WO2011128664A2

WO2011128664A2 - Method and apparatus for controlling doubly fed electrical machine and doubly fed electrical machine incorporating such apparatus

Info

Publication number: WO2011128664A2
Application number: PCT/GB2011/050672
Authority: WO
Inventors: Hamza Chaal; Milutin Jovanovic
Original assignee: University Of Northumbria At Newcastle
Priority date: 2010-04-16
Filing date: 2011-04-04
Publication date: 2011-10-20
Also published as: GB201103534D0; WO2011128664A3; GB201006361D0

Abstract

A controller (218) is disclosed for a doubly fed electrical machine comprising a stator (204), a rotor (209), a set of primary windings mounted to the stator and adapted to receive first electrical signals to generate a first rotating magnetic field, and a set of secondary windings mounted to the stator or to the rotor and adapted to receive second electrical signals to generate a second rotating magnetic field, wherein the rotor is located in said first and second rotating magnetic fields in use and is adapted to interact therewith to generate a magnetomotive force. The controller is adapted to receive current and voltage signals from the primary windings to determine real and/or reactive power of the primary windings, compare said real and/or reactive power with reference values, and apply voltage vectors as electrical signals to the secondary windings to adjust the real and/or reactive power of the primary windings.

Description

METHOD AND APPARATUS FOR CONTROLLING DOUBLY FED ELECTRICAL MACHINE AND DOUBLY FED ELECTRICAL MACHINE INCORPORATING SUCH

APPARATUS The present invention relates to a method and apparatus for controlling a doubly fed electrical machine, and relates particularly, but not exclusively, to a method and apparatus for controlling a grid connected doubly fed reluctance machine. The invention also relates to a doubly fed

electrical machine incorporating such apparatus.

Brushless doubly fed reluctance machines (BDFRM) have been investigated as a possible alternative to existing electrical generators having narrow speed ranges, such as wind turbines,^' because of their modest cost, high reliability of brushless structure and competitive performance compared with conventional doubly excited wound rotor induction machines (DEWRIM) or brushless doubly fed induction machines {BDFIM) . Such machines allow the use of a lower rated inverter which, for a typical speed range of 2:1 in wind turbines, can be 25% of the machine rating, offering a significant cost advantage.

A torque controller for a BDFRM is disclosed in

"Encoderiess Direct Torque Controller for Limited Speed Range Applications of Brushless Doubly Fed Reluctance Motors", Milutin G. Jovanovic et al. IEEE Transactions on Industry Applications, Vol 42, number 3, May/June 2006, and is explained with reference to Figures 1 and 2.

-

Figure 1 illustrates a brushless doubly fed reluctance motor 2 having a stator 4 and a rotor 6. A set of primary windings 8 connected to the grid for receiving three phase electrical power is mounted in the stator 4, and a set of secondary windings 10 connected to the grid for receiving three phase power is mounted in the stator 4 and controlled by means of an AC/DC/AC converter 12 comprising a rectifier 14 and an inverter 16 (Figure 2) for controlling the voltage applied to the secondary windings 10. The rotor 6 is provided with half the total number of primary and secondary poles and interacts with a rotating magnetic field generated by the primary 8 and secondary 10 windings.

The principle of operation of the motor illustrated in Figure 1 is described in detail in "Introduction to the Space Vector Modeling of the Brushless Doubly Fed Reluctance

Machine", M. G. Jovanovic, Electric Power Components and Systems, 31:729-755, 2003, the contents of which is

incorporated herein by reference. As will be appreciated by persons skilled in the art, as a result of the effective variation in air gap between the rotor 6 and the stator 4, the magnetic flux density in the primary windings 8 is given by:

Β (θ,ή = μ₀ηιΚpm (1)

+ -~CO$[(O)_p

where co_rm is the rotor angular velocity.

