/3) (Van + a*Vbn + a^2*Vcn) V2 = (1/3) (Van + a^2*Vbn + a*Vcn)

J11

Vll-zero sequence is fixed at 0 and is not a user input because because Vll has no ground reference and hence no Vo.

C13

Vca is not a user input because two Vl-l quantities define the third. Vca was selected as defined by equation.

P21

When copying Mem1 data to Vll, Mem1 data for Vc and Vo is not copied to Vll. Vll-ca is left as a calculated quantity and Vll-o is left as 0.

P23

Mem1 = Vln x I* (= S): This calculates per phase Watt and VAR transfer. The ABC-Rectangular form of Vln and I is used.

P24

When copying Mem2 data to Vll, Mem2 data for Vc and Vo is not copied to Vll. Vll-ca is left as a calculated quantity and Vll-o is left as 0.

P26

Mem2 = I + Mem1: The ABC-Rectangular form of I and Mem1 is used. This calculation is provided to give a means of calculating the current seen by a current differential relay. One has to first work through the effects of CT ratios, relay taps, and relay phase compensation using other features of this sheet.

D28

The voltage transformer effect calculations are used to calculate voltage transformations of an ideal transformer, The calculations for Vln, Vll, and I are independent. Each uses the ABC-Rectangular form of Vln, Vll, and I The theory applied is simply to perform the appropriate phase shift in the symmetrical components: For any type of transformer, the calculations assume negative sequence shift in the calculations will be equal and opposite the positive sequence shift. In a wye-gnd wye-gnd transformer, the zero sequence quantities will have no phase shift. In any other type of transformer, the zero sequence quantities will be blocked and will not transfer from one side to the other. The process described above only works when voltage is defined on only one side of the transformer. Be aware that fault conditions can involve defining voltages on two sides of a transformer and hence voltage drop calculations must be done to determine transformer voltages. For instance, consider a YY xfrmr with normal positive sequence voltage applied to one side of transformer, defining Van at 1pu@0 degerees. Then assume a SLG fault on the other side that defines Van to be zero; both definitions for Van cannot be true simultaneously in an ideal transformer. Calculations assume no magnetic feedback between core legs as may be found in three legged three phase core form transformers. The transformer effect on Vl-n and Vll is calculated independently. If, for example, one did not click on "convert" after entering some new Vln data above, the Vll secondary data above will still be old, and the results below will be for whatever old data was in the Vll fields above, and not be representative of the Vln data that was just entered.

L28

The current transformer effect calculations use the ABC-Rectangular format of I. For a wye connected CT the spreadsheet assumes no phase shift and only a ratio transformation occurs. For a DAB connected CT the positive sequence current is shifted by +30 degrees and the given ratio transformation is applied, the negative sequence current is shifted by -30 degrees and the given ratio transformation is applied, and the zero sequence current is blocked. The opposite positive and negative sequence phase shift is used for a DAC connected CT.

B29

Enter primary/secondary phase to phase voltage ratio.

B30

A lagging secondary would be entered in as a negative number, and a leading secondary would be entered in as a positive number (+ symbol not neeed). Phase shift example: If the secondary voltage lags the primary voltage by 30 degrees when normal phase sequence voltage is applied, enter -30. If the secondary normally leads by 30 degrees, enter 30. There is no internal sanity check on the phase shift that is entered. Normally the phase shift will be in some increment of 30 degrees, but the math will accept any value, even one that is physically impossible. This feature might be useful in seeing what occurs in a phase shifting transformer.

Zabc to Z012 Conversion

Enter the Symmetrical Component Domain Impedances Enter the ABC Domain ImpedancesMagnitude Degrees Magnitude Degrees Magnitude Degrees Magnitude

40.000 50.00 0.000 0.00 0.000 0.00 5.197Z012 = 0.000 0.00 4.000 75.00 0.000 0.00 ZABC = 2.821

0.000 0.00 0.000 0.00 2.000 80.00 2.243

Resultant ABC Domain Impedances Resultant Symmetrical Component Domain ImpedancesMagnitude Degrees Magnitude Degrees Magnitude Degrees Magnitude

15.146 53.39 12.242 50.46 12.679 45.50 10.000ZABC = 12.679 45.50 15.146 53.39 12.242 50.46 Z012 = 0.000

12.242 50.46 12.679 45.50 15.146 53.39 0.000

Doble Engineering Pvt Ltd,305-SAKAR BUILDING,OLD PADRA ROAD,VADODARAPH:(+91) (265) 555 77 15FAX: (+91) (265) 235 82 65EMAIL: [email protected]; [email protected]

"A Derivation of Symmetrical Component Theory and Symmatrical Component Networks." This sheet performs the Z012 to Zabc and Zabc to Z012 conversions discussed in the paper. It would be rather uncommon for this calculation to be done in the hand-calculations that this spreadsheet is mainly supporting, so is more of an informative page.

Enter the ABC Domain ImpedancesDegrees Magnitude Degrees Magnitude Degrees

59.94 2.243 52.51 2.821 29.3529.35 5.197 59.94 2.243 52.5152.51 2.821 29.35 5.197 59.94

Resultant Symmetrical Component Domain ImpedancesDegrees Magnitude Degrees Magnitude Degrees

350.00 0.000 0.00 0.000 0.000.00 4.000 75.00 0.000 0.000.00 0.000 0.00 2.000 80.00

"A Derivation of Symmetrical Component Theory and Symmatrical Component Networks." This sheet performs the Z012 to Zabc and Zabc to Z012 conversions discussed in the paper. It would be rather uncommon for this calculation to be done in the hand-calculations that this spreadsheet is mainly supporting, so is more of


Basic Fault Calculator

System Data:Magnitude Degrees

E prefault 63.000 0Magnitude Degrees

Z0 5.0000Z1 1.0000Z2 1.0000ZfZn

Fault Calculations

Three Phase A phase to ground Phase B to Phase C

In Fault In Fault In Fault

Mag Degrees Mag Degrees Mag DegreesI-a 63.0000 0.000 I-a 27.0000 0.000 I-a 0.0000 0.000I-b 63.0000 -120.000 I-b 0.0000 0.000 I-b 54.5596 -90.000I-c 63.0000 120.000 I-c 0.0000 0.000 I-c 54.5596 90.000I-0 0.0000 0.000 I-0 9.0000 0.000 I-0 0.0000 0.000I-1 63.0000 0.000 I-1 9.0000 0.000 I-1 31.5000 0.000I-2 0.0000 0.000 I-2 9.0000 0.000 I-2 31.5000 180.000

Other side of Xfmr Other side of Xfmr Other side of XfmrMag Degrees Mag Degrees Mag Degrees

I-a 63.0000 30.000 I-a 15.5885 0.000 I-a 31.5000 90.000I-b 63.0000 -90.000 I-b 0.0000 0.000 I-b 63.0000 -90.000I-c 63.0000 150.000 I-c 15.5885 180.000 I-c 31.5000 90.000I-0 0.0000 0.000 I-0 0.0000 0.000 I-0 0.0000 0.000I-1 63.0000 30.000 I-1 9.0000 30.000 I-1 31.5000 30.000I-2 0.0000 0.000 I-2 9.0000 -30.000 I-2 31.5000 150.000

and then converting to ABC quantities.

100+100i

User Notes:

Instructions:=> Enter in the appropriate info in the System Data fields, an then press the "Calculate" button.=> The spreadsheet is simply performing the classical fault calculations given below:

I-3ph: I1 = E/(Z1+Zf)

I-B to C: I1 = -I2 = E/(Z1+Z2+Zf)

I-A to Gnd: I1 = I2 = I0 = E/(Z1+Z2+Z0+3Zf+3Zn)


Calculate

Clear All

Z-fault

E-prefault

Z-system

30o Lead

I-fault

Zn

D6

Normally 0, but if one un-protects the sheet, another # may be entered.

D7

An inductive line would have a positive degree setting.

D14

See Instructions below for a description of the calculations that are performed.


Basic Load Flow Calculator Miscellaneous Other Calcs:

Given Es, Er:

Magnitude Degrees Magnitude Degrees

Es 0.0000 Z-line 0.0500 77.0000

Er

Given Es, I: Solution is for:

Magnitude Degrees Given Es, I

Es 480.0000 0.0000 Watts VAR VA Power Fact.

