Electrical Transmission and Distribution--Power Transformers (part 1)

1. INTRODUCTION

Excellent textbooks are already available dealing with the design theory and operation of power transformers. This Section therefore concentrates on highlighting certain important aspects of:

1. Voltage selection degrees--Calculation of transformer voltage ratio, specification of insulation levels, examples of voltage regulation, rating, tap ranges and impedance calculations.

2. Thermal aspects -- Specification of temperature rise and ambient conditions.

Some comments are made on constructional features of different types of transformer in common use together with the purpose and selection of accessories. A review of the relevant IEC Standards and summary of the parameters to be specified by the user when detailing a transformer for a particular application are given. Earthing transformer selection and the use of a delta tertiary winding are described in Section 4, Sec. 4.4.6.

Consideration of an application of the interconnected star (or zigzag) transformer winding and balancing large single phase loads onto a three phase supply is given in Section 25.

FIG. 1 Phasor diagram for single phase 1:1 turns ratio transformer supplying an inductive load of lagging power factor cosΘ₂.

2. STANDARDS AND PRINCIPLES

2.1 Basic Transformer Action

The phasor diagram for a single phase transformer with a 1:1 turns ratio sup plying an inductive load of power factor cos Θ₂ is shown in FIG. 1.The transformer no-load current, I0 consists of the physically inseparable magnetizing current and core loss components. The primary magnetizing current, Im, is lagging the primary induced emf, E1, by 90 degrees. The primary core loss component, Ic consists of hysteresis and eddy current components. The hysteresis loss is proportional to the frequency of operation and the peak flux density while the eddy current loss is a function of the frequency, rms flux density and the thinness of the core laminations. Normally the magnetizing current is much larger than the core loss component and in power transformers the no load current I0 is almost equal to Im. Typically the no-load current, I0, represents some 1.5% of full load current for small distribution transformers and may be less than 0.75% for large high voltage transformers. The no-load cur rent is small because the primary links with its own magnetic field and electromagnetic theory explains that this will induce a back-emf to oppose the voltage applied externally to the coil. The open circuit transformer therefore acts as a highly inductive choke with a power factor of some 0.15 lagging.

Virtually the whole magnetic field created by the primary is attracted into the steel core and is encircled by the secondary winding. If the magnetic field is considered common to both primary and secondary transformer windings the actual field strength (in theory at least) becomes of no importance and only the four variables of voltage and coil winding turns remain giving the fundamental transformer expression:

V1/V2 ~N1/N2 (eq.1)

Under load conditions the voltage induced in the secondary winding coil drives a current into the load. In addition, the secondary current also produces its own magnetic field which acts to oppose (and thus reduce) the original field in the steel core laminations. This in turn reduces the field in the primary and allows more current to flow until a turns balance is reached. The total primary and secondary load current, I1 and I2 produce equal and opposite magnetic fields in the core so the overall effect is to leave the magnetic field unchanged from what it was before the load was applied to the secondary coil.

This leads, at large load currents when the primary current, I1, is much greater than the no-load current, I0, to the second fundamental expression:

N1 x I1 =N2 x I2 (eq. 2)

It should be noted that the magnetic flux levels in the core do not rise in proportion to the load current. The magnetic field due to the secondary is always balanced by that due to the primary current. The net magnetizing flux is due only to the magnetizing current and magnetic flux levels do not therefore reach very high levels under abnormal short circuit conditions.

Combining the two equations gives:

V1 x I1 =V2 x I2 (eqn. 3)

2.2 Transformer Equivalent Circuit

The transformer equivalent circuit shown in FIG. 2 is a fundamental basis for transformer calculations involving voltage drop or regulation under various load conditions (short circuit currents, tap settings, power factor, load currents, etc.).

FIG. 2 Transformer equivalent circuit.

