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# EEE 576 Lecture 3 EEE 576

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This 36 page Class Notes was uploaded by Shammya Saha on Tuesday February 16, 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 40 views. For similar materials see Power System Dynamics in Electrical Engineering at Arizona State University.

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Date Created: 02/16/16

EEE 576 Spring 2016 Power System Dynamics Lecture 3 1 Reactive Capability Curves Synchronous generators are rated in terms of the maximum MVA output at a specified voltage and power factor (usually 0.85 or 0.9 lagging) which they can carry continuously without overheating. Active power – Limited by prime mover capability to a value within the MVA rating. 2 The continuous reactive power output capability is limited by 3 considerations: 1) Armature current limit 2) Field current limit 3) End region heating limit 3 Armature Current Limit Armature current causes I R losses and this results in increase of temperature of the conductor and its immediate environment. This limits the generator rating in terms of the max current carried by the armature without exceeding heating limitations. 4 Output complex power S P jQ tEtI (cos jsin) = Power factor angle In the P-Q plane the armature current limit will be a circle with its center at the origin and the radius equal to the MVA rating. 5 Armature current heating limit 6 Field Current Limit Consider the following simplified model of the synchronous machine where we assume X d X = q s E E jX I q to s to E q X i ad fd E I i R The heat resulting from the fd fd power loss imposes a second limit on the operation of the generator 7 For the synchronous machine model shown , the following phasor diagram can be drawn. Equate components in phase with and perpendicular to phasor E t (X iadsifd X I ios s t (X i )cos E X I sin ad fd i t s t X adsifd i Itcos X s X iadofd E i t Itsin X s 8 X ad P E t tos E tfdin i X s X E 2 Q E I sin ad E i cos t t t X t fd i X s s This relationship between P and Q for a Given Field Current 2 Et defines a circle centered at on the Q-axis with X s X ad E i t fd as the radius. X s 9 In a balanced design, the thermal limits for the field and armature intersect at a point A, which represents the machine MVA and P.F. rating. 10 End Region Heating Limit The localized heating in the end region of the armature poses a third limit on the operation of a synchronous machine. 11 Causes eddy currents in stator laminations – results in localized heating. In the under excited region field current is low and retaining ring is not saturated This permits an increase in End armature and turn leakage flux leakage 12 Also flux produced by armature current adds to flux produced by field current. This enhances axial flux in the end region and resulting heat limits generator output During overexcited conditions the high field current keep the end ring saturated so leakage flux is small 13 588 MVA, 22kv 0.85 p.f. machine 14 400 MVA Hydrogen cooled 15 Underexcitation Limiter (UEL) The UEL is intended to prevent reduction of generator excitation to a level where the small-signal (steady-state) stability limit or the stator core end-region heating limit is exceeded. Control signal is derived from a combination of voltage and current or active and reactive power. If input signals to UEL are stator voltage and current, the limiting characteristics are circular in the P-Q plane. With active and reactive power it would be a straight line. 16 17 Overexcitation Limiter (OXL) Protects generator from overheating due Permissible to prolonged field thermal overload overcurrent. of the field winding for round Generator field rotor generator winding designed to ANSI std C50.13- operate continuously 1977 at rated load condition. OXL detects high field current and after a time delay acts through AC regulator to ramp down the excitation preset value 18 Volts-per-Hertz Limiter and Protection Protect generator and step-up transformer from damage due to excessive flux resulting from low freq and/or over voltage 19 Field Shorting Circuits Rectifier cannot conduct in the reverse direction. Hence exciter current cannot be negative in AC and static exciters. Under pole slipping and S.C. induced current in field winding can be negative and may result in very high voltages. Special circuitry is needed to bypass the exciter Field discharge resistor 20 Modeling of excitation systems Normalization of exciter equations (PU system) The exciter equations are normalized on the basis of rated air gap voltage, i.e., exciter voltage that produces rated no-load terminal voltage with no saturation. Thus at no load and with no saturation, E FD.0pu corresponds to V=1.0put 1.0 pu exciter output current is the corresponding synchronous machine field current. 