hálózati tranzienseinek számítógépi...

EMTP Applications, Laboratory III, April – May, 2001

HÁLÓZATI TRANZIENSEINEK SZÁMÍTÓGÉPI SZIMULÁCIÓJA

VILLAMOSENERGIA-RENDSZEREK FÕSZAKIRÁNY

LABOR III.

MÉRÉSVEZETÕ: PRIKLER LÁSZLÓ

TARTALOMJEGYZÉK

OLDAL

1. AZ ATP-EMTP SZIMULÁCIÓS PROGRAMCSOMAG ÁTTEKINTÉSE 1

2. ATPDRAW GRAFIKUS FELHASZNALÓI INTERFACE 6

3. HÁLÓZATANALÍZIS AZ IDÕ- VAGY FREKVENCIA-TARTOMÁNYBAN 17

4. TÁVVEZETÉKEK ÉS KÁBEL SZIMULÁCIÓJA 21

5. TIPIKUS ALKALMAZÁSI PÉLDÁK 22

6. A LABORATÓRIUMI MÉRÉS SORÁN ELVÉGZENDÕ FELADATOK 30

2001 ÁPRILIS - MÁJUS

EMTP Applications Laboratory, April - May, 2001 ATP simulation package

Prof. Dr. Kizilcay page 1

Capabilities of the Transients Program ATP-EMTP

ATP-EMTP as world-wide mostly used universal program for digital simulation ofelectromagnetic transients in power systems has extensive modelling capabilities. Besides actualsimulation module there exist several non-simulation supporting routines, which can be used togenerate model data like computation of line parameters or derivation of coupled RL matrix torepresent multi-phase, multi-winding transformers in the time-domain simulation.

A schematic overview of available simulation modules and supporting routines and theirinteraction is shown below.



Built-in Electrical Components

Component type ATP Element Identification

LINEAR BRANCHES

‚ type 0 : Uncoupled lumped series RLC element‚ type 1,2,3,.. : Mutually coupled ð-circuit‚ type 51,52,53,.. : Mutually coupled RL elements‚ type -1,-2,-3,.. : Distributed parameter line models

• Constant parameter line model (Clark, K.C. Lee)• Special double-circuit distributed line• SEMLYEN line model• JMARTI line model• NODA line model

‚ Saturable TRANSFORMER component (multi winding)• TRANSFORMER single-phase units• TRANSFORMER THREE PHASE with zero-sequence coupling• IDEAL TRANSFORMER component

• BCTRAN supporting routine• KIZILCAY F-DEPENDENT (high order admittance branch)• CASCADED PI - type 1,2,3 element (for steady-state solution)• PHASOR BRANCH [Y] - type 51,52,53 element

(for steady-state solution and Frequency Scan computation)

NONLINEAR BRANCHES

‚ type 99 : Pseudo-nonlinear resistance‚ type 98 : Pseudo-nonlinear inductance‚ type 97 : Staircase time-varying resistance‚ type 96 : Pseudo-nonlinear hysteretic inductor‚ type 94 : User-defined component via MODELS‚ type 93 : True, nonlinear inductance‚ type 92 : – Exponential ZnO surge arrester

– Multi-phase, piece-wise linear resistance withflashover

‚ type 91 : Multi-phase time-varying resistanceTACS/MODELS controlled resistance

‚ User supplied Fortran nonlinear element


Component type ATP Element Identification

SWITCHES

‚ type 0 : Stand alone switches• Time-controlled switch• Voltage-controlled switch• MEASURING switch

‚ type 0 : Statistical switches• STATISTICS switch• SYSTEMATIC switch

‚ TACS/MODELS controlled switch• type 11 : Switch for diode and thyristor application• type 12 : Switch for spark gap and triac application• type 13 : Simple TACS/MODELS controlled switch

SOURCES

‚ Empirical Sources

‚ Analytical Sources (voltage or current)• type 11 : Step function• type 12 : Ramp function• type 13 : Two-slope linearized surge function• type 14 : Cosine function / trapped charge• type 15 : Exponential surge function• type 16 : Simplified AC/DC converter model• type 18 : Ideal transformer / ungrounded voltage source

‚ TACS/MODELS controlled sources• TACS/MODELS modulation• TACS/MODELS controlled voltage/current source

‚ Rotating Machines• type 59 : Three-phase synchronous machine

(prediction method)• type 58 : Three-phase synchronous machine

(phase-domain solution)• type 19 : Universal Machine model

USER-DEFINED

COMPONENTS

‚ type 94 : MODELS controlled electrical branch• Thevenin type model• Iterated type model• Non-transmission Norton type model• Transmission Norton type model



Simulation Modules

MODELS in ATP is a general-purpose description language supported by a large set of

simulation tools for the representation and study of time-variant systems.

% The description of each model is enabled using free-format, keyword-driven syntax of localcontext and that is largely self-documenting.

% MODELS allows the description of arbitrary user-defined control and electric circuitcomponents, providing a simple interface for connecting other programs/models to ATP.

% As a general-purpose programmable tool, MODELS can be used for processing simulationresults either in the frequency domain or in the time domain.

TACS is a simulation module for time-domain analysis of control systems. It was originally

developed for the simulation of HVDC converter controls. In TACS block diagramrepresentation of control systems is used. TACS can be used for the simulation of

% HVDC converter controls% Excitation systems of synchronous machines% power electronics and drives% electric arcs (circuit breaker and fault arcs).

Interface between electrical network and TACS is established by exchange of signals like nodevoltage, switch current, switch status, time-varying resistance, voltage and current sources.

Important Supporting Programs

LINE CONSTANTS is a supporting routine to compute electrical parameters of overhead

lines in frequency-domain like per length impedance and capacitance matrices, ð-equivalent,model data for constant-parameter distributed line (CPDL) branch. LINE CONSTANTS in ATPis internally called to generate frequency data for the line models SEMLYEN SETUP, JMARTISETUP and NODA SETUP.

CABLE CONSTANTS / CABLE PARAMETERS are supporting routines to computeelectrical parameters of power cables. CABLE PARAMETERS is newer than CABLECONSTANTS and has additional features like handling of conductors of arbitrary shape, snakingof a cable system and distributed shunt admittance model. CABLE CONSTANTS is linked toSEMLYEN SETUP and JMARTI SETUP whereas CABLE PARAMETERS is called by NODA



SETUP to generate frequency-dependent electrical parameters.

