Edsa Paladin

SYNCHRONOUS MACHINE PARAMETERS ESTIMATION

EDSA MICRO CORPORATION 16870 West Bernardo Drive, Suite 330 San Diego, CA 92127 U.S.A.

© Copyright 2008 All Rights Reserved

Version 2.95.00

October 2008

Table of Contents Program Overview ........................................................................................................................................ 1 Calculation Theory ........................................................................................................................................ 1 Overview ................................................................................................................................................... 1 Calculations .............................................................................................................................................. 2 Longhand Calculation For Program Verification and Validation / QA/QC .................................................... 6 Getting Started .............................................................................................................................................. 8 Opening or Creating a File........................................................................................................................ 8 Opening Calculation Views..................................................................................................................... 10 Calcs|AC Resistance .............................................................................................................................. 11 Calcs|D-Axis X/SCR ............................................................................................................................... 12 Calcs|D-Axis Saturated X ....................................................................................................................... 13 Open Circuit Characteristic - Data Point Dialog ..................................................................................... 14 Calcs|Q-Axis X (1) .................................................................................................................................. 14 Calcs|Q-Axis X (2) .................................................................................................................................. 16 Getting Results ....................................................................................................................................... 16 Closing Views ......................................................................................................................................... 17 Saving the File ........................................................................................................................................ 18 The Toolbar............................................................................................................................................. 19 Command Reference .................................................................................................................................. 20 File Commands....................................................................................................................................... 20 Edit Commands ...................................................................................................................................... 21 Record Commands................................................................................................................................. 22 Record|Delete ............................................................................................................................................. 22 Clipboard Commands ............................................................................................................................. 23 Window Commands................................................................................................................................ 23 Help Commands ..................................................................................................................................... 24 References .................................................................................................................................................. 28

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Synchronous Paramaters

Program Overview EDSA Synchronous Machine Parameter Calculation program provides a series of “intelligent calculators” for determining equivalent circuit parameters and short circuit ratio for synchronous machines (motors and generators). These intelligent calculations are useful for various analyses and system simulation studies. The calculation is based on data that are readily available from the manufacturer, or can be obtained from field tests. Calculated parameters are: 1. 2. 3. 4. 5. 6.

Equivalent effective AC resistance Direct-axis reactance (unsaturated Synchronous reactance) Short Circuit Ratio (SCR) Direct-axis reactance (saturated Synchronous reactance) Potier reactance Quadrature-axis reactance

Synchronous Machine calculation files are stored in two parts. The master file is always named with an extension of *.SMP. The detail file is always named with an extension of *.SMD. A *.SMP file can contain information for multiple machines. All of the input data, as well as calculated results, for a machine are organized in a record.

Calculation Theory Overview The synchronous machine characteristic curves are shown below.

In the steady-state analysis of a balanced three-phase power system, a synchronous machine is represented by a perphase (phase to neutral) model. The parameters of the per-phase model of a synchronous machine are: 1. 2.

Effective AC resistance per phase Direct-axis synchronous reactance per phase

1


3.

Quadrature-axis synchronous reactance per phase

It may be noted that the direct- and quadrature-axis synchronous reactances of a round-rotor (non-salient pole) machine have same values. In determining the saturated synchronous reactance, the following assumptions are made: (a) Armature leakage reactance is constant and independent of saturation, (b) The load saturation curve (Field current versus resultant air-gap voltage) is exactly the same with the Open Circuit Characteristic. According to assumption (b), the armature leakage reactance is equal to the Potier reactance. The program uses piece-wise linear approximation of the Open Circuit Characteristic to compute the Potier reactance. The Potier reactance value is used for armature leakage reactance. Since the load saturation curve and the Open Circuit Characteristic usually become vertically nearer together as saturation is increased to high values, the value of the armature leakage reactance can usually be measured with fair accuracy by measuring the Potier triangle at very high values of saturation. In such case, zero power factor test is to be carried out for high voltage and rated current. Usually, zero power factor test is carried out for rated voltage and rated current to determine the Potier reactance. In any case, armature leakage reactance is taken to be equal to the Potier reactance for any degree of saturation. Since saturation factor is dependent on the resultant air-gap voltage, saturated synchronous reactance is a function of resultant air-gap voltage. The program computes the saturation factor and saturated synchronous reactance for a set of voltages on Open Circuit Characteristic. Note that open circuit voltages are also resultant of the air-gap voltages. Calculations Following are the tests required to compute effective ac resistance, direct-axis synchronous reactance (unsaturated and saturated), and short circuit ratio: 1.

