generator basics

Excitation Fundamentals Training Instruction Leaflet

Turbine Control Service Associates Page i 2006

Table of Contents Table of Figures ........................................................................................................... iii Fundamentals of Generation ......................................................................................... 1

Charge and Polarity................................................................................................... 1 Conductors ................................................................................................................ 2 Electromotive Force.................................................................................................. 2 Alternating Current Generation ................................................................................ 3 Frequency.................................................................................................................. 5 Torque/Counter Torque ............................................................................................ 6

Generator Terminology and Design.............................................................................. 9 Armature ................................................................................................................... 9 Field ........................................................................................................................ 10

Number of Field Poles ........................................................................................ 10 Generator Physical Design...................................................................................... 11

Stator ................................................................................................................... 11 Rotor ................................................................................................................... 12 Cooling Considerations....................................................................................... 12

Excitation Techniques................................................................................................. 13 Rotating DC Exciter................................................................................................ 13 Rotating Alternator Exciter..................................................................................... 14 Brushless Exciter .................................................................................................... 15 Static Exciter........................................................................................................... 16

Power, Watts and VARs ............................................................................................. 17 Resistance ............................................................................................................... 17 Reactance ................................................................................................................ 17

Inductance ........................................................................................................... 17 Capacitance ......................................................................................................... 18 Resonance ........................................................................................................... 19

Apparent Power ...................................................................................................... 19 True Power or Megawatts....................................................................................... 19 Reactive Power or MegaVARs.............................................................................. 20 Power Factor ........................................................................................................... 20

Voltage Droop............................................................................................................. 21 Synchronizing the Generator ...................................................................................... 22

Excitation Fundamentals

Synchroscope ...................................................................................................... 23 Frequency............................................................................................................ 23 Voltage................................................................................................................ 23 Phase ................................................................................................................... 24 Closing the breaker ............................................................................................. 24

Motorizing the Generator........................................................................................ 24 Maintaining Synchronization.................................................................................. 25 Changing Load........................................................................................................ 26 Changing Voltage ................................................................................................... 27

Load Sharing............................................................................................................... 28 Real Load ................................................................................................................ 29

Dispatching of Real Load ................................................................................... 30 Transient Response ............................................................................................. 30

Reactive Load Sharing............................................................................................ 31 Power System Stability ........................................................................................... 32

Generator Ratings and Curves .................................................................................... 33 Nameplate ............................................................................................................... 33 Generator Saturation Curve .................................................................................... 33

Over Voltage Condition...................................................................................... 35 Over Voltage Limiting and Protection................................................................ 36

Generator VEE Curve ............................................................................................. 36 Capability Curve: .................................................................................................... 38

Curve Derivation................................................................................................. 42 Over-Excitation................................................................................................... 43 Overload.............................................................................................................. 43 Under-Excitation................................................................................................. 44

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Table of Figures

Figure 1: Charged Particles........................................................................................... 1 Figure 2: Electromotive Force ...................................................................................... 2 Figure 3: Alternating Current Generator....................................................................... 3 Figure 4: Alternating Current Generation..................................................................... 4 Figure 5: Torque vs. Counter Torque ........................................................................... 6 Figure 6: Generator Terminology ................................................................................. 9 Figure 7 : DC Rotating Exciter ................................................................................... 13 Figure 8 : AC Rotating Exciter ................................................................................... 14 Figure 9: Brushless Exciter......................................................................................... 15 Figure 10: Static Exciter ............................................................................................. 16 Figure 11: Resistance.................................................................................................. 17 Figure 12: Inductance ................................................................................................. 18 Figure 13: Capacitance ............................................................................................... 18 Figure 14: Generator Equivalent Circuit..................................................................... 21 Figure 15: Droop Characteristics ................................................................................ 22 Figure 16: Synchroscope............................................................................................. 23 Figure 17: Magnetic Coupling Analogy ..................................................................... 25 Figure 18: Simplified System Impedances ................................................................. 27 Figure 19: Simplified Distribution System................................................................. 29 Figure 22: Generator Saturation Curve....................................................................... 34 Figure 23: Generator Vee Curve................................................................................. 37 Figure 24: Idealized Generator Capability Curve....................................................... 39 Figure 25: Sample Capability Curve........................................................................... 41 Figure 26: Capability Curve Derivation ..................................................................... 42

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Fundamentals of Generation

Electricity and magnetism were originally considered separate physical phenomena. Through the pioneering work of Faraday, Clerk-Maxwell and others, the inseparable interdependency between the two phenomena is now well understood. These basic principles underlie the generation of electricity for large scale use.

Charge and Polarity

Charge and polarity are fundamental properties of protons and electrons. These two particles possess unit charges of opposite polarity. Whenever a charged particle is in motion, it creates a magnetic field. If many charged particles of the same polarity are moving together in the same direction, such as electrons in a copper wire, their magnetic fields are cumulative. If they are all moving at the same speed, then each particle contributes a quantum of magnetism to the field. Thus the strength of the magnetic field is proportional to the number of charged particles passing through the wire.

Figure 1: Charged Particles

It is this property of matter which allows for the creation of electro-magnets. The unit of measure for quantities of charged particles moving together is the ampere. Therefore, the strength of a magnetic field surrounding a wire is exclusively dependent on the amperes of current flow in the wire. By looping the wire into coils, the density of the magnetic field can be increased for the same amperage of current flow. The density can be further increased by winding the coils of wire around a magnetically permeable material called a core.

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Conductors

Conductors are materials in which the outermost electrons of the atomic structure are loosely bound and can be stripped free with ease. Most metals are good conductors, including gold, platinum, silver and copper. Materials which have the opposite characteristics are called insulators.

Electromotive Force

Any magnetic field will apply a force to a charged particle which passes through the field. The force is called potential or electromagnetic force (EMF). In free space, the force causes the particle to be deflected at a right angle to the direction of the magnetic field. If the charged particle is an electron within a conductive material such as a wire, then the electromotive force strips the electron free from its parent atom and causes it to move from atom to atom along the wire.

For example, if two magnets are placed with their opposing poles close together, a magnetic field is established between the two. The strength of the magnetic field is proportional to the inherent strength of the magnets and the distance between them. The lines between the magnets represent the density of the magnetic lines of flux. Increasing the strength of the magnets or moving them closer together will increase the field strength.

If a wire composed of a conductive material is passed through the magnetic field at an angle which cuts the lines of magnetic flux, then an electromotive force (EMF) is felt by the charged particles in the wire. If the conductor moves parallel to the lines of flux, no EMF is induced and no force is applied to the charged particles.

Figure 2: Electromotive Force

The magnitude of the induced EMF is proportional to the number of lines cut (field density) and the speed at which the conductor is moving. If the motion is perpendicular to the lines of flux, then the induced EMF is maximized. If the motion is angular at less than 90 degrees, then the magnitude of the

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induced EMF is less. If the speed is increased, then the EMF is proportionally higher. The term relative motion takes into account both the motion of the conductor and the angle of incidence between the conductor and the magnetic field. The unit of measure for electromotive force is the volt, so the voltage varies proportionally to both the relative motion of the conductor and flux density of the magnetic field.

The polarity of the EMF is determined by the direction of motion with respect to the polarity of the magnetic field. Therefore, reversing the direction of motion will result in a reversal of polarity. Conversely, reversal of the magnetic field will result also result in a polarity reversal.

