Survey

Document related concepts

Analog-to-digital converter wikipedia, lookup

Television standards conversion wikipedia, lookup

Operational amplifier wikipedia, lookup

Valve RF amplifier wikipedia, lookup

Schmitt trigger wikipedia, lookup

Josephson voltage standard wikipedia, lookup

Oscilloscope history wikipedia, lookup

Resistive opto-isolator wikipedia, lookup

Power MOSFET wikipedia, lookup

Opto-isolator wikipedia, lookup

Voltage regulator wikipedia, lookup

Surge protector wikipedia, lookup

Current mirror wikipedia, lookup

Integrating ADC wikipedia, lookup

Switched-mode power supply wikipedia, lookup

Transcript

Vector Controlled Doubly Fed Induction Generator for Wind Applications Dr. Ani Gole, Dept. of Electrical and Computer Eng., University of Manitoba. This document discusses the theory of operation behind the doubly fed generator case developed by Ani Gole (Univ. of Manitoba, Canada) and Om Nayak (Nayak Corporation, Princeton, NJ). The controller concept is based on the paper by Pena et al [1]. Description of Rotor Current Generation Circuit (Generator PWM Converter and Controls) CTRL GENERATOR PWM Converter & Controls W S a b c a b c IM GRID PWM Converter & Controls a b c ira,irb,irc A A Isa B Isb TL Va B Vb C C Isc Vc 13.8 kV, 500 HP INDUCTION GENERATOR Fig 1: Doubly Fed Induction Generator The Doubly fed induction generator/motor allows power output/input into the stator winding as well as the rotor winding of an induction machine with a wound rotor winding. Using such a generator it is possible to get a good power factor even when the machine speed is quite different from synchronous speed. Such machines can therefore operate without the need for excessive shunt compensation. The rotor currents (ira,irb,irc) of the machine can be resolved into the well known direct and quadrature components id and iq. The component id produces a flux in the air gap 1 which is aligned with the rotating flux vector linking the stator; whereas the component iq produces flux at right angles to this vector. The torque in the machine is the vector cross product of these two vectors, and hence only the component iq is contributes to the machine torque and hence to the power. The component id then controls the reactive power entering the machine. If id and iq can be controlled precisely, then so can the stator side real and reactive powers. The procedure for ensuring that the correct values of id and iq flow in the rotor is achieved by generating the corresponding phase currents references ira_ref, irb_ref and irc_ref, and then using a suitable voltage sourced converter (VSC) based current source to force these currents into the rotor. The latter action is straightforward and can be achieved using current-reference pulse width modulation (CRPWM) or other technique. The crucial step is to obtain the instantaneous position of the rotating flux vector in space in order to obtain the rotating reference frame. This can be achieved by realizing that on account of Lenz’s law of electromagnetism, the stator voltage (after subtracting rotor resistive drop) is simply the derivative of the stator flux linkage a as in eqn. (1) which is written for phase a. va ia Ra d a dt …….(1) The control structure shown in Fig. 2 can thus be used to determine the location (s) of the rotating flux vector. Isa * 0.467 Isa * 0.467 Isa * 0.467 Identification of main stator flux by integrating stator voltage after removal of resistive drop. The washout filter removes any dc component from the integrated flux without significantly ffecting the phase D + Va C 1 sT A alfa D + Vb C D + Vc C Valfa B 3 to 2 Transform beta Vbeta C 1 sT sT G 1 + sT sT G 1 + sT phisx X Y Y mag r to p X Vsmag phsmag phi phis phisy Very important signal present location ==> of rotating stator flux phis C Ra + D - rotor_angle in Angle out Resolver slpang determining the relative difference between stator flux and rotor position for resolving the rotor currents Fig 2: Determination of rotating mag. Flux vector location In Fig. 2, the three phase stator voltages (after removal of resistive voltage drop) are converted into the Clarke ( and ) components v and v , which are orthogonal in the balanced steady state. This transformation is given by: 2 v v v 1 1/ 2 1/ 2 a vb ……(2) 2 / 3 0 3 / 2 3 / 2 vc Integrating v and v, we obtain and , the Clarke components of stator flux. Converting to polar form 1 | | 2 2 , s tan ( / ) ……(3) The angle s gives the instantaneous location of the stator’s rotating magnetic field. In practical control circuits, as in Fig. 2, some filtering is required in order to rid the quantities and of any residual dc component introduced in the integration process. Now the rotor itself is rotating and is instantaneously located at angle r (labeled “rotor angle” in the figure). Thus, with a reference frame attached to the rotor, the stator’s magnetic field vector is at location s-r , which we refer to