Method for simulating circuits implemented by computers

Abstract

The invention shows and describes a computer-implemented method (1) for simulating a circuit (2) with the aid of at least one computing unit (3), the circuit (2) having a switching element (T i ) circuit components (L, R, T i ), switching element (T i ) can occupy a conducting switching state or a non-conducting switching state, the circuit (2) is described by the mathematical expression MR and the overall switching state (SST) is described by numerical solution in the calculation unit (3) i ) is expressed in terms of (MR) for each overall switching state (SST i ) calculation circuit. This allows the overall switching state (SST) of the switching element to be expressed in a mathematical expression as simply as possible and to be numerically calculated. i ) and thus all the overall switching states (SST i ) circuit (2), that is, the conducting switch element (T i ) is represented by the switch coil (7), the non-conducting switch element (T i ) is represented by the switched capacitor (8), and the electrical characteristics of the switched coil (7) and the switched capacitor (8) are expressed by the structurally consistent, time-discrete switching equation i S,k Description, so that the switching element (T i ) Using a structurally consistent, time-discrete switching equation i S,k In the case of , all the overall switching states (SST) for circuit (3) are generated i ) is a discrete-time state space representation of H, Φ, C that is independent of the switch state. d , D d , and on the basis of all the overall switch states (SST) for the circuit (2) in the calculation unit (3) i ) is a discrete-time state space representation of H, Φ, C that is independent of the switch state. d , D d Execute the simulation.

Description

Technical Field

[0001] The invention relates to a computer-implemented method for simulating an electrical circuit with the aid of at least one computing unit, wherein the electrical circuit has a circuit component comprising a switching element, wherein the switching element can assume a conducting switching state or a non-conducting switching state, wherein the electrical circuit is described by a mathematical expression and the electrical circuit is calculated on the computing unit for each overall switching state by numerically solving the mathematical expression describing the overall switching state. Background Art

[0002] The invention is in the field of real-time simulation technology of circuits for the purpose of influencing or testing technical-physical processes. Technical-physical processes can, for example, involve controllers, such as are used in large quantities in motor vehicles, aircraft, energy acquisition or energy distribution systems, etc. Technical-physical processes can also, for example, involve frequency converters of electric drives, DC / DC regulators, energy supply networks, in particular any controlled machine parts from automation technology that are controlled by simulation circuits. The first application scenario relates to the field of hardware-in-the-loop simulation (HIL), the second application scenario is often explained by the term "rapid control prototyping (RCP)".

[0003] The computing unit mentioned at the beginning of this document, with the aid of which the simulation is carried out, is therefore usually a component of a HIL simulator or a component of a real-time capable RCP computer; both systems have I / O interfaces. Electrical signals can be read or output via the I / O interfaces, wherein the electrical signals can be analog or digital communication technology signals with low power, but in the case of electrical loads or power amplifiers, large electrical powers can also be transmitted via the I / O interfaces, for example to actuate an electric motor.

[0004] The selected calculated output variables of the overall circuit are thus output as electrical signals via the I / O interface, so that they influence the technical physical process. Additionally or alternatively, process variables of the technical physical process are detected by measurement technology and read in the form of electrical signals via the I / O interface and provided to the computing unit. The simulation has a direct influence on the physical world.

[0005] In power electronics applications, for example, involving electrical drives, generators or electrical energy supply networks, the overall circuit usually has a large number of (semiconductor) switches in addition to ohmic resistors, capacitors and coils, for example, in the power output stage for realizing a converter. Then, in the overall circuit, for example, converter control data can be generated, which is used to appropriately control the power switches of the converter, wherein these power switches are usually implemented as semiconductor switching elements (such as MOSFETs, i.e. metal oxide semiconductor field effect transistors). These power switches can be actively switched on or off via control terminals. Other switching elements in power electronic circuits are diodes, which are used, for example, in reverse parallel with the power switches in the bridge circuit and can reduce the current driven by the inductor when the power switches are turned off. These freewheeling diodes, of course, cannot be actively switched on or off via the control terminals like other diodes, and their conducting state is generated by their electrical terminal parameters, i.e., by their terminal voltage or internal diode current.

[0006] The simulation of such circuits, in particular power electronic circuits, places high demands on the simulation hardware used, i.e., on the computing units used and their memory configuration, especially because the simulation usually has to be carried out in real time, since real processes are influenced or variables obtained from real processes by measurement are processed within the scope of the simulation. Therefore, it is often necessary to ensure that the requirements in terms of computing time and memory are met.

[0007] The calculation units can refer to different cores of a processor, but can also refer to different processors of a multiprocessor system, which is not uncommon in larger HIL simulators. It is also possible to implement a calculation unit or multiple calculation units based on one (or more) FPGAs (field programmable gate arrays), but this brings speed advantages but also difficulties in certain numerical operations such as division.

