ECE 476 POWER SYSTEM ANALYSIS

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

2. Reading and Homework • 1st 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/GloverSarmaSimdwnldv15.asp

3. Substation Bus

4. 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 = Pactual,tie-flow - Psched

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

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

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

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

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

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

14. 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. MISO and PJM MISO and PJM arethe reliabilitycoordinatorscovering theelectric gridin Illinois. ComEd is inPJM, and Ameren is inMISO.

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

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

18. Primary Methods for Power Transfer • The most common methods for transfer of electric power are • Overhead ac • Underground ac • Overhead dc • Underground dc • other

19. 345 kV+ Transmission Growth at a Glance

20. 345 kV+ Transmission Growth at a Glance

21. 345 kV+ Transmission Growth at a Glance

22. 345 kV+ Transmission Growth at a Glance

23. 345 kV+ Transmission Growth at a Glance

24. Magnetics Review • Ampere’s circuital law:

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

27. Magnetic Flux

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

30. Flux linkages and Faraday’s law

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

32. 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. Inductance Example, cont’d

34. 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. Flux Linkages outside of the wire

36. Flux Linkages outside, cont’d

37. Flux linkages inside of wire

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

39. Line Total Flux & Inductance

40. Inductance Simplification