EEEB443 Control & Drives

EEEB443 Control & Drives Modeling of DC Machines By Dr. UngkuAnisaUngkuAmirulddin Department of Electrical Power Engineering College of Engineering EEEB443 - Control & Drives

Outline • Introduction • Theory of Operation • Field Excitation • Separately Excited DC Motor • State-Space Modeling • Block Diagrams and Transfer Functions • Measurement of Motor Constants • References EEEB443 - Control & Drives

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 EEEB443 - Control & Drives

Introduction • Some limitations: • High maintenance (commutators & brushes) • Expensive • Speed limitations • Sparking • Commonly used DC motors • Separately excited • Series (mostly for traction applications) EEEB443 - Control & Drives

DC Machine – Theory of Operation • Field winding - on stator pole • if produces f • Armature winding –on rotor • iaproduces a • f and a mutually perpendicular • maximum torque • Rotor rotates clockwise • For unidirectional torque and rotation • ia must be same polarity under each field pole • achieved using commutators and brushes EEEB443 - Control & Drives

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 EEEB443 - Control & Drives

DC Machine – Field Excitation • Separately Excited • Field winding separated from armature winding • Independent control of if (f) and ia (T) EEEB443 - Control & Drives

DC Machine – Field Excitation • Shunt Excited • Field winding parallel to armature winding • Variable-voltage operation complex • Coupling of f (if) and T (ia) production • T vs  characteristic almost constant • AR = armature reaction (as T , ia , armature flux weakens main flux  f, ) EEEB443 - Control & Drives

DC Machine – Field Excitation • Series Excited • Field winding in series with armature winding • Variable-voltage operation complex • Coupling of f (if) and T (ia) production • T ia 2 since if= ia • High starting torque • No load operation must be avoided (T = 0,  ) EEEB443 - Control & Drives

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. Long-shunt connection Short-shunt connection EEEB443 - Control & Drives

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 demagnetisationdue to armature reaction EEEB443 - Control & Drives

Ra Lf Rf La ia + ea _ + vt _ if Electromagnetic torque Armature back e.m.f. Separately Excited DC Machine + vf _ Fieldcircuit Armaturecircuit EEEB443 - Control & Drives

Separately Excited DC Motor • Motor is connected to a load. • Therefore, where TL= load torque J = load inertia (kg/m2) B = viscous friction coefficient (Nm/rad/s) EEEB443 - Control & Drives

DC Machine - State-Space Modeling • DC motor dynamic equations: • Therefore, (1) (2) (3) (4) (5) (6) EEEB443 - Control & Drives

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: (7) (8) EEEB443 - Control & Drives

DC Machine - State-Space Modeling • Comparing (7) and (8): EEEB443 - Control & Drives

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

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 (10) (11) EEEB443 - Control & Drives

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 Va input and TL disturbance is: • The Laplace inverse of (14) gives the speed time response (t). (12) (13) (14) EEEB443 - Control & Drives

DC Machine – Measurement of Motor Constants • To analyse DC motors we need values for Ra, La and Kb • Armature Resistance Ra • DC voltage applied at armature terminals such that rated ia flows • This gives the dc value for Ra • Need to also correct for temperature at which motor is expected to operate at steady state • Similar procedure can be applied to find Rf of field circuit EEEB443 - Control & Drives

DC Machine – Measurement of Motor Constants • Armature Inductance La • Apply low AC voltage through variac at armature terminals • Measure ia • Motor must be at standstill (i.e.  = 0 and e = 0) • f = supply frequency in Hz • Ra= ac armature resistance • Similar procedure can be applied to find Lf of field circuit (variac) EEEB443 - Control & Drives

DC Machine – Measurement of Motor Constants • EMF Constant Kb = 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 Ea • Get values of ea at different speeds • Plot Ea vs.  • Slope of curve = Kb • Units of Kb= [V/rads-1] Ea(V)  (rad/s) EEEB443 - Control & Drives

References • Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001. • Chapman, S. J., Electric Machinery Fundamentals, McGraw Hill, New York, 2005. • Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008. • Ahmad Azli, N., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008. EEEB443 - Control & Drives

EEEB443 Control & Drives