[0008] It is known in the prior art that the circuits described here are described by mathematical expressions based on physical regularities. Such circuits can be mathematically expressed, for example, in the form of nodes with an impedance matrix M by setting up mesh and node equations, or by defining input and output variables and state variables in a state space with matrices A, B, C, D. In both types of mathematical expressions, large-scale systems of equations are generated. The special difficulty in circuits with switching elements is that these switching elements themselves cannot be described as terms of equations, but rather that changes in the switching state of the switching elements always lead to changes in the structure of the observed circuit and therefore also to changes in the mathematical expression. If the circuit contains, for example, n switching elements, then a 2-way equation of the circuit is generated. nThe circuit is described in two parts. n It is not difficult to see that this approach is extremely expensive.

[0009] It is known in the prior art, for example, to reduce the complexity for describing a circuit in mathematical terms by appropriately dividing the circuit while taking into account all possible overall switching states; in this regard reference is made to EP 3 418 924 A1. Summary of the invention

[0010] The object of the present invention is to design the method for simulating a circuit described at the beginning of the text in such a way that a circuit with multiple, most favorable combinations of switching states of switching elements and therefore with multiple, most favorable overall switching states can be described and numerically calculated in a mathematical expression in the simplest possible manner and method.

[0011] The above-mentioned object is firstly and essentially solved in the method for simulating a circuit explained at the outset by representing the conducting switching elements in the circuit by switching coils and representing the non-conducting switching elements in the circuit by switching capacitors. Furthermore, by means of a structurally consistent, time-discrete switching equation i S,k Describe the electrical characteristics of the switched coil and switched capacitor so that a structurally consistent, time-discrete switching equation is used for the switching element i S,k The switch-state-independent, time-discrete state space representation H, Φ, C for all the overall switch states of the circuit is generated under the condition of d , D d As a mathematical expression, and based on the switch-state-independent, time-discrete state-space representation H, Φ, C for all overall switch states of the circuit d , D d The simulation is performed on a computing unit.

[0012] By replacing the switching element with a capacitor, which is referred to here as a switched capacitor, in the non-conducting state, and by replacing the switching element with a coil, which is referred to here as a switched coil, in the conducting state, it is firstly achieved that the switching element, regardless of its type, is expressed in the mathematical expression and is therefore generally clear in the mathematical expression. This is an important difference from the prior art described at the beginning of this article, in which the switching element itself does not appear in the mathematical expression at all, but only the selection of the switching state of the corresponding switching element, i.e., conducting or non-conducting, causes a change in the mathematical expression of the circuit. The idea now is to describe the switched coil and the switched capacitor mathematically by structurally consistent switching equations, i.e., these switching equations that appear to be mathematically consistent have nothing to do with whether they describe switched coils or switched capacitors. This is possible when the equations for the switched coil and the switched capacitor are formulated within the scope of time discreteness, so in this regard what is discussed here are structurally consistent, time discrete switching equations i S,k , where k refers to the kth calculation step. These time-discrete switching equations i are further explained in detail in the accompanying drawings. S,k How exactly it looks like.

[0013] Given a consistent description of the switching coils and switching capacitors within the time discretization, it is possible to use structurally consistent, time-discrete switching equations i for the switching elements. S,k In the case of establishing a matrix with H, Φ, C d , D d The advantage of this is that H, Φ, C can be expressed based on the switch state-independent, time-discrete state space expression for all the overall switching states of the circuit. d , D d The simulation of the circuit is performed on the computing unit. It is therefore no longer necessary to switch between a plurality of different mathematical representations (a separate mathematical representation for each overall switching state), which greatly simplifies the simulation and, in particular, greatly saves memory.

[0014] In a preferred embodiment of the method, it is provided that a structurally consistent, time-discrete switching equation i for the switching element S,k A uniform conductance component G for the conductive switching state and the non-conductive switching state of the corresponding switching element S This is the central boundary condition for the time-discrete switching equation to become structurally consistent in this embodiment. In addition, the structurally consistent, time-discrete switching equation i S,k It also has a current source part I S,k The current source part IS,k (A separate current source section I is required for each switching element S,k ) describes H, Φ, C in the discrete time state space d , D d Then set as additional input, so the time-discrete state space expression H, Φ, C d , D d Then it can be called independent of the switching state, because different overall switching states can be affected only by affecting the current source part I S,k The additional input acting on it is adjusted.

[0015] An advantageous further development of the method is characterized in that, in order to shorten the transient transition when the switching state of a switching element (or also of a plurality of switching elements) changes, the corresponding current source part I S,k With additional pulse current And thus pre-adjustment is achieved. Pulse current Preferably, it is not equal to zero only in one calculation step, and quite preferably only in the switching time of the corresponding switching element, which is the presentation form (Vorstellung) of a "pulse-like" signal in the world of time discreteness. In fact, any shortening of the transient switching process is advantageous, but it is particularly advantageous for the following cases, that is, the pulse current for the switching element The intensity of is calculated according to the following settings, namely, transient transitions when the switching state of the switching element is changed are completely avoided.

