BONDIN: A new engineering simulation software for ODE
Contents
1. 96 As we have commented throughout the systems generated can be of type ODE or DAE While the former can be solved with a large quantity of algorithms the latter requires specific numerical methods to solve it for which reason Dassl 16 has been chosen for its robustness and rapid convergence 11 Conclusion The problems involved in any model made by a Bond Graph are directly related to causality and are greater the more complex the calculation Many of the options put forward in other works attempt to simplify the calculation of causality and oblige the user to carry out changes or simplifications to the original model This means that since it is the modeller that makes the decisions in many cases the results vary or the simulation is simply not carried out to completion On the other hand the difficulty of numerically solving a system of equations depends on the type of system ODE or DAE and on the number of equations that is to say the number of variables and on the integration pass that is conditioned by the appearance of certain elements Finally every calculation that is made symbolically instead of numerically allows a clearer interpretation to be made together with a global view of each and every parameter in the model ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS However it is essential to have appropriate software for solvi2. 15 Romero G F lez J Mera J M Maroto J Efficient simulation of mechanism kinematics using bond graphs Simulation Modelling Practice and Theory Vol 17 Issue 1 pags 293 308 2009 16 Petzold L Differential algebraic equations are not ODE s SIAM J Sci Stat Comput Vol 3 No 3 pp 367 384 1982 ISBN 978 960 474 052 9
3. cylinder 7 K Connecting point to the chassis i Sf Sf fixed Ax 0 3 Sf Sf fixed Ay 0 gt x Connecting point tothechassis tect ge eg Sf Sf fixed Cx 0 i Sf Sf_fixed Cy 0 Connecting point to the chassis Actuator 1 o Sf sf_actl eee I L Unloading arm C K extreme x 0 f Q Element 6 Pa CK a Bucket Extreme point of the bucket Support arm cylinder 8 Figure 7 Front loader mechanism by using subsets in Bondin As can be seen the speed with which a complex model can be prepared from previously saved and configured models makes this a very useful tool for generating large models On the other hand if it is compared with its original model its simplicity makes it much easier to understand Finally given the importance of the issue particular emphasis has been placed on the fact that a subset can be inserted into another as many times as required with no limits of levels 10 Obtaining the results When a simulation has been successfully completed the results can be shown in graphic form using a dialogue box that allows choosing the variables to be displayed either individually or as a set and lets certain areas be zoomed in on 3 326 OOo 2552 000 7 7Ge OOo T OFet OGO 2 448 009 3 340 00T Q 0er O00 3 35er 000 7 35e 000 T y3et oe 7 53er OOF v 95e 007 Figure 8 Superimposed graphs obtained ISSN 1790 5117
4. L d E G P L IG df_ PUL Are 41 161 gent TPT pij a G J Ji G OT De i l i al Betri P L E1 16 7 D o a 5 J P M d F d G P M G d P M _____ _ _ _ PD es eM Go IOE a ee 2 eee Se ai 81 LC Tga PINT l Wal Whatatesd Be rimt ilal er EIG ERA 6 7 D J ee ea al in a form that is user readable fig 5 and they can ar ree a be numerically simulated PSE STE We aa i 7 m er When a pre calculation of the DAE and ODE J To obtain the equations defining a model totally automatically that are user transparent Maple must be used This should be installed in the computer to carry out symbolic operations such as matrix manipulation deriving and simplifying expressions NON REDUCED EQUATIONS DAE Algebraic differential equations d dt VI_1 1 m1 R VI_1 1 m1 K XK_1 1 m1 m2 g 1 m1 R Vo g 1 ml m2 d dt VI_2 d dt XK_1 VI_1 Vo VI_2 VI_1 REDUCED EQUATIONS ODE Differential equations d dt VI_1 1 m2 m1 R VI_1 1 m2 m1 K XK_1 1 m2 m1 m2 g 1 m2 m1 R Vo 1 m2 m1 m1 g d dt XK_1 1 VI_1 1 Vo Algebraic equations VI_2 VI_1 equations txt d dt VI_2 d dt VI_1 Figure 5 File with equations obtained from a model composed by two inertances wi
5. Ph D Tesis Universidad de Zaragoza Spain 1989 8 Rosenberg R C ENPORT 6 User s Manual Rosencode Associates Inc Lansing MI 1985 9 Romero G F lez J Vera C Optimised procedures for obtaining the symbolic equations of a dynamic system using the Bond Graph technique Simulation Series Vol 37 N 1 pags 51 a 58 2005 10 Romero G F lez J Martinez M L Maroto J Kinematic analysis of mechanism by using Bond graph language Proceedings of European Conference on Modelling and Simulation pags 155 a 165 2006 ISSN 1790 5117 97 11 Romero G F lez J Maroto J Martinez M L Simplified bond graph models for simulations of earth moving machines Simulation Series Vol 39 pags 139 a 147 2007 12 Romero G F lez J Maroto J Mera J M Simulation of an electrical substation using the Bond Graph technique Proceedings of 10th International Conference on Modelling and Simulation de IEEE pags 584 589 2008 13 Romero G F lez J Martinez M L del Vas J J Simulation of the hydraulic circuit of a wheel loader by using the Bond Graph technique lt Proceedings of European Conference on Modelling and Simulation Pags 313 a 321 2008 14 Romero G F lez J Maroto J Martinez M L Simulation of an Asynchronous Machine by using a Pseudo Bond Graph AIP Conference Proceedings Vol 1060 Issue 1 pags 137 146 2008
