The present invention is useful in high-and medium voltage dive systems. The invention is particularly useful for synchronous machine drive systems using HV (High Voltage) converters and HV machines, such as cable wounded machines, and for HV synchronous machine drive systems in conjunctions with trans- mission systems.

PRIOR ART In a synchronous apparatus comprising a machine having a sta- tor machine part and a rotor machine part comprising a rotor field winding, excitation has to be provided in order to build up a magnetic flux. For power generation and in large drive systems electrically excited synchronous machines are used. In this case, excitation can be achieved by means of a dc voltage sup- plied to the rotor field winding via brushes and slip rings, mounted on the rotor shaft. However, in some applications, for example in delicate environments (dust, humidity, explosive, etc) slip rings are not accepted. Furthermore the brushes are

associated with periodic maintenance. This makes it attractive to supply excitation to the rotor machine part by other means. One way is via an exciter such as a rotating transformer. The syn- chronous exciter comprises a stator part and a rotor part com- prising a rectifier. The exciter can be of either synchronous type or asynchronous type.

The synchronous exciter is fed by a dc-voltage on the stator part. The rotor part comprises three phase windings. The three phase windings in the rotor part supplies a three-phase rectifier connected to the field winding of the machine. It is obvious that the shaft must rotate to induce anything in the exciter rotor winding. Therefore, the synchronous exciter is not suitable if operation at zero or low speed is desired.

The asynchronous exciter machine operates as an induction machine in plugging operation, i. e slip higher than 1. The stator windings are connected to a three phase voltage source and the rotor windings are connected to a rectifier that supplies the field winding. Since voltage is induced in the rotor, even at standstill, the asynchronous exciter machine is suitable also at zero or low speed. The three phase voltage source, feeding the exciter sta- tor, is normally a simple thyristor inverter. The thyristor inverter supplies a fixed frequency and variable voltage to the exciter.

The thyristor inverter is chosen because it is robust and low cost. Its disadvantage is the fixed frequency, large harmonic content and low control bandwidth.

A variable speed drive using a synchronous motor with a rotor field winding requires the field current to be controlled and in particular measured precisely, to obtain a high performance dy- namic and steady state control of motor torque, flux and power factor. A disadvantage of brushless excitation is that it does not allow for direct measurement of the field current. Thereby, de- tection and control of the field current becomes difficult. When brushless excitation is used, wireless current transducers has to

be mounted to the rotor shaft or the field current have to be re- constructed from the exciter stator voltages and currents. De- tection schemes using telemetry from rotor to stator exists, but with poor reliability. Thus, It is a desire to compute the field winding current from signals that are measurable on the stator side of the brushless excited motor. It I also desirable to obtain accurate information in steady state as well as during dynamic conditions.

The presence of a thyristor inverter feeding the exciter stator exciter part, and a diode rectifier between the exciter rotor part and the machine field winding makes computation of the field current rather complicated. In essence, it is a matter of solving the dynamic equations for the electrical circuit formed by the ex- citer and the machine and their non-linear power converters. To solve this problem a model for treatment of the rectifier circuit has been developed.

A model for calculating the field current in a synchronous appa- ratus, denoted a current model, has been developed. In the cur- rent model the field current is calculated based on exciter cur- rent measurement. The exciter rotor phase currents are esti- mated and the field current is calculated as the sum of the rotor currents. First, the rotor current is calculated and transformed into rotor coordinates. Second, the field current has to be esti- mated from the rotor current. A disadvantage with the current model is that there are still transient model deviations in the re- constructed currents. With the current method, the field current estimate is based on a maximum over time of the rectified rotor currents and therefore the ripple will cause a too high value of the field current estimate. With the current method the ripple in the phase currents cannot be filtered since the full bandwidth is needed for detection of short circuit. At a field current corre- sponding to full torque, the exciter will go into saturation at low speeds. Saturation cause large error in rotor current reconstruc- tion.

Thus, in the current model the magnetic flux in the exciter stator can be estimated with good accuracy. However, the relation be- tween the flux and currents is affected by saturation and iron losses. Since the effects of saturation and iron losses are of the same magnitude as the rotor current and effect the rotor current estimate directly, large errors occur.

During steady state condition free-wheeling, i. e. short circuit, in the field winding occurs due to the thyristor inverter. Free- wheeling may also occur when the field current is forced to- wards zero, for example when the speed are reduced. During the free-wheeling it is not possible to estimate the field current, since there exist no relation between field current and the rotor currents during the free-wheeling. A problem with the current model is that the field current can't be controlled during the free- wheeling since the field current can't be estimated. The problem concerning short circuit is always present in the current model.

