Electrical Machines - Synchronous Machines Complete Study Notes

Introduction of synchronous machines

Synchronous machines are one of two types: the stationary ﬁeld or the rotating dc magnetic ﬁeld. The stationary ﬁeld synchronous machine has salient poles mounted on the stator—the stationary member. The poles are magnetized either by permanent magnets or by a dc current.
The armature, normally containing a three-phase winding, is mounted on the shaft. The armature winding is fed through three slip rings (collectors) and a set of brushes sliding on them. This arrangement can be found in machines up to about 5 kVA in rating.
For larger machines—all those covered in this book—the typical arrangement used is the rotating magnetic ﬁeld. The rotating magnetic ﬁeld (also known as revolving-ﬁeld) synchronous machine has the ﬁeld-winding wound on the rotating member (the rotor), and the armature wound on the stationary member (the stator).
A dc current, creating a magnetic ﬁeld that must be rotated at synchronous speed, energizes the rotating ﬁeld-winding. The rotating ﬁeld winding can be energized through a set of slip rings and brushes (external excitation), or from a diode-bridge mounted on the rotor (self-excited).
A synchronous generator is an electrical machine producing alternating emf (Electromotive force or voltage) of constant frequency.
The synchronous motor operates at a precise synchronous speed, and hence is a constant-speed motor. Unlike the induction motor, whose operation always involves a lagging power factor, the synchronous motor possesses a variable-power-factor characteristic and hence is suitable for power-factor correction applications.
A synchronous motor operating without mechanical load is called a compensator. It behaves as a variable capacitor when the field is overexcited, and as a variable inductor when the field is under-excited. It is often used in critical positions in a power system for reactive power control.

Types of Synchronous Machines: According to the arrangement of the field and armature windings, synchronous machines may be classified as:

Rotating-armature type
Rotating-field type

Rotating-Armature Type:

The armature winding is on the rotor and the field system is on the stator.
The generated current is brought out to the load via three (or four) slip-rings.
Insulation problems, and the difficulty involved in transmitting large currents via the brushes, limit the maximum power output and the generated electromagnetic field (emf).
This type is only used in small units, and its main application is as the main exciter in large alternators with brushless excitation systems.

Rotating Field Type

The armature winding is on the stator and the field system is on the rotor.
Field current is supplied from the exciter via two slip-rings, while the armature current is directly supplied to the load.
This type is employed universally since very high power can be delivered.
Unless otherwise stated, the subsequent discussion refers specifically to rotating-field type synchronous machines.

According to the shape of the field, synchronous machines may be classified as:

Cylindrical-rotor (non-salient pole) machines and
Salient-pole machines

Cylindrical Rotor Machines

The cylindrical-rotor construction is used in generators that operate at high speeds, such as steam-turbine generators (usually two-pole machines).
This type of machine usually has a small diameter-to-length ratio, in order to avoid excessive mechanical stress on the rotor due to the large centrifugal forces.

Salient-pole machines

The salient-pole construction is used in low-speed alternating current (AC) generators (such as hydro-turbine generators), and also in synchronous motors.
This type of machine usually has a large number of poles for low-speed operation, and a large diameter-to-length ratio.
The field coils are wound on the bodies of projecting poles.
A damper winding (which is a partial squirrel-cage winding) is usually fitted in slots at the pole surface for synchronous motor starting and for improving the stability of the machine.

Flux Density Distribution in the air gap & the induced EMF in the Phase winding of Two pole & Four pole Machine

BASIC OPERATION OF THE SYNCHRONOUS MACHINE

In the above pictorial representation “Developed” view of a four-pole stator, showing the slots, the poles, and a section of the winding. The section shown is of one of the three phases. It can be readily seen that the winding runs clockwise under a north pole, and counterclockwise under a south pole. This pattern repeats itself until the winding covers the four poles. A similar pattern is followed by the other two phases, but located at 120 electrical degrees apart.

Schematic view of a two-pole generator with two possible winding conﬁgurations

Two parallel circuits winding
A two series connected circuits per phase.
On the right, the three phases are indicated by different tones.
Here we can see that some slots only have coils belonging to the same phase, while in others, coils belonging to two phases share the slot.

