Method for controlling a multiphase separately excited synchronous generator in a wind turbine
11585320 · 2023-02-21
Assignee
Inventors
- Roberto Rosso (Aurich, DE)
- Jair Cassoli (Aurich, DE)
- Sönke Engelken (Bremen, DE)
- Amgad Eldeib (Aurich, DE)
Cpc classification
H02P25/22
ELECTRICITY
F05B2270/327
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F03D7/0272
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Y02E10/72
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
International classification
F03D7/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
A method for controlling a multiphase separately excited synchronous generator in a wind turbine is provided. The generator has a stator and an armature having an excitation input, connected to an excitation controller, for inputting an excitation current or an excitation voltage. The stator has a stator output, connected to a rectifier, for delivering stator currents. The rectifier is controllable to control the stator currents by detecting a speed of the armature or rotor, determining a setpoint power to be delivered by the generator or the turbine based on the speed, determining an excitation current or voltage based on the detected speed and determined setpoint power, inputting the excitation current or voltage by excitation controller at the excitation input, determining the stator currents as setpoint stator currents based on the speed and the setpoint power, and controlling the rectifier to set the stator currents to the setpoint stator currents.
Claims
1. A method for controlling a multiphase separately excited synchronous generator in a wind turbine, comprising: detecting a speed of an armature or aerodynamic rotor of the wind turbine, wherein: the synchronous generator includes a stator and the armature, and the armature has an excitation input for receiving at least one electrical quantity, an excitation controller is connected to the excitation input for inputting the at least one electrical quantity, the stator has a stator output for delivering stator currents, a rectifier is connected to the stator output for rectifying the stator currents and for providing the stator currents to a direct current (DC) link connected to the rectifier, and the rectifier is controllable in order to control the stator currents; determining a setpoint power to be delivered by the synchronous generator based on the speed and a detected power output of the synchronous generator or the wind turbine by at least: determining an intermediate power based on the speed; determining a control error based on comparing the intermediate power with the detected power output; providing the control error to a proportional-integral (PI) controller; and determining the setpoint power by the PI controller; determining the at least one electrical quantity based on the speed and the setpoint power; inputting, by the excitation controller, the at least one electrical quantity at the excitation input; determining setpoint stator currents based on the speed and the setpoint power, wherein the setpoint stator currents are setpoint values for the stator currents; controlling the rectifier to set the stator currents to be delivered at the stator output to the setpoint stator currents; estimating parameters of the synchronous generator, wherein the parameters include at least one of: magnetization inductances, a stator resistance, or an excitation resistance; and determining, by an adaptive controller, the at least one electrical quantity or the setpoint stator currents, wherein the adaptive controller determines the at least one electrical quantity or the setpoint stator currents based on the estimated parameters.
2. The method as claimed in claim 1, comprising: determining, by the adaptive controller, the at least one electrical quantity or the stator currents based on a model of the synchronous generator; and adapting the model or relationships derived from the model based on the estimated parameters.
3. The method as claimed in claim 1, wherein the wind turbine is a gearless wind turbine, the synchronous generator is a ring generator, and the stator has at least two three-phase systems.
4. The method as claimed in claim 1, comprising: operating at least one inductance of the synchronous generator in a range of saturation to cause at least one parameter to change; and detecting the at least one parameter.
5. The method as claimed in claim 1, comprising: estimating the parameters of the synchronous generator based on: at least one stator voltage of one or more three-phase stator systems, or at least one stator current of a three-phase stator system or at least one of a plurality of three-phase stator systems.
6. The method as claimed in claim 1, comprising: estimating d/q components of the magnetization inductance of the synchronous generator.
7. The method as claimed in claim 1, comprising: determining, by the adaptive controller, the setpoint stator currents in d/q coordinates; and transforming the setpoint stator currents into a three-phase representation with one current value per phase to control the rectifier to set the stator currents to be delivered to the setpoint stator currents.
8. The method as claimed in claim 1, wherein the DC link is connected to an inverter and the inverter converts energy of the DC link into a three-phase current for supply to an electrical supply system.
9. The method as claimed in claim 1, comprising: controlling the adaptive controller such that an efficiency of the synchronous generator is maximized.
10. The method as claimed in claim 1, comprising: estimating at least one magnetization inductance using an inductance characteristic curve for the at least one magnetization inductance, wherein the inductance characteristic curve specifies a relationship between values of the at least one magnetization inductance and a magnetization current; and incrementally updating the inductance characteristic curve.
