Synchronous Machine-II

Contents

Recall the Two-Reaction Theory of Salient-Pole Synchronous Machine 1

Describe the Power Flow Equation of Cylindrical-Rotor Synchronous Machines 2

Describe the Power Flow Equation of Salient-Pole Synchronous Machines 3

Recall the Effect of change in Excitation at Constant Load 6

Recall and draw the V-Curve of Synchronous Machines 7

Recall and draw the Inverted V-Curve of Synchronous Machines 8

Recall and draw Compounding Curve of Synchronous Machines 10

Recall Hunting phenomena in Synchronous Machines 11

Describe Damper windings in Synchronous Machines 12

Describe the Synchronous Condenser 13

Describe the Dual Purpose Synchronous Motor 14

Recall the different Torques in Synchronous Motor 15

Recall the Two-Reaction Theory of Salient-Pole Synchronous Machine

The Two-Reaction theory is a method used to analyze the performance of salient-pole synchronous machines. In these machines, the rotor has projecting poles with a large air gap, which creates a significant magnetic saturation effect. This effect causes the magnetic field distribution in the air gap to be more complex than that of a cylindrical rotor machine, making the analysis of salient-pole machines more challenging.

The Two-Reaction theory divides the magnetic field in the air gap of the salient-pole machine into two components: the direct-axis (d-axis) component and the quadrature-axis (q-axis) component. The d-axis component is aligned with the axis of the rotor poles, while the q-axis component is perpendicular to the rotor poles.

The d-axis component of the magnetic field is responsible for producing the torque in the machine. The magnitude of the d-axis component depends on the excitation current of the rotor field winding and the armature reaction. The armature reaction is the effect of the stator current on the magnetic field distribution in the air gap. The armature reaction creates a demagnetizing effect on the d-axis component of the field, reducing the torque produced by the machine.

The q-axis component of the magnetic field is responsible for creating the flux linkage between the stator and rotor windings, which generates the induced voltage in the stator winding. The magnitude of the q-axis component depends on the rotor speed and the field excitation current.

The Two-Reaction theory allows us to separate the effect of the armature reaction on the d-axis component of the field from the effect of the rotor speed on the q-axis component of the field. This separation enables the analysis of the machine’s performance and the design of the machine’s excitation system to achieve the desired performance.

For example, suppose a salient-pole synchronous machine has an armature current flowing through the stator winding. In that case, the armature reaction will create a demagnetizing effect on the d-axis component of the field, reducing the machine’s torque production. However, the q-axis component of the field will remain unaffected, and the induced voltage in the stator winding will remain unchanged. This effect is essential for the proper design of the machine’s excitation system to compensate for the armature reaction and maintain the desired performance.

In summary, the Two-Reaction theory is a method used to analyze the performance of salient-pole synchronous machines. The theory divides the magnetic field in the air gap of the machine into two components: the d-axis and q-axis components. The d-axis component is responsible for producing the torque in the machine, while the q-axis component creates the flux linkage between the stator and rotor windings, generating the induced voltage in the stator winding. This separation enables the analysis of the machine’s performance and the design of the machine’s excitation system to achieve the desired performance.

Describe the Power Flow Equation of Cylindrical-Rotor Synchronous Machines

The power flow equation of a cylindrical-rotor synchronous machine describes the relationship between the electrical power input and the mechanical power output of the machine. It is based on the principle of energy conservation and is derived from the electrical and mechanical equations of the machine.

Let’s consider a cylindrical-rotor synchronous machine operating in steady-state conditions. The power flow equation can be expressed as:

P_in – P_loss = P_out

Where:

• P_in is the electrical power input to the machine.
• P_loss represents the power losses in the machine, including copper losses and core losses.
• P_out is the mechanical power output of the machine.

The electrical power input, P_in, can be calculated using the following equation:

P_in = V_phase * I_phase * cos(θ)

Where:

• V_phase is the phase voltage applied to the machine.
• I_phase is the phase current flowing through the machine.
• θ is the power factor angle, which represents the phase difference between the voltage and current waveforms.