[0016] Calculate pulse current The intensity is of course associated with some costs. Therefore, in a further development of the method, only the current source portion I of those switching elements which are evaluated as "important" - ie, for example, those with the highest actual or expected switching frequency - is selected. S,k Equipped with additional pulse current

[0017] A further development of the method described here aims to answer the question: in the case of a structurally consistent, time-discrete switching equation i for the switching element S,k How should we choose the uniform conductivity part G? S. It is obvious that an open switching element is best simulated by a switching capacitor with the smallest possible capacitance, because a switching capacitor with the smallest possible capacitance will very quickly assume its static final state with respect to current and voltage. In exactly the same way, a closed switching element is best simulated by a switching coil with the smallest possible inductance, because here too the static final state with respect to the current through the switching coil and the voltage across the switching coil is reached in the shortest possible time. However, the description of the switching coil current and the switching capacitor current according to the equation shows that, with very small capacitances of the switching capacitor, the required uniform conductance component G can only be achieved with very large values ​​of the inductance of the switching coil. S , and vice versa, which corresponds to the opposite design goal. Therefore, there is a question about the advantageous selection of a uniform conductance portion G S It should be noted that a respective uniform conductance G can be selected for each switching element. S , it is just the same that a uniform conductance G can be assumed for all switching elements of the circuit. S The optimization method described here can be used in two ways.

[0018] The uniform conductivity part G can be systematically made as follows S An advantageous option is to use the conductance portion G S The sum of the current source parts I S,k and pulse current when necessary In the case of a specific choice of (Konkret), H, Φ, C are expressed in a time-discrete state space independent of the switching state. d , D d Get the system matrix Φ * The specific, expanded, time-discrete state space representation of and represented by the system matrix Φ * Calculate the eigenvalue λ i As a stability parameter, the characteristic value provides important information about the dynamic behavior of the time-discrete overall system, ie, the time-discretely modeled circuit, and is also significant in this respect as an absolute value.

[0019] In a preferred embodiment of the method, provision is made for a time-discrete state space representation that is dependent on the switching state to be determined as a reference circuit for each overall switching state of the circuit in such a way that as small values ​​as possible are used for the inductance of the switching coil and the capacitance of the switching capacitor. When working with conductance components, this is only achieved by omitting the use of a uniform conductance component G for the conducting switching state and the non-conducting switching state of the respective switching element. sThis is the only possible condition. Then, 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 be determined, from which the reference eigenvalue λ can be calculated. Refi In practice, these reference eigenvalues ​​then correspond to the desired eigenvalue configuration, since they are based not only on an optimized configuration of the switched capacitors but also on an optimized configuration of the switched coils. The eigenvalues ​​λ of the system matrix expressed in the expanded, time-discrete state space are calculated using the quality criteria. i and the reference eigenvalue λ of the system matrix expressed in the time-discrete state space related to the switching state Refi In the case of , find the unified conductance part G for the conductive switching state and the non-conductive switching state of the corresponding switching element s The best choice.

[0020] In order to find the conductance part G for unity s The best choice is from the eigenvalues ​​λ of the system matrix expressed in the expanded, time-discrete state space i and the reference eigenvalue λ of the system matrix of the time-discrete state space representation of the corresponding reference circuit associated with the switching state Refi The sum of the differences between the two is preferably used to calculate an overall measure of the dynamic deviation as the quality assessment criterion J. Finally, the unified conductivity component G is selected which minimizes the overall measure of the dynamic deviation. S As an optimization or optimisation, preferably, the different switching states are additionally combined with reference to a time-discrete state space representation of the switching state-dependent state of the overall circuit.

[0021] Furthermore, the invention also relates to a simulator having a computing unit for simulating a circuit, wherein the computing unit is programmed with a program in such a way that the computing unit can carry out the method described above when the program is run.

[0022] Furthermore, the invention relates to a computer program which comprises instructions which, when the program is run by a computing unit, cause this computing unit to carry out the method described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Now, there are various possibilities for designing and expanding the method according to the invention for simulating a circuit in detail. For this purpose, reference is made to the dependent claims of claim 1 and to the description of preferred exemplary embodiments in conjunction with the drawings. In the drawings:

[0024] Figure 1 A circuit with a switching element and the operation of the switching element according to the prior art in order to obtain a mathematical expression and to calculate the mathematical expression on a computing unit are shown;

[0025] Figure 2 A circuit with a switching element and the operation of the switching element according to the invention in order to determine a mathematical expression and to calculate the mathematical expression on a computing unit are shown;

[0026] Figure 3 shows an L / C equivalent circuit diagram for a switching element and the addition of a pre-regulated power supply to achieve pre-regulation in order to reduce transient processes;

[0027] Figure 4 shows the switching logic of different semiconductor switching elements; and

[0028] Figure 5 A simulator is shown, on which a method for simulating a circuit is implemented. DETAILED DESCRIPTION

[0029] exist Figures 1 to 5 1 shows a computer-implemented method 1 for simulating a circuit 2 having circuit components R, L, T with different emphasis.

[0030] exist Figure 1 , such a computer-implemented method 1 for simulating a circuit 2 by means of at least one computing unit 3, as is known from the prior art. Figure 1 A simple single-phase full-bridge inverter is shown in FIG. 2 . Circuit 2 has various circuit components R, L, T, such as a coil L, an ohmic resistor R and MOSFET transistors T1, T2, T3, T4 with control terminals g1, g2, g3, g4. MOSFET transistors T1, T2, T3, T4 are switching elements T i The switching element T i A conducting switching state or a non-conducting switching state can be assumed.