It can therefore be seen from the above equation that the effect of the rotor 6 is to modulate the flux density in the primary windings 8, producing a flux density component at the same frequency as the rotating field generated by the grid power supply, and side bands at frequency ω + p_rOi_m and

In a similar manner, the flux density wave form in the secondary windings 10 can be represented as: cos(t¾t -a-ρβ) +— [cos((t¾ -p_ra>_m)t + (p_r - p_s)0 - a)

2m

+ cos((i¾ + ρ,ω^)t - (_Pr +ρ₅)θ - )]

(2)

For the arrangement shown in Figure 1, it is possible to show that:

(3) dt dt ^f const p—p άλ.

u„ = R z^' + - (4) s const

ω_Γ = dd_r I dt = p_rG>_rm = ω + ω, = (1 - s)a> (7)

Where are the three-phase inductances of the primary and secondary windings. From this it can be shown that P = L_p(i_pd + ji_pq ) + L_ps (i_sd - ji_ss_qq) . (8)

L=oL- _sL+~^l_p=aL_s(i_sd+ji_sq) + X_ps (9)

where A is the primary flux linking the secondary winding. Referring to Figure 2, the arrangement for

detecting the necessary parameters to control the apparatus is shown.

However, the arrangement shown in Figures 1 and 2 suffers from the drawback that it is necessary to know the self inductances of the windings, and the arrangement is found at low secondary currents and maximum torque per inverter ampere conditions to suffer from pronounced

sensitivity to parameter knowledge inaccuracies, which causes difficulties in real time implementation. Attempts to improve the estimation quality involves significant added complexity and computational burden, which in turn reduces the extent to which the cost of the controller can be reduced . Preferred embodiments of the present invention seek to overcome one or more of the above disadvantages of the prior art .

According to an aspect of the present invention, there is provided a controller for a doubly fed electrical machine comprising : - a stator;

a rotor;

at least one set of first electrical windings mounted to the stator and adapted to receive first electrical signals to generate a first rotating magnetic field; and at least one set of second electrical windings mounted to the stator or to the rotor and adapted to receive second electrical signals to generate a second rotating magnetic field;

wherein the rotor is located in said first and second rotating magnetic fields in use and is adapted to interact therewith to generate a magnetomotive force, and

the controller is adapted to receive current and voltage signals from at least one said set of first

electrical windings to determine real and/or reactive power of said first windings, compare said real and/or reactive power with reference values, and apply third electrical signals to at least one said set of second electrical windings to adjust said real and/or reactive power of said first windings.

The present invention is based on the surprising discovery that the instantaneous real power of the primary windings of a doubly fed reluctance machine have dynamics which largely follow those of torque, which are controllable by varying the phase difference between the magnetic flux vector in the secondary windings and the mutual flux through the primary and secondary windings. This provides the advantage that the real power can be increased or decreased in a simple manner by increasing or decreasing this phase difference and, since both the primary and secondary windings participate in establishing the resultant flux in the machine, it is possible to increase or decrease the reactive power by increasing or decreasing the magnetising current from the primary windings. This in turn provides the advantage that the controller can be used independently of machine parameters, and therefore machine type, and less processing power is required in order to operate the controller. This therefore significantly reduces the cost of operation of the controller.

The controller may be adapted to apply at least one respective third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

This provides the advantage of enabling rapid and simple control by means of a look-up table in which a small number of correction values are contained, which in turn reduces the complexity and cost of the controller.

The controller may be adapted to apply, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings . This provides the advantage of simplifying the

operation of the apparatus, which in turn enables the controller to be operated with less processing power, which in turn reduces the cost of the controller. The third electrical signals may be adapted to increase and/or decrease reactive power in at least one said set of first electrical windings by increasing and/or decreasing magnetic flux in at least one said set of second electrical windings .

The third electrical signals may be dependent on a phase difference between the magnetic flux in at least one said set of second electrical windings and the magnetic flux linking said first and second electrical windings.

This provides the advantage of enabling the controller to operate independently of machine parameters and machine type .

According to another aspect of the present invention, there is provided a double fed electrical machine comprising a stator;

a rotor;

at least one set of first electrical windings mounted to the stator and adapted to receive first electrical signal to generate a first rotating magnetic field;

at least one set of second electrical windings mounted to the stator or to the rotor and adapted to receive second electrical signals to generate a second rotating magnetic field;

wherein the rotor is located in said first and second rotating magnetic fields in use and is adapted to interact therewith to generate a magnetomotive force; and

a controller as defined above.

According to a further aspect of the present invention, there is provided a method of controlling a doubly fed electrical machine comprising:

a stator;

a rotor;

at least one set of first electrical windings mounted to the stator and adapted to receive first electrical signals to generate a first rotating magnetic field; and

at least one set of second electrical windings mounted to the stator or to the rotor and adapted to receive second electrical signals to generate a second rotating magnetic field; and

wherein the rotor located in said first and second rotating magnetic fields in use and is adapted to interact therewith to generate a magnetomotive force;

the method comprising:

receiving current and voltage signals from at least one said set of first electrical windings to determine real and/or reactive power of said first windings;

comparing said real and/or reactive power with

reference values; and

applying third electrical signals to at least one said set of second electrical windings to adjust said real and/or reactive power of said first windings.

