Iec tr 60909 2 2008

Table 1 – Actual data of typical synchronous generators, motors and condensers ...7Table 2 – Actual data of typical two-winding transformers NT: network; ST: power station .... INTERNATI

Scope and object

This part of IEC 60909 comprises data of electrical equipment collected from different countries to be used when necessary for the calculation of short-circuit currents in accordance with IEC 60909-0

Generally, electrical equipment data are given by the manufacturers on the name plate or by the electricity supplier

In certain situations, data may be unavailable; however, the information in this report can be utilized to calculate short-circuit currents in low-voltage networks, provided it aligns with the typical equipment used in the user's country The gathered data and its analysis can also serve medium- or high-voltage planning needs and facilitate comparisons with data from manufacturers or electricity suppliers Additionally, for overhead lines and cables, electrical data can sometimes be derived from physical dimensions and materials using the equations outlined in this report.

Thus this technical report is an addition to IEC 60909-0 It does not, however, change the basis for the standardized calculation procedure given in IEC 60909-0 and IEC 60909-3.

Normative references

The following referenced documents are indispensable for the application of this document

For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies

IEC 60909-0:2001, Short-circuit currents in three-phase a.c systems – Part 0: Calculation of currents

IEC 60909-3:- 1 , Short-circuit currents in three-phase a.c systems – Part 3: Currents du-ring two separate simultaneous line-to-earth short-circuit currents and partial short-circuit currents flowing through earth

General

The data required for calculating short-circuit currents is often provided in curve sheets or tabular examples For straightforward equations, calculations for positive-sequence and zero-sequence short-circuit impedances for overhead lines and cables are also included.

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Fifteen National Committees responded to a questionnaire prior to the first edition of this report, with the results detailed in Table 1 found in the Annex.

In some cases, average values or characteristic trends as function of rated power, rated voltage, etc are given.

Data of typical synchronous machines

Characteristic data of synchronous machines are listed in Table 1 The reactances are given as relative values related to Z rG =U rG 2 /S rG (see IEC 60909-0) Sometimes they are given in

Figure 1 illustrates the sub-transient reactances of synchronous machines, including generators, motors, and condensers, in the direct axis for 50 Hz and 60 Hz machines, plotted against their rated power.

Table 1 – Actual data of typical synchronous generators, motors and condensers

Relative values of reactances and d.c time constant

Czechos- lovakia a) TG2: Two-pole turbo generator

SC: Salient pole synchronous condenser b) ⎟⎟

U c) Negative-sequence reactance d) Zero-sequence reactance e) Unsaturated synchronous reactance f) Saturated synchronous reactance g) DC time constant for a three-phase terminal short circuit

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU. x '' d 100

Czechoslovakia ex-GDR Germany Hungary

Figure 1 – Subtransient reactance of synchronous machines 50 Hz and 60 Hz

(Turbogenerators, salient pole generators, motors SM and condensers SC)

In Figure 2 the rated voltages and power factors of 50 Hz or 60 Hz synchronous machines

(generators, motors) are plotted as a function of the rated power

Figure 3 illustrates the unsaturated and saturated synchronous reactances (\$x_{dsat}/x_d\$) for 50 Hz and 60 Hz turbogenerators, plotted against their rated power, which is essential for calculating the steady-state short-circuit current.

Data are also given for the zero-sequence reactance It is recommended that the relationship

Figure 2 – Rated Voltage U rG and rated power factor cos ϕ rG of synchronous machines

(Turbo generators, salient pole generators, motors and condensers 50 Hz and 60 Hz)

Czechoslovakia Denmark ex-GDR Germany

These values are excluded from the medium value x dsat / x d x dsat / x d

These values from Norway are excluded from x dsat / x d

Figure 3 – Unsaturated and saturated synchronous reactance of two-pole turbo generators 50 Hz and 60 Hz (relative values)

Data of typical two-winding, three-winding and auto-transformers

In Tables 2, 3 and 4 characteristic data of two-winding, three-winding and auto-trans-formers are listed

Table 2 – Actual data of typical two-winding transformers

(NT: network; ST: power station)