SEMLYEN SETUP is a supporting routine to generate frequency-dependent model data for

overhead lines and cables. Modal theory is used to represent unbalanced lines in time-domain.Modal propagation step response and surge admittance are approximated by secondorder rational functions with real poles and zeros.

JMARTI SETUP generates high-order frequency-dependent model for overhead lines andcables. The fitting of modal propagation function and surge impedance is performed byasymthotic approximation of the magnitude by means of a rational function with real poles.JMARTI line model is not suitable to represent cables.

BCTRAN is an integrated supporting program in the ATP-EMTP, that can be used to derive a

linear [R], [ L] or [A], [R] matrix representation for a single- or three-phase transformer usingdata of the excitation test and short-circuit test at rated frequency. For three-phase transformers,both the shell-type (low homopolar reluctance) and the core-type (high homopolar reluctance)transformers can be handled by the routine.

XFORMER is used to derive a linear representation for single-phase, 2- and 3- winding

transformers by means of RL coupled branches. BCTRAN should be preferred to XFORMER.

SATURA is a conversion routine to derive flux-current saturation curve from either RMS

voltage-current characteristic or current-incremental inductance characteristic. Flux-currentsaturation curve is used to model a non-linear inductance, e.g. for transformer modeling.ATPDraw has this feature integrated in the model Saturable 3 phase transformer.

ZNO FITTER can be used to derive a true non-linear representation (typ-92 branches) for a

zinc-oxide surge arrester, starting from manufacturer's data. ZNO FITTER approximatesmanufacturer's data (voltage-current characteristic) by a series of exponential functions of type

.i ' p@ vVref

q

DATA BASE MODULE allows the user to modularize network sections. Any module may

contain several circuit elements. Some data, such as node names or numerical data may havefixed values inside the module, whereas other data can be treated as parameters that will bepassed to the data base module, when the module is connected to the data case via $INCLUDE.

EMTP Applications Laboratory, April – May,2001 ATPDraw

L. Prikler page 6

ATPDraw the graphical front-end interface Introduction The ATP-EMTP simulation system consists of various separate supporting programs (pre- and post processors), data initialization files and the solver program (TPBIG.EXE). ATPDraw can be used as a simulation center, that provides an operating shell for other ATP-EMTP components. This shell function is supported by version 1.2 and above [1]. Fig. 1 gives a functional overview of the traditional use of ATP-EMTP program. Program components are communicating via disk files: i.e. the output of the pre-processors are used as input for the main program, while the product of the simulation can be used as input for plotting programs. When the main program is used as pre-processor for some components (e.g. BCTRAN, LINE CONSTANTS etc.), the punch file products must be re-used as input in a subsequent run. The structure of the program components is rather difficult, so having a user shell which supervises the execution of separate programs and input/output flows has a great advantage.

Fig. 1 - Schematic description of the ATPDraw user shell

ATPDraw graphical user-shell

ASCII Text editor

ATP (TPBIG.EXE)

TPPLOT

PCPLOT

DisplayNT

DspATP32

GTPPLOT

PCPLOT for Windows

.PL4, .PS, .HGL file

PL42mat

.ATP file input data

.ADP project file

.ALC line data

USP Library

.PCH Library

*.ATP

PlotXY

*.PL4

*.PS

Data Information

LCC

Introduction

ATPDraw version 1 for Window 7

1 What is ATPDraw?

ATPDraw� for Windows is a graphical, mouse-driven preprocessor to the ATP version of theElectromagnetic Transients Program (EMTP). It assists to create and edit the model of theelectrical network to be simulated, interactively. In the program the user can construct an electriccircuit, by selecting predefined components from an extensive palette. The preprocessor thencreates the corresponding ATP input file, automatically in correct format. Circuit node naming isadministrated by ATPDraw and the user only needs to give name to "key" nodes. ATPDrawcurrently supports about 70 standard components and 28 TACS objects. A simplified usage ofMODELS is also possible. In addition, the user can create his own circuit objects using the DataBase Module and the $INCLUDE option of ATP. Both single phase and 3-phase circuits can beconstructed. Multiple circuit windows are supported to work on several circuits simultaneouslyand copy information between the circuits. Most types of edit facilities like copy/paste, rotate,import/export, group/ungroup, undo and print are available. Other facilities in ATPDraw are: abuilt-in editor for ATP-file editing, support of Windows clipboard for bitmap/metafile, output ofWindows Metafile/Bitmap file format or PostScript files.

ATPDraw is most valuable to new users of ATP and is an excellent tool for educational purposes.It is to be hoped, however that even experienced users of ATP will find the program useful fordocumentation of circuits and exchanging data cases with other users. The possibility of buildingup libraries of circuits and sub-circuits makes ATPDraw a powerful tool in transients analysis ofelectric power systems. The ATPDraw package also includes the ATP_LCC program forLine/Cable constants support and a utility, that makes possible the usage of existing circuit filescreated by the previous (DOS/GIGS) versions of the program under the new environment.

The program is written in Borland Pascal. Two functionally very similar versions of ATPDrawexist. A 32-bit version which is written in Borland Delphi 2.0 runs only under Windows 95/NTand a 16-bit version compiled with Borland Delphi 1.0 for Windows 3.x.

ATPDraw� is a trademark and copyrighted by © 1996-1997 SINTEF Energy Research,Trondheim, Norway. It is programmed and maintained by Dr. Hans Kr. Høidalen. The programwas redesigned and converted to Windows by O. G. Dahl, Dahl Data Design, Norway.

The ATPDraw for Windows program is royalty free. The proprietary rights of the program belongto the Bonneville Power Administration, USA, the company who financed the development.

2 Short description of ATP

ATP (Alternative Transients Program) is considered to be one of the most widely used softwarefor digital simulation of transient phenomena of electromagnetic, as well as electromechanicalnature in electric power systems. It has been continuously developed through internationalcontributions over the past 20 years, coordinated by the Canadian/American EMTP Users Groupco-chaired by Drs. W. Scott Meyer and Tsu-huei Liu.

Introduction

ATPDraw version 1 for Windows 8

The ATP program calculates variables of interest within electric power networks as functions oftime, typically initiated by some disturbances. Basically, the trapezoidal rule of integration is usedto solve the differential equations of system components in the time domain. Non-zero initialconditions can be determined either automatically by a steady-state, phasor solution or they can beentered by the user for some components.

