Power transformers and autotransformers

Power transformers are electrical devices installed on the power plants or substations and are employed in the power network to increase or decrease the voltage level with the same frequency. Normally, the total installed power transformer capacity in the grid is four-five times higher than the generation capacity. Different power transformer’s configurations exist, though the most popular one is the three-phase power transformer. Compared to a single-phase power transformer, the power losses are 12-15% lower in three-phase power transformers and their production cost is reduced by 20-25%. The choice of power transformer type is a multifactorial process which is defined by the power transformer weight, size and transportation constraints apart from electromagnetic characteristics. Therefore, single-phase transformers are mainly used as ultra-high voltage grid transformer or the step-up transformer on the high-capacity power plant.

The reliability requirements to a power transformer operation are determined by the degree of its influence on the whole power grid security. Particularly, high requirements are associated with ultra-high voltage grid transformer or the step-up transformer on the high-capacity power plant. The power transformer design should consider the low-probability contingencies (once in ten years). GMDs accounting is not a regular practice.

Transformer replacement is costly and logistically challenging. Table 4.2 gives estimates of the recovery time for power transformer failures conjectured from the information about the response to natural hazards and supplemented with information from the technical documentation [1]. US Department of Energy estimates the average lead time of a domestically manufactured transformer between 5-12 months and internationally manufactured 6-16 months and can be up to 28-24 months in high demand periods [2]. The Royal Academy of Engineering, UK, says that it will take at least eight weeks to transport, install and commission a spare transformer unit [3]. Supply is also hampered by a surge in demand from India, China, Latin America and Middle East, where vast new grids are being constructed to cope with the increased demand for electricity power [4].

Real case of power transformer failures and corresponding repair time include following examples [5]. Transformer fire at Kriimmel Power Station, Germany, in June 2007 did not result in the unit loss, and the transformer was brought back to operation by circuit switching in 30 minutes after the event. Time for onsite repair varies from 48 hours (case of power transformer damage at Rostov Nuclear Power Plant, Russia, in October 2010) to 960 hours (case of 1,200 MVA step-up transformer failure at Salem Nuclear Power Plant, US, March 1989). In case of no replacement is available on site, the repair time rose up to 6,480 hours for the case of generator transformer failure at Longannet Power Plant, Scotland, in September 2009. The chronic of power transformer repair after Hydro-Quebec event in 1989 was the following.

Table 4.2

Power transformer repair time as a function of its type and the damage severity

Repair strategy

Repair time

Inspect, reset and re-energize

14-20 hours

Refill oil, onsite

2 days

Minor repair onsite

1-2 weeks

Change windings, onsite

3 months

Replace (with spare)

5 days

Replace (no existing spare)

1 year

Transformer T1 (phase C) at LG-4 was the first one to put back into service on April 26, 1989. Power transformer T3 at LG-4 went back to operation on December 15, 1989. Static VAR compensator CLC 12 at Chibougamau was replaced by a spare unit on June 1, 1989 and went back into service in July 1990. The sequence of events that lead to a blackout is given in Table 2.2.

Modern high-voltage power transformers have a complex structure. The main components include: tank, core, windings, isolation, tap changer, cooling system, leads and terminal arrangements. Core is the “heart” of the power transformer, its constructive basis. It creates a closed magnetic circuit with low reluctance for carrying the linkage flux through the windings. The core is stacked by a lamination of thin (ca. < 0.3 mm) electrical steel sheets, which are coated with a layer of insulation material (thickness ca. 10-20 jum). Core materials are constantly improved by introducing new materials such as oriented, hot-rolled grain-oriented (HRGO), cold- rolled grain-oriented (CRGO), high permeability cold-rolled grain-oriented (Hi-B), laser scribed steels [6]. The core consists of limbs (L) surrounded by windings and connecting yokes (Y). The core joint is the place where limbs and yokes are met to each other. The most common core joint is a mitered joint with a 45° cutting angle. Based on the number of steps, two types of core joints are considered: overlap and step-lap (more than one step).

High-voltage power transformer windings can be layer or disk. In the first case, both high-voltage and low-voltage transformer windings are made in cylindrical shape and placed concentric relative to each other. This method gives the best utilization of space and is widely used in power transformer design, however, it demands a lot of time and labour, and involves high cost and production time. In the second case, the windings are made as cylinders with the same diameters and placed above each other on the same limb. Windings are made from Cu transposed wires.