If we substitute electromagnets for the permanent magnets, then the strength of the magnetic field can be adjusted by changing the current flow through the electromagnetic coils. Consequently, the voltage induced into the conductor can be externally controlled by adjusting the current flow in the electromagnets.

Alternating Current Generation

Now, consider the case where the single conductors are replaced by one or more loops of wire that are free to rotate about some axis within the magnetic field. Since the two legs of the loop are always moving in opposite directions, the voltage generated in the two sides of the loop are of opposite polarity and when connected together become additive to each other. The total EMF can be measured at the terminals on the ends of the loop of wire.

Figure 3: Alternating Current Generator



All generators, from the smallest hand crank generator to the largest turbo-generators used in power plants operate in accordance with these principles.

Summarized, these principles state that in order to generate electricity three elements are required.

A Magnetic Field

A Current Carrying Conductor

Relative Motion between the Conductor and Magnetic Field

During the first half of the rotation, one conductor of the loop (A) is passing upward through the field while the other (B) is passing downward through the field. During the second half of the cycle, the motion of the conductors reverses. The A conductor is passing downward while the B conductor is passing upward.

Figure 4: Alternating Current Generation



At the beginning of the cycle, (T0) the conductors are both moving parallel to the field so no EMF is induced. As the rotation continues, the conductors begin cutting into the field causing an EMF to be induced into the two legs of the loop of wire. As the rotation continues, the number of lines of flux being cut, per unit time, increases as the conductors motion approaches the point where the motion is perpendicular to the field. Consequently, the induced voltage increases to its maximum when the conductors are moving perpendicular to the field. (T90)

As the rotation continues, the number of lines of flux cut per unit time lessens and the resultant voltage dissipates towards zero as conductors reach the point where the motion is parallel to the field (T180). During this entire half cycle, the induced EMF measured at the generator terminals is positive, starting at zero volts, reaching its maximum voltage at T90 and returning to zero volts at T180.

As the cycle continues, the A conductor begins to move up through the field while the B conductor moves downward. The magnitude of the induced EMF increases again proportional to the number of lines of flux cut per unit time, from it minimum at T180 to its maximum at T270 However, since the direction of the relative motion has reversed for both conductors, the polarity of the induced EMF is also reversed and the voltage as measured at the terminals will be negative for the entire second half of the cycle. After peaking at T270, the EMF drops towards zero volts again at T360 after which, the cycle repeats itself. If the voltage were traced out for one full rotation, it would appear as a sinusoidal wave form.

If the magnetic field density is held constant, then the voltage of the sine wave is directly proportional to the speed of rotation. Likewise, if the speed of rotation is held constant, then the voltage is directly proportional to the magnetic field density. Normally, the speed of rotation is held constant so the magnitude of the output voltage is controlled by adjusting the magnetic field strength.

Frequency

The time required for one cycle of the sinusoidal waveform is dependent on the speed of rotation and is typically expressed in cycles per second or hertz. In most all power generation applications, the frequency of the generated voltage is determined by the grid to which the power is being supplied. North America operates at 60 Hz whereas Europe operates at 50 Hz.

The frequency is very tightly controlled to ensure that all synchronous machines perform as designed and to avoid mechanical resonance issues with the prime movers. A change in frequency in excess of .05% of the nominal frequency is considered undesirable and will require corrective action to restore the system to normal frequency. The chart below illustrates how a variation in rotational speed influences the frequency of the generated voltage for a .05% variation.



System Frequency

Generator Poles

Nominal Speed

Frequency Deviation

Speed Deviation

60 Hz 2 3600 RPM + 0.030 Hz + 1.8 RPM

60 Hz 4 1800 RPM + 0.030 Hz + 0.9 RPM

Torque/Counter Torque

If the terminals of the generator armature are an open circuit, then no current flows in the armature windings. If a current path is connected to the armature winding, then current will flow through armature into the load and the amperage of the armature current flow will be inversely proportional to the impedance of the load.

Figure 5: Torque vs. Counter Torque

As the load current flows through the armature windings, a magnetic field is developed around the conductors of the armature winding. The polarity of the magnetic field surrounding the armature windings is such that it opposes the magnet field on the rotor and makes it more difficult to turn the



rotor through the armatures magnetic field. This phenomenon, called counter torque, is directly proportional to the true load current in the armature winding.

With infinite load impedance (open circuit), no real current flows through the armature and the counter torque is zero. Therefore, little effort i.e. torque from the prime mover, is required to sustain the rotation of the rotor. As the impedance of the load is reduced, more current flows through the armature to the load, the magnetic field surrounding the armature winding becomes stronger and consequently counter torque increases.

The magnetic field induced by the armature current interacts with the excitation magnetic field, thus acting to oppose the rotation of the rotor. In order to maintain a constant speed of rotation, more torque must be applied to the rotor from the prime mover. Therefore, as load current is increased, counter torque increases and more torque (more energy) is required to keep the rotor rotating at the same speed.

In order to maintain a constant speed of rotation, the torque applied to the rotor must always be in equilibrium with the counter torque of the load current. When the generator is connected to an infinite grid, the load current will change to match the torque of the prime mover. As long as the torque and counter torque are in equilibrium, the machine speed will remain constant.



Generator Terminology and Design

In a generator, the current carrying conductors, i.e.. the windings, in which the voltage is induced are called the armature and the element which provides the magnetic field is called the field. These two terms apply only to the function of the conductors and are not related to their physical placement. When relating to the physical placement of the armature and field, the terms stator and rotor define which element is stationary and which rotates.

Figure 6: Generator Terminology

Armature

In the previous example, the armature windings are mounted on the rotor. The permanent magnets which provide the field magnetism are mounted on a fixed, stationary base, thus the field is on the stator. However, this arrangement is not mandatory and the opposite arrangement is most common.

In practical application, connecting the load to a rotating armature is undesirable as the high voltage and current must be transferred from the rotating element to reach the stationary load. The transfer mechanism involves the use of large brushes and slip rings which will be subject to wear and other electromechanical limitations. For this reason, most generators are constructed with the armature windings mounted on the stator.



Field

If the armature windings are stationary, then the field is mounted on the rotor. Thus, by rotating the field within the armature, the relative motion between the armature and the field is restored and the voltage is induced into the armature on the stationary element.

Since the magnetic field density of a permanent magnet is not adjustable, it makes a poor choice for a field where the output voltage of the generator must be adjustable. Therefore, in most applications the field magnetism is created by an electromagnet mounted on the rotor. With this arrangement, the strength of the magnetic field can be adjusted by changing the current flow through the electromagnets coils. Consequently, the output terminal voltage can be externally controlled by adjusting the current flow in the rotating electromagnet coils.

In order for the polarity of the magnetic field to remain constant, direct current (DC) must be utilized. The DC current used to create the field magnetism is commonly called excitation current or field current. Since the amperage of the excitation current determines the magnetic field density, the amperage of the excitation current also determines the magnitude of the voltage induced in the armature.

Supplying DC current to the rotating element can be accomplished in many different ways. However, as long as the excitation current can be modulated, the output voltage of the generator can be controlled.

Recall that the magnitude of the voltage produced by a generator is dependent on:

Number of loops of conductor in the armature windings

Speed of rotation (rate of cutting lines of flux)

Strength of the magnetic field (governed by the field current)

The number of conductors in the armature windings is fixed when the generator is built and the speed of rotation is held constant by the power grid frequency. The only parameter which can be varied to control the generator output voltage is the strength of the magnetic field. Since the magnetic field is produced by a DC electromagnet, the strength of the magnetic field is solely a function of the amperes of current supplied to the field winding. Therefore, the output voltage of the main generator is directly proportional to the field current.