The magnetizing circuit is taken as a shunt-connected impedance (inductance to represent the setting up of the magnetic field and resistance to represent heat losses in the core). As an approximation this equivalent circuit assumes the no-load current, I0, to be sinusoidal and the core flux constant at all loads. In practice, the non-linear core material flux density/magnetizing force (B/H) curve, means that even for a sinusoidal-applied voltage a slightly distorted magnetizing current results. The magnetizing current is rich in harmonics which must be kept in check by keeping the flux density within specified limits. During transformer energization a 'transient' current inrush rich in second harmonic will result. The magnitude of this inrush depends upon the instant of switching and the residual core flux. Transients may be more than two times full load current with significant decay over periods between 5 and 50 cycles depending upon transformer rating. This effect can be detected by transformer protection relays in a manner whereby the presence of the second harmonic component is used as a restraint feature. In this way the relay can be used to differentiate between a true fault and inrush current and avoid anomalous tripping.

The two resistances, R1 and R2, represent the ohmic resistances of the primary and secondary windings. The two inductances, X1 and X2, which are not independent, represent the leakage reactance in a realistic transformer. In practice, not all the magnetic field of the primary is linked with the secondary coil. Leakage results in a slightly lower secondary voltage than the simple turns ratio theory predicts and the greater the load current the greater the deviation from the ideal. In addition, further losses occur from magnetostriction whereby the physical dimensions of the core laminations change by a few parts in a million in a complex pattern with the flux cycle. This in turn causes hum at audible even harmonics of the supply frequency.

FIG. 3 Transformer phase relationships -- Dyn11 connections.

2.3 Voltage and Current Distribution

Vector representation of voltage and currents in transformer windings allows the practicing engineer to visualize the relationships involved. These relation ships are shown for Dy11 and Yd11 vector group transformer connections in Figs. 3 and 4, respectively. The length of the vector is made equal to the maximum or rms value of voltage or current. The convention is for the arrow heads to point away from the source of generation towards the load.

FIG. 4 Transformer phase relationships -- YNd11 connections.

2.4 Transformer Impedance Representation

The systems engineer, as opposed to the transformer designer, is chiefly concerned with the representation and characteristics of a given power transformer in the transmission and distribution network. In fault and load flow studies transformers are represented in the network diagrams by their equivalent impedances. The positive and negative sequence impedances of two winding power transformers are equal and equivalent to the ordinary leakage impedance used in three phase calculations. Transformer impedance is usually expressed as a percentage reactance (a transformer is highly inductive) on the base of the transformer rating. For transformers with dual or triple ratings (see SEC. 4.6 for cooling codes, for example ONAN/ONAF or ONAN/ONAF/OFAF) the correct rating base and tap position must be clearly detailed when specifying the transformer impedance required.

Typical values are given in FIG. 5.

FIG. 5 Typical two winding transformer ratings and minimum positive or negative percentage impedances (Z1 and Z2) together with derivation for auto-transformer impedances.

FIG. 6 Impedance representation of three winding transformers.

There is a move in city center primary substation design towards direct con version between the highest and lowest distribution voltages (say, 132 kV to 11 kV) rather than via an intermediate voltage level (e.g. 132 kV to 66 kV to 11 kV). In such cases the transformer impedance must be carefully specified to limit the secondary fault level and still maintain good voltage regulation as described later in this Section. Three winding transformers also have equivalent positive and negative sequence impedances and may be represented in an impedance network by three, rather than a single, impedances as shown in FIG. 6. Typical auto-transformer/two winding transformer impedances may be estimated for rough fault calculation purposes as shown in FIG. 5 if actual rating plate data is unavailable.

Transformer zero sequence impedances will vary over a wide range depending upon the winding vector grouping and neutral point earthing of both transformer and/or source generators within the system. As explained in SEC. 2.2, a turns balance is normally produced within the transformer windings. However, under fault conditions the zero sequence impedance is a result of the extent to which the configuration allows the zero sequence cur rent in one winding to be balanced by equivalent ampere turns in another winding. The zero sequence impedance of star/star transformers is also dependent upon the core configuration. Several examples of the distribution of zero sequence currents (represented by arrows with no vector significance but indicating the magnitude by the number of arrows involved with a given phase) in typical transformer windings for different typical vector groupings are shown in FIG. 7 together with approximations of zero sequence impedance magnitudes.

