Synchronous and Asynchronous Machines

Posted on Aug 13, 2024 in Electronics

Asynchronous Machines

Single Phase Induction Motor

Working Principle

Basically, a single-phase induction motor comprises a squirrel cage rotor similar to that of three-phase motors and a stator with a single-phase AC-powered winding. Usually constructed with powers less than 1 hp, they are also called fractional motors.

Introducing an alternating current in the stator windings produces a magnetomotive force in the gap. This produces a magnetic field proportional in strength, which in turn induces currents in the rotor, as if it were the secondary circuit of a transformer. The torques generated by the interaction of the intensities of the two halves of the rotor winding inductor with the stator field are opposite each other. Therefore, the resultant torque acting on the rotor at rest is zero. The absence of an initial boot pair represents the characteristic feature of a single-phase motor, and so this machine cannot boot by itself.

If one phase of a three-phase motor is disconnected, it would operate similarly to a single-phase motor.

Start

The single-phase motor has no starting torque and therefore cannot start up by itself.

The procedures for starting single-phase induction motors are:

1. Engine starting phase
   This motor has two windings located on the stator, electrically 90 degrees apart in space. The first winding, called the main winding, covers 2/3 of the slots and has many turns of heavy wire, so it offers low resistance and reactance and is directly connected to the network. The other winding, called the auxiliary or starting winding, covers the rest of the stator and has few turns of thin wire, offering high resistance and low reactance. It is connected in series with a centrifugal switch located on the motor shaft.
2. Motor with capacitor
   This type of motor consists of a main winding that covers 2/3 of the slots and has many turns of heavy wire, so it offers great reactance and low resistance and is directly connected to the network. The auxiliary winding covers the rest of the stator and has few turns of thin wire, offering high resistance and low reactance. It is connected in series with a capacitor of sufficient capacity to advance the current phase by about 90 degrees for the main winding. Sometimes, to improve torque characteristics and the power factor of the machine, capacitors are used with oil-impregnated paper that works continuously.

Synchronous Machines

Introduction

Synchronous machines are electrical machines whose rotational speed (rpm) is tightly linked with the frequency (f) of the AC network with which they work: n = 60f / p, where p is the number of pole pairs of the machine.

Synchronous machines can operate as either generators or motors. However, in practice, they are more frequently used as generators (alternators) to produce alternating current electricity. On the other hand, when they convert electrical energy into mechanical energy, they operate as synchronous motors. These motors are used in industrial drives that require constant speeds, taking advantage of the fact that, unlike asynchronous motors, they can regulate the power factor with which they work. When working with a leading power factor, a synchronous motor is said to function as a synchronous capacitor or synchronous condenser.

Constructive Aspects

Synchronous machines, like other types of electrical machines, consist of two separate windings:

1. Field winding: Constructed in the form of distributed or concentrated windings in slots, fed by direct current, which creates the poles of the machine.
2. Armature winding: A distributed winding forming a three-phase alternating current circuit.

On small machines, for powers that do not exceed 10 kVA, the field winding is normally placed in the stator in concentrated form, while the armature generally forms a three-phase winding on the rotor.

In large synchronous machines, which in the case of alternators can reach 1000-1500 MVA, the placement of the windings is opposite to the previous, so that the poles are located on the rotor and the phase winding on the stator. In this situation, the rotor structure is produced in two different versions, either salient pole or cylindrical rotor. In the first case, the windings of the poles are concentrated, while for the cylindrical rotor, the winding is distributed in slots on the poles. The power inductor winding is formed by two rings placed on the moving part of the machine, introducing a continuous stream outside. There are two types of armatures: a rotating armature requires three rings, while a fixed induced armature does not need rings. It should be noted that it is more difficult to isolate the conductors in a rotating armature than in a fixed armature.