[0031] The circuit 2 is finally described by the mathematical expression MR 4. Depending on the corresponding switching element T i Depending on the respective switching states, different overall switching states SST appear in circuit 2 i The corresponding overall switching state SST is described by numerical solution i Mathematical expression of MR i The electrical characteristics of the circuit 2 are calculated. As already explained in the general description, in the n switching elements T i There is circuit 2 of 2 n This means for the commonly used mathematical expression MR of circuit 2 that the switching element T i Each different switching combination results in a respective overall switching state SST i For each overall switching state SSTi All mathematical expressions of MR i The sum of then forms a mathematical expression MR for the generality of the circuit 2.

[0032] Depending on the switch element T i Depending on the switching state of the switch (the switching element can also be a diode, a mechanical switch, another semiconductor switching element, etc.), use the corresponding appropriate mathematical expression MR i The corresponding overall switching state SST is calculated in the calculation unit 3 i .

[0033] exist Figure 1 It is also shown that the computing unit 3, which can be a component of the HIL simulator, is connected to the physical process 6 via the I / O interface 5 and influences the physical process 6 by outputting corresponding parameters calculated within the scope of the simulation and also obtains data by measuring corresponding parameters of the physical process 6, which are then introduced into the simulation of the circuit 2.

[0034] The computing unit 3 thus interacts directly with the real world and the calculations of the circuit 2 on the computing unit 3 result in a direct interaction with the physical process 6. Figure 1 The approach shown in FIG. 1 is very memory-intensive and also very complex to operate, since the switching element T i Each individual combination of the switching states of circuit 2 uses the corresponding mathematical sub-expression MR i . Switching element T i Not the corresponding mathematical expression MR i elements, but rather leads to a structural change in circuit 2, by changing the corresponding overall switching state SST i Different mathematical expressions in MR i Such structural changes are taken into account.

[0035] When for example using the state space as SST for each overall switch state i Mathematical expression of MR i When , a large number of state space expressions are generated, which is exactly the same as the overall switch state SST i For simplicity, the specific overall switching state is labeled with the letter ξ in the following equations. The time-continuous state space representation is therefore for each switching state SST i Or ξ has the following general form:

[0036] y=C (ξ) x+D (ξ) u

[0037] The letters used in the above equations are bolded to clarify that this involves matrices or vectors. The matrices A, B, C and D are the system matrix, the input matrix, the output matrix and the feedforward matrix. The state vector x generally contains all state variables of the energy storage device, i.e., for example, the voltage at the capacitor and the current in the coil, the output vector y then contains all the generated output variables, and the input vector u generally contains the values ​​of all current sources and voltage sources.

[0038] As already explained, during the simulation of the circuit 2 by the computing unit 3, it is always necessary to take into account which switching elements T i is conducting or non-conducting. Correspondingly, which switching elements T i In which switch state is SST i or ξ. Therefore, in the subsequent calculations, the selection is suitable for the overall switching state SST i Or the time-continuous state space expression of ξ. i So there are 2 n This solution is very memory-intensive and is problematic in particular when the calculation unit 3 is implemented on the basis of an FPGA (Field Programmable Gate Array).

[0039] Now, in Figure 2 Schematically it is shown how method 1 for simulating circuit 2 can be greatly simplified. Figure 2 Both the basic principle and the special embodiments which will be described in detail below can be recognized. The method 1 used here is characterized in that the conductive switching element T in the circuit 2 i The non-conducting switching element T represented by the switching coil 7 in the circuit 2 i represented by the switched capacitor 8. This measure alone always presents the problem that switching must be done back and forth between two different elements, namely between the switched coil 7 and the switched capacitor 8, so that structural differences in the mathematical description of MR cannot be ruled out. Therefore, another important feature is that the switching equation i is discretized in a time-consistent manner. S,k For each switching element T i The electrical characteristics of the switching coil 7 and the switching capacitor 8 are described.

[0040] When using the switching element T i The structurally consistent, time-discrete switching equation i S,k In the case of all the overall switching states SST for circuit 2 i The time-discrete state space expression H, Φ, C is independent of the switch state d , D dHow this happens will be explained in more detail below. Then, based on all the overall switching states SST for the circuit 2, i The time-discrete state space expression H, Φ, C is independent of the switch state d , D d The simulation is performed on the computing unit 3. By using the switching element T i By using the switching coil 7 and the switching capacitor 8 and describing the electrical characteristics of the switching coil 7 and the switching capacitor 8 in a time-discrete manner, it is possible to generate an equivalent circuit for the switching element T i The structurally consistent, time-discrete switching equation i S,k The switching equation is then introduced into the time-discrete state space expression H, Φ, C independent of the switching state d , D d The result is a unique complete representation MR of circuit 2, and for each overall switching state SST i No need for different mathematical expressions MR i The method 1 for simulating the circuit 2 is thus simplified and the resource expenditure of the computing unit 3 for such a simulation is significantly reduced compared to the methods known from the prior art.

