Introduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.) |

(introduction...) |

Preface |

1. Importance of Electrical Engineering |

2. Fundamental Quantities of Electrical Engineering |

2.1. Current |

2.2. Voltage |

2.3. Resistance and Conductance |

3. Electric Circuits |

3.1. Basic Circuit |

3.2. Ohm’s Law |

3.3. Branched and Unbranched Circuits |

3.3.1. Branched Circuits |

3.3.2. Unbranched Circuits |

3.3.3. Meshed Circuits |

4. Electrical Energy |

4.1. Energy and Power |

4.2. Efficiency |

4.3. Conversion of Electrical Energy into Heat |

4.4. Conversion of Electrical Energy into Mechanical Energy |

4.5. Conversion of Electrical Energy into Light |

4.5.1. Fundamentals of Illumination Engineering |

4.5.2. Light Sources |

4.5.3. Illuminating Engineering |

4.6. Conversion of Electrical Energy into Chemical Energy and Chemical Energy into Electrical Energy |

5. Magnetic Field |

5.1. Magnetic Phenomena |

5.2. Force Actions in a Magnetic Field |

5.3. Electromagnetic Induction |

5.3.1. The General Law of Induction |

5.3.2. Utilisation of the Phenomena of Induction |

5.3.3. Inductance |

6. Electrical Field |

6.1. Electrical Phenomena in Non-conductors |

6.2. Capacity |

6.2.1. Capacity and Capacitor |

6.2.2. Behaviour of a Capacitor in a Direct Current Circuit |

6.2.3. Types of Capacitors |

7. Alternating Current |

7.1. Importance and Advantages of Alternating Current |

7.2. Characteristics of Alternating Current |

7.3. Resistances in an Alternating Current Circuit |

7.4. Power of Alternating Current |

8. Three-phase Current |

8.1. Generation of Three-phase Current |

8.2. The Rotating Field |

8.3. Interlinking of the Three-phase Current |

8.4. Power of Three-phase Current |

9. Protective Measures in Electrical Installations |

9.1. Danger to Man by Electric Shock |

9.2. Measures for the Protection of Man from Electric Shock |

9.2.1. Protective Insulation |

9.2.2. Extra-low Protective Voltage |

9.2.3. Protective Isolation |

9.2.4. Protective Wire System |

9.2.5. Protective Earthing |

9.2.6. Connection to the Neutral |

9.2.7. Fault-current Protection |

9.3. Checking the Protective Measures |

For calculating the power of three-phase systems, the same relations are applicable as for the calculation of the power of alternating current systems. In accordance with the phase angle involved, a distinction is also made between effective power, reactive power and apparent power.

The star connection of three equal resistors is shown in Fig. 8.13.

For the total power, we have

P = 3 · U_{Str}· I_{L}· cos j

When the power is to be determined, on the basis of the
line-to-line voltage U_{L}, the following holds when using equation u.2.

_{}

_{}

(8.4.)

Fig. 8.13. Star connection of three
resistors

When three equal resistors are connected in delta (Fig. 8.14.), the total power is written as

P = 3 · U_{L}· I_{Str}· cos j

Fig. 8.14. Delta connection of three
resistors

When the line-to-line current is used, the following holds when using equation 8.3.

_{}

_{}

(8.5.)

where:

U |
line-to-line voltage |

I |
line-to-line current |

cos j |
power factor |

A comparison of the equations 8.4. and 8.5. shows that, independent of the given type of connection, the same equations for calculating the power are given.

When the phase load is unequal, the total power is obtained in the form of the sum of the powers in the three phases to be determined individually.

Example 8.3.

Three resistors of 800 W each have to be interposed in a three-phase network of 380 V one time in star connection and another time in delta connection. Calculate the effective power involved in each case.

Given:

U_{L}= 380 V

R = 800 W

cos j = 1

To be found:

effective power P for star connection and for delta connection

Solution:

star connection of the three resistors

_{}

In star connection, only the phase voltage drops at the three
resistors. Hence, for the current I_{L} we have

_{}

This expression is entered in the initial equation

_{}P = (380 V)

^{2}/800 W

P = 180.5 W

delta connection of the three resistors

_{}P = 3 · U

_{L}· I_{Str}· cos j

Since the full line-to-line voltage is applied to each resistor, we have for the phase current

I_{Str}= U_{L}/R

This expression is entered in the initial equation

P = 3 · U_{L}^{2}/R · cos j

P = 3 · (380 V)^{2}/800 WP = 541.5 W

At the three resistors, a total power of 180.5 W is obtained, in star connection and of 541.5 W in delta connection.

In practice frequently advantage is taken of the possibility of obtaining different powers by changing the type of connection of the various loads. For example, for three-phase motors, there are special switching devices which enable the changing over from star connection to delta connection and vice versa.

The power of a three-phase system can be determined from the sum of the individual powers in the three phases in ease of unequal phase loads or from the relation given in equation 8.4. in case of equal loads irrespective of the type of connection.

Questions and problems:

1. Determine the effective power of three resistors in star connection of 200 W if the latter are connected to a three-phase network with a line-to-line voltage of 220 V!2. Determine the effective power when the three resistors of problem 1. are in delta connection!

3. Three unequal effective resistances (80 W, 200 W, 500 W) have to be connected in star and in delta arrangement to a three-phase network with a line-to-line voltage of 380 V. Determine the total effective power!