OBJECTS AND SUMMARY OF THE INVENTION The object of the present invention is to provide a method for estimating the field current in a brushless excited synchronous apparatus that solves the above-mentioned problems with the prior art.

This object is achieved by means of a method characterized by: receiving measured values of the current and voltage of the ex- citer stator part, calculating the voltages of the exciter rotor part based on the values of the current and voltage of the exciter stator part by means of a mathematical model of the exciter, calculating the voltage of the field winding based on said calcu- lated voltages of the exciter rotor part by means of a mathemati- cal model of the rectifier, and calculating the field current of the field winding based on said calculated voltage of the field wind- ing by means of a mathematical model of the field winding. This method requires that the rotor position of the machine is known.

According to the invention the field current is estimated based on the field voltage. The rotor exciter voltages are estimated and the field voltage is calculated based on the exciter rotor voltages. By estimating the field voltage, instead of the field cur- rent, the effects of saturation and iron losses are reduces. The errors in flux to current relation will only cause estimation errors in the resistive and inductive voltage drops. Since the voltage drops should be magnitudes smaller than the main voltage, the total estimation error decreases significantly compare to the cur- rent model.

Also, the case when the rectifier is free-wheeling is simplified considerably since no special treatment is required. Since the field current is estimated from the field voltage, parameter sen- sitivity is transferred from the exciter to the machine. Also noise in the estimated field voltage will be effectively filtered by the field current estimations.

Further advantages with the method according to the invention is that it is provides a faster and more precise estimation of the field current than known methods, in turn giving a better control of machine torques, flux and power factor. This allows lower power rating for the same dynamic and steady state perform- ance.

The method according to this embodiment of the invention makes it possible to estimate the field current during steady state conditions.

According to a preferred embodiment of the invention, the field current is calculated with regard to the flux (ad) in the machine.

This embodiment makes it possible to estimate the field current not only during a steady state conditions, but also during a tran- sient condition.

According to a further preferred embodiment of the invention, said mathematical model of the exciter comprises a plurality of differential equations describing the exciter and that the volt- ages of the exciter rotor part is calculating by solving said dif- ferential equations.

According to a further preferred embodiment of the invention, said rectifier is a diode rectifier, and the voltage of the field winding is calculated as the difference between the maximum and minimum voltage of the exciter rotor part. The field voltage is calculated as the difference between the maximum and mini- mum phase voltage of the exciter rotor part.

A further object of the invention is to provide a field current es- timator for estimating the field current in a brushless excited synchronous apparatus. This object is achieved by a field cur- rent estimator as defined in claim 7.

According to an aspect of the invention, the object is achieved by a computer program directly loadable into the internal mem- ory of the computer or a processor, comprising software code portions for performing the steps of the method according to the invention, when said program is run on a computer. The com- puter program product is provided either on a computer readable medium or through a network, such as the Internet.

According to another aspect of the invention, the object is achieved by a computer readable medium having a program re- corded thereon, when the program is to make a computer per- form the steps of the method according to the invention, and said program is run on the computer.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will now be explained more closely by the descrip- tion of different embodiments of the invention and with reference to the appended figures.

Fig. 1 shows an example of a synchronous apparatus compris- ing an exciter.

Fig. 2 shows an exciter per-phase equivalent circuit as seen from the rotor.

Fig. 3 shows a steady state ideal supply excitation system equivalent circuit.

Fig. 4 shows a machine model for stator current reconstruction.

Fig. 5 shows numerical construction of exciter currents at stand still and zero torque.

Fig. 6 shows example of curve shapes when the exciter oper- ates at half rated speed and half rated torque.

Fig. 7 shows a reconstruction of rotor winding phase current and measured rotor phase current at field current corre- sponding to zero torque. No compensation for iron losses.

Fig. 8 shows a reconstruction of rotor winding phase current and measured rotor phase current at field current corre- sponding to nominal torque. No compensation for iron losses.

Fig. 9 shows a reconstruction of rotor winding phase current and measured rotor phase current at field current corre- sponding to zero torque. Compensation for iron losses.

Fig. 10 shows a reconstruction of rotor winding phase current and measured rotor phase current at field current corre- sponding to nominal torque. Compensation for iron losses.

