6.1 INTRODUCTION

Synchronous generators are the main source of bulk power generation at large power stations. They may be driven by prime movers such as hydro turbines, wind turbines, gas turbines, or internal combustion engines. Today's most mature science of power generation rests on synchronous-generator technology. Generators are the largest single unit of electric machines in production, having power of some 1,000 MVA. In a large power system, more than a thousand machines may be interconnected through tie-lines supplying thousands of megawatts of power to consumers dispersed over a wide area. Each machine could be driven by prime movers.

Synchronous generators are scalable and may be built for smaller power-generation applications such as domestic, commercial, and small-scale industrial needs. These could have capacities ranging from 10 kW to 500 kW. Such machines are usually driven by diesel- or gasoline-powered internal combustion engines.

6.2 SYNCHRONOUS-GENERATOR CONSTRUCTION

Synchronous machines operate at 60 or 50 Hz for utility and for larger frequency in large aircraft. Almost all synchronous machines have stationary armatures commonly called the stator and rotating field structures called the rotor. The rotor may be constructed with salient or cylindrical (round with no polar projection) poles, as shown in Figure 6.1 [9]. The prime-mover speed influences the construction of the salient poles rotors. The armature carries three-phase winding in which AC emf is generated.

Generator stator windings are similar to that of polyphase induction machines. The stator core consists of windings (built in a segmented core) of high-quality laminates with slot-embedded, double-layer, top windings, as seen in Figure 6.2 [5].

The generator stators are connected in a three-phase Y model with 60° by two-power speed. The salient-pole synchronous machine is equipped with damper windings, which are usually a set of copper or brass conductors set in pole-face slots and connected for stability, with several other useful functions such as starting synchronous machines. Their role is damping rotor oscillation, as shown in Figure 6.3 [5], reducing overvoltage under short-circuit conditions, thus helping synchronize the machines.

6.3 EXCITERS

There are different types of excitation systems for synchronous machines. However, modern excitation systems use AC power sources through a silicon-controlled, solid-state rectifier. The DC winding on the rotating field is connected to the exciting system through slip rings and brushes as seen in Figure 6.4. A reasonable model of a modern exciter is linearized and only takes account of the major time constant of the exciter T_e, which is usually very small, and an exciter gain K_e, ignoring saturation and other nonlinearities. The model of such an exciter is given in the frequency domain as

(6.1)

where V_f and V_r are the DC-field voltage and some reference voltages, respectively.

• For large hydro-generators (with low speed) there may not be self-excitation. But a self-starter or permanent-magnet-type exciter may be employed to activate the exciter.
• Silicon diodes and thyristor excitation are used to avoid wear and tear in classical excitation synchronous machines.
• Brushless systems have system-mounted rectifiers rotating with the rotor; the need for brushes is eliminated and no slip rings are needed.

6.4 GOVERNORS

The mechanical system is an input to the electrical system and a shaft connects the two systems. When there is an increase in load, the generator applies a torque, which is in opposition to the torque from the mechanical system. This brings about a resultant reduction in the speed of the shaft of the system. This change in speed is an undesirable effect in the generator because it causes a variation in the frequency of the generated voltage. Thus, a governor is applied to the mechanical system (Figure 6.5) to bring about a predictable linear relationship between speed and power, so that reduction in speed can be controlled. Frequency is also controlled by the governor by increasing the no-load speed when there is a frequency reduction of the generated voltage.

Electrical power usually exceeds that of the input mechanical power when there is a sudden increase in electrical load, and the power difference is usually supplied by the kinetic energy stored in the rotating system. This results in the kinetic energy being reduced and thus makes the turbine speed decrease, which also results in the fall in frequency. The turbine speed reduction causes the governor to act by adjusting the turbine input valve to change the mechanical power output, which will bring the speed to a new steady-state value. Most modern governors make use of electronic speed sensors.

6.5 SYNCHRONOUS GENERATOR OPERATING PRINCIPLE

Consider a synchronous generator with wound salient rotors, as shown in the simplified diagram of Figure 6.6. The rotor winding is connected to a DC-supply voltage producing a field current, I_f. The external DC excitation voltage, which can be as high as 250 V, produces an electromagnetic field around the coil with static north and south poles. When the generator's rotor shaft is turned by the prime mover (hydro, steam, or gas turbine), the rotor poles also move, producing a rotating magnetic field as the north and south poles rotate at the same angular velocity as the turbine blades (assuming direct drive). As the rotor rotates, its magnetic flux cuts the individual stator coils one by one and, by Faraday's law, an emf and therefore a current is induced in each stator coil.

