EP3881216A1 - Procédé mis en oeuvre par ordinateur pour la simulation d'un circuit électrique - Google Patents

Procédé mis en oeuvre par ordinateur pour la simulation d'un circuit électrique

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Publication number
EP3881216A1
EP3881216A1 EP19805278.9A EP19805278A EP3881216A1 EP 3881216 A1 EP3881216 A1 EP 3881216A1 EP 19805278 A EP19805278 A EP 19805278A EP 3881216 A1 EP3881216 A1 EP 3881216A1
Authority
EP
European Patent Office
Prior art keywords
switching
state
circuit
time
discrete
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
EP19805278.9A
Other languages
German (de)
English (en)
Inventor
Axel Kiffe
Katrin Witting
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Dspace GmbH
Original Assignee
Dspace GmbH
Dspace Digital Signal Processing and Control Engineering GmbH
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Dspace GmbH, Dspace Digital Signal Processing and Control Engineering GmbH filed Critical Dspace GmbH
Publication of EP3881216A1 publication Critical patent/EP3881216A1/fr
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/32—Circuit design at the digital level
    • G06F30/33—Design verification, e.g. functional simulation or model checking
    • G06F30/3308—Design verification, e.g. functional simulation or model checking using simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/32—Circuit design at the digital level
    • G06F30/33—Design verification, e.g. functional simulation or model checking
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/32—Circuit design at the digital level
    • G06F30/337—Design optimisation

Definitions

  • the invention relates to a computer-implemented method for simulating an electrical circuit by means of at least one computing unit, the electrical circuit having circuit components with switching elements, the switching elements being able to assume either a conductive or a blocking switching state, the circuit being described by a mathematical representation and the circuit is calculated for the overall switching state by numerically solving the mathematical representation describing the overall switching state on the computing unit.
  • the invention is located in the technical field of real-time simulation of electrical circuits for the purpose of influencing or testing a technical-physical process.
  • the technical-physical process can be, for example, control devices such as those used in large numbers in motor vehicles, airplanes, energy generation or energy distribution systems, etc.
  • the technical-physical process can also be, for example, the frequency converter of an electric drive, a DC / DC converter, an energy supply network, any controlled machine parts - in particular from automation technology - that are controlled by the simulated electrical circuit.
  • the first use case concerns the area of hardware-in-the-loop simulation (HIL), the second use case is often described by the term rapid control prototyping (RCP).
  • HIL hardware-in-the-loop simulation
  • RCP rapid control prototyping
  • the computing unit mentioned at the beginning, by means of which the simulation is carried out, is therefore often part of an HIL simulator or a real-time-capable RCP computer, which is usually intended to replace a control unit; both systems have an I / O interface.
  • Electrical signals can be read or output via the I / O interface, the electrical signals being analog or digital according to directional signals with low power.
  • the I / O interface le but also significant electrical power are transmitted, for example to control electric motors.
  • Selected calculated output variables are thus transmitted via the I / O interface.
  • the entire electrical circuit is output as electrical signals so that they act on a technical-physical process. Additionally or alternatively, process variables of the technical-physical process are measured and read in the form of electrical signals via the I / O interface and made available to the computing unit.
  • the simulation has a direct impact on the physical world.
  • the overall electrical circuit typically has, in addition to ohmic resistances, capacitors and coils, a large number of (semiconductor) switches, for example in power output stages for implementation of an inverter.
  • converter control data can then be generated, which are used to suitably control the power switches of the converter, these usually being implemented as semiconductor switching elements (for example MOSFET, metal-oxide-semiconductor field-effect transistor).
  • MOSFET metal-oxide-semiconductor field-effect transistor
  • diodes which are used, for example, anti-parallel to circuit breakers in bridge circuits and via which, when the circuit breakers are open, inductive currents can break down currents.
  • the computing units can be different cores of a processor, but it can also be different processors of a multiprocessor system, which is often the case with larger HIL simulators. It is also possible for one computing unit or several Computing units based on one (or more) FPGA (field programmable gate array) is or are implemented, which brings speed advantages but also difficulties with certain numerical operations such as the divisions.
