Ac Machines Fundamental
Ac generators are electrical machines that convert mechanical energy to an AC electrical energy. There are two types of machines synchronous of generators and induction (Asynchronous).
Synchronous generators are the machines whose magnetic field current is supplied by a separate DC power source.
Basic concept:
In order to understand how AC machines functions let's consider a simple loop of wire rotating within a uniform magnetic field. The rotating part of the machine is called "Rotor" whereas the stator represents the stationary part of the machine.
When the rotor starts rotating a voltage will be in induced in the loop, the voltage can be found through the following formula:
In order to determine the total induced voltage on the loop one must examine each segment of the loop separately and sum all the resulting voltages, after summing all the voltage the induced voltage will be:
With the purpose of relating this single loop behavior to the behavior of a real AC machine
Theta=Wt, assuming the rotation of the loop is constant with respect to time.
V=rw,
Now defining the maximum flux through the loop Phi(max) = AB where A = 2rL the area of the loop.
Hence, the voltage of a real AC machine can be expressed as follows:
E(induced)=Phi(max)*w*sinwt.
As it can be noticed from the above equation, the voltage in a real AC machine depends on the 2 factors:
Now introducing a third factor related to the construction of the machine. This factor is a constant depending on the number of loops in the winding.
In case of 3 phase set of coils the induced voltage in each coil will be:
Where Nc represents the number of turns in each coil.
Torque induced in a current-carrying loop
When a current flows in a loop a torque will be induced. to determine the total induced torque the following formulas must be used
F=i(LxB)
I= magnitude of the current in the segment
F represents the force on each segment.
Now the torque on each segment is given by torque = Taw = force applied*perpendicular distance = (F)*(rsin(theta))
Where theta is the angel between vector r and F.
After summation of the torque on each segment the total torque induced will be Taw(induced)=2rilBsin(theta)
Note that the maximum torque will be when the plane of the loop is parallel to the magnetic field and the minimum is when it's perpendicular.
The current in the loop will produced a magnetic flux density B(loop)=(Mu*i)/G
Where G is a factor depending on the geometry of the loop. Recall that the area of the loop is A=2rl.
Now the total torque induced can be represented as follows
Taw(induced=K*B(loop)*B(s)*Sin(theta)
Where K is the third factor introduced earlier in the voltage depending factors.
K= AG/Mu
Where Mu is the magnetic permeability.
B(s) is the stator magnetic field
B(loop) is the magnetic field generated by the rotor with theta defined to be the angle between them
The total torque induced formula will look like the following:
Taw(induced)=K*B(loop)xB(s)
Therefore as it can be noticed the torque depends on four factors:
Now defining the net magnetic field to be the sum of the rotor and the stator magnetic field yields to:
Where Delta is the angle between B(r) and B(net).
The rotating magnetic field
As showed before, two magnetic fields are present in the machine one produced by the rotor and the other is produced by the stator. The torque generated in the rotor causes the rotation in order to align both magnetic fields. Therefore, the basic concept of operation of an AC machine is to make the stator magnetic field rotates so that the rotor will be chasing the stator.
The rotation of the stator magnetic field takes place when applying a 3 phase set of currents each of equal magnitude and differing in phase in 120 degree through a three phase winding which produces a rotating magnetic field of constant magnitude. The 3 phase winding consist in 3 separate winding spaced 120 electrical degrees apart around the surface of the machine.
The relationship between electrical frequency and the speed of magnetic field rotation
Lets define the electrical speed in Hertz (frequency) Fe and the electrical speed in radians per second W(e) , also the mechanical speed in revolutions per second Fm and in radians per second Wm.
For a 2 poles machine the magnetic poles complete one mechanical rotation around the stator surface for each electrical cycle of the applied current. Therefore, Fe=Fm and We=Wm for a 2 pole machine.
Considering a 4 poles stator winding, a pole moves only halfway around the stator surface in one electrical cycle. In mechanical motion the stator moves 180 mechanical degrees; meanwhile 360 electrical degrees were completed. As a result Theta(e)=2*Theta(m).
In general
Theta(e)=P/2*Theta(m)
F(e)=P/2*F(m)
w(e)=P/2*w(m)
where P is the number of magnetic poles on an AC machine stator.
With f(m)=N(m)/60 the relationship between the electrical frequency in hertz to the resulting mechanical speed of the magnetic fields in revolutions per minute is the following:
F(e)=(N(m)*P)/120
AC machines Power Flows and Losses
The efficiency if an Ac machine the ratio between the output and the input power
N= Pout/Pin * 100%
The difference between the Output and Input power is called losses
N= (Pin - Pout)/Pin * 100%
The losses of an Ac machine is basically divided into 4 categories:
Electtical losses in a 3 phase Ac machine is found in Pscl = 3Ia^2Ra (stator copper losses) where Ia is the current flowing in each armature phase and Ra is the resistance of each one
Prlc=If^2Rf (Rotor copper losses) where If current flowing in field winding on the rotor and Rf is the resistance of the field winding.
The core losses are hysteresis losses and eddy current losses found in a motor
Mechanical Losses which are friction and windage
Stray losses are taken by convention to be 1% of full load accounting for the losses that can not be placed in any of the above categories.
Voltage regulation and Speed Regulation
The voltage regulation is the ability of the generator to keep constant voltage at its terminal as load varies and it is given by the following equation:
Vr = (Vnl-Vfl)/Vfl * 100%
Where Vnl and Vfl are the No Load voltage and Full Load Voltage respectively.
The speed regulation is the ability of the generated to keep constant shaft speed as load varies it is given by:
Sr = (Nnl-Nfl)/Nfl * 100%
Or Sr =(Wnl=Wfl)/Wfl * 100%
Where Nnl and Nfl are the No Load And Full Load shaft speed respectively
And the Wnl and Wfl are the No load and full load angular velocity respectively.
Synchronous Generator
A set of three phase voltages is induced within the stator winding of the generator by a rotating magnetic field. This magnetic field is produced by turning the rotor of the generator using a prime mover. A Dc current must be applied to the rotor winding.
Note that field windings is a term used for the windings that produce the magnetic field whereas armature winding is used for the windings that induce the voltage.
In synchronous generator the rotor winding are the field windings and the stator windings are the armature winding.
Since the field windings are located on the rotor then to supply a Dc current 2 ways are suggested:
Slip rings are metal rings installed on the shaft of the machine but insulated from it. A brush is block of graphite like carbon compound that conducts electricity and has very low friction. The brushes are stationary while the rings are rotating and connected to the filed winding so that Dc current can be supplied from an external Dc source.
Slip rings and brushes have some disadvantages such as:
Brushless exciter is created by installing a small Ac generator inside the main synchronous generator. The field winding of the small generator is located on the stator of the main machine so that the Dc current can be supplied to it directly. Its armature current is then rectified and supplied to the rotor winding (field winding) of the synchronous machine. Now by changing the field current of the small generator the field current of the synchronous machine can be controlled.
Another way to make the excitation independent from any external power source Pilot Exciter is used. It is a small generator with permanent magnet installed on the rotor of them main synchronous machine. The armature is located on the stator which by rectification supply Dc current for the exciter described above.
The Speed of rotation of synchronous generator
The rate of rotation is related to the electrical frequency by the following formula:
Fe= NmP/120
Where Fe = electrical Frequency
Nm = mechanical speed of mechanical speed in round per minute
P = Number of poles
this means that the synchronous generator runs at a constant speed depending on the number of poles existing.