[0041] Next, we will now show how the switching equation i can be obtained by means of a structurally consistent, time-discrete switching equation i S,k To describe the electrical characteristics of the switching coil 7 and the switching capacitor 8. The following time discretization of the relationship in the form of equation 1 is used here:

[0042]

[0043] Here, T is the calculation step and the corresponding discretization method (forward Euler method, Tustin method and backward Euler method for γ=0, γ=1 / 2 and γ=1) can be configured with the selected value for γ.

[0044] When the discretization described above is applied to the relationship between the current and voltage at the switching coil 7, then (Equation 2) is obtained:

[0045]

[0046]

[0047] Here, it applies to I L,k+1 and G L The ones are:

[0048]

[0049] Following the same principle, the corresponding relationship between the current flowing through the switched capacitor 8 and the voltage on the switched capacitor 8 can also be described by equation 3, wherein the following derivation (equation 3) is performed similarly:

[0050]

[0051] Here, it applies to I in equation 3 C,k+1 and G C is (Equation 3a):

[0052]

[0053] It can be seen that the mathematical structure for the current flowing through the switching coil 7 and the current flowing through the switching capacitor 8 is the conductance part G that appears in the equation L and G c The structure is consistent when the same is selected. Therefore, it can actually be the conductivity part G L and G c The conductivity part G is selected to be the same, that is, to be uniform S Find the structurally consistent, time-discrete switching equation i S,k . Under this premise, what is valid is (Equation 4):

[0054]

[0055] Therefore, it is applicable to the structurally consistent, time-discrete switching equation i S,k or S,k+1 is (Equation 5):

[0056] i S，k+1 =G S v S，k+1 +I S，k+1

[0057] In the described time-discrete equations, the indices for the calculation steps can of course also be moved, so that equation 5 specified for calculation step k+1 can simply be moved to calculation step k in the following way, that is, calculation step k+1 is replaced by calculation step k everywhere, which has the same meaning in terms of content.

[0058] As derived above, one embodiment of the method 1 is characterized in that: i The structurally consistent, time-discrete switching equation i S,k With corresponding switching element T i The uniform conductance G of the conducting and non-conducting switching states s and the current source part I S,k And the current source part I S,kIt is a discrete-time state space expression H, Φ, C that is independent of the switch state. d , D d The additional input and thus the different overall switching state SST i Only through the additional input, the current source part I S,k Be adjusted.

[0059] exist Figure 2 In the power supply part or current source part I S,k Use I SW,k Note that this has its reasons in the improved design of the method 1, which will become apparent later. Figure 2 The time-discrete state space expression H, Φ, C in the switch state is independent d , D d At least we can see from the signal flow diagram that the switch element T i The switching state of the switching element T is only affected by the additional input to the left at the input node of the state space representation (see also the input vector g of the switching element in the feedback path). i The switching on and off of the current source part I S,k Done. Equation 6 states that for a non-conducting switching element T i (off, closed) and the switching element T for conducting i (on, open) Corresponding value:

[0060]

[0061] From equation 6, we know that at the calculation time point k+1, the switching element T i The conducting state of the switch and the switching element T i The current source portion of the non-conducting switch state I S,k The value of the current source part I at the calculation time point k S,k Based on equation 3a, the derivation of the relationship in equation 6 can be expressed, for example, as follows for the non-conducting state off:

[0062]

[0063] Based on the time-discrete current equation for the switch coil, similarly for the switch element T i The on state of the conduction is deduced.

[0064] Equations 5 and 6 can be combined to form the following equation 6a by introducing the switch state variable s i , the switch state variable is equal to 1 in the conducting state and equal to 0 in the non-conducting state:

[0065]

[0066] By replacing the switching element T with an arrangement with an energy store, namely with a switching capacitor 8 and a switching coil 7 in each case, i , the simulation of circuit 2 forcibly generates a transient process associated with it, so that after a certain period of time, until the conducting or non-conducting switching element T i The originally desired static state is produced. An extended embodiment of the method 1 is therefore characterized in that, in order to i The switching state of the switch is changed to shorten the transient transition, and the current source part I S,k With additional pulse current And thus pre-adjustment is achieved. Additional pulse current Preferably, the additional pulse current is not equal to zero only in one calculation step, preferably only in the corresponding switching element T i It acts on the conversion time point.

[0067] exist Figure 3 It is shown how the switching element T can be further improved. i The switch equivalent circuit with the switch coil 7 and the switch capacitor 8 is provided so as to use the additional pulse current Implement the presetting described above. Figure 3 a, the switching element T i The equivalent circuit diagram with the switching coil 7 and the switching capacitor 8 is supplemented by an additional pre-regulated power supply, namely with a parallel pre-regulated current source I FF,k+1 and a series pre-regulated voltage source V FF,k+1 .Depend on Figure 3 a to Figure 3 b Then it can be known that for the switching element T i The L / C equivalent circuit diagram consists of a uniform conductance part G s and the current source part I S,k+1 In addition, node N is at the preset voltage source V FF,k+1 upstream, this is easily accomplished by pre-regulating one of the power supplies, i.e., either the pre-regulating voltage source V FF,k+1 Either pre-adjust the current source I FF,k+1 , is 0 in each switching state. Figure 3 b to Figure 3 c shows that the circuit components can be further merged. Figure 3 b. The node current applicable to node N is (Equation 7):

