AU614876B2 - Damping rotor oscillations in synchronous machines - Google Patents

Description

M7- COMMONWEALTH OF AUSTRALIA PATENT ACT 1952 COMPLETE SPECI FICATION 614876

(ORIGINAL)

FOR OFFICE USE CLASS INT. CLASS Application Number: Lodged: :0:0 Co 0 ego *e .0 0 0

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9. 0 00 Oe @000 0 goeS Complete Specification Lodged: Accepted: Published: Priority: Related Art-: 0000 go 0S S 00 So S

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.000 o 0@ 0S S NAME OF APPLICANT: ADDRESS OF APPLICANT: NAME(S) OF INVENTOR(S) ADDRESS FOR SERVICE: BHP ENGINEERING PTY. LTD.

2/4 Kennedy Street Kingston 2604 New South Wales

AUSTRALIA

Noel GODFREY Larry.PARKES Russell WILKIE DAVIES COLLISON, Patent Attorneys; 1 Little Collins Street, Melbourne, 3000.

00 O 000 00 0 00 O COMPLETE SPECIFICATION FOR THE INVENTION ENTITLED: "DAMPING ROTOR OSCILLATIONS IN SYNCHRONOUS MACHINES" The following statement is a full description of this invention, including the best method of performing it known to us 01, 2T 99

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ULr*i_~ la DAMPING ROTOR OSCILLATIONS IN SYNCHRONOUS MACHINES 9 @*of 10 11 12 o 13 *14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 36 37 38 This invention relates to damping rotor oscillations in synchronous machines.

An electromechanical system which includes an electrical synchronous machine and its connected power system exhibits on underdamped resonance typically in the frequency range of 1 to 3 hertz. This is due to the mathematical relationship relating input power to output power which, in its simplest form, can be described by a second order underdamped differential equation analogous to the equations of motion associated with a mass supported by a spring.

The synchronous machine is thus capable of producing power oscillations in response to a system disturbance or load disturbance, and amplification of repetitive disturbances with frequency components in the vicinity of the natural resonance frequency of the synchronous machine.

A power supply system is made up of a network of synchronous generators connected by various transmission lines. The power supply network may spread over a vast area providing electrical power to consumers in all parts of the region. It follows that the power system may respond differently from a disturbance in one part of the network to the same disturbance in another part of the network or under different load conditions. Hence there are several degrees of freedom in which a power supply may respond to a 890914,&diskname&,0469f.ws, 1 fNEW 13 1 F' 2 4 6 7 8 9 11 12 S 13 14 S 15 17 18 19 4 S, 20 21 22 23 24 26 27 28 29 31 32 33 34 36 37 disturbance both in the size of oscillations and the frequency.

The reliability of the power supply network depends on the relative stability between its connected elements of which the synchronous generator is an important part. At any node or bus within the power network there is at least one synchronous generator which may influence that bus.

Underdamped power swings at the synchronous generator natural frequency may cause loss of power at the connected bus. Hence the integrity of the power system is determined in part by the degree of damping of the synchronous generator.

Synchronous motors are often used in industry as the primary consumer of input power in many industrial processes. Being connected to the power supply network it also has to be considered in the stability of the power supply, if not in the complete supply network, then in the local area network. Annoying voltage flicker often results at the local supply bus in response to underdamped power oscillations which is usually first noticed as a flicker in the plant lighting.

If the power oscillations become too severe the synchronous motor will trip off line due to loss of synchronism or due to other motor protection devices. This can result in damage to the industrial process or even the plant equipment.

Examples of processes using synchronous motors to convert electrical power to mechanical power are draglines, rolling mills or mine winders. In these examples load torque, frequency components of which fall in the vicinity of the synchronous motor natural frequency, are amplified by the synchronous motor. Continued torque excitation in this ii: ii PI c i: e ,-e y r i 890914 ,&dlskname&,0469f.ws,2 i-- ;1 -3- 9 Ii 11 12 13 14 S 16 oeeo 17 18 19 20 21 S22 23 S 24 24 frequency range may cause the resulting power oscillations to grow or be sustained about the machine operating point.

The synchronous motor response to large transient changes in load similarly produces power overswings and subsequent oscillations which can threaten the integrity of the connected power system.