Open Circuit Characteristic

2.

Short Circuit test: (a) (b) (c)

Field current required to give rated short circuit current Three-phase short circuit load loss at rated current Average temperature of the armature winding during short circuit load loss test

3.

Zero-power factor test: Field current to give rated current and rated or higher terminal voltage at zero power factor

4.

DC resistance test: (a) (b)

Armature winding resistance per Y-phase; and Average winding temperature during the test.

In order to compute the quadrature-axis synchronous reactance for a salient-pole machine, the following tests are used: 1. 2.

Slip test Maximum lagging current test

In the following discussion, air-gap line (a-g line) refers to a line obtained from the Open Circuit Characteristic by extending the straight-line lower portion thereof. In the case lower portion is not linear, the air-gap line refers to a

2


line drawn as a straight line of maximum possible slope that passes through the origin and is tangent to the Open Circuit Characteristic. The following are the common input variables: VLB STB

= =

Rated line voltage of the machine in kV Rated three-phase MVA of the machine

Note: Machine voltage and MVA ratings are the bases for per unit quantities. The following are the output variables: R X du SCR Xp VLA , SFi , X ds,i

= = = =

Effective AC resistance in per unit (p.u.) at Ts Unsaturated direct-axis synchronous reactance in p.u. Short circuit ratio Potier reactance in p.u.

=

Resultant air-gap line voltage (also, the open circuit line voltage) in p.u. and SFi and

X ds,i are respectively the corresponding saturation factor and saturated direct-axis Xq

synchronous reactance in p.u. Quadrature-axis synchronous reactance in p.u.

=

Calculation of Effective AC resistance (R)

Below are the formulae used for calculating the effective ac resistance of armature. R dc T

= =

Ts PSCL Ta

= = =

DC resistance of armature per Y-phase in ohms Average temperature of armature winding in degree Celsius during DC resistance measurement Temperature in degree Celsius, at which effective ac resistance is to be determined Three-phase short circuit load loss in kW at rated armature current Average temperature of the armature winding in degree Celsius during short circuit load loss test

Rated line current,

Base impedance,

I LB =

ZB =

10 3 x S TB

(1)

Amps

VLB x 3

(VLB ) 2 Ohm S TB

(2)

R dc,TS = R dc,T x

(TS + F) Ohm (T + F)

(3a)

R dc,Ta = R dc,T x

(Ta + F) Ohm (T + F)

(3b)

where, F F

= =

234.5 for copper conductor, and 225.0 for aluminum conductor.

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Stray load loss, PSLL = PSCL x 10 3 - [3(I LB ) 2 xR dc,Ta ] Watt R dc,Ts + R=

(4)

PSLL 3(I LB ) 2

ZB

(5)

p.u.

Calculation of Unsaturated Direct-Axis Synchronous Reactance X du

(I f ,air , VL,air )

= Any non-zero point on the air-gap line, where I f ,air is the field current in amperes and VL,air is line voltage in kV

I fsc

= Field current in amperes corresponding to the rated short circuit current.

X du

= VL,air ,pu /(S.C. current in pu corresponding to I f ,air )

X du =

VL, air x I fsc VLB x I f, air

(6)

p.u.

Calculation of Short Circuit Ratio (SCR)

Additional variables for Short Circuit Ratio: I frv

=

Field current in amperes corresponding to the rated voltage on the Open Circuit Characteristic.

