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The equivalent complex circuit

In section 3.4 presents the general procedure for calculation by the complex amplitudes method. In this case we have to build the equivalent complex circuit (ECC). Let us consider the procedure of obtaining the ECC.

In Fig. 4.29 circuit shows of the power of three-phase asynchronous motor (AM) is shown. Here three motor windings are presented by resistances r1 , r2 , r3 , inductances L1 , L2 , L3 , and capacitance C1 , C2 , C3 . A food circuit is represented by three-phase voltage source e1, e2 , e3

 

 

Fig. 4.29

 

 

Circuit load is presented resistances r , r , r . Sources of voltages e , e , e form a three phase system. Write down their images through the complex amplitudes

 

(4.199)

 

The complex impedance of the separate phase of the circuit

 

(4.200)

 

From (4.199), (4.200) get ECC (Fig. 4.30)

 

 

Fig. 4.30

 

Here currents

 

(4.201)

Here the procedure of obtaining the ECC is the following:

1) select the conventional-positive direction of the currents in the branches of the original circuit;

2) instantaneous values of harmonic currents, voltages and EMF submit in a united trigonometric form of a record: all through the sine or all through the cosine functions;

3) the instantaneous values of voltages and currents, voltages and EMF replace their images in the form of complex amplitudes, the direction of the voltages and currents in the ECC coincide with the direction of these values in the original circuit;

Thus, the order of calculation of the circuits by the method of complex amplitudes can be defined as follows:

1) make up the equivalent complex circuit (ECC);

2) work out a system of algebraic equations in the complex form and solve it;

3) pass from images of unknown quantities in the complex form to the originals in a real form (to obtain the instantaneous values of these quantities);

4) verify the correctness of the calculation by conditions of active and reactive powers balance.

Let us consider the main methods of making and solve complex equations of the circuit.

4.5.3. Method of Kirchhoff's equations

 

The method is based on direct application of Kirchhoff laws for currents and voltages. By this the maximum number of equations of Kirchhoff's law for the current is composed. The remaining equations are based on Kirchhoff's law for the voltage. Independent values are currents in the branches. The number of equations in the system equals the number of branches of the network.
You can determine the following procedure for the calculation by the method of Kirchhoff's equations:

1) select the conditional positive direction of the currents in the branches;

2) select the independent nodes of the network, select the basic node, as the basic node it is advisable to take node, which converges the largest number of branches;

3) to construct q - 1 equations of Kirchhoff's law for the current for independent nodes (q -the total number of the network nodes);



4) select the independent loops of the network, it must be remembered that a branch with an ideal current source does not form a separate loop;

5) select the direction of path-tracing of the loops;

6) to construct p - q + 1 equations of Kirchhoff’s law for the voltages for independent loops (p - the number of the network branches);

7) the obtained system of equations of Kirchhoff's laws for the currents and the voltages solve together, find the currents of branches; if signs of calculated currents in some of the branches were negative, the actual direction of the currents in these branches are opposite of selected;

8) using the found values of currents and resistances branches determine the voltage of branches.

 


Date: 2015-12-18; view: 950


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