Various methods are available for improving the stability of synchronous machines and for minimising power oscillations within the power system itself. These methods range from switching techniques and careful design of system reactances to dynamic voltage support, use of DC links and special strategies for machine excitation control.

The present invention relates to machine excitation control and falls within the category of control strategies normally described as slip stabilisation. Slip stabilisation uses motor speedexcursions from a selected reference synchronous speed to be used as the controlled quantity in the synchronous motor excitation system, whereby machine torque components are generated via the field to oppose the speed excursions.

Most oscillatory systems can be adequately described by a second order differential equation, the coefficients of which characterise the system in terms of a natural frequency of oscillation and a damping ratio. The higher the damping ratio the more damped is the system. The general principle of damping strategies is to add an element to the system which improves the damping ratio of the system as described by the second order approximation.

In the mechanical analogy of a mass supported by a spring, this is equivalent to adding a dashpot to the system to damp the natural resonance frequency. The dashpot produces forces which oppose the difference between 890914&diskname&,0469f.ws,3 0* o• S o. S. I i. I Ei 4

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0 18 19 20 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 velocities at each end of the spring. In the case of the synchronous machine, there is a spring-like torque acting to align the rotor magnetic axis of the machine with those of other synchronous machines connected to the system. Machine torque and electrical power flow are analogous to spring force, the machine's rotating inertia is analogous to mass and the rotor slip speed corresponds to the relative velocities of each end of the spring. The generation of counter torques proportional to slip speed creates damping similar to that produced by a dashpot.

Excitation control systems for synchronous generators are primarily for automatic voltage regulation.

It is usual for modern excitation systems to incorporate a power system stabiliser to improve the damping of the machines.

Power system stabilisers are based on the measurement of speed, frequency or electrical power. The first two quantities prove to be relatively expensive to measure and have inherent difficulties in application due to signal extraction problems and noise sources. The third quantity is easily measurable and is most often used in modern slip stabilisation equipment.

The measurement of speed for use as the stabilisation signal has a number of problems. These problems include tachogenerator ripple voltage, which may degrade over time; torsional resonance in the generatorturbine or motor shaft; and the extraction of the slip speed component above the synchronous speed, which is not independent of line frequency. The resulting signal to noise ratio is therefore low and the mechanical cost involved in retrofitting a tachogenerator to the machine shaft does not make this solution cost effective.

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4 *fl 18 19 20 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 The use of slip frequency for damping control also has its shortcomings. Frequency is measured at the machine terminals and its value will lie between that of the power system and that of the machine rotor. It is therefore not as effective a control signal as actual slip speed of the rotor. If the power system is very stiff at the point of connection of the machine, frequency variations will be relatively insensitive to rotor oscillations. The degree of sensitivity can also change dramatically as the power system configuration changes by switching transmission lines, loads and generating sources in and out of service. Secondly, frequency is sensitive to power oscillations occurring within the power system itself, and may not reflect accurately the response of the machine of interest.

Uncertainties in using frequency as the controlling signal does not make this solution universal for all applications.

The basis of using active power measurement in slip stabilisation techniques is the correlation between the rate of change of active power and slip speed for which a relational expression can be devised based on linearisation of the machine equations. Phase lead or phase lag networks are required to correct for phase shifts in the control algorithm. This approach works well for a particular machine operating condition and so long as excursions from the linearised machine model are not too extreme as to make the errors due to the machine non linearities significant, the control algorithm produces beneficial results.

The object of this invention is to provide a cost effective solution to the problem of synchronous machine resonance, a solution which offers potentially better performance than methods currently employed.

Generally speaking the invention involves the use of an accurate mathematical model to derive the effective rotor slip speed and in the control strategies used to 890914.&diskname&.0469f.ws.5 i L. i i 1 6

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17 18 19 S' 20 .4 21 22 23 24 o 26 27 28 29 31 32 33 34 36 37 38 provide forceful and timely limitation of the magnitude of the true slip speed. The model also provides an output signal proportional to rotor power angle, which can be used with benefit for other purposes. The novelty is enhanced by the fact that the input to the mathematical model can be derived from inexpensive and readily available transducers, measuring real power and reactive power flowing between the power system and the synchronous machine.

More particularly, the invention provides a method of damping rotor oscillations in synchronous machines comprising the steps of determining the real power input to the machine, determining the reactive power input to the machine, determining the relative power angle of the magnetic axis of the rotor of the machine from said power inputs, determining the slip speed from the time rate of change of said power angle and controlling field excitation of the machine in accordance with said slip speed.