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FIG. 7 Zero sequence impedance approximations for different transformer vector groups and different system earthing configurations.

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2.5 Tap Changers

2.5.1 Introduction

The addition of extra turns to the secondary winding as shown in FIG. 1 allows a change in output voltage from, say, V2 to V2 1?V as the primary to secondary turns ratio is decreased. In transmission systems the control of the voltage may be achieved by varying the transformer ratios or the effective number of turns in service by using taps. There is a practical limit to the number of separate winding tap positions that can be accommodated arising from the physical size of the tap changer required and tapping winding insulation between adjacent steps. Transformer voltage control is therefore characteristically by means of small step changes in voltage. Tap changers may be motor driven or manually operated via a switch. Alternatively, the change in turns ratio may involve physically and manually changing tapping connections. Such arrangements may be found on the smaller distribution dry type transformers. Tap changer switches may be mounted separately on the side of the tank with their own separate oil insulation. This is intended to allow for easier maintenance. Alternatively, the tap changer may be mounted in the main transformer tank in order to reduce costs and result in a compact transformer design.

2.5.2 Tap Changer Types and Arrangements

Tap changers may be:

1. Off-circuit -- The tap change may only be carried out when the trans former is not energized. Off-circuit tap changers are usually relatively simple switches mounted close to the winding tappings. The switches are under oil and are designed to change position only when the transformer is de-energized. There is consequently no breaking of current flow. The tap changer is operated by a handle, or wheel, from the outside of the tank in most transformers.

2. Off-load -- The tap changer may be operated when the circuit is energized but not when the circuit is drawing load current.

3. On-load -- The tap changer may be operated under load conditions. An on-load tap changer has a much more difficult duty than the off-circuit type. An international survey on failures in large power transformers (CIGRE Working Group Study Committee 12, Electra, Jan. 1983, No. 88, pp. 21-48) showed that tap changers were the source of some 40% of transformer faults. As the name implies, the on-load tap changer may change tapping position with transformer load current flowing.

On-load tap changer selection is best completed in conjunction with the manufacturer unless some standardization policy by the electrical supply utility dictates otherwise.

On-load tap changer manufacturer's requirements are:

1. General

- Reliability

- Minimal maintenance

- Lowest cost

- Electrical supply utility preferences.

2. Technical

- Dielectric strength

- Overload and fault current capability

- Breaking capacity

- Electrical and mechanical life expectancy

- Service and processing pressure withstand capability.

There are three basic tapping arrangements (see FIG. 8) and each have their own advantages and disadvantages depending on the application. In addition, the connection point for the taps depends upon whether the transformer is a double wound unit or an auto-transformer.

The linear arrangement is generally applied for smaller tapping ranges and results in a relatively simple tap changer. It is restricted to smaller ranges because of difficulties which can arise from bringing out a large number of tapping leads from the winding and also owing to impulse voltages being developed across a large number of tapping turns.

FIG. 8 Basic arrangements of tapped windings

For larger tapping ranges the reversing arrangement can be used. The changeover selector allows the taps to be added or subtracted from the main winding, effectively halving the number of connections and giving a larger tapping range from a smaller tap winding. A disadvantage of the reversing arrangement is that on the position with the minimum number of effective turns the total tapping winding is in circuit resulting in higher copper losses in the transformer.

A coarse/fine arrangement incorporates some of the advantages of the reversing arrangement but exhibits lower copper losses on the minimum tap position. The main disadvantage of the coarse/fine scheme is the cost of pro viding separate coarse and fine tapping windings.

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FIG. 9 OLTC arrangements in double wound transformers.

Mid-winding arrangement Line-end arrangement Star-connected windings Delta-connected windings

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2.5.3 Electrical Connections to the Main Winding

For double wound transformers (see FIG. 9), the tappings may be applied to either star- or delta-connected windings. The most common connection is at the neutral end of star-connected HV windings. This results in the most economical tap winding and allows a low voltage class, three phase tap changer to be used. When tappings are applied to delta-connected windings the lack of a neutral leaves the choice of connecting the tappings at either the line end or in the middle of the main winding. The line-end connection requires the tap changer to be fully insulated from the system voltage. The mid-winding connection can be used to reduce the dielectric stresses but other parameters such as transformer impedance, winding insulation level and economic considerations will affect the final choice.

