35949705 Electrical Calculations

1 04/08/2023 document.xls

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

Disclaimer

Purpose of this Spreadsheet

Instructions, Notes

100+100i 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.

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.Rev. 3.0: 03/06; Added "Z=OHL" sheet using simplified Carson's equation from Wagner and Evans.

Basler Electric Company, P.O. Box 269, Highland, Illinois USA 62249Phone: 618/654-2341 - Fax: 618/654-2351 - Website: http://www.basler.com

This spreadsheet presents basic calculations associated with electrical power. In developing this software Basler Electric has attempted to develop accurate calculation methods, but Basler Electric does not warrant that the software is free from bugs, errors, or other program limitations. Users are encouraged to consult with a Basler Electric representative to determine the accuracy of the data and results for the specific use or purpose of the user.

By use of this program, the user agrees that Basler Electric 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 software. In no event will Basler Electric be liable for any indirect, special, or consequential damages. In the event of any litigation regarding this software, 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.=> This spreadsheet is best viewed at 1024x768 or higher resolution. To fit everything on one screen some sheets use <100% zoom. If one has a higher resolution monitor, one might raise the zoom control to 100% for clearer viewing.=> This sheet uses complex number functions from the Excel Analysis ToolPak. Enable the Analysis ToolPak feature from the Excel menu "Tools/Add-Ins." If the Analysis ToolPak is not listed as an available Add-In, then likely only a partial installation of Excel has been done on your machine. The Analysis ToolPak is distributed with Excel, but it is an optional component that might not be installed in a partial installation of Excel. See test below to verify the complex number functions are working correctly.=> Though locking and protection is used in much of the the spreadsheet, there is no password protection. If one has obtained this spreadsheet from third party source, be aware of possible changes to calculations that may have been done, and keep a backup copy of the original spreadsheet in case one inadvertently changes a calculation for the worse.=> All macros re-enable protection; editing the macros is the only way to stop this. => Most calculations are done on the Intermediate Calcs sheet and macros are used to copy data to the various other sheets.=> Send comments on this spreadsheet to "[email protected]"


Basic Complex Number Calculator

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

Quantity 1 3.00000 4.00000 5.00000 53.130

Quantity 2 3.00000 4.00000 5.00000 53.130

Memory 1 3.00000 4.00000 5.00000 53.130

Memory 2

Memory 3

Memory 4

Calculate:

Calc Results: Real Imaginary Magnitude Degrees Copy results to:

Q1 / Q2 1.00000 0.00000 1.00000 0.000

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.

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

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

►►◄◄

►►◄◄


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 415.0000 425.0000 0

Vl-n B-N 415.0000 425.0000 1C-N 415.0000 425.0000 2

A-B 0 0.0000 0.0000 0.0000 0.000Vl-l B-C 1

C-A 0.0000 0.0000 0.000 0.000 2

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(NOTE: VT Calcs Use ABC-Rect. Data) (CT Calcs 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:

Instructions/Notes:=> 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.


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

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

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 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 phase shift, and a leading secondary would be entered in as a positive phase shift (+ 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. There is also no sanity check of the current data. e.g., the system does not prevent one from saying there is 0 sequence current entering a delta winding in the source current cells.

Series Impedance of Medium Length Overhead Lines

Presently Selected Unit System: English

UnitsFrequency for impedance calculations: Hz 60

Total Line Length: mile(s) 1Ground Resistivity: Ohm-meters 100

Phase A Resistance per unit length (Ra) ohms/mile 0.11720Conductor Radius (Ds or GMR) feet 0.03730X Dimension; = 0 for A phase feet 0.00

Height above Ground (Y) feet 29.00Phase B Resistance per unit length (Ra) ohms/mile 0.11720

Conductor Radius (Ds or GMR) feet 0.03730

Horizontal Distance from Ph A (X) feet -5.00

Height above Ground (Y) feet 25.00Phase C Resistance per unit length (Ra) ohms/mile 0.11720

Conductor Radius (Ds or GMR) feet 0.03730

Horizontal Distance from Ph A (X) feet 0.00

Height above Ground (Y) feet 21.00Neutral 1 Resistance per unit length (Ra) ohms/mile 0.30000

Conductor Radius (Ds or GMR) feet 0.02000Horizontal Distance from Ph A (X) feet -2.50

Height above Ground (Y) feet 35.00Neutral 2 Resistance per unit length (Ra) ohms/mile 0.30000

Conductor Radius (Ds or GMR) feet 0.02000Horizontal Distance from Ph A (X) feet -2.00

Height above Ground (Y) feet 15.00

Instructions/Notes:

100+100i

User Notes:

Do you wish to enter data in miles and feet (English); or kilometers and meters (SI-MKS)?