ATP has many models including rotating machines, transformers, surge arresters, transmissionlines and cables. With this digital program, complex networks of arbitrary structure can besimulated. Analysis of control systems, power electronics equipment and components withnonlinear characteristics such as arcs and corona are also possible. Symmetric or unsymmetricdisturbances are allowed, such as faults, lightning surges, any kind of switching operationsincluding commutation of valves. Calculation of the frequency response of phasor networks isalso supported.

ATP includes at present the following components:

�� Uncoupled and coupled linear, lumped elements.�� Transmission lines and cables with distributed and frequency-dependent parameters.�� Elements with nonlinearities: transformers including saturation and hysteresis, surge

arresters, arcs.�� Ordinary switches, time-dependent and voltage-dependent switches, statistical switching�� Valves (diodes and thyristors).�� 3-phase synchronous machines, universal machines.�� MODELS and TACS (Transient Analysis of Control Systems).

MODELS in ATP is a general-purpose description language supported by an extensive set ofsimulation tools for the representation and study of time-variant systems. MODELS allows thedescription of arbitrary user-defined control and circuit components, providing a simple interfacefor connecting other programs/models to ATP. As a general-purpose programmable tool,MODELS can be used for processing simulation results either in the frequency domain or in thetime domain.

The following supporting routines are available in ATP:

�� LINE CONSTANTS, CABLE CONSTANTS and CABLE PARAMETERS for calculationof electrical parameters of overhead lines and cables

�� Generation of frequency-dependent line model input data: JMARTI Setup, SEMLYENSetup and NODA Setup.

�� Calculation of model data for transformers (XFORMER and BCTRAN).�� Saturation and hysteresis curve conversion.�� Data Base Modularization

ATP is available for most Intel based PC platforms under DOS, Windows 3.x/95/NT, OS/2, Linuxand for other computers, too (e.g., Digital Unix and VMS, Apple Mac’s, etc.). The program is inprinciple royalty free, but requires a license agreement signed by the requester and theCanadian/American EMTP Users Group, or the authorized regional users group representatives.

Introductory Manual


This part of the manual gives the basic information on how to get started with ATPDraw.The Introductory Manual starts with the explanation of how to operate windows and mouse inATPDraw. The manual shows how to build a circuit step by step, starting from scratch. Thenspecial considerations concerning three phase circuits are outlined.

3 Operating Windows

ATPDraw has a standard Windows user interface. This chapter explains some of the basicfunctionalities of the Main menu and the Component selection menu, and two important windows:the Main window and the Component dialog box.

The Main window

Fig. 3.1 - The Main window. Multiple Circuit windows and the floating Selection menu.

The ATPDraw for Windows program has a functionality similar to the DOS version . TheComponent selection menu is hidden, however, but appears immediately when you click the rightmouse in the open area of the Circuit window. Fig. 3.1 shows the main window of ATPDrawcontaining two open circuit windows. ATPDraw supports multiple documents and offers the user

Main menu Tool bar icons Componenttool bar

Header,circuit filename

Circuitwindows

Circuitcomments

Windowsstandard buttons

Circuitmap

Scrollbars

Currentactionmode

Component selection menu

Status bar withmenu option hints

Introductory Manual


to work on several circuits simultaneously along with the facility to copy information between thecircuits. The size of the circuit window is much larger than the actual screen, as it is indicated by the scroll bars of each circuit window. The Main window consists of the following parts:

Header + Frame:As a standard Windows element, it contains the system menu on the left side, a header text andminimize, maximize, exit buttons on the right side. The main window is resizeable.

System menu: Contains possible window actions: Close, Resize, Restore, Move, Minimize,Maximize or Resize and Next. The last one exists only if multiple circuitwindows are open.

Header text: The header text is the program name in case of the main window and thecurrent circuit file name in case of the circuit window(s). To move a window,click in the header text field, hold down and drag.

Minimize button: A click on this button will iconize the main window.Maximize button: A click on this button will maximize the window. The maximize button will

then be replaced with a resize button. One more click on this button will bringthe window back to its previous size.

Corners: Click on the corner, hold down and drag to resize the window.

Main menu:The main menu provides access to all the functions offered by ATPDraw. The menu items are explained in detail in the reference part of this manual:

File: Load and save circuit files, start a new one, import/export circuit files, createpostscript and metafile/bitmap files, print the current circuit and exit.

Edit: Circuit editing:copy/paste/delete/duplicate/flip/rotate, select, move label, copygraphics to clipboard and undo/redo etc.

View: Tool bar, status bar and comment line on/off, zoom, refresh and view options.ATP: Create node names, make ATP file, edit ATP file, ATP file settings (miscellaneous

cards and file formats, file sorting etc.), running batch jobs.Objects: Edit support files (default values, min/max limits, icon and help file), create new files

for MODELS and User Specified Objects.Tools: Icon editor, help file editor, text editor, setting of various program options.Window: Arranging of the circuit windows. Map window.Help: About box and Windows help file system.

Circuit window:The circuit is built up in this window. The circuit window is the container of circuit objects. Fromthe file menu you can load circuit objects from disk or simply create an empty window to startbuilding a new circuit. Circuit objects include standard ATP components, user specified elements,MODELS and TACS components, connections and relations. To move around in the circuit, youcan use the window scrollbars, or drag the view rectangle of the Map window to another position.

Component selection menu:This menu is hidden initially and pops-up only after a right mouse button click in an empty spaceof the Circuit window. In this menu all circuit objects can be selected. After selecting an object inone of the fields or pop-up menus, the object is drawn in the circuit window in marked andmoveable mode.

Introductory Manual


Circuit comments:A comment line below the circuit window shows a user defined circuit comment text.

MAP window:This window gives a bird's eye view of the entire circuit. The size of a circuit is 5000x5000 pixels(screen points); much larger than your screen would normally support. Consequently, the Circuitwindow displays only a small portion of the circuit. The actual circuit window is represented by arectangle in the Map window.

Press and hold down the left mouse button in the map rectangle to move around in the map. Whenyou release the mouse button, the circuit window displays the part of the circuit defined by thenew rectangle size and position. The map window is a stay-on-top window, meaning that it willalways be displayed on the top of other windows. You can show or hide the map selecting theMap Window option in the Window menu, or pressing the M character,

Status bar - Action mode field:The current action mode of the active circuit window is displayed in the status bar at the bottom ofthe main window, when the Status Bar option is activated in the View menu. ATPDraw can be invarious action modes. The normal mode of operation is MODE : EDIT , in which new objects areselected and data are given to objects. Drawing connections brings ATPDraw into CONN.ENDmode and so on. ATPDraw’s possible action modes are:

EDIT The normal mode.CONN.END After a click on a node, the action mode turns into CONN.END indicating that

the program is waiting for a left mouse click to set the end-point of a newconnection. To cancel drawing a connection, click the right mouse button orpress the ESC key to return to MODE : EDIT.