The magnitude of the voltage induced in the stator winding (Figure 6.6b) is a function of the magnetic field intensity, which is determined by the field current, the rotating speed of the rotor, and the number of turns in the stator winding. As the synchronous machine has three stator coils, a three-phase voltage supply corresponding to the windings, A, B, and C, which are electrically 120° apart, is generated in the stator windings.

The load is connected directly to the three-phase stator winding, and as these coils are stationary they do not need to go through large unreliable slip rings, commutators, or carbon brushes.

When the rotor is excited to produce an air-gap flux φ per pole and is rotating at an angular speed of ω radians per second, the flux linkage of N-turns of the conductor will be maximum when ωt = 0 and also at ωt = 90°. Assuming distributed winding, the flux linkage λ_a will vary as the cosine of the angle ωt. Thus, the flux linkage with coil a is

(6.2)

and induced voltage

(6.3)

where

The rms value of the generated voltage is then

(6.4)

In actual machines, the armature conductors are distributed in slots such that the phasor sum of the induced emf is less than the numerical sum. Hence, winding factor K_w is a factor used to account for the difference which varies between 0.85 and 0.95 for three phase windings. Consequently, for distributed-phase windings, the rms value of the generated voltage is

(6.5)

6.6 EQUIVALENT CIRCUIT OF SYNCHRONOUS MACHINES

The fundamental component of field and armature fluxes ∅_f and ∅_a, respectively, produces flux linkages with the armature, which induces corresponding components of armature voltage. The resultant ∅_r of the field and the armature mmfs produce the net air-gap flux given by

(6.6)

This results in net armature flux linkages

(6.7)

It should be noted that all the quantities in Equations 6.6 and 6.7 are phasors.

Correspondingly, each is responsible for a component of the armature voltage, represented as

(6.8)

The relationship between these quantities is shown in Figure 6.7.

The nature of leakage fluxes in a generator is similar to that of a transformer. The equivalent leakage flux φ_l and the flux φ_a of armature-magnetizing inductance are both in phase with the current in any phase of the armature winding. The magnetizing and leakage inductance L_m and L_l yield the synchronous inductance

(6.9)

The corresponding synchronous reactance is given by

(6.10)

(6.11)

6.7 SYNCHRONOUS GENERATOR EQUIVALENT CIRCUITS

From the phasor diagram of Figure 6.8, if we assume E_r is the rotor voltage, is the field voltage, and is the armature voltage, we can write the voltage in phasor form as:

(6.12)

Also,

(6.13)

so that we may write

(6.14)

Substituting Equation 6.13 into 6.14 yields

But

(6.15)

Hence,

(6.16)

The synchronous impedance of the machine may be represented by

(6.17)

Hence

Similarly,

where δ and θ are referred to as the load or torque angle and the power-factor angle, respectively.

The per-phase equivalent circuit of the synchronous generator may be derived from the phasor diagram relating E_f, terminal voltage V, and the drop across the synchronous impedance. This is given in Figure 6.9. If E_f is in series with synchronous impedance, I_a lags V_t by angle θ.

Further simplification of the phasor diagram of Figure 6.8 is presented in Figure 6.10 based on the model of the machine obtained in Equation 6.13.

6.8 OVER EXCITATION AND UNDER EXCITATION

With a magnitude of E_f > V_t, the machine is over excited. With a magnitude of E_f < V_t, the machine is under excited. The angle between excitation voltage E_f and V_t is known as the torque angle or load angle.

(6.18)

6.9 OPEN-CIRCUIT AND SHORT-CIRCUIT CHARACTERISTICS

The process of determining the synchronous-machine parameters are done by carrying out an open-circuit test and a short-circuit test, as shown in Figures 6.11, Figure 6.12, and Figure 6.13 [9].

The open-circuit test is carried out with the terminals of the machine disconnected from any external circuit. The basic test procedure is:

1. Open circuit the generator terminals.
2. Drive the machine at synchronous speed using an external mechanical system.
3. Slowly increase the field current and measure the open-circuit terminal voltage.

As there is no armature current, the measured terminal voltage is the induced voltage, from

The open-circuit characteristics or saturation curve can be obtained by plotting the armature terminal voltage (L–L) on an open circuit as a function of the field-excitation current when the machine is running at rated speed. The test produces a curve, as shown in Figure 6.11.