Fig. 11 shows an equivalent circuit for field current estimation.

Fig. 12 shows reconstructed rotor terminal voltage and meas- ured voltage at zero speed and no load.

Fig. 13 shows reconstructed rotor terminal voltage and meas- ured voltage at half speed and half rated torque.

Fig. 14 shows a flow diagram of a method for estimating the field current according to an embodiment of the inven- tion.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION Figure 1 shows a synchronous apparatus comprising an asyn- chronous exciter 1 and a machine 2. The exciter 1 is adapted for brushless excitation of the machine 2. A thyristor converter 3 supplies a fixed frequency, for example 50 Hz, and a three phase voltage, for example 400V, to the exciter 1. The exciter comprises a stator part 4 and a rotor part 5 having three rotor windings 6 and a diode rectifier 8. The exciter rotor part 5 is electrified from the exciter stator part 4 by means of induction.

The machine 2 comprises a rotor part 10 and a stator part 12 having three phase windings 13. The machine rotor part 10 com- prises a field winding 14. The machine stator part 12 is con- nected to a three phase voltage source. The exciter rotor wind- ings 6 are connected to the diode rectifier 8 that supplies the field winding 14.

In the following, a steady-state model of the excitation system is derived. The model is used to examine the differences between stiff sinusoidal supply and thyristor bridge supply. A per unit- system is assumed.

When the exciter is feed from a well defined voltage source, it is possible to derive curve shapes analytically in steady-state. If the source is a strong grid with sinusoidal voltages, the analysis is simple can can be can be approached with linear electric cir- cuit theory.

When the exciter is supplied by an ideal voltage source and op- erates in steady-state, an equivalent circuit can be derived.

Since the rotor winding of an induction machine is normally short circuited or connected to a linear passive load, the equiva- lent circuit often is derived as seen from the stator. However, in the following it is more convenient to derive the equivalent cir- cuit as seen from the rotor. According to Lenz's law, the induced

voltage in a winding is proportional to the flux density and fre- quency.

Ef oc Bw Since the stator frequency is t91 and the rotor frequency is W2 and both sides experience the same flux level, the relation between stator and rotor EMF is known as <BR> <BR> <BR> <BR> <BR> <BR> Er #2<BR> <BR> <BR> = = s, (2)<BR> Es = #1 where s is the exciter slip. The turn ration is one to one since a per unit-system is assumed.

By applying Kirchhoff's voltage law to the stator circuit, the rotor EMF can be calculated from the stator voltage and current as Er = sEs=s(Vs-RsIs-jX#sIs)=sVs-sRsIs-jsX#sIs.

The magnetising current is Es Er Im = jXm = jsXm. (4) The rotor phase voltage can be calculated from the rotor EMF, assuming rotor current reference direrction into the machine, as Vr = Er + jw2L#rIr + RrIr = Er + (jsw1L#r + Rr)Ir (5) or Vr = Er + (jsX#r + Rr)Ir. (6) Finally, applying Kirchhoff's current law, Is+Ir=Im, (7) the above equations can be translated into an equivalent circuit as in Figure 2. Figure 2 shows an exciter machine per-phase equivalent circuit as seen from the rotor.

The circuit in Figure 2 can be translated into a Thevenin- equivalent by calculating the open circuit rotor voltage and the reactance as seen from the rotor. The open circuit voltage be- comes Choosing Bth to be real the expression above simplifies to The equivalent impedance is After some calculation and separation in resistance and reac- tance yields The whole exciter, including the field winding of the synchronous machine, can then be drawn as shown in Figure 3. Figure 3 shows a steady state ideal supply excitation system equivalent circuit.

Since the inductance in the field winding is very high compared to the exciter leakage inductance, the field winding can initially be treated as a current source. If the resistive part Rth is ne- glected the analysis is simple and straightforward. However, if the resistive part is considered the analysis becomes compli- cated. Therefore, in the following, the resistive voltage drop is taken into account but its effect on current commutation is ne-

glected. The commutation angle is assumed to be less than 7r/3, since this is the case for the experimental exciter. The mean . value of the dc-voltage can be calculated as The mean voltage drop across the commutation inductance is A simple expression for the resistive voltage drop can be de- rived if the resistance Rth is moved from the ac-side of the recti- fier to the dc-side. The voltage drop then becomes #Vd,2=2RthId.

The commutation duration is also affected by the resistive part.

