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# EEE 576 Lecture 4 EEE 576

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This 35 page Class Notes was uploaded by Shammya Saha on Wednesday February 17, 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 74 views. For similar materials see Power System Dynamics in Electrical Engineering at Arizona State University.

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Date Created: 02/17/16

EEE 576 Power System Dynamics Lecture 4 1 This approach can be applied to other exciters to obtain appropriate models. The IEEE STD421.5-1992 recommends the following model for an ac exciter (excluding rectification). The general structure is similar to the dc exciter. 2 No load voltage determined by the saturation function S defined by no load E saturation curve This accounts for armature reaction demagnetizing effects 3 S (V ) A B 4 E E B As in the case of dc exciters the expression for V XV SE E ) Es the exponential function. Three-phase full-wave bridge rectifier circuits are commonly used to rectify the ac exciter output voltage. Effective ac source impedance seen by rectifier is predominantly inductive reactance (known as commutating reactance) The effect of this reactance is to delay the transfer of current from one valve to the other. 5 This reduces average output voltage of the rectifier as its load current increases E FD F EX E K c FD FEX f (IN) IN V E Kcdepends on the commutating reactance. The rectifier operates in one of 3 distinct modes as its load current varies from no load – short circuit level. The mode of operation depends on the commutating voltage drop. 6 The function f(N ) characterizing the three modes of rectifier circuit operation are 1: f (IN) 1.0 .0577 I N If I N 0.433 2 2: f (I N 0.75 I N If 0.433 I N.75 3: f (N ) 1.732(1.0 I ) N If 0.75 I N.0 See: R.L. Witzke, J.V. Kresser, & J.K. Dillard, “Influence of AC Reactance on Voltage Regulation of 6-Phase Rectifiers,” AIEE Trans., Vol. 72, pp.244-253, July 1953. & IEEE STD 421.5 for details 7 INshould not be > 1. If for some reason it is > 1 then F EX should be set to zero. 8 Amplifiers – can be magnetic, rotating, or electronic Transfer function of an Amplidyne is as shown Magnetic and electronic amplifiers characterized by a gain and may also include a time constant. Amplifier output limited by saturation or power- supply limitations This is represented by “non-windup” limits V RMAX & V RMIN 9 Integrator with Windup Limits dv u dt If L N v L x , then y v If , then y L v L x x y L If v L N , then N The variable v is not limited . y cannot come off a limit until v comes within the limit. 10 Integrator with Non-Windup Limits dy u dt dy If L N y L x , then u dt dy dy If y Lxand dt 0 , then setdt 0 , y L x If y L and dy 0 , then setdy 0 , y L N dt dt N Here the output variable is limited. It comes off the limit as 11 Windup Limit Applied to a Single Time Constant Block dv u v dt T If L N v L x , then y v If v L x , then y L x If v L N , then y L N 12 Non Wind Up Limit Applied to Single Time Constant Block f u y T dy If L N y L x , then f dt If y Lx and f 0 , then dy 0 ,y L x dt dy If y L and f 0 , then 0 ,y L N N dt 13 Gating Functions – Also known as auctioneering function. Used to give control to one of the two input signals Low value High value Depending on their relative size with respect to each other. 14 Modeling of Complete Excitation Systems The figure on the following slide shows the general structure of a detailed excitation system model. It has one-to-one correspondence with the physical equipment. Such detail not needed for system studies. Model reduction techniques are used to simplify the models. Parameters of the reduced model are selected such that the gain and phase characteristics of the reduced model matches the detailed model over 0-3Hz range. 15 16 IEEE has standardized 12 model structures in block diagram form. Intended for use in transient stability and small-signal stability studies. 