The method may further comprise applying at least one respective said third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

The method may further comprise applying, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective said third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings.

The third electrical signals may be adapted to increase and/or decrease reactive power in at least one said set of first electrical windings by increasing and/or decreasing magnetic flux in at least one said set of second electrical windings . The third electrical signals may be dependent on a phase difference between the magnetic flux in at least one said set of second electrical windings and the magnetic flux linking said first and second electrical windings.

According to a further aspect of the present invention, there is provided a computer program adapted to be run on a computer to carry out a method as defined above, the computer program comprising:

first computer code executable to receive current and voltage signals from at least one said set of first

electrical windings to determine real and/or reactive power of said first windings;

second computer code executable to compare said real and/or reactive power with reference values; and

third computer code executable to apply third

electrical signals to at least one said set of second electrical windings to adjust said real and/or reactive power of said first windings.

The third computer code may be executable to apply at least one respective said third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

The third computer code may be executable to apply, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective said third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings. A preferred embodiment of the present invention will now be described, by way of example only and not in any limitative sense, with reference to the accompanying

drawings, in which :-

Figure 1 is a schematic representation of a known brushless doubly fed reluctance machine

Figure 2 is a circuit diagram of a direct torque controller of the machine of Figure 1;

Figure 3 is a schematic diagram of a test rig for a brushless doubly fed reluctance machine including a

controller embodying the present invention;

Figure 4 is a schematic diagram of part of the machine of Figure 3, including power electronics and sensors used for controlling the machine;

Figure 5 is a schematic diagram of a first embodiment of a direct power controller of the machine of Figure 3;

Figure 6 is a per phase steady state equivalent circuit of the machine of Figure 3;

Figure 7 is a phasor diagram of operation of the machine of Figure 3;

Figure 8 shows characteristic space vectors for 60° sectors of rotation of the magnetic field of the apparatus of Figure 3;

Figure 9 illustrates a simulation of reactive power control of the machine of Figure 3;

Figure 10 illustrates a simulation of real power control of the apparatus of Figure 3;

Figure 11 illustrates a simulation of speed control of the apparatus of Figure 3;

Figure 12A shows primary voltage and current wave forms during ramp loading of the apparatus of Figure 3; Figure 12B shows primary voltage and current wave forms during the steady state of the apparatus of Figure 3;

Figures 13A and 13B show the phase current waveforms of the secondary windings of the machine of Figure 3 at

different time intervals;

Figures 14A and 14B show the inferred sector position on Figure 8 of the secondary flux through different time intervals ;

Figures ISA to 15C show fixed speed performance results of motor speed, real power and reactive power respectively of the test rig of Figure 3 with the controller of Figure 5 in super-synchronous mode;

Figures 16A to 16C show waveforms of sector, primary current and secondary current respectively while carrying out the process of Figure 15;

Figures 17A to 17D show variable speed performance results of motor speed, real power, reactive power and sector respectively of the test rig of Figure 3 with the controller of Figures in a limited speed range around synchronous speed;

Figures 18A to 18C show fixed speed performance results of motor speed, real power and reactive power respectively of the test rig of Figure 3 with the controller of Figure 5 in response to a sudden load change in super-synchronous mode;

Figures 19A to 19C show waveforms of sector, primary current and secondary current respectively while carrying out the process of Figure 18;

Figure 20 is a schematic diagram, corresponding to Figure 5, of a second embodiment of a direct power controller of the machine of Figure 3;

Figure 21 shows active power step response from

motoring to generating mode, while speed of shaft is

regulated by a prime mover DC machine at 650rpm; Figure 22 shows the reactive power waveform corresponding to Figure 21;

Figure 23 shows the variation of prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode when subjected to an unknown load change and corresponding to Figure 21;

Figure 24 shows the variation of primary phase "A" current with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode when subjected to the step change of active power of Figure 21;

Figure 25 shows the variation of secondary phase "a" current with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode when subjected to the step change of active power of Figure 21;

