Method and configuration for computer-aided determination of a system relationship function

A computer-aided method for describing electrical currents flowing between connections of a set of coupled linear components and non-linear components, the method which comprises the following steps:

• a) defining a differential equation system with equations for a set of coupled linear components;
• b) determining a predeterminable number of eigenvalues for a homogeneous differential equation system of the differential equation system;
• c) determining an error for the eigenvalues with respect to an error criterion obtained by ignoring all the eigenvalues of the homogeneous differential equation system;
• d) determining whether the error is less than a predetermined limit;
• e) if the error is not less than the limit, defining further eigenvalues and repeating the method steps b) to d) with the further eigenvalues until the error is less than the limit;
• f) if the error is less than the limit, defining the system relationship function from the equations of the differential equation system described by the determined eigenvalues;
• and
• g) outputting the system relationship function as an indication of the state of the set of coupled linear components at the connections of the electrical circuit.

A computer-aided method for describing differentiations of the electrical currents in an electrical circuit with linear components and non-linear components, the method which comprises the following steps:

• a) defining a differential equation system with equations for a set of coupled linear components;
• b) determining a predeterminable number of eigenvalues for a homogeneous differential equation system of the differential equation system;
• c) determining an error for the eigenvalues with respect to an error criterion obtained by ignoring all the eigenvalues of the homogeneous differential equation system;
• d) determining whether the error is less than a predetermined limit;
• e) if the error is not less than the limit, defining further eigenvalues and repeating the method steps b) to d) with the further eigenvalues until the error is less than the limit;
• f) if the error is less than the limit, defining the system relationship function from the equations of the differential equation system described by the determined eigenvalues;
• and
• g) outputting the system relationship function as an indication of the state of the set of coupled linear components at the connections of the electrical circuit.

In a configuration for determining a system state of coupled linear components of an electrical circuit with an arbitrary number of non-linear components and linear components, a computer unit comprising:

• a device for determining a differential equation system for a set of coupled linear components of an electrical circuit;
• a device for determining a predetermined number of eigenvalues for a homogeneous differential equation system of the differential equation system;
• a device for determining an error with respect to an error criterion obtained by ignoring all the eigenvalues of the homogeneous differential equation system;
• a checking device for checking whether the error is less than a predetermined limit, whereby
• if the error is not less than the predetermined limit, said device for determining the eigenvalues defines further eigenvalues until the error is less than the limit, and
• if the error is less than the predetermined limit, the system relationship function is defined from those equations of the differential equation system which are described by the determined eigenvalues, and
• an output device for outputting the system relationship function as an indication of the state of the set of coupled linear components at the connections of the electrical circuit.

A configuration for determining a system state of coupled linear components of an electrical circuit having an arbitrary number of non-linear components and linear components, comprising:

• a computer having an output device, said computer being programmed to:
• define a differential equation system with equations for a set of coupled linear components;
• determine a number of eigenvalues for a homogeneous differential equation system of the differential equation system;
• determine an error for the eigenvalues with respect to an error criterion obtained by ignoring all the eigenvalues of the homogeneous differential equation system;
• determine whether the error is less than a predetermined limit;
• if the error is not less than the limit, define further eigenvalues and repeat the process with the further eigenvalues until the error is less than the limit;
• if the error is less than the limit, define the system relationship function from the equations of the differential equation system described by the determined eigenvalues;
• and
• output the system relationship function as an indication of the state of the set of coupled linear components at the connections of the electrical circuit on said output device.