I 700.0000 -80.0000 Ss 58,345.8 58,345.8 336,000.0 0.1736 Per Unit / Base CalculationsSr 52,834.5 307,023.3 311,536.2 0.1696 Three Phase

Given Er, I: Sline 23,872.1 5,511.3 24,500.0 0.2250 MVA base, 3phMagnitude Degrees Real Imaginary Mag. Degrees kV Base, L-L

Er 0.0000 Es 480.0000 0.0000 480.0000 0.0000 Given Ohmic ValueI Er 445.0480 1.8318 445.0517 0.2358 Given Current Value

Es-Er 34.9520 -1.8318 35.0000 -3.0000 Given MVA ValueGiven Es, Ss: I 121.5537 -689.3654 700.0000 -80.0000 KV, Line to Gnd

Magnitude Degrees I-baseEs 0.0000 Z-base

Watts VARs Coverted ValuesSs Ohms PU

Current PUGiven Er, Sr: MVA PU

Magnitude Degrees

Er 0.0000

Watts VARs

Sr

100+100i

User Notes:

X/R to Angle Converter:

VA/PF to Watt/VAR Converter

Add the Window's Scientific Calculator to your Excel Toolbar:1) Click through the Excel menu tree: Tools/Customize.2) Select the "Commands" tab, then in the "Categories" list click on "Tools." 3) In the scroll-down list of "Commands," there will be a few items that are simply named "Custom." Select the "Custom" command that has an icon that looks like a little calculator. Left click on it and drag it to somewhere in your toolbars.4) Click on Close.5) If you want to remove the icon later, repeat step 1, left click on the icon and drag it off the toolbar.

Instructions:=> Enter in the basic data in the appropriate fields, and then press the appropriate "Calculate" button.=> The load flow calculations are simple manipulations of S = E x I* and E = I x Z in complex number format. Macros just copy data from the Intermediate Calcs sheet to this sheet.=> Calculations are for balanced systems (i.e., single phase represents all three phases).=> Calculations use per unit voltages and currents, so that S = E x I* (e.g., the equation S = Sqrt(3) x El-l x I* is NOT used).=> Generally Es or Er is the reference angle against which other angles are measured and 0 is degrees would normally be used for Es (or Er), so the angle for Es and Er defaults to 0 degrees. However, the angle for Es and Er can be set to other than 0 and the entered angle will be used in the calculations.


Z-line

Es

I, Ss

Er

I, Sr

Calculate

Calculate

Calculate

Calculate

Calculate

Clear Load Flow

H6

An inductive line would have a positive angle setting.


Graphs

Graph Data Real Imaginary Graph Data Real Imaginary

Graph Data Real Imaginary Van 0.000 0.000 Phasor Origin (0) V0,ln 0.000 0.000 Phasor Origin (0)

Q1 0 0 Phasor Origin (0) -1.179 0.000 Phasor End Point 0.000 0.000 Phasor End Point

20 15 Phasor End Point Vbn 0.000 0.000 Phasor Origin (0) V1,ln 0.000 0.000 Phasor Origin (0)

Q2 0 0 Phasor Origin (0) 0.000 0.000 Phasor End Point 3.478 2.583 Phasor End Point

10 18 Phasor End Point Vcn 0.000 0.000 Phasor Origin (0) V2,ln 0.000 0.000 Phasor Origin (0)

Calc 0 0 Phasor Origin (0) 1.179 0.000 Phasor End Point 3.189 2.583 Phasor End Point

20 33 Phasor End Point Vab 0.000 0.000 Phasor Origin (0) V1,ll 0.000 0.000 Phasor Origin (0)

10.000 8.000 Phasor End Point 2.979 6.887 Phasor End Point

Vbc 0.000 0.000 Phasor Origin (0) V2,ll 0.000 0.000 Phasor Origin (0)

0.000 -0.500 Phasor End Point 7.021 1.113 Phasor End Point

Vca 0.000 0.000 Phasor Origin (0) I0 0.000 0.000 Phasor Origin (0)

-10.000 -7.500 Phasor End Point 0.000 0.000 Phasor End Point

Ia 0.000 0.000 Phasor Origin (0) I1 0.000 0.000 Phasor Origin (0)


Ib 0.000 0.000 Phasor Origin (0) I2 0.000 0.000 Phasor Origin (0)


Ic 0.000 0.000 Phasor Origin (0)

0.000 0.000 Phasor End Point

Instructions; Setting graph plot ranges: Between limitations in the Excel plotting/graphing functions and the varieties of plots that might be desired, only a few starting point graphs are provided below. To use these graphs one task that will likely be needed is to adjust the min and max of the X and Y scales to be the same so the graphs will look "correct" for a polar type view. To set Xmax/min and Ymax/min, double left click on each axis (real and imaginary), and select the 'scale' tab on the screen that pops up, then set the min and max values.

-20 -15 -10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

Graph of Q1, Q2, Calc Results from Complex Calc Sheet

Q1 Q2 Calc

Real

Ima

gin

ary

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

Graph of Vln, Vll, I in ABC Format

Van Vbn Vcn Vab Vbc

Vca Ia Ib Ic

Real

Imag

inar

y

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

Graph of Vln, Vll, I in 012 format

V0,ln V1,ln V2,ln V1,ll

V2,ll I0 I1 I2

Real

Ima

gin

ary


This sheet contains intermediate calculations for display on other pages. Named Ranges Lista_1 =IMCalcs!$H$276

Complex Calc Sheet. Data to be copied when the appropriate macro is run. a_2 =IMCalcs!$H$277Rect. Conversion from polar data Polar Conversion from rect. Data abc_i.012 ='V&I,ABC<>012'!$K$16:$O$18Real Imaginary Magnitude Degrees abc_i.012.p ='V&I,ABC<>012'!$N$16:$O$18

Quantity 1 20.000000 15.000000 25.000000 36.869898 abc_i.012.r ='V&I,ABC<>012'!$K$16:$L$18abc_i.abc ='V&I,ABC<>012'!$D$16:$H$18

Quantity 2 10.000000 18.000000 20.591260 60.945396 abc_i.abc.p ='V&I,ABC<>012'!$G$16:$H$18abc_i.abc.r ='V&I,ABC<>012'!$D$16:$E$18

Real Imaginary Magnitude Angle abc_mem1.012 ='V&I,ABC<>012'!$K$21:$O$23Q1 + Q2 30.000000 33.000000 44.598206 47.726311 +/- Q1 -20.000000 -15.000000 25.000000 -143.130102 abc_mem1.12 ='V&I,ABC<>012'!$K$22:$O$23Q1 - Q2 10.000000 -3.000000 10.440307 -16.699244 Q1 Conjugate 20.000000 -15.000000 25.000000 -36.869898 abc_mem1.ab ='V&I,ABC<>012'!$D$21:$H$22Q1 x Q2 -70.000000 510.000000 514.781507 97.815294 +/- Q2 -10.000000 -18.000000 20.591260 -119.054604 abc_mem1.abc ='V&I,ABC<>012'!$D$21:$H$23Q1 / Q2 1.108491 -0.495283 1.214107 -24.075498 Q2 Conjugate 10.000000 -18.000000 20.591260 -60.945396 abc_mem2.012 ='V&I,ABC<>012'!$K$24:$O$26Q1^2 175.000000 600.000000 625.000000 73.739795 New Q1 10.000000 18.000000 20.591260 60.945396 abc_mem2.12 ='V&I,ABC<>012'!$K$25:$O$26Sqrt(Q1) 4.743416 1.581139 5.000000 18.434949 Q1<=>Q2 abc_mem2.ab ='V&I,ABC<>012'!$D$24:$H$251/Q1 0.032000 -0.024000 0.040000 -36.869898 New Q2 20.000000 15.000000 25.000000 36.869898 abc_mem2.abc ='V&I,ABC<>012'!$D$24:$H$26Q1 x Q2* 470.000000 -210.000000 514.781507 -24.075498 abc_results.012 ='V&I,ABC<>012'!$K$35:$O$43Q1 || Q2 7.405732 8.853695 11.542650 50.088983 abc_results.abc ='V&I,ABC<>012'!$D$35:$H$43

abc_results.ix.012 ='V&I,ABC<>012'!$K$41:$O$43abc_results.ix.abc ='V&I,ABC<>012'!$D$41:$H$43abc_results.vx.vll.012 ='V&I,ABC<>012'!$K$38:$O$40abc_results.vx.vll.12 ='V&I,ABC<>012'!$K$39:$O$40abc_results.vx.vll.ab ='V&I,ABC<>012'!$D$38:$H$39