  • FPGA field programmable gate array
  • a circuit contains, for example, n switching elements, then there are 2 n total switching states of the circuit, each of the total switching states corresponding to a separate mathematical representation of the switching device.
  • the object of the present invention is to develop the method described at the outset for simulating an electrical circuit in such a way that it is possible in the simplest possible way to combine the circuit with several - at best with all - combinations of the switching states of the switching elements and thus with several - at best with all - to represent total switching states in a mathematical representation and to calculate them numerically.
  • the previously derived task is first and essentially achieved in that a conductive switching element in the circuit is represented by a switching coil and that a blocking switching element in the circuit is represented by a switching capacitor.
  • the electrical behavior of the switching coil and the switching capacitor is described by structurally identical time-discrete switching equations i s, k , so that using the structurally identical time-discrete switching equations i s, k, a time-discrete state space representation H, F, Cd, Da for the switching elements is represented for all overall switching states the circuit results in a thematic representation, and the simulation is carried out on the computing unit for all overall switching states of the circuit on the basis of the time-discrete state space representation H, F, C d, D d, which is independent of the switching state.
  • the structurally identical time-discrete switching equations i s, k for the switching elements te have a uniform conductance component Gs for the conductive and the blocking switching state of the respective switching element. In this exemplary embodiment, this is a central boundary condition for the time-discrete switching equations to be structurally identical. Furthermore, the structurally identical time-discrete switching equations i s, k also have a current source component Is, k .
  • the current source components I s, k (a separate current source component Is , k is required for each switching element) are then provided as additional inputs in the time-discrete state space description H, F, C d, D d , which is why the time-discrete state space representation H, F, C d, D d can then be referred to as independent of the switching state, because different overall switching states can only be set by influencing the additional inputs on which the current source components I s, k act.
  • the corresponding current source component Is, k has an additional pulse current T H in order to shorten transient transitions when the switching state of a switching element (or also several switching elements) changes, and a pilot control is thus implemented.
  • the pulse current 7 FF is not equal to zero in only one calculation step, most preferably it only acts at the switching time of the respective switching element, which in the time-discrete world is the idea of a "pulse-shaped" signal. Practically any shortening of the transient switching processes is advantageous, but it is particularly favorable if the level of the pulse current I FF is calculated for a switching element with the proviso that the transient transition gear is completely avoided when changing the switching state of the switching element.
  • An advantageous choice of the uniform conductance component Gs is made systematically in that from the switching state-independent, time-discrete state space representation H, F, C d, D d using the specific choice for the conductance components Gs and the current source components I s , k and possibly the Impulse currents I FF a concrete extended time-discrete state space representation is obtained with a system matrix F * and the eigenvalues l are calculated as a stability parameter from the system matrix F * .
  • the eigenvalues make a significant statement about the dynamic behavior of the time-discrete overall system, i.e. the time-discretely modeled electrical circuit, and are also meaningful as absolute values.
  • a switching state-dependent, time-discrete state space representation is determined by assuming the smallest possible values for the inductances of the switching coils and for the capacitances of the switching capacitors. When working with the conductance components, this can only be done under the condition that a uniform conductance component Gs is used for the conductive and the blocking switching state of the respective switching element for the switching elements. For each individual overall switching state of the circuit, a system matrix of the switching-state-dependent, time-discrete state space representation of the reference circuit can then be determined, and the reference eigenvalues k e n can be calculated therefrom.
  • the reference eigenvalues then practically represent the desired eigenvalue configuration, since they are based on the optimal configuration of both the switching capacitor and the switching coil.
  • the best choice for the uniform conductance component Gs for the conductive and the blocking switching state of the respective one is then made Switching element determined.
  • a summary measure for a dynamic deviation is preferably calculated as quality criterion J, namely from the sum of the differences between the eigenvalues l, the system matrix of the expanded time-discrete state space representation and the corresponding reference eigenvalues Z Refi of the system matrix of the switching state-dependent, time-discrete state spatial representation of the respective reference circuit.
  • the uniform conductance components Gs are selected as optimal, for which the summary measure for the dynamic deviation is minimized.
  • the switching state-dependent dependent time-discrete state space representation of the overall reference circuit is selected as optimal, for which the summary measure for the dynamic deviation is minimized.