S rT U rTHV U rTLV u kr u Rr ± p T u k + u k −

1 0,63 20 0,4 6,0 1,2 Dyn5 LV ≈1 ± 5 off-load NT, 50 Hz,

2 24 33 11 24,2 1,12 YNyn0 HV, LV 0,7 10 ± 24,1 25,3 NT, 50 Hz,

3 31,5 112 22,2 12,8 0,37 YNd5 HV ≈1 ± 18 13,9 10,5 NT, 50 Hz Germany

5 a) 500 400 132 26,1 0,30 YNynd5 HV, LV ≈ 1 , 6 ± 13 NT, 50 Hz Denmark

10 780 230 21,0 15,3 0,2 YNd5 HV ≈ 0 , 8 ± 15 16,7 14,3 ST, 50 Hz Germany a) Two-winding transformer with an auxiliary winding in delta-connection (see Table 3)

Table 3 – Actual data of typical three-winding transformers

Zero-sequence reactances related to side A

S rTAB S rTAC S rTBC U rTA U rTB U rTC u krAB u krAC u krBC X (0)A X (0)B X (0)C

MVA MVA MVA kV kV kV % % % HV MV LV Ω Ω Ω

For the transformer No 6 in Table 3 the following Figure 4 gives additional information The low-voltage winding C (30 kV) is laying near the iron core, the medium-voltage winding B

The 230 kV high-voltage winding A features a primary section along with an additional tap winding linked to the on-load tap changer, positioned close to the star point on the high-voltage side of the transformer.

The reactances $X_A$, $X_B$, and $X_C$ in the positive-sequence system can be derived from the short-circuit voltages listed in Table 3 For the high-voltage side A (with $U_{rTA} = 400 \, \text{kV}$), the calculated results are $X_A = 51.1 \, \Omega$, $X_B = -4.4 \, \Omega$, and $X_C = 124.93 \, \Omega$, without considering impedance correction factors as per IEC 60909-0 Notably, the value of $X_C$ is slightly negative, similar to $X(0)B$.

When the star point at the high-voltage side is earthed, the equation \$X(0)T = X(0)A + X(0)C\$ applies Conversely, if the star point at the medium-voltage side is earthed, a different approach is required.

X (0)T = X (0)B + X (0)C is valid related to the high-voltage side or related to the medium-voltage side: X (0)Tt = (X ( 0 ) B +X ( 0 ) C )×(230 kV) 2 /(400 kV) 2

Key a terminals and rated apparent power of the windings A, B and C b position of the tree windings in relation to the iron core c positive-sequence reactances d zero-sequence reactances

SA, SB switches at the HV- and MV-side

Figure 4 – Three-winding transformer (No 6 of Table 3)

Table 4 – Actual data of typical autotransformers with and without tertiary winding

Rated voltages Rated short-circuit voltages

Zero-sequence reactances related to side A

S rTAB S rTAC S rTBC U rTA U rTB U rTC u krAB u krAC u krBC X (0)A X (0)B X (0)C

MVA MVA MVA kV kV kV % % % HV MV LV Ω Ω Ω

7 300 300 – 235 165 – 7,0 – – YN yn0 13,0 – – Denmark a)Three separate poles

Figure 5 illustrates the relationship between the rated short-circuit voltage and the rated apparent power of unit transformers (ST) in power stations, both with and without on-load tap-changers The average value for the rated short-circuit voltage is represented by the formula: \$\ln MVA\$.

USA u kr u kr u kr u kr

Figure 5 – Rated short-circuit voltage u kr of unit transformers in power stations (ST) with or without on-load tap-changer

From Figure 5 it can be seen that the following average values for u kr may be used:

In Figure 6 the rated short-circuit voltage of network transformers (NT) is plotted as a function of the rated power For low-voltage transformers u kr = 4 % and 6 % are commonly used

In general u kr values for auto-transformers are lower

The u kr values for network transformers in the UK are, on average, twice as high as those reported from other countries

The relationship X (0) /X (1) for two and three winding transformers, if only one star point is earthed, is as follows:

USA u kr u kr u kr u kr

Figure 6 – Rated short-circuit voltages u kr of network transformers

Data of typical overhead lines, single and double circuits

The positive sequence impedance may be calculated from conductor data such as cross section and conductor centre-distances (see IEC 60909-0, 3.4, Equations (14) and (15))

The effective resistance per unit length at a conductor temperature 20 °C is:

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU. n

At a conductor temperature of 20 °C for the calculation of the maximum short-circuit current, the following values may be used:

In case of aluminium/steel conductors only the aluminium cross-section shall be used for q n

The equations provided are essential for calculating the short-circuit impedances in both the positive-sequence and zero-sequence systems of overhead lines This applies to configurations with single conductors or bundled conductors, accommodating one or two three-phase a.c circuits, regardless of the presence of earth wires.