6. out from a study of the different simulation programs available this paper presents a simulation program based on the BG technique which represents a considerable advance towards improving current automatic modelling methods As will be seen in the following pages the technique contributes a causal assignation algorithm specifically designed to allow the modeller maximum freedom without their having to take any kind of decision that might affect the end calculation It also automatically provides the optimised reduced state equations required to symbolically analyse linear and non linear systems To do so it solves the problems arising when simulating models with differential causality without any need to modify the graph charts and reduces the model to the set of differential equations required to perform the simulation eliminating where possible the restriction equations thereby reducing the computation time used in the simulation Key words Bond Graph software differential equations algebraic equations causality symbolic 1 Introduction difficulty when it comes to solving them by means Efforts to automate the BG method in recent years of numerical integration a have focused on solving the problem of the Therefore an important objective that was dealt dependent co ordinates that frequently appear in with in the development of Bondin was to mechanical 2 electrical 3 and thermal 4 generate alternative procedures to existing ones
7. the most advanced applications usually generate instructions in a particular language so that once complied it can be run and simulated Some of the other computer applications can only be used with linear systems and constant parameters In other cases the user is required to make decisions that usually lead to unequal results Finally should there be any the equations obtained either symbolically or numerically are only for the user to understand the simulation model and not to be worked with in depth Therefore taking the existing software as a basis in 2002 work was begun on a tool that would be capable of correctly obtaining the causality of the models so that the modeller would have maximum freedom and the tool then automatically provide the optimised reduced state equations required to analyse linear and non linear systems symbolically and finally go on to simulate ODE and DAE systems Bondin has been used in numerous papers 10 15 and pieces of research work undertaken by the authors since then and it has now been decided to propagate it among the scientific community ISSN 1790 5117 91 3 Main characteristics This software incorporates algorithms for causal analysis and for reducing DAE systems of equations to ODE whenever possible that have been developed to that end Thus the main features are e Bond Graph model simulation and variable parameters that are user programmable either under pseudo programmi
8. 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS Classification BONDIN MCC_lathe bnd QD Electricity A Eq maneuvering File View Visualization q Elements Calculation Windows Help R Loads D Gd cola sr ise jo 4 DC motor ind tic e lev t Basic elements E ses N DC motor ser mm lt gt Parameters Associated file MCCs bnd Associated icon 6 84e 000 ngular speed rad s Time s d at VI3 1 J Re VI3 1 J C2 _VI2_ VIt AC motors DC motors DC motor dep lt i Differential Equations d dt V12 1 Lex Rex VI2 1 Lex Ue d di VI1 1 Li C2 _VI2_ VI3 1 Li Ri VI1 1 L1 U Figure 1 Schematic capabilities of Bondin In respect of the name of the elements as will be seen further on this will serve to refer to the variables associated with the different ports when the user needs to program and also to interpret the different equations and graphs produced Parameters of the element Parameters Name Value Expression mass1 gravity N m s 2 SE_weight_m1 Physic s domain Mechanics translational C Hydraulic C Acoustic Mechanics rotational C Electricity C Themal Figure 2 Parameters dialogue box In respect of the value associated with each element this may be a numerical symbolic or mixed expre