Saturation due to magnetic saliency during open-circuit test causes the open-circuit characteristics to change from a straight line to a set of curves.

From the curve, we can deduce Z_oc if R≪ X.

(6.19)

Short-Circuit Test

As the name suggests, the short-circuit test is carried out with the terminals of the machine short circuited. The basic test procedure is as follows:

1. Set the field current to zero.
2. Short circuit the armature terminals.
3. Drive the generator at synchronous speed with the external mechanical system.
4. Slowly increase the field-winding current until the short-circuit armature current reaches the rated design value. Note that very low field-current levels are required to achieve rated short-circuit armature current.

6.10 PERFORMANCE CHARACTERISTICS OF SYNCHRONOUS MACHINES

From the model of the synchronous generator E_f, V_t, and Z_s are determined. Analysis for describing the relationship between input power and output power is enabled by power angle or torque angle of rotor.

For a generator, complex power

(6.20)

where V_t is terminal voltage of machine per phase, I_a is armature current for phase, and I_a* is its complex conjugate.

If R is neglected and and ,

(6.21)

(6.22)

but

(6.23)

(6.24)

Figure 6.14 shows the steady state power or torque angle characteristics of a cylindrical rotor machine.

(6.25)

(6.26)

Three-phase power is

(6.27)

(6.28)

(6.29)

It is provided by maximum machine torque so

(6.30)

where n_s is the synchronous speed in rpm; thus we say at , the machine reaches a steady-state stability limit.

Example 1

A 100 MVA, 11.5kV, 0.8 PF lagging, 50 Hz, two-pole, Y-connected, synchronous generator has a per-unit synchronous reactance of 0.8 and a per-unit armature resistance of 0.012.

1. What are its synchronous reactance and armature resistance in ohms?
2. What is the magnitude of the internal-generated voltage EA at the rated conditions? What is its torque angle at these conditions?
3. Ignoring losses in this generator, what torque must be applied to its shaft by the prime mover at full load?

Solution:

The base phase voltage of this generator is V_φ,base = 11,500 = 6,640 V. Therefore, the base impedance of the generator is

1. The generator impedances in ohm are:
   
2. The rated armature current is
   

The power factor is 0.8 lagging, so I_A = 5, 020∠ − 36.87°A. Therefore, the internal-generated voltage is

Therefore, the magnitude of the internal-generated voltage E_A = 10, 750 and δ = 23°V.

3. Ignoring the losses, the input power would equal the output power. Since
   

and the applied torque would be

Example 2

A three-phase, Y-connected, synchronous generator is rated 120 MVA, 13.8kV, 0.85 PF lagging and 60 Hz. Its synchronous reactance is 0.7 Ω and its resistance may be ignored.

1. What is its voltage regulation?
2. What would the voltage and apparent power rating of this generator be if it operated at 50 Hz with the same armature and field losses as it had at 60 Hz?
3. What would the voltage regulation of the generator be at 50 Hz?

Solution:

1. The rated armature current is
   

   The power factor is 0.85 lagging, so I_A = 5, 020∠ − 31.8°A. Therefore, the internal generated voltage is

   
   
   

   The resulting voltage regulation is

   
2. If the generator is to be operated at 50 Hz with the same armature and field losses as at 60 Hz (so that the windings do not overheat), then its armature and field currents must not change. Since the voltage of the generator is directly proportional to the speed of the generator, the voltage rating (and hence the apparent power rating) of the generator will be reduced by a factor of 5/6.
   
   

   Also, the synchronous reactance will be reduced by a factor of 5/6.

   
3. At 50 Hz-rated conditions, the armature current would be
   

   The power factor is 0.85 lagging, so I_A = 5, 020∠ − 31.8°A. Therefore, the internal generated voltage is

   
   
   

   The resulting voltage regulation is

   

6.11 GENERATOR COMPOUNDING CURVE

A synchronous machine has a power factor that is gradually controlled by the field current. In other words, changing its field excitation can control the power factor of the stator-line current.

The curve showing the relationship between the stator current and the field current at a constant terminal voltage with a constant real power is called a synchronous machine V curve because of the slope, as shown in Figure 6.15 [3]. The V curves can be developed for synchronous generators as well as for synchronous motors and will be almost identical.

