CHAPTER 2SYNCHRONOUS MACHINES

INTRODUCTIONSynchronous Machines are called Synchronous because their speed is directly related to the supply frequency.Rotates at a constant speed in the steady state.The rotating air gap and the rotor rotate at the same speed.Synchronous Generators: A primary source of electrical energy (Convert mechanical power into AC electrical power)Synchronous Motors: Used to convert AC electrical power into mechanical power. As well as power factor compensators.Used primarily as a generators of electrical power Synchronous Generator or Alternators

INTRODUCTIONAC machine that have a field circuit supplied by an external DC source2 types:1) Generator2) MotorMost important component in the power system, since synchronous generators:Are the source of 99% of the MW in most power systemsProvide frequency regulation and load followingAre the main source of voltage controlIs an important source of oscillation damping.

Cont.The synchronous speed, Ns

where f = frequency (Hz) p = no of poles

CONSTRUCTION

Construction:

Cont..water turbine

CONSTRUCTIONSTATORStatic or non-rotating or non-movingAlso known as the armature.The stator is a ring shaped laminated iron-core with slots.Three phase windings are placed in the slots (armature winding)- the main voltage is induced.2 types of armature windings commonly used:(i) Single layer winding (ii) Double layer winding. Most three phase windings are double layer that is two coil sides are placed in each slots.

ROTOR TYPES:

There are two types of rotor structures: 1.Round or cylindrical rotor (non-salient pole)2.Salient pole rotorThe rotor winding carries DC current so as to produce constant flux per pole.Usually recieves power from a 115 or 230 V DC generator.

CONSTRUCTIONRound or Cylindrical Rotor (Non-Salient Pole)

Normally used for rotor with 2 or 4 polesUsed for steam turbine- driven alternators which run at very high speedsUtilisation: High speed synchronous machineApplication: Steam and gas turbine as prime mover

CONSTRUCTIONSalient Pole Rotor

Pole faces project out from the rotorNormally used for rotor with 4 or more polesUsed in low and medium speed (engine driven) alternatorsHas a large number of projecting (salient) polesUtilisation: Low speed synchronous machineApplication: Hydroturbine as prime mover

Example:

PRINCIPLE OF OPERATIONThe synchronous generator converts mechanical energy from the turbine into electrical energy.The turbine converts some kind of energy (steam, water, wind) into mechanical energy

PRINCIPLE OF OPERATIONIt is designed to be operating at synchronous speed, The frequency-speed relation is

The field winding is supplied with a DC currentField winding is mechanically turned (rotated) at synchronous speed

The RMF (rotating magnetic field) produced by the field current induces voltage in the armature winding

where supply frequency No. of poleswhere = Mechanical speed

EMF EQUATION INDUCED EMF EQUATION where Pitch Factor Distribution Factor Supply frequency Flux ::::::No. of turns per phase

THE SPEED OF SYNCHRONOUS MACHINESSynchronous The electrical frequency produced is locked in or synchronized with the mechanical rate of rotation of the rotor.The rate of rotation of the magnetic fields in the machine (synchronous speed) is related to the stator electrical frequency given by

where No. of poles Rotor @ mechanicalspeed (rpm)::

The internal generator voltage

Synchronous speed (rpm):

SYNCHRONOUS GENERATOR

EQUIVALENT CIRCUIT OF SYNCHRONOUS GENERATOR Per Phase Equivalent Circuit of Synchronous Generator = Internal generated voltage= Armature current = Armature resistance = Synchronous reactance = Field current = Field resistance = Terminal voltage Field winding circuit (Rotor)Armature winding circuit (Stator)

EQUIVALENT CIRCUIT OF SYNCHRONOUS GENERATOREquivalent Circuit of Synchronous Generator Therefore

PHASOR DIAGRAM OF SYNCHRONOUS GENERATOR Unity power factor (Resistive Load) Lagging power factor (Inductive Load) Leading power factor (Capacitive Load)

Example:A 9-kVA, 208 V, three-phase, Y-connected synchronous generator has a armature resistance of 0.1/phase and a synchronous reactance 0f 5.6/phase. Determine its generated voltage when the power factor of the load is:a). 80% laggingb). unityc). 80% leading

Exercise:A 60-kVA, 3-phase, 50Hz, Y-connected, synchronous generator. The power factor of the load is 0.9 lagging. The synchronous impedance is 0.15 + j1.3/phase. Determine the voltage regulation of the generator.

POWER FLOW DIAGRAM OF SYNCHRONOUS GENERATORThe input mechanical power is the shaft Power converted from mechanical to electrical

POWER FLOW DIAGRAM OF SYNCHRONOUS GENERATORPower Converted is also known as:=Mechanical power

=Induced power

=Developed power

Where =Torque induced (Nm)

=Mechanical speed (rad/s)

=Angle between and (rad/s) where = Speed in rpm

POWER IN SYNCHRONOUS GENERATOR The input mechanical power is the shaft Power converted from mechanical to electrical Where is the angle between and Real electric output power Reactive output power

Exercise:A 40-kVA, 240 V, 50Hz, 4-pole, 3-phase, Y-connected alternator has a synchronous reactance of 0.08/phase. The armature-winding resistance is negligibly small, and the revolving field is established by permanent magnets. The rotational loss is 5% of the power developed. When the generator delivers the rated load at leading power factor of 0.866, determine: a). the power angle b). the efficiency c). the voltage regulation d). the torque supplied by the prime mover.

THE MAXIMUM POWER AND TORQUE The maximum power that generator can supply.In real synchronous machines of any size, is more than 10 times smaller than. Therefore,Ra can be ignored (since Xs >>Ra).The phasor diagram for lagging power factor with ignored of Ra is shown in figure below.