SCR

=

I frv / I fsc

(7)

Calculation of Saturated Direct-Axis Synchronous Reactance, Potier Reactance (Xp) and Saturation Factor (SFi)

(I fzpf , VLzpf )

=

Specifies the zero power factor test data where I fzpf is the field current in amperes to give rated current and a line voltage VLzpf in kV at zeropower factor.

(I fl , VL1 ) , ... , (I fN , VLN )

Note:

=

The points, specified in ascending order of field current at suitable intervals, where I fi is the field current in amperes corresponding to the line voltage VLi in kV.

The program approximates the Open Circuit Characteristic specified through N points by linear segments joining these points.

(

)

In the (field current - Line voltage) plane, AA is defined to be a line passing through I fzpf − I fsc , VLzpf and parallel to the air-gap line. With (I fo , VLo ) as the point of intersection of this line with the Open Circuit Characteristic (field current in A, and line voltage in kV), Xp

=

(VLo,pu − VLzpf ,pu ) p.u.

(8)

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Saturation factors and saturated direct-axis synchronous reactance are computed for the open circuit line voltages (also, resultant air-gap line voltages), (VLi , i = 1, N ) and VLo . For the ith line voltage Vi on the Open Circuit Characteristic : Resultant air-gap voltage in p.u., VLA,i

=

Vi / VLB

(9a)

=

VL,air ,i / Vi

(9b)

Saturation factor, SFi

X ds,i = X P +

X du - X p SFi

(9c)

p.u.

where VL,air ,i is the line voltage in kV on the air-gap line corresponding to the field current for line voltage Vi in kV on the Open Circuit Characteristic;

Calculation of Quadrature-axis Synchronous Reactance From Slip Test

For quadrature-axis synchronous reactance (for salient-pole machines): I max , I min E max , E min

= =

Respectively maximum and minimum line currents in amperes Respectively maximum and minimum line voltages in kV

Method 1

Xq =

Method 2

X q = X du (E min / E max )(I min / I max )p.u.

E min x I LB VLB x I max

(10)

p.u.

(11)

Where, I LB is calculated using equation (1) and VLB is the machine rated voltage in kV. It may be noted that the best result is obtained by using Method 2.

Calculation of Quadrature-axis Synchronous Reactance From Maximum Lagging Current Test

E I

= =

Line voltage in kV Line current in amperes at stability limit.

Xq

=

E pu / I pu

p.u.

(12)

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Longhand Calculation For Program Verification and Validation / QA/QC Example: VLB = 0.22 S TB = 0.045 Conductor material: R dc = 0.0335 = 2.0 PSCL Ts = 20°C = 1.8 I f ,air

kV MVA Copper ohm at T= 25° C kW at Ta = 30°C A

VL,air

=

0.1653

kV

I fsc I frv VLzpf

= = =

2.2 2.84 0.22

A A kV

I fzpf

=

5.8

A

Open Circuit Characteristic: Field Current (A) 0.6 1.2 1.8 2.4 2.84 3.4 3.8 4.4 4.8 5.4 6.0 6.8

Line Voltage (kV) 0.0551 0.1102 0.158 0.197 0.220 0.244 0.258 0.275 0.285 0.297 0.308 0.321

Slip test data: E max I min E min I max

= = = =

0.145 85 0.108 112

kV A kV A

Maximum lagging current test data: E I

= =

0.144 162

kV A

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Solution :

Rated line current (also, the base line current) Base impedance, Z B

= =

118.094373 1.075556

A, ohm

by by

eq.(1) eq.(2)

R dc , Ts

=

0.032855

ohm

by

eq.(3a)

R dc , Ta Stray load loss, PSLL Effective AC resistance, R

= = =

0.034145 571.393043 0.043244

ohm W p.u.

by by by

eq.(3b) eq.(4) eq.(5)

= 0.918333 p.u. by

eq.(6)

by

eq.(7)

by

eq.(8)

A:

Unsaturated direct-axis synchronous reactance,

B:

Short circuit ratio

=

X du

1.290909

Point of intersection of line AA with the Open Circuit Characteristic:

C:

I fo V Lo

= =

4.1091864 0.26675

Xp

=

0.2125 p.u.