Note 1: The equations use a simplified equation for the ground loop impedance that is a partial implementation of what is referred to as Carson's Equations. See referenced paper for discussion. If one expects results that mimic Carson's Equations then one should obtain a professionally written package that fully implements those equations.Note 2: This sheet was first provided in Rev 3 of this spreadsheet. The results have not been deeply checked against a professionally written software package. Use the results with caution.

=>This sheet calculates the series impedance of overhead lines using the processes described in the paper, "Zero Sequence Impedance of Overhead Transmission Lines" (see www.basler.com).=> The spreadsheet uses a simplifed equation for the ground loop reported by many texts. See the referenced paper for the equation. => If any wire (phase or ground) does not exist, either enter a very high resistance or 0 resistance for that wire. The spreadsheet checks if R<0.00001 per unit length, and if so, it uses R =1E+6 per unit length instead.=> The X position of A phase relative to the ground plane is the X reference, so XA is fixed at 0. The X position of B, C, and N1 and N2 can be positive or negative. The calculations and X and Y input accept any conductor orientation. There is no requirement on the order of conductors; e.g., phase A could be the lowest, highest, the farthest to the right or the left, or anywhere in between. The only limitation is that phase A is expected to be at X = 0 and is the reference against which the XB, XC, XN1, and XN2 coordinates are measured, and that Y is positive for all conductors.=> This sheet does not calculate the effective diameter of bundled conductors. This is an easy calculation (see referenced paper) and is left to the user to apply and then enter the appropriate value in the cells.=> The spreadsheet will not support more than 2 ground wires, nor does it calculate the mutual impedance with a parallel line, nor does it calculate the impedance of 2+ parallel lines.


-6 -5 -4 -3 -2 -1 0

0

5

10

15

20

25

30

35

40

Conductor Locations

X Distance from Ph AH

eig

ht

Ab

ov

e G

rou

nd

English

SI-MKS

C12

This is the effective radius for the conductor or the bundled conductor for AC impedance calculations, as found in conductor characteristic tables, and when applicable, the geometric mean radius of the conductor bundle.

C13

All X (horizontal) distances are in reference to the phase A location.

F13

Should always = 0.

The impedance of the total line length in ohms:

Magnitude Degrees Magnitude Degrees0.9187 77.68 0.2946 74.96

ZABC = 0.2940 74.90 0.9350 78.080.2659 73.52 0.2940 74.92

The impedances in the above matrix refer to the ABC domain impedances below:

Resultant Symmetrical Component Domain Impedances in ohmsMagnitude Degrees Magnitude Degrees

1.4920 76.53 0.0161 -24.23Z012 = 0.0155 -150.77 0.6396 79.28

0.0153 -24.91 0.0132 23.31Z1, Z2 using K*ln(GMD/GMR) and phase A wire R, GMRThe impedances in the above matrix refer to the 012 domain impedances below.Z00, Z11, and Z22 are the values commonly referred to as Z0, Z1, and Z2.

Instructions/Notes:

The equations use a simplified equation for the ground loop impedance that is a partial implementation of what is referred to as Carson's Equations. See referenced paper for discussion. If one expects results that mimic Carson's Equations then one should obtain a professionally written package that fully implements those equations.

This sheet was first provided in Rev 3 of this spreadsheet. The results have not been deeply checked against a professionally written software package. Use the results with caution.

