Three Winding Transformer. By G. K. KAISER (Transformer Engineer, Mitsubishi Denki-Kabushikikaisha.) Abstract. Three winding transformers afford many advantages on large power systems and their use has become widely extended in recent years. Originally designed to eliminate insulation strains when operating on the star-star connection the third winding is now frequently used to supply power in the interchange of energy between two transmission lines, and for power factor correction of long high voltage lines by means of synchronous condensers. A number of concrete examples are given. A brief discussion follows of the inherent charact,rristics of three winding transformers with regard to short circuit stresses and voltage regulation; some of the limitations are indicated. In conclusion the superiority of the three winding shell type over the core type is pointed out. Many of the large power transmission companies have found it very convenient to use three winding transformers on certain portions of their systems r,,a account of the resultant improvement in the economy and the increased flexibility of operation of the transmission lines. In this article we shall briefly discuss a number of applications of the three winding transformer, and also some of the limitations in the design of this type of apparatus. The first applications of the third winding in power transformers was as an auxiliary winding in units having both high voltage and low voltage windings connected in star. Such transformers are frequently used on account of the reduced initial cost as compared with the equivalent delta-delta connected transformers of the same voltage. The saving is more evident the higher the voltages and the lower the rated output of the transformers, and is mainly due to the better space factor of the copper wire having the larger cross section, and also due to the reduced voltage stresses between the individ ual coils and between adjacent winding groups. The addition of the auxiliary winding increases the cost only slightly, as it is usually designed for low voltage. The cost of the third winding is considerably less than the amount of the saving previously mentioned. The necessity for such a winding will appear from the following. It is well known that a sine form flux wave is produced by an exciting current with a distorted wave shape, caused by the variation Paper to to read before the meting of the Kansai Local section.
Three Winding Tran former in the permeability of the iron of the magnetic circuit with changing flux density. The most prominent component of this distorted exciting current wave is the third harmonic. Being of triple frequency it occurs as a single phase current in the three phase system. This current must be allowed to flow, since its suppression will lead to the appearance of a third harmonic voltage wave in the windings, which may greatly increase the dielectric strain on the insulation and may cause the transformer to break down. If the neutral of the transformer primary ieconneeted to the neutral of the generator without an intermediate resistance the current is able to flow and no excessive insulation stresses occur. But if we have star-star connected transformers with ungrounded neutral which is not connected to any other neu'ral in the system, then we must supply a closed winding within the transformer bank to enable this current to flow. This led to the introduction of the delta connected tertiary winding in power transformers. As the actual third harmonic current flowing in this delta tertiary is rather small, many operating companies fount it convenient to use the winding for auxiliary power, either for station lighting or for other small power requirements. In time the size of the tertiary winding was increased so that in many cases the tertiary has a rated output equal to that of either of the other two windings. There has thus been developed a variety of applications of the three winding trasformer, when all three windings are used for power purposes. Some of these are enumerated below: (1) Primary receiving power, both secondaries delivering power, usually at different voltages. (2) Secondary delivering power received from two primaries supplied by two transmission line, usually at different voltages. (3) Power transferred in either direction between two transmission lines by means of an interconnecting auto-transformer. The third winding, which is indispensible in this case, can be i sed for local power distribution. (4) Step down transformer at end of transmission line with third winding supplying synchronous condenser for power factor correction and voltage regulation. As an example of the first group we might have a 5000 KVA three phase transformer designed with a 66000 volt, 5000 KVA primary windin One of the secondary windings would be designed for 22000 volt power distribution with a 4000 KVA rating, and the other for 2300 volt local distribution and 2000 KVA rating, The combined load on the two secondary windings must, however, not exceed 5000 KVA, the primary winding rating. sometimes a power transformer bank is lccated at a suistation supplied from two transmission lines operating at different voltages. Ordinarily there would be required two sepal ate banks of transformers with two different voltage ratings and with twice the KVA rating of the load to be delivered to the distribution circuit it must bo possible to supply, the entire load from either transmission line, By using, as
G.K. KAISER a three winding transformer we can effect a considerable saving in first cost of the transformers and at.the same time maintain the required flexibility of operation. As an illustration, one primary will have a 5000 KVA winding star-connected for 132000 volts, the other primary a star or delta connected 5000 KVA winding for 66000 volts, and the delta connected secondary will have a 22000 volt winding, also pith 50000 KVA rating. In such a transformer the 5000 KVA secondary load can be supplied by either primary winding alone, or by both windings combined in any proportion desired, depending on the voltage regulation of the two lines. Rapidly expanding power companies sometimes find it necessary to increase the line voltage of their main transmission lines in order to minimize the line losses resulting from the increase in the amount of power transmitted, If the voltage is doubled the amount of power to be transmitted can be quadrupled with the same percent line loss. However, it is not always feasible to change the high voltage windins of all the connected transformers to adapt them to the increased line voltage. In such a case an auto-transformer can be readily designed to step down the voltage of the new transmission line to that required for the existing apparatus, not only at a comparatively low cost but also with a very high efficiency of conversion, usually of the order of 99%. To illustrate. An operating company wishes to raise its main transmission voltage from 88000 volts to 154009 