Synchronous generators

Synchronous generators consist of an armature winding located on the stator which is connected to the three phases of the network and a field winding on the rotor which is fed from a source of direct current. The armature winding develops an mmf (magneto motive force) rotating at a speed proportional to the supply frequency. The field winding produces an mmf which is fixed with respect to the rotor. In normal operation the rotor, and hence the field winding, rotates synchronously with the mmf Figure 4.1 Generator connected to a network

98 Embedded generation

developed by the stator with its relative angle, the load angle, determined by the torque applied to the shaft. The speed of rotation can be reduced at the design stage by increasing the number of pole pairs of the gener-ator as shown in eqn. (4.1).

N= f × 60/p (4.1)

where N is the speed of rotation in rpm, f is the system frequency (50 or 60 Hz) and p is the number of pole pairs.

The stator or armature windings are similar to those found on induc-tion machines but there are a number of different rotor arrangements.

Large steam turbine generator sets use turbo-alternators consisting of a cylindrical rotor with a single DC winding to give one pair of poles and hence maximum rotational speed (3000 rpm on 50 Hz systems). Hydro-generators often operate at lower speeds and then use multiple-pole generators with a salient-pole rotor. Smaller engine driven units also generally use salient pole generators. Exceptionally the field winding may be replaced by permanent magnets but this is not commonly found in large generators as, although higher efficiencies can be achieved, direct control of the rotor magnetic field is not possible with this arrangement.

Innovative designs of permanent magnet generators are being investi-gated as they can be constructed with a large number of poles and so operate at low speed and be connected directly to slow speed prime movers, hence removing the requirement for a gearbox in the drive train.

Figure 4.2 shows the simple mechanical analogues of synchronous and

Figure 4.2 Simple mechanical analogues of generators

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induction generators. In a synchronous generator, the rotor rotates at con-stant speed and the rotor angle is a function of the applied torque. Hence the connection of the generator to the network is represented by a spring.

In an induction generator, the rotor rotates at a slip speed, slightly faster than the synchronous magnetic field of the stator, and so the rotor speed is a function of the torque applied to the shaft. Hence the connection to the network is represented by a rotational damper. Clearly the simple syn-chronous machine analogue shown would oscillate perpetually if excited by a torque either due to a disturbance from the network or from the prime mover. In practice this is controlled by damping built into the generator, for example by damper windings on a salient pole generator. These analogues only give a simple picture over a limited linear region of operation but they do allow the operation of the two types of generator to be contrasted.

4.1.1 Steady-state operation

To investigate how a synchronous generator will behave on the power system a simple model is required. Figure 4.3 shows the normal equiva-lent circuit used to represent steady-state operation, based on the assumptions that: (i) the magnetic circuits are unsaturated, (ii) the air-gap is uniform and any effects of saliency are ignored, (iii) the air-gap flux is sinusoidal, and (iv) the stator resistance is negligible. It may be seen that

V= Ef− jIXs (4.2)

where V is the terminal voltage, Ef is the internal voltage (function of the field current) and Xs is the synchronous reactance (components due to armature leakage reactance and armature reaction) .

For a small embedded generator the terminal voltage is usually held almost constant by the network and so phasor diagrams may be drawn (Figure 4.4 ) to illustrate the operation of a synchronous generator onto a fixed voltage (or infinite busbar). The power factor of the power delivered to the network is simply cos φ, while the rotor angle (the angle by which the rotor is in advance of the stator field) is given by δ (see

Figure 4.3 Steady-state equivalent circuit of a round rotor synchronous generator

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Section 3.5.1 and eqn. 3.48). This is a particular case of the two-busbar system discussed in Chapter 3, and so the active power delivered is simply

P= (EfV/Xs) sin δ (4.3)

while the reactive power delivered to the system is

Q= EfV/X_s cos δ −V²/X_s (4.4) (Note that eqn. (3.59) describes the reactive power flowing into the reactance and so the sign is reversed in eqn. (4.4).)