11. The method as claimed in claim 1, comprising: determining one of the setpoint stator currents based on a respective setpoint stator current characteristic curve and the setpoint power to be delivered, wherein the respective setpoint stator current characteristic curve specifies a relationship between the setpoint power to be delivered and the one of the setpoint stator currents.
12. The method as claimed in claim 11, wherein the respective setpoint stator current characteristic curve is changed based on at least one quantity from a list including: the estimated magnetization inductances; the estimated stator resistance; and the estimated excitation resistance, and wherein changing the respective setpoint stator current characteristic curve is performed less frequently than the one of the setpoint stator currents is determined based on the respective setpoint stator current characteristic curve.
13. The method as claimed in claim 1, comprising: determining the setpoint stator currents online based on the setpoint power and at least one quantity from a list including: the estimated magnetization inductances; the estimated stator resistance; and the estimated excitation resistance.
14. A wind turbine, comprising: a multiphase separately excited synchronous generator; an aerodynamic rotor; a stator having a stator output configured to deliver stator currents; a rectifier, connected to the stator output, configured to rectify the stator currents and provide the stator currents to a direct current (DC) link connected to the rectifier, the rectifier being controllable to control the stator currents; an armature having an excitation input configured to receive at least one electrical quantity; an excitation controller connected to the excitation input; and a controller, including a proportional-integral (PI) controller, configured to: detect a speed of the armature or the aerodynamic rotor; determine a setpoint power to be delivered by the synchronous generator based on the speed and a detected power output of the synchronous generator or the wind turbine by at least: determining an intermediate power based on the speed; determining a control error based on comparing the intermediate power with the detected power output; providing the control error to the PI controller; and determining the setpoint power by the PI controller; determine the at least one electrical quantity based on the speed and the setpoint power, wherein the excitation controller is configured to cause the at least one electrical quantity to be provided at the excitation input; determine setpoint stator currents based on the speed and the setpoint power, wherein the setpoint stator currents are setpoint values for the stator currents; control the rectifier to set the stator currents to be delivered at the stator output to the setpoint stator currents, wherein the controller is configured as an adaptive controller for determining the at least one electrical quantity and the setpoint stator currents, and wherein the at least one electrical quantity or the stator currents are control variables for the controller; and estimate parameters of the synchronous generator, wherein the parameters include at least one of: magnetization inductances, a stator resistance, or an excitation resistance.
15. The method as claimed in claim 12, wherein changing the respective setpoint stator current characteristic curve is performed at a frequency in a range of 0.01 to 10 Hertz (Hz).
Description
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
(1) The invention is explained in more detail below in exemplary fashion on the basis of embodiments with reference to the accompanying figures.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
DETAILED DESCRIPTION
(9)
(10) The disclosure relates to an adaptive control method for an adaptive rectifier for a separately excited six-phase synchronous generator. Such a system is proposed as part of a wind turbine as shown in
(11) Further explanation of the method is provided below. For this, current and voltage variables are specified predominantly in a rotor-field-oriented d/q coordinate system. The conversion of stator-oriented time characteristics, sinusoidal for the purposes of simplification, to the dq coordinate system rotating with the rotor field is widely known and is explained in the literature. This conversion is assumed below.
(12) The torque T.sub.e of a six-phase synchronous machine without damper windings can be described as follows:
(13)
where P denotes the number of pole pairs for the machine, i.sub.d1s and i.sub.q1s denote the d and q components of the stator currents of the first generator system, and i.sub.d2s and i.sub.q2s denote the d and q components of the stator currents of the second generator system. The first and second generator systems should be understood here to mean particularly the first and second stator systems. Furthermore, i.sub.fd′ denotes the excitation current with reference to the stator and is defined as follows:
(14)
(15) In equation (2), N denotes the number of turns for the machine and i.sub.fd denotes the untransformed excitation current, which can also be referred to as i.sub.e or i.sub.err. L.sub.md and L.sub.mq in equation (1) are the magnetization inductances of the generator that need to be estimated. These inductances are saturation-dependent and can differ greatly from their rated values during operation, depending on the magnetization current i.sub.m. A first estimate of L.sub.md can be obtained by means of a no-load test, according to the following equation:
(16)
where V.sub.oc denotes the RMS conductor-conductor no-load voltage and ω.sub.e denotes the electrical rated frequency of the machine in rad s.sup.−1. The magnetization current i.sub.m is defined as follows:
i.sub.m=√{square root over (((i.sub.q1s+i.sub.q2s)m).sup.2+(−i.sub.d1s−i.sub.d2s+i.sub.fd′).sup.2)} (4)
where
(17)
During the no-load test, no current flows in the stator, and therefore i.sub.m=i.sub.fd′. Analytical calculations on the basis of the generator geometry or by means of finite element simulations allow the trend of the change in the d and q components of the magnetization inductance as a function of i.sub.m to be estimated. This is depicted in
(18) For a specific generator operating point, defined by a speed and a setpoint power value, it is then possible to find an optimum combination of stator currents i.sub.d1, i.sub.q1, and i.sub.q2 and excitation current i.sub.fd that is able to minimize the stator losses P.sub.v.sub.
