Power System Dynamics and Stability Lecture Summary

ECE 576 Power System Dynamics and Stability Lecture 12: Exciters Prof. Tom Overbye Dept. of Electrical and Computer Engineering University of Illinois at Urbana-Champaign overbye@illinois.edu 1

Announcements Homework 3 is due now Homework 4 is on the website and is due on March 6 Read Chapter 4 Midterm exam is on March 13 in class Closed book, closed notes You may bring one 8.5 by 11" note sheet You do not need to write down block diagrams or the detailed synchronous machine equations; I'll give you what you need here Simple calculators allowed 2

Wind Cut-outs, 2/17/14 Plot-0 105 102 MW 103 HMW 28 MPH 80 60 40 20 0 -20 2/17/2014 12:00:00 AM 24.00 hours 2/18/2014 12:00:00 AM PAL_WIND-PWD - AVA GEN MW - AGC PRIMARY PAL_WIND-35KV GEN MW - POTENTIAL MAX GEN PAL_WIND-INSTANTANEOUS AVG WIND SPEED Graph provided by Tracy Rolstad, Avista 3

GenRou, GenTPF, GenTPJ Figure compares gen 4 reactive power output for the 0.1 second fault 4

Voltage and Speed Control ( , P ) ( ) Q, V

Exciters, Including AVR Exciters are used to control the synchronous machine field voltage and current Usually modeled with automatic voltage regulator included A useful reference is IEEE Std 421.5-2005 Covers the major types of exciters used in transient stability simulations Continuation of standard designs started with "Computer Representation of Excitation Systems," IEEE Trans. Power App. and Syst., vol. pas-87, pp. 1460-1464, June 1968 Another reference is P. Kundur, Power System Stability and Control, EPRI, McGraw-Hill, 1994 Exciters are covered in Chapter 8 as are block diagram basics 6

Functional Block Diagram Image source: Fig 8.1 of Kundur, Power System Stability and Control 7

Types of Exciters None, which would be the case for a permanent magnet generator primarily used with wind turbines with ac-dc-ac converters DC: Utilize a dc generator as the source of the field voltage through slip rings AC: Use an ac generator on the generator shaft, with output rectified to produce the dc field voltage; brushless with a rotating rectifier system Static: Exciter is static, with field current supplied through slip rings 8

Brief Review of DC Machines Prior to widespread use of machine drives, dc motors had a important advantage of easy speed control On the stator a dc machine has either a permanent magnet or a single concentrated winding Rotor (armature) currents are supplied through brushes and commutator Equations are di v i R L dt di v i R L G i dt The f subscript refers to the field, the a to the armature; is the machine's speed, G is a constant. In a permanent magnet machine the field flux is constant, the field equation goes away, and the field impact is embedded in a equivalent constant to Gif f = + f f f f = + + a a a a a m f Taken mostly from ECE 330 book, M.A. Pai, Power Circuits and Electromechanics 9

Types of DC Machines If there is a field winding (i.e., not a permanent magnet machine) then the machine can be connected in the following ways Separately-excited: Field and armature windings are connected to separate power sources For an exciter, control is provided by varying the field current (which is stationary), which changes the armature voltage Series-excited: Field and armature windings are in series Shunt-excited: Field and armature windings are in parallel 10

Separately Excited DC Exciter (to sync mach) d 1 f = + e r i N 1 1 in f in f 1 1 dt 1 = 1 is coefficient of dispersion, modeling the flux leakage 1 1 a f 1 11

Separately Excited DC Exciter Relate the input voltage, ein1, to vfd f 1 = = v K K fd a1 1 a1 a1 1 1 N K f 1 1 = N v f 1 f 1 fd Assuming a constant speed 1 a1 N K 1 d dv dt dv f 1 f 1 1 fd = N f 1 dt a1 1 N K f 1 1 fd = + e i r in in f 1 dt 1 1 a1 1 12

Separately Excited DC Exciter If it was a linear magnetic circuit, then vfd would be proportional to in1; for a real system we need to account for saturation v ( )fd v fd = + in i f v sat fd 1 K 1 g Without saturation we can write K N = a1 1 K L g1 f 1us f 1 1 Where is the L f 1us unsaturated field inductance 13

Separately Excited DC Exciter d 1 f = + e r i N 1 1 1 in f in f dt 1 Can be written as r e K L dv dt ( ) 1 1 f f us K fd = + + v r f v v 1 in fd f sat fd fd 1 1 1 g g This equation is then scaled based on the synchronous machine base values v X R X R fd = = md md E V fd fd V fd fd BFD 14

Separately Excited Scaled Values r L 1 1 f f us K g K T E E K sep 1 1 g Xmd V fd BFD V e 1 R in R ) ( V R BFD fd Xmd S E r f E 1 E fd f sat fd Vr is the scaled output of the voltage regulator amplifier Thus we have ) ( dEfd dt = + + T K S E E V E E E fd fd R sep 15

The Self-Excited Exciter When the exciter is self-excited, the amplifier voltage appears in series with the exciter field Note the additional Efd term on the end ) ( dEfd dt = + + + T K S E E V E E E E fd fd R fd sep 16

Self and Separated Excited Exciters The same model can be used for both by just modifying the value of KE ( E E E fd T K S E dt dE ) ( ) fd = + + E V fd R = = 1 typically .01 K K K E E E self sep self 17

Saturation A number of different functions can be used to represent the saturation The quadratic approach is now quite common = 2 ( ) ( ) S E B E A E fd fd 2 ( ) B E A fd E = An alternative model is ( ) S E E fd fd Exponential function could also be used ( ) B E = S E A e x fd E fd x 18

Exponential Saturation ( ) 5 . 0 E fd = 1 . 0 S E e = 1 K E fd E 5 . + 1 E fd Steady state = 1 . V e E R fd 19

Exponential Saturation Example Given: = .05 KE = 0.27 S E E fd max = .75 0.074 S E E fd max = 1.0 VR max = 6 . 4 E fd max , and A B E = Find: . 0015 A x x fd x max B xE fd = S A e = . 1 14 B E x x 20

Voltage Regulator Model dV dt Amplifier R = + T V K V Modeled as a first order differential equation A R A in min R V max R V V R V In steady state R = = V V V ref t in K A K V V Big A t ref There is often a droop in regulation 21

Feedback This control system can often exhibit instabilities, so some type of feedback is used One approach is a stabilizing transformer N dI 2 1 t = Large Lt2 so It2 0 V L F tm N dt 1 22

Feedback dI ( ) 1 t = + + E R I L L 1 1 1 fd t t t tm dt dE dV R N L fd 1 2 F t tm 1 = + V F ( ) + dt L L N R dt 1 1 t tm t 1 K T F F

IEEE T1 Exciter This model was standardized in the 1968 IEEE Committee Paper with Fig 1 shown below 24

IEEE T1 Evolution This model has been subsequently modified over the years, called the DC1 in a 1981 IEEE paper (modeled as the EXDC1 in stability packages) Note, KE in the feedback is the same as the 1968 approach Image Source: Fig 3 of "Excitation System Models for Power Stability Studies," IEEE Trans. Power App. and Syst., vol. PAS-100, pp. 494-509, February 1981 25

IEEE T1 Evolution In 1992 IEEE Std 421.5-1992 slightly modified it, calling it the DC1A (modeled as ESDC1A) VUEL is a signal from an under- excitation limiter, which we'll cover later Same model is in 421.5-2005 Image Source: Fig 3 of IEEE Std 421.5-1992 26