The power losses, P_loss, in the machine consist of two main components: copper losses and core losses. Copper losses are the resistive losses in the stator and rotor windings and can be calculated as:

P_copper = I^2 R

Where:

• I is the rms current flowing through the windings.
• R is the total resistance of the windings.

Core losses, on the other hand, are the losses due to hysteresis and eddy currents in the magnetic core of the machine. They are typically represented by a constant value and can be estimated based on the machine’s specifications.

The mechanical power output, P_out, is given by:

P_out = T_mech * ω_mech

Where:

• T_mech is the mechanical torque produced by the machine.
• ω_mech is the mechanical angular velocity of the rotor.

The power flow equation provides a relationship between the electrical power input and the mechanical power output of a cylindrical-rotor synchronous machine. By solving this equation, various operating parameters of the machine can be determined, such as torque, power factor, and efficiency.

Describe the Power Flow Equation of Salient-Pole Synchronous Machines

The power flow equation of a salient-pole synchronous machine is an equation that describes the relationship between the input electrical power, the output mechanical power, and the losses in the machine. This equation is essential for analyzing the performance of the machine and designing its excitation system to achieve the desired performance.

The power flow equation of a salient-pole synchronous machine can be expressed as follows:

P_in = P_out + P_loss

Where P_in is the input electrical power to the machine, P_out is the output mechanical power of the machine, and P_loss is the power loss in the machine.

The input electrical power to the machine is given by:

P_in = V_t * I_t * cos(theta)

Where V_t is the terminal voltage of the machine, I_t is the current flowing in the machine, and theta is the phase angle between the voltage and current.

The output mechanical power of the machine is given by:

P_out = T_m * omega_m

Where T_m is the torque produced by the machine, and omega_m is the angular speed of the rotor.

The power loss in the machine is given by:

P_loss = P_core + P_copper + P_mech

Where P_core is the core losses in the machine, P_copper is the copper losses in the machine, and P_mech is the mechanical losses in the machine.

The core losses in the machine are due to hysteresis and eddy current losses in the core material. These losses are dependent on the magnetic flux density in the core and the frequency of the magnetic field.

The copper losses in the machine are due to the resistance of the stator and rotor windings. These losses are dependent on the current flowing in the windings and the resistance of the windings.

The mechanical losses in the machine are due to friction and windage losses in the bearings and the air gap. These losses are dependent on the speed of the rotor.

In a salient-pole synchronous machine, the rotor has salient poles instead of a smooth cylindrical rotor, as in a cylindrical-rotor synchronous machine. The presence of the salient poles in the rotor causes the magnetic field to be non-uniform and to have a significant effect on the machine’s performance. The power flow equation of a salient-pole synchronous machine accounts for this non-uniform magnetic field by including additional terms for the damper winding and the field winding.

The damper winding is a short-circuited winding that is placed on the rotor to damp out oscillations that can occur during transient conditions. The damper winding has a resistance and an inductance, which contribute to the power loss in the machine.

The field winding is a winding that is used to create the magnetic field in the rotor. The field winding has a resistance and an inductance, which also contribute to the power loss in the machine.

The power flow equation for a salient-pole synchronous machine can be modified to include these additional terms as follows:

P_in = P_out + P_loss + P_damper + P_field

Where P_damper is the power loss in the damper winding, and P_field is the power loss in the field winding.

For example, suppose a salient-pole synchronous machine is used as a generator in a power plant. In that case, the power flow equation can be used to calculate the input electrical power, the output mechanical power, and the losses in the machine. The equation can also be used to design the machine’s excitation system to achieve the desired performance, such as maintaining a constant voltage at the terminal or regulating the reactive power flow.