P.sub.v_stat=6R.sub.sI.sub.srms.sup.2 (5)
(19) Here, I.sub.srms is the RMS phase current, and this is defined as follows:
(20)
(21) The excitation losses are calculated by means of the following equation:
P.sub.v_rot=V.sub.errI.sub.err (7)
where V.sub.err is the excitation voltage and I.sub.err is the excitation current. However, the limited DC link voltage, also simply just called link voltage, means that not all optimum-loss operating points are attainable. This applies particularly if the rectifier operates as a step-up rectifier and thus the DC link voltage must always be above the RMS stator voltage by a specific factor.
(22) A further limiting factor is the maximum current-carrying capability of the power-electronics elements in the rectifier, in particular of the semiconductor switches. It is thus proposed that the following constraints be taken into consideration:
(23)
(24) Here,
V.sub.qs=ω.sub.rλ.sub.ds−R.sub.sI.sub.qs (11)
V.sub.ds=−ω.sub.rλ.sub.qs−R.sub.sI.sub.ds (12)
and λ.sub.ds and λ.sub.qs are defined as follows:
λ.sub.ds=L.sub.md(−2I.sub.ds+i.sub.fd′)−L.sub.lsI.sub.ds (13)
λ.sub.qs=L.sub.mq(−2I.sub.qs)−L.sub.lsI.sub.qs (14)
Here, ω.sub.r is again the electrical speed of the operating point and L.sub.ls is the stray inductance of the stator. An iterative algorithm is used to calculate all possible setpoint stator and excitation current values that satisfy the illustrated constraints. This combination is chosen that minimizes the sum of the losses. It is also possible to use known gradient methods, or other methods for finding a maximum.
(25) It has been recognized that generator parameters can change so greatly that making allowance for such changes can improve the control or automatic control. In order to calculate setpoint values matched thereto as well as possible, knowledge of the generator parameters R.sub.s, L.sub.ls, L.sub.md and L.sub.mq is useful. The stator resistance is temperature-dependent and can be calculated empirically using the following equation:
R.sub.s(T)=R.sub.sT0(1+α(T−T.sub.0)) (15)
where R.sub.sT0 is the nonreactive stator resistance for a specific temperature T.sub.0, which can be 20° C., for example, and changes with the factor α on the basis of the temperature variation. The stray inductance L.sub.ls can be determined by means of a short-circuit test or by means of FEM simulations.
(26) The rotor resistance R.sub.e can easily be calculated from the measured variables V.sub.err and I.sub.err as follows:
(27)
(28) If the generator is in a steady state, the q and d components of the stator voltage can be calculated by means of equations (11) and (12). Calculation in the steady state is thus proposed, because in the transient state it would be necessary to make allowance for the derivation of the respective flows in the two equations, which makes the calculation more complicated. Assuming that R.sub.s and L.sub.ls are known, L.sub.md and L.sub.mq can be calculated by means of the following equations:
(29)
where v.sub.qs, v.sub.ds, i.sub.qs, i.sub.ds are the instantaneous values of the applicable stator voltages and currents. Only one of the two stator systems needs to be considered in this case, because it has been recognized that these two stator systems can be assumed to be identical. The currents and voltages in equations (17) and (18) contain many harmonics, and it is therefore proposed that they be filtered. The switching frequency of the converter is dependent on the operating point. It is thus proposed that an operating point that is as unfavorable as possible for filtering be used—in particular, an unfavorable operating point is one at which there is a low switching frequency and/or a high harmonic load, which is assumed particularly in the case of high saturation —, and that this be taken as a basis for trimming the necessary filter time constants.