=>This sheet calculates the series impedance of overhead lines using the processes described in the paper, "Zero Sequence Impedance of Overhead Transmission Lines" (see www.basler.com).=> The spreadsheet uses a simplifed equation for the ground loop reported by many texts. See the referenced paper for the equation. => If any wire (phase or ground) does not exist, either enter a very high resistance or 0 resistance for that wire. The spreadsheet checks if R<0.00001 per unit length, and if so, it uses R =1E+6 per unit length instead.=> The X position of A phase relative to the ground plane is the X reference, so XA is fixed at 0. The X position of B, C, and N1 and N2 can be positive or negative. The calculations and X and Y input accept any conductor orientation. There is no requirement on the order of conductors; e.g., phase A could be the lowest, highest, the farthest to the right or the left, or anywhere in between. The only limitation is that phase A is expected to be at X = 0 and is the reference against which the XB, XC, XN1, and XN2 coordinates are measured, and that Y is positive for all conductors.=> This sheet does not calculate the effective diameter of bundled conductors. This is an easy calculation (see referenced paper) and is left to the user to apply and then enter the appropriate value in the cells.=> The spreadsheet will not support more than 2 ground wires, nor does it calculate the mutual impedance with a parallel line, nor does it calculate the impedance of 2+ parallel lines.


-6 -5 -4 -3 -2 -1 0

0

5

10

15

20

25

30

35

40

Conductor Locations

X Distance from Ph A

He

igh

t A

bo

ve

Gro

un

d

Conductor X, Y coordinates

Magnitude Degrees X Y0.2658 73.51 A 0 290.2933 74.85 B -5 250.9167 77.63 C 0 21

The impedances in the above matrix refer to the ABC domain impedances below: N1 -2.5 35N2 -2 15

Separation between conductors (feet).dX dY Total

A-B 5.00 4.00 6.40A-C 0.00 8.00 8.00A-N1 2.50 -6.00 6.50

Resultant Symmetrical Component Domain Impedances in ohms A-N2 2.00 14.00 14.14Magnitude Degrees B-C -5.00 4.00 6.40

0.0162 -150.40 B-N1 -2.50 -10.00 10.310.0134 141.55 B-N2 -3.00 10.00 10.440.6396 79.28 C-N1 2.50 14.00 14.220.6441 79.52 C-N2 2.00 6.00 6.32

The impedances in the above matrix refer to the 012 domain impedances below. N1-N2 -0.50 20.00 20.01Z00, Z11, and Z22 are the values commonly referred to as Z0, Z1, and Z2. GMD, Phase Conductors, (feet). 6.90

Instructions/Notes:

The equations use a simplified equation for the ground loop impedance that is a partial implementation of what is referred to as Carson's Equations. See referenced paper for discussion. If one expects results that

=>This sheet calculates the series impedance of overhead lines using the processes described in the paper, "Zero Sequence Impedance of Overhead Transmission Lines" (see www.basler.com).

=> If any wire (phase or ground) does not exist, either enter a very high resistance or 0 resistance for that wire. The spreadsheet checks if R<0.00001 per unit length, and if so, it uses R =1E+6 per unit length instead.=> The X position of A phase relative to the ground plane is the X reference, so XA is fixed at 0. The X position of B, C, and N1 and N2 can be positive or negative. The calculations and X and Y input accept any conductor orientation. There is no requirement on the order of conductors; e.g., phase A could be the lowest, highest, the farthest to the right or the left, or anywhere in between. The only limitation is that phase A is expected to be at X =

=> This sheet does not calculate the effective diameter of bundled conductors. This is an easy calculation (see referenced paper) and is left to the user to apply and then enter the appropriate value in the cells.

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

Blank unprotected sheet for user's work


Basic Fault Calculator

System Data:Magnitude Degrees

E prefault 0Magnitude Degrees

Z0Z1Z2ZfZn

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 I-a I-aI-b I-b I-bI-c I-c I-cI-0 I-0 I-0I-1 I-1 I-1I-2 I-2 I-2

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

I-a I-a I-aI-b I-b I-bI-c I-c I-cI-0 I-0 I-0I-1 I-1 I-1I-2 I-2 I-2

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)


Z-fault

E-prefault

Z-system

30o Lead

I-fault

Zn

Calculate

Clear All

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 Voltage Drop & Load Flow Calculator Miscellaneous Other Calcs:

Given Es, Er:

Magnitude Degrees Magnitude Degrees

Es 0.0000 Z-line

Er

Given Es, I: Solution is for:

Magnitude Degrees

Es 0.0000 Watts VAR VA Power Fact.

