Electrical Machines : Synchronous Machines

By Yash Bansal|Updated : May 20th, 2021

Electrical Machines : Synchronous Machines











In this article, you will find the study notes on Synchronous Machines.

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




  • 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 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 NS called as Synchronous Speed by the following expression

Ns = 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 (φr), which in this case equals the stator flux (φs), magnetizes the core to the extent the applied voltage (V1) is exactly opposed by a counter electromotive force (Cemf) (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 (φs). This situation represents the under-excited condition shown in condition no load (a) in above figure.

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) (Fs). In order to maintain the required magnetizing MMF (Fr) 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.

Generator Operation

  • Let’s assume that the machine is running at no load and a positive torque is applied to the shaft; that is, the rotor flux angle is advanced ahead of the stator flux angle. As in the case of motor operation, the stator currents will change to create the new conditions of equilibrium.
  • If the machine is initially underexcited, condition (a) in Figure.
  • On the other hand, if the machine is overexcited, condition (b) in Figure.
  • It is important to note that when “seen” from the terminals, with the machine operating in the underexcited mode, the power factor angle (ϕ1) is leading (i.e., I1 leads V1).This means the machine is absorbing reactive power from the system. The opposite occurs when the machine is in the overexcited mode.
  • As for the motor operation, an overexcited condition in the generating mode also allows for greater power deliveries. As generators are normally called to provide VARs together with watts, they are almost always operated in the overexcited condition.

A 3-φ synchronous machine is double excited AC machine. Its field winding is excited by a DC source and its armature winding is excited by AC source.

Synchronous speed:


where f = Supply frequency, and p = Number of poles

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 Ea= 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 – 60oC above the ambient temperature
  • B – 80oC above the ambient temperature
  • F – 105oC above the ambient temperature
  • H – 125oC 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 Generator

The alternator is operating on no load i.e., the rotor is rotating and energized and the stator is open-circuited.

  • Its circuit diagram is shown in below.


  • An equivalent circuit of a synchronous generator shown in below.


  • Let Xs = Synchronous reactance, Xar = Fictitious reactance, Xa = Armature reactance, Ra = Armature resistance, and Zs = Synchronous impedance.

Xs = Xar + Xa

Zs = Ra + j Xs

Ea = V + Ia Zs

Phasor Diagram


  • The phasor diagram for inductive, purely resistive and capacitive loads are shown in the figure below. All these phasor diagrams apply to one phase of a 3-φ machine.
  • At lagging, power factor:


  • At unity, power factor:



  • At leading, power factor:



Power Relationship

  • Mechanical power input to the generator Pmechanical = Tsωs
  • DC power input to a wound rotor Pin electrical= If
  • Total power input: Pin = Tsωs + If
  • Real power output:


  • Reactive power output:


where, V = Terminal voltage per phase, and Ef = Excitation voltage per phase = Phase angle between Ef and V, and Xs = Synchronous reactance

Salient Pole Synchronous Machine


The component currents Id and Iq provide component voltage drops jId Xd and jId Xq as shown in the figure.

Ea = V + IaRa + jIdXd + jIqXq

I = Id + Iq

If Ra is neglected, Ea = V + jIdXd + jIqXd

  • Phasor Diagram



  • For Generating Mode: 


  • For Motoring Mode:


 Note: δ = ψ – φ (generating mode), and δ = φ – ψ (motoring mode)


  • Power Angle


Use + for synchronous generator, and - for synchronous motor (here Ra is neglected)

  • Output Power

P0 = 3V(Id sin δ + Id cos δ)

  • Total Power Developed


Cylindrical Rotor Synchronous Motor


where, V = Terminal phase voltage applied to the armature, Ef = Excitation voltage, Ra = Effective armature resistance/phase, Xs = Synchronous reactance/phase, Zs = Impedance/phase.

Ea = V – IaRa – jIaXs

  • Phasor Diagram


Salient Pole Synchronous Motor


Ea = V – IaRa – jIaXq – jId(Xd – Xq)

  • 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


The variation in the terminal voltage with load is called voltage regulation, hence 

Per-unit voltage regulation = (|VNL|-|VFL|)/|VFL| = |Ef|-|V|/|V|

  • (a) zero power factor leading
  • (b) 0.8 power factor leading
  • (c) 0.9 power factor leading
  • (d) unity power factor
  • (e) 0.9 power factor lagging
  • (f) zero power factor lagging.













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