6.12 SYNCHRONOUS GENERATOR OPERATING ALONE: CONCEPT OF INFINITE BUS

When a single synchronous machine operating in generating or motoring mode is connected to an infinite bus, the infinite-bus theory cannot be applied since there are no additional machines to compensate for field-excitation changes and prime-mover output to keep the terminal voltage and frequency constant. Since the terminal voltage changes drastically as the load changes, an automatic voltage regulator is required to control the field current in order to maintain a constant terminal voltage as the load varies.

Generally,

1. addition of inductive loads causes terminal voltage to drop drastically
2. addition of purely resistive loads has minimal effect on terminal voltage
3. addition of capacitive loads causes the terminal voltage to rise drastically

Figure 6.16 shows the constant field current volt-ampere characteristics of a synchronous generator operating alone. The curves are for three different values of constant field currents and power factors.

Figure 6.17 shows a typical set of reactive power capability curves for a large, hydrogen-cooled turbine generator along with the effect of increased hydrogen pressure on allowable machine loadings. The rotor MVA of the synchronous machine is distorted by the stator current in terms of maximum allowable stator current. The upper and lower portions of the area inside the circle with a radius of maximum S represent the generator and motor. Figure 6.18 [3] shows the reliability power capability curves.

6.13 INITIAL ELEMENTARY FACTS ABOUT SYNCHRONOUS MACHINES

We must realize that:

or

(6.31)

Thus, a polyphase winding excited by a balanced three phase produces an effect equivalent to that of a magnet or DC-rotating machine.

For a synchronous machine, space distribution of radial gap flux density is given by

(6.32)

where

(6.33)

For a pole machine

from which we can get the flux linkage λ as

(6.34)

and

(6.35)

In terms of flux density

(6.36)

where e is a sinusoidal voltage with spatial distribution.

For a two-pole, synchronous machine under steady-state conditions, operation revolves at 60 rps or 3,600 rpm in order to produce voltage with frequency 60 Hz.

For a coil passing a complete cycle every two pairs of poles sweeping in each revolution,

6.14 CYLINDRICAL-ROTOR MACHINES FOR TURBO GENERATORS

The maximum value of induced voltage is

(6.37)

(6.38)

When connected with the equation of induced voltage in Equation 6.8, if we include the winding type in the salient-pole machine either in delta or star connection,

(6.39)

where k_w is the winding factor.

Normally, k_w < 1 and is typically 0.85 − 0.95.

6.15 SYNCHRONOUS MACHINES WITH EFFECTS OF SALIENCY: TWO-REACTANCE THEORY

The saliency of a machine accounts for the reactance measurement at the terminal varying as a function of the rotor position. Armature current is resolved in two axes into the direct axis component I_d and the quadrature axis component I_q. I_d produces the armature reaction flux φ_ar along the axis of the field poles, while I_q produces an armature reaction flux φ_aq.

The sum of the two fluxes

(6.40)

E_f and I_a are out of phase by φ.

Similar to magnetizing reactance X_p of cylindrical-rotor theory, the inductive effects can be resolved into X_φd and X_φq given as

(6.41)

(6.42)

X_l is same for direct and quadrature reactances. To account for X_d and X_q in X_s we have

(6.43)

Given the phase shift between I_d and I_q we can determine the torque angle from

(6.44)

Let us show how the saliency affects the power angle.

The figure and related equations are derived as follows

(6.45)

(6.46)

(6.47)

(6.48)

solving

(6.49)

(6.50)

6.16 THE SALIENT-POLE MACHINE

The synchronizing power coefficient is

(6.51)

(6.52)

Figure 6.19 shows the power and load angle for saliency ΔP changes depend on load-angle changes Δδ

(6.53)

if

(6.54)

(6.55)

(6.56)

Efficiency Computation for Synchronous Generators

(6.57)

For the case of a generator, power flow is shown in Figure 6.20.

Generator Power Computation

(6.58)

where m is the number of armature windings, P_o is the power output per phase (VI cos φ), P_cu is the armature-winding ohmic loss (mI²R), P_f is the field-winding ohmic loss (I²_fR_f), P_s is stray losses, and P_wf is the windage and frictional loss.

Note that windage and frictional losses are obtained from the open-circuit test. From the short-circuit test, we compute the windage, friction, and armature-winding ohmic loss to give the stray loss. Compute armature core losses + eddy current losses due to the armature-winding circuit.

