Gain Matrix Distributed Computing Technique for Power System State Estimation

Abstract

The Electric Power System State Estimation problem involves large sparse matrices. The Jacobian matrix is highly sparse in nature and the computational efforts can be enhanced by avoiding arithmetic operations resulting in 'zero'. The researchers have introduced sparse matrix techniques so as to store only non-zero elements of the matrix and thereby reducing the huge dynamic memory requirements, which intern reduce the computational time. A few such techniques This paper elaborates a different technique to obtain the "effective operation" with the focus on the computational time and the storage space reduction. The "effective operation" can be achieved without applying conventional compact storage techniques to find the Jacobian product. A different style for multiplication of two large sparse Jacobian matrices is adopted to obtain this novel approach. As a result, computational time is reduced and also Jacobian array size is reduced form two dimensional array to single dimensional array. The solution gives scope for distributed/parallel computing without disturbing the network structure [6].

Power system Vertical Division State Estimation (VDSE) – A parallel processing technique

“…Hence, in ideal case, for 'm' number of measurements m-number of processors can be used to find A 1 to A m independently. On the basis of above discussions it can be seen that Jacobian two dimension memory size is now reduced to one dimension array and also multiple processors can be used to increase the computational speed [11]. The step by step analysis of ISE and JPSE is given in the Appendix 4, Sections 4.1e4.2.…”

“…If the number of processors is also increased proportionally with the increase in the system (network) bus/node, then the Computational time required to compute for [A] does not increase. It has been observed that the computational time required by this (Jacobian parallel computing) method is much less than the conventional method even if single processor is employed [11]. It can be proved that ½A ¼ ðJ T *W*JÞ ¼ P m j¼1 ½A m .…”

“…Having sufficient measurements available at each node area, using the Equations (9) and (10), the Equation (1) can be re-written as ðAÞ NAk Dx NAk ¼ ðbÞ NAk (11) where 'NA k ' refers to kth node area and Dx NAk is the state vector corresponds to kth node area.…”

“…It can be proved that ½A ¼ ðJ T *W*JÞ ¼ P m j¼1 ½A m . Hence, both methods (conventional and Jacobian parallel computing) are mathematically same, only the change is in computing style [11].…”