  • the invention also relates to a simulator with a computing unit for simulating an electrical circuit, the computing unit being programmed with a program such that it executes the method described above when the program is executed.
  • the invention relates to a computer program comprising instructions which cause a computer unit to execute the previously described method when the program is executed by a computing unit.
  • a computer program comprising instructions which cause a computer unit to execute the previously described method when the program is executed by a computing unit.
  • various options for designing and developing the method according to the invention for simulating an electrical circuit For this purpose, reference is made to the claims subordinate to claim 1 and to the description of preferred exemplary embodiments in connection with the drawing. 1 shows an electrical circuit with switching elements and the handling of the switching elements according to the prior art, in order to arrive at a mathematical representation and to calculate this on a computing unit,
  • FIG. 2 shows an electrical circuit with switching elements and the handling of the switching elements according to the invention in order to arrive at a mathematical representation and to calculate this on a computing unit
  • FIG. 4 shows the switching logic of various semiconductor switching elements and FIG. 5 shows a simulator on which the method for simulating an electrical circuit is carried out.
  • FIGS. 1 to 5 A computer-implemented method 1 for simulating an electrical circuit 2 with circuit components R, L, T is shown in FIGS. 1 to 5 with different focuses.
  • 1 shows such a computer-implemented method 1 for simulating an electrical circuit 2 by means of at least one computing unit 3, as is known from the prior art.
  • Circuit 2 is a simple single-phase full-bridge inverter in FIG. 1.
  • the electrical circuit 2 has various circuit components R, L, T, for example a coil L, an ohmic resistor R and MOSFET transistors Ti, T 2 , T, T 4 with control connections gi, g 2 , g 3 , g 4th
  • the MOSFET transistors Ti, T 2 , T, T 4 represent the switching elements T, here. These switching elements Ti can assume either a conductive or a blocking switching state.
  • the electrical circuit 2 is finally described by a mathematical Dar position MR 4.
  • different overall switching states SSTi occur in circuit 2.
  • the electrical behavior of the circuit 2 is calculated by numerically solving the mathematical representation MR describing the respective overall switching state SSTi.
  • MR mathematical representations MR of the circuit 2
  • the sum of all the mathematical representations MR for each overall switching state SSTi then forms the comprehensive mathematical representation MR for the circuit 2.
  • the switching element T (which can also be a diode, a mechanical switch, another semiconductor switching element, etc.)
  • the correspondingly appropriate mathematical representation MR is used to calculate the respective overall switching state SSTi on the computing unit 3.
  • the computing unit 3 which can be part of an HTI. Simulator here, is connected to a physical process 6 via an I / O interface 5 and by outputting corresponding ones in the context of the simulation Calculated quantities acts on the physical process 6 and by measuring corresponding quantities from the physical process 6 also receives data which then flow into the simulation of the electrical circuit 2.
  • the arithmetic unit 3 is therefore in direct interaction with the real world and the calculation of the electrical circuit 2 on the arithmetic unit 3 leads to an immediate interaction with the physical process 6. It is readily apparent that the in Fig. 1 Darge - The procedure is extremely memory-intensive and is also difficult to handle, since a corresponding mathematical representation MR of the circuit 2 must be used for each individual combination of the switching states of the switching elements Ti.
  • the switching elements T are not elements of the respective mathematical representation MR, but lead to a structural change in the circuit 2, which is taken into account by various mathematical representations MR in the respective overall switching state SST.
  • the letters used in the above equation are written in bold to indicate that these are matrices or vectors.
  • the matrices A, B, C and D are system, input, output and pass matrix.
  • the state vector x usually contains all the state variables of the energy store, for example voltages at capacitors and currents in coils
  • the output vector y contains all the resulting output variables
  • the input vector u usually contains the values of all current and voltage sources.
  • FIG. 2 shows schematically how the method 1 for simulating the electrical circuit 2 can be simplified considerably.
  • Fig. 2 shows both the basic principle, as well as special configurations, which are also described in detail below.
  • the method 1 used here is characterized in that a conductive switching element Ti is represented in the circuit 2 by a switching coil 7 and in that a blocking of the switching element U in the circuit 2 is represented by a switching capacitor 8.