17 The principal input signal to each excitation system is the output V cf the voltage transducer At the first summing point the signal V is scbtracted from the voltage reference V REF & the other signals. This produces the actuating signal. 18 The actuating signal controls the excitation system. Additional signals such as the underexcitation limiter output (V UEL) come into play only during extreme or unusual conditions. 19 Type DC2A Represents field controlled dc commutator exciters with continuously acting voltage Voltage transducer Stabilizing feedback Regulators having supplies obtained from the generator or auxiliaries bus, the voltage regulator limits are proportional to terminal voltage V T 20 AC1A – Field Controlled Alternator – Rectifier Excitation System This is proportional to field current 21 Type AC5A – Brushless Excitation System Regulator supplied from a source such as a permanent magnet generator that is not affected by system disturbances 22 Type ST2A – Uses both current and voltage sources to form the power sources. Rectifier loading and commutating effects taken into account. EFDMAX represents limit on the exciter voltage due to saturation of the magnetic components. 23 Type ST3A This utilizes a field voltage control loop to linearize exciter control characteristics. 24 Terminal Voltage Transducer and Load Compensator T R Rectification and filtering of the synchronous machine terminal voltage R C X – Compensated impedance V t I –tre in phasor form V cs the principal control signal to the excitation system 25 Block Diagram for Excitation System Assume 0.1 1.0 K 0.05 A G E 0.5 0.05 E R K A40 K G1.0 26 V t KG(s) V REF [1 KG(s)H(s)] Neglecting Saturation KG(s) K A G (1 s)(K s)(1 s) A E E G K H(s) R 1 s R K K (1 s) V t A G R VREF (1 s)(K s)(1 s)(1 s) K K K A E E G R A G R 27 Open loop transfer function = KGH+1 K A G R 40K R (1 A)(K E s)E1 s)G1 s)R (10.1s)(0.050.5s)*(10.05s)(1 s) K 400K K K A G R K (s 10)(s .01)(s 1)(s 20) 28 The response is dominated by the generator and exciter poles very close to the origin. This requires compensation that will bend the locus to a more favorable shape in the neighborhood of the j axis. This compensation is provided by either a rate or derivative feedback and lead-lag compensation. 29 In the compensation shown a rate feedback loop is included Where the constant anF gain K are iFtroduced 30 Problem 7.14 from A&F Assume , A , E , G , E , aGd K sameAas in Ex. 7.7. Let R take values of 0.001, 0.01 & 0.1. Find effect of on thR branch of the root locus near the imaginary axis. K A KG R KGH (1 A)(K E s)(E s)(1G s) R K K K A G R 1 K E 1 1 AE G Rs )(s )(s )(s n E G R K A KG R AE G RsC )(sAC )(s EC )(sCG) R 31 .01 , 1.0 , 0.5 , K E0.05 A G E R 0.1 0.01 0.001 C R 10 100 1000 Characteristic equation in terms of C R 4 3 2 s (C CAC EC )sG(C R C C A CEC G R C A G )s A R E G E R [C C (C C )C C (C C )]sC C C C A E G R G R A E A E G R K KGH (s 10)(s 0.1)(s 1)(s CR) 4 3 2 s (10.9C )R (10.9C R.9)s (10.9C )s R R KGH K1 K 2 K 3 K 4 1 s C A s C E s CG s CR (s CA)(s C E(s C )Gs 32) R 1 K1 (CEC )AC CG)(C AC )R A 1 K2 (C AC )EC CG)(C EC ) R E K 1 3 (C C )(C C )(C C A G E G R G) K 1 4 (C C )(C C )(C C ) A R E R G R Time Domain Response C A C E C G CRt K 1 K e2 K e3 K e4 Only C is negative and results in a growing exponential. E However system is stable for some values of gain less than cross over value. 33 1. 4 poles, no zeroes P=4, Z=0 2. Asymptotes (2k 1) 3 5 7 k 4 , 4 , 4 , 4 P Z 3. Centre of Gravity CG P Z 10.011C R 10.9CR P Z 4 4 CR CG For high 10 -5.22 values of R , CG quickly 100 -27.72 moves to the 34 As CG moves to the left, the locus tends to follow the asymptotes extending the stable region of operation. Characteristic eqn (s 10)(s 0.1)(s 1)(s C )R K 0 4 3 2 s (9.9C )sR (10.9C 8.9Rs (K C ) 0 R For stable operation K C R 35

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