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PHASE SHIFTING TRANSFORMERS AND QUADRATURE BOOSTERS
To control the power flow in an interconnected network it is sometimes necessary to use a phase shifting transformer. For example, in the network shown in FIG. 15(a) there are two routes for the flow of load current passing from substation A to substation B. If no external influences are brought to bear then the load would divide between the two alternative routes in inverse proportion to their impedances, or, expressed algebraically:
(a) Flow of load current from A to B determined by line impedances
(b) Additional imposed voltage, ?V, at substation A
gives rise to circulating current, iX
FIG. 15
where i is the total load current flowing between A and B and i1, i2, z1, z2 are the currents and impedances respectively in the lines as denoted by the appropriate suffixes.
However, if it is required that the load current should split in some proportion other than the inverse of the route impedances; perhaps the rating of line 1 is twice that of line 2 but its impedance only 75 percent of the line 2 impedance; then it is necessary to increase the current in line 1 by some quantity ix and reduce that in line 2 by the same amount, so that
where the new currents, i _ 1 and i _ 2 are in the required proportion, in this case i_ 1/i_ 2 _ 2.
As will be seen from FIG. 15(b) the current ix may now be regarded as a circulating current flowing around the system superimposed on the load cur rents determined by the line impedances. To cause this current to circulate requires a driving voltage ?V such that
and since the impedance (z1 + z2) is largely reactive, the voltage delta V will need to be approximately in quadrature with the line current. This quadrature volt age can be provided by the installation in the system of a suitably connected transformer. The most appropriate location for this transformer depends on the voltage profile around the system; it might be necessary to provide delta V/2 at each of the substations. The transformer, or transformers provide the necessary phase shift, or quadrature voltage, around the system to drive the required equivalent circulating current. They are thus known as phase shifting transformers or quadrature booster transformers.
In order to provide a voltage in quadrature with the line voltage the phase shifting transformer has its primary windings, or shunt windings, connected between phases of the transmission line. By interconnecting the phases as shown in FIG. 16 the transformer secondaries, or series windings, will have their output voltages at 90º to the primary phase voltages. The series windings need only consist of regulating windings with on-load tapchangers so that the amount of phase shift can be varied to suit load transfer requirements. In FIG. 16(a) the tappings are arranged in linear fashion so that the phase shift has variable magnitude but is always in the same sense (FIG. 16(b)). If the tap pings are connected in a buck/boost arrangement as shown in FIG. 16(c) then the phase shift may be positive or negative (FIG. 16(d)).
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FIG. 16 Arrangements of quadrature booster
Phasor diagram for one phase of booster in diagram (a) (b)
Basic connections of quadrature booster upper diagram shows arrangement in its functional form while physical configuration is shown in lower diagram (a)
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FIG. 16 (Continued)
(c) Workable arrangement of quadrature booster with tapped winding connected in buck/boost (d) Phasor diagram for one phase of arrangement in diagram (c)
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FIG. 17 Arrangement of 400 kV, 1200 A booster to provide a phase shift
of +/- 18º
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The arrangement shown in FIG. 16(c) represents a workable quadrature booster configuration, however it has disadvantages. The series winding is totally exposed to the transmission network conditions and, since most system interconnections operate at voltages of at least 400 or 500 kV, this represents a particularly onerous duty for a regulating winding and tapchanger, both of which would require insulating for up to 500/_3 kV to ground as well as meeting the appropriate lightning and switching impulse withstand requirements.
The most common arrangement of quadrature booster is therefore as shown in FIG. 17. This consists of two separate components having separate three phase cores. For all but the smallest units these will be housed in two separate tanks and, since by their very nature system interconnectors tend to have ratings of several hundred MVA, this means that separate tanks are normally provided. The advantage of this arrangement is that by isolating the regulating winding from the system this can operate at a somewhat lower voltage to ground as well as only needing to withstand surges transferred from the line rather than directly on its terminals. The voltage ratio of the open-delta/delta-connected series transformer can also be selected to enable the unit to be optimized to match the voltage and current capability of the available tapchanger.