From the construction type of the core and windings, the power transformer can be classified into core-form and shell-form [7]. The graphical representation of them is given in Fig. 4.4. The windings are wrapped around the core with a cylindrical shape in core-form transformers, however, the core is stacked around the windings in shell-form transformers. Each winding consists of two parts (1 and 2). Windings have a flat or oval shape in this case and are often called pancake windings. The total cost of active materials is 20-30% less for core-type transformer, which makes this type more preferable for medium- and high-voltage levels.

Power transformer construction schemes

Figure 4.4: Power transformer construction schemes: core-form transformer on the left and she 11-form transformer on the right (Courtesy of Prof. Popov, V.)

Single-phase power transformers can be made with two, three or four limbs. In case of two limbs, there is not return limb and the cross-section of the yoke is the same as for the limb. In case of three or four limbs, there are two return limbs. The return limbs are not surrounded by any windings and constructed in order to provide a closed path for the flux. The size of three- and four-limb transformers is decreased compared to two-limb one, since the cross-section of the yokes and return limbs is ca. 50% of the main limb. Three-phase transformers have three or five limbs. In the first case, all three limbs are surrounded by windings. The five-limb design is used for large power transformers to decrease their height, stray fluxes and eddy current losses.

The power transformer’s active part is located in the tank filled with the insulation oil. It is made in a rectangular cubic shape from soft magnetic steel with a thickness about few centimeters. The tank should be robust to mechanic, acoustic thermal, electric and electromechanical contingencies and sustain transportation. The tank should minimize the stray fields outside the transformer and eddy currents inside the tank. The shielding is used in large power transformers. The shielding is done by mounting the laminations of copper or high permeable material on the inner side of the tank wall that are so-called protective shunt [6].

Autotransformers are types of transformers in which the primary and secondary windings have a common part and they are electrically connected at that common point [8]. In other words, power is transmitted using both galvanic and inductive methods in autotransformers. They are characterized by a reduced size and an optimum use of construction materials together with low short-circuit impedance that prevents their widespread installation in the grid. Generally, they are used when the voltage ratio is not so big.

The power transformer passport data includes the following parameters:

  • 1. Rated power is the value of the total power indicated in the passport, at which the transformer can be continuously loaded under the rated conditions of the installation site and the cooling conditions at the rated frequency and voltage. The rated power of a two-winding power transformer is the power of each of the windings. The windings of the three-winding transformer can be made for the same power or for the different. In the last case, the rated power is the power of one of the windings.
  • 2. Rated voltage is the voltage of the first and secondary transformer windings in the no-load condition. This rated voltage of the three-phase transformer is equal to its line-voltage, or is equal to phase voltage (.U/ine//3) in case of a single-phase transformer. The transformation coefficient is specified for each pare of windings in three-winding transformer.
  • 3. Short-circuit voltage и* is the voltage of one of the windings when the current flowing over the winding is equal to the rated one whilst the other is short-circuited. Short-circuit voltage defines the windings impedance. In case of three-winding power transformer, the test is done for each pair of the windings. Short-circuit voltage is defined in the percentages of the rated voltage, and is in the range of 2-10%.
  • 4. No-load current defines active and reactive losses in the transformer’s steel and depends on the steel’s magnetic properties, power transformer design and production quality. No-load current is defined in the percentage of the rated current, and normally does not exceed the value of 2%.
  • 5. No-load losses consists of the hysteresis losses (ca. 50-80% of no-load losses) and eddy current losses (ca. 20-50% of no-load losses). Hysteresis losses are caused by the frictional movement of magnetic domains in the core laminations being magnetized and demagnetized by alternation of the magnetic field. Hysteresis losses depend on the core steel.
  • 6. Short-circuit losses consists of Ohmic heat losses (copper losses) and conductor eddy current losses. The Ohmic heat losses is determined by the power transformer total load and is caused by the resistance of the conductor. It can be reduced by increasing the cross-sectional area of conductor or by reducing the winding length.
  • 7. Connection scheme. In total, three connection scheme exist: delta (Д), star (wye), grounded star (wye0). The graphs are given in Section 2.4.3. Y connection allows us to design the inner isolation by considering the phase electromotive force which is Уз times lower than the linear electromotive force. Star connection is normally used for high-voltage winding. Delta winding is generally used for low-voltage winding, since it allows us to reduce the conductors cross-sectional area by considering phase current (УЗ times lower than the linear current). Moreover, delta connection prevents high harmonics (with the numbers n = Зк, К = 1,2,3,...) penetration to the grid.
  • 8. Transformer windings group specifies the angle between the electromotive forces of the first and the second windings. Twelve groups exist. In case both of the windings are wye-connected, even group can be achieved 2, 4,
  • 6, 8, 10, 0. In case the combination of Д/Д or Д/wye windings are used, the odd group can be achieved 1, 3, 5, 7, 9, 11. The group and connection scheme are specified as following wye/A —11.