the “slip angle” slip. The instantaneous values for the desired rotor currents can then be readily calculated using the inverse dq transformation, with respect to the slip angle, as shown in Fig. 4. The equations for all transformations are shown in the appendix. Generation of current references slpang alfa Rotor to Stator Q beta D D and Q reference currents A alfa 2 to 3 B Transform beta C Ira_ref Iraa Irb_ref Irbb Irc_ref Ircc Fig. 4: Final step in generation of rotor phase reference currents Once the reference currents are determined, they can be generated using a voltage sourced converter operated with a technique such as current reference pulse width modulation (CRPWM) as shown in Fig. 5. The Appendix gives a short introduction to CRPWM. 3 10000.0 BRK T1 D1 T1 T1 D1 T3 T1 D1 T5 CR-PWM based Rotor-side converter V 1.0 Ecap Ecapref T2 D2 T6 T2 D2 T2 Irb Irc Erc Ira Era Erb T4 T2 D2 GA GB GC Current-Reference PWM Controls. Hysteresis band can be adjusted Ira Irb C Irc C + T1 T1 E Ira_ref C + + T3 E Irb_ref T5 E Irc_ref T4 T6 T2 CPanel hysband 10 ira_ref C + + hy * -1 ira_ref C + - E nhy 0 0.1 hy E hy Fig. 5: CRPWM Converter and Controller for rotor currents 4 Grid PWM Converter and Controls: As can be seen from Fig. 5, the rotor side VSC converter requires a dc power supply. The dc voltage is usually generated using another voltage sourced converter connected to the ac grid at the generator stator terminals. A dc capacitor is used in order to remove ripple and keep the dc bus voltage relatively smooth. This grid PWM Converter is operated so as to keep the dc voltage on the capacitor at a constant value. In effect, this means that the Grid side converter is supplying the real power demands of the rotor side converter. It is possible to operate this converter using a current reference approach used for the rotor side converter. However, as mentioned earlier, CRPWM has the drawback that the switching frequency and hence the losses are not predictable. Therefore, a feedback controller is used in which the error between the desired and ordered currents is passed through a proportional-integral controller which controls the output voltage of a conventional Sinusoidal PWM Converter. The advantage of the SPWM controller is that the number of switchings in a cycle is fixed, and so the losses can be easily estimated apriori. It is possible to control the d axis current by controlling the d-component of the SPWM output waveform and the q axis current via the q component. However, this leads to a poor control system response, because attempting to change id also causes iq to change transiently. Hence, modifications have to be made to the basic P-I controller structure so that a decoupled response is possible, and a request to change id changes id and not iq; and vice-versa. If a voltage sourced converter with constant dc bus voltage is connected to an ac grid through a (transformer) inductance L and resistance R, it can be shown that that: R R – ---- – ---- 0 d id L id 1 vd – ed L x1 + --= d t iq = L – eq R iq R x2 – – ---0 – ---L L vd – ed x1 = ------------------ + id L ed = – Lx1 + vd + Lid eq x2 = – ------ – iq L … eq = – Lx2 – Liq ….(4) Here v=vd is the voltage of the ac grid, and because this is chosen as the reference, vq is by definition, zero. Ed and eq are the d and q components of the generated VSC voltage. Eqn. 4 clearly shows that attempting to change id using ed will also cause a transient change in iq. If instead, we use the quantities Lx1 and Lx2 to control the currents, the resulting equations are decoupled. Using feedback PI control, we let the error in the id loop affect L x1 and in the iq loop, L x2 as shown in Fig. 6. 5 Vd=3.22 kV idref P D +F 3.266 B + D + Vdref1 F Lx1 I 1.6 i1d L i1q 1.6 * iqref D + F - P I L D - F Vqref1 Lx2 Fig 6: Decoupled Controller. In the selected circuit, the grid transformer rating is 4 kV (secondary) , 1 MVA with 10% leakage, giving an impedance L= 1.6 . Similarly a line-line voltage of 4 kV gives a line to neutral voltage of 4/kV, and as we are using peak quantities in the dq conversion, vd = (4/kVkV. The detection of the ac grid voltage reference angle and the generation of d and q components of current (as required in Fig 6) are done in a straightforward manner using a d-q transformation block as in Fig. 7. The selection of idref for the grid side converter is through the control circuit shown in Fig 8, which attempts to keep the capacitor voltage at its rated value by adjusting the amount of real power. The reactive power order is dialed in, but could have been generated by a similar controller whose objective would be to keep the ac voltage at some set point. If these reference voltages vdref1 and vqref1 (Fig. 6) are applied at the secondary of the transformer, the desired currents idref and iqref will flow in the circuit. The remaining parts of the controls are standard PWM controls. The control blocks shown in Fig 