JB/T 10181.6-2000 Calculation of cable current carrying capacity Part 3: Sections related to operating conditions Section 2: Economic optimization of power cable cross-section
Some standard content:
Mechanical Industry Standard of the People's Republic of China
Calculation of the current rating of electric cablesPart 3: Sections on operating conditionsSection 2: Economic optimization of power cable sizeJB/T10181.6-2000
idtIEC60287-3-2:1995
This standard describes a method for selecting the economic cross-section of the conductor, taking into account the initial investment and the expected values of the joule losses during the economic life of the cable.
Note: The method recommended in this standard is not applicable to cables working under system voltage equal to or greater than the following values (see JB/T10181.1) Cable type
Impregnated paper insulated cable:
Viscous impregnated paper
Oil-filled and gas-filled
Other types of insulated cables:
Ethylene propylene rubber (EPR)
Polyvinyl nitride (PVC)
Polyethylene (PE) (HD and LD)
Cross-linked polyethylene (XLPE) (non-filled type) Cross-linked polyethylene (XLPE) (filled type) System voltage U. (kV) 2)
Matters such as maintenance, energy loss of forced cooling system and hourly electricity pricing are not included in this standard. 2 Reference standards
The provisions contained in the following standards constitute the provisions of this standard through reference in this standard. At the time of publication of the standard, the versions shown are all valid. All standards are subject to revision. Parties using this standard should explore the possibility of using the latest version of the following standards. GB/T3956--1997
JB/T 8996--1999
JB/T 10181.1--2000
JB/T10181.3—2000
Instructions for adoption:
Conductors of cables
Guidelines for the selection of high-voltage cables
Calculation of cable current carrying capacity Part 1: Calculation of current carrying capacity formula (100% load factor) and loss Section 1: General provisions
Calculation of cable current carrying capacity Part 2: Thermal resistance Section 1: Calculation of thermal resistance 1) As the influence of dielectric loss on the selection of economically optimized cross-section has been supplemented in the IEC60287--3-2 amendment, the original note has been deleted. 2) The voltage value is consistent with JB/T8996.
Approved by the State Bureau of Machinery Industry on April 24, 2000 and implemented on October 1, 2000
IEC60853
3 Symbols
JB/T 10181.6-2000
Calculation of the maximum periodic and emergency current carrying capacity of cables, the variable part of the cost per unit length related to the conductor cross-section Auxiliary quantity defined by formula (16)
The constant part of the cost per unit length related to the laying conditions, etc. Total cost of the cable system
Annual power supply cost
Auxiliary quantity defined by formula (10)
The maximum load in the first year, that is, the maximum average current value I(t) per hour
Load as a function of time
Cable length
The present value of the Joule loss cost over a period of N years The time period included in the financial calculation is also referred to as the "economic life" Number of phase conductors in the circuit
Number of circuits with the same type and load
Energy cost for 1 W·h at the corresponding voltage poleInstallation cost of the cable line
Installation cost of the adjacent larger standard conductor cross-sectionInstallation cost of the adjacent smaller standard conductor cross-sectionAuxiliary quantity defined by equation (8)
AC resistance per unit length of cable, including the added values of yp, y, lambda, lambda2 (which can be considered as constants at average operating temperature, see Chapter 4)AC resistance per unit length of the adjacent larger standard conductor cross-sectionAC resistance per unit length of the adjacent smaller standard conductor surfaceAC resistance per unit length of conductor unit length Functional relationship between AC resistance and its cross sectionCross section of cable conductor
Economic cross section of conductor
Working time under maximum Joule loss
Annual added value at Imx
Annual added value of P, excluding inflation factorDiscount rate used to calculate present value
Auxiliary quantity defined in formula (9)
Proximity effect coefficient, see JB/T10181.1
Skin effect coefficient, see JB/T10181.1
cu/m·mm*
cu/W·year
cu/W·h
Temperature coefficient of conductor resistance at 20℃||t t||Maximum allowable operating temperature of conductor
Average ambient temperature
Average operating temperature of conductor
JB/T10181.6—2000
Metal sheath loss factor, see JB/T10181.1Armor loss factor, see JB/T10181.1
Load loss factor, see IEC60853
Conductor resistivity at 20℃, see 5.2
4 Calculation of total cost
During the economic life of the cable, the total cost of cable installation and operation expressed in present value is calculated as follows. Note that the financial amount used is expressed in arbitrary monetary units, recorded as (cu).
