Resistivity and Temperature Coefficient of Resistance.

1.10 A three-phase Y-connected power system has rated numbers of 50MVA and 120kV.

Calculate the relative value of a three-phase apparent power of 40MVa for

(a) The basis is the apparent three-phase power of the system

(b) The basis is the apparent power per phase of the system.

1.11 A three-phase synchronous generator, Y connection, 6.25kVA; 220V has a capacitance of 8.4 

each phase

(a) Using the rated values ​​of the machine as a basis, calculate the relative power (b)Calculate the new relative power when choosing the new basis of 7.5 kVA; 230V

1.12 A three-phase, 13kV line supplies 8 MVA to the load. The total impedance of each phase of the line is (0.01+j0.05)tđ, calculated for the 8MVA, 13kV base. Calculate the effective voltage drop along the line.

1.13 Consider a part of a power system consisting of two generators connected in parallel, connected to a booster to supply power to a 230kV transmission line. The rated data of the above components are

Generator G 1 : 10MVA, 12% power

Generator G 2 : 5MVA, 8% power

Transformer T: 15MVA, 6% power

Line L(4+j60) , 230kV

In which the percentage electrical resistances are calculated based on the rated data of each component. Calculate the above percentage electrical resistances and impedances when choosing the new base capacity of 15MVA while the base voltages remain the same.

1.14 Draw the impedance diagram of the electrical system in Figure 1.17. Then choose a common base and calculate the relative values ​​of the circuit parameters on that common base.

1

10 KVA G

2500V

Z g1*

j. 0.2 tđ

T 1

40 KVA

Z d ( 50 j 200) 

Line

T 2

M

80 KVA

2500 /

8000

10,000 /

5000

20 KVA G2

2500V

Z T1*

j. 0.1tđ

Z T 2 *

j. 0.09 tđ

Z g2 *

j. 0.3 tđ

Figure 1.17

1.15 Draw the impedance diagram of the electrical system in Figure 1.18, in which the impedance values ​​are in %

G 1

15 MVA

6 %

66KV

(4 G 2

10 MVA

10%

5 MVA

8%

Figure 1.18 1-wire diagram of the electrical system

1.16 Draw the relative electrochemical diagram of the system in Figure 1.19.

G 2

T 1

j 60 2

G 3

G 1

20 MVA 30 MVA 30 MVA

15% 11/ 66KV 66/ 11KV T 3

15% 15%

Go to download

Figure 1.19 One-wire diagram of an electrical system

2.5 MVA

11/6.6 KV

8 %

Chapter 2

PARAMETERS OF POWER TRANSMISSION LINES

In the previous chapters, we saw that the power transmission line (or line for short) is one of the main parts of the power system. In terms of calculations, it is replaced by an equivalent circuit consisting of three characteristics or parameters: resistance, inductance, and capacitance.

2.1 RESISTOR

2.1.1 DC resistor (or DC resistor)

DC resistance of an electric wire with length l and cross-sectional charge S

To be:

R l

S

(2.1)

in which is the resistivity of the wire, in .m

2.1.2 Alternating current resistance (or AC resistance)

When a wire carries an alternating current, the current density is unevenly distributed across the wire's cross-section and depends on the frequency of the alternating current. This phenomenon is called the skin effect, or skin effect, and makes the AC resistance larger than the DC resistance (about 5 to 10%).

2.1.3 Change of resistance with temperature

The resistance of the conductor increases proportionally to the working temperature. Let R 1 and R 2 be the resistance at temperatures T 1 and T 2 respectively , we have:

R 2R 1  1    T 2 T 1 

In which called the temperature coefficient of resistance.

(2.2)

The resistivity and temperature coefficient of some metals are given in Table 2.1.

Table 2.1 Resistivity and temperature coefficient of resistance.

Material

Resistivity at 20 o c   . cm	Temperature coefficient at 20 o c o C  1
Aluminum	2.83	0.0039
Sports	6.4 - 8.4	0.0020
Cold drawn copper	1.77	0.00382
My friend	1.72	0.00393
Iron	10.0	0.0050
Silver	1.59	0.0038
Steel	12-88	0.001 – 0.005

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Note: Long lines may have additional parallel resistance (inductor) in addition to the series resistance.