V&I,ABC<>012 Sheet. Data to be copied when the appropriate macro is run. abc_results.vx.vll.abc ='V&I,ABC<>012'!$D$38:$H$40Vl-n ABC rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities abc_results.vx.vln.012 ='V&I,ABC<>012'!$K$35:$O$37

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees abc_results.vx.vln.abc ='V&I,ABC<>012'!$D$35:$H$37A-N -1.179000 0.000000 1.179000 180.000000 0 0.000000 0.000000 0.000000 0.000000 abc_vll.012 ='V&I,ABC<>012'!$K$11:$O$13

Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 -0.589500 -0.340348 0.680696 -150.000000 abc_vll.12 ='V&I,ABC<>012'!$K$12:$O$13C-N 1.179000 0.000000 1.179000 0.000000 2 -0.589500 0.340348 0.680696 150.000000 abc_vll.12.p ='V&I,ABC<>012'!$N$12:$O$13A-B -1.179000 0.000000 1.179000 180.000000 0 0.000000 0.000000 0.000000 0.000000 abc_vll.12.r ='V&I,ABC<>012'!$K$12:$L$13

Vl-l B-C -1.179000 0.000000 1.179000 180.000000 1 -0.589500 -1.021044 1.179000 -120.000000 abc_vll.ab ='V&I,ABC<>012'!$D$11:$H$12C-A 2.358000 0.000000 2.358000 0.000000 2 -0.589500 1.021044 1.179000 120.000000 abc_vll.ab.p ='V&I,ABC<>012'!$G$11:$H$12

Vl-n ABC polar conversions A-B-C Quantities 0-1-2 Sequence Quantities abc_vll.ab.r ='V&I,ABC<>012'!$D$11:$E$12Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees abc_vll.abc ='V&I,ABC<>012'!$D$11:$H$13

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 abc_vln.012 ='V&I,ABC<>012'!$K$6:$O$8Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 abc_vln.012.p ='V&I,ABC<>012'!$N$6:$O$8

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 abc_vln.012.r ='V&I,ABC<>012'!$K$6:$L$8A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 abc_vln.abc ='V&I,ABC<>012'!$D$6:$H$8

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 abc_vln.abc.p ='V&I,ABC<>012'!$G$6:$H$8C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 abc_vln.abc.r ='V&I,ABC<>012'!$D$6:$E$8

Vl-n 012 rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities bf_all.results ='Basic Faults'!$B$16:$L$34Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees cc_m1 =ComplexCalc!$D$9:$H$9

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 cc_m2 =ComplexCalc!$D$10:$H$10Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 cc_m3 =ComplexCalc!$D$11:$H$11

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 cc_m4 =ComplexCalc!$D$12:$H$12A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 cc_q1 =ComplexCalc!$D$5:$H$5

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 cc_q1.polar =ComplexCalc!$G$5:$H$5C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 cc_q1.rect =ComplexCalc!$D$5:$E$5

Vl-n 012 polar conversions A-B-C Quantities 0-1-2 Sequence Quantities cc_q1q2 =ComplexCalc!$D$5:$H$7Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees cc_q2 =ComplexCalc!$D$7:$H$7

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 cc_q2.polar =ComplexCalc!$G$7:$H$7Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 cc_q2.rect =ComplexCalc!$D$7:$E$7

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 cc_results =ComplexCalc!$B$17:$H$17A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 cc_results.data.only =ComplexCalc!$D$17:$H$17

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 ic.cc_1.over.q1 =IMCalcs!$B$18:$H$18C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 ic.cc_plusminus.q1 =IMCalcs!$K$12:$O$12

Vl-l ABC rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.cc_plusminus.q2 =IMCalcs!$K$14:$O$14Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.cc_q1.conjugate =IMCalcs!$K$13:$O$13

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.divide.q2 =IMCalcs!$B$15:$H$15Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 ic.cc_q1.minus.q2 =IMCalcs!$B$13:$H$13

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 ic.cc_q1.over.q2 =IMCalcs!$B$18:$H$18A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.parallel.q2 =IMCalcs!$B$20:$H$20

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 ic.cc_q1.plus.q2 =IMCalcs!$B$12:$H$12C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 ic.cc_q1.polar.conv.from.rect =IMCalcs!$G$7:$H$7

Vl-l ABC polar conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.cc_q1.q2.exchange =IMCalcs!$K$16:$O$18Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.cc_q1.rect.conv.from.polar =IMCalcs!$D$7:$E$7

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.squared =IMCalcs!$B$16:$H$16Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 ic.cc_q1.x.q2 =IMCalcs!$B$14:$H$14

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 ic.cc_q1.x.q2conjugate =IMCalcs!$B$19:$H$19A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q2.conjugate =IMCalcs!$K$15:$O$15

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 ic.cc_q2.polar.conv.from.rect =IMCalcs!$G$9:$H$9C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 ic.cc_q2.rect.conv.from.polar =IMCalcs!$D$9:$E$9

Vl-l 012 rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.cc_sqrt.q1 =IMCalcs!$B$17:$H$17Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.complexcheck.i =IMCalcs!$D$730

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 ic.complexcheck.r =IMCalcs!$C$730Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 ic.fault_all.results =IMCalcs!$B$221:$L$239

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 ic.i.012.p_012.p =IMCalcs!$N$108:$O$110A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 ic.i.012.p_012.r =IMCalcs!$K$108:$L$110

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 ic.i.012.p_abc.p =IMCalcs!$G$108:$H$110C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 ic.i.012.p_abc.r =IMCalcs!$D$108:$E$110

Vl-l 012 polar conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.i.012.r_012.p =IMCalcs!$N$103:$O$105Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.i.012.r_012.r =IMCalcs!$K$103:$L$105

A-N 6.666667 5.166667 8.434387 37.775684 0 0.000000 0.000000 0.000000 0.000000 ic.i.012.r_abc.p =IMCalcs!$G$103:$H$105Vl-n B-N -3.333333 -2.833333 4.374802 -139.635463 1 3.477671 2.583333 4.332183 36.606233 ic.i.012.r_abc.r =IMCalcs!$D$103:$E$105

C-N -3.333333 -2.333333 4.068852 -145.007980 2 3.188996 2.583333 4.104060 39.010150 ic.i.abc.p_012.p =IMCalcs!$N$98:$O$100A-B 10.000000 8.000000 12.806248 38.659808 0 0.000000 0.000000 0.000000 0.000000 ic.i.abc.p_012.r =IMCalcs!$K$98:$L$100

Vl-l B-C 0.000000 -0.500000 0.500000 -90.000000 1 2.979274 6.886751 7.503560 66.606233 ic.i.abc.p_abc.p =IMCalcs!$G$98:$H$100C-A -10.000000 -7.500000 12.500000 -143.130102 2 7.020726 1.113249 7.108440 9.010150 ic.i.abc.p_abc.r =IMCalcs!$D$98:$E$100

I ABC rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.i.abc.r_012.p =IMCalcs!$N$93:$O$95Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.i.abc.r_012.r =IMCalcs!$K$93:$L$95

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.i.abc.r_abc.p =IMCalcs!$G$93:$H$95Vl-n B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.i.abc.r_abc.r =IMCalcs!$D$93:$E$95

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.i_plusminus.012 =IMCalcs!$K$123:$O$125I ABC polar conversions A-B-C Quantities ic.i_plusminus.abc =IMCalcs!$D$123:$H$125

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.isum3_012 =IMCalcs!$K$170:$O$172A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.isum3_abc =IMCalcs!$D$170:$H$172

I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.ix.dab_012 =IMCalcs!$K$155:$O$157C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.ix.dab_abc =IMCalcs!$D$155:$H$157

I 012 rectangular conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.ix.dac_012 =IMCalcs!$K$160:$O$162Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.ix.dac_abc =IMCalcs!$D$160:$H$162


A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.ix.yy_012 =IMCalcs!$K$150:$O$152I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.ix.yy_abc =IMCalcs!$D$150:$H$152

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.lf_er.i =IMCalcs!$H$194:$L$203I 012 polar conversions A-B-C Quantities 0-1-2 Sequence Quantities ic.lf_er.sr =IMCalcs!$H$182:$L$191