Figure 26 shows the sector waveform of the test rig of

Figure 3 with the controller of Figure 5 in a sub-synchronous mode when subjected to the step change of active power of Figure 21;

Figure 27 shows the variation of active power with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode at constant speed;

Figure 28 shows step response of reactive power with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode at constant speed;

Figure 29 shows the variation of prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 while subjected to the step change of reactive power of Figure 21;

Figure 30 shows the variation of primary phase "A" current with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode at constant speed corresponding to the step change of reactive power of Figure 28; Figure 31 shows the variation of secondary phase "a" current with time of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode at constant speed corresponding to the step change of reactive power of Figure 28;

Figure 32 shows the sector waveform of the test rig of Figure 3 with the controller of Figure 5 in a sub-synchronous mode at constant speed corresponding to the step change of reactive power of Figure 28;

Figure 33 shows step response of active power with time of the test rig of Figure 3 with the controller of Figure 5 in a synchronous mode;

Figure 34 shows the variation of reactive power with time of the test rig of Figure 3 with the controller of Figure 5 in a synchronous mode when subjected to the active power step change of Figure 33;

Figure 35 shows the regulated prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 in a synchronous mode when subjected to the active power step change of Figure 33;

Figure 36 shows the variation of active power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode during the change of reactive power demand shown in Figure 37;

Figure 37 shows the variation of reactive power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode;

Figure 38 shows the regulated prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode during the change of reactive power demand shown in Figure 37; Figure 39 shows the step response of active power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode;

Figure 40 shows the variation of reactive power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode when subjected to the step change of active power of Figure 39;

Figure 41 shows the regulated prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode when subjected to the step change of active power of Figure 39;

Figure 42 shows the variation of primary phase "A" current with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode when subjected to the step change of active power of Figure 39;

Figure 43 shows the variation of secondary phase "a" current with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode when subjected to the step change of active power of Figure 39;

Figure 44 shows the sector waveform of the test rig of

Figure 3 with the controller of Figure 5 in a super- synchronous mode when subjected to the step change of active power of Figure 39;

Figure 45 shows the variation of active power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode while subjected to the step change of reactive power of Figure 46;

Figure 46 shows the step response of reactive power with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode;

Figure 47 shows the regulated prime mover speed with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode while subjected to the step change of reactive power of Figure 46;

Figure 48 shows the variation of primary phase "A" current with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode

corresponding to the step change of reactive power of Figure 46;

Figure 49 shows the variation of secondary phase "a" current with time of the test rig of Figure 3 with the controller of Figure 5 in a super-synchronous mode

corresponding to the step change of reactive power of Figure 46; and

Figure 50 shows the sector waveform of the test rig of Figure 3 with the controller of Figure 5 in a super- synchronous mode corresponding to the step change of reactive power of Figure 46.

Referring to Figures 3 to 5, a brushless double fed reluctance machine 202 embodying the present invention includes a stator 204 having 3-phase primary windings connected to a three phase grid supply 206, and 3-phase secondary windings connected to power electronics 208 comprising IGBT inverter 210, diode rectifier 212 and driver 214 connected to a controller 218. A rotor 209 is rotatably mounted to the stator 204.

The timing of the gate signals of the IGBT inverter 210 is controlled by the controller 218 which drives the driver 214 to directly control the real and reactive power in the secondary windings. Inductive current transformers 220a,

220b, 220c measure the current in the secondary windings and provide input signals to the controller 218. Referring to Figures 3 to 6, the space sector equations stationary reference frame for the machine of Figure 3 d ₀ dX_D

- —P

{ID

pi_p ⁺ L_mi_se^J ' - L_pi_p + L_m_i_sm

(12:

:i3)

This therefore gives rise to the steady state

equivalent circuit shown in Figure 6.

The rotor position dependent term e^{J r} in equation 12 carries out a frequency conversion from the primary windings to the secondary windings and vice versa resulting in coupled vectors / and _ i_sm . These virtual currents have the same amplitude and phase as the primary and secondary currents respectively, but different angular velocities. In other words i_pm = i_p and i_sm = i_s in the respective rotating reference frames as shown in Figure 7.

The -pole reluctance motor provides such a magnetic coupling between the two > -pole primary and the two p_s-pole secondary windings {supplied at frequencies over ω_ρ and <¾ respectively by modulating the stator MMFs in a frequency sense under the following rotor angular velocity and pole number conditions

where the generalised slip is $ = -ω₅ Ι ω_ρ . It can therefore be seen that the secondary flux vector _s is ahead of the mutual flux vector λ for motoring operation (as shown in Figure 7), and that it lags behind the latter in generating mode.