No-Load Operation

When the ideal machine is connected to an inﬁnite bus, a three-phase balanced voltage (V₁) is applied to the stator winding (within the context of this work, three-phase systems and machines are assumed).

As described above, it can be shown that a three-phase balanced voltage applied to a three-phase winding evenly distributed around the core of an armature will produce a rotating (revolving) magneto-motive force (MMF) of constant magnitude (Fs). This MMF, acting upon the reluctance encountered along its path, results in the magnetic ﬂux (φ_s) previously introduced.

The speed at which this ﬁeld revolves around the center of the machine is related to the supply frequency and the number of poles is N_S called as Synchronous Speed by the following expression

N_s = 120/P

f = electrical frequency in Hz

P = number of poles of the machine

Ns = speed of the revolving ﬁeld in revolutions per minute (rpm)

Phasor Diagrams of Cylindrical-Rotor Ideal Machine

If no current is supplied to the dc ﬁeld winding, no torque is generated, and the resultant ﬂux (φ_r), which in this case equals the stator ﬂux (φ_s), magnetizes the core to the extent the applied voltage (V₁) is exactly opposed by a counter electromotive force (C_emf) (E₁).
If the rotor’s excitation is slightly increased, and no torque is applied to the shaft, the rotor provides some of the excitation required to produce (E₁), causing an equivalent reduction of (φ_s). This situation represents the under-excited condition shown in condition no load (a) in above figure.

Alternator (Synchronous generator)

The construction of an alternator consists of field poles placed on the rotating fixture of the machine. An alternator is made up of two main parts: a rotor and a stator. The rotor rotates in the stator, and the field poles get projected onto the rotor body of the alternator. The armature conductors are housed on the stator.

An alternator is basically a type of AC generator. The field poles are made to rotate at synchronous speed N_s = 120 f/P for effective power generation. Where, f signifies the alternating current frequency and the P represents the number of poles.

In most practical construction of alternator, it is installed with a stationary armature winding and a rotating field unlike in the case of DC generator where the arrangement is exactly opposite. This modification is made to cope with the very high power of the order of few 100 Megawatts produced in an AC generator contrary to that of a DC generator.

To accommodate such high power the conductor weighs and dimensions naturally must be increased for optimum performance. For this reason, is it beneficial to replace these high-power armature winding by low power field windings, which is also consequently of much lighter weight, thus reducing the centrifugal force required to turn the rotor and permitting higher speed limits.

A synchronous machine essentially consists of two parts:

Armature (rotor)
Field magnet system

Small AC generators and of low voltage rating are commonly made of rotating armature. In such generators, the required magnetic field is produced by DC electromagnet placed on the stationary member called stator and the current generated is collected by means of brushes and slip ring on the revolving member called the rotor.

Practically all large rating generators are made of revolving field. In such generators revolving field structure or rotor has slip rings and brushes for supply of excitation current from an outside DC source and the stationary armature, which is made of thin silicon sheet steel laminations securely clamped and held in place of steel frame, accommodates coils or winding in the slots. The slots are provided on the stator core and of mainly two types viz. open type or semi-closed type. Totally closed type slots are never used.

EMF equation of Alternator

The emf equation of Synchronous Generator or Alternator is given as

Let,

Φ = Flux per pole, in Wb

P = Number of poles

N = Synchronous speed in rpm

f = Frequency of induced emf in Hz

Z = Total number of conductors

Z_ph = Conductors per phase connected in series = Z/3 as number of phases = 3

Consider a single conductor placed in a slot.

The average value of emf induced in a conductor = dΦ/dt.

For one revolution of a conductor,

E_avg per conductor = (Flux cut in one revolution/Time taken for one revolution).

Total flux cut in one revolution is Φ x P.

Time taken for one revolution is 60/N_s seconds.

But in ac circuits, RMS value of an alternating quantity is used for the analysis. The form factor is 1.11 of sinusoidal emf.

Pitch Factor or Coil Span Factor (K_c)

In practice, short pitch coils are preferred. So coil is formed by connecting one coil side to another which is less than one pole pitch away. So actual coil span is less than 180°. The coil is generally shorted by one or two slots. The angle by which coils are short pitched is called angle of short pitch denoted as ‘ alpha’ where = Angle by which coils are short pitched.

