Fundamental Equations for Analogue Studies of Synchronous Machines [includes discussion]

Breedon, D. B.; Ferguson, Russ

doi:10.1109/aieepas.1956.4499306

Cited by 11 publications

(2 citation statements)

References 3 publications

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“…The first simulates equation (3), which is the equation of the synchronous machine in the direct-axis. The second simulates equation (4), which is the equation of the machine in the quadratureaxis. Both give as its output the corresponding axis current and flux linkage.…”

Section: The Principle Of the Simulationmentioning

confidence: 99%

An Improved Teaching Simulation of Synchronous Machines

El-Serafi

Badr

1972

International Journal of Electrical Engineering & Education

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List of Symbols Einduced e.m.f, of synchronous machine G(p) fild . I f ' (Rkd+Xkkd.p)Xad-Xa~·P e operationa unction = 2 (Rf d+ Xffd'P) (Rkd+ Xkkd·P)-Xaf·p i a , i b , i, armature currents of synchronous machine i d , i q direct-and quadrature-axis armature currents, respectively d P differential operator dt armature resistance external resistance shaft torque of synchronous machine developed electrical torque of synchronous machine bus-bar voltage components of the bus-bar voltage in the direct-and quadrature-axis, respectively initial values of V d and V q before disturbance excitation voltage external reactance direct-axis operational reactanceRfd+Xffd·P Rkd+Xkkd'P -Xad·p quadrature-axis operational reactance = X q _ X;q.p Rkq+ Xkkq.P X d , X q direct-and quadrature-axis synchronous reactances, respectively X kkd, X kkq direct-and quadrature-axis damping winding reactances, respectively X ad, X aq direct-and quadrature-axis magnetizing reactances, respectively Xffd field winding reactance R f d field winding resistance R kd, R kq direct-and quadrature-axis damping winding resistances, respectively 9 0 angle of phase a from the direct-axis at the instant of disturbance (pO) angular velocity of synchronous machine (pO)o angular velocity of synchronous machine at instant of disturbancẽ load angle of synchronous machinẽ o load angle of synchronous machine at instant of disturbance "' d' "' 11. direct-and quadrature-axis flux linkages, respectively e inertia constant of synchronous machine and its prime-mover at East Carolina University on June 6, 2016 ije.sagepub.com Downloaded from 4Introduction.The performance of synchronous machines can be described by the well-known Park equations 1. These equations are greatly simplified at steady state and the performance of the machine is easily studied through the use of equivalent circuits and vector diagrams. This is not the case for transient and dynamic operation as the differential equations describing such performance are nonlinear. Numerous numerical methods are available for solving the nonlinear differential equations on digital computers. However, the analog computer still has its own advantages which make it preferred for many studies. Some of these advantages are:

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Section: The Principle Of the Simulationmentioning

confidence: 99%

An Improved Teaching Simulation of Synchronous Machines

El-Serafi

Badr

1972

International Journal of Electrical Engineering & Education

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“…Krause (68) developed this form further and Nandi (86) converted the representation to conform to proposed IEEE definitions (59) . Numerous other studies using analog computer representa tions are to be found in the literature (2,3,8,10,15,109).…”

Section: B Analog Computer Simulationmentioning

confidence: 99%

Compensation of synchronous machines for stability

Schröder

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IX. APPENDIX A. DEVELOPMENT OF ANALOG COMPUTER REPRESENTATION OF A SYNCHRONOUS MACHINE 119 A. Development of Synchronous Machine Equations 125 vil Figure Page 19 Elimination of feedback path through Block diagram of synchronous machine and exciter after reduction 36 21 Block diagram of synchronous machine and exciter after putting feedback loop over a common denominator 38 22 Root-locus of uncompensated synchronous machine and exciter with K=K^ 41 23 Block diagram after closing regulator loop 43 24 Root-locus of synchronous machine and exciter with excitation rate feedback and K«Kp., Tj,=0.05 sec 46 25 Root-locus of synchronous machine and exciter with excitation rate feedback and K=Kj,, Tp=10 sec 48 26 Root-locus of synchronous machine and exciter with power system stabilizer and K=GBN=+3.3 pu, T,=0.2 sec, T2=.05 sec and T=3 sec 50 27 Root-locus of synchronous machine and exciter with power system stabilizer and K=GRN=-3.3 pu, T2=0.02 sec, T2=.05 sec and T=3 sec 51 28 Root-locus diagram of synchronous machine and exciter with bridged-T network placed In exciter forward loop and K=K^, 0)^=23 rad/sec, r=.l and n=2 53 29 Root-locus diagram of synchronous machine and exciter with bridged-T network placed in exciter forward loop and K=K^, 0)^=19.7 rad/sec, r=.l and n=2 54 30 Root-locus diagram of synchronous machine and exciter with bridged-T network placed In exciter forward loop and K=K^, 0^=26 rad/sec, r=.4 and n=2 55 31 Block diagram showing addition of bridged-T filter to regulator feedback loop 57 32 Root-locus of synchronous machine and exciter with brldged-T in regulator loop, 2-stage lead-lag network in exciter feedforward loop and speed feedback through GRN with K"K^, UQ=21 rad/sec, r=.l, n=2, T]^=.2 sec, T2=.05 sec and GRN=+3.3 pu 59 viii Figure Page 33 Movement of zeros of Equation 21 with K=+GEN Movement of zeros of Equation 21 with K=-GSN 62 35 Root-locus resulting from cancellation of torque-angle loop and field poles with K=K^ 69 36 Movement of zeros of Equation 44 with K=+l/Kp 71 37 Movement of zeros of Equation 44 with K=-1/Kp 72 38 Root-locus after third order pole cancellation and addition of excitation rate feedback 73 39 Block diagram of Figure 18 after moving the takeoff point for Kg 75 40 Reduced block diagram of synchronous machine and exciter in which torque-angle loop has not been closed 76 41 Block diagram after neglecting excitation rate feedback, moving the Ka loop to the torque summing junction and placing all feedback loops over a common denominator 77 42 Root-locus showing results of torque-angle loop cancellation 81 43 Uncompensated system 83 44 Excitation system rate feedback with Kp=.04 pu and Tp=.05 sec 85 45 Power system stabilizer with T=3 sec, T-j^=.2 sec, T2=.05 sec and GRN=0.5 pu 86 46a Bridged-T filter placed in regulator loop with 01(5=21 rad/sec, r=.l and n=2 87 46b Bridged-T filter placed in regulator loop with u)Q=23 rad/sec, r=.l and n=2 88 46c Bridged-T filter placed in regulator loop with a)Q=19.7 rad/sec, r=.l and n=2 89 46d Bridged-T filter placed in regulator loop ...

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Analogue Computer Representations of Synchronous Generators in Voltage-Regulation Studies [includes discussion]

Riaz

1956

Trans. AIEE, Part III: Power Appar. Syst.

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Fundamental Equations for Analogue Studies of Synchronous Machines [includes discussion]

Cited by 11 publications

References 3 publications

An Improved Teaching Simulation of Synchronous Machines

An Improved Teaching Simulation of Synchronous Machines

Compensation of synchronous machines for stability

Analogue Computer Representations of Synchronous Generators in Voltage-Regulation Studies [includes discussion]

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