For the purpose of illustration it is possible to put some typical values on the booster arrangement of FIG. 17. This might be required to provide a phase shifting capability of +/- 18º on a 400 kV transmission line having a current rating of 1200 A. The tangent of 18º is 0.325 so that the series winding must pro duce a maximum quadrature output of 0.325 x 400 _/3 = 75 kV. With a rated current of 1200 A, the series unit will have a three-phase rating of 3 x 75 x 1200 = 270 MVA. (Note that this unit has its output winding in open delta so that 75 kV and 1200 A are the respective phase voltage and current. The three phase unit thus has a rating of 3 times the product of these phase quantities, and no _/3 factor is involved.) A typical current rating of tapchanger which might be considered for such a unit is 1600 A. If maximum use is to be made of tapchanger current capability, the open-delta/delta series transformer must have a voltage ratio such as to produce this line current from the delta winding, that is the delta winding must have a phase current of 1600 _/3 = 924 A and hence a phase voltage of 97.4 kV. Connecting the regulating windings in star means that each phase must have a total all-taps-in voltage of 97.4 _/3 = 56.2 kV. This represents the maximum voltage across the range for the tap changer and based on an 18 step, 19 position, tapchanger is equivalent to 3120 V per step. These values are just about on the limit of the capability of a commercial 1600 A tapchanger. The rating of the shunt transformer will be 3 x 56.2 x 1600 = 270 MVA, and the combined rating of the complete unit will be 540 MVA. At full output for the series winding the shunt winding will draw a current (270 _/3 x 10^6 )/400 000 = 390 A from the 400 kV system.
It should be noted that the figure of 18º phase shift assumed for the above example is an open circuit value and would be reduced at full load due to regulation. The impedance of the series unit adds to the system impedance to determine the fault level on the system and thus must be set to meet system requirements. The impedance of the shunt unit will vary considerably between the all-taps-in and the all-taps-out condition, but it has very little effect on the system fault level and so the lower it can be made the less will be the effect of its variation on the overall impedance variation of the unit. The fault infeed for faults on the interconnections between shunt and series units is effectively limited only by the supply system impedance plus their respective impedances acting in parallel. This will therefore be very high and the design should be such as to make the likelihood of phase-to-phase faults on these connections as low as possible. If the units are in separate tanks one way of achieving this is by enclosing the connections in gas-insulated bus ducting. Alternatively oil-filled phase-isolated trunking may be used. The series transformer, in particular, requires a very large number of very high voltage connections and if some of these are gas-insulated or enclosed in oil-filled trunking this enables the terminal spacing to be reduced and thus reduces the overall space required on the tank for connections.
Testing
Testing large quadrature boosters presents particularly difficult problems for manufacturers. Shunt and series units need to be erected in the test bay which generally means that the available space is stretched to the limit. The large number of interconnections, particularly those across phases, mean that lightning impulse voltage distribution and the transfer of surge voltages between windings is difficult to predict with accuracy so that the manufacturer will wish to have confirmation of his design calculations at the earliest opportunity. It is likely, therefore, that he will wish to connect up the units in air in order to carry out recurrent surge oscillograph (RSO) measurements before these are installed in their tanks.
When the units have been installed in their tanks and filled with oil the RSO measurements will be repeated. To provide access to those interconnections which are enclosed, it may be necessary to install additional temporary bushings. It will also be necessary to have access to these interconnections in order to make resistance measurements for the temperature rise tests.
To carry out the temperature rise test a short-circuit may be applied to each of the open-delta phases of the series transformer and a supply connected to the regulating windings on the shunt transformer which must be at the all taps-in position. A current can then be circulated through both transformers of sufficient magnitude to generate full-load losses, that is no load plus load losses in each of the two transformers. Because of the differing requirements between shunt and series transformers as regards impedance and insulation requirements it is unlikely that their core sizes will be the same and so their no-load losses will differ. This means that supplying all the losses as copper losses in this way will result in some inaccuracy in the measured top oil temperature rises. Loss distribution on test will, however, be within a few percent of the correct figures so that the measured top oil rises can be corrected in accordance with the EN 60076-2 procedure with very little error.
FIG. 18 2000 MVA, 400/400 +/- j80 kV quadrature booster on final test
For the induced overvoltage test the booster can be supplied with the test generator connected to the regulating winding in the same way as for the temperature rise test. Alternatively it is possible to provide an additional winding on the shunt transformer which is used solely for this purpose. Lightning impulse and switching surge tests may be applied to all winding terminals as a test of the dielectric integrity of the individual windings but in addition it is usual to apply an impulse and switching surge test to both output winding terminals (i.e. source and load terminals) of the series transformer connected together as a simulation of service conditions. FIG. 18 shows a large quadrature booster erected for test in the factory.