It is defined as the ratio of resultant emf when the coil is short pitch to the result emf when the coil is full pitched. It is always less than one.

Distribution Factor (K_d)

Similar to full pitch coils, concentrated winding is also rare in practice. Attempt made to use all the slots available under a pole for the winding which makes the nature of the induced emf more sinusoidal. Such a winding is called distributed winding.

Consider 18 slots 2 pole alternator.

So, slots per pole i.e. n = 9.

m = Slots per pole per phase = 3

β = 180°/9 = 20°

Let E = Induced emf per coil and there are 3 coils per phase.

In concentrated type, all the coil sides will be placed in one slot under a pole. So, induce emf in all the' coils will achieve maxima and minima at the same time i.e. all of them will be in phase. Hence resultant emf after connecting coils in series will be algebraic sum of all the emf's as all are in phase.

The distribution factor is defined as the ratio of the resultant emf when coils are distributed to the resultant emf when coils are concentrated. It is always less than one.

Armature reaction in Alternator

Every rotating electrical machine works based on Faraday’s law of electromagnetic Induction. Every electrical machine requires a magnetic field and a coil (Known as armature) with a relative motion between them.

In case of an alternator, we supply electricity to rotor to produce magnetic field and output power is taken from the armature. Due to relative motion between field and armature, the conductor of armatures cut the flux of magnetic field and hence there would be changing flux linkage with these armature conductors. According to Faraday’s law of electromagnetic induction there would be an emf induced in the armature. Thus, as soon as the load relates to armature terminals, there is a current flowing in the armature coil.

As soon as current starts flowing through the armature conductor there is one reverse effect of this current on the main field flux of the alternator (or synchronous generator). This reverse effect is referred as armature reaction in alternator or synchronous generator.

In other words, the effect of armature (stator) flux on the flux produced by the rotor field poles is called armature reaction.

In an alternator like all other synchronous machines, the effect of armature reaction depends on the power factor i.e. the phase relationship between the terminal voltage and armature current.

Reactive Power (lagging) is the magnetic field energy, so if the generator supplies a lagging load, this implies that it is supplying magnetic energy to the load. Since this power comes from excitation of synchronous machine, the net reactive power gets reduced in the generator.

Hence, the armature reaction is demagnetizing. Similarly, the armature reaction has magnetizing effect when the generator supplies a leading load (as leading load takes the leading VAR) and in return gives lagging VAR (magnetic energy) to the generator. In case of purely resistive load, the armature reaction is cross magnetizing only.

The armature reaction of alternator or synchronous generator depends upon the phase angle between, stator armature current and induced voltage across the armature winding of alternator.

The phase difference between these two quantities, i.e. Armature current and voltage may vary from -90^o to + 90^o

Motor Operation

However, this section presents an introductory discussion of the synchronous machine, and thus the motor mode of operation is also covered. If a braking torque is applied to the shaft, the rotor starts falling behind the revolving-armature-induced magnetomotive force (MMF) (F_s). In order to maintain the required magnetizing MMF (F_r) the armature current changes. If the machine is in the under-excited mode, the condition motor in the Figure (a) represents the new phasor diagram.

On the other hand, if the machine is overexcited, the new phasor diagram is represented by Motor in Figure (b). The active power consumed from the network under these conditions is given by

Active power=V₁×I₁×cosϕ₁ (per phase)

If the braking torque is increased, a limit is reached in which the rotor cannot keep up with the revolving ﬁeld. The machine then stalls. This is known as “falling out of step,” “pulling out of step,” or “slipping poles.” The maximum torque limit is reached when the angle δ equals π/2 electrical.
The convention is to deﬁne δ as negative for motor operation and positive for generator operation. The torque is also a function of the magnitude of φr and φf. When overexcited, the value of φf is larger than in the under-excited condition.
Therefore synchronous motors are capable of greater mechanical output when overexcited. Likewise, the under-excited operation is more prone to result in an “out-of-step” situation.

Apparent power and Power factor

Two factors limiting the power of electric machines are

Mechanical torque on its shaft (usually, the shaft can handle much more torque)
Heating of the machine’s winding.