When tappings are applied to auto-transformers the choice of connection is even more involved. From a dielectric viewpoint the ideal position for the tappings is at the neutral end. As with double wound transformers this has the advantage of a smaller, lower cost tap changer. In core form transformers the physical disposition of the windings greatly affects the transformer impedance. The neutral tap changer position therefore results in a possibly advantageous, low impedance variation over the tapping range. However, since the operation of auto-transformers differs from double wound types this advantage may be outweighed by other considerations as shown in FIG. 10. The main disadvantage of the neutral end tapping connection arises from the fact that reducing the turns of the LV circuit also reduces turns in the HV circuit and therefore a larger tapping winding is required for a given voltage change. For auto-transformers with high ratios this is not a great disadvantage and the neutral end connection can usually prove the most economic solution for auto-transformer ratios above 2.5/1. The disadvantage becomes more pronounced on transformers with low ratios and large tapping ranges. This is one of the reasons why the majority of the 400/132 kV auto-transformers on the UK National Grid system have neutral end tap changers whereas the line-end tap changer is much more common for 275/132 kV units.

Another effect of varying the turns in the LV and HV auto-transformer circuits simultaneously is that the volts per turn, and therefore the flux density of the transformer core, varies over the tapping range. Consequently, the voltage induced in any auxiliary winding such as a tertiary will vary with tap position. The line-end connection has the advantage of constant flux density and therefore constant tertiary voltage over the tapping range. Also, the change in turns ratio is achieved in a more cost effective manner particularly for lower transformer ratios. The main disadvantages are the higher cost of the line-end tap changer and the higher impedance variation over the tapping range resulting from the preferred disposition of the windings.

===FIG. 10 Auto-transformer tapping arrangements. ==

NEUTRAL-END TAPS Advantages Lower-cost tap changer Lower-impedance variation over tapping range More economical at high transformation ratios Disadvantages Variable flux Tertiary voltage variation

LINE-END TAPS Advantages Constant flux Constant tertiary voltage More economical at low transformation ratios Disadvantages Higher-cost tab changer Higher-impedance variation over tapping range

===

2.5.4 Dielectric Stresses

FIG. 11 illustrates the critical stresses of a three phase neutral-end coarse fine tap changer. The most onerous stresses appear during the transformer dielectric tests and their magnitude depends upon the transformer design parameters and the tapping position during the tests. The magnitude and precise location of maximum stresses is determined at the design stage through numerical simulation.

FIG. 11 On-load tap changer critical stresses.

2.5.5 Tap Changer Duty

FIG. 12 illustrates the switching sequence of the tap changer selector and diverter switch. The purpose is to transfer connection from the selected tap to a preselected adjacent tapping without interrupting the power supply to the load.

FIG. 12 Operating sequence of tap selector and divertor switch.

During the short time that the transfer switch is in transit between contacts M1 and M2 the load is carried by a transition impedance. With the exception of some units in North America (which use reactors) the transition impedance is nowadays normally a resistor. The transition resistors (RT) are designed according to the step voltage and rated through current, and the very fast transfer time in the order of tens of milliseconds means that the transition resistors need only be short time rated. The main contacts M1 and M2 are called upon to carry the full load current continuously. The diverter switch contacts T1 and T2 must be capable of sustaining arc erosion and mechanical duty resulting from making and breaking full load current. The arcing of these contacts produces gases which saturate the adjacent oil and a barrier must be provided to separate this oil from the main transformer oil.

2.5.6 In-Tank Tap Changers

FIG. 13 illustrates the physical arrangement of the in-tank tap changer.