A kV

Using eqs.(9a,b,c): Resultant Air-gap Voltage in p.u. 0.25045 0.5009 0.71818 0.89545 1.0 1.109091 1.172727 1.2125 1.25 1.295454 1.35 1.4 1.459091

Saturation Factor 1.0 1.0 1.0462 1.118782 1.185485 1.279643 1.352585 1.414659 1.469335 1.546667 1.669697 1.788961 1.945379

Saturated Direct-axis Synch. Reactance in p.u. 0.918333 0.918333 0.88716 0.84339 0.80789 0.76408 0.73434 0.71144 0.69287 0.66885 0.63523 0.60704 0.57532

Quadrature-axis synchronous reactance: From slip test,

D:

Method 1:

Xq

=

0.48886 p.u.

by

eq.(10)

Method 2:

Xq

=

0.49026 p.u.

by

eq.(11)

From maximum lagging current test, E:

Xq

=

0.47714 p.u. by eq.(12).

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Getting Started

In the following paragraphs, several Calculation windows are shown with example data. The machine used for these example screens is a design class A, 220 Volt, 45 kVA, 1200 rpm salient pole machine. This example is also referenced in the Longhand Calculations. Opening or Creating a File

From the main menu select “Analysis/Rotating Machine Parameters/Synchronous Machines Param” After starting Synchronous Machine Parameter Calculation, the first thing you need to do is either create a new project file, or open an existing one. This is done via the File|Open or File|New command shown below.

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Either creating, or opening a file, the Machine ID view (shown below) is opened. From the main menu select “New”.

This view will be blank if you have created a new file. This is the form where machines are described. Each machine in your project file must have a unique Machine ID. Beyond that, there are very few restrictions upon what may go into the ID and description fields. Rated voltage and kVA are input here since these values are required by all calculations. At this time minimize the screen (do not quit).

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Opening Calculation Views

The importance of the program is in the Calculation views that are accessed by the Calcs menu illustrated below:

The various Synchronous Machine Parameter calculations are largely independent of each other, so input parameters and results have been organized in a single view for each calculation. The calculations options are: 1. 2. 3. 4. 5.

Calculation of AC resistance Calculation of D-axis reactance and SCR Calculation of D-axis saturated reactance Calculation of Quadrature-axis reactance, using Slip test method Calculation of Quadrature-axis reactance, using Maximum Lagging Current test method

Note: In order to use any of the Calcs commands, a machine parameter file must be open.

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Calcs|AC Resistance

The Calcs|AC Resistance command opens an AC resistance calculation view for the active machine parameter file. The input data fields in this calculation view are described below:

Armature Conductor Material

Select either copper or aluminum. This affects the characteristic temperature for resistance calculations.

DC Resistance - Ohms/ Y-phase

Enter the published or measured DC resistance of the armature per Yphase in ohms.

DC Resistance - temp, C

Enter the armature winding temperature in degrees Celsius at which the DC resistance measurement was taken.

SC Load Loss - kW at Rated Armature Current

Enter the 3-phase short circuit load loss in kW at rated armature current.

SC Load Loss Temp, C

Enter the average temperature of the armature winding during short circuit load loss measurement in degrees Celsius.

Operating temp, C

Enter the operating temperature at which AC resistance is to be calculated.

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Calcs|D-Axis X/SCR

The Calcs|D-Axis X/SCR command opens a Direct-axis unsaturated reactance / short-circuit-ratio calculation view for the active machine parameter file. The input data fields in this calculation view are described below:

Optional Calculation

Check the Short Circuit Ratio (SCR) box if you want to calculate short circuit ratio. This opens an additional input field that is required for SCR calculation.

Air-gap Data Point - Field Current

Enter any non-zero point on the air-gap line. Enter field current in amps. See line-voltage, V. This field is repeated on the D-Axis Saturated X calculation view.