The practical steady-state limits is set by heating in the windings. The maximum acceptable armature current sets the apparent power rating for a generator

If the rated voltage is known, the maximum accepted armature current determines the apparent power rating of the generator

The power factor of the armature current is irrelevant for heating the armature windings.

Synchronous Machine Ratings

The purpose of ratings is to protect the machine from damage. Typical ratings of synchronous machines are voltage, speed, apparent power (kVA), power factor, field current and service factor.

Voltage, Speed, and Frequency: The rated frequency of a synchronous machine depends on the power system to which it is connected. The commonly used frequencies are 50 Hz (Europe, Asia), 60 Hz (Americas), and 400 Hz (special applications: aircraft, spacecraft, etc.). Once the operation frequency is determined, only one rotational speed in possible for the given number of poles.

The change in frequency would change the speed. Since E_a= Kφω, the maximum allowed armature voltage changes when the frequency changes. Specifically, if a 60 Hz generator will be operating at 50 Hz, its operating voltage must be derated to 50/60 or 83.3 %.

Synchronous Machine Temperature Rating

The maximum temperature rise that a machine can stand depends on the insulation class of its windings. The four standard insulation classes with they temperature ratings are:

A – 60^oC above the ambient temperature
B – 80^oC above the ambient temperature
F – 105^oC above the ambient temperature
H – 125^oC above the ambient temperature

The higher the insulation class of a given machine, the greater the power that can be drawn out of it without overheating its windings.

Note: The overheating is a serious problem and synchronous machines should not be overheated unless absolutely necessary. However, power requirements of the machine not always known exactly prior its installation. Because of this, general purpose machines usually have their service factor defined as the ratio of the actual maximum power of the machine to the rating on its plate. For instance, a machine with a service factor of 1.15 can actually be operated at 115% of the rated load indefinitely without harm.

Cylindrical Rotor Synchronous Motor

where, V = Terminal phase voltage applied to the armature, E_f = Excitation voltage, R_a = Effective armature resistance/phase, X_s = Synchronous reactance/phase, Z_s = Impedance/phase.

E_a = V – I_aR_a – jI_aX_s

Phasor Diagram

Salient Pole Synchronous Motor

E_a = V – I_aR_a – jI_aX_q – jI_d(X_d – X_q)

Phasor Diagram:

Power Developed:

Experimental Determination of Circuit Parameters

In the per phase equivalent circuit model illustrated above first for Generator & Second For Motor, there are three parameters need to be determined: winding resistance Ra, synchronous reactance Xs, and induced emf in the phase winding Ea. The phase winding resistance Ra can be determined by measuring DC resistance of the winding using the volt-ampere method, while the synchronous reactance and the induced emf can be determined by the open circuit and short circuit tests.

Open Circuit Test
Drive the synchronous machine at the synchronous speed using a prime mover when the stator windings are open circuited. Vary the rotor winding current, and measure stator winding terminal voltage. The relationship between the stator winding terminal voltage and the rotor field current obtained by the open circuit test is known as the open circuit characteristic of the synchronous machine.

Short Circuit Test
Reduce the field current to a minimum, by using the field rheostat, and then open the field supply circuit breaker. Short the stator terminals of the machine together through three ammeters; Close the field circuit breaker; and raise the field current to the value noted in the open circuit test at which the open circuit terminal voltage equals the rated voltage while maintaining the synchronous speed. Record the three stator currents. (This test should be executed quickly as the stator currents may be greater than the rated value).

Under the assumptions that the synchronous reactance Xs and the induced emf Ea have the same values in both the open and short circuit tests,

and that Xs >> Ra, we have

Effect of Excitation

By controlling the rotor excitation current such that the synchronous condenser draws a line current of leading phase angle, whose imaginary component cancels that of the load current, the total line current would have a minimum imaginary component.

Therefore, the overall power factor of the inductive load and the synchronous condenser would be close to one and the magnitude of the overall line current would be the minimum.

It can also be seen that only when the power factor is a unit or the stator current is aligned with the terminal voltage, the magnitude of the stator current is minimum.

By plotting the magnitude of the stator current against the rotor excitation current, a family of “V” curves can be obtained. It is shown that a larger rotor field current is required for a larger active load to operate at unity power factor.

Voltage Regulation