The invention also provides a control system for damping rotor oscillations in synchronous machines, said system including means for measuring real power input to the machine, means for measuring reactive power input to the machine, compensating means for determining the relative power angle of the magnetic axis of the rotor of the machine and for determining the slip speed from the time rate of change of said power angle, and coupling means for coupling output of the compensating means to a field excitation circuit for the machine.

The invention will now be further described with reference to the accompanying drawings, in which: Figure 1 is a simplified line diagram of a power system including a large synchronous machine; Figure 2 illustrates a synchronous machine system incorporating the invention; 890914.&diskname&.0469f.ws.6

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'to., 1"~i 7 1 2 3 4 6 7 8 9 11 12 13 14 15 15 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 38 Figure 3 is a diagram useful in understanding the operation of the invention; Figure 4 is the preferred form of control circuitry of the invention; Figures 5 and 6 show graphically oscillations of a synchronous machine without slip stabilisation; Figures 7 and 8 show graphically oscillations of a synchronous machine damped in accordance with the system of the invention; and Figures 9 and 10 show more detailed circuit diagrams of the control circuitry.

Figure 1 shows a simplified single line diagram of a power system connecting a large synchronous machine source 2 to the machine 4 to be controlled. In practice, this large reference machine is an effective composite of the many synchronous machines connected to the complete power supply network. The principle purpose of the invention is to improve the damping of the electromechanical system generally speaking by forcing the field excitation of the synchronous machine 4 to produce torque components which act to reduce the magnitude of variation of the machine's rotor speed from the effective corresponding frequency of the power system voltages. The departure from synchronism, commonly known as "slip speed" or "slip frequency" is calculated from a compensating circuit 6 (see Figure 2) which, generally speaking, can be regarded as a mathematical model of the machine's relative rotor angle, also known as the "load angle", "power angle", or "torque angle".

Figure 2 diagramatically illustrates a system incorporating the compensating circuit 6 of the invention.

The diagram shows a three phase power supply 8 supplying power to the synchronous machine 4 to be controlled. The machine 4 is coupled by an output shaft 10 to a mechanical load 12. The machine 4 includes a field exciter circuit 14 which in turn is controlled by error signals from a summing 890514 &diskname&,0469f.ws.7 )r 8 1 2 3 4 6 7 8 9 11 12 13 400 14 15 16 17 18 19 21 *0 22 23 24 26 27 28 29 31 32 junction 16. The summing junction also receives a field current, a feedback signal on line 18 and the output from a primary controller 18 which includes set point inputs and feedback control signals from the motor 4 in the usual way.

In accordance with the invention, the summing junction 16 includes input from the compensating circuit 6. The compensating circuit 6 includes a real power transducer coupled to the power supply 8 for measuring the real power flow to the machine 4. The circuit includes a reactive power transducer 22 coupled to the supply 8 for measuring the reactive power flow to the machine 4. The compensating circuit 6 uses the measurements of the real and reactive power flow to the machine to calculate the relative power angle of the rotor magnetic axis from a mathematical model which is based upon the machine's circle diagram with appropriate compensation for source impedance. Slip speed is calculated from the time rate of change of power angle.

The magnitude of the slip speed is then adjusted in inversed proportion to the power angle, with appropriate limits, and then passed to the summing junction 16 to produce components of machine torque which act to reduce the magnitude of the machine slip speed.

Figure 3 illustrates the preferred embodiment of the compensating circuit 6 shown in block diagram of Figure 4. The circuit receives input from the real power transducer 20 which passes to the numerator input of a divider circuit 26. The denominator znput to the divider circuit 26 is derived from a summing junction 28 which sums a signal from the reactive power transducer 26 with output from a function generator circuit 30. The function generator circuit 30 produces a value equal to: 1 Xq Xe 38 890914,&diskname&.0469f.ws. 8 i -9- Where: Xq Quadrature axis Synchronous Reactance Xe Series reactance between the machine to be controlled and the measurement bus The output from the divider circuit 26 represents TAN d where d represents the load angle.

