AC Machine CHAPTER 3 EKT 415

AC Machine  Alternating current (ac) is the primary source of electrical energy.  It is less expensive to produce and transmit than direct current. For this reason, and because ac voltage is induced into the armature of all generators, ac machines are generally more practical.  May function as a generator (mechanical to electrical) or a motor (electrical to mechanical)

DC Machine & AC machine DC motor - ends of the coil connect to a split ring to 'rectify' the emf produced AC motor - no need recification, so don't need split rings.

AC Motor As in the DC motor case, a current is passed through the coil, generating a torque on the coil. DC motor Since the current is alternating, the motor will run smoothly only at the frequency of the sine wave.

AC Generator This process can be described in terms of Faraday's law when you see that the rotation of the coil continually changes the magnetic flux through the coil and therefore generates a voltageFaraday's lawmagnetic flux

Generator and Motor

How Does an Electric Generator Work?

AC Machine  Two major classes of machines; (i) Synchronous machines. (ii) Induction machines.

 Synchronous machines are ac machine that have a field circuit supplied by an external dc source. –DC field winding on the rotor, –AC armature winding on the stator  Origin of name: syn = equal, chronos = time  Synchronous machines are called ‘synchronous’ because their mechanical shaft speed is directly related to the power system’s line frequency. Synchronous Machine

where P is the number of magnetic poles f e is the power line frequency. Typical machines have two-poles, four-poles, and six-poles The frequency of the induced voltage is related to the rotor speed by:

Construction Energy is stored in the inductance As the rotor moves, there is a change in the energy stored Either energy is extracted from the magnetic field (and becomes mechanical energy – motor) Or energy is stored in the magnetic field and eventually flows into the electrical circuit that powers the stator – generator Synchronous Machine

Construction DC field windings are mounted on the (rotating) rotor - which is thus a rotating electromagnet AC windings are mounted on the (stationary) stator resulting in three-phase AC stator voltages and currents  The main part in the synchronous machines are  i) Rotor  ii) Stator Synchronous Machine

Rotor  There are two types of rotors used in synchronous machines: cylindrical (or round) rotors and salient pole rotors.  Salient pole rotors are less expensive than round rotors.  Cylindrical ( round) rotor – low speed machines (hydro- turbines)  Salient-Pole rotor - high speed machines (steam- turbines)

Construction-Rotor  i) Cylindrical (or round) rotor Synchronous Machine  i) Salient-pole rotor

 Synchronous machine rotors are simply rotating electromagnets built to have as many poles as are produced by the stator windings.  Dc currents flowing in the field coils surrounding each pole magnetize the rotor poles.  The magnetic field produced by the rotor poles locks in with a rotating stator field, so that the shaft and the stator field rotate in synchronism.  Salient poles are too weak mechanically and develop too much wind resistance and noise to be used in large, high-speed generators driven by steam or gas turbines. For these big machines, the rotor must be a solid, cylindrical steel forging to provide the necessary strength.

 Axial slots are cut in the surface of the cylinder to accommodate the field windings.  Since the rotor poles have constant polarity they must be supplied with direct current.  This current may be provided by an external dc generator or by a rectifier. In this case the leads from the field winding are connected to insulated rings mounted concentrically on the shaft. Stationary contacts called brushes ride on these slip rings to carry current to the rotating field windings from the dc supply. The brushes are made of a carbon compound to provide a good contact with low mechanical friction. An external dc generator used to provide current is called an “exciter.

Synchronous Machine Stator  The stator of a synchronous machine carries the armature or load winding which is a three-phase winding.  The armature winding is formed by interconnecting various conductors in slots spread over the periphery of the machine’s stator. Often, more than one independent three phase winding is on the stator. An arrangement of a three-phase stator winding is shown in Figure below. Notice that the windings of the three-phases are displaced from each other in space.

Construction  Stator Synchronous Machine

Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine Flux produced by a stator winding

Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine

Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine Two Cycles of mmf around the Stator

Synchronous Generator Equivalent circuit model – synchronous generator

 If the generator operates at a terminal voltage V T while supplying a load corresponding to an armature current Ia, then;  In an actual synchronous machine, the reactance is much greater than the armature resistance, in which case;  Among the steady-state characteristics of a synchronous generator, its voltage regulation and power-angle characteristics are the most important ones. As for transformers, the voltage regulation of a synchronous generator is defined at a given load as;

Synchronous Generator Phasor diagram of a synchronous generator The phasor diagram is to shows the relationship among the voltages within a phase (E φ,V φ, jX S I A and R A I A ) and the current I A in the phase. Unity P.F (1.0)

Synchronous Generator Leading P.F. Lagging P.F

Synchronous Generator Power and Torque In generators, not all the mechanical power going into a synchronous generator becomes electric power out of the machine The power losses in generator are represented by difference between output power and input power shown in power flow diagram below

Synchronous Generator Losses Rotor - resistance; iron parts moving in a magnetic field causing currents to be generated in the rotor body - resistance of connections to the rotor (slip rings) Stator - resistance; magnetic losses (e.g., hysteresis) Mechanical - friction at bearings, friction at slip rings Stray load losses - due to non-uniform current distribution

