Mehran University Of Engineering & Technology, SZAB Khairpur Mirs Campus

ENGR. AHSANULLAH MEMONLECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS

EQUIVALENT CIRCUIT AND POWER EQUATION OF SYNCHRONOUS MOTOR

2

Figure shows the equivalent circuit model for one armature phase of a cylindrical rotor synchronous motor.

All values are per phase. Applying KVL to the circuit:

faralaaaT EXjIXjIRIV +++=

Combining reactances

arlS XXX += ( )SaafT XjRIEV ++= SafT ZIEV +=

A phasor diagram showing the component phasor and tip to tail determination of VT is shown

The phase angle of the excitation voltage is called the load angle or power angle. The torque angle is also called the load or power angle.

N.N.SHAIKH 4

SYNCHRONOUS MOTOR POWER EQUATION (MAGNET POWER)

Except for very small machines, Ra of synchronous motor is relatively small and neglected; therefore the terminal voltage can be approximated as

1...+= SafT XjIEV

The equivalent circuit and phasor diagram corresponding to equation (1), is shown below are normally used for the analysis of synchronous motor behavior, as motor responds to changes in load and/ or changes in field excitation.

N.N.SHAIKH 5

From the geometry of the phasor diagram,

2...sin-=cos fiSa EXI

Multiplying through by VT and rearranging terms,

3...sin-

=cos S

fTiaT X

EVIV

Since Left side of equation (3) is an expression for active power – input, the magnet power/phase developed by the synchronous motor may be expressed as

4...cos=1, iaTin IVP

5...sin-

=1, S

fTin X

EVP

OR

Mehran University Of Engineering & Technology, SZAB Khairpur Mirs Campus

ENGR. AHSANULLAH MEMONLECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS

SHAFT LOAD, POWER ANGLE & DEVELOPED SHAFT LOAD,POWER ANGLE AND DEVELOPED TORQUE

SHAFT LOAD AND POWER ANGLEAt normal operating condition, the rotor of a synchronous motor rotates in synchronism with the rotating flux of the stator.

Increase in shaft load cause the rotor magnets to change their angular position with respect to the rotating flux. This displacement angle can be seen by viewing the rotor with a strobe light synchronized with the stator frequency.

As the machine is loaded, the rotor changes its relative position with respect to the rotating flux of the stator, lagging behind it by angle δ .

Angle δ, expressed in electrical degrees, is called the power angle, load angle, or torque angle.

A synchronous motor operates at the same average speed for all values of load from no-load to its peak load.

When the load on a synchronous motor is increased, the motor slows down just enough to allow the rotor to change its angular position in relation to the rotating flux of the stator, and then goes back to synchronous speed. [???]Similarly, when the load is removed, it accelerates just enough to cause the rotor to decrease its angle of lag in relation to the rotating flux, and then goes back to synchronous speed.When the peak load that the machine can handle is exceeded, the rotor pulls out of synchronism.

9

DEVELOPED TORQUEThe torque developed by all synchronous motors has two components:

1. The Reluctance Torque Component:

It is due to the normal characteristics of magnetic materials in a magnetic field to align themselves so that the reluctance of the magnetic circuit becomes minimum

2. The magnetic torque component:

It is due to the magnetic attraction between the field poles on the rotor and the corresponding opposite poles of the rotating stator flux.

Mehran University Of Engineering & Technology, SZAB Khairpur Mirs Campus

ENGR. AHSANULLAH MEMONLECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS

EFFECT OF CHANGES IN SHAFT LOAD ON ARMATURE CURRENT, POWER ANGLE, AND POWER FACTOR

EFFECTS OF CHANGES IN SHAFT LOAD (Synch Motor)

Assuming applied voltage, frequency, and field excitation are constant. Changes in shaft load effects on armature current, power angle, and power factor.

1) Phasor digram when no changes are made

ilaodshaft ↓↑ Resulting an increase in power factor

VT, Ef1, Ia1, and δ1 are the initial load conditions.

Ef2, Ia2, and δ2 indicate the new steady – state conditions that

correspond to doubling the shaft load.

Doubling the shaft load, doubles both sincos fia EAndI

If the excitation is not changed, increasing the shaft load causes the locus of Ef phasor to a circular arc, increasing its phase angle with increasing shaft load. It should be noted that:

During increase on motor loading, the average speed of the machine does not change, until a point is reached at which a further increase in δ fails to cause a corresponding increase in motor torque, and rotor pulls out of synchronism.

1) Phasor diagram when changes in Ia

1) Phasor diagram when changes in Ef

The point of maximum torque occurs at a power angle of approximately 90o for a cylindrical rotor machine.The critical value of torque that causes a synchronous motor to pull out of synchronism is called the pull – out torque.

1) Phasor diagram when changes in both Ia and Ef

Mehran University Of Engineering & Technology, SZAB Khairpur Mirs Campus

ENGR. AHSANULLAH MEMONLECTURER DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS

EFFECT OF CHANGES IN FIELD EXCITATION ON SYNCH MOTOR PERFORMANCE

Increasing the strength of the magnets will increase the magnet attraction, and cause the rotor magnets to have a closer alignment with the corresponding opposite poles of the rotating stator flux; that results in a smaller power angle (δ).

EFFECT OF CHANGES IN FIELD EXCITATION (Synch Motor)

Proof of this behavior can be seen in the following equation.

ASSUMING:A constant shaft load, the steady – state value of must be constant.

sin3S

fTin X

EVP

sinfE

A step increase in Ef will cause a transient increase in Ef sin δ , and rotor will accelerate. As rotor changes its angular position, δ decreases until Ef sin δ has the same steady – state value as before, at this time the rotor again rum at synchronous speed. The change in angular position of the rotor magnets relative to the rotating flux of the stator occurs in a fraction of a second.

Figure shows under excitation Ef<VT

Diagram when Ef<VT

Figure shows normal excitation Ef=VT

Diagram when Ef=VT

Figure shows over excitation Ef>VT

Diagram when Ef>VT

The effect of changes in field excitation on Ia, δ, and power factor of a synchronous motor operating with a constant shaft load, from a constant voltage, constant frequency supply, is illustrated in the figure;

Figure shows under, normal ,over excitation

For a constant shaft load,

332211 sin=sin=sin fff EEE

Similarly: from equation

iaIP cos

for a constant shaft load.

iaiaiaia IIII cos=cos=cos=cos 332211

NOTE

changes the angle of the current phasor (power factor) to go from lagging to leading. The value of field excitation that results in unity power factor is called “Normal Excitation”. Excitation greater than normal is called “Over excitation”. Excitation less than normal is called “under excitation”. Tf VE >

31↑ ff EToE