  • a switching coil 7 is represented in the circuit 2 by a switching coil 7
  • a blocking of the switching element U in the circuit 2 is represented by a switching capacitor 8.
  • a switching-state-independent time-discrete state space representation H, F, C d, D d for all total switching states SSU of the circuit 2 then results. Exactly how this can be done is explained below by way of example. The simulation can then be carried out on the arithmetic unit 3 on the basis of the time-discrete state space representation H, F, Cd, D d, which is independent of the switching state.
  • Equation 3 the derivation being analog (Equation 3): The following applies for I c, k + i and for Gc in equation 3 (equation 3 a):
  • the index for the calculation step can of course also be shifted, so that the equation 5 given for the calculation step k + 1 can also simply be shifted to the calculation step k, that is to say the calculation step k + 1 everywhere through the calculation step k is replaced, which is equivalent in terms of content.
  • an embodiment of method 1 is characterized in that the structurally identical, time-discrete switching equations i s , k for the switching elements Ti have a uniform conductance component Gs for the conducting and the blocking switching state of the respective switching element Ti and a current source component I s, k and which have Stromierennkom components I s, k additional inputs of the switching state independent zeitdis kreten state space representation is H, F, Cd, As are so different overall tikschaltzulets SstI only by influencing of the additional inputs, i.e. the current source components I s , k, can be set.
  • Equation 6 From equation 6 it can be seen that the value for the current source components I s , k + i in the conductive switching state of the switching elements Ti and in the blocking switching state of the switching elements Ti at the time of calculation k + 1 depends on the value of the current source components I s, k for the calculation time k.
  • the derivation of the relationship in equation 6 can be represented, for example, for the blocking state off as follows, starting from equation 3a:
  • Equation 5 and 6 can be combined into the following equation 6a by introducing the switching state variable Si, which is 1 in the conducting state and 0 in the blocking state:
  • the switching elements Ti are each replaced by an arrangement with energy stores, namely in each case with a switching capacitor 8 and a switching coil 7, associated transient processes occur in the simulation of the circuit 2, so that a certain amount of time passes until set the actually desired stationary states for a conductive or a blocking switching element Ti.
  • a further development of method 1 is therefore characterized in that, in order to shorten transient transitions when the switching state of the switching elements T; the current source components I s , k have an additional pulse current / ⁇ and so a pilot control is implemented.
  • the additional pulse current T FF is preferably not equal to zero in only one calculation step, and preferably it only acts at the switchover time of the respective switching element Ti.
  • Fig. 3 it is shown how the switch equivalent circuit for a Wegele element Ti with a switching coil 7 and with a switching capacitor 8 can be further developed in order to implement the pilot control described above with the additional pulse current I FF .
  • Fig. 3a the above-described equivalent circuit diagram for a switching element U with the switching coil 7 and the switching capacitor 8 is supplemented by additional pilot control sources, namely with the pilot control current source I F F, k + i connected in parallel and with the pilot control voltage source V F connected in series F, k + i ⁇ From Fig. 3a to Fig.
  • Equation 8 has the same structure as equation 5.
  • I S w , k is set to zero and the pulse current I FF is activated for the duration of a simulation step.
  • the pulse required for the pilot control is caused by the different pulse strengths according to equation 10.
  • the level of the pulse current T FF for a switching element Ti is calculated with the measure that the transient transition when the switching state of the switching element Ti is completely avoided.
  • the current source components Is, k of such switching elements Ti are preferably equipped with the additional pulse current I FF which appear to be “important”, in the present case those switching elements Ti with the highest actual or expected switching frequency.
  • the switching-state-independent, time-discrete state space representation H, F, C d, D d is already shown in the computing unit 3. It is possible to use this time-discrete state space representation H, F, C d, D d , which is independent of the switching state, starting from the circuit 2 using the equivalent circuit for switching elements Ti with switching coil 7 and switching capacitor 8 and with a discretization approach, for example the discretization approach according to equation 1 to derive directly. It may be easier to understand, to begin with a time-continuous representation of the state space with the usual system matrices A, B, C, D.
  • switching elements Ti are replaced by an equivalent circuit with switching coils 7 and switching capacitors 8 and the continuous-time representation of the state space with a discretization approach into the switching-state-independent, time-discrete state spatial representation H, F, C d, Da transferred.