The load angle d is determined by arc tan circuit 32 which performs the following function, as can be appreciated from the circle diagram of Figure 3: d ARC TAN Pe Qe+'/(Xq+Xe) For a cylindrical rotor machine this function becomes: d ARC TAN Pe Qe+'/(Xs+Xe) a all scalar quantities are in per unit and Pe Machine Electrical Power Qe Machine Reactive Power (Positive for Exported Vars) Xs Synchronous reactance of a cylindrical rotor machine.

This forms the basic circuit, which is easily implemented to estimate rotor angle relative to the effective power angle of the supply system bus at which power and reactive power are measured.

In cases where the polarity of input power can reverse, the absolute value of the power ,agle as determined 910702,gcpsp.006,42379.sp,9 -i 1 10 8 9 ii S: 12 13 14 16 17 18 19 21 22 23 S 24 26 27 28 29 31 32 33 34 36 37 38 by an absolute valve circuit 24 coupled to the output of circuit 32 is used for control purposes to maintain correct polarity of the negative feedback damping loop. If such excursions are only transient, damping can be inhibited when the polarity of power angle reverses as an alternative to the use of an absolute valve.

Output from the circuit 24 is differentiated in a differentiating circuit 34 to yield the slip speed estimate.

This estimated slip speed is then used as the feedback quantity to the damping regulator D(s) in circuit 35. The frequency response of the damping regulator circuit 35 is designed to provide the necessary compensation to achieve an optimum closed loop frequency response of the system. The output from the damping regulator circuit 35 is modified by a gain adaption circuit 36. The output from circuit 24 is also modified by a limit circuit in circuit 37 which provides upper and lower bounds as well as any necessary dynamic compensation to provide the gain adaption signal to circuit 36. This gain adaption circuit 36 compensates for gain changes in the power/field current transfer function within the synchronous machine as the load angle changes.

Output from the compensating circuit 6 is then inputted to the summing junction 16, as mentioned pieviously so as to affect the field exciter circuit 14 of the machine 4.

The speed of the response of the damping control should be several times faster than the oscillations that are to be damped. This requirement would normally favour direct static excitation, but other forms of excitation systems may be adequate with appropriate dynamic compensation in the control system. This can be determined for each application.

For a synchronous generator an AVR (automatic voltage regulator) is the primary excitation control loop, the reference to which usually incorporates the power system 890914. &diskname&.0469f.ws. 11 12 13 14 16 18 19 21 23 S. 24 26 27 28 29 31 32 33 34 36 37 38 stabilisation signal. For a synchronous motor, field excitation is usually controlled to provide fixed field current, power factor control or reactive power control, depending on the design philosophy.

As illustrated in Figures 2 and 4 the preferred embodiment of the slip stabilisation control scheme incorporates a high performance field current regulator as an inner control loop. The set point of the field current regulator includes the field current reference provided by the primary control strategy, which could be the AVR for the synchronous generator or the power factor or reactive power control of the synchronous motor. The slip stabilising signal is also applied to the field current regulator summing junction 16 and functions to damp the machine's natural resonance, regardless of the form of the primary control loop.

In the damping control algorithm the argument is calculated from power and reactive power measurements and a are -h-qn two term approximation to the AAN function determined by the circuit 32 gives the estimated value of load angle. The time derivative of estimated angle provides a signal proportional to slip speed which is then applied, via a gain adaption circuit 36, to the excitation system.

Alternatively the stabilising controller may be connected in a number of different configurations other than the control scheme described in the preferred embodiment, including connection as an exclusive parallel controller to the AVR or synchronous motor excitation control strategy or connection to the summing input of the primary controller.

The circuit of Figure 4 can be implemented using readily available electronic building blocks and therefore does not require any specialised electronic design. For instance, the -A4ta-* function in circuit 32 has been i: r;

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ii; 'il 890914, &diskname&.0469f.ws ,1i i- 1 12 implemented using a two term approximation to the tan function. That is, the first two terms of the Taylor series representation to the tan function as follows: x 3 2x tan x x 3 for Ixl< 2 The approximation becomes: 0 10 0* x 3 tan x x 3 for Ixl<A 2 To obtain the arc tan function an operational amplifier 50 with the tan x approximation circuit 52 as the feedback element gives the arc tan equivalent as shown in Figure 9. The x 3 term in the tan x series is then simply calculated using two multipliers 54 and 56 as shown in the final circuit of Figure The Taylor series expansion for arc tan x becomes: x 3 x ARC TAN x x for Ix 1 3 7t 1 1 ifx 1 2 x 2x 3 ifx -1 Since the argument has a value less than one, the following approximation is made:

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3 ARC TANx x xfor Ix 1 3 910702,gcpspe.00 6 ,42379.sp,12 I i II I 13 qfL 4iiai therefore in the -aan circuit 32: a 1 b -1 3 7 8 9 11 12 13 14 1 15 S. 16 17 0** 18 19 21 22 23 24 26 27 *2 27 o* 28 The control algorithm does not rely on a linearised machine model and therefore works well for different machine operating points. The larger the machine angle the easier it is to control and therefore best performance is achieved at higher powers.