(30)
(31)
(32)
(33) The control structure 300 in
(34) Part of the automatic control is formed by the estimating device 312, which can also be referred to as an observer, but in this instance estimates parameters, namely the two magnetization inductances L.sub.md and L.sub.mq. The input quantities for the estimating device 312 are the stator voltage V.sub.S and the stator current I.sub.S in this regard. The values are obtained by the estimating device 312 from the generator 302. In this regard, it is also possible for these quantities to have already been captured otherwise and to be available in a control computer, for example, and for the estimating device 312 to be able to resort to these quantities therein. The estimating device 312 thus does not absolutely have to provide measuring means or devices of its own on the generator 302.
(35) The result of the estimating device 312 is the two magnetization inductances L.sub.md and L.sub.mq, or can also be referred to as the d and q components of the magnetization inductance. These two quantities are input into the adaptive controller 314.
(36) The adaptive controller 314 additionally receives the present speed n and the present setpoint power value P.sub.soll as input quantities. The present setpoint power value P.sub.soll is obtained from a speed/power characteristic curve stored in the speed/power characteristic curve block, referred to in simplified terms as n-P block 316. The speed n describes the speed of the aerodynamic rotor, as the speed/power characteristic curve stored in the n-P block 316 matches the aerodynamics. This speed n therefore also has a decisive effect on the generator 302 and is therefore shown as an input variable for the generator 302. In the case of a gearless wind turbine as proposed in the present case, the speed n of the aerodynamic rotor corresponds to the speed of the generator, that is to say to the armature speed.
(37) The adaptive controller 314 then uses the present speed n and the currently prescribed setpoint power P.sub.soll to calculate an excitation voltage V.sub.e that an excitation controller is supposed to provide in order to ensure an excitation power in the generator 302, which is embodied as a separately excited generator. Additionally, the adaptive controller 314 calculates setpoint values for the stator current, or setpoint values for the individual phase currents of the dual three-phase stator current. The reason is that the setpoint values for the three phase currents i.sub.a, i.sub.b and i.sub.e for the first three-phase stator current and the values i.sub.x, i.sub.y and i.sub.z of the second three-phase stator current are calculated or prescribed. These setpoint values for the stator current, or the components thereof, are then converted by the active rectifier 304.
(38) For this calculation or stipulation, the adaptive controller 314 makes allowance for changes in the magnetization inductance by taking into consideration the applicable d and q components that it receives from the estimating device 312.
(39) The values for the stator current, or the components thereof and the excitation power, or instead the excitation voltage, can therefore be matched to one another in optimum fashion by the adaptive controller 314. Additionally, changes in the properties of the generator 302 can be taken into consideration at that time.
(40)
(41) The characteristic curve for the two components L.sub.md and L.sub.mq of the magnetization inductance is changed accordingly, as indicated by the lower graph in the adaptation block 413. These two characteristic curves accordingly contain a kink, but, optimally, it is possible for further values of the characteristic curves to be adapted little by little too and to lead to an overall change in the characteristic curves.
(42) The result is then provided to the optimization block 414, which can then produce setpoint values on the basis thereof. The parameters transferred from the adaptation block 413 to the optimization block 414 are not shown in detail in
(43) The optimization block 414 continues to receive a setpoint power value P.sub.set denoting the power value that currently needs to be set, namely for the power output to be delivered by the generator or the wind turbine.
(44) This setpoint power value P.sub.set that actually needs to be set is the result of a setpoint power value controller 416, which is in the form of a PI controller in the present case. This PI controller 416 receives a desired power output P.sub.soll and an actual value of the present power output P.sub.m, which therefore also denotes a measured power. If the setpoint power value is now changed, that is to say if P.sub.soll is changed, it is not desirable for an accordingly possibly sudden change to also thus be passed to the optimization block. Accordingly, there is provision for this setpoint P value controller 416, which tracks the power value P.sub.set that actually needs to be set at present to the prescribed setpoint power value P.sub.soll with a dynamic range.