I Ss Per Unit / Base CalculationsSr Three Phase

Given Er, I: Sline MVA base, 3phMagnitude Degrees Real Imaginary Mag. Degrees kV Base, L-L

Er 0.0000 Es Given Ohmic ValueI Er Given Current Value

Es-Er Given MVA ValueGiven Es, Ss: I 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) 415.000 425.000 Phasor End Point 0.000 0.000 Phasor End Point

3 4 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) 415.000 425.000 Phasor End Point 0.000 0.000 Phasor End Point

3 4 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) 415.000 425.000 Phasor End Point 0.000 0.000 Phasor End Point

1 0 Phasor End Point Vab 0.000 0.000 Phasor Origin (0) V1,ll 0.000 0.000 Phasor Origin (0)

0.000 0.000 Phasor End Point 0.000 0.000 Phasor End Point

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


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


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 3.000000 4.000000 5.000000 53.130102 abc_i.012.r ='V&I,ABC<>012'!$K$16:$L$18abc_i.abc ='V&I,ABC<>012'!$D$16:$H$18

Quantity 2 3.000000 4.000000 5.000000 53.130102 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$23Q1 + Q2 6.000000 8.000000 10.000000 53.130102 +/- Q1 -3.000000 -4.000000 5.000000 -126.869898 abc_mem1.12 ='V&I,ABC<>012'!$K$22:$O$23Q1 - Q2 0.000000 0.000000 0.000000 0.000000 Q1 Conjugate 3.000000 -4.000000 5.000000 -53.130102 abc_mem1.ab ='V&I,ABC<>012'!$D$21:$H$22Q1 x Q2 -7.000000 24.000000 25.000000 106.260205 +/- Q2 -3.000000 -4.000000 5.000000 -126.869898 abc_mem1.abc ='V&I,ABC<>012'!$D$21:$H$23Q1 / Q2 1.000000 0.000000 1.000000 0.000000 Q2 Conjugate 3.000000 -4.000000 5.000000 -53.130102 abc_mem2.012 ='V&I,ABC<>012'!$K$24:$O$26Q1^2 -7.000000 24.000000 25.000000 106.260205 New Q1 3.000000 4.000000 5.000000 53.130102 abc_mem2.12 ='V&I,ABC<>012'!$K$25:$O$26Sqrt(Q1) 2.000000 1.000000 2.236068 26.565051 Q1<=>Q2 abc_mem2.ab ='V&I,ABC<>012'!$D$24:$H$251/Q1 0.120000 -0.160000 0.200000 -53.130102 New Q2 3.000000 4.000000 5.000000 53.130102 abc_mem2.abc ='V&I,ABC<>012'!$D$24:$H$26Q1 x Q2* 25.000000 0.000000 25.000000 0.000000 abc_results.012 ='V&I,ABC<>012'!$K$35:$O$43Q1 || Q2 1.500000 2.000000 2.500000 53.130102 abc_results.abc ='V&I,ABC<>012'!$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$37A-N 415.000000 425.000000 594.011784 45.682060 0 415.000000 425.000000 594.011784 45.682060 abc_vll.012 ='V&I,ABC<>012'!$K$11:$O$13

Vl-n B-N 415.000000 425.000000 594.011784 45.682060 1 0.000000 0.000000 0.000000 0.000000 abc_vll.12 ='V&I,ABC<>012'!$K$12:$O$13C-N 415.000000 425.000000 594.011784 45.682060 2 0.000000 0.000000 0.000000 0.000000 abc_vll.12.p ='V&I,ABC<>012'!$N$12:$O$13A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 abc_vll.12.r ='V&I,ABC<>012'!$K$12:$L$13

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 abc_vll.ab ='V&I,ABC<>012'!$D$11:$H$12C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 abc_vll.ab.p ='V&I,ABC<>012'!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 abc_vln.012 ='V&I,ABC<>012'!$K$6:$O$8Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 abc_vln.012.p ='V&I,ABC<>012'!$N$6:$O$8