Number of Field Poles

Each electromagnet used in the generator is called a field pole. The number of field poles on the rotor is correlated to the rotational speed of the generator and the mechanical limitations of its prime mover.



In general, the larger the prime mover then the slower is its permissible speed of rotation. Since AC generators must operate at a common frequency, the different speeds are accommodated by varying the number of field poles.

The minimum number of poles is two (one dipole): one north, one south. A single rotation of the two pole rotor results in one cycle in the output voltage. Adding a second field winding, i.e., another pair of field poles, mounted perpendicular to the first results in two cycles per revolution of the rotor.

If the speed of rotation is the same then the four pole generator will operate at twice the frequency of the two pole machine, which will be problematic for parallel operation of the generators. By reducing the speed of rotation proportional to the number of poles, the frequency can be held constant to a standard value and machines of different speeds can be synchronized and operated in parallel.

Frequency Poles Speed Prime Mover

60 Hz 2 3600 RPM Fossil Steam Turbine

60 Hz 4 1800 RPM Nuclear Steam Turbine

60 Hz 48 150 RPM Hydro Turbine

420 Hz 28 3600 RPM PMG

Generator Physical Design

All generators used in large scale power generation are configured with a stationary armature and a rotating field. Generators driven by steam turbines, combustion turbines and internal combustion engines are horizontally mounted. Most hydro turbine-generators are vertically mounted with the generator on top of the water wheel.

Stator

A typical armature winding has 8 to 11 turns of conductor per armature phase. The conductors are wound onto a core of permeable metal to concentrate the magnetic flux and to provide mechanical strength and integrity. The design of the stator core has been under constant improvement in design, materials and manufacturing techniques to achieve higher generating capacity. Improvements include:

Silicon Steel to improve permeability and strength



Laminated construction to limit eddy current heating

Stepped End Iron Laminations to accommodate higher flux densities

Rotor

The electrical and mechanical design of the rotor varies considerably with the number of poles and the speed of rotation. The field winding of a typical large steam turbine generator contains 8 to 10 turns per pole.

Cooling Considerations

The greatest impediment to increased capacity has been the ability to remove the waste heat from the generator windings. Considerable design and experimentation have taken the capacities from the kilowatt range to the gigawatt range. Due to their physical size, most hydro generators are still air cooled. However, nearly all other turbine driven generators are cooled with hydrogen. Some of the advantages of hydrogen cooling include:

Low windage losses due to low molecular mass

Good heat transfer characteristics

Good insulating characteristics

Cheaper than noble gases

The largest capacity generators have water-cooled armature windings to permit even higher rates of heat removal.



Excitation Techniques

There are many different schemes employed to provide DC excitation current to the rotating field of the main generator. The four following examples are representative of the common schemes in use today. It should be noted that the voltage regulator technology used to control excitation is generally independent of the excitation scheme.

Rotating DC Exciter

The rotating exciter is a relatively small DC generator driven by the prime mover or a large motor. The DC output of the exciter is supplied to the main generator field through brushes and slip rings. A field breaker is usually provided to interrupt excitation current upon shutdown of the unit.

Figure 7 : DC Rotating Exciter

The resistance of the generator field winding presents a constant load resistance to the exciter, so the magnitude of field current is determined by the voltage output of the exciter. The voltage output of the exciter is a function of the magnetism supplied by the exciter field(s). In early machines, multiple fields were used to control the exciter output and consequently the generator output voltage.

Shunt Field fed by the exciters own output and adjusted with a rheostat to provide a base level of excitation



Buck/Boost Fields Windings which aid or oppose the shunt field to provide trim control of excitation, fed by the voltage regulator.

Later systems abandoned the buck/boost fields in favor of a single field fed directly by an electronic regulator. The power source to the regulator is typically station service power or an even smaller shaft driven permanent magnet generator called a pilot exciter.

Rotating Alternator Exciter

The alternator based excitation scheme is similar to the rotating DC Exciter with the exception that the exciter is a small AC generator (alternator) and the rectification of AC to DC is accomplished by diode bridges between the alternator and the generator brushes and slip rings. Just as with the large turbine-driven generators, the AC alternator also requires a power source to supply its own field windings and regulate output. The power source to the alternator field regulator is taken from the alternator output, upstream of the diode rectifiers.

Figure 8 : AC Rotating Exciter

This scheme is inherently unstable due to the fact that the excitation source voltage varies markedly with the excitation requirements of the generator. This scheme requires a closed loop feedback controller to be in service at all times.



Since the alternator field is self excited, the boost CTs are intended to preclude a collapse of the system during transient and fault conditions.

The rectification diodes are typically water-cooled, which presents a number of maintenance issues as the units age.

Brushless Exciter

The brushless exciter scheme consists of a shaft driven AC generator with a rotating rectifier assembly which supplies DC field current directly to the generator field through the generator coupling. No brushes or slip rings are required.

Figure 9: Brushless Exciter

The resistance of the generator field winding presents a constant load resistance, so the magnitude of field current is determined by the voltage output of the AC exciter though the rotating rectifier. The voltage output of the AC exciter is a function of the exciter field current which is supplied by the power amplifiers in the voltage regulator. Therefore, the generator output voltage is controlled by the voltage regulator by adjusting the output voltage of the power amplifiers. The power amplifiers are powered by a small shaft driven permanent magnet generator, so the system is self-powered once the prime mover is up to speed. Although the generator field current cannot be directly measured, it is inferred from the exciter field current.



Static Exciter

The static exciter scheme consists of large power amplifiers which convert AC into DC current for application to the generator field through brushes and slip rings. The AC supply provided by the generator output so the system is self exciting once the voltage of the generator is initially raised to its nominal level. An AC field breaker is supplied to apply and remove excitation.

Figure 10: Static Exciter

The resistance of the generator field winding presents a constant load resistance, so the magnitude of field current is determined by the voltage output of the power amplifiers. The voltage output of the power amplifiers is a function of the voltage regulator. Therefore, the generator output voltage is controlled by the voltage regulator by adjusting the output voltage of the power amplifiers.

The static exciter scheme requires additional subsystems to remove excitation in a controlled manner and to protect the generator rotor during fault conditions.



Power, Watts and VARs

Generators operate in an alternating current environment. A review of the characteristics of AC circuits is useful for understanding of the parameters and behavior of generators in the real world.

Resistance

Resistance is a property of a material defined by the degree to which it can oppose current flow. The unit of measure for resistance is the Ohm. In a resistive only load, the voltage and current are in phase with each other and the power is all converted to light, work or heat. The unit of measure for the power in a resistive circuit is the Watt.

Figure 11: Resistance

Reactance

Inductive and capacitive components are known as reactive components. The term derives from the phenomenon whereby the devices interact with the AC power to produce a phase shift between the voltage and current flow. When present in an AC circuit, the reactive components store energy in the form of magnetic fields and stored charge. The power associated with the flow of stored energy in the reactive components is called reactive power. Reactive current circulates between the reactive components in the circuit and does not perform any work. The unit of measure for reactive power is the volt-amp-reactive or VAR.