(45) The optimization block 414 then takes the cited inputs as a basis for calculating stator currents and an excitation voltage. The excitation voltage can be output directly as an excitation voltage V.sub.e that needs to be set. The stator currents that need to be set are initially output for each stator subsystem in d/q components. Accordingly, the values I.sub.qs1, I.sub.ds1, I.sub.qs2, I.sub.ds2 are output. However, they are initially provided to the transformation block 415, which transforms these d/q components into a, b, c components. The result for the dual three-phase stator systems under consideration is then six single instantaneous values, namely ia, ib, ic, ix, iy and iz. These six current values can then, as indicated in
(46)
(47) The six stator currents of the six-phase generator are set on the basis of the desired power P.sub.set and hence the excitation voltage V.sub.e. In this regard, it is useful to know the magnetization inductances L.sub.md and L.sub.mq. The relationships in d/q components are provided particularly in equation (1) and in the additional explanations and equations. On the basis of equation (1), a recursive solution can be found, for example.
(48) However, it has been recognized that the magnetization inductances are not constant, but rather may be dependent on the present operating point of the generator. In particular, they are dependent on the magnetization current, as shown in
(49) The optimization block 414 makes allowance for the magnetization inductances L.sub.md and L.sub.mq being variable by using the respective present values. In this regard, it can find a recursive solution based on equation (1), for example, at the present operating point each time, and can take this as a basis for determining the stator currents I.sub.qs1, I.sub.ds1, I.sub.qs2 and I.sub.ds2 in d/q coordinates. It is naturally also possible for recursive solutions of this kind or other solutions to be determined beforehand and stored in a table, from which they are then retrieved during operation. Intermediate values can be interpolated.
(50) The optimization block 414 therefore prescribes the stator currents that are set, and, for this purpose, at least adapts the magnetization inductances used. The magnetization inductances are parameters, and therefore the optimization block 414 is an adaptive controller or part of an adaptive controller.
(51) In this regard, the optimization block 414 receives these magnetization inductances from the adaptation block 413. The adaptation block 413 is particularly supposed to illustrate that the magnetization inductances are subject to a change, and this change is also taken into consideration. The adaptation block 413 together with the optimization block 414 can therefore also be understood to be an adaptive controller.
(52) In fact, the adaptation block 413 is used particularly to illustrate the assumed change. The initial starting point in this case, namely in accordance with the upper graph of the adaptation block 413, is a relationship between the magnetization current I.sub.m and the magnetization inductances, which was initially stored as a characteristic.
(53) However, it has been recognized that there can be differences therefrom. In order to make better allowance therefor, magnetization inductances can then be observed for the respective magnetization current I.sub.m, by an observer, this also being able to be referred to as estimation. The observer is represented as observer block 412. It can receive the excitation current I.sub.e, the stator voltage V.sub.S and the stator current I.sub.S as input quantities and observe or estimate and output the magnetization inductances L.sub.md and L.sub.mq and the magnetization current I.sub.m.
(54) On that basis, the observer block 412 thus has the function of determining the magnetization inductances L.sub.md and L.sub.mq and the magnetization current I.sub.m from said input quantities.
(55) This can be accomplished by using a conventional observer based on a system description, as provided particularly by equations (4), (17) and (18). Alternatively, the observer block 412 can use an estimation algorithm or a calculation to determine the magnetization inductances L.sub.md, L.sub.mq and the magnetization current I.sub.m. This can also be effected on the basis of equations (4), (17) and (18). Equations (4), (17) and (18) also relate to present measured values, which means that they involve actual influences, especially thermally independent influences, being used for the determination. The application of the equations therefore allows temperature-dependent changes to be detected and taken into consideration. The characteristic curve shown in
(56) The values thus observed for L.sub.md, L.sub.mq and I.sub.m are subsequently input into the adaptation block 413 after they have been determined for an operating point by the observer block 413.
(57) This is indicated by the two arrows “e” in the upper graph in the adaptation block 413. The arrow “e” therefore illustrates two values, determined by the observer block, for L.sub.md and L.sub.mq at a specific operating point in the upper graph of the adaptation block 413. These operating-point-dependent values for L.sub.md and L.sub.mq are transferred to the lower graph of the adaptation block 413 and result in the two kinks shown. Initial values are thus stored in the adaptation block 413 for the magnetization inductances, for example, in the form of a characteristic curve or a lookup table, which are then constantly updated with the present values from the observer block 413. The updated or adapted values for L.sub.md, L.sub.mq and I.sub.m are subsequently transferred to the optimization block 414, which takes into consideration the updated values to determine the stator currents.
