Patent ID: 7490026

Claim:
A method for simulating an electrical network, whereby the inconsistencies in a system of differential equations of the electrical network are detected by the following steps: providing a computer system including a memory, an arithmetic unit, an input device and an output device; providing a system of equations describing the electrical network, the equations having the form f (t, x (t), {dot over (x)} (t), . . . , x (k) (t), p )= 0 , including: f 1 ⁡ ( t , x _ ⁡ ( t ) , x . _ ⁡ ( t ) , … ⁢ , x _ ( k ) ⁡ ( t ) , p _ ) = 0 , f 2 ⁡ ( t , x _ ⁡ ( t ) , x . _ ⁡ ( t ) , … ⁢ , x _ ( k ) ⁡ ( t ) , p _ ) ≂ 0 , ⋮ f n ⁡ ( t , x _ ⁡ ( t ) , x . _ ⁡ ( t ) , … ⁢ , x _ ( k ) ⁡ ( t ) , p _ ) = 0 , wherein x (t) and derivatives {dot over (x)} (t), . . . , x (k) thereof in each case have m number of_elements, and p is a parameter vector that can occur in the system of equations; and executing a test method for providing error information relating to inconsistencies in the system of equations on the computer system, the test method having the following steps 1 to 3: step 1: setting up a dependence matrix A with m number of columns and n number of rows, and setting an element A to A (i, j)≠0 when an i th row of f (t, x (t), {dot over (x)} (t), . . . , x (k) (t),p) defined with f i (t, x (t), {dot over (x)} (t), . . ., x (k) (t)) is a function of a) a j th element of x expressed as x j (t); or b) one of the derivatives of the j th element of x defined as x j (s) (t); and otherwise setting the element A (i, j)=0; step 2: determining a set of row ranks each having the numbers of those rows of the dependence matrix A that are mutually dependent and determining a set of column ranks of the dependence matrix A each having the numbers of those columns of the dependence matrix A that are mutually dependent if such row ranks and/or column ranks are present; and step 3: outputting at the output device error information containing the numbers contained in each row rank determined in step 2 and in each column rank determined in step 2; wherein the row rank includes a set C 2 of natural numbers i, where 1≦i≦n, of the matrix A with the n number of rows and the m number of columns when it fulfils the conditions of: i) no transversal T of the matrix A such that C z is contained in the set of row indices of T, and ii) for each element c of C z there is a transversal T of the matrix A such that C z \{c} is wholly contained in the set of the row indices of T, and the column rank comprises a set C s of natural numbers i, where 1≦i≦m, of the matrix A with the n number of rows and the m number of columns when it fulfils the conditions of: i) no transversal T of the matrix A such that C s is contained in the set of row indices of T, and ii) for each element c of C s there is a transversal T of the matrix A such that C s \{c} is wholly contained in the set of the column indices of T.