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Bus admittance matrix is widely used in power engineering for modelingnetworks. Being highly sparse, it requires fewer CPU operations when used forcalculations. Meanwhile, sparse matrix calculations involve numerous indexingand scalar operations, which are unfavorable to modern processors. Withoutusing the admittance matrix, nodal power injections and the correspondingsparse Jacobian can be computed by an element-wise method, which consists of ahighly regular, vectorized evaluation step and a reduction step. This paperrevisits the admittance matrix from the computational performance perspectiveby comparing it with the element-wise method. Case studies show that theadmittance matrix method is generally slower than the element-wise method forgrid test cases with thousands to hundreds of thousands of buses, especially onCPUs with support for wide vector instructions. This paper also analyzes theimpact of the width of vector instructions and memory speed to predict thetrend for future computers.

Bus Admittance Matrix Revisited: Is It Outdated on Modern Computers?