(58) The adaptation block 413 therefore illustrates, particularly in comparison with
(59)
(60) In this regard,
(61) In a further embodiment in
(62) In an alternative embodiment to
(63) For the inductances, namely particularly L.sub.md and L.sub.mq, values from one or more tables are used, which can also be referred to as “lookup tables.” These one or more tables are updated on the basis of the magnetization current i.sub.m during generator operation, specifically whenever there is a steady operating state for a respective operating point. In the steady state, equations (11) and (12) describe the d and q components of the stator voltage, and the inductances L.sub.md and L.sub.mq can therefore be estimated by means of equations (17) and (18), and then the values can be updated.
(64) In order to compensate for both modeling inaccuracies and ignored losses, a PI controller changes the setpoint power value of the control. This PI controller is active only in proximity to the setpoint power values and serves as a basis for setpoint current value generation until the desired power output is reached. In the event of large differences from the setpoint value, the I component can be deactivated. On account of a rather large time constant for the generator, the setpoint values are calculated at a low frequency, which can be 100 Hz for example, this being a comparatively low value in comparison with a maximum clock frequency of 10 kHz in standard microcontrollers.
(65) Control of an active rectifier for a separately excited synchronous machine with optimized machine efficiency is therefore proposed. The separately excited synchronous machine can also be referred to as a separately excited synchronous generator. In particular control for a synchronous machine having two generator systems has been described. The method can alternatively be adapted for a different number of generator systems or stator systems; specifically, besides two three-phase systems, there is also the possibility of four or more stator systems.
(66) Provided herein is operating a separately excited synchronous machine having multiple generator systems or stator systems and highly saturation-dependent parameters at optimized efficiency using an active rectifier. The saturation characteristic of the machine, or the estimate of the correct response of the magnetization inductance, can be achieved using the described solution and can be used for a control method for active rectifiers, and this also allows the saturation characteristic of the machine to be taken into consideration. Additionally, the presented solution is suitable for separately excited synchronous machines.
(67) Literature references [a] and [b] cited below describe solutions for separately excited synchronous generators.
(68) Literature reference [a] shows a method for controlling a separately excited synchronous machine. Setpoint current values are calculated analytically by means of the “Lagrange multiplier” method in order to minimize the total stator and rotor losses. A self-tuning algorithm is presented, which can change some parameters of the analytical calculation during operation, assuming that the machine is in the steady state. However, only the i_d component of the stator current and the excitation current i_err are adapted.
(69) In regard to the parameter estimation, methods are often proposed that are based on RLS (Recursive Least Square) methods, or the like, and the assumption of the steady state is necessary for this in order to ignore the derivation of the flows. To improve matters, the estimation of the inductances L.sub.md and L.sub.mq in the proposed solution is based on a method in which the applicable parameters are simply calculated by means of algebraic equations.
(70) The techniques described herein can be used, at least in some embodiments, for controlling a separately excited synchronous machine having multiple generator systems. Assuming that the parameters of the machine are consistent with the actual properties of the machine, the algorithm can calculate the respective globally optimum operating point in order to minimize the stator and rotor losses for a specific setpoint power. The method affords the opportunity to correct the lookup tables for the inductances by means of online parameter estimation, which can be performed by means of algebraic evaluation of the measured generator quantities, namely the voltages, the currents and the speed.
(71) Since the operating points are determined by means of a numerical iterative calculation, an appropriate computing power is required. The problem has been recognized and the calculation can be performed at a lower frequency in comparison with the clock frequency of modern microcontrollers owing to the high mechanical inertia of the machine and the large time constant of the rotor.
THE VARIOUS REFERENCES
(72) [a] Chi D. Nguyen and W. Hoffman, “Self-Tuning Adaptive Copper-Losses Minimization Control of Externally Excited Synchronous Motors,” International Conference on Electrical Machines (ICEM) 2014, pp. 897-902, Sep. 2-5, 2014. [b] D. Kowal, P. Sergeant, L. Dupre' and H. Karmaker, “Comparison of Frequency and Time-Domain Iron and Magnet Loss Modeling Including PWM Harmonics in a PMSG for Wind Energy Application,” IEEE Trans. on Energy Conversion, vol. 30, no. 2, pp. 476-486, June 2015.