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close this bookIntroduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.)
View the document(introduction...)
View the documentPreface
View the document1. Importance of Electrical Engineering
close this folder2. Fundamental Quantities of Electrical Engineering
View the document2.1. Current
View the document2.2. Voltage
View the document2.3. Resistance and Conductance
close this folder3. Electric Circuits
View the document3.1. Basic Circuit
View the document3.2. Ohm’s Law
close this folder3.3. Branched and Unbranched Circuits
View the document3.3.1. Branched Circuits
View the document3.3.2. Unbranched Circuits
View the document3.3.3. Meshed Circuits
close this folder4. Electrical Energy
View the document4.1. Energy and Power
View the document4.2. Efficiency
View the document4.3. Conversion of Electrical Energy into Heat
View the document4.4. Conversion of Electrical Energy into Mechanical Energy
close this folder4.5. Conversion of Electrical Energy into Light
View the document4.5.1. Fundamentals of Illumination Engineering
View the document4.5.2. Light Sources
View the document4.5.3. Illuminating Engineering
View the document4.6. Conversion of Electrical Energy into Chemical Energy and Chemical Energy into Electrical Energy
close this folder5. Magnetic Field
View the document5.1. Magnetic Phenomena
View the document5.2. Force Actions in a Magnetic Field
close this folder5.3. Electromagnetic Induction
View the document5.3.1. The General Law of Induction
View the document5.3.2. Utilisation of the Phenomena of Induction
View the document5.3.3. Inductance
close this folder6. Electrical Field
View the document6.1. Electrical Phenomena in Non-conductors
close this folder6.2. Capacity
View the document6.2.1. Capacity and Capacitor
View the document6.2.2. Behaviour of a Capacitor in a Direct Current Circuit
View the document6.2.3. Types of Capacitors
close this folder7. Alternating Current
View the document7.1. Importance and Advantages of Alternating Current
View the document7.2. Characteristics of Alternating Current
View the document7.3. Resistances in an Alternating Current Circuit
View the document7.4. Power of Alternating Current
close this folder8. Three-phase Current
View the document8.1. Generation of Three-phase Current
View the document8.2. The Rotating Field
View the document8.3. Interlinking of the Three-phase Current
View the document8.4. Power of Three-phase Current
close this folder9. Protective Measures in Electrical Installations
View the document9.1. Danger to Man by Electric Shock
close this folder9.2. Measures for the Protection of Man from Electric Shock
View the document9.2.1. Protective Insulation
View the document9.2.2. Extra-low Protective Voltage
View the document9.2.3. Protective Isolation
View the document9.2.4. Protective Wire System
View the document9.2.5. Protective Earthing
View the document9.2.6. Connection to the Neutral
View the document9.2.7. Fault-current Protection
View the document9.3. Checking the Protective Measures

8.4. Power of Three-phase Current

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 · UStr · IL · cos j

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


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 · UL · IStr · 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.




line-to-line voltage


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.


UL = 380 V
R = 800 W
cos j = 1

To be found:

effective power P for star connection and for delta connection


star connection of the three resistors

In star connection, only the phase voltage drops at the three resistors. Hence, for the current IL 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 · UL · IStr · cos j

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

IStr = UL/R

This expression is entered in the initial equation

P = 3 · UL2/R · cos j
P = 3 · (380 V)2/800 W
P = 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!