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The bus admittance matrix is central to many power system simulationalgorithms, but the link between problem size and computation time (i.e., thetime complexity) using modern sparse solvers is not fully understood. It hasrecently been suggested that some popular algorithms used in distributionsystem power flow analysis have cubic complexity, based on properties of densematrix numerical algorithms; a tighter theoretical estimate of complexity usingsparse solvers is not immediately forthcoming due to these solvers'problem-dependent behaviour. To address this, the time complexity of admittancematrix-based distribution power flow is considered empirically across a libraryof 75 networks, ranging in size from 50 to 300,000 nodes. Results across fouradmittance matrix-based methods suggest complexity coefficient values between1.04 and 1.12, indicating complexity that is instead almost linear. Theproposed empirical approach is suggested as a convenient and practical way ofbenchmarking the scalability of power flow algorithms.

Demonstrating Almost Linear Time Complexity of Bus Admittance Matrix-Based Distribution Network Power Flow: An Empirical Approach