J. A. Domínguez Vázquez, I. Valle González,
S. Lorenzo Matilla, J. M. Ruiz González.
Dpto Tecnología Electrónica. - E.T.S.I.I.
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Abstract Usually loads attached to AC/DC converters are unbalanced and/or variables, preventing the application of Oriented Field Theory (O.F.T.) and loosing its advantages. In this paper, a possible solution is exposed.
Actually the two cases aren’t going to modify substantially the system, although it will change the regulator’s control strategy.
In the case (a) (see next scheme), the target is to feed the unbalanced load with a constant voltage and frequency.
I.- Introduction.
Loads attached to AC/DC converters are sometimes unbalanced and/or variables. As it’s known, to apply O.F.T., it’s necessary a balanced load to simplify a three-phases AC system to a one - phase DC one. The basic idea, that is exposed in this paper, is to consider a three-phases balanced load which allows an easy application of O.F.T. and the unbalanced load considered as perturbations, compensated by a controller. The threephases balanced load is the appropriate to keep a reference voltage and not to consume active power.
II.- Modeling.
As it has been mentioned before, the balanced load that is needed for the control is compound by three capacitors, attached in parallel to the unbalanced load getting the two targets: it’s possible to apply O.F.T
because it is balanced and it doesn’t consume active power.
There are two cases to consider: a.-) converter attached to the power line.
b.-) converter not attached to the power line.
Vd
C C C z1 z2 z3
The unbalanced load is named as z1, z2, z3 and the balanced one are the capacitors named as C.
Applying O.F.T. to the capacitors, high value capacitors to get a low time response system, and avoiding momentarily the unbalanced load, it can be obtained:
Is where the voltage vector Vs coincides with the active component axis "d". Thus it’s easy to obtain the

next expression for Is, w and C, every of them O.F.
magnitudes:
I sq
= C · w · V s
· q
I sd
= C · (s V s
) · d where q is the reactive component axis unitary vector.
As we have considered the load as a perturbation, it is only necessary to control the next parameters:
*.- The required unbalanced load power.
*.- The voltage and the frequency.
The next scheme shows how to make it:
This is the theoretical modeling, but in a real case, the system needs the presence of inductances to control the current’s slopes. Then, the real implementation is as it’s shown in the next page, where “L” represents the inductances and the unbalanced load is connected by a transformer with neutral point attached. to battery. .
The inductances and the capacitors, actually, are an L-C filter to conform the currents and voltages that the converter injects to the load.
The presence of them, hardly modify the control.
Only a regulator for I sd
is needed to maintain the V sq
in zero value.
L z1
L
L z
2 z3
C C C
Vs1
Vs2
Vs1
Vq
.
O.F
Vd
Vd*
1 / s
p k/s
i1*
Id*
Iq*
.
-1
O.F
i2*
i3*
iL1 iL2 iL3 i1 i2 i3 w (fixed)
A control of the phase voltage it’s made in O.F.
with a appropriate regulator, so it’s possible to consider it a constant value. The high capacity capacitors will provide an slow time response for the voltage to face the instantaneous consumptions, also faced by the Id* regulator, faster time response than the Iq* one.. This provides the references currents *i1, *i2, *i3 that feed the capacitors which maintain the phase voltage. The consumed currents (measured) by the unbalanced loads iL1, iL2, iL3 will be the perturbations that added to the first references currents will compose the real currents references I1, I2, I3. These currents will control the converter in "sliding" mode.
Obviously, the regulator for the I sq
has an integrator part only, and the regulator for the I sd
is only a proportional one, faster than the first one.
A simulation is shown on the next pages, after several cycles .
The parameters used in the simulation are: w = 50 Hz. ; Wc = 7500 Hz;V phase = 127v.
L = 0.1 mH. ; C = 1500 uF. ;
Z1 = 1 Oh + 1 mH ;
Z2 = 10 Oh + 0.5 mH ;
Z3 = 1K Oh + 0.01 mH; and 13.33 10
-6 seconds as time control. It has been estimated considering the use of an DSP to control the converter and to calculate all the algorithm, for example the DSP32c of AT&T, can make it.

The figures 1, 2 represent the start of the system:
In spite of it, with the decreasing of I d
* this effect disappears.
figure 1 figure 4
In the next three cycles, figure 5, the system has already corrected this effect and is going to the permanent.
figure 2
In the figures 3 it is shown the permanent response after 60 cycles from the start: figure 5
The stationary state is got in the next 6 cycles.
The three last of them are shown in the figure 6, on next page.
figure 3
In the next cycles, the unbalanced load is attached to the system. This is done at the half time of the interval.
The response is instantaneously. The I sd
regulator reacts quick facing the new consumptions. The voltage is always between the 90% an the 110% of reference voltage. Notice the good transient.
the rising of I d
* causing the appearance of a continuous voltage.
It’s remarkable the creasing of V q observed
due to figure 6

figure 7:
In the next 3 cycles, the permanent is reached, The filter L-C proves its utility when these currents are compared with the ones that circulate by the capacitors, showed in figures 1 to 7 for the phase 1, graphic named as “CAP. CURR.”.
figure 7
The next three figures 8, 9 and 10 show the phase currents and voltages in detail in the permanent response.
figure 10
The system’s response is good and without any troubles, when the loads are disconnected. The filter L-C has to be designed carefully for it.
The results confirm, as it had been supposed, that the system is an instantaneous time response one.
Other configurations for the balanced load are still in study.
figure 8 figure 9
In the case b), converter attached to the power line only the strategy control changes and the new target now, could be to give a determined reference of active power to the power line. This is the new scheme, shown below:
+
Vcc
Icc
i1 i2 i3
C C
ic3 ic2 ic1 iL1 iL2
C iL3
Z3 Z2 Z1 iR1 iR2 iR3
Power Line
It’s possible to make two different possibilities in it:
*.- The converter feeds the unbalanced load or not.
*.- The converter feeds the capacitors or not.
factor.
The last chance depends on the desirable power

This is the control scheme, see next figure: vs1 vs2 vs3
3/2 e jp
Vsq=0
Vsd
C.w
Isq
("fixed") w.t
2/3 e
-jp
* i1
* i2
+
* i3
+
+ i1 i2 i3 iL1 iL2 iL3 w
(power line)
So if it is wanted to feed the capacitors, it’s the
Isq the parameter that, according to the phase voltage, will supply the reference. If the unbalanced loads were feed from the converter iL1, iL2, iL3 will be added to the references currents as perturbations. So the currents iR1, iR2, iR3, will be actives currents, Isd in O.F.
III.- Conclusions
This system is a causal one because the current consumption in the unbalanced load is provided by the reference voltage imposed in the capacitors, working all the system as the usual power line. Besides the system is an instant time response one when the voltage regulators are fast enough and the capacitors have high capacity to face the instant consumptions generated by the variables loads.
Any power line observer method has been omitted in this paper although it is necessary to obtain the voltage and the frequency for the last case. This case
(b) is easier to control than the first one, case (a), because of the voltage regulator is not fundamental for the good system’s performance