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.lf_es.er =IMCalcs!$B$182:$F$191A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.lf_es.i =IMCalcs!$B$206:$F$215

I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.lf_es.ss =IMCalcs!$B$194:$F$203C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.s3_012 =IMCalcs!$K$165:$O$167

+/- Vl-n A-B-C Quantities 0-1-2 Sequence Quantities ic.s3_abc =IMCalcs!$D$165:$H$167Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vll.012.p_vll.12.p =IMCalcs!$N$89:$O$90

A-N 1.179000 0.000000 8.434387 -142.224316 0 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vll.12.r =IMCalcs!$K$89:$L$90Vl-n B-N 0.000000 0.000000 4.374802 40.364537 1 -3.477671 -2.583333 4.332183 -143.393767 ic.vll.012.p_vll.ab.p =IMCalcs!$G$88:$H$89

C-N -1.179000 0.000000 4.068852 34.992020 2 -3.188996 -2.583333 4.104060 -140.989850 ic.vll.012.p_vll.ab.r =IMCalcs!$D$88:$E$89+/- Vl-l A-B-C Quantities 0-1-2 Sequence Quantities ic.vll.012.p_vln.012.p =IMCalcs!$N$85:$O$87

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vll.012.p_vln.012.r =IMCalcs!$K$85:$L$87A-N -10.000000 -8.000000 12.806248 -141.340192 0 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vln.abc.p =IMCalcs!$G$85:$H$87

Vl-l B-C 0.000000 0.500000 0.500000 90.000000 1 -2.979274 -6.886751 7.503560 -113.393767 ic.vll.012.p_vln.abc.r =IMCalcs!$D$85:$E$87C-A 10.000000 7.500000 12.500000 36.869898 2 -7.020726 -1.113249 7.108440 -170.989850 ic.vll.012.r_vll.12.p =IMCalcs!$N$81:$O$82

+/- I A-B-C Quantities 0-1-2 Sequence Quantities ic.vll.012.r_vll.12.r =IMCalcs!$K$81:$L$82Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vll.012.r_vll.ab.p =IMCalcs!$G$80:$H$81

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.012.r_vll.ab.r =IMCalcs!$D$80:$E$81I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.012.r_vln.012.p =IMCalcs!$N$77:$O$79

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll.012.r_vln.012.r =IMCalcs!$K$77:$L$79Voltage Xfmr ic.vll.012.r_vln.abc.p =IMCalcs!$G$77:$H$79Wye-Wye Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vll.012.r_vln.abc.r =IMCalcs!$D$77:$E$79

A-N -0.680696 0.000000 0.680696 180.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vll.12.p =IMCalcs!$N$73:$O$74Vl-n B-N -0.680696 0.000000 0.680696 180.000000 1 -0.340348 -0.589500 0.680696 -120.000000 ic.vll.abc.p_vll.12.r =IMCalcs!$K$73:$L$74

C-N 1.361392 0.000000 1.361392 0.000000 2 -0.340348 0.589500 0.680696 120.000000 ic.vll.abc.p_vll.ab.p =IMCalcs!$G$72:$H$73A-B 5.773503 4.907477 7.577379 40.364537 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vll.ab.r =IMCalcs!$D$72:$E$73

Vl-l B-C 5.773503 4.041452 7.047458 34.992020 1 -0.863249 7.453739 7.503560 96.606233 ic.vll.abc.p_vln.012.p =IMCalcs!$N$69:$O$71C-A -11.547005 -8.948929 14.608787 -142.224316 2 6.636751 -2.546261 7.108440 -20.989850 ic.vll.abc.p_vln.012.r =IMCalcs!$K$69:$L$71A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vln.abc.p =IMCalcs!$G$69:$H$71

I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vln.abc.r =IMCalcs!$D$69:$E$71C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vll.12.p =IMCalcs!$N$65:$O$66

Voltage Xfmr ic.vll.abc.r_vll.12.r =IMCalcs!$K$65:$L$66Other Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vll.abc.r_vll.ab.p =IMCalcs!$G$64:$H$65

A-N -0.680696 0.000000 0.680696 180.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vll.ab.r =IMCalcs!$D$64:$E$65Vl-n B-N -0.680696 0.000000 0.680696 180.000000 1 -0.340348 -0.589500 0.680696 -120.000000 ic.vll.abc.r_vln.012.p =IMCalcs!$N$61:$O$63

C-N 1.361392 0.000000 1.361392 0.000000 2 -0.340348 0.589500 0.680696 120.000000 ic.vll.abc.r_vln.012.r =IMCalcs!$K$61:$L$63A-B 5.773503 4.907477 7.577379 40.364537 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vln.abc.p =IMCalcs!$G$61:$H$63

Vl-l B-C 5.773503 4.041452 7.047458 34.992020 1 -0.863249 7.453739 7.503560 96.606233 ic.vll.abc.r_vln.abc.r =IMCalcs!$D$61:$E$63C-A -11.547005 -8.948929 14.608787 -142.224316 2 6.636751 -2.546261 7.108440 -20.989850 ic.vll_plusminus.12 =IMCalcs!$K$119:$O$120A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll_plusminus.ab =IMCalcs!$D$118:$H$119

I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.012.p_vll.12.p =IMCalcs!$N$57:$O$58C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.012.p_vll.12.r =IMCalcs!$K$57:$L$58

Current Xfmr ic.vln.012.p_vll.ab.p =IMCalcs!$G$56:$H$57Wye Sec. Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vln.012.p_vll.ab.r =IMCalcs!$D$56:$E$57

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vln.012.p_vln.012.p =IMCalcs!$N$53:$O$55I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.012.p_vln.012.r =IMCalcs!$K$53:$L$55

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.012.p_vln.abc.p =IMCalcs!$G$53:$H$55Current Xfmr ic.vln.012.p_vln.abc.r =IMCalcs!$D$53:$E$55DAB Sec. Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vln.012.r_vll.12.p =IMCalcs!$N$49:$O$50

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vln.012.r_vll.12.r =IMCalcs!$K$49:$L$50I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.012.r_vll.ab.p =IMCalcs!$G$48:$H$49

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.012.r_vll.ab.r =IMCalcs!$D$48:$E$49Currrent Xfmr ic.vln.012.r_vln.012.p =IMCalcs!$N$45:$O$47DAC Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vln.012.r_vln.012.r =IMCalcs!$K$45:$L$47

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vln.012.r_vln.abc.p =IMCalcs!$G$45:$H$47I B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.012.r_vln.abc.r =IMCalcs!$D$45:$E$47

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vll.12.p =IMCalcs!$N$41:$O$42Mem1 = S = V x I* ic.vln.abc.p_vll.12.r =IMCalcs!$K$41:$L$42

Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vln.abc.p_vll.ab.p =IMCalcs!$G$40:$H$41A 0.000000 0.000000 0.000000 180.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vll.ab.r =IMCalcs!$D$40:$E$41

S B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vln.012.p =IMCalcs!$N$37:$O$39C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vln.012.r =IMCalcs!$K$37:$L$39

Mem2 = Isum = I + Mem1 ic.vln.abc.p_vln.abc.p =IMCalcs!$G$37:$H$39Real Imaginary Magnitude Degrees Real Imaginary Magnitude Degrees ic.vln.abc.p_vln.abc.r =IMCalcs!$D$37:$E$39

A 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.r_vll.12.p =IMCalcs!$N$33:$O$34Isum B 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.r_vll.12.r =IMCalcs!$K$33:$L$34

C 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.r_vll.ab.p =IMCalcs!$G$32:$H$33ic.vln.abc.r_vll.ab.r =IMCalcs!$D$32:$E$33ic.vln.abc.r_vln.012.p =IMCalcs!$N$29:$O$31ic.vln.abc.r_vln.012.r =IMCalcs!$K$29:$L$31ic.vln.abc.r_vln.abc.p =IMCalcs!$G$29:$H$31ic.vln.abc.r_vln.abc.r =IMCalcs!$D$29:$E$31ic.vln_plusminus.012 =IMCalcs!$K$113:$O$115ic.vln_plusminus.abc =IMCalcs!$D$113:$H$115

Load Flow. Data to be copied when the appropriate macro is run ic.vx.other_012 =IMCalcs!$K$139:$O$147ic.vx.other_abc =IMCalcs!$D$139:$H$147

Given Es, Er Given Er, Sr ic.vx.yy_012 =IMCalcs!$K$128:$O$136Watts VAR VA Power Fact. Watts VAR VA Power Fact. ic.vx.yy_abc =IMCalcs!$D$128:$H$136

Ss 0 0 0 0 Ss 0 0 0 0 JJH =IMCalcs!$C$990Sr 0 0 0 0 Sr 0 0 0 0 lf_results ='Other Calcs'!$F$11:$J$20

Sline 0 0 0 0 Sline 0 0 0 0 m_30 =IMCalcs!$K$676Real Imaginary Mag. Degrees Real Imaginary Mag. Degrees p_30 =IMCalcs!$K$675

Es 0 0 0 0 Es 0 0 0 0 Print_Area =IMCalcs!$A$1:$R$731Er 0 0 0 0 Er 0 0 0 0 sqrt3 =IMCalcs!$K$276

Es-Er 0 0 0 0 Es-Er 0 0 0 0

I 0 0 0 0 I 0 0 0 0

Given Es, Ss Given Er, I

Watts VAR VA Power Fact. Watts VAR VA Power Fact.