Excitation Systems

The windings that form the poles of a synchronous machine are fed with direct current. In the traditional system, this DC comes from an exciter generator mounted on the shaft of the group, and its output is applied to the alternator rotor through slip rings with corresponding brushes. The exciter is a conventional DC generator, which sometimes replaces all or part of its excitation with a pilot exciter to improve speed of response. Synchronous machines often have a smaller pilot exciter, and the main exciter works as a shunt inductor, directly feeding the alternator field.

In modern times, a brushless excitation system is used. In this case, the phase winding of the exciter is mounted on the rotor, and the field winding on the stator. The AC output of the DC exciter is converted by rectifiers mounted on the shaft and directly feeds the alternator rotor without rings or brushes (rotating rectifiers).

In modern alternators used on generators to supply electricity to isolated installations, self-excitation of the alternator is used. This is necessary to obtain the DC poles from the generator output itself, which is then rectified.

Working Principle of an Alternator

Running on Empty

By rotating the rotor at speed n, electromotive forces (EMFs) are induced in the windings of the three phases of the stator, which are outdated by 120 degrees in time. If we consider the N turns of each phase to be concentrated, and the concatenated flow for the same varies between the limits + Φm – Φm, the average value of EMF induced in each phase during half a period of the alternating current is:

E_med = 4fNΦm

The effective EMF E will have a magnitude:

E = 4KfNΦm

The open-circuit characteristic curve is an important feature of the synchronous machine’s operation with no load, as it expresses the terminal EMF of the machine when disconnected, depending on the load current.

Performance Under Load: Armature Reaction

If, while running a loaded generator with a given excitation current, we close the armature circuit by connecting a load impedance to the terminals, we obtain a voltage V across the machine below the value it had at no load (E0). The reduction in the output voltage of the generator is due to the appearance of a current in the armature, which causes a voltage drop in this circuit. At the same time, it produces a magnetomotive force (MMF) that reacts with the inductor air-gap flux, modifying the machine. It should also consider the armature’s reactance, due to the stator leakage flux, which does not interact with the rotor flux. This leakage flux can define an inductance Lσ, that, multiplied by the current pulse, results in the stator leakage reactance X_σ = ωLσ = 2πfLσ. The effect caused by the armature MMF on the inductor MMF modifies the air-gap flux of the machine. This phenomenon is known as armature reaction.

Membership of the inductor and armature MMFs as the load is resistive, inductive, or capacitive:

1. Resistive load
   If the load is purely resistive, the power factor is unity, and if one ignores the impedance of the armature, it may be considered that the phase angle between the EMF and the current is φ = 0. To calculate the direction and magnitude of the induced EMFs, Faraday’s law must be applied in the form: e = L (v x B), where v indicates a velocity vector, contrary to the direction of rotation of the rotor, equal to the peripheral speed, which is the result of taking into account the relative motion between the two circuits. The EMFs are highest when the sides of the coils are located directly across from the centers of the poles. As the phase angle between the EMF and the current is zero, this moment coincides with the maximum intensity. It is noted that for a resistive load, the armature reaction is transverse, i.e., it is displaced 90 degrees from the MMF.
2. Inductive load
   When the load is purely inductive, the phase angle between the EMF and the current is about 90 degrees. In this case, the maximum flow will be moved in space from a peak of EMF at an angle of 90 degrees in the opposite direction of rotation of the rotor. Whatever the EMFs are highest when the sides of the turns are in the center of the poles, the current will be highest when the north pole of the rotor is advanced 90 electrical degrees to the position of maximum MMF. It is noted that the armature reaction MMF opposes the inductor, which means that a purely inductive load produces a demagnetizing reaction, which tends to reduce the resultant MMF, reducing the flow in the gap, thus causing a reduction of the induced EMF.
3. Capacitive Load
   When the load is purely capacitive, the stator current will peak 90 electrical degrees before the driver faces forming the turns of the armature, which is when the EMF is at its maximum. At this time, there is a reinforcement of the MMF of the inductor, which means that capacitive loads help the action of the field at the poles, causing a magnetizing effect on them.
   When loads are not pure, a phase angle between -90 degrees and +90 degrees is present.
   Thus, in synchronous machines, both salient-pole and cylindrical rotor, the armature reaction causes a resultant change in the MMF acting on the magnetic circuit, which in turn changes the magnitude of the air-gap flux and hence the value of the EMF obtained in the armature.