THE MAXIMUM POWER AND TORQUESubstitute into Therefore : Torque angle

POWER AND TORQUE IN SYNCHRONOUS MACHINESMaximum power that generator can supply occurs when:Maximum power Torque induced

Example:A 2400kVA, 16kV, 50Hz, three-phase generator is Y-connected. The generator has a synchronous reactance of 100/phase and armature resistance is negligible. If the generator is operating at 0.75 leading power factor, determine:i) the armature current ii) the excitation voltage, Ea iii) torque angle iv) maximum power supplied by generator v) with the excitation voltage held and the driving torque is reduced until generator is delivering 10MW. Determine the armature current and the power factor of the generator.

DETERMINATION OF THE SYNCHRONOUS REACTANCE , XsThe synchronous reactance is an important parameter in the equivalent circuit of the synchronous machine. This reactance can be determined by performing two tests, an open-circuit test and a short-circuit test.

OPEN CIRCUIT TEST Circuit for Open Circuit Test Open Circuit Characteristic

DETERMINATION OF THE SYNCHRONOUS REACTANCE, XsOpen Circuit Test on Generator

The generator is turned at the rated speedThe terminals are disconnected from all loadsField current is set to zeroIncrease the field current gradually in stepMeasure the terminal voltage at each step of field currentWith the terminals open, so is equal toThus plot a graph or versus . The graph is known as open circuit characteristics (OCC).

DETERMINATION OF THE SYNCHRONOUS REACTANCE , XsShort Circuit Test

Adjust the field current to zeroShort-circuit the terminal of the generator through a set of ammeters.Measure the armature current or the line current as the field current is increasedPlot a graph versus . The graph is known as short circuit characteristics (SCC).Circuit for Short Circuit Test Short Circuit Characteristic

DETERMINATION OF THE SYNCHRONOUS REACTANCE , XsOpen and Short Circuit Characteristics

DETERMINATION OF THE SYNCHRONOUS REACTANCE , XsArmature current is given by

Magnitude of armature current is given by

The internal machine impedance is given by

The synchronous reactance is given by

PROBLEMS1)A 200kVA, 480V,50 Hz, Y connected synchronous generator with a rated field current of 5A was tested, and the following data was taken:VT,OC at the rated IF was measured to be 540IL,SC at the rated IF was found to be 300 Awhen a DC voltage of 10V was applied to two of the terminals, a current of 24A was measuredFind the values of the armature resistance and the approximate synchronous reactance in ohms that would used in the generator model at rated conditions.

Example:The test data obtained at the rated speed on a 3-phase , Y-connected, synchronous generator are given as follows:Short circuit test: Field current = 1.2 AShort cct current = 25 AOpen circuit test:Field current = 1.2 AOpen cct voltage = 440 VThe per-phase winding resistance is 1.2. Determine the synchronous reactance of the generator.

VOLTAGE REGULATION OF SYNCHRONOUS GENERATORThe variation in the terminal voltage with load is called voltage regulation. Mathematically, voltage regulation is defined as the fractional rise in the terminal voltage when a given load is removed Voltage regulation

VOLTAGE REGULATION OF SYNCHRONOUS GENERATORIf a synchronous generator operating at:

Unity power factor:has a small positive value of VRLeading power factor:has a fairly large positive value of VRLeading power factor:has a negative value of VR

EFFICIENCY OF SYNCHRONOUS GENERATOREfficiency for any electrical machine is defined as:

SYNCHRONOUS MOTOR

EQUIVALENT CIRCUIT OF SYNCHRONOUS MOTOR A synchronous motor is the same physical machine as a synchronous generator, all of the basic speed, power and torque equations earlier in this chapter apply to synchronous motor also.A synchronous motor is the same in all respects as a synchronous generator, except that the direction of power flow is reversed, the direction of current flow is reverse also

EQUIVALENT CIRCUIT OF SYNCHRONOUS MOTOR= Internal generated voltage= Armature current = Armature resistance = Synchronous reactance = Field current = Field resistance = Terminal voltage

EMF EQUATION

Because of the change in direction of , the Kirchoffs Voltage Law equation for the equivalent circuit changes too. Equation describing is: Finally, EMF equation

PHASOR DIAGRAM OF SYNCHRONOUS MOTOR

POWER FLOW DIAGRAM OF SYNCHRONOUS MOTOR is also known as:=Mechanical power

=Induced power

=Developed power

TORQUE OF SYNCHRONOUS MOTOR Torque induced

where =Angle between and =Load angle

=Torque angle

(rad/s) where = Speed in rpm

VOLTAGE REGULATION OF SYNCHRONOUS MOTORThe variation in the terminal voltage with load is called voltage regulation. Mathematically, voltage regulation is defined as the fractional rise in the terminal voltage when a given load is removed: in other word Voltage regulation

EFFICIENCY OF SYNCHRONOUS MOTOR Efficiency for any electrical machine is defined as:

Example: (Synch. Motor)A 10-hp, 230 V, three-phase. -connected, synchronous motor delivers full load at a power factor of 0.707 leading. The synchronous reactance of the motor is j5/phase. The rotational loss is 230 W and the field winding loss is 70 W. Calculate the generated voltage and the efficiency of the motor. Neglect the armature winding resistance.

PROBLEMS

PROBLEMS

PROBLEMThe full load current of a 3.3kV, Y- connected synchronous motor is 60A at 0.8 pf lagging. The armature resistance and synchronous reactance of the motor are 0.8/phase and 5.5/phase respectively. With an assumption that the mechanical stray load loss to be 30kW, determine: i)excitation emf [ 1.69 kV ] ii) torque angle [ 7.99 deg] iii) shaft output and efficiency iv) voltage regulation

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