Air-gap Data Point Line Voltage, V

Enter any non-zero point on the air-gap line. Enter line voltage in Volts. See field current. This field is repeated on the D-Axis Saturated X calculation view.

Field Current at Rated SC Current

Enter the field current in amps corresponding to the rated short circuit current. This field is repeated on the D-Axis Saturated X calculation view.

Field Current at Rated Voltage on OC Characteristic

Enter the field current in amps corresponding to the rated voltage on the Open Circuit Characteristic. This field is activated when the Short Circuit Ratio box is checked.

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Calcs|D-Axis Saturated X

The Calcs|D-Axis Saturated X command opens a direct-axis saturated reactance calculation view for the active machine parameter file. The input data fields in this calculation view are described below.

Air-gap Data Point - Field Current

Enter any non-zero point on the air-gap line. Enter field current in amps. See line-voltage, V. This field is repeated on the D-Axis X / SCR calculation view.

Air-gap Data Point Line Voltage, V

Enter any non-zero point on the air-gap line. Enter line voltage in Volts. See field current. This field is repeated on the D-Axis X / SCR calculation view.

Field Current at Rated SC Current

Enter the field current in amps corresponding to the rated short circuit current. This field is repeated on the D-Axis X / SCR calculation view.

Rated current, Zero PF Field Current

Enter the field current in amps to give rated line current and a specified line voltage at zero power factor.

Rated current, Zero PF Line Voltage

Enter the line voltage corresponding to the specified field current to give rated line current at zero power factor.

Open Circuit Data Add

The machine’s Open Circuit Characteristic is defined by a series of fieldcurrent, line-voltage points. Click the Add button to open the Open Circuit Characteristic dialog to add a data point. Points are automatically ordered by increasing field current, regardless of the order in which they are entered. Up to 100 points may be used to describe the Open Circuit Characteristic.

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Open Circuit Data Delete

Click the Delete button to delete the currently highlighted Open Circuit Characteristic data point.

Open Circuit Data Edit

Click the Edit button to open the Open Circuit Characteristic dialog to change a data point.

Open Circuit Characteristic - Data Point Dialog

The Open Circuit Characteristic - Data Point dialog is executed in response to either the Add or Edit command buttons on the D-Axis Saturated X calculation view. The input data fields in dialog are described below:

Field Current

Enter the open circuit field current in amps for a corresponding line voltage.

Line Voltage

Enter the line voltage in Volts corresponding to the specified field current.

Calcs|Q-Axis X (1)

The Calcs|Q-Axis X (1) command opens a quadrature-axis reactance, slip-test method, calculation view for the active machine parameter file. This calculation can take one of two forms, depending on whether a valid unsaturated direct-axis reactance calculation has been performed for the machine. If there is no valid unsaturated reactance calculation, the calculation uses maximum line current and minimum line voltage of the slip test data. In this case, the calculation view appears as follows.

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15


The input data fields in this calculation view are described below: Line Current - Minimum

Enter the minimum line current from the slip test.

Line Current - Maximum

Enter the maximum line current from the slip test.

Line Voltage - Minimum

Enter the minimum line voltage from the slip test.

Line Voltage - Maximum

Enter the maximum line voltage from the slip test.

Calcs|Q-Axis X (2)

The Calcs|Q-Axis X (2) command opens a quadrature-axis reactance, maximum-lagging-current-test method, calculation view for the active machine parameter file. The input data fields in this calculation view are described below.

Line current

Enter the line current in amps at the stability limit.

Line voltage

Enter the line voltage in Volts at the stability limit.

Getting Results

As soon as the program detects valid inputs, the calculation is updated. If invalid data are entered into an input field, the calculation window is immediately blanked.

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Closing Views

To close a Calculation view, select the Close command from the system menu for the view you want to close. The system menu for a view (or any other window) is accessed by clicking the small gray box in the upper left corner of the view’s window. This is illustrated below:

If you close the Machine ID view, all other views of the associated project file are also closed. This has the same effect as selecting the File|Close command.