Phasor Diagram of an Alternator: Voltage Regulation

The phasor diagram of an alternator graphically determines the relationship between EMF and voltage in different operating regimes of the machine.

In principle, to analyze the phasor diagram, a synchronous machine with a uniform air gap (cylindrical rotor) is considered because then the armature reaction does not depend on the position of the rotor, as the reluctance is the same in all positions. It is assumed that the leakage reactance Xσ is constant and that hysteresis losses in iron can be neglected. This last condition is equivalent to saying that the resultant MMF is in phase with the flow it produces.

Consider a machine operating as a synchronous generator with a phase voltage V, which carries an inductive current induced in a phase angle φ. To determine the resulting EMF, the voltage drops produced in the resistance and leakage reactance will be added to the terminal voltage, resulting in:

E_r = V + RI + jX_σI.

The flow needed to produce the previous EMF will advance 90 degrees for E_r, and if hysteresis is neglected, the direction of flow will also correspond to the resultant MMF F_r. F_r is the sum of the excitation or inducing MMF F_e and the reaction-induced MMF F_i, i.e.:

F_r = F_e + F_i.

If this excitation MMF is represented by F_e, the machine is left empty in the absence of armature reaction, i.e., F_i = 0, the resultant MMF becomes the excited MMF F_e = F_r, and the flow placed in the gap increases in phase with F_e and determines the synchronous open-circuit characteristic curve. The above process is the general method to calculate the MMF required in the excitation when the machine delivers a current I at a given voltage V.

Define voltage regulation of a synchronous machine as the quotient:

A = [(E₀ – V) / V] * 100%,

which expresses the change in terminal voltage from no load to full load for a particular excitation at the poles. With resistive loads and especially inductive loads, due to the demagnetizing effect of the armature MMF, there is a decrease in blood flow as output grows, leading to positive regulation values. For capacitive loads, having the armature MMF magnetizing effect, the load voltage is higher than the no-load voltage, leading to a negative regulation value.

Linear Analysis of a Synchronous Machine: The Equivalent Circuit

General

In synchronous behavior, it is necessary to consider the effect of armature reaction, which requires the simultaneous use of electrical quantities (EMF, voltage, and current) and magnetic quantities (MMFs and flow). This analysis procedure is called a general method and accurately reproduces the physical phenomena involved, but it has the disadvantage that handling two types of quantities leaves no choice but to resort to using phasor diagrams.

Behn-Eschenburg Method: Synchronous Impedance

This method is applied to cylindrical rotor machines working in a linear regime, which means that the flows are proportional to the MMFs, and therefore, the principle of superposition can be used. The advantage of this method is that it leads to an equivalent electrical circuit of the synchronous machine, with the analytical advantages that this entails. It is known that there is actually a single stream in the air gap of a synchronous machine that is produced by the joint action of the excitation MMF F_e and the reaction MMF F_i. However, it is more convenient to consider that each MMF produces an independent flow that creates a corresponding induced EMF. This will work only with EMFs and electrical variables, apart from the magnetic ones. This idea involves three streams:

1. The leakage flux Φ_σ, which results in a voltage drop in the reactance of the same name X_σ: + jX_σI, i.e., the voltage drop caused by the leakage reactance is advanced 90 degrees with the armature current.
2. The excitation flow Φ_e, which is responsible for the EMF produced at no load, E₀.
3. The armature reaction flux Φ_i, which results in an EMF E_p delayed 90 degrees with the flow.

Finally, with a new phasor diagram, we arrive at the final expression:

E₀ = V + RI + jX_σI + jX_pI,

indicating that the air-gap induced EMF E₀ due to the excitation MMF F_e can be considered as the result of adding the voltage V across the machine to the voltage drops of the resistance: RI.