  • the sole use of the equivalent circuit for the switching elements Ti according to FIG. 3c leads to the following time-constant and switching-state-independent representation of the state space (equation 11, superscript T here means "transposed”):
  • Isw contains all currents of the current source components of the L / C equivalent circuit diagram for the switching elements Ti and U L represents all other sources in the circuit 2 modified by the L / C equivalent circuit diagram for the switching elements Ti.
  • V S w includes all switching element voltages and isw includes all switching element currents .
  • the output vector y L contains all other quantities which are of interest in the circuit 2 with regard to the simulation.
  • the output variables in i S w are used to evaluate all switching element currents and switching element voltages in the "Switch logic".
  • H, F, C d, Da are the time-discrete system, input, output and through matrices.
  • the interaction of all variables in terms of signal flow is shown graphically in computing unit 3 in FIG. 2.
  • dead time elements 9 have been inserted symbolically in the state space representation in FIG numerical calculation itself can be effected.
  • FIG. 4 How the "switch logic" works is shown in FIG. 4 by way of example on various switching elements U.
  • the signals at the control inputs g of the switching elements Ti must be taken into account as well as the existing currents in the respective switching element T ,.
  • the relationships shown in FIG. 4 are readily apparent and do not need to be explained in detail.
  • the method 1 is designed so that from the switching state-independent time-discrete state space representation H, F, C d, D d using the specific choice for the Feitwertkomponents Gs and the current source components I s , k and, if necessary, the pulse currents ⁇ H a concrete, expanded, time-discrete state space representation is obtained with a system matrix F * and the eigenvalues l are calculated as a stability parameter from the system matrix F * . Since the eigenvalues l make a significant statement about the dynamic behavior of the time-discrete overall system, their values are in themselves suitable as an assessment measure for the stability and the dynamic behavior of the circuit 2.
  • the system Matrix F * can be obtained from Equation 9 if it is formulated as a vector equation, as shown in Equation 14: The relationships according to Equation 15 apply here:
  • the diagonal matrix S contains all switching states s; of each switching element Ti.
  • the diagonal matrix G contains all the uniform conductance components Gsi for each individual switching element Ti. It is therefore possible to choose an individual uniform tail unit component Gsi for each switching element Ti, which differs, for example, from all other uniform conductance components Gsi differs from the other switching elements Ti, however, identical values could also be selected for the uniform tail unit components Gsi for all switching elements Ti. With similar switching elements Ti, it may be more plausible to choose identical values for the uniform tail assembly components Gsi, especially if they are part of a common assembly, such as a bridge circuit.
  • the eigenvalues l 1 can be calculated in a known manner from this comprehensive expanded system matrix F * .
  • the eigenvalue configuration that appears most suitable on the basis of these evaluations then allows a conclusion to be drawn as to which choice is best for the values of the conductance components Gs.
  • desired reference eigenvalues Z Refi are specified and that the best is achieved by calculating a quality criterion J using the eigenvalues I, the system matrix F *, the expanded time-discrete state space representation and the reference eigenvalues Z Refi Choice for the uniform conductance component G s for the conductive and the blocking switching state of the respective switching element T) is determined.
  • the reference eigenvalues are preferred.
  • e n is determined in such a way that a time-discrete state space representation dependent on the switching state is determined as the reference circuit for each overall switching state SST, the circuit 2, by assuming the smallest possible values for the inductances of the switching coils 7 and for the capacitances of the switching capacitors 8, which is only a task the condition that a uniform conductance component Gs for the conductive and the blocking switching state of the respective switching element T is used for the switching elements Ti (equation 4).
  • the reference eigenvalues k Re n (here the index i denotes the respective eigenvalue) for each overall switching state SSR (here the index i denotes the respective overall switching state) of the circuit 2 ) calculated.