MOVE LABEL Indicates a text label move. Clicking the left mouse button on a text label, thenholding it down and dragging it enables you to move the label to a newposition. If the text label is overlapped by a component icon, the text label canbe moved using Move Label in the Edit menu. Then the action mode turns intoMOVE LABEL. Releasing the mouse at the new text label location, the actionmode returns to MODE : EDIT.

GROUP Indicates region selection. Double clicking the left mouse button in an emptyspace of the active circuit window enables you to draw a polygon shapedregion. To end the selection, click the right mouse button. Any objects withinthe selected region are marked then for selection. To cancel region selection,press the Esc key.

INFO.START Indicates the start of a relation when TACS | Draw relation is activated in theselection menu. Clicking the left mouse button on a component node or on theend-point of another relation will initiate the drawing of a new relation.Relations are used to visualize information flow into FORTRAN statementsand are drawn as blue connections, but do not influence the connections ofcomponents. To cancel, click the right mouse button or press the Esc key.

INFO.END Indicates the end of a relation. The program is waiting for a left mouse buttonclick to set the end-point of the new relation. To cancel drawing relation, clickthe right mouse button or press the Esc key.

Introductory Manual


Status bar - Modified and Hints field:The middle field of the status bar is used to display the Modified state of the active circuit. Assoon as you alter the circuit (moving a label, deleting a connection, inserting a new component,etc.), the text 'Modified' appears, indicating that the circuit must be saved before exit. The fieldwill be empty when you save the circuit or undo all modifications. The rightmost field of thestatus bar displays the menu option hints.

The Component dialog box

After selecting a component in the Component selection menu the new circuit object appears inthe middle of the circuit window enclosed by a rectangle. Click on it with the left mouse button tomove, or the right button to rotate, finally click in the open space to unselect and place the object.The object input window appears when you click the right mouse button (or double click with theleft button) on a circuit object. Assuming you have clicked on the icon of an RLC element, adialog box shown in Fig. 3.2 appears.

Fig. 3.2 - The Component dialog box.

The Component dialog box has the same layout for all circuit objects. In this window the usermust specify the required component data. The number of DATA and NODES menu fields are theonly difference between input windows for standard objects. The nonlinear branch componentshave a Characteristic page too, in addition to the normal Attributes page, where the nonlinearcharacteristics and some include file options can be specified.

Carriage return, Tab or the mouse can be used to move the cursor between input fields. The arrowkeys can be used to move the cursor inside of a menu field. When the cursor is moved out to theright side of the field the menu content is scrolled.

Introductory Manual


Numerical values in the data input windows can be specified as real or integer, with an optionalexponential integer, identified by ‘E’ or ‘e’. An “Illegal numeric specification” message isproduced, when the characters are non-numeric. Legal formats are: 3.23e4, 323E+02, 32300,32.3e+3 etc.

Input texts in the node input menus can be specified with any characters (remember that characterslike * - + / $ etc. should not be used in ATP node names, also avoid space and lower case letters).The user does not need to give names to nodes, in general. The name of the nodes without specialinterest are recommended to be left unspecified. ATPDraw will then give a unique name to thosenodes. The node dot of these nodes are displayed in red color in the circuit window.

Below the data input column there is a Group No input field. This is an integer field where anoptional group number can be specified to the object, which could be used as a sorting criteria (thelowest group number will be written first into the ATP file).

Below the node input column there is a Label input text field. The content of this field is writtenon the screen and also into the circuit file. The label text is movable. The component dialog boxhas a Comment input text field. If you specify a text in this field, it will be written to the ATP fileas a comment (i.e. as the first line of the object’s data).

The radio buttons of the Output group specify the branch output requests. If the Hide box isselected, the object becomes hidden (which means that it is not written to the ATP file) and itsicon becomes light gray in the circuit window. The Lock option is not yet implemented in thepresent version of the program.

The OK button will close the dialog box and the object’s data and its properties are updated in thedata structure. The red drawing color which indicates that no data is given to the object will beturned off. When you click on the Cancel button, the window will be closed without updating theobject’s data. The Help button invokes the Help Viewer showing the help text of the object. Forobtaining further help press the F1 key.

4 Operating the mouse

This chapter contains a summary of the various actions taken dependent on mouse operations. Theleft mouse button is generally used for selecting objects or connecting nodes; the right mousebutton is used for specification of object or node properties.

Left simple click: On object:

Selects object (also connection).If the Shift key is pressed, the object is added to the current group.

On object node:Begins to draw a connection.Moves the mouse to the end node, left click to place, right to cancel.

In the open area of the circuit window:Unselects object.

Right simple click:On object node:

Introductory Manual


Opens the node dialog box.On unselected object:

Opens the component dialog box.On unselected object, when you hold down the Shift key:

Opens the circuit window shortcut menu.On selected object(s):

Rotates object(s).In the open area of the circuit window:

Cancels connection made.Left click and hold:

On object:Moves object(s).

On node:Resizes connection (it is often necessary to select connection first).

In the open area of the circuit window:Draws a rectangle for group selection.Objects inside the rectangle become a group when the mouse button is released.

Left double click:On object node:

Performs the Node dialog box.On unselected object:

Performs the Component dialog box.On selected object:

Performs a Group Number specification window.In the open area of the circuit window:

Starts the group selection facility. Click left to create corners in an enclosing polygon,click right to close. Objects inside the polygon become a group.

5 Edit operations

ATPDraw offers the most common edit operations like copy, paste, duplicate, rotate and delete.The edit options operate on a single object or on a group of objects. Objects must be selectedbefore any edit operations can be performed. Selected objects can also be exported to a disk fileand any circuit files can be imported into another circuit.

Tool Shortcut key Equivalent in menusCopy Ctrl+C Edit | CopyPaste Ctrl+V Edit | PasteDuplicate Ctrl+D Edit | DuplicateRotate Ctrl+R Edit | Rotate (or right click)Flip Ctrl+F Edit | FlipGroup Ctrl+G Edit | Select group (or left double click in open space)All Ctrl+A Edit | Select AllLabel Ctrl+L Edit | Move LabelUNDO Alt + BkSp Edit | UndoREDO Shft+Alt+BkSp Edit | RedoZoom In/Out + / - View | Zoom In / OutZoom window Z View | Zoom

Introductory Manual


The ground symbol is drawn at the selected node when you exit the window as Fig. 3.3 shows.

