An improved recursive Fourier algorithm for numerical relays

Computation burden of non-recursive Fourier algorithm is well-known heavy, limiting its application in numerical relays. Although recursive form of Fourier algorithm reduces computation burden greatly, errors caused by finite word-length effect and truncated data bits seriously affect accuracy and long-term stable operation because the errors will be cumulated step by step. Based on sources and characteristic analysis of cumulative errors mentioned above, the paper proposes an improved method calculating alternatively using recursive and non-recursive forms to minimize cumulative errors. Moreover, employing distribution and synchronous calculation technology for weighted product terms, the improved method maintains inherent advantages of recursive algorithm, whose calculation amount only increases 2 additions compared with continuous recursive algorithm. The proposed method is applied in busbar protection and substation-area protection for smart substation requiring access of large number of analog channels. Digital simulation and prototype long-term running experiments show that the improved method can effectively reduce cumulative errors and drastically decrease computation burden in comparison to non-recursive algorithm. © 2016, Power System Technology Press. All right reserved.