From equation (14), the following mechanical power balance equation can be established, showing individual contributions of each BDFRM winding:

where the electromagnetic torque can be represented by:

Neglecting copper losses in the apparatus of Figure 3 and the rate of change of energy stored in the magnetic field, the instantaneous electric power becomes approximately equal to the mechanical power. The former assumption will be familiar to persons skilled in the art, especially with larger machines having inherently lower resistances, and the latter approximation is justified on the basis that the rate of change of stored energy dW/dt is directly proportional to dX_p l dt and is approximately equal to 0. It can therefore be concluded that the real power dynamics will largely follow those of torque which, as can be deduced from equation {16} above, is controllable by varying angle 9_S of X_s , and in turn angle δ . If P_p is to be increased/decreased, therefore, then it is necessary to increase/decrease 9_S and therefore s .

Referring to Figure 8, the effects of applying a particular secondary voltage vector U_k on the secondary flux X_s , and therefore its effect on P_p or Q_p values, depend on the position of the flux vector at a given time instant. For example, as shown in Figure 8, if X_s is located in sector 1, the application of either voltage vector t¾ or ¾ will move X_s anti-clockwise, increasing both the angle δ and the real power _p (>0) drawn by the primary winding. Under the same voltage conditions when the BDFRM is operated as a generator, i.e. when leads X_s and P_p <0 (positive real power being produced by the machine in this case) , the angular separation between the two flux vectors reduces, resulting in P_p

increasing (i.e. becoming less negative) which is equivalent to the machine generating less power to the grid. It can therefore be seen that the effect of U₂ or ¾ increasing P_p is invariant of the operating mode, as is the P_p decreasing effect of U_$ or Ug. It can therefore be concluded that if X_s lies in the k^th sector, then the vectors U_k+1 or U_k+2 will increase P_p, and U_k-i or U_k-2 will decrease it in the actual sense. Which of the voltage vectors is to be selected will also depend upon the specific reactive power Q requirement that has to be simultaneously satisfied. The Q_p > 0 consumption can be directly controlled by the changes in _s. For example, it can be seen from Figure 8 that any of the vectors ¾, ¾ or U_e would increase the magnetising d-axis component (i.e. along λ ) of X_s . This would indicate a larger amount of reactive power to be fed by the inverter and a consequent reduction in the Q_p demand. On the other hand, either ¾, U₄ or t¾ would have the completely opposite effect, requiring more Q_p to be taken from the grid. It can also be seen that these qualitative properties are unaffected by the operating mode of the BDFRM. It can therefore be appreciated that if the _s is in the k^th sector, then the vectors U_k-i, U_k or U_k+1 would decrease, and U_k+2r U_k+3 or U_k-2 would increase Q_p. The operation of the controller shown in Figure 3 will now be described.

A Q_p reference is set to achieve the desired line power factor. A conventional PI speed controller with an

integrated power limiter provides the necessary P_p reference for a given set-point with its integral action effectively compensating for the machine losses. The actual power inputs to the hysteresis comparators are computed using the primary currents and voltages. The primary winding is usually derived with an isolated neutral point allowing the use of only two current sensors because of balanced conditions.

However, the primary supply voltages may not be always balanced and three voltage transducers can be employed for this reason.

The phase quantities are first transformed into stationary dq components (with the respective d-axis being aligned with the A-phase) , and then the 3-phase real and reactive powers are calculated using the following well-known expressions :

P_p=i_d-u_d+i_q-u_q

(17)

where i_d = i_a,i_q = (i_a+2_ib)/[3,u_d = u_a -(u_b +u_c)/2 and u_q = - (u_b -u_c)l2 for a Y-connected primary winding with ^ABC phase sequence. The outputs of hysteresis comparators 124, 126 (Figure

5) giving errors between desired and measured powers, in addition to the information about the secondary flux sector, make it possible to index relevant look-up tables in the control software and choose an appropriate voltage vector to be applied to the secondary terminals at any given time.