Ss 0 0 0 0 Ss 0 0 0 0

Sr 0 0 0 0 Sr 0 0 0 0

Sline 0 0 0 0 Sline 0 0 0 0

Real Imaginary Mag. Degrees Real Imaginary Mag. Degrees

Es 0 0 0 0 Es 0 0 0 0

Er 0 0 0 0 Er 0 0 0 0

Es-Er 0 0 0 0 Es-Er 0 0 0 0

I 0 0 0 0 I 0 0 0 0


Given Es, I

Watts VAR VA Power Fact.

Ss 58345.7876960885 58345.7876960885 336000 0.17364817766693

Sr 52834.4868646638 307023.338424864 311536.215133652 0.16959340294353

Sline 23872.0665872383 5511.30083142472 24500 0.224951054343866

Real Imaginary Mag. Degrees

Es 480 0 480 0

Er 445.04796628359 1.83175846850308 445.051735905216 0.235820506209618

Es-Er 34.9520337164101 -1.83175846850308 35 -3.00000000000004

I 121.553724366851 -689.365427108546 700 -80

Fault Calc. Data to be copies when the appropriate macro is run.

Three Phase A phase to ground Phase B to Phase C

In Fault In Fault In Fault

Mag Degrees Mag Degrees Mag Degrees

I-a 63 0 I-a 27 0 I-a 0.000000 0.000000

I-b 63 -120 I-b 9.76996261670138E-15 0 I-b 54.559600 -90.000000

I-c 63.0000000000001 120 I-c 9.76996261670138E-15 0 I-c 54.559600 90.000000

I-0 0 0 I-0 9 0 I-0 0 0

I-1 63 0 I-1 9 0 I-1 31.5 0

I-2 0 0 I-2 9 0 I-2 31.5 180

Other side of Xfmr Other side of Xfmr Other side of Xfmr

Mag Degrees Mag Degrees Mag Degrees

I-a 63.0000000000001 30 I-a 15.5884572681199 0 I-a 31.500000 90.000000

I-b 63 -90.0000000000001 I-b 1.08051568231428E-14 0 I-b 63.000000 -90.000000

I-c 63.0000000000001 150 I-c 15.5884572681199 180 I-c 31.500000 90.000000

I-0 0 0 I-0 0 0 I-0 0 0

I-1 63.0000000000001 30 I-1 9 30 I-1 31.5 30

I-2 0 0 I-2 9 -30 I-2 31.5 150

Complex Calc sheet - calculations

Rectangular to Polar conversions Polar to Rectangular conversions

Complex format Mag Degrees Radians Radians Real Imaginary

Q1 20+15i 25.000000 36.869898 0.643501 0.643501 20.000000 15.000000

Q2 10+18i 20.591260 60.945396 1.063698 1.063698 10.000000 18.000000

Math calculations

Restating Data: Real Imaginary Complex Mag Degrees Radians

Q1 20.000000 15.000000 20+15i 25.000000 36.869898 0.643501

Q2 10.000000 18.000000 10+18i 20.591260 60.945396 1.063698

Q2 Conjugate 10.000000 -18.000000 10-18i 20.591260 -60.945396 -1.063698

Performing Calcs: Radians, basic calc Simplified Radians

Q1+Q2 30.000000 33.000000 30+33i 44.598206 47.726311 0.832981

Q1-Q2 10.000000 -3.000000 10-3i 10.440307 -16.699244 -0.291457

Q1xQ2 -70.000000 510.000000 -70+510i 514.781507 97.815294 1.707199 1.707199

Q1/Q2 1.108491 -0.495283 1.10849056603774-0.495 1.214107 -24.075498 -0.420197 -0.420197

Q1^2 175.000000 600.000000 175+600i 625.000000 73.739795 1.287002 1.287002

Sqrt(Q1) 4.743416 1.581139 4.74341649025257+1.58 5.000000 18.434949 0.321751 0.321751

1/Q1 0.032000 -0.024000 0.032-0.024i 0.040000 -36.869898 -0.643501 -0.643501

Q1xQ2conjugate 470.000000 -210.000000 470-210i 514.781507 -24.075498 -0.420197 -0.420197

1/Q2 0.023585 -0.042453 0.0235849056603774-0.0 0.048564 -60.945396 -1.063698 -1.063698

1/Q1 + 1/ Q2 0.055585 -0.066453 0.0555849056603774-0.0 0.086635 -50.088983 -0.874218 -0.874218

Q1||Q2 = 1/[1/Q1 + 1/Q2] 7.405732 8.853695 7.40573152337859+8.85 11.542650 50.088983 0.874218 0.874218

V&I,ABC<>012 sheet - calculations

Vll Vca Real Imaginary a1, a2 constants: Square Root 3

Vab 10.000000 8.000000 a_1 -0.5+0.866025403784439i sqrt3 1.73205080756888

Vca, rect. Vbc 0.000000 -0.500000 a_2 -0.5-0.866025403784438i

Vca = -sum -10.000000 -7.500000

Vab rectangular 10.000000 8.000000

Vca, polar Vac rectangular 0.000000 -0.500000 Complex Format Magnitude Degrees Radians

Vca = -sum -10.000000 -7.500000 -10-7.5i 12.500000 -143.130102 -2.498092

V conversions, starting with Vln ABC rectangular

Given: Real Imaginary Complex Format Magnitude Degrees Radians

AN -1.179000 0.000000 -1.179 1.179000 180.000000 3.141593

Vl-n BN 0.000000 0.000000 0 0.000000 0.000000 0.000000

CN 1.179000 0.000000 1.179 1.179000 0.000000 0.000000

Calculated Line to Line, ABC format

AB -1.179000 0.000000 -1.179 1.179000 180.000000 3.141593

Vl-l BC -1.179000 0.000000 -1.179 1.179000 180.000000 3.141593

CA 2.358000 0.000000 2.358 2.358000 0.000000 0.000000

ABC to 012 conversion Cmplx ABC Data/3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AN -0.393 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n BN 0 -0 0 1 -0.5895-0.3403479836872 -0.589500 -0.340348 0.680696 -150.000000 -2.617994

CN 0.393 -0.1965+0.340347983687 -0.1965-0.3403479836872 2 -0.5895+0.340347983687 -0.589500 0.340348 0.680696 150.000000 2.617994

AB -0.393 0 -1.11022302462516e-16 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.393 0.1965-0.3403479836872 0.1965+0.3403479836872 1 -0.5895-1.0210439510618 -0.589500 -1.021044 1.179000 -120.000000 -2.094395

CA 0.786 -0.393+0.6806959673745 -0.393-0.68069596737456 2 -0.5895+1.021043951061 -0.589500 1.021044 1.179000 120.000000 2.094395

V conversions, starting with Vln ABC polar

Given: Magnitude Angle Radians Real Imaginary Complex Format

AN 8.434387 37.775684 0.659310068332858 6.66666666666666 5.16666666666666 6.66666666666666+5.16666666666666i

Vl-n BN 4.374802 -139.635463 -2.437099 -3.333333 -2.833333 -3.33333333333333-2.83333333333333i

CN 4.068852 -145.007980 -2.530867 -3.333333 -2.333333 -3.33333333333333-2.33333333333332i

Calculated Line to Line, ABC format

AB 12.806248 38.659808 0.674741 10.000000 8.000000 9.99999999999999+7.99999999999999i

