Powe system analysis by grainger

POWER SYSTEM ANALYSIS McGraw-Hill Series in Electrical and Computer Engineering Senior Consulting Editor Stephen W Director, Carnegie-Mellon University Circuits and Systems Communications and Signal Processing Computer Engineering Control Theory Electromagnetics Electronics and VLSI Circuits Introductory Power alld Eflergy Radar and An tennas Previous Consulting Editors Ronald N Bracewell, Colin Cherry, James F Gibbons, Willis W Harman, Hubert Heffn er, Edward W Herold, John G Linvill, Simon Ramo, Ronald A Rohrer, Anthony E Siegman, Charles Susskind, Frederick E Terman, John G Truxal, Ernst Weber, and John R Whinnery Power and Energy Senior Consulting Editor Stephen W Director, Carnegie-Mellon University Chapman: Ele c tric Machinery Fundamentals Fitzgerald, Kingsley, and Umans: Electric Machinery Elgerd: Electric Energy Systems Theory Gonen: Electric Power Distribution System Engineering and Stevenson: Power System Analysis Krause and Wasynczuk: Electromechanical Motion Devices Stevenson: Elements of Power System Analysis Gr ainger Also available from McGraw-Hill Schaum's Outline Series in Electronics & Electrical Engineering Most outlines include basic theory, definitions and hundreds of example problems solved in step-by-step detail, and supplementary problems with answers Related titles on the current list include: Circuit A n alysis An alog & Digita l Communications Basic Basic Electrical Engineering Basic Mathematics for Electricity & Electronics Basic Electricity Digital Principles Electric Circliits Electric Machines & Electromt'c/zallics Electric Power System,\ Eleclrolnagllclics Llcctl"Ollic Circuits EleClrollic Commllnic(I{ion Electronic Dccias & Cirelli/s Eleccronics TecIII IO/OJ:,T)' Ellgilleering Ecol/omics FCI'dhuck & Conrrol Systems Ill/roell/Clioll 10 Digila! Systems Aficroprlarquette University, and North Profes�or Grainger has aho «llight at the of University Wisconsin­ ity Supply Board of Ireland; Commonwealth Edison Company, Chicago; \Vis­ consin Electric Po\vcr Company, MilwaUKee; and Carolina Pmver & Light Company, Raleigh Dr Grainger is an active consullant with t h e Pacific Gas and El e ct ric Company, San Francisco; Southern California Edison Company, Rose­ mead; a n d mimy other power industry organizJtions His educational ane! Carolina State University His industrial experience has been with the Electric­ Am eri c a n Society of Engineering Education, the American Power Conference, technical involvements erRED, and CIGRE include the IEEE Povv'cr Engineering Society, The Dr Grainger is the aut h or of numerous papers in the IEEE Power Engineering So c i e ty ' s Transactiotls and was recognized by the IEEE Transmis­ s ion and Distribution Committee for the 1985 Prize Paper Award In 1984, P ro fessor Grainger was chosen by the Edison Electric Institute for the EEl Power Engineering Ed u ca tor Award William D Stevenson, Jr (deceased) was a professor and the As oci at e Head of the Electrical Engineering De p a rt m e n t of N ort h Carolina State University A Fellow of the I n sti tu te of Electrical and Electronics E ng i n ee r s , he worked in private industry and taught at both Clemson U ni v e rs i ty and P r inc e t on Univer­ s en?ineering for t h e McGraw-HilI Encyc!opedin of Science and Technology, He was the recipient of several teaching and professional awards, sity Dr Stevenson also served as a consulting editor in electrical power B.2 SPARSITY OF THE JACOBIAN 775 from which the new jacobian elements and the power mismatches of ' the second iteration are calculated The final converged solution is shown in Fig 9.4 Because of the order in which we have solved the mismatch equations of this ex amp le nO fill-ins have occurred and the zero elements of the original j acobian are repeated in the triangular matrices L and U The elements 0.000 appearing in U are actually the result of truncating the numerical results to d isplay only three significant decimal figures It is straightforward to confirm that the numerical product of L and U e q u a l s the original jacobian matrix within the rou nd-off accu racy d isplayed , INDEX ABCD constants, 201 i n circle-di agram equations, 216, for networks (table), 753 in power-flow equa tions, Acceleration factors, 339 A d mittance: branch, 240 drivi n g point, 32 equival ent admi ttance, ne twork, 25 -255 mutual of nodes, 32 in pow e r Il o w s tu d ies, 329, admi ttance, ;IS d a t