The diode voltage drop is calculated as #Vd,3=2Vf where tuf ils the diode forward voltage drop.

The dc-sided voltage becomes I"d d=Vd0-#Vd,1-#Vd,2-#Vd,3 or The direct voltage can in steady state be calculated as Vd=IdRff. (19) From equations (13-19), the direct current as a function of input voltage in steady state can be derived as

As an alternative to the analysis above simulation might be used.

Figure 4 shows a machine model for stator current reconstruc- tion. No proper analysis of stator current and power factor is carried out in this thesis. However, if the stator and rotor resis- tance are neglected, the rotor current can be reconstructed nu- merically. By neglecting the stator resistance and leakage reac- tance, the simple machine model according to Figure 4 can be used. The magnetizing current can then be calculated as Figure 5 shows a numerical construction of exciter currents at standstill and zero torque.

Then, the stator current becomes is(t)=im(t)-ir (t) (22) Finally, the RMS value of the stator current and power factor can be calculated. As an alternative, simulation can be used.

The thyristor bridge introduce three main difficulties to the analysis. First, the introduction of harmonics. The analysis in the previous section was based on a fixed magnitude and frequency supply. If the harmonics cannot be neglected the concept of slip is of no use. Since the harmonics influence the commutation of the rectifier circuit, the analysis cannot be done for each har- monic separately.

Second, the two commutating circuits influence each other.

Since the rotor rotates asynchronously to the stator supply there is no periodicity in the commutation pattern, not even in steady- state. It is therefore hard to define the stationary properties for

the circuit. If at all possible, statistical methods should be con- sidered.

Third, the field winding is short circuited by the rectifier for parts of the time even in normal steady state operation, as seen in Figure 6. Figure 6 shows example curve shapes when exciter is operating at half rated speed and half rated torque. The short circuits are clearly visible in the rotor line-to-line voltage. Top graph: stator current (solid) and rotor current (dashed). Bottom graph: Stator line-to line voltage (solid) and rotor line-to-line voltage (dashed).

When a thyristor in the converter is turned off, the field current will be forced to go through the magnetizing inductance. Since the magnetizing inductance is many times larger then the leak- age inductance, any commutation will nearly be stopped, or "suspended". As the voltage drops below zero due to resistive losses, the field winding is short circuited through the diodes in the rectifier. During the short-circuit, it is impossible to observe the field current from the exciter stator.

These three difficulties make the analytical approach trouble- some. Simulation of the circuit is possible but does not fit into the framework, since a stiff voltage source is required. The ap- proach in this thesis is experimental verification, since simula- tion of the two commutating circuits together is time-consuming and a platform for experimental implementation was readily available. Setting up the rules describing the combination of the two commutating circuits is a time consuming task.

The stator of the exciter machine was connected to the supply grid via an auto transformer. The rotor was rotated by a speed controlled induction machine on the same shaft. The synchro- nous machine was at standstill with the stator circuit open. The stator voltage, stator current, field voltage, field current, active

and reactive power was measured. From the measured quanti- ties the Thevenin-equivalent was calculated according to (9), (11) and (12). The direct current was calculated according to (20). Also the individual voltage drops was calculated assuming a diode forward voltage drop of 1 Volt or 0.0215 p. u. The rela- tive error in both calculated dc-voltage and dc-current was cal- culated according to From the measurements the mean value of the field current is found to be approximately half the RMS value of the stator cur- rent. The estimation error in both dc-current and dc-voltage is approximately one percent except for very small stator voltages.

The same setup is used as for stiff sinusoidal supply except that the auto transformer is replaced by a thyristor converter. The <BR> <BR> <BR> converter is controlled by a current signal, In, which is in the fol- lowing normalized where zero corresponds to no output voltage and one corresponds to full output voltage. The same measure- ments, as well as calculations, were done as for stiff voltage supply. If the equations derived for the sinusoidal case are ap- plied large deviation occur the estimation errors for both current and voltage are above 50% even for moderately high stator volt- ages. The expected field current show large deviations from the ideal case with respect to stator voltage.

The experimental results for stiff sinusoidal supply is in good agreement with the model. There are some large deviations for very low voltage levels. This is probably due to the crude esti- mation of the diode forward voltage drop. The power factor and stator currents have the expected properties. The steady state

model described can with good accuracy be used for estimation of field voltage and field current when stiff sinusoidal voltage supply is used.

