A new method for fast calculation of Jacobian matrices: automatic differentiation for power system simulation

Many numerical methods used in power system simulation require the computation of Jacobian matrices. This being particularly true for implicit integration algorithms, and not for explicit ones. These computations often take a significant proportion of the overall CPU time. This paper presents an application of the automatic differentiation method which results in large savings in the computation of Jacobian matrices. An original application of this method is in a software which simulates power systems dynamics. As the program enables the users to introduce their own models, automatic differentiation becomes particularly efficient. In comparison with numerical differentiation, it leads to a saving of 80% of the time required for the computation of the Jacobian matrices and up to 28% of the total CPU time. Automatic differentiation is a very efficient method which should be valuable to other power system software, in particular those which offer users the possibility of defining their own models