Found 1011 Articles for Digital Electronics

A three-phase star-connected autotransformer is shown in the figure. The three-phase autotransformers are used for small ratios of transformation.In practice, the star connected three-phase autotransformers are used and the delta connected autotransformers are avoided. The primary application of three phase autotransformers is for interconnecting two power systems of different voltage levels such as 66 kV to 132 kV power systems, 110 kV to 220 kV power systems, 220 kV to 400 kV power systems etc.Numerical ExampleA three-phase star-connected autotransformer supplies a balanced three-phase load of 100 kW at 380 V and at 0.85 power factor lagging. If the supply voltage ... Read More

The non-sinusoidal nature of the magnetising current in a three phase transformer produces some undesirable phenomena. The phase magnetising current should contain third and higher order harmonics which is necessary to produce a sinusoidal flux.If the phase voltage across each phase is sinusoidal, then the phase magnetising currents are given as follows −$$\mathrm{𝐼_{𝑅𝑁} = 𝐼_{𝑚}\:sin\:𝜔𝑡\:+\:𝐼_{3𝑚 }sin(3𝜔𝑡\:+\:φ_{3})\:+\:𝐼_{5𝑚}\:sin(5𝜔𝑡\:+\: φ_{5})\:+\:… (1)}$$$$\mathrm{𝐼_{𝑌𝑁} = 𝐼_{1𝑚}\:sin(𝜔𝑡 − 120°)\:+ \:𝐼_{3𝑚}\:sin[3(𝜔𝑡 − 120°)\:+\:φ_{3}]\:+\:𝐼_{5𝑚} \:sin[5(𝜔𝑡 − 120°)\:+\:φ_{5}] +....}$$$$\mathrm{\Rightarrow\:𝐼_{𝑌𝑁} = 𝐼_{1𝑚}\:sin(𝜔𝑡 − 120°)\:+\:𝐼_{3𝑚}\:sin(3𝜔𝑡\:+\:φ_{3})\:+\:𝐼_{5𝑚}\:sin(5𝜔𝑡\:+\:120°\:+\:φ_{5}) +..…\:(2)}$$And$$\mathrm{𝐼_{𝐵𝑁} = 𝐼_{1𝑚}\:sin(𝜔𝑡 − 240°)\:+ \:𝐼_{3𝑚}\:sin[3(𝜔𝑡 − 240°)\:+\:φ_{3}]\:+\:𝐼_{5𝑚}\:sin[5(𝜔𝑡 − 240°)\:+\:φ_{5}] +...}$$$$\mathrm{\Rightarrow\:𝐼_{𝐵𝑁}= 𝐼_{1𝑚}\:sin(𝜔𝑡 − 240°)\:+\:𝐼_{3𝑚}\:sin(3𝜔𝑡\:+\:φ_{3})\:+\:𝐼_{5𝑚}\:sin(5𝜔𝑡\:+\:240°\:+\:φ_{5}) +\:… (3)}$$Hence, from the eqns. (1), (2) and (3), it is clear that ... 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

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

The procedure for determining the voltage regulation of a 3-winding transformer is given as follows −Step 1Determine the kVA in each winding (primary, secondary and tertiary) for the given load. Determine x for each winding. Where, x is the ratio of actual kVA loading of the winding to the base kVA used in determining the network parameters. Hence, $$\mathrm{For\:primary\:winding, \:𝑥_{1 }=\frac{Primary\:kVA\:loading}{Base\:kVA}}$$$$\mathrm{For\:secondary\:winding, \:𝑥_{2 }=\frac{Secondary\:kVA\:loading}{Base\:kVA}}$$$$\mathrm{For\:tertiary\:winding, \:𝑥_{3 }=\frac{Tertiary\:kVA\:loading}{Base\:kVA}}$$Step 2Calculate the voltage regulation for each winding at its operating power factor.Let cosφ1, cosφ2 and cosφ3 are the operating power factors of primary winding, secondary winding and tertiary winding respectively. If vr1, vr2 and vr3 ... Read More

In case of the delta-star connection of a 3-phase transformer, the primary winding is connected in delta while the secondary winding is connected in star (see the figure).Primary Winding − As the primary winding is connected in delta. Hence, the line voltage and the phase voltage on the primary side are the same and the line current is √3 times of the phase current.Secondary Winding − The secondary winding is connected in star fashion. Thus, the secondary line voltage is √3 times of the phase voltage and the line current is equal to the phase current.The delta-star connected 3-phase transformers ... Read More

A conventional two-winding transformer can be converted into an autotransformer as shown in the figures given below. It can be converted into a step-up autotransformer by connecting the two windings electrically in series with additive polarities. If the windings are connected electrically in series with subtractive polarities, then a step-down autotransformer is obtained.To understand the conversion of a two winding transformer into an autotransformer, consider a conventional two-winding transformer of 20 kVA, 11000/400 V. This transformer has to be connected in autotransformer.Case 1 – With Additive PolarityThe figure shows the series connections of the winding with additive polarity. As the ... Read More

A full-load test on the large transformer is to be conducted to determine the maximum temperature rise of the transformer which is called as back-to-back test. The back-to-back test is also known as Sumpner’s test or regenerative test.In case of small transformers, the full-load test is conveniently possible, but for large transformers, full load test is very difficult. It is because, a suitable load to consume full-load power of a large transformer may not be available. It will also be very expensive as a large amount of energy will be wasted in the load during the test.The figure shows the ... Read More

Approximate Voltage Drop in a TransformerThe figure shows the approximate equivalent circuit of a practical transformer referred to secondary side.At no-load i.e. with I2= 0, the secondary terminal voltage is, $$\mathrm{V_{2}=KV_{1} .....(1)}$$When an inductive load of power factor cosφ2 (lagging) is connected across the secondary winding of the transformer, the secondary winding carries a current I2 and hence the voltage drops occur in $(R_{2} + K^2R_{1})$ and $(X_{2} + K^2X_{1})$. As a result, the secondary voltage drops from KV1 to V2 across the load terminals.By applying KVL to the circuit, we get, $$\mathrm{V_{2}=KV_{1}-I_{2}[(R_{2} + K^2R_{1})+J(X_{2} + K^2X_{1})]}$$$$\mathrm{⇒ V_{2}=KV_{1}-I_{2}(R_{02} +jX_{02}) = ... Read More

There are different types of DC generators are available for the various types of applications. The applications of various types of DC generators based on their characteristics are as follows −Applications of Separately Excited DC GeneratorsA separately excited DC generator requires an independent external DC source for the excitation of field winding. Thus, it is expensive and being rarely used. Following are some application of separately excited DC generators −These are able to produce a wide range of voltage output, they are primarily used in laboratory and commercial testing.These are used in speed regulation tests.These generators operate in a stable ... Read More