In the context of electrical engineering, the variable $ n $ represents the number of subconductors, which can take values of 1, 2, 3, 4, or 6 When $ n = 1 $, there is a single conductor present The radius of each subconductor is denoted as $ r $, while $ d $ is defined as the geometric mean distance between the conductors, calculated as $ d = 3 d_{L1L2} d_{L1L3} d_{L2L3} $ Additionally, the effective bundle radius $ r_B $ is given by the formula $ r_B = n \cdot r \cdot R^{n - 1} $, where $ R $ is the radius of the circle on which the subconductors are arranged, as illustrated in the accompanying figure.

Zero-sequence system impedance without earth wire:

The zero-sequence system impedances in Figures 7 and 8 and in Table 5 are referred to an earth resistivity of ρ0Ωm and therefore to an equivalent depth of current return of

930m δ = (50 Hz) or δ 0m (60 Hz) For the calculation of δ see IEC 60909-3, Equation

Zero-sequence impedance with one earth wire Q:

Example for a bundle conductor with two subconductors

Z =ω μ + ω μ δ , and d QL = 3 d QL 1 d QL 2 d QL 3 μrQ depends on the material and structure of the earth wire

Zero-sequence impedance with two earth wires Q1 and Q2:

NOTE In case of 60 Hz, the values shall be multiplied by 1,2

Figure 7 – Positive-sequence reactance X ( ' 1 ) =X L ' of low-voltage and medium-voltage overhead lines 50 Hz, Cu or Al, with one circuit according to Equation (15) of

Positive-sequence impedance per circuit:

3 L1M 1 L2M 2 L3M 3 mL1M1 d d d d = and d mL1M2 = 3 d L1M 2 d L1M 3 d L2M 3 , if the line conductors of both circuits are symmetrical to the tower, otherwise use:

6 L1M2 L1M3 L2M3 L2M1 L3M1 L3M2 mL1M2 d d d d d d d In many cases the quotient, d mL1M2 /d mL1M1 , has results in the neighbourhood of one and then the positive sequence impedance per circuit is Z ' ( II 1 ) ≈Z ( I' 1 )

Table 5 – Actual data of typical overhead lines 50 Hz and 60 Hz

Geometric data (see 2.4 and Figure 8) r d d mL1M2

Voltage Conductors/ subconductors number material q n

Earth wire number material q n r B d LM d mL1M1 d Q1Q2 d QL

No Type of line/ number of circuits

(Fig 9) kV mm 2 mm 2 mm m m m m Ω / km Ω / km

(60 Hz) a) Impedances per circuit and resistances at a temperature of 20 °C b) Special design Two separate lines in one single right-of-way c) Since 2006, a new configuration of conductors is typical: 3×Al/St 635/117

Zero-sequence impedance with one earth wire Q per circuit:

LM d d d = ; d mL1M 1 = 3 d L1M 1 d L2M 2 d L3M 3 ; d mL1M2 = 3 d L1M2 d L1M3 d L2M3 , if the line conductors of both circuits are symmetrical to the tower

For Z ' QQE and Z ' QLE see the information following Equation (5)

Figure 8 – Positive-sequence reactance X ( ' 1 ) =X L ' of overhead lines 50 Hz

(60 Hz-values converted to 50 Hz)

Zero-sequence impedance with two earth wires Q1 and Q2:

For Z ' LME , see the information following Equation (8) respectively for Z ' Q1Q2E and Z ' Q1Q2LE , see the information following Equation (6)

Figure 9 – Type of overhead lines

Data of typical high-voltage, medium-voltage and low-voltage cables

The impedances of high-, medium-, and low-voltage cables are influenced by national techniques and standards, and can be sourced from textbooks or manufacturers' data Table 6 presents the characteristic data for 50-Hz cables.