Recall the Effect of change in Excitation at Constant Load

The excitation of a synchronous machine refers to the magnetic field that is created by passing current through the field winding. The strength of the magnetic field is proportional to the excitation current, and it affects the performance of the machine. Changing the excitation current at a constant load can have a significant effect on the machine’s performance, as described below:

1. Change in Terminal Voltage: Changing the excitation current can change the terminal voltage of the synchronous machine. If the excitation current is increased, the magnetic field strength increases, which increases the terminal voltage. Conversely, if the excitation current is decreased, the magnetic field strength decreases, which decreases the terminal voltage. Therefore, changing the excitation current can be used to control the terminal voltage of the machine.
2. Change in Power Factor: Changing the excitation current can also change the power factor of the synchronous machine. The power factor is the ratio of the real power (measured in watts) to the apparent power (measured in volt-amperes) of the machine. If the excitation current is increased, the power factor of the machine increases, and if the excitation current is decreased, the power factor of the machine decreases. Therefore, changing the excitation current can be used to control the power factor of the machine.
3. Change in Reactive Power: Changing the excitation current can also change the reactive power (measured in volt-amperes reactive or VAR) of the synchronous machine. The reactive power is the component of the apparent power that is due to the magnetic field in the machine. If the excitation current is increased, the reactive power of the machine increases, and if the excitation current is decreased, the reactive power of the machine decreases. Therefore, changing the excitation current can be used to control the reactive power of the machine.
4. Change in Power Transfer Capability: Changing the excitation current can also affect the power transfer capability of the synchronous machine. The power transfer capability is the maximum amount of real power that the machine can transfer at a given power factor and terminal voltage. If the excitation current is increased, the power transfer capability of the machine increases, and if the excitation current is decreased, the power transfer capability of the machine decreases. Therefore, changing the excitation current can be used to increase or decrease the power transfer capability of the machine.
5. Change in Stability: Changing the excitation current can also affect the stability of the synchronous machine. The stability of the machine refers to its ability to maintain a constant speed and output voltage under varying load conditions. If the excitation current is increased, the stability of the machine increases, and if the excitation current is decreased, the stability of the machine decreases. Therefore, changing the excitation current can be used to improve or worsen the stability of the machine.

In summary, changing the excitation current of a synchronous machine at a constant load can have a significant effect on the machine’s performance, including the terminal voltage, power factor, reactive power, power transfer capability, and stability. Therefore, the excitation system of the machine must be carefully designed and controlled to achieve the desired performance.

Recall and draw the V-Curve of Synchronous Machines

The V-curve of synchronous machines is a graphical representation of the relationship between the excitation current and the power factor of the machine. The V-curve is obtained by plotting the power factor of the machine on the y-axis and the excitation current on the x-axis. The V-curve is so named because of its shape, which resembles the letter “V.”

The V-curve of synchronous machines is useful for analyzing the performance of the machine under different operating conditions. The V-curve is typically divided into three regions: under-excited, normal-excited, and over-excited. The under-excited region is located on the left-hand side of the V-curve and represents the operating conditions where the machine is under-excited. The over-excited region is located on the right-hand side of the V-curve and represents the operating conditions where the machine is over-excited. The normal-excited region is located in the middle of the V-curve and represents the operating conditions where the machine is operating at the rated excitation current.

The V-curve is typically used to determine the maximum power transfer capability of the synchronous machine. The maximum power transfer capability occurs at the boundary between the under-excited and normal-excited regions of the V-curve. At this point, the power factor of the machine is unity, and the machine is operating at the maximum power transfer capability.

The V-curve of synchronous machines is affected by various factors, including the load on the machine, the voltage regulation of the machine, and the power factor of the load. For example, if the load on the machine increases, the V-curve shifts downwards, indicating a decrease in the power factor. Similarly, if the voltage regulation of the machine is poor, the V-curve shifts to the left, indicating a decrease in the maximum power transfer capability of the machine.

In summary, the V-curve of synchronous machines is a graphical representation of the relationship between the excitation current and the power factor of the machine. The V-curve is useful for analyzing the performance of the machine under different operating conditions and determining the maximum power transfer capability of the machine. The V-curve is affected by various factors, including the load on the machine, the voltage regulation of the machine, and the power factor of the load.

Recall and draw the Inverted V-Curve of Synchronous Machines

The inverted V-curve of synchronous machines is a graphical representation of the relationship between the field current and the armature current at constant terminal voltage. The curve is obtained by plotting the armature current on the x-axis and the field current on the y-axis. The curve is so named because of its shape, which is the inverse of the V-curve.