Characteristics of Open-Circuit and Short-Circuit of a Synchronous Machine: Determination of the Synchronous Impedance

To study the behavior of this machine, it will be necessary to determine the parameters included in this circuit: E₀ and Z_s. The value of E₀ may be determined by analyzing the open-circuit condition:

Open circuit: I = 0 => E₀ = V (open circuit)

That is, the EMF E₀ is the terminal voltage of the machine when the armature current is zero. Finally, we reach the open-circuit characteristic:

E₀ = f(I_e), which is a curve.

The calculation of the synchronous impedance Z_s requires a short-circuit test:

Short circuit: V = 0 => E₀ = (R + jX_s) * I_short = Z_s * I_short

Where the modular value of the synchronous impedance is Z_s = E₀ / I_short, i.e., the synchronous impedance is the ratio between the open-circuit voltage and the short-circuit current. Having completed the steps… The curve representing I_cc = φ(I_e) is called the short-circuit characteristic and is virtually a straight line because, under these conditions, the magnetic circuit is not saturated, as both the excitation and the resulting flow are of low value.

For small excitations, the synchronous impedance Z_s is constant since the open-circuit characteristic coincides with the air-gap line and leads to the so-called unsaturated synchronous impedance:

Z_s (unsaturated) = O_d / O’_e

In the different proposals for standards and instructions from electrotechnical committees of different countries, it is customary to take the so-called saturated (or adjusted) synchronous impedance, which is obtained from the rated voltage O_d, which accounts for an exciting current O_b and produces a current in the armature O’_f:

Z_s (saturated) = Z_s = O_d / O’_f.

Finally, and after several operations, we can arrive at the equation that shows that the short-circuit ratio is the inverse of the saturated synchronous impedance values expressed in per unit:

1 / Z_s (pu) = O’_f / O’_g = O_b / O_c = SRC (short-circuit ratio).

Nonlinear Analysis of a Synchronous Machine: Potier’s or Zero Power Factor Method: Calculation of Regulation

Potier’s method is applied to cylindrical rotor synchronous machines operating in the saturation zone. In these machines, the saturated Behn-Eschenburg method leads to appreciable errors since the EMFs are not proportional to the MMFs due to the nonlinearity of the magnetic circuit area where it works.

Potier’s method determines the value of the decrease in the leakage reactance X_σI and the MMF produced by the armature reaction, so that the calculation of the regulation is based on constructing a general phasor diagram. To calculate the adjustment by Potier’s method, knowledge of the open-circuit characteristic curve is required, and it is also necessary to perform a test with a pure inductive short circuit, plotting the output voltage curve with respect to the excitation MMF, for a constant armature current equal to the rated current. Using Potier’s triangle, points on the characteristic curve are determined. Furthermore, Potier’s reactance is slightly greater than X_σ.

Operation of an Alternator on an Isolated Network

The behavior of a synchronous generator under load varies greatly depending on the power factor of the load and whether the generator operates alone or in parallel with other alternators. First, we will study the analysis of the behavior of the machine running in isolation. There are two important controls: first, the voltage regulator, which is incorporated in the exciter and, by varying the generator field current, can control the output voltage. On the other hand, the prime mover that drives the alternator has a speed regulator that acts on the water inlet, thereby allowing the group to control the speed and hence the frequency.

Assuming that the machine moves at a constant speed, the frequency is a fixed parameter. As the load increases, the armature current increases, and both the armature reaction MMF F_i and the resultant MMF F_r increase, resulting in a lower EMF E_r and a lower output voltage.

The equation governing the electrical behavior of the machine will be:

V = E₀ – jX_sI

In short, for an alternator operating on an isolated system, we have:

1. The frequency depends entirely on the speed of the prime mover that drives the synchronous machine.
2. The power factor of the generator is the power factor of the load.
3. The output voltage depends on: a) speed, b) exciting current, c) armature current, d) power factor of the load.