Examining suitable voltage vectors to satisfy both real and reactive power demands for a given sector k suggest the exclusion of the not-applicable vectors U_k and U_k+3 as shown in Table 1. The corresponding binary patterns showing the switching status of inverter legs can be found in Figure 6. Implementing the switching logic in Table 1 ensures the control of P_p and Q_p within a narrow, user-specified, band around the reference values, i . e . [p^* -AP,P^* +AP] and

|ρ· - Δβ,β' + Δβ] . Table 1: Optimum Switching Vectors

The secondary voltage effects on power control

discussed above are valid, regardless of the relative position of the X_s sector within its residing sector. For the purposes of operating the controller, therefore, it is only necessary to know which sector _s is located in at a certain time instance. A sector detection technique based on monitoring the rate of change of Q_p {AQ_P) under particular voltage conditions is carried out as follows.

Assuming that X_s lies in sector 1, for example as illustrated in Figure 6, applying the vectors U₂ or U₆ results in reduction of Q_pi and !¾ or ¾ results in its increase, as shown in Table 1. If the machine speed is super-synchronous, X_s rotates anti-clockwise and moves to sector 2. Once in sector 2, the influence of voltage vectors U₃ and" U₆ on Q_p variations are opposite from those in sector 1. Such reversal in the sign of AQ_P (from positive to negative or vice-versa} enables sector determination, and their proper detection can be used to make a decision for a sector transition to be taken by the controller. Similarly, if the machine is operated in sub-synchronous mode, _s

travels clockwise, entering sector 6 where the effect of vectors U₂ and U₅ becomes different. There are therefore two voltage vectors that can serve as indicators for a change in sector. Since _s cannot jump through sectors over a short control interval, the sector counter will therefore either be incremented or decremented by one. The predictions of AQ_P for possible (sector, voltage) combinations are recorded in Table 2, where ^Λ+' refers to the increase of Q_p and ~' to its decrease, and χ' indicates situations that should not occur. The actual AQ_P variations can be calculated from measurements at the current and previous sampling instance using equation (17) above. If there is a mismatch in AQ_P sign between the expected and true values, this means that a change of sector has taken place, and that the sector number information should therefore be updated, in accordance with Table 3.

Table 2: Expected rate of change of Q_p

Table 3: Inferred direction of sector change

Sector/Vector Ui u₂ u₃ u₄ Us u_e

1 X -1 +1 X -1 +1

2 +1 X -1 +1 X -1

3 -1 +1 X -1 +1 X

4 X -1 +1 X -1 +1

5 +1 X -1 +1 X -1

6 -1 -1 X -1 +1 X Simulation

To demonstrate the invention and test its theoretical performance for generating operating mode of the machine, a 4.5kW, 750 rpm, 6/2-pole BDFRM machine used for simulation studies is self-started as an induction machine by shorting the secondary windings, and after reaching the synchronous speed (750 rpm) , the control is enabled on-the-fly' followed by a gradual reduction of Q_p reference {Q^* in Table 1) down to zero for unity power factor operation.

The accurate and smooth Q_p control in the pre-set hysteresis bandwidth (2AQ in Table 1) can be observed from Figure 9. At t=1.3s, a load torque of -40 Nm is applied in a ramp fashion (at -lOONm/s) and subsequently kept constant throughout the rest of the simulation. Figure 10 shows the excellent dynamic and steady state response of P_p. It is important to notice the inherently decoupled control of real and reactive power. For maximum power point tracking (MPPT) of wind turbines, the outer PI speed control loop may be required to ensure effective variable speed operation at optimum tip-speed ratio. Figure 11 depicts the controller response to different desired speeds. The disturbance that appears at t=1.3s comes from the machine ramp loading at this time instant and is normal for the selected PI gains. At t=2.5s the speed reference is set gradually (1000 rpm/s) to 1000 rpm, and at t=3.5s changed to 500 rpm, in order to evaluate the control quality over the limited speed range of interest to the BDFRM target applications. Finally, Figure 10 illustrates the respective phase voltage and current waveforms which are n rad out of phase as expected for unity (-1 in generating mode) power factor control under both transient and steady-state loading conditions. Experimental Verification

Referring again to Figure 3, the power electronics 208 is in the form of a frequency converter comprising a Semikron intelligent power module supplied by Semikron Limited,

Hertford, UK, connected to a controller 218 comprising a DS1103 rapid prototyping board supplied by dSPACE Limited of Hertford, UK. The timing of the gate signals of the power electronics 208 is controlled by the controller 218 to directly control the real and reactive power in the primary windings. Inductive current transformers 220a, 220b and 220c measure the current in the secondary windings and provide input signals to the controller 218. Although secondary current sensors are not required for controlling the real and reactive power, these are monitored in the apparatus of

Figure 3 to confirm the theory of operation of the apparatus.