Table 6 – Actual data of typical electric cables

No kV - - mm 2 - - - - Ω /km - Ω /km

2 6/10 3 × 1 Cu 120 rST R h) SC W+T Cu 0,16+j0,116 S+E - Hungary

3 10 3 Cu 240 rST NR TC M Pb 0,088+j0,069 S+E +j0,242 China

4 22 3 Cu 120 rST NR i) TC FW Cu 0,153+j0,104 S+E - Norway

6 110 3 × 1 Cu 240 HO R j) SC M Pb/Al 0,079+j0,12 S+E 0,51+j0,30 Germany

7 132 3 × 1 Cu 220r HO R SC M Pb 0,084+j0,12 S 0,58+j0,061 Italy

The article discusses the specifications of a cable identified as 10 380 3 × 1 Cu 1200sST R SC M Al, which features a line-to-line voltage and a round, hollow, sector form with stranded construction It highlights the distinction between radial and non-radial fields, indicating that the cable is a single core (SC) type Key components include tapes, wires, and a metallic sheath, with AC resistance measured at 20°C The cable's sheath (S) provides shielding, while the earth (E) and a fourth conductor (4th) are also mentioned Additional identifiers include N2YSY and DKAB, along with considerations for oil pressure.

Table 7 presents the equations for calculating the positive-sequence and zero-sequence impedance of single-core cables, both with and without a metallic sheath or shield earthed at both ends Notably, Case No 2 applies to low-voltage systems featuring four equal cores (N = PEN).

Table 7 – Equations for the positive-sequence and the zero-sequence impedance of cables

Cable configuration Positive-sequence and zero-sequence impedance

Cable without metallic sheath or shield ⎟⎟

3 d L1L2 d L1L3 d L2L3 d = and δ from Equation (36) of IEC 60909-3

Cable without metallic sheath or shield

Four equal single-core cables (low voltage)

Z ω μ (12) Current return through the fourth conductor N

Current return through the fourth conductor N and the earth E

(14) with Z ' ( 0 ) from Equation (11) and d LN = 3 d L1N d L2N d L3N

Cable with metallic sheath (shield) S earthed at both ends

Current return through sheath (shield) and earth

= (16) with Z ' ( 1 ) from Equation (10), Z ' ( 0 ) from Equation (11) and the medium radius r Sm =0,5(r Si +r Sa ) of the sheath or the shield

Case No 3 in Table 7, represented by Equations (15) and (16), applies to three single-core high-voltage cables, such as those rated at 64 kV/110 kV, which have a metallic sheath or shield that is earthed at both ends In both positive-sequence and zero-sequence current systems, currents flow through the sheaths or shields of these cables Consequently, the calculation of the reduction factor, as outlined in IEC 60909-3, must also consider the three sheaths or shields.

2 conductor screen: semi-conducting XLPE

4 insulation screen: extruded semi-conducting XLPE

Figure 10 – Single-core cable 64 kV / 110 kV with lead sheath [4] 2

Table 8a presents data and results derived from Equations (15) and (16) in Table 7 for Case No 3a, which involves a triangular configuration of three high-voltage single-core cables with a lead sheath rated for 64/110 kV (U m = 123 kV) 2XK2Y, as provided by the manufacturer [4] Additionally, Table 8b addresses the flat configuration of the cables, requiring the calculation of arithmetic mean values.

2 Figures in square brackets refer to the Bibliography

Table 8 – Single-core cables 64/110 kV, 2XK2Y,

3×1×240 1 200 rm, Cu with lead sheath a) in triangular configuration

Zero-sequence impedance Z ' (0)SE =R (0)SE ' =jX (0)SE ' in case of current return through the sheath and the earth, f = 50 Hz, ρ = 100 Ωm, q n r L q S a) r Sm a)

X c) r 3 d) mm 2 mm mm 2 mm mm mm Ω /km Ω /km Ω /km - - -

0,177 0,170 a) q S =2πr Sm d S with S d thickness of the lead sheath b) d ≈1,06D a in case of a triangle configuration c) '

Z ( according to Equation (16) d) Reduction factor of the three sheaths of the single-core cables, see Equation (17) b) in flat configuration q n r L q S a) r Sm a)

X X c) r 3 d) mm 2 mm mm 2 mm mm mm Ω /km Ω /km Ω /km - - -

The lead sheath thickness is represented by \$d S\$ in the equation \$q S = 2\pi r d S\$ For a flat configuration, the diameter is calculated using \$d = (D a + 70 \text{ mm}) \cdot 3^2\$ The parameter \$Z' (0)SE\$ is defined according to Equation (16) Additionally, the reduction factor for the three sheaths of single-core cables is detailed in Equation (17).

The calculated results for single-core cables, based on German Standards, are presented for conductors made of copper or aluminum, featuring cross-linked polyethylene (XLPE) insulation, a copper wire and tape shield, and a polyethylene sheath The tables provide the positive-sequence and zero-sequence impedance for current return through the shield and the earth, specifically for selected cross sections of 6-/10-kV and 12-/20-kV cables Additionally, the reduction factor $ r_3 = \frac{I_E}{3I_0} $ is included, considering the shield of all three single-core cables.