CT=CI+CJ（eu）
Where: CI—Total cost of cable line installation (cu): (1)
CJ The equivalent cost of energy loss is calculated from the date of purchase of the cable line device, that is, the present value of Joule loss (cu) during the economic life of N years.
Estimation of C value
The total cost of loss consists of two parts: a) energy cost and b) additional cost of power supply loss. a) Energy cost
Energy loss in the first year=（Im2RLN,N）TWhere: Imar-Maximum load of the cable in the first year (A):
L—Cable length (m);
(W·h)
R-AC resistance per unit length of conductor (2/m) taking into account skin effect and proximity effect (y, y) and losses in metal shielding and armor (,).
Because the economic cross-section of the conductor is often larger than the cross-section of the conductor determined by thermal conditions (i.e., the size determined by JB/T10181.1, JB/T10181:3 and/or IEC60853), the conductor temperature is lower than its maximum allowable value. In the absence of more accurate information, it is more convenient to assume that it is a constant, that is, R is a constant, and the corresponding temperature is (8-0.)/3+0. Where: 0-corresponds to the maximum rated temperature of the conductor of this cable type: 0. Average ambient temperature. Factor 3 is an empirical value, see Appendix B. Note: If higher accuracy is required (for example, when the calculation cannot clearly determine what is the nominal cross-section of the conductor to be selected, or the load increase in the last few years is significantly greater than that in the first year), the above can be used. The conductor section obtained by the approximate temperature is used as the starting point for calculation, and a more accurate estimate of the conductor temperature is required.
Appendix B gives a method for more accurate estimation of conductor temperature and resistance value. Then the economic section is determined again using the corrected value of the conductor resistance. The influence of conductor resistance on the economic section is very small, so a single alternative calculation is sufficient, N,--the number of phase conductors in each circuit;;
N is the number of circuits with the same type and load value:
T—operating time under maximum joule loss (h/year), that is, the number of annual hours of the maximum current Imax to be applied to equal the total annual energy loss generated by the actual variable load current. JB/T1018116-2000
8760 1(t)2
If the load loss factor II is known and can be assumed to be constant during the economic life, then: T=μx8760
See IEC60853 for deriving the loss factor μ. Time, h;
I(t) Load current as a function of time, A. The energy loss cost in the first year is:
= (Im2XRXLXN,XN,) XTXP
Energy cost per watt-hour at the corresponding voltage level, cu/W·h. Where: P
b) Additional power supply cost
The cost of additional power supply required to provide energy loss is: =(ImXRXLXN,XN) XD
Where: D-the additional cost required per year, cu/W·year. Therefore, the total cost of energy loss in the first year is: (cu/year)
= (Ima2XRXLXN,XN)× (TXP+D)
If the cost is paid at the end of that year, the present value of the cost on the date of purchase of the device is: (Imax×R×L×N,×N,)x(T×P+D)1+i/100
Where: i
Discount rate excluding the effect of inflation, %. Similarly, the present value of the cost discounted to the purchase date within the N-year operating period is: (Imax -RLN,N.)(T.P+ D).Q
1+i/100
(cu）
(cu）
Where: O - the increase in energy costs within N years taking into account the increase in load and the discount rate coefficient is: 1-
r=(1+ a /100 )*(1 + b /100 )1+/100
Where: a
-annual load increase, %;
b-annual increase in energy costs excluding inflation, %. (3)
· (9)
When it is necessary to take into account the series calculation of different conductor cross-sections, all parameters except conductor current and resistance can be expressed by a coefficient F: F=N,·N,·(T· P+D).