In the preferred embodiment, consistent performance is achieved throughout the operating range by using gain adaption to increase the controller gain as rotor angle decreases. Using this method consistent performance can be achieved with loaded machines down to approximately 0.25 pu load with decreasing performance down to the unloaded machine condition.

The model accuracy is enhanced or limited by the following phenomena: The accuracy of the model under transient conditions is very good and can be enhanced further if appropriate dynamic compensation is applied to this static model.

The effects of machine saturation are inherent in the model definition, hence errors due to saturation are minimized.

Small transient errors do arise due to internal damping torques of the machine which cannot be observed with the above function. Closer transient estimation can be achieved using appropriate compensation. However, these errors prove to be unimportant in the final result.

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Mi 14 11 12 13 14 15 16 17 18 19 21 22 9 o 23 24 26 27 28 29 31 32 33 34 36 37 38 Although this model effectively calculates power angle between the machine rotor and that of the voltage at the point of measurement, the model can be enhanced to move the apparent point of measurement further back into the power system.

The measurement of active and reactive power flows also provides flexibility in the choice of location in the power system at which the measurements are made.

Figures 5 to 8 illustrate recorded machine power oscillations taken under similar loading conditions with and without the compensating circuit of the invention. The recordings relate to the case where the synchronous machine 6 comprises a synchronous motor driving the motor-generator sets which power a five stand cold rolling mill.

Figures 5 and 6 show the first and last halves of coil of strip steel of a known control system which does not include the compersating circuit of the invention.

In Figures 5 and 6 the oscillatory behaviour is caused by transient powers drawn by the main mill drive machine 4 supplied by the generators coupled to the machine source 2. The input power to the synchronous motor has an underdamped oscillatory response to changes in shaft power.

In these tests, the cold mill rolls steel strip which has been coiled up for ease of handling. The rolling process reduces the gauge of the strip to produce strip at varying gauge and metalurgical qualities. The coil is threaded through the mill at slow speed. Once threaded the mill accelerates to rolling speed for the remainder of the coil.

Near the end of the coil the mill decelerates to allow the tail of the strip to pass through the mill safely. Figure shows the synchronous motor 4 response during and immediately after acceleration of the mill during which time most corrections are made by the gauge control system.

Figure 6 shows the transient response associated with the 890914&diskname&.0469f.ws. 14 15 1 mill deceleration. In this instance, the oscillations 2 result due to either the acceleration or deceleration of the 3 mill speed or from the action of automatic gauge controls of 4 the cold rolling mill with subsequent movements in the screw down adjusters. Subsequent power demands from the mill 6 drives reflect in the increase in load angle of the 7 synchronous machine and subsequent power overswing which 8 results in oscillatory behaviour due to the low damping of 9 the machine.

11 Figures 7 and 8 correspond to Figures 5 and 6 O w. 12 respectively but show the oscillatory behaviour with the 13 compensating circuit 6 for slip stabilisation in accordance 14 with the invention.

16 In all cases: 17 18 TRACE A Recording of the estimate of load 19 angle d, that is, the output of circuit 32.

21 Signal Scaling 8 volts n radians or S 22 4 23 45 degrees 24 Recorder Sensitivity 2 volts/ division.

26 a 27 TRACE B Recording of the synchronous motor 28 power Pe, that is, the signal from 29 the power transducer, circuit 31 Signal Scaling 8 volts 1 per unit power 32 33 1 per unit power rated machine power 34 Recorder Sensitivity 2 volts/ division.

36 37 TRACE C Recording of the synchronous 38 890914.gcpspe.001.0469f.ws.15 .I -1

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TRACE D machine reactive power Qe, that is, the signal from the reactive power transducer, circuit 22.

