[{"key":"dc.contributor.author","value":"Calvin\u0303o-Fraga, Jesu\u0301s","language":null},{"key":"dc.date.accessioned","value":"2009-11-17T00:00:00","language":null},{"key":"dc.date.available","value":"2009-11-17T00:00:00","language":null},{"key":"dc.date.issued","value":"2003","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/15027","language":null},{"key":"dc.description.abstract","value":"This report presents the development of a new family of difference equations for the\r\nnumerical solution of systems of differential equations arising in electric power circuits. The\r\nmain advantage of these difference equations is their adjustability, which allows for the\r\ntuning of the resulting formulas while using large time steps. The tuned formulas have been\r\nused successfully in the time-domain simulation of 50\/60-Hz solutions of electric power\r\ncircuits for linear and non-linear problems. The linear steady state and the non-linear power\r\nflow problems can be solved, with no error either in magnitude or in phase, at a comparable\r\ncomputational cost to traditional techniques such as the well-known phasor analysis and\r\nNewton-Raphson iterations. Additionally, the techniques developed do not use complex\r\nnumbers, resulting in a faster matrix factorization for linear systems, or a smaller Jacobian\r\nmatrix for non-linear systems. The main advantage of the proposed techniques is that due to\r\nthe time-domain nature of the simulation, where the transition from one time solution to the\r\nnext represents a small transition between states, the technique is able to closely follow the\r\ntrajectory of the system even for ill-conditioned power flow problems where traditional\r\nNewton-Raphson iterations fail to converge, such as when the system buses are beyond or\r\nnear the point of voltage collapse. With the proposed novel formulas, the computational cost\r\nof generating PV curves across all busses of the power system network is greatly reduced,\r\nand the resulting curves clearly show the point of voltage collapse as well as any unstable\r\nvoltage\/power combination thereafter. The ability to quickly obtain PV curves makes the\r\nproposed techniques particularly well suited for online power system monitoring of operating states. Also, since these new difference equations introduce very little error for frequencies\r\nlower than the tuned frequency, they are also well suited for the solution of dynamic power\r\nflow problems such as those resulting from loads variation, transformers tap change, and\r\noutages.","language":"en"},{"key":"dc.format.extent","value":"4700737 bytes","language":null},{"key":"dc.format.mimetype","value":"application\/pdf","language":null},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":null},{"key":"dc.rights","value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","language":null},{"key":"dc.title","value":"Tunable difference equations for the time-domain simulation of power system operating states","language":"en"},{"key":"dc.type","value":"Text","language":null},{"key":"dc.degree.name","value":"Doctor of Philosophy - PhD","language":"en"},{"key":"dc.degree.discipline","value":"Electrical and Computer Engineering","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":null},{"key":"dc.date.graduation","value":"2003-11","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Applied Science, Faculty of","language":null},{"key":"dc.description.affiliation","value":"Electrical and Computer Engineering, Department of","language":null},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]