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Saving the File

To save the file, from the main menu select “Save”

Enter file name “Tutorial.smp” and press

.

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The Toolbar

Single button short-cuts for several of the menu commands are provided on the toolbar. Command equivalents for the toolbar buttons illustrated above are as follows, from left to right: File|New Create a new document File|Open Open an existing document File|Save Save this document Edit|Cut Cut the record into a buffer Edit|Copy Copy the record into a buffer Edit|Paste Paste a record from the buffer Edit|Undo Undo the last action Record|First Record|Prev Record|Next Record|Last File|Print

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Command Reference File Commands

New

The File|New command opens a new, untitled machine parameter file, and opens a blank Machine ID view of the file. The application prompts you to give a name to an untitled file when it is closed.

Open

The File|Open command displays the Open a File dialog box so you can select an existing machine parameter file to load. You can also create a new file by giving it a name that doesn't currently exist. The default directory for opening existing files is defined in the EDSAMPRM.INI file in your Windows directory.

Close

The File|Close command checks to see if unsaved changes have been made to the active machine parameter file. If there are unsaved changes, the option is provided to save or discard the changes. All view windows for the file are then closed.

Save

The File|Save command saves the machine parameter file in the active view window to disk. If the file is unnamed, the Save/File As dialog box is displayed so you can name the file, and choose where it is to be saved.

Save As

The File|Save As command allows you to save a file under a new name, or in a new location on disk. The command displays the Save/File As dialog box. You can enter the new file name, including the drive and directory. All view windows containing this file are updated with the new name. If you choose an existing file name, you are asked if you want to overwrite the existing file.

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Output

The File|Output command allows you to save records as a text file.

Print

The File|Print command generates a formatted report of all input and results for the active machine parameter file, and spools it to the default windows printer, or to the printer selected under the Print Setup command.

Print Setup

The File|Print Setup command displays the Windows printer setup menu. Printer settings may be changed, or a printer other than the default may be selected. Settings will only affect printout generated by the machine parameter calculation program.

Exit

The File|Exit command ends the machine parameter program session. If changes have been made since the file was saved, options are provided to save the changes, discard the changes or cancel the Exit command.

Edit Commands

The Edit commands can be used to manipulate text in the various data input and result fields of the machine parameter calculation program. Edit|Undo

Reverse the action of the last command: Edit|Cut, Edit|Paste or Record|Delete.

Edit|Cut

Cut the machine record and put it on the clipboard and data buffer. Select Edit|Undo or Edit|Paste command to reverse this action, if necessary.

Edit|Copy

Copy the machine record and put it on the clipboard and data buffer.

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Record Commands

Multiple machines are managed by the Synchronous Machine Parameter Calculation program within a single file. Each machine occupies a “record” within the file. The Record commands provide for navigation through and manipulation of the various machine parameter records in a file. Records within the file are always alphabetically sorted according to the Machine ID assigned to it.

Record|First

Move to the first machine record.

Record|Prev

Move to the previous machine record.

Record|Next

Move to the next machine record.

Record|Last

Move to the last machine record.

Record|Insert

Open a blank machine record in the active file.

Record|Delete

Delete the currently displayed record from the active file. Select Edit|Undo command to reverse this action if necessary.

22


Clipboard Commands

The Clipboard menu provides command to output text data from a machine record. This command will make a user easily bind synchronous machine parameters in a documentation or text file. Export

The Clipboard|Export command converts a printing formated data to text data, and then copies the text to Clipboard.

Window Commands

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Window commands provide control over the arrangement of calculation View Windows within the application window area.

Cascade

The Window|Cascade command sizes all View Windows at their normal size, and arranges them so that the captions of all View Windows are visible.

Tile

The Window|Tile command sizes all View Windows to an equal size so that they can be arranged in a tile pattern within the application Window area.

Arrange Icons

The Window|Arrange Icons arranges the icons for any minimized Windows (see System Menu) in a row at the bottom left of the application Window area.