When the exciter is supplied by a thyristor converter, slow varia- tions in the field current appears even for a constant control an- gle. This is expected to cause problems not only in estimation but also in the field current control. The results for thyristor con- verter supply show little resemblance to the ideal model. This is believed to be the result of the large harmonic content. Also the short circuit condition is not included in the model. The steady state model is not well suited for estimation of the field current when thyristor supply is used. The stator current magnitude is approximately three times higher then the rotor current magni- tude. This implies a great demand on the quality of magnetizing current and iron losses. Steady-state evaluation of the power factor indicates errors in the estimation of these currents. For a real exciter, the magnetizing current will be much smaller com- pared to the rotor current when operating at full speed, since the number of poles is greater.

In the following the current model will be described. In a stator reference frame, the following complex relation is valid between the stator flux linkage and machine current Since the stator flux is not directly known it has to be estimated.

One possible way is to use the voltage model for estimation of the flux. It is known that Simulating (25) directly results in an open integration and can- not be used. Instead the integration is replaced by a low pass filter. The flux estimate then becomes

where P is the differentiation operator. The cut-off frequency wo has to be chosen so the phase is close to-90 degrees at the fundamental frequency and that low frequency noise is sup- pressed sufficiently.

Now, the rotor current space vector can be calculated from (25) as The rotor current then has to be transformed from stator refer- ence frame into rotor reference frame, irr = irse-j# (29) where # is the electrical rotor position.

The two phase complex representation of the rotor current has to be transformed into three phase representation The rectified rotor current is This is however not equal to the field current since the field winding will be short circuited by the rectifier for a part of the fundamental period, even in normal operation. When the field winding is short circuited, a short circuit current will flow from the negative rail to the positive rail. The sum of this short circuit

current and the rectified exciter rotor current will be the total field current.

In steady-state, i. e the synchronous machine d-axis current is constant, the maximum decrease is set from the field winding time constant. When a short circuit is detected, the field current is estimated by letting it decrease as it would, if the synchro- nous machine d-axis current was constant. The field current can however be forced to decrease faster if the synchronous ma- chine stator current in the d-axis is increased.

The principle chosen in this thesis is to limit the rate of field cur- rent decrease. The decrease is however not limited to the extent set from the field winding time constant since short circuit is not expected to extend over a time longer than one sixth of a elec- trical period in the rotor and a faster decrease let spikes caused by noise decay faster. The limit of decrease simply becomes a computational light way to calculate the maximum. The estimate of the field current then becomes iff[n]=max (irect[n],K#iff[n-1]) where K < 1 iS a decay factor.

The current model above depends on a good relation between flux and stator and rotor current. If the iron losses are low and the exciter operates at a low magnetic utilization the linear rela- tion (25) holds. If the machine operates at a high magnetic utili- zation, saturation has to be taken into account.

Normally, exciter machines are designed to operate at low mag- netic utilization and therefore the exciter will normally not run saturated. However, the machine used for experimental verifica- tion becomes saturated even at steady state when the synchro- nous machine operates at nominal torque.

The iron losses have a non linear dependency of frequency.

Since the electric frequency in the rotor varies with speed the equivalent magnetizing resistance is expected to vary with rota- tional speed. It is also likely that the harmonics injected into the stator by the thyristor converter will produce iron losses which are not possible to reconstruct by an equivalent resistance, Iron losses is here compensated for by introducing a compensated stator current If the rotor position is not known, it is impossible to use (29) to reconstruct the rotor currents. If the exciter can be looked upon as a strong grid the effects of commutations can however be neglected. If the commutations are neglected, the current can be assumed to flow only in two phases with opposite direction. The rotor currents can in this case be written The complex rotor current is Substituting (36) into (37) yields Since the magnitude of the complex rotor current is the same in both stator and rotor reference frame, the field current can be calculated as The field current is then calculated in the same way as when the position is known.

The following aspects of the current model performance are evaluated be experiments: The reconstruction of the rotor cur- rents with the stator of the synchronous machine disconnected with and without compensation for iron losses and the recon- struction of the field current with the stator of the synchronous machine disconnected with and without compensation for iron losses.

The rotor current reconstruction is verified at field currents cor- responding to no torque and nominal torque. The reconstruction is performed with and without iron loss compensation. Figure 7 shows reconstruction of rotor winding phase current (solid) and measured rotor phase current (dashed) at field current corre- sponding to zero torque. No compensation for iron losses. Fig- ure 7 shows reconstruction of rotor winding phase current (solid) and measured rotor phase current (dashed) at field current cor- responding to nominal torque. No compensation for iron losses.

