# Functions, variations and application areas of magnetic components

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1 Westring Büren Germany T F energy efficiency and reliability 1.1 Transformers The transformer is one of the traditional components of electrical engineering. It is used in all areas of every day life. Transformers are used to match electrical energy, which is supplied on various voltage levels to the respective application. Its area of application ranges from power levels of just a few Watts (small transformers) right up to 1000MW (distribution transformers). The principle of transformers lies in the magnetic alternating flux of two coils, which are mounted on a common iron core (Fig. 1.1). Based on this construction and in accordance with the laws of induction, the voltages act pretty much like the number of turns. However, transformers will be subject to power loss due to losses occurring in the materials used (copper and iron). It is differentiated between single-phase transformers and three-phase transformers. Figure 1.1 Basic construction of a transformer Assuming that this transformer is an ideal transformer, the ratio of transformation is calculated as follows: (Remark to the formulas: voltages are designated in German as U, in English as V ) U1 N1 ü = = U N In the case of an ideal transformer the input power must be equal to the output power U 1 I1 = U I hence, the following equation shows the transformer ratio of the current. 1 I1 ü = I The effective voltage value or the numbers of turns are calculated according to the following formula. π w B A = U L

2 / Designs, applications Single-phase transformers The single phase transformer consists of a magnetic circuit, which is constructed from two coils coupled together by an iron core. The wound parts of the cores are referred to as legs, the connecting elements are known as the yoke (Fig. 1.). The legs and the yoke are packaged by individually insulated metal sheets, in order to reduce eddy-current losses, which develop from the magnetisation of the iron. Any losses suffered by the transformer are divided into no-load loss (magnetisation of the iron core, iron losses), short-circuit losses (which occur from the resistance of the windings) and extra losses (stray magnetic fields, which cause a current displacement within the conductor). Figure 1. Single-phase transformer designs Single-phase transformers are divided into core type transformers and shell type transformers. The core type transformer carries half the number of turns on each coil and the iron cross section is the same throughout (Fig. 1.a). The shell type transformer carries the complete winding on one central coil thereby saving construction height through the division of the return path, because each side of the yoke carries only half of the flux (Fig. 1.b). These two types of transformer design are used for small to medium power levels Three-phase transformers Since the power grid is designed as a three phase system, three-phase transformers are required for higher power. Three phase transformers are differentiated between symmetrical and non-symmetrical types. The symmetrical three-phase transformer may be compared with a transformer array, comprising three individual single-phase transformers.

3 3/11 The non-symmetrical three-phase transformer comprises three iron packages, which are located on one level (Fig. 1.3a). In this type of construction the linkage point of the transformer is located in the centre of the yoke and different magnetising currents are created in the coils. Fig. 1.3b depicts a five-coil transformer with lesser construction height through two additional returns paths. Figure 1.3 Three phase transformer designs Various configurations are available for three phase transformers in a symmetrical three-phase system, i.e. the star configuration; the delta configuration and the zigzag connection. The appropriate configuration depends on the application of the transformer. Calculation of a three phase transformer is carried out analogue to the one phase transformer Rectifier transformers Rectifier transformers are transformers that are predominantly used to feed equipment with rectifier frontend. These transformers may be designed as a single or a three phase transformer. Such rectifiers load the transformers with non-sinusoidal currents, which considerably reduce the load factor of the transformer. Hence, in comparison to transformers with a sinusoidal load, the calculated power of rectifier transformers is considerably increased (B 11%, B6 5%, M-3 34% and M1 309% through DC-components in the electric current). Even though the use of a transformer may not be required at the rectifier input in most cases, it can be used to boost or buck the voltage between AC and DC circuit, or for the provision of a galvanic separation between primary and secondary for safety reasons (Fig. 1.4). Commutation reactors in the line may then be omitted, because the commutating current can flow through the transformer.

4 4/11 To increase the commutating reactance, transformers may be fitted with built-in reactors, which will, in addition, reduce the harmonic content, in order to comply with international EMC regulations. Figure 1.4 Example of circuitry and harmonics in a B rectifier Autotransformers Autotransformers are a special form of transformer design without a galvanic separation between input and output. It is predominantly used as a matching transformer for different voltage levels. In comparison with the isolation transformer, the autotransformer with the same power rating is considerably smaller. It also has a lower short-circuit impedance compared with an isolation transformer (typical 1%). For rectifier applications, transformers may be designed with various phase angles of 0, e.g. 11 or ± 15. Figure 1.5 Example of an autotransformer circuit