The leads from the tapping winding are connected to the selector contacts within the main transformer oil. The diverter switches are enclosed in an oil-filled insulating cylinder which is piped to its own conservator. The oil con tact with the diverter switch is therefore isolated ensuring that degradation products resulting from the switching process do not contaminate the transformer oil. Maintenance is confined to the diverter compartment and the selector contacts are considered maintenance free. Access to the selector contacts and separation of the selector oil from the transformer oil to increase the selectivity of dissolved gas-in-oil analysis may be specified. In these cases it is necessary either to separate the in-tank tap changer from the trans former by a barrier board as shown in FIG. 13(b) or alternatively to supply a separate bolt-on tap changer. If access to the selector contacts without dropping the transformer oil level below the level of the windings is specified then a weir may be fitted inside the transformer as shown in FIG. 14.

The tap changer oil may then be drained independently of the main transformer oil.

FIG. 13 In-tank tap changers.

[In-tank OLTC Separate diverter oil Common selector oil Barrier board OLTC Separate diverter oil Separate selector oil ]

FIG. 14 Weir-type tap changer.

FIG. 15 Bolt-on tap changers.

2.5.7 Bolt-On Tap Changers

The two main types of bolt-on tap changers are shown in FIG. 15.

The double-compartment type separates the selector contacts from the diverter switch forming two main compartments. This system allows the tap changer manufacturer to separate the mechanical drives to the selector and diverter mechanisms. The diverter may be operated by a spring-loaded device at switching speed and the selector can be driven directly from the output shaft of the motor drive mechanism at slower speeds. This is the traditionally preferred type for larger transformers built.

The single-compartment bolt-on tap changer utilizes selector switches which combine the function of selection and transfer in one mechanical device. The fact that arcing products are in contact with insulation subjected to high voltages limits the application of single-compartment tap changers to the lower ratings.

2.6 Useful Standards

The principal reference for power transformers is IEC 60076. A number of other standards are also relevant, but work is in hand to supersede many of them by sections of 60076, thus making one easier reference. Reference to the IEC index, accessible via the internet, will enable the current status to be checked as work progresses (see also TABLE 1).

3. VOLTAGE, IMPEDANCE AND POWER RATING

3.1 General

The correct specification of transformer voltages, impedance(s) and kVA rating(s) are described in this section.

3.2 Voltage Drop

As shown in FIG. 2, there is an internal voltage drop in a transformer under secondary load conditions. The volt drop is due to the leakage reactance and the winding resistance. Rather than express the impedance in ohms per phase the normal convention with transformers is to express the impedance as a percentage value referred to the kVA (or MVA) rating of the transformer.

The change in transformer terminal voltage from no load to full load is the regulation of the transformer. This change corresponds with the volt drop appearing at full load. Several formulae are available to calculate volt drop, the more accuracy required the more complex the formula. The following is adequate for most purposes:

ΔU =[(R p) ² + (X q) ²]^1/2 + 100%

where:

X=leakage reactance (%)

R=winding resistance (%)

p=power factor, cos Φ (in %)

q=sin Φ (in %)

ΔU=volt drop at full load (%)

[coming soon] TABLE 1 Useful Standards

For example, a transformer with a leakage reactance of 10%, a resistance of 0.5% and supplying a load at 0.85 (85%) power factor will have the following full load volt drop:

ΔU =5.3%

Notice that the formula includes the winding resistance which is small compared with the leakage reactance but may be included to retain accuracy.

3.3 Impedance

The short circuit impedance or internal impedance is a main parameter for a transformer. Extreme values are limited by design factors; the lowest value by the minimum physical distance between windings, the highest by the effects of the associated high leakage flux.

For any given rating and voltage the size and weight of a transformer are functions of its percentage reactance. A small percentage reactance means a large main flux requiring larger iron cross-section. As reactance is increased the iron cross-section decreases, iron loss decreases but copper loss increases.

The ratio of copper loss to iron loss is appreciably increased and the total loss increased slightly. High reactance has the disadvantage of a large voltage drop (requiring a large tapping range to compensate and maintain secondary voltage) and a large amount of reactive power consumed within the transformer itself. For larger transformer ratings a high reactance may, however, be considered desirable because it limits the short circuit current and there fore maintains the rating of associated system switchgear. Some compromise must be arrived at between these conflicting requirements and minimum values are shown in FIG. 5.