Vl-l BC 0.500000 -90.000000 -1.570796 0.000000 -0.500000 -0.500000000000011i

CA 12.500000 -143.130102 -2.498092 -10.000000 -7.500000 -9.99999999999999-7.49999999999998i


ABC to 012 conversion Cmplx ABC Data/3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AN 2.22222222222222+1.72222222222222i 0 3.99680288865056e-15i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n BN -1.11111111111111-0.94 1.37346843690752-0.490 -0.262357325796413+1.4 1 3.47767090063074+2.58 3.477671 2.583333 4.332183 36.606233 0.638899

CN -1.11111111111111-0.77 1.22913086961011-0.573 -0.118019758499004+1.3 2 3.18899576603592+2.58 3.188996 2.583333 4.104060 39.010150 0.680856

AB 3.33333333333333+2.66666666666666i 0 -4.44089209850063e-16i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.16666666666667i 0.144337567297409+0.0 -0.144337567297409+0.0 1 2.97927405783632+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.49 3.83173017612775-1.636 -0.498396842794422+4.1 2 7.02072594216367+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

V conversions, starting with Vln 012 rectangular


0 0.000000 0.000000 1.79476517395799e-15 0.000000 0.000000 0.000000

Vl-n 1 3.477671 2.583333 3.47767090063074+2.58 4.332183 36.606233 0.638899

2 3.188996 2.583333 3.18899576603592+2.58 4.104060 39.010150 0.680856

012 to ABC conversion Complex 012 data *a_1 *a_2 Complex ABC Data Real Imaginary Magnitude Degrees Radians

0 1.79476517395799e-15 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

Calculated Line to Line, ABC format Magnitude Angle Radians Real Imaginary Complex Format

AB 12.806248 38.659808 0.674741 10.000000 8.000000 9.99999999999999+7.99999999999999i

Vl-l BC 0.500000 -90.000000 -1.570796 0.000000 -0.500000 -0.50000000000001i

CA 12.500000 -143.130102 -2.498092 -10.000000 -7.500000 -9.99999999999999-7.49999999999998i

V Line to Line, ABC to 012 Conversion Cmplx ABC Data/3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AB 3.33333333333333+2.66666666666666i 0 -4.44089209850063e-16i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.16666666666667i 0.144337567297409+0.0 -0.144337567297409+0.0 1 2.97927405783632+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.49 3.83173017612775-1.636 -0.498396842794422+4.1 2 7.02072594216367+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

V conversions, starting with Vln 012 polar


0 0.000000 0.000000 0.000000 0.000000 0.000000 1.79476517395799e-15

Vl-n 1 4.332183 36.606233 0.638899 3.477671 2.583333 3.47767090063074+2.58333333333333i

2 4.104060 39.010150 0.680856 3.188996 2.583333 3.18899576603592+2.58333333333333i


0 1.79476517395799e-15 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

Calculated Line to Line, ABC format Magnitude Angle Radians Real Imaginary Complex Format

AB 12.806248 38.659808 0.674741 10.000000 8.000000 9.99999999999999+7.99999999999999i

Vl-l BC 0.500000 -90.000000 -1.570796 0.000000 -0.500000 -0.50000000000001i

CA 12.500000 -143.130102 -2.498092 -10.000000 -7.500000 -9.99999999999999-7.49999999999998i

V Line to Line, ABC to 012 Conversion Cmplx ABC Data/3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AB 3.33333333333333+2.66666666666666i 0 -4.44089209850063e-16i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.16666666666667i 0.144337567297409+0.0 -0.144337567297409+0.0 1 2.97927405783632+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.49 3.83173017612775-1.636 -0.498396842794422+4.1 2 7.02072594216367+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

V conversions, starting with Vll ABC rectangular


AB 10.000000 8.000000 10+8i 12.806248 38.659808 0.674741

Vl-l BC 0.000000 -0.500000 -0.5i 0.500000 -90.000000 -1.570796

CA -10.000000 -7.500000 -10-7.5i 12.500000 -143.130102 -2.498092

ABC to 012 conversion Cmfplx ABC Data / 3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AB 3.33333333333333+2.66666666666667i 0 3.10862446895044e-15i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.166666666666667i 0.144337567297407+0.0 -0.144337567297407+0.0 1 2.97927405783631+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.5i 3.83173017612776-1.636 -0.498396842794431+4.1 2 7.02072594216368+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

Calculated Line-Line, 012 format Magnitude Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 1.79476517395799e-15

Vl-n 1 4.332183 36.606233 0.638899 3.477671 2.583333 3.47767090063074+2.58333333333333i

2 4.104060 39.010150 0.680856 3.188996 2.583333 3.18899576603592+2.58333333333333i

012 to ABC conversion Complex 012 Data *a_1 *a_2 Complex ABC data Real Imaginary Magnitude Degrees Radians

0 1.79476517395799e-15 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

V conversions, starting with Vll ABC polar Comment: V0 was included in calculations in the next 4 conversions below as a check. It should always be zero.


AB 12.806248 38.659808 0.674740942223553 10 8 10+8i

Vl-l BC 0.500000 -90.000000 -1.5707963267949 3.06161699786838E-17 -0.5 3.06161699786838e-17-0.5i

CA 12.500000 -143.130102 -2.49809154479651 -10 -7.5 -10-7.5i

ABC to 012 conversion Cmplx ABC Data / 3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AB 3.33333333333333+2.66666666666667i 0 3.10862446895044e-15i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 1.02053899928946e-17-00.144337567297407+0.0 -0.144337567297407+0.0 1 2.97927405783631+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.5i 3.83173017612776-1.636 -0.498396842794431+4.1 2 7.02072594216368+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

Calculated Line-LIne, 012 format Magnitude Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 1.79476517395799e-15

Vl-n 1 4.332183 36.606233 0.638899 3.477671 2.583333 3.47767090063074+2.58333333333333i

2 4.104060 39.010150 0.680856 3.188996 2.583333 3.18899576603592+2.58333333333333i

012 to ABC conversion Complex 012 Data *a_1 *a_2 Complex ABC data Real Imaginary Magnitude Degrees Radians

0 1.79476517395799e-15 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

V conversions, starting with Vll 012 rectangular


0 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-l 1 2.979274 6.886751 2.97927405783631+6.88 7.503560 66.606233 1.162498

2 7.020726 1.113249 7.02072594216368+1.11 7.108440 9.010150 0.157257

Calculated Line to Neutral, 012 format Magnitude Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 1 4.332183 36.606233 0.638899 3.477671 2.583333 3.47767090063074+2.58333333333333i

2 4.104060 39.010150 0.680856 3.188996 2.583333 3.18899576603592+2.58333333333333i


0 0 AB 9.99999999999999+7.99 10.000000 8.000000 12.806248 38.659808 0.674741

Vl-l 1 2.97927405783631+6.88 -7.45373864405591-0.86 4.47446458621959-6.023 BC -0.500000000000001i 0.000000 -0.500000 0.500000 -90.000000 -1.570796

2 7.02072594216368+1.11 -4.47446458621959+5.52 -2.54626135594409-6.63 CA -10-7.49999999999999i -10.000000 -7.500000 12.500000 -143.130102 -2.498092

0 0 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

V conversions, starting with Vll 012 polar

Given: Magnitude Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l 1 7.503560 66.606233 1.162498 2.979274 6.886751 2.97927405783631+6.88675134594812i

2 7.108440 9.010150 0.157257 7.020726 1.113249 7.02072594216368+1.11324865405187i

Calculated Line to Neutral, 012 format Magnitude Degrees Radians Real Imaginary Complex Format


0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 1 4.332183 36.606233 0.638899 3.477671 2.583333 3.47767090063074+2.58333333333333i

2 4.104060 39.010150 0.680856 3.188996 2.583333 3.18899576603592+2.58333333333333i


0 0 AB 9.99999999999999+7.99 10.000000 8.000000 12.806248 38.659808 0.674741

Vl-l 1 2.97927405783631+6.88 -7.45373864405591-0.86 4.47446458621959-6.023 BC -0.500000000000001i 0.000000 -0.500000 0.500000 -90.000000 -1.570796

2 7.02072594216368+1.11 -4.47446458621959+5.52 -2.54626135594409-6.63 CA -10-7.49999999999999i -10.000000 -7.500000 12.500000 -143.130102 -2.498092