The nodes not given a name by the user will automatically be given a name by ATPDraw, startingwith XX followed by a four digit number. Nodes got the name this way (i.e. from the program) aredistinguished by red color from the user specified node names.

Fig. 3.3 - Click on the voltage source node with the right mouse button and specify the source node name.

6 Storing the circuit file

You can store the circuit in a disk file whenever you like during the building process. This is donein the main menu with File | Save (or Ctrl+S). If the current circuit is a new one which has notbeen previously saved, a Save As dialog box appears where you can specify the circuit name. Twodifferent styles of the Save As dialog boxes are available, depending on the Open/Save dialogsetting in the Tools | Options | General menu: a Windows 95 standard dialog box and a Windows3.1 style. The default extension is .CIR in both cases and it is automatically added to the file nameyou have specified.

When the circuit once was saved, the name of the disk file appears in the header field of the circuitwindow. Then if you hit Ctrl+S or press the Save circuit icon in the Toolbar, the circuit file isupdated immediately on the disk. The File + Save As option or the Save As icon from the Toolbarallows the user to save the circuit currently in use under a name other than that already allocated tothis circuit.

7 Creating ATP file

The ATP file is the file required by ATP to simulate a circuit. The ATP file is created by selectingMake File command in the ATP main menu.

Before you create the ATP file, you must specify some miscellaneous parameters (i.e. parameters,that are printed to Misc. Data card(s) of the ATP input file). The default values of theseparameters are given in the ATPDraw.ini file. Changing these default values can either be donein the Settings | Simulation sub-menu under the ATP main menu for the current circuit, or underthe Tools | Options | View/ATP | Edit settings for all new circuits created henceforth.

Fig. 3.4 shows an example of the ATP’s 1st miscellaneous data card settings (specifying timestep, time scale of the simulation etc.). This window appears if you select the Simulation tab of the ATP | Settings menu.

Introductory Manual


Select:� Time step �T in sec.� End time of simulation Tmax in sec.� Xopt=0: Inductance in mH.� Copt=0: Capacitance in �F.

Press Help to get more information or OKto close the dialog box.

The simulation settings are stored in thecircuit file, so you should save the file afterchanging these settings.

Fig. 3.4 Simulation settings.

The first integer miscellaneous data card is changed under the ATP | Settings | Integer page, andthe statistic/systematic switch control card is specified under the ATP | Settings | Switch settings.

Under the File format page the user canselect precision mode and the ATP-filesorting criteria. The main characteristic ofthe simulation (time domain or frequencyscan) can also be set on this page. If youselect the File format page, the windowshown in Fig. 3.5 appears:

Select:

� Sorting by cards: First /BRANCH, then/SWITCH and then /SOURCE.

All other check boxes are unselected

Fig. 3.5 - The file format menu.

To create an ATP file you must select the Make File in the ATP menu. This selection will start aprocedure which examines your circuit and gives node names to circuit nodes. Then a standardWindows’ Save As file window appears, where you can specify the name and path of the ATP file.The same name as the circuit file with extension .ATP is suggested.

You can load an old circuit whenever you like (select File | Open) and create the correspondingATP file (select ATP | Make File).

��

Prof. Dr. Kizilcay 17

Solution Methods in ATP

The time-domain and frequency-domain solution methods in ATP will be reviewed briefly.

Detailed analysis of numerical modeling of system components and electrical networks are given

in the EMTP Theory Book (TB). The review focuses rather to the applicational features and

limitations of the solution methods.

� Time-domain solution methods

The electric network is described in ATP-EMTP using node equations, i.e. node voltages are

selected as state variables. Branch currents are expressed therefore as functions of the node

voltages.

The solution for each element in time-domain is performed using time step discretization. The

value of all system variables are supposed to be known at t – �t and their value is to be

determined at time t. The time step �t is assumed to be so small that the differential equations are

approximated by difference equations.

For example, a simple algebraic relationship is obtained by replacing the differential equation for

a inductance

(1)v � L didt

with a central difference equation that is equivalent to the numerical integration of i using

trapezoidal rule for one time step.

(2)v(t) � v(t��t)

2� L i(t) � i(t��t)

�t

(3)i(t) � G�v(t) � Ihist(t–�t)

with . G is the equivalent conductance that remains constant, when the time step �t ofG �

�t2L

the computation is constant. Ihist(t – �t) is the history term composed of know quantities from the

��

1Brackets are used to indicate matrix and vector quantities.

Prof. Dr. Kizilcay 18

preceding time step having the unit of Ampere. A similar formulation can be written for capacitor

and resistors. For multi-phase coupled elements this basic formulation still holds. The equations

of multi-phase coupled elements are incorporated into the nodal admittance matrix of the

electrical network.

For any type of network with n nodes, a system of n such equations can be formed1,

(4)[G] [v(t)] � [i(t)] � [Ihist]

with [G] : n x n symmetric nodal conductance matrix,

[v(t)] : vector of n node voltages,

[i(t)] : vector of n current sources, and

[I hist] : vector of n known "history" terms.

Normally, some nodes have known voltages either because voltage sources are connected to

them, or because the node is grounded. In this case Eq. (4) is partitioned into a set A of nodes

with unknown voltages, and a set B of nodes with known voltages. The unknown voltages are

then found by solving

(5)[GAA] [vA(t)] � [iA(t)] � [IhistA] � [GAB] [vB(t)]

for [vA(t)].

The actual computation in the EMTP proceeds as follows: Matrices [GAA] and [GAB] are

built, and [GAA] is triangularized with ordered elimination and exploitation of sparsity. In each

time step, the vector on the right-hand side of Eq. (5) is updated from known history terms, and

known current and voltage sources. Then the system of linear equations is solved for [vA(t)],

using the information contained in the triangularized conductance matrix. In this "repeat

solution" process, the symmetry of the matrix is exploited in the sense that the same

triangularized matrix used for downward operations is also used in the backsubstitution. Before

proceeding to the next time step, the history terms included in [IhistA] are then updated for use in

future time steps.

The transient simulation can be started from

1) zero initial conditions

2) a.c. steady-state initial conditions at a given frequency.