The inverted V-curve is important in analyzing the stability of synchronous machines. The curve is typically divided into two regions: stable and unstable. The stable region is located on the left-hand side of the curve, and the unstable region is located on the right-hand side of the curve. The boundary between the stable and unstable regions is called the critical field current.

If the machine is operating at a field current that is less than the critical field current, the machine is stable. In this region, an increase in the armature current results in a decrease in the field current, which causes the machine to slow down. Conversely, a decrease in the armature current results in an increase in the field current, which causes the machine to speed up. The machine is said to be stable because it can return to its original operating point after a disturbance.

If the machine is operating at a field current that is greater than the critical field current, the machine is unstable. In this region, an increase in the armature current results in an increase in the field current, which causes the machine to speed up. Conversely, a decrease in the armature current results in a decrease in the field current, which causes the machine to slow down. The machine is said to be unstable because it cannot return to its original operating point after a disturbance.

The inverted V-curve is affected by various factors, including the machine’s rotor angle, the machine’s excitation system, and the machine’s damping characteristics. For example, if the machine’s damping characteristics are poor, the inverted V-curve will shift to the left, indicating a decrease in the critical field current and a decrease in the stability of the machine.

In summary, the inverted V-curve of synchronous machines is a graphical representation of the relationship between the field current and the armature current at constant terminal voltage. The curve is important in analyzing the stability of synchronous machines and is affected by various factors, including the machine’s rotor angle, the machine’s excitation system, and the machine’s damping characteristics.

Recall and draw Compounding Curve of Synchronous Machines

The compounding curve of synchronous machines is a graphical representation of the relationship between the terminal voltage and the field current at constant speed and load. The curve is obtained by plotting the terminal voltage on the y-axis and the field current on the x-axis.

The compounding curve is important in determining the machine’s performance under varying load conditions. The curve is typically divided into two regions: over compounding and under compounding. The over compounding region is located on the left-hand side of the curve, and the under compounding region is located on the right-hand side of the curve. The boundary between the over compounding and under compounding regions is called the rated field current.

If the machine is operating at a field current that is less than the rated field current, the machine is under compounded. In this region, an increase in the load results in a decrease in the terminal voltage, which causes the machine to slow down. Conversely, a decrease in the load results in an increase in the terminal voltage, which causes the machine to speed up. The machine is said to be under compounded because it cannot maintain a constant terminal voltage under varying load conditions.

If the machine is operating at a field current that is greater than the rated field current, the machine is over compounded. In this region, an increase in the load results in an increase in the terminal voltage, which causes the machine to speed up. Conversely, a decrease in the load results in a decrease in the terminal voltage, which causes the machine to slow down. The machine is said to be over compounded because it can maintain a constant or even increasing terminal voltage under varying load conditions.

The compounding curve is affected by various factors, including the machine’s excitation system and the machine’s armature reaction. For example, if the machine’s excitation system is weak, the compounding curve will shift to the right, indicating a decrease in the rated field current and a decrease in the machine’s ability to maintain a constant terminal voltage under varying load conditions.

In summary, the compounding curve of synchronous machines is a graphical representation of the relationship between the terminal voltage and the field current at constant speed and load. The curve is important in determining the machine’s performance under varying load conditions and is affected by various factors, including the machine’s excitation system and the machine’s armature reaction.

Recall Hunting phenomena in Synchronous Machines

Hunting is an undesirable phenomenon that occurs in synchronous machines when the rotor and stator magnetic fields are not properly synchronised. Hunting is characterized by small variations in speed and torque, which can lead to machine instability and damage. Hunting typically occurs in salient-pole machines, which have a large air gap between the rotor and stator.

Hunting can occur in two different modes: subsynchronous oscillations and supersynchronous oscillations. Subsynchronous oscillations occur when the rotor speed is less than the synchronous speed, while supersynchronous oscillations occur when the rotor speed is greater than the synchronous speed.