For three phase systems the zero sequence impedance of the transformer is also of importance since it determines the magnitude of fault currents flowing between the neutral of a star-connected winding and earth during phase-to-earth faults. The transformer zero sequence impedance is dependent upon the core configuration (three or five limb for core type transformers) and whether or not a delta-connected auxiliary winding is fitted (refer to FIG. 7 and SEC. 5.2.3).

3.4 Voltage Ratio and Tappings -- General

A transformer intended to connect, for example a 132 kV system to a 20 kV system may, at first sight, simply require a voltage ratio of 132/20 kV. In practice, this may not be the most appropriate ratio to specify to the manufacturer since the following aspects need to be taken into account:

1. The 132 kV system voltage is not constant and may vary as much as 610% from the nominal value.

2. Volt drop on load will depress the voltage at the 20 kV terminals.

To accommodate these effects virtually every practical transformer will need tappings to allow selection of different voltage ratios to suit different circumstances. In some situations, where the transformer regulation and the primary voltage variations are small, a change from one tapping to another would be very infrequent, if ever, in the transformer life. In such cases 'off circuit' or 'off-load' tappings are adequate.

In the majority of transmission system applications, system voltage control is achieved by changing transformer taps and an 'on-load' tap changer facility is needed for frequent changes in tapping without removing the transformer from service.

3.5 Voltage Ratio with Off-Circuit Tappings

In domestic and industrial distribution systems, transformers stepping down from 11 kV to 3.3 kV or 0.415 kV will normally be satisfactory without on load tap changers. Such transformers will usually have impedances of around 4% to 6% giving a full load volt drop at 0.85 pf of 3% or 4%. In many cases the primary voltage will be fairly well controlled to, say, 63% of the nominal value. Combining the primary voltage variation effect with the transformer regulation effect gives an overall reasonably satisfactory 9-10% voltage variation on the secondary terminals. The voltage ratio is usually chosen to give approximately nominal secondary voltage at full load. Thus a ratio of 11 kV to 433 V is commonly chosen to feed a 415 V system. Distribution transformer off circuit tappings giving 25.0%, 22.5%, 0%, 12.5% and 15.0% variation in ratio are conventionally specified and will be adequate for the majority of situations. The middle tap of a transformer is referred to as the 'principal tap.' The role of the off-circuit tap changer is then to match the transformer to the circumstances of the installation. For example, an 11 kV/433 V transformer close to a main 33/11 kV feeder substation may see an 11 kV voltage level biased towards the high side -- for example, 11.3 kV 62%. On the other hand, a remote 11 kV/433 V transformer may see an 11 kV voltage biased towards the low side -- for example, 10.8 kV 63%. In the former case the 12.5% tapping would be used (giving a ratio 11.28 kV/433 V), and in the latter the 22.5% tapping would be used (giving a ratio 10.7 kV/ 433 V). For standardization, both transformers use the same specification; only the tapping is changed for the particular service condition.

3.6 Voltage Ratio and On-Load Tappings

The procedure for specifying voltage ratio and tapping range for on-load tap changes is quite involved and often causes problems. SEC. 3.9 gives an example of some of the factors to be considered.

IEC 60076-1 defines three categories of voltage variation for transformers with tappings. They are defined as follows:

-- Constant flux voltage variation (CFVV) - The tapping voltage in any untapped winding is constant from tapping to tapping. The tapping voltages in the tapped winding are proportional to the tapping factor.

-- Variable flux voltage variation (VFVV) - The tapping voltage in the tapped winding is constant from tapping to tapping. The tapping voltages in any untapped winding are inversely proportional to the tapping factor.

-- Combined voltage variation (CbVV) - The transformer is specified using both principles, but applied to different parts of the range. This approach is particularly used in instances of a large tapping range.

Particular care must be taken in attempting to specify the impedance variation with tapping, as this can restrict the design. Refer to IEC 60076-1 for extensive guidance.