Table 9 – 10-kV-cables N2XS2Y a) in triangular configuration (Table 7, Case No 3a) q n a)d)

X r 3 mm 2 mm mm mm Ω /km Ω /km Ω /km - - -

0,34 0,34 0,34 a) rST, see Table 6 b) d = 1,05×D a c)κ VSm/mm 2 d) Dataq n , R ' L D a , r Sm according to [3] and [4]. b) in flat configuration (Table 7, Case No 3b) q n a)d) D a b)d) r L r Sm d)

0,36 0,36 0,37 a) rST, see Table 6 b) d = (D a + 70 mm) 3× 2 c) κ VSm/mm 2 d) Data q n , R L ' , D a , r Sm according to [3] and [4].

Table 10 – 20-kV-cables N2XS2Y a) in triangular configuration (Table 7, Case No 3a) q n a)d)

0,34 0,34 0,34 a) rST, see Table 6 b) d = 1,05×D a c) κ VSm/mm 2 d) Data q n , R L ' Δa, r Sm according to [3] and [4] b) in flat configuration (Table 7, Case No 3b) q n a)d)

0,37 0,37 0,37 a) rST, see Table 6 b) d = (D a + 70 mm) 3× 2 c) κ VSm/mm 2 d) Data q n , R L ' , Δa, r Sm according to [3] and [4].

Results for Case No 2a in Table 7 are given as an example in Table 11 in the case of four low-voltage (0,6/1 kV) single-core cables NYY 4×1× q n

Table 11 – Positive-sequence and zero-sequence impedance of four low-voltage single-core cables NYY 4×1× q n (Case No 2a in Table 7) with

R , X ( ' 0 ) N /X ( ' 1 ) N in case of current return through the fourth conductor N and

R , X ( ' 0 ) NE /X ( ' 1 ) N in case of current return through the fourth conductor N and the earth

X d) r e) mm 2 mm Ω /km mm Ω /km - - -

0,18 0,16 0,15 a) See Table 6; b) D a = D amax, outer diameter of the single-core cable, 6 a

Z ( according to Equation (14) e) See Equation (21)

The results R (0)NE ' /R (1)N ' , X (0)NE ' /X (1)N ' given in Table 11, are valid for an earth penetration depth of δ = 931 m and a cable length of at least 1 000 m In case of short cables

(l < 1 000 m ≈ δ ) the results, R (0)NE ' /R (1)N ' ,X (0)NE ' /X (1)N ' are smaller than those given in

Table 11 In this case δ should be replaced by the expression d E =(2/e)l C e − l C /( e δ ) with l C as the cable length ( l C < δ ) and e = 2,718 and ωμ 0 /8 should be replaced by 0 , 75 (ωμ0 / 8 ) d E /δ

Low-voltage cable according to German Standards (N) [3]:

Cable with copper or aluminium (A) conductors

(example: four-core cable), insulation of thermoplastic material based on PVC (Y) and a protective covering in the form of a sheath of thermoplastic material based on

Current return through the fourth conductor N (with full cross section):

Current return through the fourth conductor N and the earth E:

Reduction factor (Current through earth: I E =r3I ( 0 ) , see IEC 60909-3):

Table 12 – Low-voltage cable NYY a) with four copper conductors q n a) r L '

X r mm 2 mm Ω/km mm mm mm Ω/km - - - - -

0.17 0.15 0.14 a) See Table 6 b) Resistance at 20 °C c) Thickness of insulation d) d=3 d L1L2 d L1L3 d L2L3 e) Outer diameter of the four-core cable b) with four aluminium conductors q n r L R L ' a) d b) D a c)

X r mm 2 mm Ω/km mm mm Ω/km - - -

L2L3 L1L3 L1L2 d d d d= c) Outer diameter of the four-core cable.

Three-and-a-half–core cable NYY:

Current return through the fourth conductor N (with reduced cross section):

Current return through the fourth conductor N (with reduced cross section) and the earth E:

Table 13 – Low-voltage cable NYY with three and a half copper conductors q n r L R L ' r N R N ' d

X r mm 2 mm Ω/km mm Ω/km mm Ω/km - - -

The N(A)YCWY cable features three or four conductors made of copper or aluminum, insulated with thermoplastic material based on PVC It includes a helically applied concentric copper conductor and is encased in a PVC-based thermoplastic sheath.