In normal operation, the rotor angle δ is usually less than 30° and so the cosine term of eqn. (4.4) remains fairly constant. Thus, increasing the torque on the rotor shaft increases the rotor angle (δ) and results in more active power exported to the network. Increasing the field current and hence increasing the magnitude of Ef results in export of reactive power.

The phasor diagrams of Figure 4.4 show the same rotor angle (and hence the same active power export) but with two different values of excitation:

(a) Underexcited

|Ef| < |V|

a leading power factor (using a generator convention and the direction of I as shown), importing reactive power.

Figure 4.4 Phasor diagrams of a round rotor synchronous generator connected to a voltage V

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(b) Overexcited

|Ef| > |V|

a lagging power factor (using a generator convention and the direction of I as shown), exporting reactive power.

It may be noted that if the direction of the definition of the current I is reversed, and the machine considered as a motor rather than a generator, then an underexcited motor has a lagging power factor and an over-excited motor has a leading power factor. Of course, if torque is still applied to the shaft then active power will be exported to the network, and if |Ef|>|V| then reactive power will still be exported irrespective of whether the same machine is called a motor or generator. Therefore, it is often helpful to consider export/import of real and reactive power rather than leading/lagging power factors which rely on the definition of the direction of the current flow.

Values of Xs are available from generator manufacturers and some typical ranges are quoted in References 3 and 4. References 1 and 2 show how the analysis can be extended to include the effects of saliency in the rotor and saturation of the magnetic circuits. In practice good power systems analysis programs will include these effects if sufficient data are provided.

The operating chart of a synchronous generator is formed directly from the phasor diagram of Figure 4.4. The phasor diagram is simply scaled by multiplying by V/Xs, which is a constant, to give the phasor diagram of Figure 4.5. The locus of the new phasor VI then describes the operation of the generator. Various limits are applied to account for: (i) the maximum power available from the prime mover, (ii) the maximum current rating of the stator, (iii) the maximum excitation and (iv) the minimum excitation for stability and/or stator end winding heating. These limits then form the boundaries of the region within which a synchronous generator may oper-ate. In practice there may be additional limits including a minimum power requirement and the effect of the reactance of the generator transformer.

The operating chart illustrates that a synchronous generator con-nected to an infinite busbar of fixed voltage and frequency has essentially independent control over real and reactive power. Real power is varied by adjusting the torque on the generator shaft and hence the rotor angle, while reactive power is adjusted by varying the field current and hence the magnitude of Ef. For example, at point (x) both real and reactive power are exported to the network, at (y) rather more real power is being exported at unity power factor, while at (z) real power is exported and reactive power imported.

Figure 4.6 shows a notional 5 MW synchronous embedded generator driven by a small steam turbine. If the short-circuit level at the point of connection (C) is, say, 100 MVA, with an X/R ratio of, say, 10, then the total source impedance on a 100 MVA base will be approximately 102 Embedded generation

Z= 0.1 + j1.0

and with a realistic value of Xs of 1.5 per unit on rating, then, again on a 100 MVA base,

X_s= j30

Thus it can be seen immediately that |Xs|>>|Z| and, to a first approxima-tion, the synchronous generator will have a very small effect on network voltage. As a small generator cannot affect the frequency of a large interconnected power system, then the embedded generator can be con-sidered to be connected directly to the infinite busbar. Figure 4.6 is an oversimplification in one important respect in that the other loads on the network are not shown explicitly and these will alter the voltage at the point of connection of the generator considerably. In some power sys-tems, changes in total system load or outages on the bulk generation system will also cause significant changes in frequency.