3.7 Basic Insulation Levels (BIL)

The amount of insulation applied to the winding conductors is usually influenced by the impulse voltage rating of the winding rather than by the power frequency voltage rating. Impulse voltages due to lightning or switching activity appearing at the terminals of the transformer stress the winding insulation and this effect may be reduced by the application of surge arresters.

The factors involved in correct specification of the transformer basic insulation level are explained in Section 9. See also IEC 60076-3 which gives particular guidance on insulation levels for transformers.

FIG. 16 Winding arrangements.

3.8 Vector Groups and Neutral Earthing

Three phase windings of transformers will normally be connected in a delta con figuration, a star (wye) configuration, or, less commonly, in an interconnected star (zigzag) configuration as shown in FIG. 16. The vector grouping and phase relationship nomenclature used is as follows:

- Capital letters for primary winding vector group designation.

- Small letters for secondary winding group designation. D or d represents a primary or secondary delta winding.

- Y or y represents a primary or secondary star winding.

- Z or z represents a primary or secondary interconnected star winding.

- N or n indicates primary or secondary winding with an earth connection to the star point.

- Numbers represent the phase relationship between the primary and secondary windings. The secondary to primary voltage displacement angles are given in accordance with the position of the 'hands' on a clock relative to the mid-day or twelve o'clock position. Thus, 1 (representing one o'clock) is 230 deg. ,3 is 290 deg. ,11 is 130 deg. and so on.

Therefore a Dy1 vector grouping indicates that the secondary red phase star voltage vector, Vrn, is at the one o'clock position and therefore lags the primary red phase delta voltage vector, Vrn, at the twelve o'clock position by 30_ , that is the one o'clock position is 30_ lagging the primary twelve o'clock position for conventional anti-clockwise vector rotation.

Similarly a Dyn11 vector grouping indicates that the secondary red phase voltage leads the primary voltage by 30 degr. , that is the eleven o'clock position leads the twelve o'clock position by 30 degr. . The secondary star point is earthed.

Yy0 would indicate 0 degr. phase displacement between the primary and secondary red phases on a star/star transformer.

Dz6 would indicate a delta primary interconnected star secondary and 180 degr. secondary-to-primary voltage vector phase displacement.

The system designer will usually have to decide which vector grouping arrangement is required for each voltage level in the network. There are many factors influencing the choice and good summaries of the factors of most interest to the manufacturer can be found in Ref. [1]. From the user's point of view, the following aspects will be important:

1. Vector displacement between the systems connected to each winding of the transformer and ability to achieve parallel operation.

2. Provision of a neutral earth point or points, where the neutral is referred to earth either directly or through an impedance. Transformers are used to give the neutral point in the majority of systems. Clearly in FIG. 16, only the star or interconnected star (Z) winding configurations give a neutral location. If for various reasons, only delta windings are used at a particular voltage level on a particular system, a neutral point can still be provided by a purpose-made transformer called a 'neutral earthing trans former' or 'earthing compensator transformer' as shown in FIG. 16 and also as described in Section 4.

3. Practicality of transformer design and cost associated with insulation requirements. There may be some manufacturing difficulties with choosing certain winding configurations at certain voltage levels. For example, the interconnected star configuration is bulky and expensive above about 33 kV. Of considerable significance in transmission systems is the cost and location of the tap changer switchgear as explained in SEC. 2.5.

4. The Z winding reduces voltage unbalance in systems where the load is not equally distributed between phases, and permits neutral current loading with inherently low zero-sequence impedance. It is therefore often used for earthing transformers (see also Section 25, Section 25.4).

3.9 Calculation Example to Determine Impedance and Tap Range

3.9.1 Assumptions and Data

It is required to calculate the impedance and tap changer range for a star/star auxiliaries transformer.

- The voltage variation on the primary side is 132 kV 610%.

- The maximum allowable voltage variation on the secondary side is 21 kV 20%, 15%.

- The maximum allowable 3.3 kV voltage is 3.54 kV (17.5%).

- The maximum transformer load is anticipated to be initially 31.9 MVA at 0.9 pf and increased to an ultimate future figure of 38.3 MVA at 0.9 pf.