Cable with four conductors NYCWY:

Current return through the fourth conductor N and the concentric copper conductor S:

2π 4 (27) with the medium radius r Sm = 0 , 5 ( r Sa + r Si )

Current return through the fourth conductor N, the concentric copper conductor S and the earth E:

N LS S LN NS LN LS

Table 14 gives the results found with Equations (26) to (29) for cables NYCWY with four equal conductors The data r L ,R L ' ,r N =r L ,R N ' =R L ' and d =d LN are the same as in Table 12a

Table 14 – Low-voltage cable NYCWY with four copper conductors q n a)

X r mm 2 mm mm Ω/km Ω/km - - - - -

L,R ,r r ,R R r = = and d are given in Table 12a a) See Table 6 b) r Sm = 0 , 5 ( r Sa + r Si ) c) 2

Cable with three conductors N(A)YCWY:

Current return through the concentric copper conductor (shield S):

Z ω μ (31) with the medium radius of the shield or sheath r Sm =0,5(r Sa +r Si )

Current return through the concentric copper conductor (shield S) and the earth E:

Table 15 – Low-voltage cable NYCWY a) with three copper conductors q n r L a)

X r mm 2 mm Ω/km mm Ω/km mm Ω/km - - -

0,35 0,27 0,22 0,18 a) See Table 12a b) See Table 12a c) r Sm=0 , 5 ( r Sa+r Si ) d) κS =56 Sm/mm 2 e) 3

LICENSED TO MECON Limited - RANCHI/BANGALORE FOR INTERNAL USE AT THIS LOCATION ONLY, SUPPLIED BY BOOK SUPPLY BUREAU. b) with three aluminium conductors q n r L a)

X r mm 2 mm Ω/km mm Ω/km mm Ω/km - - - - -

0,21 0,17 0,14 a) See Table 12b b) See Table 12b c) r Sm =0 , 5 ( r Sa+r Si ) d) κS =56 Sm/mm 2 e) 3

The belted cable features three conductors made of copper or aluminum, insulated with mass-impregnated paper for both the conductors and the belt It is encased in a smooth extruded aluminum sheath, complemented by a protective covering that includes a layer of elastomer tape or plastic film Additionally, the cable is finished with a thermoplastic sheath made from PVC, designated as N(A)KLEY.

Equations (30) to (33) apply to the positive-sequence and zero-sequence impedance, as well as the reduction factor for type B cables with three conductors Historically, N(A)KLEY cables were utilized in local networks, where an aluminum sheath served as a neutral conductor (N) or a protective earth and neutral (PEN) conductor.

The cable features four (or three and a half) conductors made of copper or aluminum, insulated with mass-impregnated paper It is protected by a lead sheath reinforced with steel tape armoring, and finished with an outer layer of fibrous material, designated as N(A)KBA.

These cables are used in former times in low-voltage distribution networks, if the additional earthing by the lead-sheath was necessary [3]

The positive-sequence and zero-sequence impedance calculations, along with the reduction factor, can be performed by neglecting the steel tape armoring For four (or three and a half) conductors, refer to Equations (26) to (29), while for four conductors, use Equations (30) to (33).

The reduction factor for a lead sheath and armoring with a minimum of two overlapping steel tapes is determined through measurement, as detailed in the results presented in [3].

Figure 11 – Reduction factor depending on the inducing current for cables with one lead sheath and two overlapping steel tapes, f = 50 Hz [3]

Figure 12 – Reduction factor depending on the inducing current for cables with three lead sheaths and two overlapping steel tapes, f = 50 Hz [3]

Data of typical asynchronous motors

The locked-rotor current to rated current ratio (\$I_{LR}/I_{rM}\$) varies between low- and medium-voltage motors For low-voltage motors, this average ratio is around 6.7 for power ratings between 2 kW and 300 kW per pair of poles In contrast, medium-voltage motors exhibit an average ratio of approximately 5.5 for power ratings ranging from 30 kW to 6 MW per pair of poles.

In Table 16 actual data of asynchronous motors are given

Table 16 – Actual data of typical asynchronous motors

Number of pair of poles p

Figure 13 illustrates the ratio of \$I_{LR}/I_{rM}\$, while Figure 14 depicts the product of the power factor \$\cos \phi_{rM}\$ and efficiency \$\eta_{rM}\$ as a function of the active power per pair of poles \$P_{rM}/p\$.