9. It initially attempts to assign causality using the first algorithm but if this cannot be done successfully it does so with the second one If this is the case a message appears to inform of this with the only purpose of stating which of the two algorithms has been satisfactorily used Karnopp and Rosemberg 1 introduced the sequential causality assignation procedure SCAP this being the conventional procedure to use This procedure consists of the following steps 1 Assign appropriate causality to one of the sources and extend across the other nodes Repeat until all the sources have been taken account of 2 Choose any I or K element and assign integral causality Extend it across the other nodes Repeat until all the I and K ports have been taken into account 3 a Examine the state of the BG If there is an incomplete causality with no conflicts continue in step 4 3 b Examine the state of the BG If there is an incomplete causality with conflicts stop and correct the model by the user 3 c Examine the state of the BG If there is a complete causality finalise 4 Choose a resistance port without assigned causality assign an arbitrary causality and extend it Repeat until all the resistances have been taken into account 5 Choose an intermediate bond without assigned causality assign an arbitrary causality and extend it Repeat until all the bonds have been completed In order to study a greater numb
10. Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS BONDIN A new engineering simulation software for ODE and DAE systems with symbolic notation based in the Bond Graph technique ROMERO G FELEZ J CABANELLAS J M MAROTO J Dep of Mechanical Engineering Engineering Graphics Group Escuela T cnica Superior de Ingenieros Industriales Universidad Polit cnica de Madrid C Jos Guti rrez Abascal N 2 28006 Madrid Spain Tel 34 91 336 31 15 FAX 34 915 618 618 e mail gregorio romero jesus felez josemaria cabanellas joaquin maroto upm es Abstract The concept of Bond Graph BG introduced by Paynter and perfected by Karnopp and Rosenberg 1 contributed a unified method to describe dynamic models of multidisciplinary systems since they can be modelled using elements possessing the properties of generation Se Sf storage I C dissipation R and transformation of energy TF GY These elements interrelate in a conservative energy field by means of bonds that indicate the energy transfer and bonds 0 1 which symbolise the system s dynamic behaviour The resulting structure offers a global view of the system and its physical structure Moreover after obtaining causality this technique also offers the computational structure and reveals any possible mathematical problems in simulating it The entire system remains open and accessible unlike the classical methods Starting
11. cate the speed or the independent variable associated with the inertance 7_n and _X _n_ to indicate its movement or the integral of the previous independent variable If dealing with Compliance type ports named C_n the variable to be taken into account is its movement X in translational mechanics its integral having no physical sense Therefore in this type of port the letter X should be placed before the name of the element in question C_n and the character _ placed before and after th X name_port_Compliance _ Thus we will get XC_n_ to indicate the movement made by the spring C_n or the independent variable associated with that element 8 Programming scripts and dlls Sometimes when it is wished to perform a simulation with greater realism and therefore greater complexity it is not sufficient to insert constant parameters or variables that are governed by a particular expression What must be done is to program a series of conditions that will make these variables vary in one way or another While on some occasions it is sufficient to write some simple conditions on others it is not and functions belonging to more complex external libraries need to be called on To this end two modules have been designed through which conditions can be inserted in one way or another Should it be wished to insert conditions directly each of them must begin with the reserved word if and imme
12. diately after in brackets the requirement wished to be met must be written Then in brace brackets the numerical value must be placed or the expression linked to the condition Finally in order to indicate that writing the condition has concluded a semi colon must be put in place Should there be several requirements in a single condition each of these must be in brackets and separated by the reserved word and Thus in order to program a variable damper so that depending on the difference of speed between its ends inertances Il and 2 the damper is softer or harder it would suffice to write it as shown in figure 6 ISSN 1790 5117 95 if abs _VI1_ _VI2_ gt 0 and abs _VI1_ _V1I2_ lt 5 if abs _VI1_ _VI2_ gt 5 and abs _VI1_ _VI2_ lt 10 1000 if abs _VI1_ _VI2_ gt 10 Figure 6 Pseudo code of a variable parameter Calling a function from an external dll type library will be done when the code is too complex to do it using simple conditions and must be compiled as a dynamic library DLL To make the call the reserved word DLL must first appear to indicate that an external library needs to be loaded and then the name of the dll dynamic library that it is wished to load and the name of the function to be called Finally the different variables must be indicated in the appropriate order whose nu