  • the quality criterion J can be determined, for example, according to the following calculation rule (equation 20), where the index j here runs through all of the switching states SST j and the index i all eigenvalues in the respective overall switching state:
  • J is a summary measure of a dynamic deviation, which is calculated from the sum of the differences between the eigenvalues l, the system matrix of the extended time-discrete state space representation and the corresponding reference eigenvalues Z Refi of the system matrix of the switching state-dependent time disc - th state space representation of the overall reference circuit. So that the greatest possible approximation of the eigenvalues l, the system matrix of the expanded time-discrete state space representation and the corresponding reference eigenvalues Z Refi of the system matrix of the switching state-dependent time-discrete state space representation is achieved, J is the measure for Dynamic deviation minimized.
  • the spatial representation of the reference circuit is also summed up via the various switching states of the expanded, time-discrete state.
  • FIG. 5 shows a simulator 10, here an HIL simulator, with a computing unit 3 for simulating an electrical circuit 2, where the computing unit 3 is programmed with a program such that the previously described method 1 with the computing unit 3 is executed. Via the I / O interface 5, the simulator 10 is connected to a control unit 11, which here is the physical process 6.

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Abstract

L'invention concerne un procédé (1) mis en oeuvre par ordinateur pour la simulation d'un circuit électrique (2) au moyen d'au moins une unité de calcul (3), le circuit électrique (2) présentant des composants (L, R, Ti) dotés d'éléments de commutation (Ti), les éléments de commutation (Ti) pouvant prendre soit un état de commutation conducteur, soit un état de commutation bloquant, le circuit (2) étant décrit par une représentation mathématique MR et le circuit étant calculé pour chaque état de commutation global (SSTi) par déclenchement numérique de la représentation mathématique MR qui décrit l'état de commutation global (SSTi) , sur l'unité de calcul (3). Une manière simple de représenter le circuit (2) avec plusieurs - dans le meilleur des cas avec toutes les - combinaisons des états de commutation globaux (SSTi) des éléments de commutation (Ti) et ainsi avec plusieurs - dans le meilleur des cas avec tous les - états de commutation globaux (SSTi) sous la forme d'une représentation mathématique, et de le calculer numériquement, consiste à représenter un élément de commutation conducteur (Ti) dans le circuit par une bobine de commutation (7), à représenter un élément de commutation bloquant (Ti) dans le circuit (2) par un condensateur de commutation (8), à décrire le comportement électrique de la bobine de commutation (7) et du condensateur de commutation (8) par des équations de commutation iS, k discrètes dans le temps, de structure identique de sorte que l'utilisation des équations de commutation iS, k discrètes dans le temps, de structure identique pour les éléments de commutation (Ti) permet d'obtenir une représentation d'espace d'état H, Φ, Cd, Dd discrète dans le temps et indépendante de l'état de commutation pour tous les états de commutation globaux (SSTi) du circuit (3), et d'effectuer la simulation sur la base de la représentation d'espace d'état H, Φ, Cd, Dd discrète dans le temps et indépendante de l'état de commutation pour tous les états de commutation (SSTi) du circuit (2) sur l'unité de calcul (3).
EP19805278.9A 2018-11-15 2019-11-15 Procédé mis en oeuvre par ordinateur pour la simulation d'un circuit électrique Pending EP3881216A1 (fr)

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DE102018128653 2018-11-15
PCT/EP2019/081535 WO2020099659A1 (fr) 2018-11-15 2019-11-15 Procédé mis en oeuvre par ordinateur pour la simulation d'un circuit électrique

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WO2023275347A1 (fr) * 2021-07-02 2023-01-05 Dspace Gmbh Simulateur et procédé de fonctionnement d'un simulateur
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AU2002243494A1 (en) * 2001-01-11 2002-07-24 P.C. Krause And Associates, Inc. Circuit simulation
JP5943269B2 (ja) * 2011-11-29 2016-07-05 学校法人 中央大学 回路シミュレーション方法、回路シミュレーション装置、および回路シミュレーションプログラム
JP6197314B2 (ja) * 2013-03-13 2017-09-20 富士電機株式会社 電力系統のシミュレーション方法および電力系統シミュレータ
DE102017113594A1 (de) 2017-06-20 2018-12-20 Dspace Digital Signal Processing And Control Engineering Gmbh Computerimplementiertes Verfahren zur Simulation einer elektrischen Gesamtschaltung

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CN113039548A (zh) 2021-06-25
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JP7420803B2 (ja) 2024-01-23
JP2022507574A (ja) 2022-01-18

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