Inductance

When inductors are introduced into the AC circuit, the interaction of the magnetic field surrounding the inductors causes a shift in phase relationship of the voltage and current. Twice in each power line cycle, some of the energy of the system is stored in the build up of the magnetic field surrounding the inductor. As the voltage cycles back toward zero on each half cycle, the magnetic field collapses, returning the stored energy back into to the circuit. In the case of a pure inductor, the current flow is shifted out of phase with the voltage such that the current lags the voltage by 90 degrees.



Figure 12: Inductance

The unit of measure for the inductance of a coil is the Henry. The effect of the inductor in the circuit is called inductive reactance and is measured in Ohms.

XL=2* (PI)* Frequency (Hz)*Inductance

When the circuit includes both inductive and resistive elements, the lagging phase shift will be less than 90 degrees in proportion to the resistance and inductive reactance.

Capacitance

With a capacitive load element, some of the energy in the system is stored as a charge in the capacitor. During each frequency cycle, current is supplied to build up the charge in the capacitor, but as the voltage alternates the capacitor discharges, thereby giving back the stored current. In the case of a purely capacitive load, the current flow is shifted out of phase with the voltage such that the current leads the voltage by 90 degrees.

Figure 13: Capacitance



The unit of measure for the inductance of a capacitor is the Farad. The effect of the capacitor in the circuit is called capacitive reactance and is measured in Ohms.

XC=1/ 2* (PI)* Frequency (Hz)*Capacitance

When the circuit includes capacitive and resistive elements, the leading phase shift will be less than 90 degrees in proportion to the resistance and capacitive reactance.

Resonance

When an AC circuit contains both inductive and capacitive elements, the capacitors and inductors will interact with each other as a resonant circuit. Since the devices operate with opposing phases shifts, they can support each other in the storing of system energy. When the inductors magnetic field is collapsing, the energy can be stored on a capacitor. When the capacitor discharges, the energy is transferred into the inductor as a magnetic field. The combination of the two elements creates a circuit that allows the energy to circulate between the inductors and capacitors rather than requiring external support for the reactive current. If the values of the inductive reactance and capacitive reactance are similar, the reactive current will circulate between the two elements in the system.

Apparent Power

In an AC circuit which contains both resistive and reactive components, the total power is the vector sum of the true power and the reactive power. This vector sum is referred to as an AC circuits apparent power. The unit of measure of apparent power is the voltamp or VA. In a three phase AC system, the constant of the square root of three corrects for the phase-to-phase flow of current, yielding the total or apparent power formula.

Volt-Amps = Apparent Power = 1.732* Terminal Volts * Stator Amps

The nameplate rating of the generator is in units of apparent power because all of the electric current flows through the generator armature and causes heating of the generator windings. Apparent power is expressed in mega volt amps (MVA) or kilo-volt-amps (KVA).

True Power or Megawatts

True or real power is the portion of the apparent power (MVA) which services the resistive component of the load. The true power is also that portion of the total current flow which is in phase with the voltage. True power is expressed in watts and the value is calculated by multiplying the apparent power by the cosine of the angle (theta) of the phase shift between voltage and current.

Watts = 1.732 * Terminal Volts* Stator Amps * (COS Theta)



The generator is not given a rating in watts, whereas the prime mover is usually rated in watts or horsepower.

Reactive Power or MegaVARs

When the load has an inductive or capacitive component, current flow must be provided by the generator beyond that which is required to perform real work. This portion of the apparent power is called reactive power and it is expressed in units of Volt-Amps Reactive or VARs.

The reactive power is found by multiplying the apparent power by the sin of the phase shift angle.

VARs = 1.717 * Terminal Volts* Stator Amps * (SIN Theta)

The term lagging is applied when the reactive component of the load is predominantly inductive. The VARs associated with inductive loads are also known as VARs Out or positive VARs. The term leading is applied when the reactive component of the load is predominantly capacitive. The VARs associated with capacitive loads is known as VARs In or negative VARs. Regardless of the phase shift, the VARs are amperes of current which flow through the generator and contribute to the heating of the armature windings.

Power Factor

The Power Factor is a common term which describes the fraction of the total power which is performing real work. The value of the power factor is derived from the cosine of the phase shift between voltage and current and cannot exceed a value of 1. However, since the phase angle can be leading or lagging, the cosine can have a positive or negative value. If the generator is servicing an inductive load, then the power factor is defined as lagging. If the load is predominantly capacitive then the power factor is defined as leading.

If the power factor is 1 or unity then the load is entirely resistive and all of the MVA is making Megawatts. If the power factor is less than 1, then the MVA is divided between megawatts and megaVARs, but the relationship is not linear.

For example, consider a generator operating at its rating of 1000 MVA at a .9 lagging power factor. The power factor is defined as the cosine of the phase angle, therefore the inverse cosine of .9 yields the phase angle in degrees.

Phase Angle = COS-1 (PF) = COS-1 (.9 ) = 25.8o Phase Angle (Theta) Watts = MVA * (COS 25.8o) = 1000 * .900= 900 Megawatts



VARs = MVA * (SIN 25.8o) = 1000 * .436 = 436 MegaVARs Out. The generator nameplate usually specifies the rated power factor, which defines how much of the rated MVA is permissible as megawatts and megaVARs. The rated power factor is always assumed to be a lagging power factor as the nature of the load is almost always inductive.

Voltage Droop

Voltage Droop refers to an inherent characteristic of the generator whereby the output voltage of the generator falls off or droops as the armature current increases. The magnitude of the effect is proportional to the impedance of the armature windings of the generator. Since the armature winding has properties of resistance and inductance, the generator will exhibit droop characteristics for both real and reactive load.

Figure 14: Generator Equivalent Circuit

The armature winding can be approximated as a series circuit of a resistor and an inductor. The impedance (R+XL) of the armature winding varies with the design of the generator.

The voltage induced into the armature by the excitation field is called the voltage behind the generator. The voltage measured at the generator output is called the terminal voltage. The armature winding constitutes an impedance in series between the voltage behind the generator and the voltage measured at the generator terminals. The terminal voltage is equal to the voltage behind the generator less the voltage drop across the armature winding impedance.



The armature current is composed of both real and reactive current. The resistive component responds to the portion of the armature current which is in phase with the voltage, while the inductive component responds to the reactive current, i.e. the VAR load. The voltage drop across the impedance results in heating of the armature winding.

With no armature current, the voltage drop of the winding is null and the voltage behind the generator can be felt at the terminals. (i.e. the no load condition) As current through the armature increases, the voltage drop across the armature winding increases proportional to the amperage. The voltage drop across the impedance causes the terminal voltage to drop accordingly.

In order to maintain a constant output voltage, the voltage behind the generator must be increased to counteract the drop across the winding. To increase voltage behind the generator, the operator must increase excitation current. Thus, when changing load on the generator, the operator must also adjust excitation to keep the generator output voltage constant. The voltage drop is sensitive to changes in both watts and VARs.

Figure 15: Droop Characteristics

It is this phenomenon that brought about the development and implementation of automatic voltage regulators. The automatic voltage regulator monitors the output voltage and adjusts excitation as needed to keep the output voltage constant.

Synchronizing the Generator

Generators used for large scale power generation are almost always operated in parallel with many other generators connected to a large power grid. Before a generator can provide load to the grid, it must first be synchronized. Once synchronized, the generator will share real and reactive load with all of the other generators connected to the grid.

The process of synchronizing the generator to the grid requires that a circuit breaker be closed to electrically connect the output of the generator to the grid. In order to safely synchronize, three parameters must be aligned between the generator and the grid prior to closing the breaker. The parameters are aligned using the speed controls of the prime mover and the voltage controls on the generator. When synchronized manually, the operator typically uses a specialized indicator called a



synchroscope and two voltmeters to ensure that the three parameters are properly aligned and it is safe to close the breaker.