Subsynchronous oscillations can be caused by a variety of factors, including unbalanced magnetic pull, unbalanced mechanical forces, and unbalanced stator or rotor winding currents. Supersynchronous oscillations can be caused by a variety of factors, including variations in the rotor magnetic field, variations in the stator magnetic field, and variations in the rotor or stator winding currents.

The effects of hunting can be severe, leading to increased mechanical stresses on the rotor and stator, increased wear and tear on the bearings, and increased losses in the machine. To prevent hunting, various techniques are used, including the use of damping windings, the use of rotor or stator damper windings, and the use of solid-state controllers.

In summary, hunting is an undesirable phenomenon that occurs in synchronous machines when the rotor and stator magnetic fields are not properly synchronised. Hunting can occur in two different modes: subsynchronous oscillations and supersynchronous oscillations. The effects of hunting can be severe, leading to increased mechanical stresses on the rotor and stator, increased wear and tear on the bearings, and increased losses in the machine. To prevent hunting, various techniques are used, including the use of damping windings, the use of rotor or stator damper windings, and the use of solid-state controllers.

Describe Damper windings in Synchronous Machines

Damper windings are a type of winding that is often used in synchronous machines to reduce the effects of hunting. Hunting is an undesirable phenomenon that occurs when the rotor and stator magnetic fields are not properly synchronised, leading to small variations in speed and torque that can cause machine instability and damage.

A damper winding is typically a set of conductive bars or coils that are mounted on the surface of the rotor, and that are electrically connected to the rotor winding. The damper winding is designed to produce a magnetic field that interacts with the magnetic field produced by the rotor winding, damping out any subsynchronous oscillations that may be present.

The design of the damper winding depends on a variety of factors, including the size and shape of the machine, the type of rotor winding, and the expected operating conditions of the machine. In general, the damper winding should be designed to produce a magnetic field that is out of phase with the magnetic field produced by the rotor winding, so that the two fields oppose each other and cancel out any subsynchronous oscillations.

In addition to reducing the effects of hunting, damper windings can also help to reduce the effects of transient disturbances, such as sudden changes in load or voltage. This is because the damper winding acts as a sort of electrical shock absorber, absorbing any sudden changes in magnetic field or mechanical forces that might otherwise cause the machine to become unstable.

In summary, damper windings are a type of winding that is often used in synchronous machines to reduce the effects of hunting and other types of instability. Damper windings are typically a set of conductive bars or coils that are mounted on the surface of the rotor and that are designed to produce a magnetic field that interacts with the magnetic field produced by the rotor winding. The design of the damper winding depends on a variety of factors, including the size and shape of the machine and the expected operating conditions of the machine.

Describe the Synchronous Condenser

A synchronous condenser is a synchronous machine that is operated as a reactive power source rather than a mechanical power source. It is essentially a synchronous generator that is connected to the power system but is not connected to any mechanical load. Instead, the synchronous condenser is used to supply or absorb reactive power as needed to support the voltage and stability of the power system.

The operation of a synchronous condenser is based on the fact that a synchronous machine can operate as a capacitor or an inductor depending on the excitation level. When the excitation level is increased beyond the normal operating level of a synchronous generator, the machine begins to absorb reactive power, effectively operating as a capacitor. Conversely, when the excitation level is decreased below the normal operating level, the machine begins to supply reactive power, effectively operating as an inductor.

Synchronous condensers are often used in power systems to improve voltage regulation, reduce voltage fluctuations, and improve system stability. They can also be used to improve the power factor of the system, which is a measure of the efficiency of the system in delivering real power to loads.

One example of the use of synchronous condensers is in high-voltage transmission systems. In these systems, long transmission lines can cause voltage drops and other instabilities that can affect the reliability and efficiency of the system. By installing synchronous condensers at strategic locations along the transmission line, operators can effectively compensate for these voltage drops and improve the stability of the system.

Another example of the use of synchronous condensers is in renewable energy systems, particularly those based on wind or solar power. These systems often generate variable amounts of power depending on weather conditions and other factors, which can create instabilities in the power system. By using synchronous condensers to supply or absorb reactive power as needed, operators can help to stabilize the power system and improve the overall reliability and efficiency of the renewable energy system.