0 0 AN 6.66666666666666+5.16 6.666667 5.166667 8.434387 37.775684 0.659310

Vl-n 1 3.47767090063074+2.58 -3.97606774342517+1.72 0.498396842794426-4.30 BN -3.33333333333333-2.83 -3.333333 -2.833333 4.374802 -139.635463 -2.437099

2 3.18899576603592+2.58 -3.83173017612776+1.47 0.642734410091836-4.05 CN -3.33333333333333-2.33 -3.333333 -2.333333 4.068852 -145.007980 -2.530867

I conversions, starting with ABC rectangular


A 0.000000 0.000000 0 0.000000 0.000000 0.000000

I B 0.000000 0.000000 0 0.000000 0.000000 0.000000

C 0.000000 0.000000 0 0.000000 0.000000 0.000000


A 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

I B 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

C 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

I conversions, starting with ABC polar


A 0.000000 0.000000 0.000000 0.000000 0.000000 0

I B 0.000000 0.000000 0.000000 0.000000 0.000000 0

C 0.000000 0.000000 0.000000 0.000000 0.000000 0

ABC to 012 conversion Cmplx ABC Data / 3 *a_1 *a_2 Complex Format 012 Data Real Imaginary Magnitude Degrees Radians

A 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

I B 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

C 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

I conversions, starting with 012 rectangular


0 0.000000 0.000000 0 0.000000 0.000000 0.000000

I 1 0.000000 0.000000 0 0.000000 0.000000 0.000000

2 0.000000 0.000000 0 0.000000 0.000000 0.000000


0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n conversions, starting with 012 polar


0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0

012 to ABC conversion Complex 012 Data *a_1 *a_2 Complex ABC Data Real Imaginary Magnitude Degrees Radians

0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Transformer calculations. First copy in base ABC data, then convert to 012 formats again. Then do the Xfmr conversion math.

Restating Primary Data: Real Imaginary Complex format mag degrees radians

AN -1.179000 0.000000 -1.179 1.179000 180.000000 3.141593

Vl-n BN 0.000000 0.000000 0 0.000000 0.000000 0.000000

CN 1.179000 0.000000 1.179 1.179000 0.000000 0.000000

AB 10.000000 8.000000 10+8i 12.806248 38.659808 0.674741

Vl-l BC 0.000000 -0.500000 -0.5i 0.500000 -90.000000 -1.570796

CA -10.000000 -7.500000 -10-7.5i 12.500000 -143.130102 -2.498092

A 0.000000 0.000000 0 0.000000 0.000000 0.000000

I B 0.000000 0.000000 0 0.000000 0.000000 0.000000

C 0.000000 0.000000 0 0.000000 0.000000 0.000000

ABC to 012 conversion, rectangular format, then convert to polar

Cmplx ABC Data / 3 *a_1 *a_2 Complex 012 Data Real Imaginary Magnitude Degrees Radians

AN -0.393 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n BN 0 -0 0 1 -0.5895-0.3403479836872 -0.589500 -0.340348 0.680696 -150.000000 -2.617994

CN 0.393 -0.1965+0.340347983687 -0.1965-0.3403479836872 2 -0.5895+0.340347983687 -0.589500 0.340348 0.680696 150.000000 2.617994

AB 3.33333333333333+2.66666666666667i 0 3.10862446895044e-15i 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC -0.166666666666667i 0.144337567297407+0.0 -0.144337567297407+0.0 1 2.97927405783631+6.88 2.979274 6.886751 7.503560 66.606233 1.162498

CA -3.33333333333333-2.5i 3.83173017612776-1.636 -0.498396842794431+4.1 2 7.02072594216368+1.11 7.020726 1.113249 7.108440 9.010150 0.157257

A 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

I B 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

C 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

Voltage Transformer, Wye-Wye

Transformer Effect on: Magnitude Phase shift, degrees

Zero Sequence 1 0

Positve sequence 1 30

Negative sequence 1 -30

Secondary Sequence Quantities Seq. Mag. / VT ratio Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 1 0.680696 -120.000000 -2.094395 -0.340348 -0.589500 -0.340347983687285-0.5895i

2 0.680696 120.000000 2.094395 -0.340348 0.589500 -0.340347983687284+0.589500000000001i

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l 1 7.503560 96.606233 1.686097 -0.863249 7.453739 -0.863248654051865+7.4537386440559i

2 7.108440 -20.989850 -0.366342 6.636751 -2.546261 6.63675134594812-2.54626135594408i

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0


0 0 AN -0.680695967374569+9.9 -0.680696 0.000000 0.680696 180.000000 3.141593

Vl-n 1 -0.340347983687285-0.580.680695967374569-8.32 -0.340347983687284+0.5 BN -0.68069596737457 -0.680696 0.000000 0.680696 180.000000 3.141593

2 -0.340347983687284+0.5 -0.340347983687286-0.580.680695967374569-8.88 CN 1.36139193474914-1.720 1.361392 0.000000 1.361392 0.000000 0.000000

0 0 AB 5.77350269189625+4.90 5.773503 4.907477 7.577379 40.364537 0.704494

Vl-l 1 -0.863248654051865+7.4 -6.02350269189626-4.47 6.88675134594811-2.979 BC 5.77350269189624+4.04 5.773503 4.041452 7.047458 34.992020 0.610726

2 6.63675134594812-2.546 -1.11324865405187+7.02 -5.52350269189624-4.47 CA -11.5470053837925-8.94 -11.547005 -8.948929 14.608787 -142.224316 -2.482283

0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Voltage Transformer, Other than wye-wye



Zero Sequence 0 0



Secondary Sequence Quantities Mag. / VT Ratio Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 1 0.680696 -120.000000 -2.094395 -0.340348 -0.589500 -0.340347983687285-0.5895i

2 0.680696 120.000000 2.094395 -0.340348 0.589500 -0.340347983687284+0.589500000000001i

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l 1 7.503560 96.606233 1.686097 -0.863249 7.453739 -0.863248654051865+7.4537386440559i

2 7.108440 -20.989850 -0.366342 6.636751 -2.546261 6.63675134594812-2.54626135594408i

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0


0 0 AN -0.680695967374569+9.9 -0.680696 0.000000 0.680696 180.000000 3.141593

Vl-n 1 -0.340347983687285-0.580.680695967374569-8.32 -0.340347983687284+0.5 BN -0.68069596737457 -0.680696 0.000000 0.680696 180.000000 3.141593

2 -0.340347983687284+0.5 -0.340347983687286-0.580.680695967374569-8.88 CN 1.36139193474914-1.720 1.361392 0.000000 1.361392 0.000000 0.000000

0 0 AB 5.77350269189625+4.90 5.773503 4.907477 7.577379 40.364537 0.704494

Vl-l 1 -0.863248654051865+7.4 -6.02350269189626-4.47 6.88675134594811-2.979 BC 5.77350269189624+4.04 5.773503 4.041452 7.047458 34.992020 0.610726

2 6.63675134594812-2.546 -1.11324865405187+7.02 -5.52350269189624-4.47 CA -11.5470053837925-8.94 -11.547005 -8.948929 14.608787 -142.224316 -2.482283

0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Current Transformer, Wye secondary


Zero Sequence 1 0


Negative sequence 1 0

Secondary Sequence Quantities Seq. Mag / CT Ratio Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0

012 to ABC conversion Complex Format 012 data *a_1 *a_2 Complex ABC Data Real Imaginary Magnitude Degrees Radians

0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Current Transformer, DAB Secondary

Transformer Effect on: Magnitude Phase Angle, degrees

Zero Sequence 0 0



Secondary Sequence Quantities Seq. Mag. / CT Ratio Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0


0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Current Transformer, DAC Secondary

Transformer Effect on: Magnitude Phase Angle, degrees

Zero Sequence 0 0

Positve sequence 1 -30

Negative sequence 1 30

Secondary Sequence Quantities Seq. Mag. / CT Ratio Degrees Radians Real Imaginary Complex Format

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 1 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0


0 0 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I 1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Mem 1 = S = V x I* Real Imaginary Complex Format Magnitude Degrees Radians

AN -1.179 0 -1.179 1.179000 180.000000 3.141593

V BN 0 0 0 0.000000 0.000000 0.000000

CN 1.179 0 1.179 1.179000 0.000000 0.000000

A 0 0 0 0.000000 0.000000 0.000000

I* B 0 0 0 0.000000 0.000000 0.000000

C 0 0 0 0.000000 0.000000 0.000000

A 0 0 -0 0.000000 180.000000 3.141593

S = V x I* B 0 0 0 0.000000 0.000000 0.000000

C 0 0 0 0.000000 0.000000 0.000000


AN -0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

S = V x I* BN 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CN 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