Denmark ex-GDR Germany Hungary

Active power of the motor per pair of poles m = P rM /p

Low-voltage motors ex-Czechoslovakia

Figure 13 – Ratio I LR / I rM of low-voltage and medium-voltage asynchronous motors, 50 Hz and 60 Hz

Australia Bulgaria China Denmark ex-GDR Germany Hungary Italy

Japan Norway USA ex-USSR

Medium-voltage motors Low-voltage motors

Figure 14 – Product cosϕ rM xη rM of low-voltage and medium-voltage motors, 50 Hz and 60 Hz

Busbars

Collected data of busbars are given in Table 17

Table 17 – Actual data of distribution busbars

I r Num- ber Mate- rial Cross section

No kV A - - mm 2 - Ω/km Ω/km

USSR a) Split bar 2× 1 600 A b) Current return through sheath (S) and earth (E)

The medium positive-sequence reactance per unit length of busbars, which do not have sheath or shielding, can be calculated for configurations with one, two, or three parallel bars made of copper (Cu) or aluminum (Al) for the main conductors L1, L2, or L3 This calculation utilizes the theory of geometric mean distance.

Approximations for the geometric mean distance g L1L1 are given in Figure 15 g L1L1 = (0,23+0,222 5 × n) × a g L1L1 = (0,74+0,226 5 × n) × a g L1L1 = (1,218+0,227 5 × n) × a

Figure 15 – Geometric mean distance g L1L1 = g L2L2 = g L3L3 of the main conductors

The factors α =g L1L2 /d L1L2 and β =g L1L3/d L1L3 are given in the Figures 16a, 16b, 16c for one, two or three bars per main conductor (Figure 15), depending on the distance d L1L2 (d L1L3

= 2ãd L1L2 ) and the factor n= 2, 4, 6, (see Figure 15) a) For one bar per main conductor; a = 10 mm

IEC 2044/08 b) For two bars per main conductor; a = 10 mm

IEC 2045/08 c) For three bars per main conductor; a = 10 mm

Figure 16 – Factor α and β for the calculation of X ( ' 1 ) given in Equation (34)

Table 18 – Example for the calculation of X ( ' 1 ) for busbars using Figures 15 and 16

L1, L2, L3 a n a× × (Fig 15) mm 60 10 × 2 × 60 × 10 3 × 60 × 10 q n mm 2 600 1 200 1 800 g L1L1 (Figure 15) cm 1,565 2,099 2,583 g L1L2 = α×d L 1 L 2

Data given in the Tables 1, 2, 3, 4, 5, 6, 16 and 17 of this publication are collected from different countries In all, 15 National Committees provided information for the first edition of

IEC/TR 60909-2: 1992 Information received at that time is listed in the following Table A.1

(see Table 1 of IEC/TR 60909-2: 1992)

Table A.1 – Information received from National Committees

Number of answers to questionnaire tables National

[1] Balzer, G., Impedanzmessungen in Niederspannungsnetzen zur Bestimmung der

Kurzschluòstrửme (Measurement of impedances in low-voltage networks for the determi-nation of short-circuit currents) Diss TH Darmstadt 1977

Meyer, E P explores the phenomenon of current return through the earth, focusing on the impedances and inductive interference associated with conductors of finite length in his dissertation at TH Darmstadt.

[3] Heinhold, L., Kabel und Leitungen für Starkstrom, Part 1:1987, Part 2:1989 Siemens

[4] NEXANS, Energy Networks Germany Insulated Cables for High and Extra High

Voltage Nexans Deutschland Industries AG & Co KG, 2000

[5] Oeding, D., Oswald, B R., Elektrische Kraftwerke und Netze, 6 Edition: Springer 2004

[7] IEC/TR 60909-1:2002, Short-circuit currents in three-phase a.c systems – Part 1:

Factors for the calculation of short-circuit currents according to IEC 60909-0

[8] IEC/TR 60909-4:2000, Short-circuit currents in three-phase a.c systems – Part 4:

Examples for the calculation of short-circuit currents

Tiêu đề	Short-circuit Currents in Three-phase AC Systems – Part 2: Data of Electrical Equipment for Short-Circuit Current Calculations
Trường học	International Electrotechnical Commission
Chuyên ngành	Electrical Engineering
Thể loại	Technical report
Năm xuất bản	2008
Thành phố	Geneva

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