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 abc_vln.012.r ='V&I,ABC<>012'!$K$6:$L$8A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 abc_vln.abc ='V&I,ABC<>012'!$D$6:$H$8

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 abc_vln.abc.p ='V&I,ABC<>012'!$G$6:$H$8C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 abc_vln.abc.r ='V&I,ABC<>012'!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 cc_m2 =ComplexCalc!$D$10:$H$10Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 cc_m3 =ComplexCalc!$D$11:$H$11

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 cc_m4 =ComplexCalc!$D$12:$H$12A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 cc_q1 =ComplexCalc!$D$5:$H$5

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 cc_q1.polar =ComplexCalc!$G$5:$H$5C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 cc_q1.rect =ComplexCalc!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 cc_q2.polar =ComplexCalc!$G$7:$H$7Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 cc_q2.rect =ComplexCalc!$D$7:$E$7

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 cc_results =ComplexCalc!$B$17:$H$17A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 cc_results.data.only =ComplexCalc!$D$17:$H$17

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.cc_1.over.q1 =IMCalcs!$B$18:$H$18C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.cc_plusminus.q1 =IMCalcs!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.divide.q2 =IMCalcs!$B$15:$H$15Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.minus.q2 =IMCalcs!$B$13:$H$13

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.over.q2 =IMCalcs!$B$18:$H$18A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.parallel.q2 =IMCalcs!$B$20:$H$20

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.plus.q2 =IMCalcs!$B$12:$H$12C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.polar.conv.from.rect =IMCalcs!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.squared =IMCalcs!$B$16:$H$16Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.x.q2 =IMCalcs!$B$14:$H$14

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.cc_q1.x.q2conjugate =IMCalcs!$B$19:$H$19A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.cc_q2.conjugate =IMCalcs!$K$15:$O$15

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.cc_q2.polar.conv.from.rect =IMCalcs!$G$9:$H$9C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.cc_q2.rect.conv.from.polar =IMCalcs!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.complexcheck.r =IMCalcs!$C$730Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.fault_all.results =IMCalcs!$B$221:$L$239

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.i.012.p_012.p =IMCalcs!$N$108:$O$110A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.i.012.p_012.r =IMCalcs!$K$108:$L$110

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.i.012.p_abc.p =IMCalcs!$G$108:$H$110C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.i.012.p_abc.r =IMCalcs!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.i.012.r_abc.p =IMCalcs!$G$103:$H$105Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.i.012.r_abc.r =IMCalcs!$D$103:$E$105

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.i.abc.p_012.p =IMCalcs!$N$98:$O$100A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.i.abc.p_012.r =IMCalcs!$K$98:$L$100

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.i.abc.p_abc.p =IMCalcs!$G$98:$H$100C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.i.abc.p_abc.r =IMCalcs!$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 -415.000000 -425.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vll.12.r =IMCalcs!$K$89:$L$90Vl-n B-N -415.000000 -425.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vll.ab.p =IMCalcs!$G$88:$H$89

C-N -415.000000 -425.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 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$87A-N 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vln.abc.p =IMCalcs!$G$85:$H$87

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.012.p_vln.abc.r =IMCalcs!$D$85:$E$87C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll.012.r_vll.12.p =IMCalcs!$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 415.000000 425.000000 594.011784 45.682060 0 415.000000 425.000000 594.011784 45.682060 ic.vll.abc.p_vll.12.p =IMCalcs!$N$73:$O$74Vl-n B-N 415.000000 425.000000 594.011784 45.682060 1 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vll.12.r =IMCalcs!$K$73:$L$74

C-N 415.000000 425.000000 594.011784 45.682060 2 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vll.ab.p =IMCalcs!$G$72:$H$73A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vll.ab.r =IMCalcs!$D$72:$E$73

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vln.012.p =IMCalcs!$N$69:$O$71C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.p_vln.012.r =IMCalcs!$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 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vll.ab.r =IMCalcs!$D$64:$E$65Vl-n B-N 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vln.012.p =IMCalcs!$N$61:$O$63

C-N 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vln.012.r =IMCalcs!$K$61:$L$63A-B 0.000000 0.000000 0.000000 0.000000 0 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vln.abc.p =IMCalcs!$G$61:$H$63

