PPT-Non-Linear Programming © 2011 Daniel Kirschen and University of Washington

Author : calandra-battersby | Published Date : 2018-02-26

1 Motivation Method of Lagrange multipliers Very useful insight into solutions Analytical solution practical only for small problems Direct application not practical

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Non-Linear Programming © 2011 Daniel Kirschen and University of Washington: Transcript


1 Motivation Method of Lagrange multipliers Very useful insight into solutions Analytical solution practical only for small problems Direct application not practical for reallife problems because these problems are too large. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations (Part 2). Daniel Kirschen. Optimization . with . inequality constraints. Objective function. Equality constraints. Inequality constraints. © 2011 D. Kirschen and University of Washington. 2. Example: Economic Dispatch. (Part 1). Daniel Kirschen. Economic . d. ispatch problem. Several generating units serving the load. What share of the load should each generating unit produce?. Consider the limits of the generating units. and . Ancillary Services. © 2011 D. Kirschen and the University of Washington. 1. Introduction. Participants in electricity . markets rely on the power system infrastructure. All participants, but especially consumers, . Daniel Kirschen. 1. © 2011 D. Kirschen and the University of Washington. Perspectives. The investor’s perspective. Will a new plant generate enough profit from the sale of energy to justify the investment?. LP formulation of Economic Dispatch. © 2011 D. Kirschen & the University of Washington. 1. 1. 2. 3. L. x. 1. P. 1. MAX. x. 2. P. 2. MAX. x. 3. P. 3. MAX. P. 1. MIN. P. 2. MIN. P. 3. MIN. Objective function is linear . © 2011 Daniel Kirschen and University of Washington. 1. Motivation. Many optimization problems are linear. Linear objective function. All constraints are linear. Non-linear problems can be linearized:. and . Ancillary Services. © 2011 D. Kirschen and the University of Washington. 1. Introduction. Participants in electricity . markets rely on the power system infrastructure. All participants, but especially consumers, . Daniel . Kirschen. © 2011 Daniel Kirschen and the University of Washington. 1. Economic . Dispatch: Problem Definition. Given load. Given set of units on-line. How much should each unit generate to meet this load at minimum cost?. © 2011 Daniel Kirschen and University of Washington. 1. Which one is the real maximum?. © 2011 Daniel Kirschen and University of Washington. 2. x. f(x). A. D. Which one is the real optimum?. © 2011 Daniel Kirschen and University of Washington. on Electricity Markets. © 2011 D. Kirschen and the University of Washington. 1. Introduction. No longer assume that all generators and loads are connected to the same bus. Need to consider:. Congestion, constraints on flows. 1. Participating in Electricity . Markets. Perspective. Generator. Consumer. Retailer. Operator of a pumped-hydro plant. © 2011 D. Kirschen and the University of Washington. 2. Participating in . Electricity Markets. The Desired Brand Effect Stand Out in a Saturated Market with a Timeless Brand

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