13. ed out on matrices the method is capable of obtaining a system of reduced equations all of which is done by using symbolic notation As can be seen from the paper mentioned above 9 any model can be condensed into a general one that contemplates ports with integral and differential causality and type R elements or ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS intermediate bonds where it has been necessary to assign arbitrary causality The way to proceed is exactly the same in the singular cases but obviously the complexity will be somewhat greater as there will now be three interrelated systems instead of two In these cases once the three systems of equations have been formed Se_Ri SeT dalp 1 Pm i t Se_i t Sf_Ri i eae fea EN uy FY sei TE Se_gr_i 3 Sf_gr_i To reduce the systems 1 to 3 which are composed by differential and algebraic equations we can reformulate the systems and a final system of differential equations can be obtained dy Se_Ri 7 PMC i nPop fio Sf_Ri Disc d do ae XK_i t SE Serd sc 1 gi TA bp oe aes ae T Sf_gr_i A Xk r PRAN pen St iC 4 Se_Ri Se_Ri eti Sf_Ri eae Pm_i t ee Se_i t mn Sf_Ri Se_gr_i Pan o se_gri 2 The equations 4 can be generated Sf gri Sf gri automatically simply by operating and deriving the different matrices as follows P
14. er of cases without having to change the BG model structure some modifications have been made to this procedure These are in point 3 b where the option of causal compatibility or conflicts has been considered Firstly if the conflict occurs in a node to which a type I or C port is attached the causality of these ports changes automatically They will initially have integral causality and then become differential When all the type I or C ports have been concluded if a conflict is produced in a node to which no type I or C element is attached the next step is to eliminate all information referring to causality in resistances and intermediate bonds Then after changing ISSN 1790 5117 93 automatically one of the integral causalities to differential causalities the study can be continued If another similar conflict is again found the same Operation is performed on successive integral causalities By this procedure there should only remain as many ports with integral causality as there are degrees of freedom If the algorithm is incapable of continuing and enters into a recurring loop the causality assignation starts again and checks that each time a causality is imposed if a conflict is created or not If the case is affirmative go back and clean everything that has happened since this latest imposition of causality and carry on with the following element or intermediate bond If the causal analysis has been successfully comp
15. he dependent and independent variables the number of algebraic and differential equations and detect any possible problems It is for this reason that the only option activated at the beginning is this one its eee Windows Help Causality Figure 3 Calculation menu Using the Causality option a causal analysis of the model is performed and the result is shown by means of the causality lines on the graphs and their being assigned one colour or another la2 Lex ol sS SE2 Uex 1 S SEi Ki integral fiow l_in R R2 Rex wd 11 Li l i3 Jshatt Shera OF I ee Oe SF1 U 1 6Y Gy7 C gt fiow l gt 1 R R3 Rshaft R R1 Ri RwRaRgeart 1 i lq4 Jgear1 SE SEp Kp fiow l_in SF SF ref flow I5 183 5 r TF TF 1 r RWRe Rgeara i1 la5 Jgear2 SE SE3 Mc Figure 4 Electrical operation of a lathe by using PI type regulators with solved causality in Bondin ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS The colour blue is assigned to the graphs where causality has been obtained from other pre calculated causalities or due to the imposition of integral or differential causalities on the different I or C ports fig 4 while pink is reserved for the graphs where causality needed to be imposed in order to obtain a correct analysis The program consists of two causal assignation algorithms
16. leted the Parameters option will be activated in the menu below the Causality menu from which strictly speaking the simulation will be performed after assigning numerical values or programming on the user inserted parameters To do this the program automatically analyses each and every one of the written expressions and deduces the names of the different parameters 6 Obtaining the equations Having calculated causality and inserted the different parameters requested the following two options of the submenu fig 3 become active and from here we proceed to calculate the differential and or algebraic differential equations of the model in a symbolic form depending on the independent variables and those inserted by the user According to the compelexity of the model reducing the system of equations can involve a large amount of computation time At ICBGM 05 New Orleans USA 9 two of the authors presented a procedure for obtaining the minimum number of equations necessary and for reducing a system of algebraic differential equations to a purely differential one within a simulation model carried out with a bond graph and based only on causal assignation The method employs a series of basic rules for assigning causality correctly in order to avoid any type of incompatibility Subsequently depending on the different types of causal paths and algebraic loops coexisting through a succession of algebraic operations carri