The whole set of power transformer parameters is rarely available. Parameters which differ from those specified above can be requested to the manufacturer. Some parameters can be obtained from terminal measurements. For instance, leakage inductance and winding resistances can be obtained when the high voltage winding is energized and low voltage winding is short circuited. Power transformers of types described above can be constructed for any rated power or voltage level, and from any magnetic material. Moreover, the construction type does not influence the functional principle, electromagnetic processes or the ability to ensure required outputs.

The GMD poses several ill effects to power transformer operation. In order to understand what happens at the moment of GIC appearance, a saturation simplified magnetization curve is given in Fig. 4.5. Transformers are designed to operate under the sinusoidal voltage and current. GIC as a quasi DC imposes a unidirectional flux in the transformer’s core. In turn, the DC flux adds to the AC flux in one half-cycle and subtracts from the AC flux in the other half. In other words, magnetization current becomes very high in one half-cycle and decreases a little in the other half-cycle. If large enough, GIC can result in power transformer’s half-cycle saturation. Since the high-voltage power transformers have a big number of windings turns, even small GIC may saturate the core. Whenever the iron core saturates, its relative permeability tends to decrease. In case of a deep saturation, permeability is equal to the one of the air n, = 1. The improved saturation curve for single-phase transformer which enables a consistent depiction of real BH data is given in [9].

Magnetic flux curve shape

Figure 4.5: Magnetic flux curve shape

The magnetic properties of electrical steel are usually measured with a sinusoidal magnetic flux density at a fixed level of magnetic induction [10]. Hi-В electrical steel type materials with higher saturation flux densities, lower permanent flux values, and larger linear portion of magnetic curve compared to regular grain-oriented (RGO) materials are used for power transformer’s core. The numerical representation of saturation core for a single-phase four-limb power transformer is shown in [11]. As the transformer core saturates, magnetic flux looks for new paths with relatively low reluctance, e.g. structural components of the transformer made of the ferromagnetic material. As these parts are not designed to minimize eddy currents, induction from the leakage flux heats up the elements. The response of power transformer to GIC as function of its core design was in the scope of various studies [12], [13], [14], [15], [16].

According to the principle of duality between electric and magnetic circuits, each flux path can be represented as an inductor [17]. Magnetic flux paths differ in different transformer designs. The generalized magnetic circuit is shown in Fig. 4.6. The magnetic circuit of a single-phase transformer is represented with two side branches. Three middle branches correspond to the three-phase three-limb transformer magnetic circuit. The full circuit in Fig. 4.6 constitutes to three-phase five-limb transformer magnetic circuit.

Generalized power transformer magnetic circuit

Figure 4.6: Generalized power transformer magnetic circuit

The DC flux path, connection scheme, and insulation characteristics determine power transformer’s robustness to GMD effects. The analysis result shows that the single-phase transformers are the most vulnerable regardless to the number of limbs. In contrast, three-phase three-limb is the most robust and reacts with minor asymmetries, since DC fluxes compensate each other in the main limbs and connecting yokes. In other words, the paths of the positive and zero sequence fluxes are different, where positive and zero sequence fluxes are the representation of the physical fluxes in the transformer’s core in the sequence domain 0-1-2, following the rule that any set of unbalanced three-phase quantities can be represented as the sum of three symmetrical set of balanced phasors. The positive sequence fluxes are the normal power system phase sequence quantities whereas zero sequence fluxes are a set of three phasors with similar phase information. The zero sequence path is closed through an air gap with high magnetic reluctance. The positive and zero sequence flux paths are both closed within the core in a single-phase transformer, which is the most vulnerable type. Three-phase five-limb power transformers fall between these two extremes. Although both direct and zero sequence fluxes are closed inside the core, they have different paths. The return branches are the paths for the zero sequence fluxes. In case the magnetic tank of a three-phase three-limb transformer is designed in a way that an air distance to a core is small, there is a chance that the tank acts as a path for zero-sequence fluxes. Hence, the limbs of three-limb core saturate, since the zero sequence reluctances are reduced. The relative power transformer susceptibility is given in [18]. The flux distribution in power transformers core due to GIC is presented in Fig. 4.7a-4.7c [19]. The correlation between the transformers magnetization current (/„,) and GIC (/G/c) can be described as follows (Eq. 4.6):

where a is saturation angle. Saturation angle is the angle corresponding to the time duration when the core flux exceeds the knee point to reach its maximum in case one considers a voltage cycle as 360°.