In summary, a synchronous condenser is a synchronous machine that is operated as a reactive power source rather than a mechanical power source. It is used to supply or absorb reactive power as needed to support the voltage and stability of the power system. Synchronous condensers are often used in high-voltage transmission systems and renewable energy systems to improve system stability, reduce voltage fluctuations, and improve the power factor of the system.

Describe the Dual Purpose Synchronous Motor

A dual purpose synchronous motor is a type of synchronous motor that can be operated either as a motor or as a generator. It is designed to have a very high power factor when operated as a motor, and to deliver a high output voltage when operated as a generator. These characteristics make dual purpose synchronous motors ideal for use in applications where both motor and generator functions are required, such as in power generation, traction systems, and other industrial applications.

The construction of a dual purpose synchronous motor is similar to that of a standard synchronous motor, with a rotor and stator assembly. The rotor contains the field winding, which is excited by a DC source to create a magnetic field. The stator contains the armature winding, which is connected to the power source and supplies the current to drive the motor.

When operated as a motor, a dual purpose synchronous motor is designed to have a very high power factor, which is the ratio of real power to apparent power. This means that the motor is very efficient at converting electrical power into mechanical power, and produces a high torque output. The high power factor also helps to reduce the reactive power consumption of the motor, which can result in significant energy savings.

When operated as a generator, a dual purpose synchronous motor is designed to deliver a high output voltage, which is typically higher than the voltage of the power source. This is achieved by adjusting the excitation level of the field winding to create a higher voltage output. The high output voltage makes dual purpose synchronous motors ideal for use in applications such as power generation, where the generated power must be stepped up to a higher voltage level for transmission over long distances.

One example of the use of dual purpose synchronous motors is in traction systems for electric vehicles. In these systems, the motor is used to drive the vehicle forward, while the regenerative braking system uses the motor as a generator to convert the kinetic energy of the vehicle into electrical energy, which is then stored in a battery or fed back into the power grid.

Another example of the use of dual purpose synchronous motors is in power generation systems. In these systems, the motor is used to drive a generator to produce electrical power, while the generator can be used as a motor to start the motor when the power source is not available.

In summary, a dual purpose synchronous motor is a type of synchronous motor that can be operated either as a motor or as a generator. It is designed to have a very high power factor when operated as a motor, and to deliver a high output voltage when operated as a generator. Dual purpose synchronous motors are ideal for use in applications where both motor and generator functions are required, such as in power generation, traction systems, and other industrial applications.

Recall the different Torques in Synchronous Motor

Synchronous motors are used in various industrial applications, including compressors, pumps, and generators. The torque produced by a synchronous motor depends on the excitation current and the power factor. There are two types of torques in synchronous motors: Pull-in torque and Pull-out torque.

1. Pull-in torque:

The pull-in torque is the minimum torque required to start the synchronous motor. The pull-in torque occurs when the rotor speed is less than the synchronous speed, and the stator magnetic field pulls the rotor towards the synchronous speed. The pull-in torque is maximum when the motor is operated at unity power factor.

1. Pull-out torque:

The pull-out torque is the maximum torque that can be produced by the synchronous motor without losing synchronization. The pull-out torque is dependent on the motor’s excitation current and varies with the power factor. It is highest at leading power factor and decreases as the power factor becomes more lagging.

1. Cogging torque:

Cogging torque is an unwanted torque that occurs due to the interaction between the salient poles of the rotor and stator. It is a pulsating torque that can cause the motor to vibrate and produce noise. Cogging torque is more prominent in salient pole synchronous motors than cylindrical rotor synchronous motors.

1. Damper winding torque:

In synchronous motors, damper winding is used to provide damping effect during the hunting phenomenon. The damper winding also produces torque, known as the damper winding torque, which opposes the hunting motion of the rotor. The magnitude of the damper winding torque is proportional to the rotor displacement from its equilibrium position.

In summary, synchronous motors have different types of torques, including pull-in torque, pull-out torque, cogging torque, and damper winding torque. Understanding these torques is crucial in designing and operating synchronous motors in various applications.