Then the total cost is:
1+i/100
CT=CI+Ima2×RXLXF
5 Determine the economical cross-section of the conductor
5.1 The first method: The economical current range of each conductor in the series cross-section 96
(cu/w)
JB/r10181.6-2000
For given installation conditions, all conductor cross-sections have an economical current range. The upper and lower limits of the economical current of a given conductor cross-section can be obtained by the following formula:
The lower limit of the maximum current:
CI-CI,
F.1(R, - R)
Upper limit of maximum current:
cI, cr
NF.1.(RR,)
Where: CI refers to the installation cost of the conductor cross-section cable, cu; R-the AC resistance per unit length of a conductor cross-section cable, /mCI,-the installation cost of the adjacent smaller conductor standard cross-section cable, cu:Cl-the installation cost of the adjacent larger conductor standard cross-section cable, cu;(A)
R,-the AC resistance per unit length of the adjacent smaller conductor standard cross-section cable, α/m;R,-the AC resistance per unit length of the adjacent larger conductor standard cross-section cable, 2/m. Note
1 The upper and lower limits of the economic current of each conductor cross-section can be listed in a table to select the most economical conductor cross-section under a specific load. 2 The upper limit of the economic current of a conductor cross-section is the lower limit of the economic current of the adjacent larger cross-section. 5.2 Second method: Economic cross-section of conductor for a given load 5.2.1 General formula
Economic cross-section The general formula is the cross-section that minimizes the total cost function, namely: CT (s) = CI (s) + Im2XR (s)XLXF(cu) Where: CI (s), R (s) - expressed as a function of the conductor cross-section S, see 5.2.2. (12)
· (13)
(14)
The relationship between CI (s) and conductor cross-section can be derived from the known prices of standard cross-sections: Generally, if a linear relationship can be reasonably fitted within the limited range of conductor cross-sections, it should be adopted. Taking into account the fact that there may be some uncertainty in the financial parameters assumed during the selected economic life, the calculated results will have a small error. R (s) is expressed as a function of the cross-section. For aluminum stranded wire, it can be obtained according to JB/T10181.1: R (s) = B· P2ol1 + α20 (8.-20)] × 10° (2/m)..S
B=(1ty,ty,)(1+^ + α2)
Where: P20 conductor DC resistivity (α·m); (15)
（16)
Note: The economic cross section of the conductor is unlikely to be equal to the standard cross section of the conductor, so it is necessary to provide a continuous relationship between the conductor cross section and resistance. It can be obtained by setting the resistivity of various materials. P2 recommended value; copper is 18.35×10-9, aluminum is 30.3×10~9, this value is not the actual value of the material, but the attenuation value, so that the conductor resistance can be calculated directly from the nominal cross section instead of the actual cross section. J, yp - skin effect and proximity effect coefficient, see JB/T10181.1^^z - metal sheath and armor loss factor, see JB/T10181.1; - resistance temperature coefficient of actual conductor material at 20℃, 1/K; a20
0 - conductor temperature, see the definition of R in formula (2), ℃: B - auxiliary quantity in formula (16), assuming that the conductor cross-section is a certain possible value, this value is calculated by JB/T10181.1: 97
- cable conductor cross-section (mm).
S-Linear cost function for cable cost
JB/T 10181.6-2000
5.2.2 If the linear model can be adapted to the cable type under consideration and the original cost of installation, then: CI (s) = LX (AXS + C)
Where: A - variable cost part related to conductor cross section, cu/m mm2; C - constant cost part not related to conductor cross section, cu/m: L - cable length, (m).
From formula (14), S can be derived and made equal to zero to obtain the optimal cross section S (mm2): Ss = 1000x
[Imax × F × P20 ×B×[1 + α20 ×(0m - 20]A
（18）
1When the economic cross section is unknown, it is necessary to assume a possible cable cross section in order to calculate the rational values of "'s, and input, person,. If the economic cross section is too different, it is necessary to repeat the calculation.
2The constant part of the cost C in formula (17) does not affect the calculation of the economic cross section SscSc. It is unlikely to be exactly equal to the standard cross section (see GB/T3956). Therefore, it is necessary to calculate the costs of adjacent larger and smaller standard cross sections and then select the most economical cross section.
