Energy Systems

, Volume 1, Issue 3, pp 273–289 | Cite as

Numerical methods for on-line power system load flow analysis

  • Siddhartha Kumar KhaitanEmail author
  • James D. McCalley
  • Mandhapati Raju
Original Paper


Newton-Raphson method is the most widely accepted load flow solution algorithm. However LU factorization remains a computationally challenging task to meet the real-time needs of the power system. This paper proposes the application of very fast multifrontal direct linear solvers for solving the linear system sub-problem of power system real-time load flow analysis by utilizing the state-of-the-art algorithms for ordering and preprocessing. Additionally the unsymmetric multifrontal method for LU factorization and highly optimized Intel® Math Kernel Library BLAS has been used. Two state-of-the-art multifrontal algorithms for unsymmetric matrices namely UMFPACK V5.2.0 and sequential MUMPS 4.8.3 (“Multifrontal Massively Parallel Solver”) are customized for the AC power system Newton-Raphson based load flow analysis. The multifrontal solvers are compared against the state-of-the-art sparse Gaussian Elimination based HSL sparse solver MA48. This study evaluates the performance of above multifrontal solvers in terms of number of factors, computational time, number of floating-point operations and memory, in the context of load flow solution on nine systems including very large real power systems. The results of the performance evaluation are reported. The proposed method achieves significant reduction in computational time.


Load flow analysis Linear solvers Multifrontal methods MUMPS UMFPACK MA48 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Siddhartha Kumar Khaitan
    • 1
    Email author
  • James D. McCalley
    • 1
  • Mandhapati Raju
    • 2
  1. 1.Department of Electrical and Computer EngineeringIowa State UniversityIowaUSA
  2. 2.Optimal Inc.PlymouthUSA

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