A Feasibility Study of Direct-Mapping-Type Parallel Processing Method to Solve Linear Equations in Load Flow Calculations Hiroaki Inayoshi, Non-member

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A Feasibility Study of Direct-Mapping-Type Parallel Processing Method to Solve Linear Equations in Load Flow Calculations Hiroaki Inayoshi, Non-member (University of Tsukuba), Yasuharu Ohsawa, Member (Kobe University), Takuya Homma, Member (University of Tsukuba) Owing to the growing size and complexity in power systems, system analysis, such as the transient calculation, take much time hence fast calculation methods are required. Although the parallel processing is a hopeful method, there was a difficulty in the parallel solution of the linear equation which appears in the power-flow calculation through the Newton-Raphson method. This paper aims at the fast calculation of the power-flow ploblem via parallel processing. In order to improve the suitability to the parallel solution of the differential equation in transient calculation, we assume the use of a direct-mapping-type parallel processing machine, which directly maps the network of a power system onto the network of processors. Under this assumption, we propose a new parallel-processing-oriented method, where the linear equation is solved by linear-iterations between nodes with the Aitken acceleration. We simulate the method on three model power systems and compare this Parallel Iterative Method (PIM) with a Parallel Direct Method (PDM), which uses the banded matrix, according to the number of operations required. As the results, we can expect that the PIM may solve the linear equations faster than the PDM with m processors, although the PIM might be inferior to the PDM with mxm processors, where m denotes the half band-width of the banded matrix.

870 T. IEE Japan, Vol. 111-B, No. 8, '91

Fig. 1. PAD representation of parallel iterative method. Fig. 2. Convergence of linear iteration (one-dimension). Fig. 3. Graphic explanation for Aitken acceleration. 872 T. IEE Japan, Vol. 111-B, No. 8, '91

Fig. 4. PAD representation of the algo rithm to calculate both x(v) and accerelat ed y(v) simultaneously.

Fig. 5. Process flow in one node. 874 1 IEE Japan, Vol. 111-B, No. 8,'91

Fig. 7. Result of simulation for 118-node system. Fig. 6. Result of simulation for 39-node system. Fig. 8. Result of simulation for 283-node system.

Table 1. Number of nodes etc for 3 model systems. 876 T. IEE Japan, Vol. 111-8, No. 8, '91

(3) S. Narita, et al.: "A Parallel Processing Algorithm for Fast Load-Flow and Stability Calculations", 7th PSCC, 0.1078 (1981) (5) Han Zhenxiang, et al.: "Parallel Load Flow Algorithm Studies in Power Systems", 9th PSCC, p. 927 (1987) (6) A. Abur : "A Parallel Scheme for the Forward/Backward Substitutions in Solving Sparse Linear Equations", IEEE Trans. Power Systems, 3, 1471 (1988) (8) J. Ward & H. Hale "Digital computer solution of power flow problems", Trans. Amer. Inst. Elect., Power Apparat us Syst.), 75, 398 (1956-6) pany : On-line stability analysis study RP70-1 for the Edison Electric Institute (1970) (11) North American Rockwell Information Systems Com

878 T. IEE Japan, Vol. 111-B, No. 8, '91

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