5 5/ Reactors, chokes A reactor (inductive component) is constructed in a similar way to a transformer, whereby a reactor may comprise of a coil (known as an air coil) or of a coil with an iron core. In the case of a coil with an iron core, the iron core is separated by defined air gaps and just like a transformer core it is constructed with layers of electrical grade laminated steel. The layered iron core design will prevent eddy currents within the core. Fig. 1.6 depicts the schematic construction of a reactor with iron core with an air gap. Figure 1.6 Coil with iron core The inductance L of this coil is determined by the following equation: L = ψ i whereby ψ represents the coil flux and i stands for the corresponding electric current. Calculation of the inductance is carried out in accordance with the law of magnetic flux: H tdl H L δ L + H Fe lfe = i ϕ h BL = AL ϕ h BFe = A = w Fe The air gap (δ L ) and the average length of the iron core (l Fe ) have the same magnetic flux (ϕ h ) determined by the coil with its component's electric current (i) and the number of windings (w). Using these equations will determine the induction, which goes into the cross section of the core and the induction of the air gap. The magnetic field intensity (H Fe ) of B Fe will be determined from the magnetisation curves of the core material used. By adapting parameters B Fe and H Fe and using different core materials, any type of reacor can be designed for any intended application or purpose.

6 6/11 The field intensity H L will be established using the following equation B H = L L μ 0 which then results in the flux of a coil with ψ = w ϕ h 1..1 Construction types, applications Fig. 1.7 depicts the construction of three and single phase reactors. It is clearly visible that the illustrated air gap is not one large gap, but a calculated overall air gap divided into several smaller air gaps. Dividing the air gaps reduces the leakage flux of the reactor and thereby minimizes the extra losses. Figure 1.7 Construction of reactors with an iron core

7 7/ Commutation reactors Commutation means the transfer of electric current from a diagonal pair of valves onto the corresponding pair of valves inside a rectifier circuit. For the valves this means that the electric current increases in one branch and decreases in the other branch (Fig. 1.8a,c). Subsequently, the AC side and the DC side are short-circuited during this (short) period. The thyristors and power diodes used are not ideal components, hence only a certain rise time for the current may be allowed (di/dt = 50A/µs up to 00A/µs). For this reason, the commutation reactor is applied to limit the increase of electric current on the mains side. In addition, the commutation inductor reduces the harmonics, which are caused by the way the rectifier draws current from the grid. Figure 1.8 Course of commutation in a B rectifier circuit

8 8/ Filter reactors Filter reactors are used to reduce the amount of harmonic currents, because harmonics cause increased power losses, mechanical vibrations and higher insulation stress within the electric motor. In order to clarify the term harmonics, Fig. 1.9 depicts a square wave and its transformation into its sine wave components. Figure 1.9 Example of the transformation of a square wave into its individual sine waves Filter inductors now have the task to remove such unwanted frequency components and, if possible, only allow the fundamental frequency to pass through to the motor. Fig depicts the output current inside the load, which flows with the use of pulse width modulation. Figure 1.10 Pulse pattern and resulting electric current of a motor drive

9 9/11 Fig 1.11 depicts the location of filter reactor (MVD) in the electrical output circuit of a traction application. Figure 1.11 Block diagram of a drive unit pertaining to an electric locomotive Filter reactors may also be used in connection with a capacitor as a trap filter inside the DC link (SK, Fig. 1.11) of a drive unit. This circuitry will filter out harmonics by making use of the series resonance DC reactors (smoothing reactors) DC reactors are used in rectifiers (Fig. 1.1) to act as follows: Prevent intermittent operation up to a defined minimum current level Reduce the ripple to a defined value Figure 1.1 DC reactor in a rectifier circuit

10 10/11 Preventing intermittent operation DC reactors are used to prevent intermittent operation, if the mean DC current becomes smaller than the peak value of the harmonic current. Hence, in order to calculate the inductance, it is necessary to know the respective rectifier (harmonic content) used. The inductance is calculated in accordance with the following formula: Udi L = f1 I d min. U di I dmin. f 1 = no-load DC voltage = Intermittent current = Interval coefficient (in consideration of the respective rectifier) Reducing the ripple with a DC reactor The DC reactor used to reduce the ripple is an inductor, which is pre-magnetised through direct current. This means, that the induction B no longer fluctuates around the zero point, but around an operating point on the magnetizing curve (Fig. 1.13). Figure 1.13 Construction and pre-magnetization response curve of a DC reactor

11 11/11 The DC reactor is therefore designed for a particular nominal current. The required inductance is calculated in accordance with the following formula: UdN L = S 1 ω I dn U dn = Rated DC voltage I dn = Rated DC current ω S = Angular frequency of the lowest present harmonic = Filter factor This operating point of the reactor is positioned in the magnetizing response curve of the core material in use in such a fashion that the core material does not get into saturation Storage chokes Storage chokes are used in switch-mode power supplies. One of the fundamental characteristics of magnetic components i.e. the storage of energy through a magnetic field is being utilized for storage chokes. Different circuits allow for the design of both step-down converters (output voltage < input voltage) and step-up converters (output voltage > input voltage). Because of the pulsed voltage mode the reactor will be loaded with a broad harmonic spectrum (Fig. 1.14) and with fast rise and fall times of the voltage pulses (dv/dt). Figure 1.14 Current and voltage patterns and bock schematic of a step-down converter.

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