1. Lecture 5 Power System Operation, Transmission Lines Professor Tom Overbye Department of Electrical and Computer Engineering ECE 476 POWER SYSTEM ANALYSIS

2. 1 Reading and Homework 1 st Exam moved to Oct 11 (in class) For lectures 4 through 6 please be reading Chapter 4 – we will not be covering sections 4.7, 4.11, and 4.12 in detail though you should still at least skim those sections. HW 1 is 2.9, 22, 28, 32, 48; due Thursday 9/8 For Problem 2.32 you need to use the PowerWorld Software. You can download the software and cases at the below link; get version 15. http://www.powerworld.com/gloversarma.asp Direct PowerWorld download page is http://www.powerworld.com/DemoSoftware/GloverSarmaSimdwnl dv15.asp

3. 2 Substation Bus

4. 3 Power Transactions Power transactions are contracts between areas to do power transactions. Contracts can be for any amount of time at any price for any amount of power. Scheduled power transactions are implemented by modifying the area ACE: ACE = P actual,tie-flow - P sched

5. 4 100 MW Transaction Scheduled 100 MW Transaction from Left to Right Net tie-line flow is now 100 MW

6. 5 Security Constrained ED Transmission constraints often limit system economics. Such limits required a constrained dispatch in order to maintain system security. In three bus case the generation at bus 3 must be constrained to avoid overloading the line from bus 2 to bus 3.

7. 6 Security Constrained Dispatch Dispatch is no longer optimal due to need to keep line from bus 2 to bus 3 from overloading

8. 7 Multi-Area Operation If Areas have direct interconnections, then they may directly transact up to the capacity of their tie-lines. Actual power flows through the entire network according to the impedance of the transmission lines. Flow through other areas is known as “parallel path” or “loop flows.”

9. 8 Seven Bus Case: One-line System has three areas Area left has one bus Area right has one bus Area top has five buses

10. 9 Seven Bus Case: Area View System has 40 MW of “Loop Flow” Actual flow between areas Loop flow can result in higher losses Scheduled flow

11. 10 Seven Bus - Loop Flow? 100 MW Transaction between Left and Right Transaction has actually decreased the loop flow Note that Top’s Losses have increased from 7.09MW to 9.44 MW

12. 11 Pricing Electricity Cost to supply electricity to bus is called the locational marginal price (LMP) Presently some electric makets post LMPs on the web In an ideal electricity market with no transmission limitations the LMPs are equal Transmission constraints can segment a market, resulting in differing LMP Determination of LMPs requires the solution on an Optimal Power Flow (OPF)

13. 12 3 BUS LMPS - OVERLOAD IGNORED Line from Bus 1 to Bus 3 is over-loaded; all buses have same marginal cost Gen 1’s cost is $10 per MWh Gen 2’s cost is $12 per MWh

14. 13 LINE OVERLOAD ENFORCED Line from 1 to 3 is no longer overloaded, but now the marginal cost of electricity at 3 is $14 / MWh

15. 14 MISO and PJM MISO and PJM are the reliability coordinators covering the electric grid in Illinois. ComEd is in PJM, and Ameren is in MISO.

16. 15 MISO LMPs 8/31/11 at 11:05 AM www.midwestmarket.org

17. 16 Development of Line Models Goals of this section are 1) develop a simple model for transmission lines 2) gain an intuitive feel for how the geometry of the transmission line affects the model parameters

18. 17 Primary Methods for Power Transfer The most common methods for transfer of electric power are 1) Overhead ac 2) Underground ac 3) Overhead dc 4) Underground dc 5) other

19. 18 18 345 kV+ Transmission Growth at a Glance

20. 19 19 345 kV+ Transmission Growth at a Glance

21. 20 20 345 kV+ Transmission Growth at a Glance

22. 21 21 345 kV+ Transmission Growth at a Glance

23. 22 22 345 kV+ Transmission Growth at a Glance

24. 23 Magnetics Review Ampere’s circuital law:

25. 24 Line Integrals Line integrals are a generalization of traditional integration Integration along the x-axis Integration along a general path, which may be closed Ampere’s law is most useful in cases of symmetry, such as with an infinitely long line

26. 25 Magnetic Flux Density Magnetic fields are usually measured in terms of flux density

27. 26 Magnetic Flux

28. 27 Magnetic Fields from Single Wire Assume we have an infinitely long wire with current of 1000A. How much magnetic flux passes through a 1 meter square, located between 4 and 5 meters from the wire? Direction of H is given by the “Right-hand” Rule Easiest way to solve the problem is to take advantage of symmetry. For an integration path we’ll choose a circle with a radius of x.

29. 28 Single Line Example, cont’d For reference, the earth’s magnetic field is about 0.6 Gauss (Central US)

30. 29 Flux linkages and Faraday’s law

31. 30 Inductance For a linear magnetic system, that is one where B=  H we can define the inductance, L, to be the constant relating the current and the flux linkage = L i where L has units of Henrys (H)

32. 31 Inductance Example Calculate the inductance of an N turn coil wound tightly on a torodial iron core that has a radius of R and a cross-sectional area of A. Assume 1) all flux is within the coil 2) all flux links each turn

33. 32 Inductance Example, cont’d

34. 33 Inductance of a Single Wire To development models of transmission lines, we first need to determine the inductance of a single, infinitely long wire. To do this we need to determine the wire’s total flux linkage, including 1.flux linkages outside of the wire 2.flux linkages within the wire We’ll assume that the current density within the wire is uniform and that the wire has a radius of r.

35. 34 Flux Linkages outside of the wire

36. 35 Flux Linkages outside, cont’d

37. 36 Flux linkages inside of wire

38. 37 Flux linkages inside, cont’d Wire cross section x r

39. 38 Line Total Flux & Inductance

40. 39 Inductance Simplification