[0068] i SW，k+1 =G S v S，k+1+I S，k+1 +I FF，k+1

[0069] =G s (v SW，k+1 -V FF，k+1 )+I S，k+1 +I FF，k+1

[0070] This equation can be described as follows Figure 3 The equation of the circuit in c (Equation 8) is transformed:

[0071] i SW，k+1 =G S v SW，k+1 +I SW，k+1

[0072] I SW，k+1 =I S，k+1 +I FF，k+1 -G S V FF，k+1

[0073] Equation 8 above has the same structure as Equation 5. When I of Equation 6a S,k+1 When used in the following equation 8, Figure 3 b relation v S，k+1 =v SW，k+1 -V FF，k+1 When (Equation 9)

[0074]

[0075] Among them, it is applicable to pulse current is (Equation 10):

[0076]

[0077] The result in Equation 10 is derived from Equation 9 with the following mathematical considerations:

[0078]

[0079]

[0080] When the switching element T i When the switch state changes, I SW,k Set to zero and pulse current is activated for the duration of the simulation step. The pulses required for preconditioning are brought about by different pulse intensities according to equation 10.

[0081] For switching element T i Pulse current The strength is calculated as follows, that is, to completely avoid the switching element T i Preferably, the switching element T that shows "important" i — The switching element T with the highest actual or expected switching frequency at the moment i —The current source part I S,k Equipped with additional pulse current

[0082] exist Figure 2 In the calculation unit 3, the time-discrete state space expression H, Φ, C, which is independent of the switch state, has been shown. d , D d It is possible that based on the circuit 2, when using the switching element T i The time-discrete state space representation H, Φ, C, which is independent of the switching state, is directly derived from the equivalent circuit with the switching coil 7 and the switching capacitor 8 and using a discretization scheme, i.e., for example, a discretization scheme according to equation 1. d , D d It may be easier to implement if we first start with a time-continuous state-space representation with the familiar system matrices A, B, C, D.

[0083] As has been shown in detail above, the switching element T i The equivalent circuit with the switch coil 7 and the switch capacitor 8 is used to replace the time-continuous state space expression and the discretization scheme is used to transform the time-discrete state space expression H, Φ, C which is independent of the switch state. d , D d . Use the button alone Figure 3 The switching element T i The equivalent circuit of leads to the following time-continuous and switch-state-independent state-space expression (Equation 11, where the superscript T refers to “transpose”):

[0084]

[0085]

[0086] I SW Contains the switching element T i All currents in the current source part of the L / C equivalent circuit diagram and u L Represents the i The L / C equivalent circuit diagram corrects all other power supplies in circuit 2. SW Including all switching element voltages and i SW Including all switching element currents. Output vector yL Contains all other parameters in circuit 2 that are important for the simulation. SW The output variables in are used to evaluate all switching element currents and switching element voltages in the "switching logic".

[0087] The discretization of the time-continuous and switching state-independent state space representation according to equation 11 using the discretization scheme according to equation 1 leads to the following relationship, namely, the switching state-independent, time-discrete state space representation H, Φ, C according to equation 12 d , D d (T here is the calculation stride from the discretization scheme):

[0088] Φ=(E-γTA) -1 (E+(1γ)·TA),

[0089] H=(Φ·(E-γTA) -1 γ+(E-γTA) -1 (1-γ))TB,

[0090] C d =C,D d =(E-γTA) -1 γTB+D.

[0091] In addition, the relationship according to equation 13 applies here:

[0092]

[0093]

[0094] H, Φ, C d , D d is the time-discrete system matrix, input matrix, output matrix and feedforward matrix. The interaction of all parameters according to signal flow is in Figure 2 In the example, the calculation unit 3 is shown graphically. For the purpose of illustration, the variables involved are calculated discretely in time in the corresponding variables by explicit equations, i.e. without having to solve an algebraic loop by an ambiguous calculation method. Figure 2 A time-delay element 9 is symbolically inserted into the state-space representation of , but this time-delay element is caused by the numerical calculation itself.

[0095] exist Figure 4 In the example, different switching elements T i Figure 1 shows how the “switching logic” works. For the state transition on / off, it must be taken into account that the switching element T i The signal at the control input g is like the corresponding switching element T i The same current exists in Figure 4 The relationship shown in is easy to understand and does not need to be explained in detail.

[0096] As mentioned before, the switching element T i The structurally consistent, time-discrete switching equation i S,k (or i SW,k , taking into account the presetting), with a corresponding switching element T i The unified conductance part G of the conducting switch state and the non-conducting switch state S and the current source part I S,k (or I SW,k , when taking presetting into account). The question arises as to how the switching element T i The structurally consistent, time-discrete switching equation i S,k Specifically choose the uniform conductivity part G S The boundary conditions from equation 4 show that a desirably small value for the capacitance of the switching capacitor 8 is in conflict with a likewise desirably small value for the inductance of the switching coil 7 .