The sensitivity of different transformer types to the effects of GIC’s is sometimes compared and ranked according to the iron area which is available to the DC-flux generated by the windings [20]. A value of 0 stays for the most robust and a value of 1 stays for the most sensitive construction. The results are presented in Table 4.3.

Table 4.3

Power transformer's sensitivity to GIC as a function of construction scheme

Transformer type

Number of phases

Number of legs


sensitivity, p.u.

Full-wound, core-form




Full-wound, core-form




Autotransformer, shell-form




Full-wound, shell-form




Autotransformer, shell-form




The winding connection scheme influences the power transformer robustness to GICs. In case the GICs are applied to a Wyc/Д power transformer, the following current and magnetic fluxes distribution are observed. The harmonics with the numbers n = 3к, К = 1,2,3,... do not exist. Therefore, magnetic flux has highly non-sinusoidal character and contains high harmonics together with the main one (Fig. 4.8). High harmonics of magnetic flux Фу generate electromotive difference

(a) Flux distribution due to a high value GIC in a core of a three-phase three-limb power transformer;

Figure 4.7: (a) Flux distribution due to a high value GIC in a core of a three-phase three-limb power transformer; (b) Flux distribution due to a low level GIC in a core of a three-phase five-limb power transformer; (c) Flux distribution due to a very low level GIC in a core of a single-phase two-limb power transformer [19] of equal amplitude and coincident in phase in the Д connected winding. These electromotive difference induce inductive currents. Fluxes induced by these currents Фд almost fully compensate the Фу fluxes. Therefore, the resulting flux is almost sinusoidal.

Magnetic flux curve shape

Figure 4.8: Magnetic flux curve shape

In case GICs are applied to Д connected winding, the harmonics with the numbers n = Зк, К = 1,2,3,... do not exist in linear currents. Currents of these harmonics circulate within the closed triangular. Magnetic fluxes of the harmonics with the numbers n= Ik, n = 2k (K = 1,2,3,...) of the primary are almost fully compensated by the fluxes from the secondary winding. Therefore, implementation of Д winding is a practical GIC mitigation measure.

The power transformer’s half-cycle asymmetrical saturation also leads to high harmonics generation. High harmonics are recognized as a drawback because they result in a sudden increase in the load and variation. Also they lead to the distortion of current and voltage waveforms that causes, as an example, thermal stress of equipment or unwanted tripping of protection circuit components. The specific feature of the generated spectrum is its richness in even and odd harmonics with low order harmonics reaching high levels [21]. In contrary, harmonics generated by FACTS, SSSCs, HVDC equipment and non-linear loads have the prevalence of odd harmonics. The value of total harmonic distortion (THD) is chosen in accordance with power system conditions (Eq. 4.7). The THD cannot exceed the following value THD< 0.05 [22]. THD is defined as in Eq. 4.7. The harmonic spectrum ranges normalized to the fundamental harmonic for three cases: normative distribution, single-phase power transformer saturation, three-phase five-limb power transformer saturation are given in Table 4.4. The values given in Table 4.4 are the average value for different GIC levels based on literature research. It is shown in [ 19] that damping of high harmonics at high GIC level occurs faster for all the transformer types.

where /, - is a relative amplitude of i current harmonic and I - is an amplitude of a main current harmonic.

Table 4.4

High harmonic distribution in case of GIC appearance



IEC 61000-4-7




































GMDs may lead to an immediate power transformer outage or its postponed loss due to its accelerated insulation degradation. Following accidents are already registered. The GSU power transformer loss at PSE& G in NJ, US, during the March, 19, 1989 event is the example of an immediate transformer loss [231. The shell-form transformer with an old winding lead design that made it susceptible to overheating caused by high circulating current was taken out of service a week later because of significant gassing [24]. A dissolved gas-to-oil detector showed an increase of 50 ppm. Visual inspection of the failed transformers revealed a severe damage to one of the two long series connections of the outer low-voltage winding paths. Phases A and C had a 20-25% conductor damage and phase В experienced insulation discoloration. In terms of power grid operation, this power transformer loss is separated from Hydro-Quebec blackout. It also noted that within two years after 1989 event GSU transforms experienced failures at 11 nuclear power plants [23]. Photos of the damaged transformer are shown in many publications to illustrate consequences of GICs [25]. Nevertheless, there was no direct measurement of magnetic and thermal effects inside transformers during real GIC events so far.

