Synchronous Machines notes Part – II for Electrical Engineering

By Deepak Yadav|Updated : July 15th, 2023

In this continuation of our series, we delve deeper into the fascinating world of synchronous machines, exploring their operation, characteristics, and applications. Building upon the foundational concepts covered in Part I, these notes will equip you with a comprehensive understanding of synchronous machines, empowering you to analyze, design, and optimize their performance. Whether you are a student, a practising engineer, or an enthusiast looking to expand your knowledge, this resource will serve as an invaluable guide to mastering the intricacies of synchronous machines.

In Part II of our notes on Synchronous Machines, we embark on an in-depth exploration of critical topics such as synchronous machine modelling, phasor diagrams, and synchronous machine parameters. You will gain a solid understanding of the mathematical models used to describe synchronous machines, enabling you to analyze their behaviour under different operating conditions. Furthermore, we will delve into the intricacies of phasor diagrams, providing you with a visual representation of the machine's voltage, current, and power relationships. By comprehending these diagrams, you will develop an intuitive grasp of how synchronous machines respond to changes in load and excitation conditions. Lastly, we will delve into the significance of synchronous machine parameters and their influence on machine performance, offering insights into optimization techniques for achieving efficient and reliable operation. Join us on this exciting journey as we unlock the mysteries of synchronous machines in Part II of our comprehensive series.

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Table of Content

Cylindrical Rotor Synchronous Generator

The Cylindrical Rotor Synchronous Generator is a vital component in power systems, characterized by its cylindrical rotor construction. This introductory guide provides insights into its design, operation, and applications. 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 below.


  • An equivalent circuit of a synchronous generator is shown 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 Salient Pole Synchronous Machine is a type of synchronous machine characterized by its distinctive pole shape, offering unique advantages in terms of simplicity, robustness, and suitability for low-speed applications.


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

The cylindrical rotor synchronous motor is a type of electric motor known for its cylindrical rotor construction, which offers several advantages such as high torque, efficient operation, and excellent stability.


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 the Motor, there are three parameters that 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 the 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 the 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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FAQs about Synchronous Machines notes Part – II for Electrical Engineering

  • Synchronous machine modelling allows engineers to mathematically represent the behaviour and characteristics of synchronous machines, enabling analysis and prediction of their performance under different operating conditions.

  • Phasor diagrams provide a graphical representation of voltage, current, and power relationships in synchronous machines. They offer a visual tool to analyze and comprehend the machine's response to load and excitation changes.

  • Important parameters of a synchronous machine include synchronous reactance, armature resistance, and field resistance. These parameters determine the machine's efficiency, power factor, and ability to synchronize with the grid.

  • Synchronous machines find applications in various fields, including power generation, industrial processes, and renewable energy systems. They are commonly used in power plants, synchronous condensers, and grid stabilization systems.

  • Optimization techniques for synchronous machines involve adjusting parameters such as field excitation, load angle, and power factor control. These adjustments aim to maximize efficiency, minimize losses, and maintain stable operations within design limits.

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