Synchroscope

The synchroscope is a circular meter with a pointer that rotates 360 degrees around like a clock hand. The pointer provides information regarding the phasing and frequency of the generator with respect to the grid. The speed of rotation indicates the difference in frequency of the generator versus the grid. The faster the pointer rotates, the greater the frequency difference. The direction of rotation indicates whether the generator frequency is slower or faster than the grid. The position of the pointer indicates the phase relationship between the generator and the grid. The synchroscope does not provide any information on matching the generator voltage to that of the grid.

Figure 16: Synchroscope

Frequency

The generator is brought up to the synchronous speed using the prime mover speed control system (governor). The shaft speed varies with the type of prime mover and the number of generator field poles. The speed is raised until the synchroscope rotates slowly in the clockwise direction, indicating that the generator is moving slightly faster than the sync speed.

Voltage

The generator output voltage and the grid voltage are indicated on independent volt meters. The grid voltage is fixed, so the operator uses the voltage regulator to adjust the generator output voltage to



match the grid. The generally accepted practice is to raise the generator voltage slightly above the grid before closing the breaker. This will ensure that any VAR load assumed by the generator is minimal and in the VARs Out direction.

Phase

The power grid is a three phase AC system. One of the characteristics of the three phase power paradigm is the phenomenon of the rotating magnetic field. The generators three phase output creates a rotating magnetic field and the grid, being supplied by other generators also has its own three phase rotating magnetic field. The output phasing of the generators rotating magnetic field must be aligned to the phasing of the grid. The synchroscope provides indication of proper phasing when the pointer is at the 12 oclock position.

Closing the breaker

With the voltages matched and the synchroscope rotating slowly in the fast direction, the operator is prepared to close the breaker. When the pointer reaches 11 oclock, the operator rotates the switch to close the breaker. It is expected that the breaker will take a second or two to close and in the meantime, the synchroscope will have moved closer to the 12 oclock position. Thus the generator and the grid will be very nearly in perfect synchronization at the moment the breaker contacts close.

Once the main generator breaker is closed, the generator rotor and the prime mover are magnetically coupled to every other generator on the grid. The excitation field magnetically binds the rotor to the rotating magnetic field of the grid and the strength of that coupling is directly proportional to the magnitude of excitation current.

Motorizing the Generator

At the point of synchronization, the prime mover is providing only enough torque to overcome friction losses of the rotating components. If the torque from the prime mover decreases, the generator will begin to act as a motor, being powered by the grid. Motorization will not normally damage the generator but may have adverse mechanical impact on the prime mover, especially steam turbines which are subject to blade resonance issues resulting from abnormal steam flow conditions.

To preclude damage to the prime mover (where applicable), the generator protection relay scheme usually includes a device for detecting the motorized condition such as a Reverse Current Relay or a first stage pressure switch. If the generator remains motorized for an excessive period of time (more than a minute or so), then the generator output breaker is tripped open.



Maintaining Synchronization

The coupling between the generator excitation field and the rotating magnetic field of the grid can be analogized as a magnetic coupling between the prime mover and a mechanical load. The coupling must be maintained in order to transmit power to the load.

As torque from the prime mover is increased, the power supplied to the grid increases. The prime mover attempts to speed up the system but the mass of the system inhibits a significant increase in speed.

Figure 17: Magnetic Coupling Analogy

As torque from the prime mover is increased, the rotor attempts to move faster than the grid. However, the magnetic coupling between them is strong enough to preclude the rotor from pulling out of synchronization and the rotor merely advances it position with respect to the rotating magnetic field of the grid. The angle of advance between the excitation field and the armature magnetic field is known as the power angle. Additional increases in torque from the prime mover will further stretch the coupling and in order to maintain the integrity of the coupling, excitation current will need to be increased as torque from the prime mover is increased. Thus, an increase in excitation will tighten the



coupling, reducing the power angle, whereas a decrease in excitation current will weaken the coupling, increasing the power angle.

If excitation continues to decrease, the magnetic coupling can be stretched to the point where it is not strong enough to maintain synchronization. The torque of the prime mover will break the coupling and accelerate the rotor beyond synchronous speed. As the rotor accelerates out of synchronization, the generator will continue to generate an output voltage that will now be now out of phase with the grid. Each time the rotor passes the point of synchronization it is said to have slipped a pole.

As the generator slips poles, its output will be out of phase with the grid. At the extreme condition of 180 degrees out of phase, the difference of potential between the generators output vs. the grid results in theoretically infinite armature current flow and correspondingly infinite counter torque. The end result of pole slippage will likely be major damage to the generator armature windings due to the high armature current and extreme magnetic mechanical forces. The high armature currents can also induce extreme AC current flow into the rotor winding, resulting in mechanical and electrical damage to the rotor and the exciter. The generator and the prime mover common shaft are also subjected to extreme torsional mechanical forces which have been known to shear the shaft of the prime mover.

The only way to safely break the coupling between the generator and the grid is to open the main generator breaker. This is best done with the unit load at minimum to reduce the excess energy in the prime mover. Loss of synchronization in any other way will likely have catastrophic consequences on the generator, exciter, prime mover and all of the associated transmission equipment. It is to be avoided at all cost.

Changing Load

When connected to a large power grid, the speed of the generator is determined by the grid frequency. The energy input to the prime mover is provided by fluid or gas flow through a turbine or fuel to an engine. If more energy is supplied to the prime mover, then more torque is supplied to the generator.

In response to the added torque, the rotor attempts to accelerate to a speed greater than the grid frequency, but it cannot overcome the magnetic coupling of the rotor magnetic field to the magnetic field of the armature. As the rotor attempts to speed up, its power angle advances. The net effect of the advance in rotor power angle is that the generator will increase its share of the total system real load.

Recall that in order for a generator to have a constant speed, the energy supplied by the prime mover must be exactly equal to the energy being supplied to the load by the generator. In other words, the torque of the prime mover must be equal to the counter torque of the generator. Counter torque comes from the magnetic field of the armature windings. The armature winding magnetic field strength is a direct manifestation of the amperes of true power being supplied by the generator.



Therefore, if the torque of the prime mover increases, the armature current must increase to re-establish the equilibrium or the rotor speed will increase. Since the speed cannot increase due to being synchronized, the effect of the advance in power angle is that the generator armature current increases until the counter torque is in equilibrium with the torque of the prime mover and the real load carried by the generator is increased.

Thus the magnitude of the real load, i.e. megawatts, carried by the generator is exclusively a function of the energy being supplied to the prime mover. If the energy input to the prime mover changes, the megawatt load on the generator will follow. The prime mover control system controls the megawatt load on the generator.

Changes in excitation have no effect on the megawatt loading of the generator. However, because of the inherent voltage droop of the generator, a change in real load will affect the generator output voltage unless the voltage regulator is in automatic control of voltage.

Changing Voltage

The relationship of the generators output voltage as compared to the system to which it is connected determines the reactive loading on the generator. A change in generator output voltage by adjusting excitation will change the reactive loading of the generator. Likewise, a change in system voltage will also change the reactive loading, even with no change in excitation.

If the generator voltage is exactly matched to the system, then the system load will appear to be entirely resistive. The generator will operate at unity power factor and it will not be carrying any VAR load at all.