Close All

The Window|Close All command closes all Window Views. selecting the File|Close command.

1 (etc.)

Each open window or calculation view will have an entry in the Window menu. Selecting one of these entries will bring that view to the top of the stack of View Windows in the application area.

This is equivalent to

Help Commands

Help commands provide access to on-line information designed to help you use the Machine Parameter Calculation program.

Contents

Displays the master table of contents for the Help system.

24


Using help

Displays general information about how to use the Help system.

About

Displays information about the program, including version ID and copyright notice.

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Output Results EDSA Synchronous Machine Parameter Estimation Input File: D:\EDSA_VV\SYNCH\TUTORIAL.SMP Output File: C:\EDSA\OUTPUT\TUTORIAL.txt Date: Machine ID:

TUTORIA 45 kVA, 220 Volts 1200 RPM, 60 Hz Machine Rating

Voltage: 220

kVA: 45

Input Machine Parameters DC Resistances Ohms/Y-phase: 0.0355 at temp: 25.0 C Short Circuit Load Loss KW at rated armature current: 2.0000 at temp: 30.0 C Operating Temp: 20.0 C Air-gap data point Field Current:1.80amp Line Voltage:165.30volts Field Current At rated short circuit current: 2.20 At rated voltage on open circuit characteristic: 2.84 Rated Current,zero PF data point Field Current:5.80amp Line Voltage:220.00volts Slip Test Data Minimum Maximum Line Current: 85.00 112.00 Line Voltage: 102.00 145.00 Maximum Logging Current Test Data Line current:162.00amp Line voltage:144.00volts at stability limit. Calculated Machine Parameters Effective AC Resistance: 0.0432 p.u. (0.0464 ohms) Unsaturated Sync Reactance: 0.9183 p.u. (0.9877 ohms) Short Circuit Ratio: 1.291 Potier Reactance from Zero PFTest: 0.2125p.u. (0.2286 ohms) Q-Axis Sync X from Slip Test: 0.4903 p.u. (0.5273 ohms) Q-Axis X from Max. Lagging Cur Test: 0.4771 p.u. (0.5132 ohms) Saturated Direct-axis Reactance Fld Current Line Voltage 0.60 55.1 1.20 110.2 1.80 158.0 2.40 197.0 2.84 220.0 3.40 244.0 3.80 258.0 4.11 266.8 4.40 275.0 4.80 285.0 5.40 297.0 6.00 308.0 6.80 321.0

Air-Gap V 0.250 0.501 0.718 0.895 1.000 1.109 1.173 1.213 1.250 1.295 1.350 1.400 1.459

Sat Factor 1.000 1.000 1.046 1.119 1.185 1.280 1.353 1.415 1.469 1.547 1.670 1.789 1.945

X-p.u. 0.918 0.918 0.887 0.843 0.808 0.764 0.734 0.711 0.693 0.669 0.635 0.607 0.575

X-ohms 0.988 0.988 0.954 0.907 0.869 0.822 0.790 0.765 0.745 0.719 0.683 0.653 0.619

Note: If the field current is not entered by the user, EDSA will calculate this value (bolded text for this example).

PROGRAM RESULTS AND LONGHAND CALCULATIONS MATCH 100% PROGRAM

LONGHAND

% DEVIANCE

A

0.9183

0.9183

0%

B

1.291

1.290909

0%

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C

0.2125

0.2125

0%

D

0.4903

0.49026

0%

E

0.4771

0.47714

0%

27


References

1.

Fitzgerald, A. E., and Kingsley, C., Jr., 'Electric Machinery', McGraw-Hill, New York, 1961.

2.

IEEE Guide : Test Procedures For Synchronous Machines, IEEE Std 115-1983.

3.

Mablekos, V. E., 'Electric Machine Theory For Power Engineers', Harper & Row, New York, 1980.

4.

Matsch, L. W., and Morgan, J. D., 'Electromagnetic And Electromechanical Machines', Harper & Row, New York, 1986.

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Edsa Paladin

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