Speed Governor EEE 576
Popular in Power System Dynamics
Popular in Electrical Engineering
This 40 page Class Notes was uploaded by Shammya Saha on Sunday April 3, 2016. The Class Notes belongs to EEE 576 at Arizona State University taught by Dr. Vittal in Fall 2015. Since its upload, it has received 17 views. For similar materials see Power System Dynamics in Electrical Engineering at Arizona State University.
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Date Created: 04/03/16
EEE 576 Spring 2016 Power System Dynamics Lecture 8 1 Speed Governing The basic function of a governor is to control speed and/or load. In a steam or hydraulic turbine- generator system, the governing is accomplished by a speed transducer, a comparator, and one or more force- stroke amplifiers. 2 A block diagram for a steam turbine generator is shown below. The speed governor is a speed transducer. The output of this is typically the position (stroke) of a rod that is proportional to speed. The stroke is compared mechanically to a preset reference. 3 This gives a position error that is proportional to speed error. The force corresponding to this position error is small and must be amplified in both force and stroke. The speed relay and the servo motor perform this function. This same schematic also applies to a hydraulic system if the valve position is changed to a gate position and the steam valve block is replaced by a wicket gate and hydro turbine system. 4 The speed transducer is the critical component of the governor system. It must measure shaft speed and provide an output signal in appropriate form – position, pressure, or voltage, for comparison against the reference. The speed transducer can be a mechanical, hydraulic, or an electronic device. 5 Flyball Governor This governor is depicted in the following figure. We will develop a model for it to describe the procedure followed. 6 7 Assume gravitational force <<< Centrifugal Force F C Two forces act on the flyballs: Outward centrifugal force F on the masses C Downward spring force F on the throttle rod S Reference position r corresponds to the desired speed. Figure 10.5 and equation 8 2 2mv F C R v R Shaft angular velocity N F 2mN R 2 2 N C b x1 Rd x C r a R d C xr b C r a Leverconstant ratio F C 2mN d C x r 2 Now writing Newton'slawfor the ball-head 9 F F mx 1 Forces C Bx 1 s 2 2 1 1 2 F ssin 2 Fsasin 1 K s x Fs Fs C r C r K Springconstant s Substituting the expressionfor the forces 2mx 2Bx K s x 2mN d C x 2 1 1 C r r 10 Now x C x Substituting thisweget 1 r 2mN 2 K s d C xr 2mx 2Bx K x s C r K s WhereK s C 2 r Linearizing theaboveequationsusing x x0 x 0 r r0 r And at thequiescentpoints x x 0 0 0 11 2mN 2 2 K s 0 d C xr 0 0 K x s 0 C r Thisgives 2 K r 4mN 0 d C x 2mx 2Bx K 2mN x 2 2 s C r 0 s 0 r The ballheadforceF acCsin the x dire1tionon the totalmass2m. Thiscreatesan equivalentforcein the x direction,which wecall F C F C F 2mN C 2 d C x 2 C r c r r 12 F K x K C x F K x C 2mN C r 0 x 0 FC 2 K 4mN C r d C xr 0 0 0 K K x K rs 2 2mx 2x K s 2 x C r C r K K K s 2 K s 2 x C r C r K s K K K xs x 13 + 1 2 ' r - 2ms 2Bs s Kx x ' K 14 The flyball governor senses change in speed and responds by making a small change in displacement or stroke (x). The force corresponding to the stroke is too small to move a throttle mechanism. Hence a force- stroke amplifier is needed to magnify the stroke and exert sufficient force to manipulate the valve. This is done by a hydraulic amplifier or servomotor. 15 Isochronous Governor The piston shown in the figure is capable of exerting a large linear Force. The equations for the flyball governor are the same as before, except that a new force, the hydraulic reaction force due To the pilot valve must be added. 16 Thesteady-statehydraulic reactionforcecan be written as: F K x h h K r K K K x K x ' K x s s x h g ' K gK Ks K x h The hydraulic piston movesin the y directionaslongas thereisa positive x -displacement of thepilot valve. 