transformer engineering design and practice 1_phần 4

2 Magnetic Characteristics The magnetic circuit is one of the most important active parts of a transformer. It consists of laminated iron core and carries flux linked to windings. Energy is transferred from one electrical circuit to another through the magnetic field carried by the core. The iron core provides a low reluctance path to the magnetic flux thereby reducing magnetizing current. Most of the flux is contained in the core reducing stray losses in structural parts. Due to on-going research and development efforts [1] by steel and transformer manufacturers, core materials with improved characteristics are getting developed and applied with better core building technologies. In the early days of transformer manufacturing, inferior grades of laminated steel (as per today’s standards) were used with inherent high losses and magnetizing volt-amperes. Later on it was found that the addition of silicon content of about 4 to 5% improves the performance characteristics significantly, due to a marked reduction in eddy losses (on account of the increase in material resistivity) and increase in permeability. Hysteresis loss is also lower due to a narrower hysteresis loop. The addition of silicon also helps to reduce the aging effects. Although silicon makes the material brittle, it is well within limits and does not pose problems during the process of core building. Subsequently, the cold rolled manufacturing technology in which the grains are oriented in the direction of rolling gave a new direction to material development for many decades, and even today newer materials are centered around the basic grain orientation process. Important stages of core material development are: non-oriented, hot rolled grain oriented (HRGO), cold rolled grain oriented (CRGO), high permeability cold rolled grain oriented (Hi-B), laser scribed and mechanically scribed. Laminations with lower thickness are manufactured and used to take advantage of lower eddy losses. Currently the lowest thickness available is 0.23 mm, and the popular thickness range is 0.23 mm to 0.35 mm for power transformers. Maximum 35 Copyright © 2004 by Marcel Dekker, Inc. 36 Chapter 2 thickness of lamination used in small transformers can be as high as 0.50 mm. The lower the thickness of laminations, the higher core building time is required since the number of laminations for a given core area increases. Inorganic coating (generally glass film and phosphate layer) having thickness of 0.002 to 0.003 mm is provided on both the surfaces of laminations, which is sufficient to withstand eddy voltages (of the order of a few volts). Since the core is in the vicinity of high voltage windings, it is grounded to drain out the statically induced voltages. If the core is sectionalized by ducts (of about 5 mm) for the cooling purpose, individual sections have to be grounded. Some users prefer to ground the core outside tank through a separate bushing. All the internal structural parts of a transformer (e.g., frames) are grounded. While designing the grounding system, due care must be taken to avoid multiple grounding, which otherwise results into circulating currents and subsequent failure of transformers. The tank is grounded externally by a suitable arrangement. Frames, used for clamping yokes and supporting windings, are generally grounded by connecting them to the tank by means of a copper or aluminum strip. If the frame-to-tank connection is done at two places, a closed loop formed may link appreciable stray leakage flux. A large circulating current may get induced which can eventually burn the connecting strips. 2.1 Construction 2.1.1 Types of core A part of a core, which is surrounded by windings, is called a limb or leg. Remaining part of the core, which is not surrounded by windings, but is essential for completing the path of flux, is called as yoke. This type of construction (termed as core type) is more common and has the following distinct advantages: viz. construction is simpler, cooling is better and repair is easy. Shell-type construction, in which a cross section of windings in the plane of core is surrounded by limbs and yokes, is also used. It has the advantage that one can use sandwich construction of LV and HV windings to get very low impedance, if desired, which is not easily possible in the core-type construction. In this book, most of the discussion is related to the core-type construction, and where required reference to shell-type construction has been made. The core construction mainly depends on technical specifications, manufacturing limitations, and transport considerations. It is economical to have all the windings of three phases in one core frame. A three-phase transformer is cheaper (by about 20 to 25%) than three single-phase transformers connected in a bank. But from the spare unit consideration, users find it more economical to buy four single-phase transformers as compared to two three-phase transformers. Also, if the three-phase rating is too large to be manufactured in transformer works (weights and dimensions exceeding the manufacturing capability) and Copyright © 2004 by Marcel Dekker, Inc. Magnetic Characteristics 37 transported, there is no option but to manufacture and supply single-phase units. In figure 2.1, various types of core construction are shown. In a single-phase three-limb core (figure 2.1 (a)), windings are placed around the central limb, called as main limb. Flux in the main limb gets equally divided between two yokes and it returns via end limbs. The yoke and end limb area should be only 50% of the main