Figure 18: Simplified System Impedances



As more excitation current is applied to the generator field, the output voltage increases above the system voltage and the generator is said to be over-excited. An over-excited generator behaves as a capacitive device, which means that it produces inductive VARs, or VARs Out. The generators power factor drops below unity and is said to be lagging, as seen by the generator.

If the excitation current is reduced from the unity power factor condition, the generator terminal voltage drops below the system voltage and the generator is said to be under-excited. An under-excited generator acts as an inductive load and absorbs capacitive VARs or VARs In. The power factor of the grid as seen by the generator drops below unity and is said to be leading.

Thus the reactive load on the generator is normally changed by adjusting excitation. However, the reactive load will also be affected by changes in the system voltage.

Load Sharing

The load on the generator from the distribution system is a combination of resistive and reactive load elements. The resistive loads include lighting, heating, machines which do work and heat (I2R) losses in devices such as transformers and transmission lines. The power which services the resistive load is called the true power and is measures in Watts.

Reactive loads are devices which exhibit capacitive or inductive characteristics. Inductive loads are devices which contain coils of wire such as transformers, motors and other devices. Capacitive loads are less common, consisting principally of the capacitance of transmission lines. Oddly, over-excited synchronous machines such as motors and generators also behave as capacitive devices. The power which services the inductive and capacitive loads is called the reactive power and is measured in Volt-Amps-Reactive (VARs).

The summation of residential, industrial and transmission/distribution related loads typically results in a total load which is largely resistive and somewhat inductive. The actual Megawatt and VAR load requirements at any given time are determined by the transmission and distribution system design, and the nature of the loads connected by customers. The magnitude of the load varies considerably from hour to hour and month to month. The real and reactive load is shared by all of the generating units connected to the grid at a given time. In order to maintain a stable grid, the generators and their control systems must be continuously responsive to the changes in the magnitude and character of the load.



Figure 19: Simplified Distribution System

Real Load

The supply and consumption of real load constitutes an energy balance between the combined torque of the prime movers and the counter torque induced by the consumption of power by the customers. In order to maintain system stability, the energy balance between supply and consumption must be maintained at equilibrium at all times.

For example, if the consumption goes down without a change in the supply, there will be an excess of power in the system. The excess power causes all of the generators to speed up in synchrony. Conversely, a reduction in the supply with without a change in demand will cause the generators to be overloaded and they will slow down in synchrony. In this way, changes in the balance between supply and demand result in a change in system frequency felt by all of the generators on the grid.

In order for system frequency to remain constant, an increase in load on one generator must be counteracted by a reduction in load on another unit. Similarly, a change in customer consumption must be compensated for by a change in generation. It is the duty of the system operator (dispatcher) to make the adjustments.



Dispatching of Real Load

During normal conditions, base load power plants carry the bulk of the anticipated load. The changes in consumption throughout the day are small enough and slow enough that the system operators can adjust the supply to match the changes in consumption by controlling one or more generators as swing units. A portion of the other available generating facilities will be operated such that they have the ability to pick up load quickly. The collective capacity of the swing units and those with extra capacity is known as the spinning reserve.

Even still, the system frequency will periodically deviate from 60 Hz by a small fraction. In general, no system operator action is required until the frequency deviates by more than .03Hz. The minor deviations in frequency are continuously recorded and the dispatcher will compensate for the irregularities by running the system a bit slower or faster to even out the average frequency over a 24 hour period.

Transient Response

Large and rapid changes in supply or consumption will result in significant frequency disturbances.

For example, if a power plant trips off line, the supply of power to the grid is instantaneously reduced to a level well below that being consumed by the customers. The excess electrical demand is immediately shifted onto the remaining generators as an increase in load. The increase in electrical load causes the counter torque in each generator to increase without a corresponding increase in torque from the prime movers. Consequently all of the generators begin to slow down and system frequency drops. With no action, the system frequency will quickly drop below safe operating levels and the generators will be tripped off line to protect the equipment. Conversely, if a tie line, substation or large industrial customer trips, there will instantaneously be an excess of power in the system and the frequency will rise.

In order to stabilize the system, the prime movers must be quickly adjusted to restore the balance between supply and demand. To ensure that the response will occur expeditiously, an automatic control feature is incorporated into all prime mover control systems. The common names for this feature are speed droop and frequency correction.

Figure 20: Speed Droop



Since the generators are all synchronized, a change in the system frequency will result in a proportional change in shaft speed of each machine. The action of the function is to automatically increase or decrease power to the prime mover of the generator in proportion to a change in speed.

For example, if speed is increasing, it is because there is excess power being supplied to the grid. The speed droop controller senses the change and acts to reduce power to the prime mover in proportion to the change in speed. If speed is decreasing, it is because there is insufficient power being supplied to the grid. The speed droop controller senses the change and acts to increase power to the prime mover in proportion to the change in speed. The relationship between a change in speed and a change in power to the prime mover is normally an adjustable feature. The chart illustrates a typical speed droop characteristic curve showing a 5% regulation ratio.

When the power being supplied to the grid has been adjusted such that it is again in equilibrium with the consumption of power, then the system frequency will stabilize and the machine speed will be constant. The speed droop controllers will hold the supply steady at that level.

Although the system will be stable, it will not longer be operating at 60 Hz. To return the system to normal operating frequency, the dispatcher will be required to adjust the units in his spinning reserve to compensate for the overall load change.

Reactive Load Sharing

In order for the grid to be stable, the VAR load of the grid must be met with VAR supply from the network of parallel generators. The system must have a balance of inductance and capacitance to achieve this condition.

When the grid load conditions are normal, the reactive demands of the load are predominantly inductive, i.e. there are more inductors connected to the grid than capacitors. In order to service the magnetizing current needs of the inductive grid, the generators must behave as capacitors. The network of parallel generators supplements the inherent capacitance of the grid to achieve the balance of inductance and capacitance. In order to exhibit capacitive behavior, a generator must be over-excited. That is, its output voltage must be higher than the local system voltage.

Conversely, under low load conditions, the transmission line capacitance can shift the impedance of the grid to become predominantly capacitive. This requires that the generators behave as inductors. In order to exhibit inductive behavior, a generator must be under-excited. That is, its output voltage must be lower than the local system voltage.

Ideally, all generators would be operated slightly over-excited or under-excited to the extent that each generator carries its proportional fraction of the VAR load. However, transmission of VAR current over long distances is inefficient due to the resulting line losses. Therefore it is desirable to have the



generators closest to the VAR load carry the bulk of the load. On the other hand, each generator has limits on the VAR load it can carry due to the heating induced by VAR current in the armature. Additionally, excessive local VAR current can result in undesired overheating of step up transformers and transmission lines.

It is the system operators responsibility to distribute the VAR load across the available generating units in the most efficient manner. Dispatchers do not have remote control of the generator voltage regulators in the power plants. In order to change the VAR load at a particular plant, the dispatcher must request the change from the local plant operator. Dispatchers do have other tools for adjusting VAR load in the form of tap changers on transformers, and capacitor banks and line reactors in switchyards and substations.

Since the VAR load is a smaller fraction of the MVA load on the system, VAR disturbances are less severe than real load disturbances. Beyond the action of the normal automatic voltage regulators, no special controls are in place to act during VAR disturbances.

Power System Stability

When generators are operated in parallel over long distances, the combined characteristics of the generators, their voltage regulators and exciters and the transmission lines can develop resonant frequencies which will cause the power sharing of the generators to be oscillatory and unstable under both steady state and transient conditions.

