Solving the load flow problem using Gröbner basis

ABSTRACT

In Electrical Engineering one of the most important problems to be solved for electrical networks is the load flow problem [6] [3]. Currently numerical solutions are provided by Newton's method, which involves recomputing the solution whenever the input data change. Given that this problem must be solved very often with different input data, the Gröbner basis can be an interesting approach since it can, in principle, provide a more algebraic solution of the input parameters and has to be solved completely only once, supplying formulas to compute single simulations. In this paper the basic ideas and a practical example are reported. Nevertheless, the required computations for practical network sizes are very complex and cannot yet be solved with the present algorithms.

REFERENCES

• 1: David A. Cox , John Little , Donal O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics), Springer-Verlag New York, Inc., Secaucus, NJ, 2007
• 2: [2] L.L. FRERIS AND A.M. SASSON, Investigation on the load- flow problem, Proc. IEE (London), 115, (1968), 1459-1470.
• 3: [3] CH. GROSS, "Power System Analysis", John Wiley & Sons, 1986.
• 4: D. Lazard, Solving zero-dimensional algebraic systems, Journal of Symbolic Computation, v.13 n.2, p.117-131, Feb. 1992 [doi>10.1016/S0747-7171(08)80086-7]
• 5: [5] A. MONTES, Numerical conditioning of zero dimensional Gröbner bases, Universitat Politcnica de Catalunya, Dept. Matemtica Aplicada 2, Research Report MA2-IR-94-008, (1994).
• 6: [6] G.W. STAGG, "Computer Methods in Power System Analysis", Mc. Graw-Hill, 1968.
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INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Electronics

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
  G.2 DISCRETE MATHEMATICS
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
  I.6 SIMULATION AND MODELING

General Terms:
Algorithms, Measurement, Performance, Theory