The conventional method of controlling the output power of a gener-ating unit is to set up the governor on a droop characteristic. This is shown in Figure 4.7, where the line (a–b) shows the variation in fre-quency (typically 4%) required to give a change in the power output of the prime mover from no-load to full-load. Thus with 1 per unit fre-quency (50Hz) the set will produce power P1. If the frefre-quency falls by 1%

the output power increases to P3, while if the system frequency rises by Figure 4.5 Operating chart of a round rotor synchronous generator connected to

an infinite busbar

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1% the output power is reduced to P2. This, of course, is precisely the behaviour required from a generator which can influence the system quency; if the frequency drops more power is required, while if the fre-quency rises less power is needed. The position of the droop line can be changed using the ‘speeder gear’ and so by moving the characteristic to (a′–b′) the power output can be restored to P1 even with an increased system frequency or by moving to (a″–b″) for a reduced system frequency.

A similar characteristic can be set up for voltage control (Figure 4.8) with the axes replaced by reactive power and voltage. Again, consider the droop line (a–b). At 1 per unit voltage no reactive power is exchanged with the system (operating point Q1). If the network voltage rises by 1%

then the operating point moves to Q2 and reactive power is imported by the generator, in an attempt to control the voltage rise. Similarly if the network voltage drops the operating point moves to Q3 and reactive power is exported to the system. Translating the droop lines to (a′–b′) or (a″–b″) allows the control to be reset for different conditions of the network. The slope of both the frequency and voltage droop character-istics can also be changed if required.

These conventional control schemes may not be appropriate for small embedded synchronous generators. For example, an industrial CHP plant may wish to operate at a fixed power output, or fixed power exchange with the network, irrespective of system frequency. Similarly, operation with no reactive power exchange with the network may be desirable to minimise reactive power charges. If the generators are oper-Figure 4.6 Control of an embedded generator

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ated on the simple droop characteristics illustrated in Figures 4.7 and 4.8 then both real and reactive power outputs of the generator will change constantly with network conditions, as the network voltage and fre-quency vary under external influences.

Therefore, for many relatively small embedded generators on strong networks, control is based on real and reactive power output rather than on frequency and voltage, as might be expected in stand-alone installa-tions or for large generators. As shown in Figure 4.6, voltage and current signals are obtained at the terminals of the generator and passed to transducers to measure the generated real and reactive power output. The main control variables are MW, for real power, and MVAR or cos φ for reactive power. A voltage measurement is also supplied to the automatic voltage regulator (AVR) and a speed/frequency measurement to the gov-ernor but, in this mode of control, these are supplementary signals only.

It may be found convenient to use the MW and MVAr/cos φ error signals indirectly to translate the droop lines and so maintain some of the bene-fits of the droop characteristic, at least during network disturbances, but this depends on the internal structure of the AVR and governor.

However, the principal method of control is that, for real power con-trol, the measured (MW) value is compared to a set point and then the error signal fed to the governor which, in turn, controls the steam supply to the turbine. In a similar manner the generator excitation is controlled to either an MVAr or cos φ setting. The measured variable is compared Figure 4.7 Conventional governor droop characteristic

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to a set point and the error passed to the AVR and exciter. The exciter then controls the field current and hence the reactive power output.

It may be noted that the control scheme shown in Figure 4.6 pays no attention to the conditions on the power system. The real power output is controlled to a set point irrespective of the frequency of the system while the reactive power is controlled to a particular MVAr value or power factor irrespective of network voltage. Clearly for relatively large embed-ded generators which can have an impact on the network this is unsatis-factory and more conventional control schemes such as voltage control with quadrature droop and the use of supplementary frequency signals to improve the governor response are likely to be appropriate [6]. These are well established techniques used wherever a generator has a signifi-cant impact on the power system but there remains the issue of how to influence the owners/operators of embedded generation plant to apply them. Operating at non-unity power factor increases the electrical losses in the generator while varying real power output in response to network frequency will have implications for the prime mover and steam supply if it is operated as a CHP plant. Moreover, as increasing numbers of small embedded generators are connected to the network it will become important to co-ordinate their response both to steady-state network conditions and to disturbances. At present, in the UK at least, the tech-nical and commercial/administrative arrangements for the co-ordination Figure 4.8 Quadrature droop chacteristic for generator excitation control 106 Embedded generation

of the operation of large numbers of small (<50 MW), independently owned embedded generators are not yet in place.