[0097] In order to find the optimal unified conductivity part G S , so that method 1 is designed, that is, when using the conductivity part G S and the current source part I S,k and pulse current when necessary In the case of a specific choice, H, Φ, C are expressed in a time-discrete state space independent of the switch state. d , D d We obtain the system matrix Φ * The concrete, expanded, time-discrete state space representation of , and as a stability parameter, the system matrix Φ * Calculate the eigenvalue λ i . Because the eigenvalue λ i The dynamic characteristics of the total system with time discreteness are given important explanations, so their values ​​are suitable as evaluation indicators of the stability and dynamic characteristics of circuit 2. The system matrix Φ * It can be obtained based on Equation 9, when this equation is expressed as a vector equation, as shown in Equation 14:

[0098]

[0099] The relationship according to equation 15 applies here:

[0100]

[0101]

[0102] The diagonal matrix S contains each switching element T i All switch states s i The diagonal matrix G contains for each individual switching element T i All uniform conductance parts G Si It is therefore possible to provide for each switching element T i Select the respective uniform conductance part G Si , which is different from the remaining switching elements T i All other uniform conductance parts G Si , but it can also be all switching elements T i Select the conductance part G for unity Si The same type of switching element T i It may be more reasonable to use the uniform conductivity part G Si Choose consistent values, especially when they are part of a common assembly, such as a bridge circuit. i (or also in the same type of switching element T i When these switching elements are installed in different assemblies or are mounted differently externally) it may be meaningful to provide a uniform conductance G Si Select values ​​that are different from each other. When replacing the name x used for the state parameter k Now under the name w k When the transition is made identifiable by discretizing the state parameters described in equation 12, the following equation 16 is obtained from equation 12:

[0103]

[0104] and Equation 17

[0105]

[0106] From this, we can deduce that the current source part I SW,k The general state space expression (Equation 18) including the calculation of

[0107]

[0108]

[0109] What applies here is (Equation 19)

[0110]

[0111] In a known manner, this generalized extended system matrix Φ can be * Calculate the eigenvalue λi By targeting the conductivity part G S With a change in the value of , different eigenvalue configurations are obtained, which must be subjected to corresponding evaluation. It can then be inferred based on these evaluations of the eigenvalue configurations that show the most appropriateness that the conductivity part G S Which choice of value is the best?

[0112] In an advantageous further development of the method, it is provided that a desired reference characteristic value λ is predetermined. Refi And by means of the calculation of the quality assessment criterion J, the system matrix Φ is expressed in the state space using the extended time discretization * The eigenvalue λ i and the reference eigenvalue λ Refi Under the condition of i The unified conductance part G of the conducting switch state and the non-conducting switch state S The best choice.

[0113] It is preferred to find the reference characteristic value λ in this way Refi , so that as for each overall switching state SST of circuit 2 i The reference circuit of the invention determines the time-discrete state space representation dependent on the switching state in such a way that the smallest possible values ​​are assumed for the inductance of the switching coil 7 and for the capacitance of the switching capacitor 8, which is only possible if the switching element T is omitted. i Use the corresponding switching element T i The uniform conductance G of the conducting and non-conducting switching states s Under this condition (Equation 4), the system matrix represented by the time-discrete state space associated with the switching state of the reference circuit is given by SST for each overall switching state of circuit 2. i (the index i here refers to the corresponding overall switching state) Calculate the reference characteristic value λ Refi (The index i refers to the corresponding eigenvalue in this case). The calculation of the quality criterion J is performed using the system matrix Φ represented in the expanded, time-discrete state space. * The eigenvalue λ i and the reference eigenvalue λ Refi Under the condition of i The unified conductance part G of the conducting switch state and the non-conducting switch state s The best choice.

[0114] The quality assessment criterion J can be determined, for example, according to the following calculation rule (Equation 20), wherein the index j is calculated over all the overall switching states SST jAnd the index i goes through all the eigenvalues ​​in the corresponding overall switching state:

[0115]

[0116] This quality criterion J involves a general measure of the dynamic deviation, which is represented by the eigenvalues ​​λ of the system matrix in the expanded, time-discrete state space i and the reference eigenvalue λ of the system matrix of the time-discrete state space representation of the reference total circuit related to the switch state Refi In order to make the eigenvalues ​​λ of the system matrix expressed in the expanded, time-discrete state space i and the corresponding reference eigenvalue λ of the system matrix in the time-discrete state space representation associated with the switching state Refi As close as possible, J is minimized as a measure for the dynamic deviation. In the previous examples, the different switching states of the extended, time-discrete state space representation of the reference circuit were also summed.

[0117] exist Figure 5 Finally, a simulator 10 is shown, here a HIL simulator, with a computing unit 3 for simulating a circuit 2, wherein the computing unit 3 is programmed in such a way that the method 1 described above is carried out by the computing unit 3. The simulator 10 is connected to a control 11, which is a physical process 6 in this case, via an I / O interface 5.