Connecting an Alternator to the Grid

In today’s world, it is very rare to have a single alternator in isolation that feeds its own load. This situation only occurs in some applications, such as generators. The general rule is that alternators in power stations are located near the primary energy sources.

To increase the performance and reliability of the system, the different power plants are connected in parallel through transmission and distribution lines. The network thus formed is a huge generator in which the voltage and frequency remain virtually constant.

For example, in Spain, the total installed electrical power of the entire country is about 65,000 MW, but the maximum unit power of alternators does not reach 1000 MW. In electrical terminology, we then say that there is an infinite power network (constant voltage and frequency) to which the various generators in the country are connected. The parallel connection of an alternator to the grid involves a series of complex operations that constitute the so-called synchronization of the machine. For such a connection to be made without any disturbance, it is necessary that the instantaneous value of the generator voltage has the same magnitude and phase as the instantaneous value of the mains voltage. This requirement leads to the following conditions, which are necessary to connect an alternator in parallel to the network:

1. The phase sequence of the alternator and the network must be the same.
2. The generator voltage must have an effective value equal to the voltage of the network, and its phases must match.
3. The frequency of the two voltages must be equal.

To verify these conditions, devices called synchroscopes are used in practice, which in the simplest case consist of three incandescent lamps. The operation begins by starting the machine through the prime mover at a speed approaching that of synchronism: n ≈ 60f / p. Excitation is then introduced into the inductor of the alternator, and it is gradually increased until the terminal voltage of the generator matches that of the mains.

In practice, in large alternators, the three-lamp synchroscope has been replaced by a needle synchroscope. The position of the needle shows the phase angle between the voltages of the generator and the network. When the frequencies are equal, the needle is stationary, and when the frequencies differ, the needle rotates in either direction, depending on whether the generator is running faster or slower than the network.

Active and Reactive Power Developed by a Synchronous Machine Connected to an Infinite Power Network

Consider a cylindrical rotor synchronous machine in which the induced resistance can be neglected compared to the synchronous reactance, whose magnitude is assumed constant. The active and reactive power delivered by the machine will be:

P = 3E₀Vsin(δ) / X_s = P_max * sin(δ),

Q = 3[(E₀Vcos(δ) – V²) / X_s]

Where the angle δ is called the power angle or load angle. The maximum active power is:

P_max = 3E₀V / X_s

If δ > 0, the active power developed by the machine is positive and corresponds to operation as a synchronous generator or alternator. If δ < 0, the active power is negative, i.e., it receives active power from the network and therefore works as a synchronous motor, delivering mechanical power at the shaft.

If E₀cos(δ) > V, the synchronous machine delivers inductive reactive power to the network, or equivalently, it receives capacitive power from the network. In this case, the machine is said to be overexcited. If E₀cos(δ) < V, the reactive power supplied by the generator is negative, i.e., capacitive, or equivalently, it receives inductive power from the network. We then say that the generator is underexcited.

Operation of a Synchronous Machine Connected to an Infinite Power Grid

When an alternator is connected to an infinite power network, it becomes part of a system that includes hundreds of other alternators, all feeding millions of loads. Unlike a generator operating on an isolated network, where the load is well defined, it is now impossible to know the nature of the load (large or small, resistive or inductive) connected to the terminals of a specific alternator. It is known that the group has two controls: a) the voltage regulation system that controls the alternator field current and, in the case of an isolated generator, was used to regulate the output voltage, and b) the speed regulation system of the prime mover, which in the isolated generator was used to control the frequency.

But the network to which the alternator is connected has infinite power, which means that the frequency and voltage are constant and are imposed by the network.