An electric motor 250 in the form of a commercially available 3kw machine with a commercial four quadrant Parker SSD drive 252 supplied by Parker Hannifin Corporation of Cleveland, Ohio, USA is used as a prime mover or a load, depending on the desired operating mode and application of the apparatus 202. The actual speed of the shaft of the motor 250 is controlled by a PI controller 160 (Figure 5) sitting on top of the controller 218 and providing a reference power signal as input to the controller 218.

The sampling time of the apparatus 202 was selected to be 0.1ms, implying a maximum switching frequency if 10kHz for IGBT inverter 210 of the apparatus 202. However, the actual switching rate was found to be about 5kHz. A full DC link voltage obtained from a 3-phase, 415V, 50Hz supply was used { approximately 600V) , and hysteresis bands were set to

AP=±50W for real power and AQ = ± 100 VAr for reactive power. The apparatus was then started with the shorted secondary windings as an induction machine, and upon reaching the steady no-load speed, the controller 218 was activated on the fly.

Reactive Power Control Referring to Figures ISA to 15C, performance of regulation of reactive power is illustrated by a ramp down response from Q* = 1400 VAr to Q* = 800 VAr at 800 rev/min. The non-optimum design of the apparatus 202 and the

inherently modest magnetic coupling between the windings causes the particular apparatus 202 of Figure 3 to have significant magnetising currents, which made it impossible to achieve unity primary power factor without exceeding the secondary current rating. The active power waveform of Figure 15B shows that the average active power P remains substantially constant during the Q* transient, demonstrating decoupled PQ control.

Figure 16A suggests the expected anti-clockwise

rotation of the secondary flux vector for super-synchronous machine operation, as indicated by the step up variations at the respective sector numbers (see Figure 8) . As a

consequence of reduced demand for magnetisation from the primary winding, the corresponding current amplitude

decreases and the secondary currents increase in magnitude, as can be seen from Figure 16C. Also, equation (14) suggests that the secondary frequency for 800 rev/min speed should be around 3.33Hz, which is confirmed by the 0.3 second current cycles in Figure 16C. Variable Speed Operation

Referring to Figures 17A to 17D, the effective speed tracking performance is shown in synchronous (750 rev/min) , super-synchronous (950 rev/min} and sub-synchronous (550 rev/min) modes of the unloaded apparatus operated as a motor. The reference speed profile is set as a ramp (of 400 rpm/s slope) in order to emulate dynamically less demanding target applications of the machine 202, such as wind turbines or large pumps. The measured active power waveform shown in Figure 17B indicates a speed dependent power loss of

approximately 400W under steady state conditions. This phenomenon is typical for lossy machines of this type, and comes from the integral action of the speed PI controller which compensates for the iron losses not being taken into account in the direct power control algorithm.

As shown in Figure 17C, the reactive power is

controlled well at its natural value of 1300 VAr. The inferred sector changes of the secondary flux positions during a short transient from super-synchronous (anticlockwise rotation and ascending sector numbers as in Figure 16A) to sub-synchronous (clockwise rotation and descending sector numbers) can be observed. While riding through the synchronous speed, the secondary flux vector becomes

stationary as the secondary winding is then DC.

Load Test

Referring to Figures 18A to 18C, the shaft speed is kept constant at 800 rev/min while the apparatus 202 is subjected to a sudden load torque change of -lONm {as read on the torque transducer display) at 1300 VAr as shown in Figure 18C. Such a load disturbance, which tends to accelerate the machine, is effectively rejected by the speed controller through the operating mode reversal to allow for the excess mechanical power to be first converted to electrical power and then delivered to the grid to maintain the speed fixed. As can be seen in Figure 18B, the apparatus 202 shifts smoothly from motoring to the generating regime and starts producing 500 {i.e. consuming -500W) .

As shown in Figure 19A, similarly to the previous cases, the increasing sector numbers indicate the anticlockwise rotation of the secondary flux vector at super- synchronous speed. Figure 19B shows that the primary winding current magnitude appears to be unaffected by the prime mover 250 driving the apparatus 202, while the secondary current amplitude shown in Figure 19C notably increases in response to the new loading conditions. This can be explained by the predominately magnetising (d-axis) current in the primary and torque producing (g-axis) currents in the secondary winding. Furthermore, the magnetic coupling is fairly weak in the particular apparatus described and therefore does not cause any significant coupled g-axis primary current component and consequent variations in the overall current amplitude.