9 convert the above references to phase and magnitude, taking care to limit the magnitude 6 to the maximum rating of the grid side VSC converter. The reference for each of the three phase voltages is then generated by an inverse dq transformation. Ea A Detection of system voltage mag X r to p Valfas B 3 to 2 Transform Y Y X phi beta Vbetas C Va alfa Vb Ed Vsmag phi phivs Vc Detection of d-q components of currents. The washout filters remove dc components. Phase change of 0.01326 rad corrects washout filter phase error i1a i1alfa phi A i1a alfa i1b B 3 to 2 Transform beta C G mag mag sT X 1 + sT r to p sT Y Y G 1 + sT X i1c Y phi D + 0.01326 i1beta X alfa D Stator to Rotor Q beta p_to_r phi X Y i1d G 1 + sT i1d i1q G 1 + sT i1q F Fig 7: Generation of quantities required for the controller in Fig. 6 Kpcvc Ticvc P EcaprefD G 1 + sT Ecap + D - + I F idref + F Ecap G sT 1 + sT Fig 8: Voltage controller Fig.10 shows a standard sinusoidal PWM controller, in which each of the phase voltages is compared with a high frequency triangle wave to determine the firing pulse patterns. 7 Generation of PWM Reference Voltages mag_of_v mag mag X r to p phi X Vdref1 vdref Y Y Y phi X phi Vqref1 X Y A alfa Rotor to Stator Q beta D p_to_r vqref alfa 2 to 3 B Transform beta C Varef Vbref Vcref Magnitude Limiter Fig 9: Phase reference voltage generator 1.26 kHz SPWM Firing Pulse generator phi phi phi PWM and tri IGBT Firing tri Vamag Varef Control * 0.2 A Delay Comparator B T Delay T Vbmag Vbref * 0.2 A IGBT T Vcref A PULSES T3s Delay T * 0.2 T4s Delay Comparator B Vcmag T1s T6s Delay Comparator B T T5s Delay T T2s Fig 10: SPWM pulse generator Tests: The following tests can be conducted to check the operation. Set the generator on “speed Control”, i.e., the machine will run at the speed designated by the slider. This is realistic because any externally connected wind turbine model would interface to the machine module through the “speed signal”. Set the speed to 0.8 pu. Set idref=0.5 pu and iqref =0 pu for the rotor side converter and vref = 10 kV and iqref (Q order) for the grid side converter. Start the system. Observe that the powers are indeed 8 FIRING as expected. Increase idref (rotor converter) to 1 pu. The change should be effected without any change in the reactive power. Similarly change iqref to 0.3 pu. And observe that P does not change. Change machine speed to 1.1 pu., with (rotor side) idref=0.5 pu and iqref =0. Notice that the torque stays the same, but the power goes up with no change in reactive power. This is because keeping idref constant maintains constant torque, and so P is proportional to speed. Monitor grid side converter currents. Observe that the dc capacitor voltage remains fixed at its rated value and grid side currents are in phase with the ac voltage. References: 1) R. Pena, J.C. Clare and G.M. Asher, “Doubly fed induction generator using back to back PWM converters and its application to variable speed wind energy generation”, IEE Proc. Electrical Power Applications, Vol. 143., No.3., May 1996. Appendix A. Current Ref. PWM (CRPWM) Current Reference PWM allows for the generation of any arbitrary current waveform in an R-L load. As shown in Fig. A1, an upper and lower tolerance band is placed around the desired reference waveform for the current as in the above figure. If the actual current is below the lower threshold, the upper switch (T1/D1) is turned on which applies a positive voltage (E/2) to the load. The current in the source thus rises in response to this voltage. When the current rises above the upper threshold, the upper switch is turned off and the lower switch (T2/D2) is turned on. This applies a negative voltage (-E/2) to the load and causes the current to drop. Thus the difference between the desired and actual currents is kept to within the tolerance band. By making the thresholds smaller, the desired current can be approximated to any degree necessary. Note however, that there is a limit to which this can be done, because the smaller the threshold, the smaller the switching periods, i.e., the higher the switching frequency and losses. Using this technique, any given current waveform can be synthesized. A method that removes all harmonics can be constructed using the approach shown in Figure A1. This approach suffers from the drawback that the switching frequency is not predictable and can be very high making the circuit less attractive for larger ratings such as ac side filters. 9 E/2 E/2 Fig A1: CRPWM Controller and Waveforms B: Transform Equations: Clarke’s Transformation A A alfa alfa B 3 to 2 Transform beta C 2 to 3 B Transform beta C ( Forward (abc to Reverseto abc) a 1 1/ 2 1/ 2 b 2 / 3 3 / 2 3 / 2 0 c 0 a 1 b 1/ 2 3 / 2 (A1) c 1/ 2 3 / 2 Park’s Transformation theta theta alfa D Stator to Rotor Q beta alfa Rotor to Stator Q beta Forward (to dq) d cos( ) sin( q sin( ) cos( ) D Reverse (to dq) cos( ) sin( d sin( ) cos( ) q …….(A2) 10