17. merical values are required to be passed to the function in question it not being necessary to do it with the time variable t since this is an internal variable The different names and variables mentioned above must be separated by the reserved character DLLSlibrary SfunctionSparameterl1 S parameterNs Therefore if it is wished to define the value of the damper in the previous example by calling the hardness function corresponding to the library characteristics dll by passing on to it as parameters the speed of the inertances situated at the ends Il and I2 VII and _V 2_ it will need to be written in the following form DLL characteristics hardness _VI1_ _VI2_ 9 Creating and handling subsets When it is required to repeatedly create models containing several similar structures as for example a hydraulic circuit 13 or a mechanism comprising several bars 15 this task can be simplified by saving these structures individually and then inserting them where they are needed as if they were new elements To create a subset all that needs to be done Is to design the model in question and leave a series of incomplete nodes through which the remaining elements of the end model will be connected at a future time ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS Strut J I g A Actuator 2 Unloading
18. ng or by calling on external dynamic libraries without the need to do any compilation whatsoever The different elements are parametrically and symbolically defined Subset libraries are east to create A model can be given unlimited hierarchical structuring using subsets Automatic generation of causality The equations resulting from the model can be obtained symbolically and legibly Obtaining the minimum set of equations by reducing the number of constraint equations and using symbolic operations automatically e Numerical resolution of the model and graphic output Throughout the following sections a brief description will be made of the visible part and of the different algorithms developed that have been used 4 Interface The software described here basically consists of a menu bar a tool bar and a work window where the model to be simulated is defined fig 1 either by the notation of ports and graphs or by means of subsets encapsulated under icons that are hierarchically structured in the program installation directory and automatically reflected in a pop up window As each element is inserted the program asks the user for the symbolic expression associated with its definition in order to be able to relate the different parameters with one another and thus be able to go on to produce an optimal formulation of the equations associated with the model once it has been fully implemented fig 2 ISBN 978 960
19. ng the causality of a BG model for simplifying the resulting system of equations working symbolically and finally carrying out the simulation In Bondin the algorithms proposed in this paper have been developed in a condensed way that allows the software to meet all of these conditions References 1 Rosemberg R C and Karnopp D C Introduction to Physical System Dynamics N Y McGraw Hill Book Company 1983 2 Bos A M Modelling mulibody systems in terms of multibond graphs with application to a motorcycle Ph D Thesis Twente University Enschede The Netherlands 1986 3 van Dijk J On the role of bond graph causality in modelling mechatronic systems Ph D Thesis Twente University Enschede The Netherlands 1994 4 Breedveld P C Thermodynamic bond graphs an the problem of thermal inertances Journal of the Franklin Institute Vol 314 No 2 pp 15 40 1982 5 Bos A M and Tiernego M J L Formula manipulation in bond graph modeling and simulation of large mechanical systems Journal of the Franklin Institute Vol 319 No 1 2 pp 51 65 1985 6 Karnopp D C and Margolis D L Analysis and simulation of planar mechanisms using bond graphs Trans ASME Journal of Syst Dyn Meas amp Control Vol 101 pp 187 191 1979 7 F lez J A method for the unified an lisis of the kinematic and dynamic of the vehicular systems based in the Bond Graph technique