��

19

� Frequency-domain Solution Methods

Frequency-domain solution methods implemented in ATP are based on the a.c. steady-state

solution of the linear network. Nodal equations are written using complex phasor quantities for

currents and node voltages. For any type of network with n nodes, a system of n such equations

can be formed,

(10)[Y] [V] � [I]

with [Y] : symmetric nodal admittance matrix, with complex elements,

[V] : vector of n node voltages (complex phasor values),

[I] : vector of n current sources (complex phasor values).

Eq. (10) is partitioned into a set A of nodes with unknown voltages, and a set B of nodes with

known voltages. The unknown voltages are then found by solving the system of linear, algebraic

equations

(11)[YAA] [VA] � [IA] � [YAB] [VB]

Bringing the term [YAB][V B] from the left-hand side in Eq. (10) to the right-hand side in Eq. (11)

is the generalization of converting Thevenin equivalent circuits (voltage vector [VB] behind

admittance matrix [YAB]) into Norton equivalent circuits (current vector [YAB][V B] in parallel

with admittance matrix [YAB]).

�� FREQUENCY SCAN Feature

The FREQUENCY SCAN (FS) feature of the ATP allows for the repetition of steady-state phasor

solutions, as the frequency of sinusoidal sources is automatically incremented between a

beginning and an ending frequency. Rather than conventional time-response output, a frequency-

response output of desired quantities like node voltage, branch current or driving-point

impedance/admittance is obtained. When plotted, the time axis of conventional ATP simulations

becomes the frequency axis, with the result being a frequency curve. Either polar coordinates

(magnitude and angle) or rectangular coordinates (real and imaginary parts) of the phasor

solution variables are used for output purposes.

Typical applications of the FREQUENCY SCAN are:

� Analysis and identification of resonant frequencies of power networks and individual system

components;

��

� Computation of frequency response of driving-point network impedances or admittances seen

from a busbar, for example, positive-sequence or zero-sequence impedance;

� Analysis of harmonics propagation in a power system using extended feature Harmonic

Frequency Scan (This subject will be handled in detail separately).

�� HARMONIC FREQUENCY SCAN (HFS) Feature

HFS is a companion to Frequency Scan (FS). Both FS and HFS performs a series of phasor

solutions. FS solves the network for the specified sources, incrementing in each subsequent step

the frequency of the sources, but not their amplitudes or phase angles. HFS on the other hand,

performs harmonic analysis by executing a string of phasor solutions determined by a list of type-

14 sources entered by the user. This procedure is the same as the procedure for harmonic analysis

used by all commercial harmonic analysis software. The main advantage of this approach

compared with the time domain harmonic analysis is a reduction in runtime of ten times or more,

and avoidance of accuracy problems with Fourier analysis.

Models developed for HFS analysis using ATP are:

� Frequency-dependent R-L-C elements

� Frequency-dependent load based on the CIGRE type C model [4]

� Harmonic current/voltage sources with frequency-dependent amplitude and phase.

�� Load Flow Option (FIX SOURCE)

This option adjusts the magnitudes and angles of sinusoidal sources iteratively in a sequence of

steady-state solution, until specified active and reactive power, or specified active power and

voltage magnitude, or some other specified criteria, are achieved. This will create the initial

conditions for the subsequent transient simulation.

EMTP Applications, Laboratory III, April – May,2001 Line/Cable models

21

Line Cable models in EMTP The separate Line/Cable Constant supporting program ATP_LCC was on the prototype level and contained some bugs and inconsistencies. The latest development resulted significant change in the LINE/CABLE CONSTANTS support. The process of creating a line/cable models in ATPDraw via the program ATP_LCC, needed several steps. This complicated the usage and resulted in some extra work when modifying the model. To use the built-in line/cable module of ATPDraw the user must first select a line/cable component with the desired number of phases (1..9) under Line/Cable item in the selection menu. This will display a component in the circuit window which is connected to the circuit as any other component. Clicking on this component will bring up a special input dialog box called the Line/cable dialog as shown in Fig. 1. When the required data are specified the user can close the dialog by clicking on OK. This will store the specified data to disk and run ATP to produce the required punch and lib files.

Fig. 1 - Line/Cable dialog window

In the Line/cable dialog the user can select System type: Overhead line: LINE CONSTANTS Single core cables: CABLE PARAMETERS Enclosing pipe: CABLE PARAMETERS Model: Bergeron: Constant parameter KCLee or Clark models PI: Nominal PI-equivalent (short lines) JMarti: Frequency dependent model with constant transformation matrix Noda: Frequency dependent model Semlyen: Frequency dependent simple fitted model

EMTP Applications, Laboratory III, April – May, 2001 Typical EMTP studies

22

Typical EMTP studies The ATP version of the Electromagnetic Transients Program (EMTP) is an effective and widely-used tool for simulating high-speed transients in electric power systems. ATP modelling capabilities cover electromagnetic and electromechanical oscillations spanning the frequency range from mHz to MHz. The EMTP is used worldwide for switching and lightning surge analysis, insulation coordination, shaft torsional oscillations, protective relay modelling, harmonics and power quality studies, HVDC and FACTS models. Because of its widespread acceptance and use, it can be considered to be a standard analysis tool. ATP has extensive modelling capabilities and additional important features besides the computation of transients. It is out of scope of this report to give a complete collection of engineering problems where ATP could be applied. Without completeness, some typical application fields are listed below, and some examples are given. Typical EMTP studies are: - Lightning studies - Switching transients and faults - Statistical and systematic studies - Very fast transients in GIS and groundings - Machine modelling - Transient stability studies, motor startup - Shaft torsional oscillations - Transformer and shunt reactor/capacitor switching - Ferroresonance - Power electronics applications - Circuit breakers and arc, current chopping - FACTS devices - Harmonic analysis - Frequency scans of network impedances - Protective device testing The following examples show how to use ATP for real engineering problems in the field of line energization and fault studies, lightning studies or for transformer inrush transients simulations.

1 Single-line to ground fault on a 750 kV line (Lab01.adp) A single-line to ground fault on a 750 kV interconnection are investigated in this study. In this example the usage of the Line/Cable objects in combination with transposition objects are demonstrated. The one-line diagram of the simulated network and the equivalent ATPDraw circuit is shown in Fig. 1.1 Three transposition points exist along the route, the Overhead Line objects represent line sections between transpositions.