Vl-l B-C 0.000000 0.000000 0.000000 0.000000 1 0.000000 0.000000 0.000000 0.000000 ic.vll.abc.r_vln.abc.r =IMCalcs!$D$61:$E$63C-A 0.000000 0.000000 0.000000 0.000000 2 0.000000 0.000000 0.000000 0.000000 ic.vll_plusminus.12 =IMCalcs!$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$41A 0.000000 0.000000 0.000000 45.682060 0 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vll.ab.r =IMCalcs!$D$40:$E$41

S B 0.000000 0.000000 0.000000 45.682060 1 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vln.012.p =IMCalcs!$N$37:$O$39C 0.000000 0.000000 0.000000 45.682060 2 0.000000 0.000000 0.000000 0.000000 ic.vln.abc.p_vln.012.r =IMCalcs!$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 0 0 0 0

Sr 0 0 0 0

Sline 0 0 0 0

Real Imaginary Mag. Degrees

Es 0 0 0 0

Er 0 0 0 0

Es-Er 0 0 0 0

I 0 0 0 0

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 0 0 I-a 0 0 I-a 0.000000 0.000000

I-b 0 0 I-b 0 0 I-b 0.000000 0.000000

I-c 0 0 I-c 0 0 I-c 0.000000 0.000000

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

I-1 0 0 I-1 0 0 I-1 0 0

I-2 0 0 I-2 0 0 I-2 0 0

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

Mag Degrees Mag Degrees Mag Degrees

I-a 0 0 I-a 0 0 I-a 0.000000 0.000000

I-b 0 0 I-b 0 0 I-b 0.000000 0.000000

I-c 0 0 I-c 0 0 I-c 0.000000 0.000000

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

I-1 0 0 I-1 0 0 I-1 0 0

I-2 0 0 I-2 0 0 I-2 0 0

Complex Calc sheet - calculations

Rectangular to Polar conversions Polar to Rectangular conversions

Complex format Mag Degrees Radians Radians Real Imaginary

Q1 3+4i 5.000000 53.130102 0.927295 0.927295 3.000000 4.000000

Q2 3+4i 5.000000 53.130102 0.927295 0.927295 3.000000 4.000000

Math calculations

Restating Data: Real Imaginary Complex Mag Degrees Radians

Q1 3.000000 4.000000 3+4i 5.000000 53.130102 0.927295

Q2 3.000000 4.000000 3+4i 5.000000 53.130102 0.927295

Q2 Conjugate 3.000000 -4.000000 3-4i 5.000000 -53.130102 -0.927295

Performing Calcs: Radians, basic calc Simplified Radians

Q1+Q2 6.000000 8.000000 6+8i 10.000000 53.130102 0.927295

Q1-Q2 0.000000 0.000000 0 0.000000 0.000000 0.000000

Q1xQ2 -7.000000 24.000000 -7+24i 25.000000 106.260205 1.854590 1.854590

Q1/Q2 1.000000 0.000000 1 1.000000 0.000000 0.000000 0.000000

Q1^2 -7.000000 24.000000 -7+24i 25.000000 106.260205 1.854590 1.854590

Sqrt(Q1) 2.000000 1.000000 2+1i 2.236068 26.565051 0.463648 0.463648

1/Q1 0.120000 -0.160000 0.12-0.16i 0.200000 -53.130102 -0.927295 -0.927295

Q1xQ2conjugate 25.000000 0.000000 25 25.000000 0.000000 0.000000 0.000000

1/Q2 0.120000 -0.160000 0.12-0.16i 0.200000 -53.130102 -0.927295 -0.927295

1/Q1 + 1/ Q2 0.240000 -0.320000 0.24-0.32i 0.400000 -53.130102 -0.927295 -0.927295

Q1||Q2 = 1/[1/Q1 + 1/Q2] 1.500000 2.000000 1.5+2i 2.500000 53.130102 0.927295 0.927295

