  The bus admittance matrix is central to many power system simulation
algorithms, but the link between problem size and computation time (i.e., the
time complexity) using modern sparse solvers is not fully understood. It has
recently been suggested that some popular algorithms used in distribution
system power flow analysis have cubic complexity, based on properties of dense
matrix numerical algorithms; a tighter theoretical estimate of complexity using
sparse solvers is not immediately forthcoming due to these solvers'
problem-dependent behaviour. To address this, the time complexity of admittance
matrix-based distribution power flow is considered empirically across a library
of 75 networks, ranging in size from 50 to 300,000 nodes. Results across four
admittance matrix-based methods suggest complexity coefficient values between
1.04 and 1.12, indicating complexity that is instead almost linear. The
proposed empirical approach is suggested as a convenient and practical way of
benchmarking the scalability of power flow algorithms.