23

750 kV tr. line

6000 MVA

6000 MVA

Single phaseto ground fault

478 km 7503

∆

∆

750 kV400 kV

1100 MVA

1100 MVA

400 kV 10000 MVA

a) one-line diagram of the simulated network

b) ATPDraw circuit

Fig.1.1 - Single phase-to-ground fault study (Lab01.adp)

The Line/Cable Constant support is integrated part of ATPDraw program, so calculating the electrical parameters of the line (and running a JMarti Setup run in the background) are all automated. The line configuration is shown in Fig. 1.2.

Fig. 1.2 - Tower configuration of the 750 kV line The supply side networks connected to the 750 kV transmission line at the sending end and at the receiving end are rather simple. Only the positive sequence short circuit impedance has been taken into account by 3-phase RLC objects, connected parallel with a resistor representing the equivalent surge impedance seen from the terminals. An uncoupled series

At tower = 41.05 m Midspan = 26.15 m

Separ=60 cm Alpha=45 ° NB=4

13.2 m

17.5 m At tower = 27.9 m Midspan = 13.0 m


24

reactance represents the short circuit inductance of the transformer bank consisting of three single-phase units. The shunt reactors, -which are also single-phase devices- have been represented by linear RLC components, because the amplitude of the reactor voltages are below the saturation level of the air gapped core. The arc resistance of the fault is assumed to be constant, and was approximation by a 2 ohms resistance. Results of the simulation are shown in Fig 1.3.

(file Cours99c.pl4; x-var t) v:SENDA v:SENDB v:SENDC 0.0 0.1 0.2 0.3 0.4 0.5

-2.500

-1.875

-1.250

-0.625

0.000

0.625

1.250

1.875

2.500*106

(file Cours99c.pl4; x-var t) c:SENDA -LN1A c:SENDB -LN1B c:SENDC -LN1C 0.0 0.1 0.2 0.3 0.4 0.5

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

Fig. 1.3 - Calculated sending end voltages (above) and line currents (below) when single phase-to-ground fault appers at the receiving end terminal

2 Lightning overvoltage study (Lab02.adp) This example demonstrates how to use ATPDraw effectively in a substation lightning protection study. Fig. 2.1 shows the one-line diagram of the cable connected 120 kV substation.. The simulated incident is a single phase backflashover on the line arising 0.25 km from the cable terminal. The simplified, single phase simulation model is shown on Fig 2.2.


25

SOROKSÁR

4.2km

Megszakító

Zno korlátozó

CSEPEL II

70m50m

Kábel

Szabadvezeték

8.5km

4.4km

HFKV

8.5km

FOJTÓ

Fig 2.1 Network connection of Csepel II Power Plant

4.2km 50m

KABL CSEP FOJ TRAF

25.5mH

HFKV2.86mH

188uF

a) simplified single phase diagram

KABL CSEP HFKV TRAFVCSP FOJ

b) ATPDraw simulation model (Lab02.adp)

Fig. 2.2

Fig. 2.3 shows the protection characteristics of metal-oxide arresters.


26

0

50000

100000

150000

200000

250000

300000

350000

400000

1E-3 10E-3 100E-3 1E+0 10E+0 100E+0 1E+3 10E+3 100E+3I [A]

U [V]SB 102/10.2Exlim R108HSR 108Pexlim 108

Fig. 2.3 – U-I characteristics of some 120 kV ZnO arresters

Fig 2.4 shows a typical simulation result obtained with the following assumptions:

- the lightning hits the line 258 m before the cable junction - zno arrester at both terminals

(fi le sorcsep.pl4; x-var t) v:KABL v :CSEP v :FOJ v :TRAF 0.00 0.05 0.10 0.15 0.20 0.25 0.30

*10 -3-200

-100

0

100

200

300

400

500

600

Fig. 2.4: Voltage stresses at the cable terminals and at the step-up transformer

3 Modelling transformers with hysteresis (Lab03.adp) When energising transformers, very often a transient magnetising inrush current occurs. This is caused by the fact, that the flux in the iron core can not be changed abruptly. The phenomena is easier to understand in a single phase transformer. At the zero crossing of the power frequency voltage the magnetising current and the flux have their maximal values, and delay with 90 electrical degrees. To satisfy the principle of the flux steadiness, it is necessary to build an equalising flux with the same magnitude, but opposite polarity, in order to start the flux from the remanent flux, as a starting point. The resultant flux reaches its highest value after a half period, which can be significantly higher then the saturation point of the iron core. This excess of flux is diverted to the coil system around the iron core (as it is written in the technical literature into the „air”, which is not fully exact), where it can be kept only with high current value. The transient current, which is generated in this way, is damped very slowly, and its


27

highest value can be close to the short-circuit current of the transformer, causing dangerous dynamic and thermal stresses. 3.1 Physical explanation of the inrush current When the transformer is energized at the zero crossing of the voltage, with no remanent flux present, the equalising flux has the same magnitude but opposite polarity as compared to the highest operational flux. The resultant flux reaches the double of the normal operational flux (nominal flux), which saturates the iron core. To keep the flux in the air, the inrush current reaches the range of the rated current of the transformer. If the transformer is energised at the peak value of the voltage with remanent flux equal zero, the transient current does not exceed the steady state magnetising current of the transformer. The phenomena in three-phase transformers are more complicated because of the galvanic and magnetic connection between the phases. The amplitude of inrush current is depend on many factors including the type of the iron core, the connection of the individual phases and the way of neutral grounding. When the switching operation starts with the central phase B at the voltage maximum of this phase, the circuit is closed through the earth and the magnetic flux is formed without transients. The magnetising current of the energised phase excites the open phases A and C to the 50% of the steady state value. The flux of phases A and C reaches the values according to the steady state momentary value after 5 ms, so at this moment both phases could be switched on without high inrush current. 3.2 Calculation of the inrush current using hand-book formulas The peak value of the inrush current is determined by the type of the iron core, the magnetic parameters of the iron material and the construction of the coil system. High peak value resultsin if the flux produced by the excitation voltage is added to the remanent flux with the same polarity. The maximal inrush current can be calculated with the following formula:

( )iAA

lN

B B Bmv

ln r t= ⋅ ⋅ ⋅ ⋅ + −

12

0µ,

where ( )µ π0

7 14 10= ⋅ ⋅ − −Vs Am , the permeability of the air (oil) Br the remanent induction, Bn the peak value of the rated induction in the iron core

Av the cross section of the iron core Al cross-section of the air , Bt saturation induction,

N is the number of turns in the energised coil, l is the length of the magnetic flux curve in the air

The less favourable case of transformer energising is, if the switching on happens at the

zero crossing of the network voltage and at the remanent flux has its maximal value with the polarity equivalent with the sign of the derivative of the voltage time function.