The Power System Stabilizer is an independent device which was developed to counteract these instabilities. The inputs to the PSS are usually system frequency and power. The PSS utilizes the excitation system as its final control element for implementing its control actions to stabilize the power flow through out the system. Further discussion is beyond the scope of this document.



Generator Ratings and Curves

The manufacturer of the generator specifies the ratings of the generator on the nameplate. In addition, the manufacturer usually supplies three engineering curves which are important for understanding the concepts of generator operation and protection and are useful in evaluating the settings of limiting and protection features of the voltage regulator.

Nameplate

The generator nameplate specifies the ratings of the generator. The relevant parameters usually identified on the nameplate include: Frequency, Terminal Voltage, KVA, Power Factor, Stator Amps, Hydrogen Pressure, Excitation Voltage and Field Current

Generator Saturation Curve

The saturation curve defines the response of the generator output

voltage to the application of excitation current to the field. The generator output voltage is shown on the vertical axis and is usually scaled in kilovolts or sometimes as a per unit value. The rated machine voltage may be shown as a horizontal line at the rated voltage. The generator field current is charted on the horizontal axis. The curve assumes that the generator is being operated at 60 Hz.

Figure 21: Nameplate



Figure 22: Generator Saturation Curve



The air gap line illustrates linear relationship of excitation current to output voltage and it represents the theoretical behavior of the machine. The no load saturation curve follows the air gap line until the voltage approaches the rated condition where the curve becomes slightly non-linear, bending to the right. This represents the actual behavior of the generator and the change is due to the density of the magnetic flux approaching the saturation point of the armature winding cores. Operating with the armature cores in saturation will result in induction heating of the cores and is not allowed for extended periods of time.

The no load point is labeled as AFNL (amps field no load) and identifies the excitation current required to bring the generator output up to the rated voltage in preparation for synchronizing the generator to the grid. For this unit, the value of no load field current is 1743 amps, which is approximately 40% of the rated field current specified by the nameplate.

The excitation system is normally sized to provide at least 130% of the rated field current. Since only 40% of the rated current is needed to reach the rated voltage before the generator is synchronized, the excitation system is capable of causing extremely high voltage output and complete armature core saturation. Whether due to operator error or equipment malfunctions, operation with the armature core saturated must be avoided. Since the heating of the cores does not occur instantaneously, the limiting and protective features may incorporate time delays to allow for momentary fluctuations.

Over Voltage Condition

The voltage rating of the generator is specified on the nameplate and plotted on the saturation curve which assumes that the operating frequency is at 60 Hz. If a generator is operated at a lower frequency than the nameplate value, then core saturation will occur at a lower voltage. The relationship between frequency and armature core saturation is linear such that a reduction in operating frequency requires a corresponding reduction in the rated voltage. This property is especially significant if excitation is inadvertently initiated during start up when the generator is being operated at a low speed or if excitation is not removed as the generator coasts down after being taken out of service.

In most power plants, the main transformer is connected between the generator and the synchronizing breaker. Therefore, the transformer is subjected to the generators output voltage and frequency as soon as excitation is applied during start up. Transformers, being constructed of coils wound on permeable cores, have the same volts/Hz properties as generators. For this reason, operators must also consider the main transformer ratings in evaluating the settings of the limiting and protective features.

Using potential transformers, the generator terminal voltage is typically stepped down for metering and protection purposes to a nominal voltage of 120 VAC at the rated terminal voltage. The rated frequency of the generator is specified as 60Hz, thus the nominal voltage to frequency ratio is 120



VAC/60 Hz or a ratio of 2.0. A drop in frequency or a rise in voltage will both result in a ratio in excess of the normal 2.0.

Over Voltage Limiting and Protection

Over voltage conditions are most likely to occur prior to synchronization. Once synchronized, over voltage can occur but the limits may be less restrictive than other limiting factors. The damage mechanism associated with the over voltage condition is overheating of the generator stator cores from operating in magnetic saturation.

When the voltage regulator is operating in automatic, the over voltage limit is enforced by the volts/hertz limiter function (VHL or HXL). The limiter is a control function of the automatic voltage regulator and acts to prevent the generator from exceeding the specified volts/Hz ratio using the automatic voltage regulator output. The action of the volts/Hz limiter is not usually time delayed.

The limiter is usually backed up by a volts/Hz protection scheme (VHP or HXP). The implementation of the volt/Hz protection is quite variable among sites and manufacturers, with some installations choosing to disable the volts/Hz protection once the generator is synchronized.

The most common version of volts/Hz protection utilizes dual set points, each with their own time delays, where the lower set point device has a long time delay and the higher set point device has a shorter time delay. In some cases, the automatic voltage regulator (AVR) is tripped to manual operation as part of the sequence in expectation that the AVR has malfunctioned. If the AVR was at fault, the generator output voltage should be reduced, the transient terminated and a unit trip avoided.

In all cases, if the over voltage condition persists for too long, the final result of the protection scheme is removal of excitation from the generator, either through opening of the field breaker or tripping of the generator lockout relay.

Generator VEE Curve

The VEE Curve illustrates the relationship of generator excitation to the range of generator operating load conditions. The ratings of the generator are listed across the top of the graph. The vertical axis is scaled in per unit MVA (fractional percent). The horizontal axis is scaled in amps of field current. Throughout the curve, the generator is assumed to be at rated voltage and rated frequency. The effects of reduced cooling capability are shown with the three hydrogen pressure values. Reduced cooling capability mandates reductions in the maximum allowable MVA and field current.



Figure 23: Generator Vee Curve



A set of vertical curves emanate from a locus at 1743 amps, the no load field current for this generator. Each line represents a constant power factor for a varying MVA and field current. The curvature of the lines is related to the combined effects of resistive and reactive voltage droop of the generator.

Constant megawatt curves are drawn horizontally across the power factor lines at three arbitrary values. The shape of the constant megawatts curve illustrates the non linear relationship of MVA to megawatts and megaVARs for varying power factors.

The nameplate rated operating point of the generator is found at the upper right corner where the 0.90 PF line intersects the 1.0 per unit MVA line. Following that point straight down to the horizontal axis yields the nameplate rated field current of 4396 amps. If the generator is operated at unity PF, the field current at the rated MVA will be 3550 amps, which equates to approximately 80 percent of the rated field current.

No Load =1743 amps = 39.7% of rated field current

Full Load at Unity PF = 3550 amps = 80.8% of rated field current

Full Load at Rated PF = 4396 amps = 100% of rated field current

From these values, one can see that the field current required to carry resistive load is approximately twice that required to achieve no load rated voltage. The increase in field current is needed to compensate for the effect of the resistive voltage droop of the generator as the unit carries real load. In order to carry the rated reactive load, a further increase in field current of approximately 20% is required to compensate for the reactive voltage droop. The relative proportionality of field current to these three operating conditions will generally hold true for all generators.

If the excitation current is not increased beyond the no load rated value, one can see that as the unit load is increased, the power factor will begin to shift away from unity toward the under-excited condition such that power factor will decrease from unity to 0.80 as the load just exceeds 350 megawatts. This exemplifies the effect on output behavior due to the inherent voltage droop of the generator and the importance of having an automatic voltage regulator.

Capability Curve:

The Generator Capability curve is provided by the generator manufacturer for the use by plant operators as a guideline for ensuring that the generator is operated safely. It is a composite of four families of curves, each of which is a limit, protecting the generator from damage due to overheating or pole slippage. These shapes of these four families give the composite curve its characteristic D shape.



