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Modeling of DC Machines By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 20081EEEB443 - Control & Drives

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Outline Introduction Theory of Operation Field Excitation Separately Excited DC Motor State-Space Modeling Block Diagrams and Transfer Functions Measurement of Motor Constants References Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives2

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Introduction DC motor in service for more than a century Dominated variable speed applications before Power Electronics were introduced Advantage: Precise torque and speed control without sophisticated electronics Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives3

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Introduction Some limitations: High maintenance (commutators & brushes) Expensive Speed limitations Sparking Commonly used DC motors Separately excited Series (mostly for traction applications) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives4

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DC Machine – Theory of Operation Field winding - on stator pole i f produces f Armature winding –on rotor i a produces a f and a mutually perpendicular maximum torque Rotor rotates clockwise For unidirectional torque and rotation i a must be same polarity under each field pole achieved using commutators and brushes Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives5

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DC Machine – Field Excitation Depends on connections of field winding relative to armature winding Types of DC machines: Separately Excited Shunt Excited Series Excited Compounded Permanent Magnet Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives6

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DC Machine – Field Excitation Separately Excited Field winding separated from armature winding Independent control of i f ( f ) and i a (T) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives7

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DC Machine – Field Excitation Shunt Excited Field winding parallel to armature winding Variable-voltage operation complex Coupling of f (i f ) and T (i a ) production T vs characteristic almost constant AR = armature reaction (as T , i a , armature flux weakens main flux f , ) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives8

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DC Machine – Field Excitation Series Excited Field winding in series with armature winding Variable-voltage operation complex Coupling of f (i f ) and T (i a ) production T i a 2 since i f = i a High starting torque No load operation must be avoided (T = 0, ) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives9

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DC Machine – Field Excitation Compounded Combines best feature of series and shunt Series – high starting torque Shunt – no load operation Cumulative compounding shunt and series field strengthens each other. Differential compounding shunt and series field opposes each other. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives10 Long-shunt connection Short-shunt connection

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DC Machine – Field Excitation Permanent Magnet Field provided by magnets Less heat No field winding resistive losses Compact Armature similar to separately excited machine Disadvantages: Can’t increase flux Risk of demagnetisation due to armature reaction Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives11

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LfLf RfRf ifif +ea_+ea_ LaLa RaRa iaia +vt_+vt_ +vf_+vf_ Separately Excited DC Machine Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives12 Electromagnetic torque Armature back e.m.f. Armature circuit Field circuit

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Separately Excited DC Motor Motor is connected to a load. Therefore, where T L = load torque J = load inertia (kg/m 2 ) B = viscous friction coefficient (Nm/rad/s) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives13

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DC Machine - State-Space Modeling DC motor dynamic equations: Therefore, Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives14 (1)(2) (3)(4) (5) (6)

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DC Machine - State-Space Modeling From (5) and (6), the dynamic equations in state-space form: where s = differential operator with respect to time This can be written compactly as: Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives15 (7) (8)

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DC Machine - State-Space Modeling Comparing (7) and (8): Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives16

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DC Machine - State-Space Modeling The roots of the system are the eigenvalues of matrix A 1 and 2 always have negative real part, i.e. motor is stable on open-loop operation. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives17 (9)

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DC Machine – Block Diagrams and Transfer Functions Taking Laplace transform of (1) and (3) and neglecting initial conditions: These relationships can be represented in the following block diagram Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives18 (10)(11)

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DC Machine – Block Diagrams and Transfer Functions From the block diagram, the following transfer functions can be derived: Since the motor is a linear system, the speed response due to simultaneous V a input and T L disturbance is: The Laplace inverse of (14) gives the speed time response (t). Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives19 (12) (13) (14)

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DC Machine – Measurement of Motor Constants To analyse DC motors we need values for R a, L a and K b Armature Resistance R a DC voltage applied at armature terminals such that rated i a flows This gives the dc value for R a Need to also correct for temperature at which motor is expected to operate at steady state Similar procedure can be applied to find R f of field circuit Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives20

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DC Machine – Measurement of Motor Constants Armature Inductance L a Apply low AC voltage through variac at armature terminals Measure i a Motor must be at standstill (i.e. = 0 and e = 0) f = supply frequency in Hz R a = ac armature resistance Similar procedure can be applied to find L f of field circuit Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives21 (variac)

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DC Machine – Measurement of Motor Constants EMF Constant K b = K Rated field voltage applied and kept constant Shaft rotated by another dc motor up to rated speed Voltmeter connected to armature terminals gives value of E a Get values of e a at different speeds Plot E a vs. Slope of curve = K b Units of K b = [V/rads -1 ] Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives22 E a (V) (rad/s)

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References Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, Chapman, S. J., Electric Machinery Fundamentals, McGraw Hill, New York, Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, Ahmad Azli, N., Short Course Notes on Electrical Drives, UNITEN/UTM, Dr. Ungku Anisa, July EEEB443 - Control & Drives

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