Signal Scaling 8 volts 1 per unit reactive power 1 per unit reactive power rated machine power Recorder Sensitivity 2 volts/ division.

Recording of the synchronous machine field current. This is the feedback quantity associated with the field regulator, circuit 14.

Signal Scaling 5 volts 1 per unit field current 1 per unit field current rated machine field current at rated load and rated power factor Recorder Sensitivity 2 volts/ division.

graphs of Figures 7 and 8 show a dramatic damping of the rotor of the machine.

21 22 23 24 26 S 27 28 Thus, the improvement in the In summary, the invention provides slip stabilisation for electrical synchronous machines and departs from current practices of inferring the value of machine slip speed from measurement of power, speed or frequency, or combinations thereof. The invention uses measurements of both real power and reactive power to calculate the relative power angle of the rotor magnetic i t j 'i 1 -li 890914,&diskname&,0469f.ws.16 1'- 17 1 axis from a mathematical model based on the machine's circle 2 diagram, with appropriate compensation for source impedance.

3 Slip speed is calculated from the time rate of change of 4 power angle. The magnitude of the slip speed signal is then adjusted in inverse proportion to the power angle, with 6 appropriate limits, and fed into the excitation control 7 system to produce components of machine torque which act to 8 reduce the magnitude of machine slip speed.

9 The point in the power system at which flow of real 11 and reactive power are measured can be chosen for best 12 effect to suit the application. The transducers used to 13 measure these quantities are commercially available from 14 many sources of supply.

*S S 16 The preferred embodiment calculates rotor power 17 angled from the arguments.

18 19 Pe for a cyclindrical rotor machine Qe+l/(Xs+Xe) 21 22 and Pe for a salient rotor machine 23 Qe+l/(Xq+Xe) 24 Other embodiments could calculate similar functions 26 of the form: 27 28 kl(Pe+k 2 where kl,k 2 and k3 can be constants or 29 variable quantities.

Qc+k3 31 32 The values of kl, k 2 and k3 are determined by the 33 specific variation of the preferred embodiment and as such 34 have no deterministic value. The constants kl, k 2 or k 3 may represent on alternative measurement quantity such as stator 36 current, stator volts or any other machine variable or a 37 38 890914.gcpspe.001.0469f.ws.17 9 11 12 13 14 16 17 18 19 21 S* 22 23 24 26 27 28

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18 constant the value of which is determined from the specific machine parameters.

Such functions would represent variations of the basic formulae. The k values can also be adjusted to move the apparent point of measurement to other locations in the power supply system.

The slip speed is calculated from the time derivative of the calculated rotor angle. In the preferred embodiment, the slip speed signal is connected to the excitation control via a gain adaption circuit which adjusts to the signal magnitude in inverse proportion to the calculated power angle. A minimum limit is imposed on the magnitude of the adapting signal. A two term polynomial has been used to execute the non-linear arctangent function.

Variations to the preferred embodiment could use different forms of gain adaption, or no gain adaptation at all. The sine or tangent of the power angle signal itself could be used as the adapting signal, or other means of approximating the power angle. The functions executed in separate sequential circuits shown in Figure 3 can be merged into a fewer number of circuits. The description and diagram serve to facilitate explanation and not to define the physical realisation of the functions.

The preferred embodiment describes an internal field current regulator subordinated to the external primary controller of the synchronous machine excitation system.

The stabilising signal is applied to the setpoint and feedback summing point of the field current regulator.

The principle covered by the invention is not limited to this arrangement. It is not necessary to use an internal field current regulator and the system can be made to work successfully by feeding the slip stabilisation 890914.gcpspe.001,0469f.ws,18 p-l" 19 00*O 0 0 0 0of* 00 so 00 signal to other control points within the excitation system, provided that appropriate dynamic compensation is provided to suit the application.

Appropriate dynamic lead/lag compensation can be used throughout the slip stabilisation and excitation system to improve the accuracy of calculation and compensate for various effective time constants in the measuring equipment, calculation circuits, excitation system, power supply system and within the machine itself.

The control circuit shown in Figure 4 of the invention may also be implemented in digital form. The only constraint is the circuit response time which determines the execution speed in the microprocessor design.

An analog interface would however be necessary to accommodate the power and reactive power transducer outputs (circuits 20 and 22) which are low level analog signals.