28

The calculation method presented before includes some simplifications:

a) it supposes that the feeding network is infinite. In the reality the voltage at the transformer is not independent on the magnitude of the current flowing into the transformer. In real cases the supply voltage decreases considerably at the transformer terminal point, if the current increases to the value higher than the rated current because of the saturation, which acts against the further increase of the current.

b) the simplified method of calculation neglects the losses, however its effect to the first, highest peak current is really not considerable.

c) the calculation neglects the multiphase properties of the transformer.

3.3 Modelling the iron core The magnetizing branch of the transformer can be represented by a hysteretic nonlinear inductor. ATP-EMTP supports only one type of magnetic material, but it could be used as first approximation for other oriented silicon steel materials. Fig 3.1 shows the hysteresis loop of the magnetic core of the transformer investigated in this study.

-1.5

-1

-0.5

0

0.5

1

1.5

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

I [%]

PSI [p.u.]

Hyst+Hyst-Armco

Fig. 3.1 - The shape of the hysteresis loop of the transformer

Beside the 132/15 kV Wye/delta connected unit transformer, this model takes into account the the capacitance of the 500 m overhead line connected directly to the 120 kV side of the transformer. The ATPDraw model is drawn in Fig. 3.2.

Fig. 3.2 - ATPDraw circuit of the 120 kV study case (Lab03.adp)


29

The transformer model is a three phase Ynd11 type coil configuration with non-linear inductance containing hysteresis as well, according to the real transformers. The hysteresis loop of the 155 MVA transformer has been simulated with Type-96 hysteretic inductances.

( f i l e C o u r s 9 9 j .p l 4 ; x-va r t ) c : S U P L A - T R 1 3 2 A c : S U P L B - T R 1 3 2 B c : S U P L C - T R 1 3 2 C

0 1 0 2 0 3 0 4 0 5 0[m s ]- 1 .0

- 0 .5

0 .0

0 .5

1 .0[ A ]

Fig. 3.3 - Calculated steady magnetizing current

( f i l e C o u rs 9 9 j .p l 4 ; x-va r t ) v :TR 1 3 2 A v :TR 1 3 2 B v :TR 1 3 2 C

0 .0 8 0 .0 9 0 .1 0 0 .1 1 0 .1 2[s ]-1 2 0

-8 0

-4 0

0

4 0

8 0

1 2 0[ k V ]

Fig. 3.4 – Transformer phase voltages at a subsequent energization

close to the zero crossing of phase A

( f i le C o u rs 9 9 j.p l4 ; x-va r t ) c :S U P L A - T R 1 3 2 A c :S U P L B - T R 1 3 2 B c :S U P L C - T R 1 3 2 C

0 .0 8 0 .0 9 0 .1 0 0 .1 1 0 .1 2 0 .1 3 0 .1 4 0 .1 5[s ]- 4 0 0 0

- 2 0 0 0

0

2 0 0 0

4 0 0 0[A ]

Fig. 3.5 - Calculated inrush current


30

Mérési feladatok

Otthoni, elõkészítõ feladatok:

1. Készítse el a Lab02.adp hálózat ( 2.2/a ábra) koncentrált R-L-C elemekbõl összeállítható helyettesítõ áramkörét. A távvezeték és a kábel hullámimpedanciája 400, ill. 40 ohm.

2. Számítsa ki a 3.2 ábrán felrajzolt 120/15 kV-os transzformátor (Lab03.adp hálózat) bekapcsolási áramlökésének maximális értékét. A transzformátor adatai az alábbiak:

Rated voltage: 132 ± 5% / 15 kV Rated current: 678 / 5966 A Rated power: 155 MVA Connection: Ynd11 Short circuit reactance: 14 % Magnetising current: 0.3 / 2.67 A Cross section of the iron core: Av = 0.535 m2

Cross section of the air channel between the iron core and high voltage core Al = 1.21 m2

Number of the energised turns in case of tap changer position -5%: N = 375 Rated induction: Bn = 1.62 T Remanent induction: Br = 1.52 T (75% of the saturation induction) Saturation induction: Bt = 2.03 T Length of the flux line in the air: l = 2 m

Mérési feladatok:

1. mérõcsoport : A + B feladatsor 2. mérõcsoport: A + C feladatsor

A mérés végén a mérõcsoportok az önállóan elvégzett B és C mérés eredményeirõl 10 perces elõadás keretében számolnak be a másik csoport tagjainak és a mérésvezetõnek.

A.1. A Lab01.adp fájl felhasználásával határozza meg a terheletlen 750 kV-os vezeték végpontján fellépõ feszültségemelkedés mértékét állandósul állapotban 0, 2 ill. 3 söntfojtókészlet bekapcsolt állapotát feltételezve.

A.2. A Lab01.adp hálózaton határozza meg a nyitott vezetékvégen kialakuló bekapcsolási túlfeszültséget a fázisfeszültség-maximum pillanatban történõ bekapcsolás esetén.

B.1. A Lab02.adp fájl felhasználásával határozza meg a hálózaton beépítendõ korlátozókészletek számát és optimális elhelyezését úgy, hogy a feszültség a hálózat egyetlen pontján se haladja meg a 120 kV-os berendezések próbafeszültsége (550 kV) 80%-át.

B.2. Ellenõrizze az otthoni felkészülés során kiszámított helyettesítõ áramkör jóságát. Vesse egybe a túlfeszültségvédelem nélküli Lab02.adp hálózat és a helyettesítõ áramkör azonos pontjain mért feszültséglengés amplitudóját és frekvenciáját.

C.1. A Lab03.adp hálózat felhasználásával határozza meg a transzformátor-fázisok remananes fluxusát a kikapcsolás idõpillanatának függvényében. A megszakítópólusok kikapcsolási sorrendje CB - A, (0+x)(0+x) - (5+x) ms.

C.2. Határozza meg a legkisebb és a legnagyobb áramlökést eredményezõ bekapcsolási pillanatot, a fenti A-CB (0-5-5 ms) bekapcsolási sorrendû megszakí tó alkalmazása esetén a remanens fluxus elhanyagolásával, illetve figyelembe vételével.

hálózati tranzienseinek számítógépi...

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