Synchronous Generator The input mechanical power is the shaft power in the generator given by equation: The power converted from mechanical to electrical form internally is given by The real electric output power of the synchronous generator can be expressed in line and phase quantities as and reactive output power

Synchronous Generator In real synchronous machines of any size, the armature resistance R A is more than 10 times smaller than the synchronous reactance X S (X s >> R A ). Therefore, R A can be ignored

Synchronous Motor

Power Flow

Example : Synchronous Generator.  A three-phase, wye-connected 2500 kVA and 6.6 kV generator operates at full-load. The per-phase armature resistance R a and the synchronous reactance, X d, are (0.07+j10.4) . Calculate the percent voltage regulation at (a)0.8 power-factor lagging, and (b)0.8 power-factor leading.

Solution.

 The machines are called induction machines because of the rotor voltage which produces the rotor current and the rotor magnetic field is induced in the rotor windings.  Induction generator has many disadvantages and low efficiency. Therefore induction machines are usually referred to as induction motors. Induction Machine

Induction motor Induction motors use shorted wire loops on a rotating armature and obtain their torque from currents induced in these loops by the changing magnetic field produced in the stator (stationary) coils.torqueinducedmagnetic field The current in the stator coil is in the direction shown and increasing. The induced voltage in the coil shown drives current and results in a clockwise torque. induced voltage

Induction motor Induction in Armature Coils

Induction motor A large percentage of small AC motors are classed as induction motors. This implies that there is no current supplied to the rotating coils. These coils are closed loops which have large currents induced in them because of their low resistance.induction motorsinduced An induction motor must achieve a rotating magnetic field to continue to exert a torque on the armature coils. In this example, the rotating field is achieved by the extra coils on the pole pieces.

Induction motor

 There are two different types of induction motor rotors that can be placed inside the stator. 1. Squirrel cage – the conductors would look like one of the exercise wheels that squirrel or hamsters run on. 2. Wound rotor – have a brushes and slip ring at the end of rotor Induction Machine  The magnetic field's rotation of induction motors is given by

1. Squirrel cage – the conductors would look like one of the exercise wheels that squirrel or hamsters run on. Induction Machine

2. Wound rotor – have a brushes and slip ring at the end of rotor Induction Machine

 The stator’s rotating field cuts the rotors conductors thereby inducing voltages in the rotor circuit.  The induced (Faraday) voltages cause currents to flow in the rotor.  The rotor’s currents produce a rotating (rotor) field which is always aligned (travels with) the stator’s rotating field.  The whole process is essentially that of a transformer.  The induction motor is sometimes referred as a rotating transformer. Induction Machine - Operation

Speed of rotation ( synchronous speed) P is the number of magnetic poles designed into the machine, f e is the power line frequency.

The Concept of Rotor Slip  The voltage induced in a rotor bar of an induction motor depends on the speed of the rotor relative to the magnetic fields 1. Slip speed – defined as the difference between synchronous speed (magnetic field's speed) and rotor speed. n slip = n sync - n m n slip = slip speed of the machine n sync = speed of the magnetic fields n m = mechanical shaft speed of motor

The Concept of Rotor Slip 2. Slip – defined as the relative speed expressed on a per-unit (or sometimes as percentage) basis If the rotor turns at synchronous speed, s = 0, while if the rotor is stationary (standstill), s = 1. Mechanical speed (rotor's speed) can be expressed in term of synchronous speed and slip as below:

The Electrical Frequency on the Rotor The rotor frequency can be expressed as f r = sf e where f r = rotor frequency s = slip f e = electrical frequency Alternative to find f r is defined as below

Induction Motor – Equivalent Circuit Same as a transformer Stator is connected to the ac source, and the rotor’s voltage and current are produced by induction. The primary of the transformer corresponds to the stator of the machine, whereas the secondary corresponds to the rotor Stator and Rotor as Coupled Circuits

Induction Motor – Equivalent Circuit

Induction Motor – Power and Torque The power flow diagram

Induction Motor – Power and Torque Example A 480-V, 50Hz, 50hp, three phase induction motor is drawing 60A at 0.80 PF lagging. The stator copper losses are 2 kW, and the rotor copper losses are 700W. The friction and windage losses are 600W, the core losses are 1800 W, and the stray losses are negligible. Fine the following quantities: a. The air gap power P AG b. The power converted P conv c. The output power P out d. The efficiency of the motor

Induction Motor – Equivalent Circuit

Induction Motor – Power and Torque The output power can be found as P out = P conv – P F&W – P misc The induced torque or developed torque:

Induction Motor – Power and Torque Exercise A 460 V, 25-hp, 60Hz, four pole, Y-connected induction motor has the following impedances in ohms per phase referred to the stator circuit: R1 =0.641Ω R2 =0.332Ω X1 =1.106Ω X2 =0.464Ω Xm =26.3Ω The total rotational losses = 110 W, Rotor slip = 2.2% at rated voltage and frequency. Find the motor's i) Speed, ii) Stator Current, iii) Power factor, iv) Pconv, v) Pout vi)  ind, vii)  load and viii) Efficiency