6.17 SYNCHRONOUS MOTORS

Synchronous machines are reversible. If the rotor is driven by a prime mover, the machine is a generator, converting the mechanical energy input to electrical energy output. If the machine draws electrical energy from a supply, it will require a motor to drive a mechanical load connected to its shaft.

The motor is a constant-speed machine. It rotates at the synchronous speed n_s, given in terms of the frequency f and the number of pole pairs P. The generator theory is also applicable to synchronous motors.

As noted, the magnitude of the excitation of a generator connected to an infinite bus affects the power factor.

Applications

Synchronous motors are useful where constant speed is required for power-factor correction. However, synchronous motors are not self-starting; their applications are for low-speed drives.

The power-flow diagram for a synchronous motor is shown in Figure 6.21.

(6.59)

Motor Analysis

For a round rotor motor

(6.60)

(6.61)

The voltage equation for the round-rotor motor is given by

(6.62)

(6.63)

Figure 6.22 shows the phasor diagram of a synchronous motor for leading, unity and lagging power factor respectively.

Examples

1. A hydraulic turbine running at 200 rpm is connected to a synchronous generator. If the induced voltage has a frequency of 60 Hz, determine the number of rotor poles.

Solution:

Number of poles

2. A 3,600 rpm, 60 Hz, 13.8kV, synchronous generator has a synchronous reactance of 20 Ω. The generator is operating at rated voltage and speed with the excitation voltage E_f = 11.5kV and the torque angle δ = 15°. Calculate:
   1. stator current
   2. power factor
   3. total output power

Solution:

3. A 100 MVA, 13.8kV, 60 Hz, salient-pole, synchronous generator with eight poles has X_d = 1.9 Ω and X_q = 1.1 Ω. The stator-coil resistance is negligible. The generator is supplying rated apparent power at a power factor of 0.866 lagging. Determine the value of excitation voltage E_f and torque angle δ.

Solution:

Thus,

E_f = 13, 623.8V at a machine angle of 21.21°.

6.18 SYNCHRONOUS MACHINES AND SYSTEM STABILITY

Stability refers to the ability of the generators in a power system to operate in synchronism both under normal conditions and following disturbances. Three categories of instability are:

1. steady-state instability
2. transient instability
3. dynamic instability

Steady-State Instability

Steady-state instabilty refers to the condition where the equilibrium of the generators connected to the power system cannot accommodate increases in power requirements that occur relatively slowly or when a transmission line is removed from service for maintenance.

Since the power flow from one point to another is proportional to the sine of the angular difference between the voltages at the two points and inversely proportional to the total impedance of the circuits connecting the two points, there is a maximum level of power flow, that is, the delivery level at which the angular difference is 90° and the sine is equal to one.

The fact that the power flow is dependent on the sine of the angular difference between the voltages has an important significance in that it defines the maximum amount of power that can be moved across the facilities connected by the impedance X12. If the power required by the customers at bus two is greater than the amount that can be delivered at a 90° separation in the voltages, the system is unworkable. When the customer load at bus two slowly increases and the angular spread responds until it reaches the 90° point and then goes beyond 90°, the system becomes unstable and will collapse.

If the net impedance is increased by removing a line, less power can be transmitted. If there are a number of lines connecting bus one with bus two, the loss or outage of any one of them will increase the impedance between the two buses and the system can again become unstable. Conversely, if the net impedance is reduced, more power can be transmitted. The value of the net impedance can be reduced by:

• building additional lines in parallel
• raising the design voltage of one or more of the existing lines
• decreasing the impedance of any of the existing lines by inserting a capacitor in series (remember XC cancels out XL)

Transient Instability

Transient instability refers to the condition where there is a disturbance in the system that causes a disruption in the synchronism or balance of the system. The disturbance can be a number of types of varying degrees of severity:

• opening a transmission line, increasing the XL of the system
• occurrence of a fault-decreasing voltage on the system (voltage at the fault goes to zero, decreasing all system voltages in the area)
• loss of a generator disturbing the energy balance and requiring an increase in the angular separation as other generators adjust to make up the lost energy
• loss of a large block of load in an exporting area

When there is a disturbance in the system, the energy balance of generators is disturbed. Under normal conditions, the mechanical energy input to the generator equals the net electrical energy output plus losses in the conversion process within the turbine generator and the power consumed in the power plant.