21 This is NOT the same base voltage as that chosen for the field (Ch. 4 A&F)normalizing the synchronous machine equations V B B S B V FB V IFB IFB This is based on the idea of equal mutual flux linkage. This base is usually a very large number. The base voltageFDould be on the order of 100V or so. 22 The exciter base voltage and the synchronous machine base for the field voltage differ. A change of base between the two quantities is required. This relationship is given by (4.59)(A&F) LAD BM F EFD ( )vFpu ( )vFV 3rF 3rF Hence any exciter differential equation may be divided by V to obtain an equation in v and then multiplied by FB Fu L AD 3rF to convert to an equation in E FDU 23 Brief Review of Eqn (4.59 A&F) Basis for converting field quantity to an equivalent stator EMF→At open circuit i A corresponds to an EMF of F iFRM F peak. If the RMS value of the EMF is E, then i M 2E F R F and iF RM fE 3 k 2 M Fnd = Rnown constants for a given machine 24 {Field current corresponds to a given EMF by a simple scaling factor} E→Stator air gap RMS voltage corresponding to field current F in pu In a similar manner a field flux linaFecan also be converted to a corresponding stator EMF. L i iF F L At steady-state O.C. F F F or F This value of field currFnt i , when multiplieR bF M , gives a peak stator voltage qf E′ (RMS) 25 The q-axis stator EMF corresponding to F is RM F 3E F LF q Using the same reasoning, a field voltage v Forresponds to a current v FrF. This in turns corresponds to a peak stator EMF (v /F )F MR. IF the peak value of this EMF is denoted as E FDthe d-axis stator EMF corresponds to a v field voltage vFor Fr RkM F 3E FD F 26 Modeling of Excitation System Components Basic Elements DC exciters – self and separately excited AC exciters Rectifiers – controlled or non controlled Amplifiers – magnetic, rotating, or electronic Excitation system stabilizing circuits Signal sensing and processing circuits 27 Separately Excited dc Exciter Ri v E P N Ri v E P v F k 1 a E a c a E (1c) a a v Ri v N E F P E k 1 28 The output voltage v is a nonlinear function F of the exciter field current i due to magnetic saturation. The voltage v Fs also affected by the load on the exciter The common approach is to account for saturation and load regulation approximately by combining the two effects. This is done using a constant resistance load-saturation curve. 29 Air-gap line tangent to the lower linear portion of the O.C. saturation curve R = slope of the air gap line. g i = departure of load saturation curve from air- gap line v i F i i Nonlinear function of vF 30 Rg i v SF(vE) F Where S (v ) = saturation function dependent on v E F F vF dv F v pR i E Rg dt R dv v p vF Rv S Fv EF E F R dt g v E FB FDB I E FDB FB R g R R gB g 31 Dividing by the Base Quantities vp R vF vF d vF v R v RS (E ) F v E dt v FB g FB FV FB v R v 1S (v ) d v pu R u Eu Fu Edt Fu g i S Ev F ) u R g Ev )F u u vF u With vFand i expressed in pu S (v ) A B Eu Fu B 32 33 v k F N a 1 E a vF E N E E v v a F F LF i L F i LFi E FDB I B g LF u vF vF vF R g F E u u FDB Corresponding to any given operating point (i ,v ) o Fo iu LFu L u L F E vFu R g dv v K v S (v )v Fu pu E Fu E Fu Fu E dt R R K S (v ) S (v ) 34 E R E u Eu Fu R g g For a separately excited exciter input voltage v = regulator output p vR. Output voltage v iF directly applied to the field of the synchronous machine Several convenient expressions to approximate exciter saturation. V v S (v ) v A e BEX F x F E F F EX We can reduce the block diagram given above to get the effective gain and time constant 35 For Any Operating Point vF E FD E Fo 1 K B EX(E FDo ) K E T E BEX (E FD ) K E o Where B EXEFDo S EE FD o ) A eEX 36

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