volts but does not desire to rewind its high voltage step down transformers for the new operating voltage. By placing an interconnecting auto-transformer between the 154 00 volt line and the 88000 volt line, all of the old apparatus can be continued in use without change. The autotransformer would be star connected on both sides with solidly grounded neutral to minimize the insulation stresses and in addition would be supplied with a delta connected tertiary winding. To show the saving effected by using an auto-transformer for this service, let us assume the amount of power to be transformed as 100000 KVA. Then the equivalent two winding transformer rating of the auto-transformer bank would be 43000 KVA. At a somewhat higher cost the tertiary winding can be designed to deliver power also, lot us say 25000 KVA at 44000 volts. This auto. transformer bank can therefore be operated un'er the following conditions ; (1) To deliver 100000 KVA at 154 to 83 KV (2) " " 25000 " " 154 " 44 " (3) " " 25000 " " 88 " 44 " The use of a three winding transformer at the end of a transmission line tc supply a synchronous condenser offers a distinct saving in the initial cost compared with separate banks of two winding transformers of the same total KVA rating at the delivery side. The tertiary winding supplying the condenser load at zero power factor leading does not greatly increase the size of the primary winding, as it is so far out of phase with the secondary winding. Also since the tertiary is usually designed for low voltage, it only molerately increases the weight and dimensions of the transformer. The application of such transformers to this service can perhaps
Three Winding Transformer best be illustrated by one or two actual problems. A 15000 KVA bank of transformers at the end of a transmission line has a tertiary winding which is connected to a synchronous motor generator set for power factor correction. The input to the primaries of the bank is to be limited to 15000 KVA at unity power factor. (a) If no load is being taken from the D. C, end of the set and the A.C. end draws 5000 KVA at zero power factor, what load can be delivered on the secondary side and at what power factor? Fig. 1 Since the primary is limited to 15000 KVA at unity power factor and supplies both secondary and tertiary windings, the out-put of the secondary will be 15800 KVA, and its power fac'or will be 95% lagging. This is a simple problem in geometry. As shoe n in Fig 1, we complete the third side of a right angle triangle of which the other two sides are both known. The power factor is the quotient of primary to secondary loads. (b) Assume a load of 1000 KW on the D.C. end and an efficiency of the set of 90%i also that the synchronous motor is drawing 4500 KVA from the line at leading power factor. How much power can be drawn from the secondary and..t what power factor without exceeding 15000 KVA on the primary? Fig. 2 Again the solution is by right angle triangles. The motor generator set draws 4500KVA of which 1110 KW represents actual energy at a power factor of 1110/4500
G.K. KAISER =24.7% leading. The reactive power will be 4369 KVA which combined with the 13890 KW available after supplying the motor generator set will give a secondary output of 14600 KVA at a power factor of 14.6/15=97.2% lagging. Three winding transformers have certain inherent characteristics which somewhat limit their application and these must be carefully considered in their relation to the transmission system. Many of the modern power sestems generate and. transmit power on such, a large scale that when a short circuit occurs on any part of the system, the amount of power feeding into the short circuit can be considered as practically unlimited. The connected apparatus must therefore be designed to be self protecting, that is, mechanically strong enough to withstand indefinitely the stresses sets up in the windings under short circuit conditions. In large power transformers this is frequently a serious problem as the mechanical forces developed are naturally very high. Their magnitude is determined largely by the internal impedance of the transformer which must of course not be too high, otherwise the cost of the transformer will be greatly increased and the regulation adversely affected. What has been said applies generally to two winding transformers, but the problem becomes rather more complicated in three winding transformers. The relation etween the impedances of the three windings is not a simple one and under bcertain conditions of short circuit the tertiary winding may carry moat of the short circuit current, if it is not properly designed. When we have a balanced three phase short circuit on the primary or secondary, all the power is supplied to the short circuit directly from the primary and secondary windings and thee is no short circuit current flowing in the delta tertiary winding. If on the other hand we have one of the lines grounded, that is, a single phase short circuit from line to neutral and power supplied.from both primary and secondary, then the tertiary serves to transfer energy from the supply circuits into the short circuit, and may carry a very heavy current. It is this cindition which must be carefully investigated in every case, and steps taken to design the tertiary winding in such a manner that this current will not be excessive. When three winding transformers are used to supply two secondary loads from one primary or to supply one secondary from two primaries it is necessary to determine the regulation under the different conditions. The regulation is not as simple a matter as in two winding transformers, but must be made in separate steps. The regulation some times even comes out as a negative value in one of the circuites which implies that there is a rise in voltage on that winding instead of a drop. For best regulation and proper tdivision of load under all operating conditions the tran - sformer should be designed for approximately equal percentage reactance between all three pairs of windings. This is accomplished by thoro inte lacing of all the coils of the different circuits, as only in this manner can the reactances be equalized shell type transformer construction is especially well adapted, for meeting this requirement as the windings consist of a number of thin flat pancake coils assembled on a central core and can be interlaced to any desired degree.. The
Three Winding Transformer The concentric cylindrical core type transformer on the other hand has the inherent disadvantage of an inflexible arrangement of windings, no interlacing of the coils being feasible. The secondary winding is usually placed between primary and tertiary and the reactance of these two pairs of windings can therefore be controlled to some extent. However the reactance between primary and tertiary is proportional largely to the sum of the other two reactance values and is therefore usually too high for proper load distribution between the windings.