ECEN 460 Power System Operation and Control

1. ECEN 460Power System Operation and Control Lecture 5: The Synchronous Machine Adam Birchfield Dept. of Electrical and Computer Engineering Texas A&M University abirchfield@tamu.edu Material gratefully adapted with permission from slides by Prof. Tom Overbye.

2. High Voltage Transmission Line Worker Source: www.youtube.com/watch?v=LIjC7DjoVe8

3. Three Bus PowerWorld Simulator Case Load with green arrows indicating amount of MW flow Note the power balance at each bus Used to control output of generator Direction of green arrow is used to indicate direction of real power (MW) flow; the blue arrows show the reactive

4. Power Balance Constraints • Power flow refers to how the power is moving through the system. • At all times in the simulation the total power flowing into any bus must be zero! • This is known as Kirchhoff’s law. And it can not be repealed or modified. • Power is lost in the transmission system.

5. Basic Power Control • Opening or closing a circuit breaker causes the power flow to instantaneously(nearly) change. • No other way to directly control power flow in a transmission line • Phase shifting transformers do provide some limited control options • By changing generation or load, or by switching other lines, we can indirectly change this flow.

6. Modeling Consideration – Change is Not Really Instantaneous! • The change isn’t really instantaneous because of propagation delays, which are near the speed of light; there also wave reflection issues • This is covered in chapters 5 and 13 but isn’t part of 460 Red is the vs end, green the v2 end

7. Transmission Line Limits • Power flow in transmission line is limited by heating considerations. • Losses (I2 R) can heat up the line, causing it to sag. • Each line has a limit; Simulator does not allow you to continually exceed this limit. Many utilities use winter/summer limits.

8. Overloaded Transmission Line

9. Announcements • Read book chapters 4 and 5 • First in-class quiz 9/13 • Covers any material through 9/6 • Lab 2 will be Friday Sept. 14, Monday Sept. 17, and Tuesday Sept. 18. • Career fair this week • Chevron Phillips presenting at end of class today • MISO info session with pizza, Thursday 4-6 pm in CHEN room 104

10. Machines: generators and motors • Electric machines are used to convert energy • Generators: mechanical into electrical • Motors: electrical into mechanical • Many devices can operate in either mode, but are usually customized for one or the other • Vast majority of electricity is generated using synchronous generators and some is consumed using synchronous motors • Much literature on subject, and sometimes overly confusing with the use of different conventions and nomenclature

11. Stator and rotor • Stator • The part of the machine that does not move • Contains sets of windings or “armature windings” surrounding the rotor • Rotor • Internal part of the machine that rotates • Separated from the stator by airgap • Also has one or more windings or “field windings” • There may be some electrical connection between the spinning rotor windings and the stator • Occasionally the rotor is a permanent magnetic, but this limits control of the machine

12. Main types of ac machines • Synchronous • Rotor windings have dc current powered separately • Stator is connected to the machine terminals • In steady state, rotor speed stays in-synch with the electrical frequency (i.e., some constant multiple) • Induction • Rotor windings are shorted through an impedance • Stator is connected to the machine terminals • In steady state, the rotor speed may vary from the electrical frequency according to a “slip” • Both can be 1 phase or 3 phase

13. Three-phase synchronous machines • Our focus today is on three-phase synchronous machines. • The three stator windings have a three-phase voltage. In a motor or interconnected generator this voltage is supplied. In a stand alone generator it is induced. • The stator ac electrical currents are arranged to create a rotating magnetic field. • The rotor dc current creates a constant magnetic field which mechanically spins “in synch” with the stator field.

14. Diagram of synchronous machine 3 bal. windings (a,b,c) – stator Field winding (fd) on rotor Damper in “d” axis (1d) on rotor 2 dampers in “q” axis (1q, 2q) on rotor

15. Round and salient pole rotors • Machines may have multiple pole pairs • With more poles, the rotor can spin slower than the stator electrical frequency • Round rotor • Air gap is constant, usually with higher speed machines • Salient pole rotor • Air gap varies circumferentially • Used with slow, many-pole machines such as hydro

16. Rotor examples • Rotors are essentially electromagnets Two pole (P)round rotor Six pole salient rotor Image Source: Dr. GlebTcheslavski, ee.lamar.edu/gleb/teaching.htm

17. Large salient rotor example High polesalient rotor Shaft Part of exciter,which is usedto control the field current Image Source: Dr. GlebTcheslavski, ee.lamar.edu/gleb/teaching.htm

18. Magnetic flux

19. Flux linkages and Faraday’s law

20. 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)

21. 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 • all flux is within the coil • all flux links each turn

22. Inductance example, cont’d Let N=100, A=0.0006 m2, R=0.03 m,mr=1000; then L is0.04 H;

23. Creating a voltage in an open-circuited generator • With zero stator current, the only flux is due to the field current • When the generator is at standstill, the flux linking each coil depends on its angle relative to the rotor’s position (and hence the field winding) • The three phases are physically shifted by 120 degrees from each other The maximumflux depends on the field current

24. Creating a voltage in an open-circuited generator • No voltage is generated at standstill • Now assume the rotor is spinning at a uniform rate, w = 2pf, so

25. Creating a voltage in an open-circuited generator • Then by Faraday’s law a voltage is induced

26. Creating a voltage in an open-circuited generator • For a linear magnetic circuit we can also write this as proportional to field current The negative signcould be removedwith a change inthe assumedpolarity

27. Magnetic saturation and hysteresis • A linear magnetic circuit assumes the flux density B is always proportional to current, but real magnetic materials saturate Magnetization curves of 9 ferromagnetic materials, showing saturation. 1.Sheet steel, 2.Silicon steel, 3.Cast steel, 4.Tungsten steel, 5.Magnet steel, 6.Cast iron, 7.Nickel, 8.Cobalt, 9.Magnetite; highest saturation materials can get to around 2.2 or 2.3T H is proportional to current Image Source: en.wikipedia.org/wiki/Saturation_(magnetic)

28. Magnetic saturation and hysteresis • Magnetic materials also exhibit hysteresis, so there is some residual magnetism when the current goes to zero; design goal is to reduce the area enclosed by the hysteresis loop To minimize the amountof magnetic material,and hence cost andweight, electric machinesare designed to operateclose to saturation Image source: www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/BHCurve.gif

29. Frequency Impacts • Assuming no saturation, the generated voltage is then proportional to frequency • To create the same voltage with less flux, we just need to increase the frequency; this is why aircraft operate at a higher frequency (e.g., 400 Hz) • When controlling motors with variable frequency, common control is to use constant volt/Hz, preventing saturation

30. Synchronous machines with output current • When operating with an output current, the terminal voltage is not equal to the internally generated voltage • This is due to several factors • Resistance in the stator windings • Self-inductance in the stator windings • Distortion of the air-gap magnetic field due to the stator current; that is, the stator current induces a magnetic field • Salient pole characteristics of the machine • The stator reactance is called the synchronous reactance, XS, and is sometimes broken into two parts Xl is due to the windingself inductance

31. A synchronous machine model • This gives us the following per phase model, which can be helpful in considering how the steady-state real and reactive output of the machine changes with changes in the field current • This model is not particularly good for saturation and understanding the generator’s dynamic response, something we’ll revisit later

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