Figure 24: Idealized Generator Capability Curve

The axes of the curve are watts on the horizontal axis and volt-amps reactive on the vertical axis. Since VARS can be inductive or capacitive, the VAR axis is zero centered and divided into two segments: overexcited (lagging) and under-excited (leading). The lines drawn outward from the origin trace the watt/VAR relationships at various power factors.



Note that there are three concentric D shaped curves, each labeled for a different value of hydrogen pressure. Since hydrogen is the cooling medium used in the generator, higher pressure implies a greater capacity for heat removal. Several of the curve segments are based on temperature limits, so if more heat can be removed, higher loads can be safely maintained.

The interior of the curve defines the allowable safe operating region. To find the actual operating point at any given time, the operator would determine the current megawatt and megaVAR load from existing control room indications. He would then plot megawatts on the horizontal axis and megaVARs on the vertical. If the power factor is lagging, then MVARs are plotted above the origin on the Over-Excited segment of the MVAR axis. If the power factor is leading, then the MVAR value is plotted below the origin on the Under-Excited segment. The intersection of the MW and MVAR lines identifies the present operating point. The length of the vector line drawn from the origin to the operating point indicates the apparent power in MVA.



Figure 25: Sample Capability Curve



Curve Derivation

As previously stated, the Generator Capability curve is a composite of four families of curves, each of which is a limit, protecting various parts of the generator from damage. Usually, the generator voltage regulator contains limiting and protection features to help prevent operating limits from being exceeded. The nomenclature of such features varies among manufacturers of voltage regulators and protective relays, but the functionality is largely the same.

Figure 26: Capability Curve Derivation



Over-Excitation

The segment across the top, from point A to point B is intended to protect the generator in the event it is excessively overexcited. Since excitation is a function of the current supplied to the field windings on the generator rotor, the rotor windings are the component which will be damaged first if the unit is operated outside the curve. The top line represents 100% of rated excitation at the normal hydrogen pressure. Lower hydrogen cooling pressures require that the maximum allowable excitation be reduced.

The excitation current flow is accompanied by I2R losses which result in heating of the rotor winding conductors. Excessive current flow will result in overheating of the insulation between the conductors and subsequent shorting of the windings. In extreme cases, the rotor windings will become soft enough to deform, causing unacceptable vibration of the rotor.

Since overheating does not occur instantaneously, the limiting and protection for over-excitation is usually time delayed. The time delay is usually designed to be inversely proportional to the severity of the transient, such settings are designed to follow the heating characteristics of the field winding.

When the voltage regulator is operating in automatic, this limit is enforced by a maximum excitation limiter (MXL/OEL) function. The limiter action is inhibited for period of time to allow for momentary transients. Once activated, the limiter acts to prevent field current from exceeding the specified value using the automatic voltage regulator output.

The limiter is backed up by a protective feature, Over-Excitation Protection (OXP) which operates in a sequence of actions to protect the rotor from damage. As part of the sequence, the AVR is tripped to manual operation under the assumption that the AVR has malfunctioned. If the AVR was at fault, the field current should be reduced and the transient terminated, avoiding a unit trip.

If the over-excitation condition persists too long, the final result of the OXP sequence is removal of excitation from the generator by tripping of the generator lockout relay.

Overload

The segment from point B to point C is intended to protect the generator from overload. Load current is carried by the armature windings, therefore overload conditions will result in overheating of the armature windings. Overheating can cause breakdown of insulation and internal shorts in the stator windings.

Since the real load current is a function of the prime movers control system, the voltage regulator does not include any limiting or protective features which respond to the overload condition.



Under-Excitation

The segment of the curve from point C to point D protects the generator from under-excitation. Operation in the under-excited region at high load is limited by heating of the end iron. At low loads, the temperature limitation is insignificant and the limit is based on the minimum excitation required to maintain synchronization.

End iron overheating results from the presence of extreme magnetic field density. Concentrated magnetic fields induce a form of circulating electrical current into the metal of the armature core, a phenomenon known as eddy currents. Eddy currents generate heat as they circulate in the silicon steel of the armature core. The flow of eddy currents is minimized by using laminated stator pole pieces, but eddy currents are still not completely avoidable. Excessive eddy currents will result in overheating of the core laminations and the pole pieces can be damaged.

The density of magnetic flux at the ends of the stator core pole pieces is proportional to armature current. It is also inherently high in the end iron region due to the fact that the armature windings physically turn at that point, concentrating the field on the inside of the turns. At low unit loads, the flux densities experienced at the end iron are insufficient to induce eddy current heating, thus end iron overheating is only an issue at high loads.

The excitation field of the rotor opposes the armatures magnetic field. A strong excitation field tends to reduce the concentration of flux at the end iron by pushing the armature field away from the end iron. As excitation is reduced, the armature field pulls in closer to the end iron, allowing the flux density at the end iron to increase. Thus reduced excitation at high loads results in optimum conditions for the development of eddy currents and end iron overheating that they induce.

At low loads, the heating of the end iron becomes insignificant and the operating limit is based on the minimum excitation required to maintain synchronization. The segment, point D to point E, is called the Steady State Stability Limit (SSSL) or pull out curve. Note that towards point D, the SSSL becomes more limiting than the under excitation limits. This is why the three temperature curves merge as they approach the no load axis.

The SSSL is a function of the generator design and is based on a relationship between the generators internal impedance and the system impedance. If the SSSL is exceeded, the generators field strength is insufficient to keep the generator in sync with the grid and the turbine will accelerate the generator out of synchronization with the grid. This phenomenon is commonly called slipping poles. Pole slippage will almost certainly damage the generator.

When the voltage regulator is operating in automatic, the limit for operation in the under-excited condition is enforced by a minimum excitation limiter (MEL/URAL) function. The limiter acts to prevent the operating point from exceeding the specified relationship of megawatts/megaVARs, using



the automatic voltage regulator output to boost excitation as necessary to stay above the limit. The limiter does not discriminate as to whether the damage mechanism will be end iron overheating or loss of synchronization, it simply limits operation in the under-excited direction thereby accounting for both possibilities.

The minimum excitation limiter function is usually backed up by some form of protection, albeit not usually a part of the voltage regulator. The most common practice is to rely upon an externally mounted Loss of Field or Out of Step relay to immediately take the generator out of service by tripping the generator lockout relay.




Table of FiguresFundamentals of GenerationCharge and PolarityConductorsElectromotive ForceAlternating Current GenerationFrequencyTorque/Counter Torque

Generator Terminology and DesignArmatureFieldNumber of Field Poles

Generator Physical DesignStatorRotorCooling Considerations

Excitation TechniquesRotating DC ExciterRotating Alternator ExciterBrushless ExciterStatic Exciter

Power, Watts and VARsResistanceReactanceInductanceCapacitanceResonance

Apparent PowerTrue Power or MegawattsReactive Power or MegaVARsPower Factor

Voltage DroopSynchronizing the GeneratorSynchroscopeFrequencyVoltagePhase Closing the breakerMotorizing the GeneratorMaintaining SynchronizationChanging LoadChanging Voltage

Load SharingReal LoadDispatching of Real LoadTransient Response

Reactive Load SharingPower System Stability

Generator Ratings and CurvesNameplateGenerator Saturation CurveOver Voltage ConditionOver Voltage Limiting and Protection

generator basics

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