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

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. 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. 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. Motivation. Method of Lagrange multipliers. Very useful insight into solutions. Analytical solution practical only for small problems. Direct application not practical for real-life problems because these problems are too large. (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, . 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 . of Electricity Markets. Daniel . Kirschen. Differences between electricity and other commodities. Electricity is inextricably linked with a physical delivery system. Physical delivery system operates much faster than any market. © 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. 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. © 2011 D. Kirschen and the University of Washington. 1. Let us go to the market.... © 2011 D. Kirschen and the University of Washington. 2. Opportunity for buyers and sellers to:. compare prices. estimate demand.