- The maximum allowable secondary 21 kV side fault current is 12.5 kA.

- Maximum primary side 132 kV source fault level is 2,015 MVA.

3.9.2 Rating Calculation

The HV principal tapping voltage is 132 kV.

The LV no-load voltage at principal tap is chosen as 22.05 kV. This volt age should be adequately high to cater for the on-load voltage drop and also adequately low to avoid over-voltage problems under specific load rejection conditions.

The initial LV maximum current =31.9√3 x 22.05=0.835 kA.

According to IEC 60076, rated power equals the product of no-load volt age and rated LV current.

Thus the initial required transformer-rated power= √3 x 22.05 x 0.83=5 32.54 MVA.

The ultimate LV maximum current=38.3√ 3 x 22.05=1.003 kA.

The ultimate required transformer-rated power= √3 x 22.05 x 1.003 = 39.09 MVA.

The auxiliaries power transformer rating chosen was 35/40 MVA ONAN/ ONAF.

3.9.3 Network Impedance Representation

FIG. 17 shows the system configuration comprising two 132/21 kV auxiliary power transformers (the details for which we are investigating), 21 kV cable network, 21/3.3 and 3.3/0.4 kV transformers, and 3.3 and 0.4 kV loads.

In this calculation the base MVA is chosen as 10 MVA. Base voltages are 132 and 21 kV. It is necessary to determine the auxiliary transformer impedance required to limit the fault level to the specified 12.5 kA.

The system configuration is reduced to an impedance network for making and breaking duties as shown in Figs. 14.18a and 14.18b. For readers wishing to work through such an impedance estimation the following network parameters may be used:

21 kV, 3c, XLPE, 18,700/22,000 V, 120 mm2 copper cable

Resistance at 90 degrees C=0.196 ohm per km

Reactance=0.108 ohm per km

Capacitance=0.25 µF per km or 78.5 micro mho per km at 50 Hz.

The per unit values may be obtained from this data as follows:

Base impedance=(21 kV)^2/10

MVA=44.1 ohm

pu resistance=0.196/44.1=0.0044 pu/km

pu reactance=0.108/44.1=0.0024 pu/km

pu susceptance=(78.5 * 10^-6 ) * 44.1=0.00346 pu/km

The effect of cable capacitance is negligible and may therefore be ignored in a simple hand calculation.

Motor Contribution to Fault Level

When a fault occurs near an induction motor the motor will contribute to the fault current. The motor may be represented as a voltage source behind a reactance. This reactance can be obtained using contribution factors.

For breaking duty calculation, two contribution factors apply:

1. Xm =1.5Xd v for a motor with a rating above 250 hp

2. Xm =3.0Xd v for a motor with a rating below 250 hp where Xm is the effective motor reactance during the fault period, and Xd v is the sub-transient reactance -- see, for example IEEE-recommended practice for electrical power distribution for industrial plants. It may be assumed here that Xd v =0.9Xd where Xd is the transient reactance. The motor starting cur rent is typically specified as six times full load current for 400 V motors and four times full load current for 3.3 kV motors. The transient motor reactance Xd =1/(starting current). Using this information the effective reactance, for the breaking duty calculation, of all the motor loads shown in FIG. 17 may be calculated.

FIG. 17 System configuration.

FIG. 18a System impedances on 10 MVA base for breaking duty.

FIG. 18b System impedances on 10 MVA base for making duty.

FIG. 19 Equivalent circuit for breaking duty (top) and making duty (bottom).

FIG. 20 Transformer regulation: (a) equivalent circuit; (b) no load equivalent circuit; (c) full load equivalent circuit.

3.9.6 Conclusions

The nominal impedance of the auxiliaries transformers in this example should therefore be 23% in order to limit the fault level to 12.5 kA under the worst case conditions (two transformers in parallel, maximum source fault level and maximum motor contribution). For satisfactory operation of the 21 kV system, a tap range of 218.75 to 118.75% should be specified when placing the order for the transformers.

cont. to part 2 >>