Effect of Varying the Excitation Current

To connect this machine to the network, it will have to produce an EMF E₀ equal in magnitude and phase to the network voltage V. If E₀ and V are identical, no current will flow through the armature of the alternator. Although the generator has been connected to the network, it does not supply (or receive) any power: it is said to be working in floating mode. If the exciting current is now increased, the induced EMF E₀ will increase, and being above the line voltage, it will cause a circulating current induced by I = (E₀ – V) / jX_s = E_x / jX_s. The current lags the voltage difference E_x by an angle of 90 degrees.

Effects of Changes in Mechanical Torque (Speed Regulator)

The active power supplied by a synchronous machine connected to an infinite power network comes from the mechanical power supplied by the turbine, which in turn depends on the water inflow (or steam in the case of thermal power plants), which is governed by the position of the speed regulator. If we consider floating mode as a new baseline and open the water inlet to the turbine, the rotor speed will increase, which will cause the voltage produced to be below the line voltage at an angle. The electrical power transferred by the generator to the grid will be: P = 3E₀Vsin(δ) / X_s, which is a function of the power angle δ. This indicates that if the excitation is constant, i.e., the EMF E₀ remains fixed, as the active power increases, the angle δ between V and E₀ also increases. In short, we can say that the change in the speed regulator of the turbine causes a change in the active power delivered by the machine, which is physically reflected as a change in the angle δ between the EMF E₀ and the voltage V.

For a given excitation, the active power will be maximum for δ = π / 2, which corresponds to the limit of static overload capacity or static stability limit of the alternator. A further increase in the input to the prime mover (turbine) causes the active power to decrease, and the excess power is converted into acceleration torque, which causes an increase in the generator speed, causing it to lose synchronism.

If it receives active power from the network and has a positive imaginary part, which means that it delivers inductive reactive power to the network or, in other words, receives capacitive power from the network, the machine is said to be overexcited.

Synchronous Motor: Features and Applications

The synchronous machine can switch from operating as a generator to operating as a motor by disconnecting the prime mover. Then, a useful torque is exerted on the axis, transforming the electrical energy absorbed from the network into mechanical rotational energy. The motor speed is expressed by the relationship: n = 60f / p, which is the network synchronous speed.

The synchronous motor has the major drawback that the torque retains a single direction only when the machine is already synchronized, i.e., when the rotor rotates at the same speed as the armature field. If the rotor is at rest or rotates at a different speed than the synchronous speed, the average torque developed when connected to the network is zero.

In synchronous motors that can start at no load, the implementation is done by means of an auxiliary motor, usually asynchronous, with the same number of poles as the main motor, so that a nearly synchronous rotation speed is obtained, and the network connection is performed using synchronization equipment, as was done with an alternator connected to the network. DC motors can also be used for this purpose because of their advantage of speed control, or induction motors with one less pole pair than the synchronous motor.

Another more practical procedure for starting these motors is to start them as asynchronous motors. For this purpose, it is necessary to place a squirrel cage winding on the poles of the machine. To perform asynchronous starting, the field winding must be closed on a resistance whose magnitude is 10-15 times higher than its own. This process is called self-synchronization of the motor. After the synchronous motor has started, its flow and excitation can be controlled so that the machine operates in an underexcited or overexcited regime to regulate its power factor, which makes this machine capable of fulfilling the dual mission of driving a mechanical load and compensating for the reactive current of the network.

Generally, the squirrel cage winding placed in these motors, used here to produce asynchronous starting, is also placed in generators and is called the damper winding because it reduces the fluctuations that occur in the transient processes of synchronous machines: connection to the network, abrupt changes in electrical or mechanical load. The effect of damper windings is zero in steady state since, when the machine is rotating at synchronous speed, no currents are induced in them.

The synchronous motor can be used to drive mechanical loads. In its low-power versions (less than 1 hp), DC is used for excitation, and its operation is based on the variation of the rotor reluctance (reluctance motors). Hysteresis synchronous motors are also used to power electric clocks and other time-measuring devices.

For high powers, one of the biggest advantages of this motor over the asynchronous motor is the possibility of regulating the power factor.