V&I,ABC<>012 sheet - calculations

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

Vab 0.000000 0.000000 a_1 -0.5+0.866025403784439i sqrt3 1.73205080756888

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

Vca = -sum 0.000000 0.000000

Vab rectangular 0.000000 0.000000

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

Vca = -sum 0.000000 0.000000 -0 0.000000 0.000000 0.000000

V conversions, starting with Vln ABC rectangular

Given: Real Imaginary Complex Format Magnitude Degrees Radians

AN 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

Vl-n BN 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

CN 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

Calculated Line to Line, ABC format

AB 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-l BC 0.000000 0.000000 0 0.000000 0.000000 0.000000

CA 0.000000 0.000000 0 0.000000 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 138.333333333333+141.666666666667i 0 414.999999999999+425.0 415.000000 425.000000 594.011784 45.682060 0.797302

Vl-n BN 138.333333333333+141.6 -191.85359886946 53.5202655361292-1 1 2.1316282072803e-13-3. 0.000000 0.000000 0.000000 0.000000 0.000000

CN 138.333333333333+141.6 -191.85359886946 53.5202655361292-1 2 1.98951966012828e-13-3 0.000000 0.000000 0.000000 0.000000 0.000000

AB 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

V conversions, starting with Vln ABC polar


Given: Magnitude Angle Radians Real Imaginary Complex Format

AN 0.000000 0.000000 0 0 0 0

Vl-n BN 0.000000 0.000000 0.000000 0.000000 0.000000 0

CN 0.000000 0.000000 0.000000 0.000000 0.000000 0

Calculated Line to Line, ABC format

AB 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l BC 0.000000 0.000000 0.000000 0.000000 0.000000 0

CA 0.000000 0.000000 0.000000 0.000000 0.000000 0

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

AN 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 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

AB 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

V conversions, starting with Vln 012 rectangular


0 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-n 1 0.000000 0.000000 0 0.000000 0.000000 0.000000

2 0.000000 0.000000 0 0.000000 0.000000 0.000000

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

0 0 AN 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

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

AB 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l BC 0.000000 0.000000 0.000000 0.000000 0.000000 0

CA 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

V conversions, starting with Vln 012 polar


0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 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 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

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

AB 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l BC 0.000000 0.000000 0.000000 0.000000 0.000000 0

CA 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

V conversions, starting with Vll ABC rectangular


AB 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-l BC 0.000000 0.000000 0 0.000000 0.000000 0.000000

CA 0.000000 0.000000 -0 0.000000 0.000000 0.000000

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

AB 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA -0 0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 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 AN 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

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 0.000000 0.000000 0 0 0 0

Vl-l BC 0.000000 0.000000 0 0 0 0

CA 0.000000 0.000000 0 0 0 0

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

AB 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA 0 -0 0 2 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-n 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 AN 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

V conversions, starting with Vll 012 rectangular


0 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-l 1 0.000000 0.000000 0 0.000000 0.000000 0.000000

2 0.000000 0.000000 0 0.000000 0.000000 0.000000

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 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 AB 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l 1 0 -0 0 BC 0 0.000000 0.000000 0.000000 0.000000 0.000000


2 0 -0 0 CA 0 0.000000 0.000000 0.000000 0.000000 0.000000

0 0 AN 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

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 0.000000 0.000000 0.000000 0.000000 0.000000 0

2 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 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 AB 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l 1 0 -0 0 BC 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 CA 0 0.000000 0.000000 0.000000 0.000000 0.000000

0 0 AN 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 0 -0 0 BN 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

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 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

Vl-n BN 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

CN 415.000000 425.000000 415+425i 594.011784 45.682060 0.797302

AB 0.000000 0.000000 0 0.000000 0.000000 0.000000

Vl-l BC 0.000000 0.000000 0 0.000000 0.000000 0.000000

CA 0.000000 0.000000 -0 0.000000 0.000000 0.000000

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 138.333333333333+141.666666666667i 0 414.999999999999+425.0 415.000000 425.000000 594.011784 45.682060 0.797302

Vl-n BN 138.333333333333+141.6 -191.85359886946 53.5202655361292-1 1 2.1316282072803e-13-3. 0.000000 0.000000 0.000000 0.000000 0.000000

CN 138.333333333333+141.6 -191.85359886946 53.5202655361292-1 2 1.98951966012828e-13-3 0.000000 0.000000 0.000000 0.000000 0.000000