The main danger posed by GICs to power transformers located in the “low-risk” regions is a number of partial discharge growth. Partial discharge stays for an electrical discharge or spark that bridges a small portion of an insulation between two conducting electrodes. It was reported that the series of geomagnetic events in 2003/4 caused significant winding overheating in a few large core-form power transformer in South Africa [26]. These incidents were found to coincide with winding overheating attributed to high sulphur content in some types of transformer’s oil. Another example is the Transformer T4 at Halfway, New Zealand, failure one minute after the GIC occurrence. It does not seem possible for a transformer of this sort to fail this quickly due to saturation of the core creating hotspots. However, deterioration of transformers is cumulative and caused by events such as power system faults, electrical overloading GICs, etc. which over time degrades the transformer. It is possible that the transformer was already prone to failure and the GIC was the final contributor, hence failing very soon after the event [27].

The transformer health is directly related to long-, medium-, and short-term condition of the insulation [28]. Ambient temperature is an important factor in determining the load capability of a transformer [29]. The document also notes that the performance may be affected by the higher operation temperature. Many long-term aging processes originate in oil and insulating paper. Paper condition is affected by oxygen levels and high temperature, with degree of polymerization being an indicator of paper degradation [30]. It reduces the heat transfer and accelerates degradation. Common approach of measuring the top oil and winding temperatures can not access delayed GIC impact. Therefore, low energy degradation triangle method is proposed in [31]. The three components of the triangle are the dissolved gasses Fb, CH4, CO, each measured in parts per million. The explanation of power transformer insulation degradation during 2003/4 events is given in Fig. 4.9.

Low energy insulation degradation triangle for power transformer during 2003/4 geomagnetic events (Courtesy of Gaunt. C.T.)

Figure 4.9: Low energy insulation degradation triangle for power transformer during 2003/4 geomagnetic events (Courtesy of Gaunt. C.T.)

The field tests of power transformer behavior under GIC were performed. In the first case, the 400 kV 400/400/125 MVA full-wound three-phase power transformer with a five-limb iron core was subjected to DC [33]. The stepwise neutral current increase from 50 A to 200 A was made. The highest temperature (ca. 130 °C) was recorded on the inside of a top yoke clamp, though the largest temperature rise was seen on the inside of a bottom yoke clamp. The highest temperature gradient, inside the bottom yoke clamp to surrounding bottom oil, was about 110 K. The time constant was 10 min. The test was done with the low ambient temperature -2 °C, hence, the temperature of 170-180 °C could be achieved with the regular ambient temperature conditions. This can pose risk to old transformers and result in some dangerous gassing in an oil.

The “effective GIC” which considers different GIC values in the series and common windings of an autotransformer is under the scope while assessing GMD impact on power transformer operation. The term was introduced by [34]. The application of “effective GIC” for two-winding and three-winding power transformer modeling was adopted by [35] and [36] respectively. The “effective GIC” is the GIC that flows from the high voltage level (HVW) to ground and produces the same magnetic flux in the core as the combination of GIC in all the windings. In other words, effective GIC is the effective per phase current. Equations for equivalent flux and effective GIC for different power transformer types is given in Table 4.5. In general, the “effective GIC” equation has the common structure for which the winding current is proportional to the number of turns of the windings and inverse to the number of turns of the windings in which the effective GIC is considered to flow.

Table 4.5

List of equations for effective GIC determination

Transformer type

Equivalent flux

Effective GIC









The proper information on power transformer’s susceptibility to GMD helps to develop optimal mitigation strategies (see Chapter 5). Just the knowledge on GIC amplitude cannot justify “pass” or “suffer the damage”. [37] proposes to divide power transformers in four categories as a function to their technical-geographical vulnerability to GMD such as Category> I transformers not susceptible to GIC effects, Category’ II transformers least susceptible to core saturation. Category III transformers susceptible to core saturation but only some overheating of windings and structural parts registered, Category’ IV transformers susceptible to core saturation as well as possible damaging windings appearance or structural parts overheating registered.

These four categories define designed-based power transformers susceptibility to GIC which refers to total GIC susceptibility by considering actual GIC amplitude at a certain node.

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