A transformer needs less magnetic material if it is operated at a higher core flux density. Thus, from the economic point of view, a transformer is designed to operate in the saturation region of the magnetic core.When a sinusoidal voltage is applied to the primary winding of the transformer, then the mutual flux set-up in the core is assumed to be sinusoidal and the no-load or exciting current (I0) will be non-sinusoidal due to hysteresis loop. It contains fundament and all odd harmonics.Consider the hysteresis loop of the core of the given transformer as shown in the figure below. Since, ... Read More

There is a sudden inrush of the primary current, when the transformer is initially energized and the maximum value of the magnetic flux is more than twice the normal value of the flux. Hence, due to the very high peak of the magnetising current, the core is driven far into saturation.Let a sinusoidal voltage is applied to the primary winding of a transformer is$$\mathrm{𝑣_{1} = u_{1𝑚}\:sin(\omega 𝑡 + 𝜃) … (1)}$$And the secondary winding of the transformer is kept open circuited. Here, θ is the angle of the voltage at t = 0.Now, if the core losses and the primary ... Read More

The three-phase transformer vector groups are divided into four main groups depending on the phase difference between the corresponding line voltages on the high-voltage and lowvoltage sides. The angle by which the line voltage on the low-voltage side lags behind the line voltage on the high-voltage side is called as the phase difference and it is measured in the units of 30° in the clockwise direction.The four transformer vector groups are −Group 1 – No Phase Displacement, i.e., 0° Phase DisplacementGroup 2 – Phase Displacement of 180°Group 3 – Phase Displacement of -30°Group 4 – Phase Displacement of +30°Now, instead ... Read More

A three phase transformer is required to step-up or step-down the three phase voltages in a power system. The 3-phase transformers can be constructed in one of the following ways −Three separate 1-phase transformers can be connected for the 3-phase operation. Such an arrangement is known as 3-phase bank of transformers.A single three phase transformer can be constructed in which the cores and windings for all the three phases are combined in a single structure.Construction of a Three Phase TransformerThe figure shows the core type and the shell type construction of the three-phase transformer. The 3-phase transformer consists of a ... Read More

The circuit arrangement of the transformers for three-to-twelve phase transformation is shown in the figure.Here, two banks of three 1-phase transformers or two 3-phase transformers are required. In this connection, the secondary windings are arranged in the form of pair of double-star connections. The primary windings of one set of transformers or of one of 3-phase transformers being connected in star while the primary windings of the other being connected in delta. Hence, the arrangement can be named as star-delta / double-star connection for transforming 3-phase to 12-phase. The phasor diagrams of both sets of transformers are shown in the ... Read More

An electrical transformer is tested at the transformer manufacturer premises and at the consumer’s site and also periodically in regular and emergency basis during its service life to confirm its specifications and performance.Types of Transformer TestsTests of transformer done at the manufacturer’s premises −Type testsRoutine testsSpecial testsTests of transformer done at the consumer’s site −Pre-commissioning testsPeriodic testsEmergency testsType Tests of TransformerThe type tests of a transformer are performed at the manufacturer’s premises to prove the design expectations and consumer’s specifications. The type tests are performed in a prototype unit, not in all manufactured units and these tests confirm the basic ... Read More

The star-star connection of transformer is shown in the figure. Here, the one terminal of three windings on each of the primary and the secondary sides being connected at a common point (called neutral point) and the other end of each winding is taken out as the line terminal.In the case of star-star connection, the phase current is equal to the line current and they are in phase. The line voltage is √3 times of the phase voltage. Also, there is a phase difference of 30° between the line voltages and phase voltages.For an ideal transformer the voltage ratios are ... Read More

In case of the star-delta connection of a transformer, the primary winding of the transformer is connected in star while the secondary winding is connected in delta (see the figure).Primary Winding – Since the primary winding is connected star fashion. Therefore, the primary line voltage is equal to the √3 times of the primary phase voltage and the primary line current is same as the primary phase current.Secondary Winding – The secondary winding is connected in delta manner. Therefore, on the secondary side of the transformer, the line voltage will be the same as the phase voltage whereas the line ... Read More

The rectifiers are used to convert alternating current (AC) to direct current (DC). The advantages of increased number of phases of the AC supply are given as follows −A smoother waveform is obtained on the DC side as the number of phases of the AC supply is increased.The objectionable harmonics in the AC being reduced with the increase in the number of phases.With the increase in the number of phases, the efficiency of the converter unit (rectifier) is also increased.Therefore, because of these advantages 6-phase is preferred instead of 3-phase for rectification. In order to obtain three to six phase ... Read More

Short-circuit and open-circuit tests are to be performed on a 3-winding transformer to determine the parameters of the equivalent circuits of it.Short-Circuit TestThe equivalent impedances Z1, Z2 and Z3 referred to a common base can be determined by performing three short-circuit tests as follows −Test 1In the first test, the secondary winding is short circuited, the tertiary winding is kept open circuited and a low voltage being applied to the primary winding so that full-load current flows in the secondary winding (see the figure above). Then, the voltage, current and power input to the primary winding is to be measured.Let ... Read More