AB 0 0 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l BC 0 -0 0 1 0 0.000000 0.000000 0.000000 0.000000 0.000000

CA -0 0 0 2 0 0.000000 0.000000 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

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

0 594.011784 45.682060 0.797302 415.000000 425.000000 414.999999999999+425.000000000001i

Vl-n 1 0.000000 0.000000 0.000000 0.000000 0.000000 4.51404394376271e-13

2 0.000000 0.000000 0.000000 0.000000 0.000000 4.38526345880333e-13

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l 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 0.000000 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


0 414.999999999999+425.000000000001i AN 415+425.000000000001i 415.000000 425.000000 594.011784 45.682060 0.797302

Vl-n 1 4.51404394376271e-13 -2.2570219718813 -2.25702197188135e- BN 414.999999999999+425.0 415.000000 425.000000 594.011784 45.682060 0.797302

2 4.38526345880333e-13 -2.1926317294016 -2.19263172940166e- CN 414.999999999999+425.0 415.000000 425.000000 594.011784 45.682060 0.797302

0 0 AB 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l 1 0 -0 0 BC 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 CA 0 0.000000 0.000000 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

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 0.000000 0.000000 0.000000 0.000000 0.000000 4.51404394376271e-13

2 0.000000 0.000000 0.000000 0.000000 0.000000 4.38526345880333e-13

0 0.000000 0.000000 0.000000 0.000000 0.000000 0

Vl-l 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 0.000000 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 8.89930740256604e-13 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-n 1 4.51404394376271e-13 -2.2570219718813 -2.25702197188135e- BN -4.44965370128301e-13-1 0.000000 0.000000 0.000000 0.000000 0.000000

2 4.38526345880333e-13 -2.1926317294016 -2.19263172940166e- CN -4.44965370128301e-13+ 0.000000 0.000000 0.000000 0.000000 0.000000

0 0 AB 0 0.000000 0.000000 0.000000 0.000000 0.000000

Vl-l 1 0 -0 0 BC 0 0.000000 0.000000 0.000000 0.000000 0.000000

2 0 -0 0 CA 0 0.000000 0.000000 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

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 415 425 415+425i 594.011784 45.682060 0.797302

V BN 415 425 415+425i 594.011784 45.682060 0.797302

CN 415 425 415+425i 594.011784 45.682060 0.797302

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 45.682060 0.797302

S = V x I* B 0 0 0 0.000000 45.682060 0.797302

C 0 0 0 0.000000 45.682060 0.797302


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 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0.000000

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 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0.000000 0.000000 0.000000 0.000000 0.000000 0

I 0.000000 0.000000 0.000000 0.000000 0.000000 0

Zline 0.000000 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

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 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 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0.000000 0.000000 0.000000 0.000000 0.000000 0

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 0.000000 0.000000 0.000000 0.000000 0.000000 0 Add/subtract 30 degrees for Xfmr effect

Z1 0.000000 0.000000 0.000000 0.000000 0.000000 0 p_30 0.866025403784439+0.5i

Z2 0.000000 0.000000 0.000000 0.000000 0.000000 0 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 0.000000 0.000000 0.000000 0.000000 0.000000 0

Three Phase Fault


Ztotal 0.000000 0.000000 0.000000 0.000000 0.000000 0

Io 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

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 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0.000000 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0.000000 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

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

Io 0.000000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0.000000 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

A Phase to Ground


Ztotal 0.000000 0.000000 0.000000 0.000000 0.000000 0

Io 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000


I1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000


Io 0.000000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0.000000 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0.000000 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000


Io 0.000000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

B Phase to C Phase


Ztotal 0.000000 0.000000 0.000000 0.000000 0.000000 0

Io 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0.000000 0.000000 0.000000 0.000000 0.000000 -0


Io 0.000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0.000 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 -0 0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000


Io 0.000000 A 0 0.000000 0.000000 0.000000 0.000000 0.000000

I1 0 -0 0 B 0 0.000000 0.000000 0.000000 0.000000 0.000000

I2 0 -0 0 C 0 0.000000 0.000000 0.000000 0.000000 0.000000

Cell Used to check for Analysis ToolPak Installation

100+100i 100 100

Documents

35949705 Electrical Calculations