Referring to Figure 20, which differs from the

arrangement of Figure 5 in that instead of controlling the speed of the shaft of motor 250 by means of a PI controller 160, the motor 250 controls the speed of the shaft which is subjected to unknown load changes (as happens in some schemes emulating varying wind speed on the rotor speed) . This particular scenario is important because it allows DPC performance to be assessed alone without being part of a higher master logic or controller. The user inputs directly desired reference values for real power P and reactive power Q as shown in Figure 20. Referring to Figures 21 to 32, a sub-synchronous speed

(650rpm) is maintained constant by the DC drive of motor 250, and the active power response is tested as shown in Figures 21 to 26. The reactive power response is then tested in

Figures 27 32. Decoupled control is demonstrated, good performance of step changes in P, Q shown, and relevant variables monitored (primary current, secondary current, rotor speed, and sector information) .

For a synchronous speed of 750 rpm, the results of active power performance testing are shown in Figures 33 to 35, and the results of reactive power testing are shown in Figure 36 to 38.

Referring to Figures 39 to 50, for super-synchronous mode the results of active power performance testing are shown in Figures 39 to 44, and the results of reactive power testing are shown in Figures 45 to 50.

It will be appreciated by persons skilled in the art that the above embodiment has been described by way of example only, and not in any limitative sense, and that various alterations and modifications are possible without departure from the scope of the invention as defined by the appended claims. For example, although the specific

embodiment described above has secondary windings on the stator, the secondary windings could be provided on the rotor instead.

Claims

1. A controller for a doubly fed electrical machine

comprising : - a stator;

a rotor;

wherein the rotor is located in said first and second rotating magnetic fields in use and is adapted to interact therewith to generate a magnetomotive force;

wherein the controller is adapted to receive current and voltage signals from at least one said set of first electrical windings to determine real and/or reactive power of said first windings, compare said real and/or reactive power with reference values, and apply third electrical signals to at least one said set of second electrical windings to adjust said real and/or reactive power of said first windings.

2. A controller according to claim 1, wherein the controller is adapted to apply at least one respective third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

3. A controller according to claim 2, wherein the controller is adapted to apply, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings .

4. A controller according to any one of the preceding claims, wherein the third electrical signals are adapted to increase and/or decrease reactive power in at least one said set of first electrical windings by increasing and/or decreasing magnetic flux in at least one said set of second electrical windings .

5. A controller according to any one of the preceding claims, wherein the third electrical signals are dependent on a phase difference between the magnetic flux in at least one said set of second electrical windings and the magnetic flux linking said first and second electrical windings.

6. A double fed electrical machine comprising:

a stator;

a rotor;

at least one set of first electrical windings mounted to the stator and adapted to receive first electrical signals to generate a first rotating magnetic field;

a controller according to any one of the preceding claims .

7. A method of controlling a doubly fed electrical machine comprising:

a stator;

a rotor;

the method comprising:

comparing said real and/or reactive power with

reference values; and

8. A method according to claim 7, further comprising applying at least one respective said third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

9. A method according to claim 8, further comprising

applying, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective said third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings.

10. A method according to any one of claims 7 to 9, wherein the third electrical signals are adapted to increase and/or decrease reactive power in at least one said set of first electrical windings by increasing and/or decreasing magnetic flux in at least one said set of second electrical windings.

11. A method according to any one of claims 7 to 10, wherein the third electrical signals are dependent on a phase difference between the magnetic flux in at least one said set of second electrical windings and the magnetic flux linking said first and second electrical windings.

12. A computer program adapted to be run on a computer to carry out a method as defined above, the computer program comprising :

third computer code executable to apply third

13. A computer program according to claim 12, wherein the third computer code is executable to apply at least one respective said third electrical signal for each of a plurality of sectors of rotation of said second rotating magnetic field.

14. A computer program according to claim 13, wherein the third computer code is executable to apply, for each of a plurality of said sectors of rotation of the second rotating magnetic field, a respective said third electrical signal causing increase or decrease of real power and/or causing increase or decrease of reactive power in at least one said set of first electrical windings.