This interface would provide necessary signal conditioning including any filtering or amplification of the transducer outputs.

Many modifications will be apparent to those skilled in the art without departing from the spirit and scope of the invention.

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Claims (6)

1. A method of damping rotor oscillations in synchronous machines comprising the steps of determining the real power input to the machine, determining the reactive power input to the machine, determining the relative power angle of the magnetic axis of the rotor of the machine from said power inputs, determining the slip speed from the time rate of change of said power angle and controlling field excitation of the machine in accordance with said slip speed.

2. A method of damping rotor oscillations in a synchronous machine comprising the steps of generating a first signal derived from the real power input to the machine, generating a second signal derived from the reactive power input to the machine, determining the relative power angle d of the magnetic axis of the rotor of the machine from said first and second signals, determining the slip speed from the time rate of change of said power angle d and controlling field excitation of the machine in accordance with said slip speed.

3. A method as claimed in claim 2 wherein: the method includes the step of applying the first signal to the numerator of a divider, applying the second signal to one input of a summer applying a third signal derived from the inverse quadrature reactance of the machine to another input of the summer to provide a summed signal and applying the summed signal to the denominator of the divider to thereby obtain an output signal which is the tangent of the relative power angle d.

4. A method as claimed in claim 3 wherein where the third signal is derived by the following formula: 890914, gcpspe.001.0469f .ws, ;odd 21 1 Xq+Xe Where: Xq Quadrature axis Synchronous Reactance Xe Series reactance between said machine and the measurement bus A method as claimed in claim 4 wherein the relative power angle d is generated by operating on said output signal in accordance with the following formula: d ARC TAN Pe Qe /(Xs +Xe) all scalar quantities are in per unit and Pe Real power input to the machine 10 Qe Reactive power input to the machine, and Xs Synchronous reactance of the machine *o a

6. Apparatus for damping rotor oscillations in a synchronous machine which includes a primary control system for controlling the machine said control system including a field exciter and a field current feedback path, said apparatus including first signal generating means for generating a first signal derived from real power S input to the machine, second signal generating means for generating a second signal derived from the reactive power input to the machine, means for determining the relative power angle d of the magnetic axis of the rotor of the machine from said first and second signals, means for determining the time rate of change of said power angle d to generate third signals representative of the slip speed of the machine, and means to apply the third signals to said field exciter of the machine. L a r i 910702,gcppc.006,42379.spe,21 {/I

22- 7. Apparatus as claimed in claim 6 wherein said means to apply includes a summing circuit which has one input coupled in use to he primary control system, another input coupled in use to the feedback path and another input coupled in use to receive said third signals, and wherein the output of the summing circuit is coupled in use to the field exciter. 8. Apparatus as claimed in claim 6 or 7 wherein said means for determining the relative power angle d includes a function generator for generating a function signal equal to: 1 Xq+Xe Where: Xq Quadrature axis Synchronous Reactance Xe Series reactance between the machine to be controlled and the measurement bus *1 a divider the numerator input of which receives said first signal and the denominator input of which receives the sum of said function signal and said second signal, the output of the divider being the tangent of the relative power angle d. 9. Apparatus as claimed in claim 8 wherein the output of the divider is-coupled to an arc tan circuit which determines the relative power angle d as follows: Pe d ARC TAN Qe +Xe) all scalar quantities are in per unit and Pe Real power input to the machine Qe Reactive power input to the machine, and Xs Synchronous reactance of the machine T Of 910702,gcpspc.00642379.spe.22 23 Apparatus as claimed in claim 8 wherein said means for determining the time rate of change of said power angle d comprises a differentiator circuit coupled to receive OrC.. +tA output from the *AAN- circuit. 11. Apparatus as claimed in claim 10 including means for controlling the sign and limiting the size of the third signals. 12. A method of damping rotor oscillations in a synchronous machine substantially as hereinbefore described with reference to the accompanying drawings. 13. Apparatus for damping rotor oscillations in a synchronous machine substantially as hereinbefore described with reference to the accompanying drawings. 4 11 12 13 14 15 16 17 17 f 21 22 23 24 DATED this 27th day of September, 1989 BHP ENGINEERING PTY. LTD. By its Patent Attorneys DAVIES COLLISON S 28 S 29 31 32 33 34 36 37 38 I 890 92 6.gcpspe.O1.,0469f.ws 23 J