Mem 2 = Isum = I + Mem1 Real Imaginary Complex Format Magnitude Degrees Radians

A 0 0 0 0.000000 0.000000 0.000000

I sum B 0 0 0 0.000000 0.000000 0.000000

C 0 0 0 0.000000 0.000000 0.000000


A 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

I sum B 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

C 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

Load Flow Calculations

Given Es, Er * = conjugate in stated equations

Magnitude Degrees Radians Real Imaginary Complex

Es 0.000000 0.000000 0.000000 0.000000 0.000000 0

Er 0.000000 0.000000 0.000000 0.000000 0.000000 0

Z-line 0.050000 77.000000 1.343904 0.011248 0.048719 0.0112475527171933+0.0487185032392618i

Esr = Es-Er 0.000000 0.000000 0.000000 0.000000 0.000000 0

I = Esr/Z 0.000000 0.000000 0.000000 0.000000 0.000000 0

I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Ss = Es x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0


Sline = dE x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sr = Er x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Given Es, Ss


Es 0.000000 0.000000 0.000000 0.000000 0.000000 0

Ss 0.000000 0.000000 0.000000 0.000000 0.000000 0

Z-line 0.050000 77.000000 1.343904 0.011248 0.048719 0.0112475527171933+0.0487185032392618i

I* = Ss/Es 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I = (Ss/Es)* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Esr = I x Zline 0.000000 0.000000 0.000000 0.000000 0.000000 0

Er = Es-Esr 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sline = Esr x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sr = Er x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Given Es, I


Es 480.000000 0.000000 0.000000 480.000000 0.000000 480

I 700.000000 -80.000000 -1.396263 121.553724 -689.365427 121.553724366851-689.365427108546i

Zline 0.050000 77.000000 1.343904 0.011248 0.048719 0.0112475527171933+0.0487185032392618i

I* 700.000000 80.000000 1.396263 121.553724 689.365427 121.553724366851+689.365427108546i

Ss=Es x I* 336000.000000 80.000000 1.396263 58345.787696 330895.405012 58345.7876960885+330895.405012102i

Esr = I x Zline 35.000000 -3.000000 -0.052360 34.952034 -1.831758 34.9520337164101-1.83175846850308i

Er = Es-Esr 445.051736 0.235821 0.004116 445.047966 1.831758 445.04796628359+1.83175846850308i

Sline = Esr x I* 24500.000000 77.000000 1.343904 5511.300831 23872.066587 5511.30083142472+23872.0665872383i

Sr = Er x I* 311536.215134 80.235821 1.400379 52834.486865 307023.338425 52834.4868646638+307023.338424864i

Given Er, Sr


Er 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sr 0.000000 0.000000 0.000000 0.000000 0.000000 0

Z-line 0.050000 77.000000 1.343904 0.011248 0.048719 0.0112475527171933+0.0487185032392618i

I* = Sr/Er 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I = (Ss/Es)* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Esr = I x Zline 0.000000 0.000000 0.000000 0.000000 0.000000 0

Es = Er+Esr 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sline = Esr x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Ss = Es x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Given Er, I


Er 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 0.000000 0.000000 0.000000 0.000000 0.000000 0

Zline 0.050000 77.000000 1.343904 0.011248 0.048719 0.0112475527171933+0.0487185032392618i

I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sr=Er x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Esr = I x Zline 0.000000 0.000000 0.000000 0.000000 0.000000 0

Es = Er+Esr 0.000000 0.000000 0.000000 0.000000 0.000000 0

Sline = Esr x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Ss = Es x I* 0.000000 0.000000 0.000000 0.000000 0.000000 0

Fault Calculations


Z0 5.000000 0.000000 0.000000 5.000000 0.000000 5 Add/subtract 30 degrees for Xfmr effect

Z1 1.000000 0.000000 0.000000 1.000000 0.000000 1 p_30 0.866025403784439+0.5i

Z2 1.000000 0.000000 0.000000 1.000000 0.000000 1 m_30 0.866025403784439-0.5i

Zf 0.000000 0.000000 0.000000 0.000000 0.000000 0

3Zf 0.000000 0.000000 0.000000 0.000000 0.000000 0

3Zn 0.000000 0.000000 0.000000 0.000000 0.000000 0

E prefault 63.000000 0.000000 0.000000 63.000000 0.000000 63

Three Phase Fault


Ztotal 1.000000 0.000000 0.000000 1.000000 0.000000 1

Io 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I1 63.000000 0.000000 0.000000 63.000000 0.000000 63

I2 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

In Fault I-012, repeated *a_1 *a_2 Complex Real Imaginary Magnitude Degrees Radians

Io 0.000000 A 63 63.000000 0.000000 63.000000 0.000000 0.000000

I1 63 -31.5+54.5596004384197 -31.5-54.5596004384196i B -31.5-54.5596004384196i -31.500000 -54.559600 63.000000 -120.000000 -2.094395

I2 0.000000 -0 0 C -31.5+54.5596004384197 -31.500000 54.559600 63.000000 120.000000 2.094395

Across Xfmr I-012, w/xfmr effects *a1 *a2 Complex Real Imaginary Magnitude Degrees Radians

Io 0.000000 A 54.5596004384197+31.5i 54.559600 31.500000 63.000000 30.000000 0.523599

I1 54.5596004384197+31.5i -54.5596004384197+31.5 -4.9737991503207e-14-63 B -4.9737991503207e-14-63 0.000000 -63.000000 63.000000 -90.000000 -1.570796

I2 0.000000 -0 0 C -54.5596004384197+31.5 -54.559600 31.500000 63.000000 150.000000 2.617994

A Phase to Ground


Ztotal 7.000000 0.000000 0.000000 7.000000 0.000000 7

Io 9.000000 0.000000 0.000000 9.000000 0.000000 9

I1 9.000000 0.000000 0.000000 9.000000 0.000000 9

I2 9.000000 0.000000 0.000000 9.000000 0.000000 9


Io 9 A 27 27.000000 0.000000 27.000000 0.000000 0.000000

I1 9 -4.5+7.79422863405995i -4.5-7.79422863405994i B 9.76996261670138e-15i 0.000000 0.000000 0.000000 0.000000 0.000000

I2 9 -4.5+7.79422863405995i -4.5-7.79422863405994i C 9.76996261670138e-15i 0.000000 0.000000 0.000000 0.000000 0.000000


Io 0.000000 A 15.5884572681199 15.588457 0.000000 15.588457 0.000000 0.000000

I1 7.79422863405995+4.5i -7.79422863405995+4.50 -3.10862446895044e-15-9 B -1.77635683940025e-15+ 0.000000 0.000000 0.000000 0.000000 0.000000

I2 7.79422863405995-4.5i 1.33226762955019e-15+9-7.79422863405995-4.5i C -15.5884572681199+9.76 -15.588457 0.000000 15.588457 180.000000 3.141593

B Phase to C Phase


Ztotal 2.000000 0.000000 0.000000 2.000000 0.000000 2

Io 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I1 31.500000 0.000000 0.000000 31.500000 0.000000 31.5

I2 31.500000 180.000000 3.141593 -31.500000 0.000000 -31.5


Io 0.000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 31.5 -15.75+27.279800219209 -15.75-27.2798002192098 B -54.5596004384196i 0.000000 -54.559600 54.559600 -90.000000 -1.570796


I2 -31.5 15.75-27.2798002192098 15.75+27.2798002192098 C 54.5596004384196i 0.000000 54.559600 54.559600 90.000000 1.570796


Io 0.000000 A 31.5i 0.000000 31.500000 31.500000 90.000000 1.570796

I1 27.2798002192098+15.75-27.2798002192098+15.7 -31.5i B -1.59872115546023e-14-6 0.000000 -63.000000 63.000000 -90.000000 -1.570796

I2 -27.2798002192098+15.7 -1.59872115546023e-14-327.2798002192098+15.75 C 31.5i 0.000000 31.500000 31.500000 90.000000 1.570796

Cell Used to check for Analysis ToolPak Installation

100+100i 100 100

Basic Electrical Simulator

Documents

Transcript of Basic Electrical Simulator