If a generator sees the electric demand at its terminal in excess of its mechanical energy input it will tend to slow down as rotational energy is removed from its rotor to supply the newly increased demand. If a generator sees an electric demand at its terminal less than its mechanical energy input, it will tend to speed up due to the sudden energy imbalance. This initial reaction is called the inertial response.

Disturbances may also change the voltage at the generator's terminals. In response, the generator's automatic voltage regulating system will sense the change and adjust the generator's field excitation, either up or down, to compensate.

Transient stability or instability considers that period immediately after a disturbance, usually before the generator's governor and other control systems have a chance to operate. In all cases, the disturbance causes the generator angles to change automatically as they adjust to find a new stable operating point with respect to one another. In an unstable case, the angular separation between one generator or group of generators and another group keeps increasing. This type of instability happens so quickly, in a few seconds, that operator corrective action is impossible.

If stable conditions exist, the generator's speed-governor system, sensing the beginning of a change in speed, will react to either admit more mechanical energy into the rotor to regain its speed or to reduce the energy input to reduce the speed. Directives may also be received by the generator from the company or area control center to adjust its scheduled output.

In addition to the measures noted above to improve steady-state stability, other design measures are available for selected disturbances to mitigate this type instability:

• improving the speed by which relays detect the fault and the speed by which circuit breakers operate to disconnect the faulted equipment sooner
• use of dynamic braking resistors, which, in the event of a fault, are automatically connected to the system near generators to reduce export from the generators
• installation of fast-valving systems on turbines, allowing rapid reduction in the mechanical-energy input to the turbine generator
• automatic generator tripping
• automatic load disconnection
• special transmission line-tripping schemes

Dynamic Instability

Dynamic instability refers to a condition where the control systems of generators interact in such a way as to produce oscillations between generators or groups of generators that increase in magnitude and result in instability, that is, there is insufficient damping of the oscillations. These conditions can occur either in normal operation or after a disturbance.

Results of Instability

In cases of instability, as the generator angles separate, the voltage and current angular relationships at points on the system change drastically. Some of the protective line relays will detect these changes and react as if they were due to fault conditions, causing the opening of many transmission lines.

The resulting transmission system is usually segmented into two or more electrically isolated islands, some of which will have excess generation and some that will be generation deficient. In excess-generation pockets, the frequency will rise. In generation-deficient pockets, the frequency will fall. If the frequency falls too far, generator auxiliary systems (motors, fans) will fail, causing generators to be automatically disconnected by their protective devices. Industry practice is to provide for situations where there is insufficient generation by installing under-frequency, load-shedding relays. These relays, keyed to various levels of low frequency, will actuate the disconnection of blocks of customer load in an effort to restore the load-generation balance.

In situations where the frequency rises because of excess generation, generators will be automatically removed from service by protective devices detecting an over-speed condition. If studies indicate potential excess-generation pockets, special selective-generation disconnection controls can be installed.

Illustrative Problems and Examples

1. At what speed must a six-pole, three-phase, synchronous generator run to generate 50 Hz voltage?

   Given f = 50 Hz, p = 6

   

2. An eight-pole, three-phase, synchronous generator is operated at 900 rpm. What is the frequency of the output voltage?

   Given p = 8, N_S = 900 rpm,

   

3. A 60 kVA, three-phase, Y-connected, 440 V, 60 Hz, synchronous generator has a resistance of 0.15 Ω and a synchronous reactance of 3.5 Ω per phase. At rated load and unity power factor, find the internal excitation voltage magnitude and the power angle.

   Given R_q = 0.15 ohm, X_S = 3.5 ohm, since it is Y connected,

   

   and since the power factor (pf) is unity,

   

   excitation voltage is

   

   where

   

   Therefore,

   

   Hence, the excitation voltage is 382.64V and the power angle is 46°.

6.19 CHAPTER SUMMARY

The synchronous machine is at the heart of power generation in any conventional power system. Because of its scalability, it is also useful in small-scale power-generation applications. In this chapter, we presented the principles of this machine and its characteristics, which are essential for students to relate with such machines in a microgrid environment. The concepts include modeling, performance measures, and characteristics of the machines. Since the synchronous machine is a key energy source in any power system, the student also may want to explore its place in nontraditional power systems, especially in the presence of unconventional energy resources such as solar photovoltaics and wind energy. This chapter therefore prepares the student for future exercises in the application of this machine in an unconventional power network. Several working examples are given to illustrate the main features of synchronous machines under different conditions.