20. nning of the 90s the same research group that had developed THTSIM TUTSIM produced CAMAS based on the SIDOPS simulation language that would eventually evolve into 20 SIM Also at the beginning of the 90s Madrid Technical University the University of California and the University of Michigan developed other similar software BONDYN CAMP G and CAMBAS the two latter with the purpose of converting a BG into a series of data that would be valid for digital simulation languages DSL and for working with machines running the SUN operating system respectively Halfway through the 90s Research Park Ideon Sweden developed DYMOLA a general purpose modelling and simulation program developed in the language oriented towards MODELICA objects which offered the possibility of representation using BG Also halfway through the 90s the University of Glasgow generated software called MTT At the end of the 90s a modelling workbench developed in partnership with EDF Electricit de France generated MS1 which performed a symbolic manipulation of the equations in the model by means of causal analysis generating the code required to run the simulation Also in the same period the Indian Institute of Technology carried out SYMBOLS which permitted hierarchic modelling using objects and systems control Apart from the tools specified above there are other less widespread applications ARCHER PASION 32 BONDLAB HYBRSIM In sum it may be said that
21. ssion In the latter case the expression may be dependent on the generic variable t time or on the independent variables Besides the basic operators contained in the whole expression these expressions may contain any of the following typical functions or constants e Trigonometric functions sin cos tan cot asin acos atan ascot sinh cosh tanh coth arsinh arcosh artanh arcoth e Mathematical functions sqr sqrt exp lg In abs sgn round fac rand e Universal constants pi e e Operators factorial power percentage ISSN 1790 5117 92 So that the results graphs show a correct result displacement speed pressure temperature angle and the values associated with each port have the correct units of measurement the physical domain to which the different elements of a model simulation belong can be selected Once the composition of a BG model has been completed as to both the form and the values associated with the different elements everything is now ready for proceeding to the simulation To do this initially almost all the options are disabled since the functions associated with each option require a certain order Due to this as one function or another is completed new menu options will be automatically activated 5 Obtaining causality In order to carry out the simulation of a model firstly an analysis of causality must be made to indirectly determine t
22. systems Some solutions that have appeared up to that would automatically implement causality now consist in handling the state equations either analyse the BG and obtain the break variables if manually 2 or with the help of symbolic calculators PeTeneehys and consider the DAE equations 5 Other solutions add stiff type elements that allow associated with the break variables inside the relaxing the system by increasing its degrees of differential equations and finally solve the resulting freedom 6 Finally some authors propose system of equations introducing Lagrange multipliers to solve the problem 2 7 Another mainly unsolved problem is that of 2 State of the art automatically obtaining the mathematical model of The first simulation program performed using complex systems where there is any number and type the BG technique was called ENPORT 8 and was of zero order causal paths ZCP that is paths along developed at the beginning of the 70s at the which there are no integration operations These University of Michigan At the end of this decade ZCPs generate mathematical models comprising the University of Twente in Holland developed DAE systems that can present varying degrees of ISSN 1790 5117 90 ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS another BG based tool called THTSIM in Europe and TUTSIM in the United States Later at the begi
23. th a rigid union As soon as the calculation of the ODE DAE expressions has been concluded these can be viewed ISSN 1790 5117 94 system equations has been made they can then be simulated independently in order to conclusions and undertake time studies reach 7 Calling the variables To define the value associated with the different elements it has been seen that those values can be numerical or symbolic expressions In the latter case the parameters can be constant conditioned variables inserted by the user or the dependent and independent variables associated with the different ports In order to be able to call a dependent or independent variable either when writing the expression associated with a specific parameter or when writing a certain condition these variables must take the form shown below Should the variable correspond to an Inertance type port named I_n that variable must be the speed V of that port in translational mechanics and its integral and X the movement also in translational mechanics which means it will be called by placing the letter V or X before ISBN 978 960 474 052 9 Proceedings of the 8th WSEAS Int Conference on SOFTWARE ENGINEERING PARALLEL and DISTRIBUTED SYSTEMS the name of the port _n in addition the character reserved _ will need to be placed before and after rer V or XK name_port_Inertance _ Thus V _n_ would be used to indi
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