István Schmidt, Károly Veszprémi
Budapest University of Technology and Economics Department of Electric Power Engineering
The circuit diagram of the converter-fed synchronous motor (CFSM) drive is given in Fig.9.1. Here all of the converters: the line-side ÁH, the motor-side ÁM and the excitation-side ÁG converter operate with line commutation. The line commutation of the thyristors in ÁM is possible, while the overexcited synchronous machine can provide the reactive power necessary for the commutation. In ÁM the commutations are done by the subtransient voltages of the SZ synchronous machine, that is why this commutation is called machine (load) commutation also. The supply is current-source-type, caused by the DC filter choke Le.
The converter ÁM can be controlled to rectifying and to inverter mode, so in spite of the unidirectional DC current mean value (Iek>0) the CFSM is capable of motor and generator mode operation. In motor mode ÁH is a rectifier, ÁM is an inverter, the mean value of the DC voltage is negative: Uek<0. In generator mode the converter modes are exchanged, consequently: Uek>0. Reversing the phase sequence of firing the thyristors of ÁM bidirectional rotation in driving and braking mode is possible (4/4 quadrant operation).
Fig.9.2. shows the block diagram of the flux and speed controlled CFSM. αh firing angle is the acting signal of the speed controller, αg firing angle is that of the flux (excitation) controller. Usually both controllers have subordinated current control loop. The α firing angle of ÁM is set by a self-controlled firing controller operated from signals of the synchronous machine SZ. By the self-controller the torque development can be optimized in motor (M) and generator (G) mode.
From the DC sides of converters ÁH and ÁG the self-controlled ÁM CFSM (the dotted-line surrounded part of Fig.9.2.) looks like a DC machine. In a real DC machine only ue and ug can be modified, the modification of the brush rocker position corresponding to the firing angle of the machine-side converter (α) is not used for this purpose. In a CFSM the excitation must be controlled always, because of the large armature reaction of the synchronous machine.
Assuming ideal, zero resistance (Rr=0) rotor winding, for a given excitation current ig zero rotor voltage is necessary: ūr=0. In this way in wk=w coordinate system the (3.6.c) rotor voltage equation is the (3.6.d) rotor flux equation is . This is the principle of the so called flux constancy: the resistanceless short-circuited coil does not allow the variation of the flux linked with it. So in every operating point the subtransient flux vector linking with the rotor winding is constant. In stationary coordinate system (wk=0) the subtransient flux vector and the corresponding induced voltage vector are (assuming constant speed operating point: w=dαr/dt=const., αr is the angle of the rotor):
It means, that in steady-state both and ū” rotate with W=W1=2πf1 rotor/fundamental angular speed and their amplitudes (Ψ” and U”) are constant. Selecting t=0 instant to the positive maximum of ua”:
The stator voltage equation in stationary reference frame (3.6.a) considering (3.7) is:
Using (9.3) the equivalent circuit of CFSM can be drawn (Fig.9.3). Comparing with Fig.2.7. high similarity can be found with R→Rt, L”→Lt, ua”→uta substitution.
In the ÁM motor-side converter according to the 6 thyristors the commutation frequency is variable: 6f1 since the fundamental frequency is variable. Considering ideal thyristors, smooth DC current (ie=Ie) and R=0 stator resistance the classical line-commutated converter theory with overlap for steady-state can be applied (the overlap must be considered, since L” is much greater -with one order- than Lt). This theory gives the following expressions for the DC voltage and current mean values:
Where . The α firing angle, the κ extinction angle (δ=κ-α is the overlap angle) and the μ=180o-κ commutation-reserve angle are related to the subtransient voltage. Fig.9.4.shows the vectors of the terminal voltage (ū), the subtransient voltage (ū”) (9.2.b) and the current (ī) in inverter mode operation. The 60° sector started with the firing of the NC thyristor is drawn in bold. Using (9.3) (and approximation R=0) the derivative of the current vector (ī) is:
E.g. this is the speed of the current vector movement during the commutation NB→NC from point 1 to point 2. Considering the L”dī/dt vector movement speed, the control limits of the thyristor NC (B: firing ON limit (α=0º); K: extinction limit (µ=0º)) are marked on ū”. In generator/rectifier mode the drive can operate at the firing ON limit: α=αmin=0o also. In motor/inverter mode for the sake of safety the extinction limit (κ=κmax=180o) must not be reached, only maximum κmeg=160o extinction angle is allowed approximately.