From Figure 7 and Figure 8 it is clear that a great improvement is gained when iron toss compensation is used. However, there are still large high frequency ripple in the reconstructed cur- rents. With the current method, the field current estimate is based on a maximum over time of the rectified rotor currents and therefore the ripple will cause a too high value of the field current estimate. At field current corresponding to full torque the exciter will go into saturation at low speeds. The remaining error is belied to be caused by saturation. Figure 9 shows reconstruc- tion of rotor winding phase current (solid) and measured rotor phase current (dashed) at field current corresponding to zero torque. Iron losses are compensation for. Figure 10 shows re- construction of rotor winding phase current (solid) and measured rotor phase current (dashed) at field current corresponding to nominal torque. Iron losses are compensation for. Saturation cause large error in rotor current reconstruction as seen in Fig- ure 10.

Since the field current estimation is based on a maximum over time of the reconstructed phase currents the current model is very sensitive to exciter machine parameters. With the current method the ripple in the phase currents cannot be filtered since the full bandwidth is needed for detection of short circuit. Satu- ration cause large errors in the experimental setup. The stator flux is believed to be well estimated. The error in rotor current estimation is mainly due to the flux to current relation (25). The flux to current relation is considerably affected by saturation and iron losses. Using compensation for iron losses and fine tuning of the machine parameters, the error in field current estimation is approximately 10%. The problems concerning short circuit is always present in the current model.

In the current model the magnetic flux in the exciter stator can be estimated with good accuracy. However, the relation between the flux and currents is affected by saturation and iron losses.

Since the effects of saturation and iron losses are of the same magnitude as the rotor current and effect the rotor current esti- mate directly, large errors occur. One way to avoid this is to es- timate the field voltage instead of the field current. The errors in flux to current relation will then only cause estimation errors in the resistive and inductive voltage drops. Since the voltage drops should be magnitudes smaller than the main voltage, the total estimation error should decrease significantly.

Also, the case when the rectifier is short circuited is simplified considerably since no special treatment is required. Since the field current has to be estimated from the field voltage parame- ter sensitivity is transferred from the exciter machine to the main machine. Also noise in the estimated field voltage will be effec- tively filtered by the field current estimator.

The complex rotor voltage in stator reference frame is given by

The rotor flux is given by Substitution of the rotor current (28) into (41) yields If the total leakage inductance is introduced as the rotor flux becomes Substitution of (44) and (28) into (40) yields In n the above expression, the terms containing stator vottage and flux should be dominant and therefore the voltage estimate should be influenced by saturation and iron losses to a notably lesser extent compared with the current model.

If the estimation of the rotor phase voltages is correct the posi- tive conducting phase is the phase with maximum phase volt- age. Likewise the negative conducting phase is the phase with minimum phase voltage.

Vra, Vrb, Vrc is the three phase voltage of the exciter rotor part.

The third voltage should be somewhere in between the two con- ducting voltages or at the same voltage as one of the other dur- ing commutation. Since the dc voltage is calculated as the dif- ference between a maximum and a minimum, estimation errors and noise is expected to raise the estimated voltage above the real value. Also, during short circuit, the dc-link is short circuited and therefore all phases are at zero potential. It is clear that during this condition, the voltage model is most sensitive for es- timation errors in the three phase voltages.

Due to the diode voltage drop, the field voltage is calculated as vff=vpn-2Vf. (47) By choosing the voltage model, sensitivity to exciter parameters is reduced at the expense of increases sensitivity to main ma- chine parameters.

Figure 11 shows an equivalent circuit for field current estima- tion. Any damper-windings are neglected. Using the synchro- nous machine equivalent circuit in Figure 11, the field winding flux linkage can be expressed by The field winding flux linkage is the sum of the field winding leakage flux 21) and the air gap flux'Z/) ad, #ff=#f#+#ad (49) The field winding leakage flux is the product of field current and field winding leakage reactance.

#f#=Xf##iff (50)

Replacing all time derivatives by the operator p and solving for the field current yields <BR> <BR> <BR> <BR> <BR> <BR> <BR> 1 vff 1 p#ad<BR> f= -<BR> Xf# p+Rff/Xf# Xf# p+Rff/Xf# (51) Since the air gap flux and field voltage is not known, they are replaced by the estimate to produce a field current estimate, <BR> <BR> <BR> <BR> <BR> <BR> <BR> 1 ûff 1 p#ad<BR> <BR> <BR> <BR> 'Iff =- The air gap flux estimate must be provided by the main flux con- trol.