5.2.3 Dielectric loss
The dielectric loss of some types of cables can be significant (see Table 3 of JB/T10181.1-2000). When selecting the most economical conductor size for such cables, the dielectric loss should be considered and the dielectric loss is calculated using the formula in JB/T10181.1. For a given voltage level and insulation thickness, an increase in conductor size leads to an increase in cable capacitance; as a result, voltage-related losses increase. Therefore, when dielectric loss is included in the analysis, as opposed to losses due to current, reducing dielectric loss tends to reduce Conductor diameter. When dielectric loss is considered, the costs CI, CI, and CI will include the total dielectric loss during the economic life. Because the calculation formula for the optimal conductor cross-section including the influence of dielectric loss is very complicated, the following method will be used. First, the economic cross-section of the conductor is obtained from formula (18) without considering the dielectric loss. Then, the cost and the two adjacent smaller standard cross-sections including the dielectric loss cost are calculated, and the most economical cross-section is selected.
A1 Overview
JB/T10181.6-2000
Appendix A||t t||(Appendix of Prompt)
Example of Calculation of Economic Conductor Section
Take the calculation of 10 cable lines with the same load and equal spacing along the line as an example, the situation is as follows: a) The first method (see 5.1) - economic current range method is used to determine the cable section between adjacent loads: b) The second method (see 5.2) - conductor economic section method is used to determine the cable section between adjacent loads: c) When a cable with a single section is used for the entire line - the above two methods are used to determine the most economical cable section. The results summarized in A6 show that to save costs, the conductor section should be selected according to the reduction of total costs rather than the minimum initial investment.
A2 Detailed Description of Cable and Power Supply System
Load and Line Data
To transmit power from a 150kV/10kV distribution station to 10 10kV/0.4kV substations using a cable line with equal spacing along the line, the 10kV cable section must be determined (see Figure A1). (It is only a three-phase circuit, so N,=1N=3). The cable length between substations is 500m.
The average maximum hourly current Im of each substation on this line in the first year is: Substation
Current (A)
Each substation decreases by 16A
For all cycles, the load factor M=1.11 (see 853). It is assumed that the factor is constant during the economic life of the cable. The cable section is selected for each line section according to the following criteria: a) the sum of the initial cost plus the present value of the Joule loss during the economic life of the cable is the minimum; b) the current carrying capacity required for the load in the last year of the economic life of the cable. The current carrying capacity required in this example is 0.9 times the maximum load, that is, the maximum load divided by the cycle load factor of 1.11; c) This example does not consider other factors, such as the short circuit and voltage drop, but can be handled according to the description in the 3rd clause of the corresponding IEC60287-3-2 in the IEC introduction of this standard.
Financial data
Economic life
Operating time under maximum loss (the value 2250 includes the effective or daily cycle load time)
10kV Joule loss price at the end of the year
Additional capacity increase fee for supply loss
Cable cost and installation fee per unit length, see Table A1JB/T10181.6-2000
The part of the installation cost that depends on the conductor cross-section in this exampleThe coefficient of annual load growth rate
Annual energy cost (price of kW-h)Increase rateAnnual discount rate
Cable data:
60.9×10-6
cu/W·h
cuW·year
cu/m·mm2
For this example, the calculation is based on the assumption of 6/10kV three-core cable. The conductor AC resistance at 40℃ and 80℃ is shown in columns (2) and (3) of Table A1, and its detailed financial data is shown in columns (4) to (6). When the soil ambient temperature is 20℃, the steady-state operating current carrying capacity at the maximum allowable conductor temperature of 80℃ is shown in A3.3.
