ECE4762011_Lect17 - ECE 476 POWER SYSTEM ANALYSIS Lecture...

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Lecture 17 Economic Dispatch, OPF, Markets Professor Tom Overbye Department of Electrical and Computer Engineering ECE 476 POWER SYSTEM ANALYSIS
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2 Announcements Be reading Chapter 7 HW 7 is 12.26, 12.28, 12.29, 7.1 due October 27 in class. US citizens and permanent residents should consider applying for a Grainger Power Engineering Awards. Due Nov 1. See http://energy.ece.illinois.edu/grainger.html for details. The Design Project, which is worth three regular homeworks, is assigned today; it is due on Nov 17 in class. It is Design Project 2 from Chapter 6 (fifth edition of course). For tower configuration assume a symmetric conductor spacing, with the distance in feet given by the following formula: (Last two digits of your UIN+50)/9. Example student A has an EIN of xxx65. Then his/her spacing is (65+50)/9 = 12.78 ft.
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3 Inclusion of Transmission Losses The losses on the transmission system are a function of the generation dispatch. In general, using generators closer to the load results in lower losses This impact on losses should be included when doing the economic dispatch Losses can be included by slightly rewriting the Lagrangian: G 1 1 L( , ) ( ) ( ( ) ) m m i Gi D L G Gi i i C P P P P P λ = = = + + - P
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4 Impact of Transmission Losses G 1 1 G This small change then impacts the necessary conditions for an optimal economic dispatch L( , ) ( ) ( ( ) ) The necessary conditions for a minimum are now , ) ( ) m m i Gi D L G Gi i i i Gi Gi C P P P P P dC P P d λ = = = + + - = P P 1 ( ) (1 ) 0 ( ) 0 L G Gi Gi m D L G Gi i P P P P P P P P = - - = + - =
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5 Impact of Transmission Losses th i i Solving each equation for we get ( ) ( ) (1 0 ( ) 1 ( ) 1 Define the penalty factor L for the i generator 1 L ( ) 1 i Gi L G Gi Gi i Gi Gi L G Gi L G Gi dC P P P dP P dC P dP P P P P P P λ - - = = - ÷ = - ÷ The penalty factor at the slack bus is always unity!
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6 Impact of Transmission Losses 1 1 1 2 2 2 i Gi The condition for optimal dispatch with losses is then ( ) ( ) ( ) 1 Since L if increasing P increases ( ) 1 ( ) the losses then 0 1.0 This makes generator G G m m Gm L G Gi L G i Gi L IC P L IC P L IC P P P P P P L P λ = = = = - ÷ i i appear to be more expensive (i.e., it is penalized). Likewise L 1.0 makes a generator appear less expensive. <
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7 Calculation of Penalty Factors i Gi Unfortunately, the analytic calculation of L is somewhat involved. The problem is a small change in the generation at P impacts the flows and hence the losses throughout the entire system. However, Gi using a power flow you can approximate this function by making a small change to P and then seeing how the losses change: ( ) ( ) 1 ( ) 1 L G L G i L G Gi Gi Gi P P P P L P P P P P -
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8 Two Bus Penalty Factor Example 2 2 2 ( ) ( ) 0.37 0.0387 0.037 10 0.9627 0.9643 L G L G G Gi P P P P MW P P MW L L - = - = = - =
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9 Thirty Bus ED Example Because of the penalty factors the generator incremental costs are no longer identical.
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ECE4762011_Lect17 - ECE 476 POWER SYSTEM ANALYSIS Lecture...

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