Presentation on theme: "Announcements Be reading Chapter 6."— Presentation transcript:
0 ECE 476 POWER SYSTEM ANALYSIS Lecture 11Ybus and Power FlowProfessor Tom OverbyeDepartment of Electrical and Computer Engineering
1 Announcements Be reading Chapter 6. HW 4 is 3.4, 3.10, 3.14, 3.19, 3.23, 3.60; due September 29 in class.First exam is October 11 during class. Closed book, closed notes, one note sheet and calculators allowed
2 Multiple Solution Example 3 The dc system shown below has two solutions:where the 18 wattload is a resistiveloadWhat is themaximumPLoad?
3 Bus Admittance Matrix or Ybus First step in solving the power flow is to create what is known as the bus admittance matrix, often call the Ybus.The Ybus gives the relationships between all the bus current injections, I, and all the bus voltages, V, I = Ybus VThe Ybus is developed by applying KCL at each bus in the system to relate the bus current injections, the bus voltages, and the branch impedances and admittances
4 Ybus Example Determine the bus admittance matrix for the network shown below, assuming the current injection at eachbus i is Ii = IGi - IDi where IGi is the current injection into thebus from the generator and IDi is the current flowing into theload
6 Ybus Example, cont’d symmetric matrix (i.e., one where Aij = Aji) For a system with n buses, Ybus is an n by nsymmetric matrix (i.e., one where Aij = Aji)
7 Ybus General FormThe diagonal terms, Yii, are the self admittance terms, equal to the sum of the admittances of all devices incident to bus i.The off-diagonal terms, Yij, are equal to the negative of the sum of the admittances joining the two buses.With large systems Ybus is a sparse matrix (that is, most entries are zero)Shunt terms, such as with the p line model, onlyaffect the diagonal terms.
13 Power Flow AnalysisWhen analyzing power systems we know neither the complex bus voltages nor the complex current injectionsRather, we know the complex power being consumed by the load, and the power being injected by the generators plus their voltage magnitudesTherefore we can not directly use the Ybus equations, but rather must use the power balance equations
17 In the News: Renewable Energy Finance Last week IEEE Spectrum had an opinion piece on how wind, water and solar could power the world.The piece was very sparse on financial detailsYesterday the News—Gazette had an article on the difficulties the first US offshore wind farm, Cape Wind, has in attracting customersNational Grid is buying one half of their output at an average cost of 24 cents per kWh ($240/MWh!!)Without committed buyers Cape Wind is unlikely to find financing for the full $2.6 billion project (454 MWs of capacity)