17 This motionisgovernedby K q a y 1 K K K K y s q r q (*) K a K a g 1 g 1 Itisconvenienttonormalizetheaboveequation on the basisof thefullload rating of thegeneratordesignated by R. 18 x r x pu r pu u x u r R R y y pu pu u yR u R K K r K y s s q R r R u K a y s u K r u g 1 R s R Assumesystemisinitiallyatsteadystatei.e., y 0 and at ratedfullloadcondition r r when theload R issuddenlydropped,causinga changeinspeedof R rad/s R R 19 Substitutinginto(*) K s q K q 0 rR R R K g 1 K g 1 K 1 R C K r R g s R r C g K g 1 R y s u u , 1 u 1s K s rq R 20 This results in an integrating governor system and is described by the figure below and is called the Isochronous governor since it attempts to integrate the speed error until the error vanishes. 21 Performance of Governor The governor is the control system that senses speed output from the generator and then controls the turbine input in order to raise or lower speed. In order to study the performance of the governor it is important to develop the incremental equations of the controlled plant. 22 We are also interested in the behavior only in the neighborhood of the steady-state operating point. Weneeda generalrelationship for theplant transfer functionG s pnd thedisturbancefunction N s for 23 Fluid flow rateW through the valveisproportional to the product of valvearea Aand fluid pressureP W k AP Valvearealinearlyrelated tostroke y W kyP W W W k y k P y P 24 Assuming pressureto beconstant W k y y K 1 Tm 1 ss 2H m T e D pu Suppose K C G 0 ,CK N 0 N K H 0 H K P G 0 ,PK A 0 A K A K C P ss K N v P ss C ss 1 K KCK P H 1 K C K P H 25 For the Isochronousgovernor Lim K K C s 0 1 1 1 s s Since K C the error must be zerofor steady state operation.This isa unique charactristicof any integral controlsystem.This impliesthat followingany deviationinspeedthe controller willdrivethe system until r &C areequalor g the steadystatespeedisindependent of loadtorque. 26 Thesteadystateperformancefor zeroerroris given by 1 r Rr ss C ss ss g Thesteadystatevalueof is a constantfor anyT e 27 The transientresponseof theIsochronousgovernor canbeevaluatedby plotting theroot locus OLTF K 1 g K 1s 1ss D2Hs s sb sc 28 The Speed Droop Governor Although the Isochronous governor has good steady state characteristic it has a sluggish response and nearly unstable for reasonable values of gain. In order to counter this effect a more effective control scheme using proportional control rather than integral control is used. 29 This is achieved using mechanical feedback via the “Summing Beam” x’ Summing beam 30 Continuing with theequationsdevelopedfor the Isochronousgovernorwehavefor thesumof forces in the x -direction K x x K x K x K 0 ' s x h ' K s K Kx hx K x s K g K K s K x h ' K g K x sK 31 From thesummingbeam,forsmalldisplacements a b x y r L L L a b Ksa Ksb ' K g y r K L L For thehydraulic piston K x a y q 1 K a g 1 y K s y K s r K K L L q 32 Normalizingand rearranging a1K g brR KL R s 1 y us ru u aK s q ay R aK s R Now consider thesystemisatfullloadand atsteady stateratedspeed 0 y y R r r y 0 R s Ks rR a yR rR y R b 33 Coefficient of r u in the normalizedequationis1. Now removetheload.Allow thespeed toincreasebut hold r t thesameposition.We then getatsteadystate r r R y y R SpRedchangegoingfromfullload tono load R R K s ' 0 rR K R R L 34 K s r K R L R R a R yR b aK R s y R KLR Thecoefficient of uin the normalizedequation is C 1 g R 1 s y r C 1 g a K L 1 g 1 aK s q 35 The block diagram is then given by 1 Wenow notethat theIsochronousintegrator 1 hasbeen trans formedinto anamplifier 1 1 1 by meansof mechanicalfeedback t hrough thesumming a beam. 1anbeadjustedbychanging L 36 Wecan now analyze the steady-state performanceof the speeddroopgovernor as wedidbeforefor the Isochronousgovernor with K 1, K 1, K K , K 1 A N C 1 P D, K H C g K1 ss T ess Then ss D K C1 g D K C1 g for the speeddroopgovernor. 37 is a function of both reference setting r and generator ss ss loadT ess AsT increases e ss In steadystate T m ss K e1 ssr C 1 ss g ss 38 K 1 g K OLTF 1 1 1 s s2Hs sa sb sc a 1 , b 1 , c D K K1C g 1 s 2H, 2H 1 s 1 s s 2 1 This governor is widely used for steam turbines and 39 The poles of the speed droop governor have much larger negative real parts than the Isochronous governor. The system can hence be operated at much higher values of gain with improved damping and smaller settling time. 40
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