2.2 INDUCTION

2.2.1 Single phase, 2 wire line

I

r

X

D

I

r

Y

a) b)

Figure 2.1: Illustration of 1-phase 2-wire line

The straight cross-section of a two-wire single-phase line is given in Figure 3.1a, where D is the distance between the centers of the two conductors and r is the radius of the conductor. The inductance per meter of a wire is:

L 1 L t L n (2.3)

L   0   0 ln D

(H/m) (2.4)

1 8 2 r

0

Where L t is the internal inductance, that is, the induction with the internal loop flux

in the wire, L n is the external inductance. Because of the vacuum, we have:

= 4 x10 -7 H/m (absolute permeability of

L = 1 x 10  7  1  4ln D 

(H/m)

r

1 

2 

Or L = 2 x 10  7  1  ln D 

(H/m) (2.5)

4

r

1 



1 1 1

Because  ln e 4  ln

4 1

e 4

so we have: (2.6)





L 1 = 2 x 10  7  ln





D 

 1  

(H/m) (2.7)

e 4 r 

With

r , r . e

 1

4  0.7788 r

(2.8)

is the geometric mean radius (BTN) of the wire, we have:

L = 2 x 10  7  ln D 

(H/m) (2.9)





1 r ' 

Thus, the total inductance, or loop inductance per meter, is:

L = 4 x 10  7  ln D 

(H/m) (2.10)





v r ' 

2.2.2 Three-phase, three-wire line

The single-phase inductance (or line-to-neutral inductance) of a three-phase line with three equally spaced conductors (the three centers of the three conductors are the three vertices of an equilateral triangle) is:

L = 2 x 10  7  ln D 

(H/m) (2.11)





n r ' 

Where D is the distance between the two conductors (i.e. the sides of an equilateral triangle) and r , is the BTN of each conductor.

However, in practice the three conductors of a three-phase line are rarely equidistant, so the inductance of the three different phases causes the voltage drop along the three different phases:

The line is unbalanced. To overcome this bad effect, people swap the three-phase circuits with each other at regular intervals along the line as shown in Figure 2.2.

D ab

D bc

b

a

c

c

b

a

a a c b

b D ca

c

Figure 2.2: Asymmetrical three-phase line layout

In this case, the average inductance of one phase of the commutation line is given by the same formula (2.11):





L = 2 x 10  7  ln D e 

(H/m) (2.12)

In there

n r ' 

3 D ab D bc D ca

D e (2.13)

is the geometric mean of the three distances D ab , D bc , D ca, also known as the equivalent distance of the three-phase line.

2.2.3 Lines made of mixed conductors (bundle wires)

A mixed conductor consists of many elements (or strands) connected in parallel. A twisted pair is also a type of mixed conductor. We will only consider the case where all the strands are identical and carry the same current.

Figure 2.3 shows a single-phase line consisting of 2 conductors. Conductor X consists of n wires; conductor Y consists of m wires, arranged arbitrarily. These wires are cylindrical, identical, and carry equal currents. Thus, each wire of X carries current I/n and each wire of Y (return wire) carries current – ​​I/m. The distance between 2 wires is denoted by D with the appropriate index.

b

c'

b'

c

a

a'm'

n

X-Line Y-Line

Figure 2.3: Single-phase line consisting of 2 mixed conductors. The inductance of wire X is:

mn ( D ' D ' ... D ' )( D ' D ' ... D ' )( D ' D ' ... D ' )

n 2 ( DD ... D )( DD ... D )( DD ... D )

aa ab am

three​

bb bm na nb nm

x

L  2 x 10  7 lnaa ab am ba ' bb bm na ' nb nm(H/m) (2.14)

In there:

°D aa' is the distance between (center of) fiber a and (center of) fiber a , .

r

a

° D aa = ' = 0.7788 r a is the BTN of fiber a.

Note that the expression in the root in the numerator of (2.14) is a product of mn terms, that is, the distances from each fiber of X to each fiber of Y. For each fiber of X there are m distances to m fibers of X, and since X has a total of n fibers, there are mn distances altogether.

distance. The mnth root of mn of this distance is called the geometric mean distance between wire X and wire Y; denoted by KTN or D m .

The expression in the square root in the denominator of (2.14) is the product of n 2 terms, which are the distances from each fiber of X to each fiber of X. Corresponding to each fiber of X

There are n distances to n fibers of X (including the 'distance' to the fiber itself), and since X has n fibers in total, there are n 2distance. square root of n2belong to

n 2 This distance is called the geometric mean radius of wire X, denoted by BTN or D s . So (2.14) becomes

L  2 x 10  7 ln D m ​​x D

(H/m) (2.15)

S

The inductance L Y of the Y wire is calculated similarly, and the inductance of the line made of mixed conductors is:

L = L X + L Y (2.16)

2.2.4 Three-phase, double-circuit line

Figure 2.4 is an example of a three-phase line, a double-circuit phase a consists of two conductors a and a' mace in parallel. Similarly, phase b consists of b,b' and phase c consists of c,c'. To overcome the imbalance of the three-phase inductance, the phases are permuted at equal intervals, similar to Figure 2.2

D

G

F

a c'c

b b'a

c a' b

b'ca'

a'bb'

c'a c'

Stage 1 Stage 2 Stage 3

Figure 2.4: Permutation line, three phase, double circuit