Two important factors influence the quality of the estimated field voltage. First the quality of the rotor voltage estimation from sta- tor quantities and second, the quality of field voltage estimation from rotor voltage.

The rotor terminal voltages are reconstructed by calculation of the rotor phase voltages according to (45) and transforming these into the rotor reference frame. The line-to-line voltages are calculated and compared to the measured values. The error is approximately constant at 10%. Figure 12 shows recon- structed rotor terminal voltage (solid) and measured voltage (dashed) at zero speed and no load. Figure 13 shows recon- structed rotor terminal voltage (solid) and measured voltage (dashed) at half rated speed and half rated torque. The instan- taneous rotor voltage in Figure 12 and Figure 13 show a good agreement between reconstructed rotor voltage and measured rotor voltage.

Figure 14 is a flow chart illustration of the method and the com- puter program product according to the present invention. It will

be understood that each block of the flow chart can be imple- mented by computer program instructions. The position of the rotor is a necessary input parameter to the method according to the invention. Measured values of the current (is) and voltage (uS) of the exciter stator part 4 is received. The voltages (Vra, vrb, Vrc) of the exciter rotor part 5 is calculated based on the values of the current (is) and voltage (Us) of the exciter stator part 4 by means of a mathematical model of the exciter, box 10.

The mathematical model used for calculating the exciter rotor voltages (Vra, Vrb, Vrac) is base on the exciter equivalent circuit shown in figure 2, and the previously discussed mathematical formulas (26), (28), (30) - (32).

The voltage (Vff) of the field winding 14 is calculated based on the calculated voltages (vra, vrb, vrc) of the exciter rotor part 5 by means of a mathematical model of the rectifier. The mathemati- cal model of the rectifier is the previously discussed mathemati- cal formula (46). Finally, the field current (iff) of the field winding 9 is calculated based on the calculated voltage (Vff) of the field winding by means of a mathematical model of the field winding.

The mathematical model used for calculating field current (iff) is base on the exciter equivalent circuit shown in figure 4.

The voltage model is sensitive to model parameters since the calculation of field voltage is based on two extreme functions, a maximum and a minimum. The field current estimator based on the voltage model is found to have about the same steady-state performance as the estimator based on the current model. How- ever, the voltage model is found to be more stable and have a higher bandwidth. Since the properties of the main machine used for experimental verification are well known compared to the properties of the exciter machine, the voltage model is fa- vorable over the current model. With the voltage model, the field current becomes possible to observe even during short circuit.

The voltage model also takes actions from the stator of the main machine into account.

The present invention is not limited to the embodiments dis- closed but may be varied and modified within the scope of the following claims. estimated stator flux linkage, complex w angular frequency owl electrical angular frequency, stator w2 electrical angular frequency, rotor wr rotor angular frequency rotor flux linkage, complex stator flux linkage, complex # electrical rotor angular position flux density Ef induced voltage in a winding Er rotor EMF Eg stator EMF Eth exciter thevenin equivalent voltage source Id rectified mean exciter voltage Ir rotor current, RMS ir rotor current, rotor current, complex Is stator current, is stator current, complex Iff field current, mean value iff field current, local value irect rectified sum of three-phase currents iuvw exciter rotor phase currents K field winding digital decay constant la total leakage inductance Lm magnetising inductance Lr rotor inductance ts stator inductance Lr rotor leakage inductance P active power, mean value p time derivative operator PF power factor Q reactive power, mean value Pm magnetising resistance Rr rotor resistance Pus stator resistance Rff field winding resistance Rth exciter Thevenin equivalent resistance S apparent power, mean s slip t time Ur rotor voltage, complex us stator voltage, complex Vd rectified mean exciter voltage Vf forward diode voltage drop vn negative rail potential, neglecting diod voltage drop vp positiv rail potential, neglecting diod voltage drop Vr rotor terminal voltage, RMS Vs stator terminal voltage, RMS Vff field voltage, mean value Vf f field voltage, local value vpn dc-link voltage, neglecting diod voltage drop Xm magnetising inductance Xr rotor reactance Xs stator reactance X#r rotor leakage reactance X#s stator leakage reactance Xad d-axis armature reactance X fe field winding leakage reactance Xth exciter Thevenin equivalent reactance