[0118] Reference numerals list

[0119] 1 Methods

[0120] 2 Circuit

[0121] 3 Computational Unit

[0122] 4 Description of circuits by mathematical expressions

[0123] 5 I / O Interface

[0124] 6 Physical Processes

[0125] 7 Switch coil

[0126] 8 Switched capacitors

[0127] 9 Time-delay element

[0128] 10. Emulator

[0129] 11 Controller

Claims

1. A computer-implemented method for simulating an electrical circuit by means of at least one computing unit, the electrical circuit having a circuit component including a switching element, the switching element being able to assume a conducting switching state or a non-conducting switching state, wherein: The circuit is described by a mathematical expression, and the circuit is calculated on the calculation unit for each overall switching state by numerically solving the mathematical expression describing the overall switching state, It is characterized in that The conducting switching element in the circuit is represented by the switching coil, and the non-conducting switching element in the circuit is represented by the switching capacitor. The electrical properties of the switching coils and the switching capacitors are described by means of structurally consistent, time-discrete switching equations, so that when using structurally consistent, time-discrete switching equations for the switching elements, a switching-state-independent, time-discrete state space representation H, Φ, C is produced for all overall switching states of the circuit. d , D d , and on the computing unit based on the switch state-independent, time-discrete state space representation H, Φ, C for all overall switch states of the circuit d , D d Perform simulation, where H is the system matrix, Φ is the input matrix, C d is the output matrix, D d is the feedforward matrix, wherein the structurally consistent, time-discrete switching equation for the switching element has a current source part, and In order to shorten the transient transitions when the switching state of the switching element changes, the current source part has an additional pulse current and thus achieves a pre-regulation.

2. The method according to claim 1, characterized in that The structurally consistent, time-discrete switching equation for the switching element has a unified conductance part for the conductive switching state and the non-conductive switching state of the corresponding switching element, and the current source part is an additional input of the time-discrete state space expression that is independent of the switching state, so that different overall switching states can be adjusted only by influencing the additional input, i.e., influencing the current source part.

3. The method according to claim 2, characterized in that At calculation time k+1, the value for the current source portion in the conductive switching state of the switching element and in the non-conductive switching state of the switching element depends at least on the value of the current source portion at calculation time k.

4. The method according to claim 2 or 3, characterized in that The pulse current is not equal to zero only in one calculation step.

5. The method according to claim 4, characterized in that The pulse current acts only at the switching time of the corresponding switching element.

6. The method according to any one of claims 1 to 3, characterized in that The intensity of the pulse current for the switching element is calculated in such a way that transient transitions are completely avoided when the switching state of the switching element changes.

7. The method according to any one of claims 1 to 3, characterized in that The additional pulse current is allocated to the current source part of the switching element having the highest actual or expected switching frequency.

8. The method according to claim 2 or 3, characterized in that: Using specific choices for the conductance component and the current source component, a specific, expanded, time-discrete state-space representation of the system matrix is ​​obtained from the time-discrete state-space representation that is independent of the switching state, and eigenvalues ​​are calculated from the system matrix as stability parameters.

9. The method according to claim 2 or 3, characterized in that: Using a specific selection for the conductance portion and the current source portion and the pulse current, a specific, expanded, time-discrete state-space representation of the system matrix is ​​obtained from the time-discrete state-space representation that is independent of the switching state and eigenvalues ​​are calculated from the system matrix as stability parameters.

10. The method according to claim 7, characterized in that A time-discrete state-space representation associated with the switching state is determined as a reference circuit for each overall switching state of the circuit in the following manner, i.e., the minimum possible values ​​are adopted for the inductance of the switching coil and the capacitance of the switching capacitor, and reference eigenvalues ​​are calculated from a system matrix of the time-discrete state-space representation associated with the switching state of the reference circuit for each switching state of the circuit, and an optimal selection of a unified conductance component for the conducting switching state and the non-conducting switching state of the corresponding switching element is determined by calculation of a quality assessment criterion using the eigenvalues ​​of the system matrix of the expanded time-discrete state-space representation and the reference eigenvalues.

11. The method according to claim 7, characterized in that A time-discrete state-space representation associated with the switching state is determined as a reference circuit for each overall switching state of the circuit in the following manner, i.e., while abandoning the condition of using a unified conductance component for the conductive switching state and the non-conductive switching state of the corresponding switching element for the switching element, the minimum possible values ​​are adopted for the inductance of the switching coil and the capacitance of the switching capacitor, and reference eigenvalues ​​are calculated from a system matrix of the time-discrete state-space representation associated with the switching state of the reference circuit for each switching state of the circuit, and the best selection of the unified conductance component for the conductive switching state and the non-conductive switching state of the corresponding switching element is determined by calculation of a quality assessment criterion using the eigenvalues ​​of the system matrix of the expanded time-discrete state-space representation and the reference eigenvalues.

12. The method according to claim 10 or 11, characterized in that From the sum of the differences between the characteristic values ​​of the expanded, time-discrete state space representation and the corresponding reference characteristic values ​​of the time-discrete state space representation of the reference total circuit, which is dependent on the switching state, an overall measure for the dynamic deviation is calculated as a quality assessment criterion and an overall stability parameter is minimized.

13. The method according to claim 12, characterized in that In addition, the different switching states of the reference circuit are summed up in a time-discrete state-space representation that is dependent on the switching state.

14. A simulator having a computing unit for simulating a circuit, wherein: The arithmetic unit is programmed with a program in such a way that the arithmetic unit carries out the method according to any one of claims 1 to 13 when the program is run.

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