In steady-state, neglecting the losses the Pmk mechanical power is equal to the mean values of the Pℓk air-gap power and the Pek DC link power (in motor/inverter mode: Pmk>0, Pek<0):
Using (9.4) and (9.6) the mean values of the speed and the torque can be expressed:
The maximal torque is developed by the CFSM at κmax=180o extinction limit in motor mode, and at αmin=0o firing ON limit in generator mode. Using (5.9, 5.10) the expression of the torque is:
According to (8.2.b) the amplitude of the fundamental current (I1) is proportional to the DC current (ie=Ie) with good approximation:
With given Ψ” and I1 the maximal Mk is at ϑ1=±90o torque angle. Fig.9.5. shows Mk/Mn relative torque (referred to Mn=(3/2)ΨnIn nominal torque) vs. I1/In≌Ie/Ien (where ). Besides the machine (load) commutation operation limits of ÁM (αmin=0o-os and κmax=180o) the safe motor/inverter mode limit curve is also drawn (κmeg=160o extinction angle). It can be established, that similarly to the separately excited DC machine the torque is proportional to the DC current. In motor mode: Mk=KMIe, in generator mode: Mk=KGIe, KM>0, KG<0. In the shaded areas the drive can operate only with forced commutation (VSI or CSI supply). A given Mk torque should be developed with the possibly minimal I1 current. For the CFSM it requires a two-stage self controlled firing controller, which provides κ=κmeg operation in motor/inverter mode, and α=αmin operation in generator/rectifier mode. In practice the controls from the position of the shaft (α) or from the position of the subtransient flux vector (αψ”) are used. The former is called: firing control from the shaft, the later: firing control from the flux.
The firing controller from the subtransient flux vector results in field-oriented firing control. Fig.9.6.a. presents the block diagram, Fig.9.6.b. shows the firing levels (for w>0 and a,b,c phase sequence). The flux vector is provided by stator machine model (detailed in Fig.5.14), the αψ” angle and the ψ” amplitude are provided by the blocks ARC and AMPL respectively. The M/G motor/generator two-stage signal changes the comparing levels according to the κmeg and αmin operation modes. In motor mode to the κ=κmeg=const. extinction angle a operation point dependent firing angle is corresponding (α=κmeg-δ). Therefore in this case the Δ signal of the FG function generator corrects the firing comparing levels using the load dependant input value Ie (in field-weakening more accurately Ie/ψ”). The firing control from the subtransient flux vector is identical with the firing control from the subtransient voltage vector, since e.g. at w>0: αu”=αψ”+90°.
More practical to fire from , since it moves on a more smooth path than the voltage vector, and its amplitude in the normal range is constant, while the amplitude of ū” is proportional to w. The firing from the shaft position (α) has larger load dependency in motor/inverter mode, and Δ correction is necessary in generator/rectifier mode also.
Fig.9.7. shows the current vector loci in coordinate system fixed to the flux vector (field coordinate system) with field-oriented firing control and machine commutation, assuming smooth DC current (ie=Ie). The marked amplitudes and angles come from Fig.9.4.; Fig.9.4.a. and Fig.9.7.b. correspond to operation point with κ=κmeg=160° and approx. nominal motor mode I1 current. In this case approx. ϑ1=120° can be reached as best torque angle.
It can be proved, that in the range R>WL” the safe machine commutation is not possible. The border angular speed is:
With the usual machine parameter it is reached at f1h≌5Hz. In the W<Wh, f1<f1h range step commutation is used. Since in this case fh/f1>50 Hz/5 Hz=10, so there are at least 10 firings in ÁH between two firings of ÁG. Consequently in this case the commutation can be done by ÁH, by controlling the current vector to zero in every 1/6th machine period (Fig.9.8.a.). The step commutation using the ī=0 current vector can be made faster, if during the commutation the TE thyristor connected parallel with Le (Fig.9.1.) is fired ON. Therefore the current flowing in Le can remain unchanged (ie=Ie) during the commutation, only the motor current must be reduced to zero, and then must be increased back to Ie. There is not a limit for the phase angle of Ī1 in step mode, so the torque angle in motor mode can be ϑ1=90°, in generator mode ϑ1=270°(-90°) also (Fig.9.8.b.,c).
In the range W>Wn, f1>f1n field weakening must be applied. In this case the amplitude of the subtransient flux vector must be controlled in the following way approximately:
Fig.9.9. presents the possibly covered operation range, assuming 4/4 quadrant and field weakening operation on the W(Mk) plane. In the step commutation range there is not continuous operation usually.
Let’s mention, that the largest variable speed drive in the word is a CFSM. This 101MW drive is used for a fan of a wind tunnel of the NASA. This huge wind tunnel is used for aerodynamic investigations of supersonic aircrafts.
If a cage rotor induction machine is made resultantly capacitive by parallel capacitors (Fig.8.7) it is also capable of operating from line commutated converter (Fig.9.1.). This so called capacitively compensated converter-fed induction machine is capable of operating in narrow frequency range only, that is why it is rarely used only.