4.1.2 Excitation systems

The performance of a synchronous generator is strongly influenced by its excitation system particularly with respect to transient and dynamic sta-bility, and the ability of the generator to deliver sustained fault current.

Supply of sustained fault current is particularly important for embedded generators due to their relatively small ratings and the long clearance times typically found in distribution protection systems. A small embed-ded generator, with the same per unit machine parameters on rating as a large generator, will provide fault current only in proportion to the machine ratings. Further, distribution networks are often protected with time-delayed overcurrent protection which, because of the way it is set (or graded) can require fault currents considerably higher than the circuit continuous rating in order to operate quickly. Thus, the ability of a small generator to provide adequate fault current requires careful attention during the design of the embedded generation scheme.

On some older generators, a DC generator, with a commutator, was used to provide the field current, which was then fed to the main field via slip rings on the rotor. Equipment of this type can still be found in service, although often with modern AVRs replacing the rather simple voltage regulators which were used to control the field of the DC gener-ator and hence the main excitation current. However, more modern excitation systems are generally of two types: brushless or static.

Figure 4.9 is a schematic representation of a brushless excitation

Figure 4.9 Brushless excitation system

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system. The exciter is simply an alternator, much smaller than the main generator and with a stationary field and a rotating armature. A full wave diode bridge is mounted on the rotating shaft to rectify the three-phase output of the exciter rotor to DC for the field of the main generator. The exciter field is controlled by the AVR, which, as discussed earlier, is itself controlled by the power factor controller to allow control either to a constant power factor or to a defined reactive power output. Power for the exciter may be taken either from the terminals of the main generator (self-excited) or from a permanent magnet generator (separately excited).

The permanent magnet generator is mounted on an extension of the main generator shaft and continues to supply power as long as the gener-ator is rotating. In contrast, a simple self-excited scheme may fail to operate correctly if a close-up fault reduces the voltage at the terminals of the generator as the generator cannot then provide fault current just when it is needed. This is of particular concern for embedded generators connected directly to the distribution network as the impedance of a generator transformer will tend to help maintain the generator terminal voltage in the event of a network fault. It is possible to use current transformers as well as a voltage transformer to supply excitation power in a separately excited scheme but, if costs allow, a more reliable method is to use a permanent magnet pilot exciter.

Figure 4.10 shows a static excitation system in which controlled DC is

Figure 4.10 Static excitation system 108 Embedded generation

supplied by a controlled thyristor rectifier and fed to the generator field via slip rings. The power supply for the thyristor rectifier is taken from the terminals of the generator. The main advantage of the static exciter is improved response as the field current is controlled directly by the thyris-tor rectifier but, of course, if the generathyris-tor terminal voltage is depressed too low then excitation power will be lost. It is again possible to provide the power supply from both voltage and current transformers at the generator terminals but it is doubtful whether the improved response of the static exciter over a permanent magnet brushless scheme can be justi-fied for many small embedded generators.

In addition to the main types described, there are a large number of innovative designs of excitation systems which have been developed over the years particularly for smaller generators. These include the use of magnetic circuits for the no-load excitation and current transformer compounding for the additional excitation required as current is drawn.

Although such techniques may work robustly on stand-alone systems they are almost impossible to model for studies of embedded generation schemes. For larger generators and their excitation systems the manu-facturers are usually able to supply the so-called IEEE exciter models.

Although such techniques may work robustly on stand-alone systems they are almost impossible to model for studies of embedded generation schemes. For larger generators and their excitation systems the manu-facturers are usually able to supply the so-called IEEE exciter models.