limb area for the same operating flux density. This type of construction can be alternately called as single-phase shell-type transformer. Zero-sequence impedance is equal to positive-sequence impedance for this construction (in a bank of single-phase transformers). Sometimes in a single-phase transformer windings are split into two parts and placed around two limbs as shown in figure 2.1 (b). This construction is sometimes adopted for very large ratings. Magnitude of short-circuit forces are lower because of the fact that ampere-turns/height are reduced. The area of limbs and yokes is the same. Similar to the single-phase three-limb transformer, one can have additional two end limbs and two end yokes as shown in figure 2.1 (c) to get a single-phase four-limb transformer to reduce the height for the transport purpose. Figure 2.1Various types of cores Copyright © 2004 by Marcel Dekker, Inc. 38 Chapter 2 The most commonly used construction, for small and medium rating transformers, is three-phase three-limb construction as shown in figure 2.1 (d). For each phase, the limb flux returns through yokes and other two limbs (the same amount of peak flux flows in limbs and yokes). In this construction, limbs and yokes usually have the same area. Sometimes the yokes are provided with a 5% additional area as compared to the limbs for reducing no-load losses. It is to be noted that the increase in yoke area of 5% reduces flux density in the yoke by 5%, reduces watts/kg by more than 5% (due to non-linear characteristics) but the yoke weight increases by 5%. Also, there may be additional loss due to cross-fluxing since there may not be perfect matching between lamination steps of limb and yoke at the joint. Hence, the reduction in losses may not be very significant. The provision of extra yoke area may improve the performance under over-excitation conditions. Eddy losses in structural parts, due to flux leaking out of core due to its saturation under over-excitation condition, are reduced to some extent [2,3]. The three-phase three-limb construction has inherent three-phase asymmetry resulting in unequal no-load currents and losses in three phases; the phenomenon is discussed in section 2.5.1. One can get symmetrical core by connecting it in star or delta so that the windings of three phases are electrically as well as physically displaced by 120 degrees. This construction results into minimum core weight and tank size, but it is seldom used because of complexities in manufacturing. In large power transformers, in order to reduce the height for transportability, three-phase five-limb construction depicted in figure 2.1 (e) is used. The magnetic length represented by the end yoke and end limb has a higher reluctance as compared to that represented by the main yoke. Hence, as the flux starts rising, it first takes the path of low reluctance of the main yoke. Since the main yoke is not large enough to carry all the flux from the limb, it saturates and forces the remaining flux into the end limb. Since the spilling over of flux to the end limb occurs near the flux peak and also due to the fact that the ratio of reluctances of these two paths varies due to non-linear properties of the core, fluxes in both main yoke and end yoke/end limb paths are non-sinusoidal even though the main limb flux is varying sinusoidally [2,4]. Extra losses occur in the yokes and end limbs due to the flux harmonics. In order to compensate these extra losses, it is a normal practice to keep the main yoke area 60% and end yoke/end limb area 50% of the main limb area. The zero-sequence impedance is much higher for the three-phase five-limb core than the three-limb core due to low reluctance path (of yokes and end limbs) available to the in-phase zero-sequence fluxes, and its value is close to but less than the positive-sequence impedance value. This is true if the applied voltage during the zero-sequence test is small enough so that the yokes and end limbs are not saturated. The aspects related to zero-sequence impedances for various types of core construction are elaborated in Chapter 3. Figure 2.1 (f) shows a typical 3-phase shell-type construction. Copyright © 2004 by Marcel Dekker, Inc. Magnetic Characteristics 39 Figure 2.2 Overlapping at joints 2.1.2 Analysis of overlapping joints and building factor While building a core, the laminations are placed in such a way that the gaps between the laminations at the joint of limb and yoke are overlapped by the laminations in the next layer.This is done so that there is no continuous gap at the joint when the laminations are stacked one above the other (figure 2.2). The overlap distance is kept around 15 to 20 mm. There are two types of joints most widely used in transformers: non-mitred and mitred joints (figure 2.3). Non-mitred joints, in which the overlap angle is 90°, are quite simple from the manufacturing point of view, but the loss in the corner joints is more since the flux in the joint region is not along the direction of grain orientation. Hence, the non-mitred joints are used for smaller rating transformers. These joints were commonly adopted in earlier days when non-oriented material was used. In case of mitred joints the angle of overlap (α) is of the order of 30° to 60°, the most commonly used angle is 45°. The flux crosses from limb to yoke along the grain orientation in mitred joints minimizing losses in them. For airgaps of equal length, the excitation requirement of cores with mitred joints is sin α times that with non-mitred joints [5]. Figure 2.3 Commonly used joints Copyright © 2004 by Marcel Dekker, Inc. ... - tailieumienphi.vn