Calculation of auxiliary quantities
+0.5/10) ×(+2/10) = 0.9117
1+5/100
Q=1-0.981230
3×1×(2250 × 60.9 ×10° + 0.003)×23.08众
1+5/100
A3 Calculation by economic current range method (see 5.1) A3.1 Calculation of economic current range for a cross-section As an example, use formulas (12) and (13) to calculate the economic current range of a 240mm2 conductor. The lower limit of I=
The upper limit of I=
500 × (52.20 - 45.96)×103
-1/2=128(A)
9.2341×500×(0.181-0.140)
500 × (58.99 - 52.20)×103
-/2 =168(A)
9.2341× 500 × (0.140 -0.114)(Formula (9))
(Formula (8))
(Formula (10))
（Formula 12)
(Formula 13）
When the installation conditions are assumed in this example, the upper limit of the current of a certain range of standard conductor cross-sections can be similarly calculated. Since the lower limit of the current of a given conductor is also the upper limit of the adjacent smaller conductor cross-section, the calculated value can be expressed as the current range as shown in the following table: Economic current range of cables with conductor cutting surface 25~400mm2 mm?
Nominal cross-section
Current range (A)
JB/T10181.6—2000
The relationship between the maximum load during the year and the total cost per unit length of cables with three conductor cross-sections is shown in Figure A2. It can be seen that each cable has a current within the cross-section current range that makes the installation cost most economical. When the load is determined, the impact of changes in conductor cross-section on the total cost is shown in Figure A3. Here, the cable and financial parameters of this example are still maintained, but it is assumed that the fixed load 1ma is 100A. It can be seen that in the most economical cross-section area, the selection of cable cross-section will not have a great impact on the total cost, but the cost reduction is very obvious compared with those cross-sections selected according to thermal properties. A3.2 Selection of economical conductor cross-section for each line segment According to the economic current range table in A3.1 above, the appropriate conductor cross-section can be selected for each section of the cable line according to the respective 1mar value in the first year. Table A2 gives the conductor cross-section selected for each section and the cost calculated according to formula (11). A typical example of cost calculation is as follows: First line segment, Imgr is 1160A.
The economic conductor cross-section selected from A3.1 is 240mm2, and its economic current range is 128~168A. CT = (52.2 × 500) + [1602 × (0.140/1000) × 500 × 9.2341] = 26100 + 16548
= 42648 (cu)
The costs of each section of the line are summarized in Table A2.
From Table A2, it can be seen that the total cost of the cable line for 30 years of operation based on economic considerations is 290535 (cu). A3.3 Conductor cross-section determined by maximum load - selection according to thermal rating The cable cross-section of each line section is selected to be able to transmit the expected maximum load in the last year of economic life without exceeding the maximum allowable conductor temperature.
For the first line section:
Imar (first year)
The maximum current in the next year
=160 (A)
=160×[1+(0.5/100)j30-
=160×1.1556
=185 (A)
The current carrying capacity (100% load factor) required in the last year is not less than: 185/1.11=167
The 1.11 in the formula is the cycle load factor set in A2b). (A)
From the following current carrying capacity table (according to JB/T10181.1 and JB/T10181.3 methods), the required conductor cross-section is 70mm2 when calculating the current carrying capacity of this cable buried.
Nominal cross section mm2
Current carrying capacity A
In order to make a fair comparison between the losses calculated for the economically selected conductor cross section and the economic figures, a suitable conductor temperature must be assumed for calculating the losses. For the economic cross section selection, the conductor temperature is assumed to be about 40°C (see Chapter 4). It is recommended that the more suitable conductor temperature for the thermal selection is the maximum allowable value of 80°C. The conductor resistance at 80°C is shown in Table A1.
The total cost of the first section within 30 years is obtained by formula (11): 101
JB/T10181.6-2000
CT=[32.95×500]+[160*×(0.553/1000)×5009.2341]=16475+65363
=81838 (cu)
Compared with the cost of this line section when estimating the economic cross-section of the conductor in A3.2, the cost savings are: (81838-42648)×100/81838=48%. A similar calculation is made for the entire line based on the calculation method of the maximum thermal current carrying capacity, see Table A3. The total cost savings for the 10 line sections are: (547864-290535) X100/547864=47%. A4 conductor economic cross-section method calculation (see 5.2) Take the first line section as an example:
Imax160A
P%=30.3×10-9.0·m (see 5.2.1)azo-0.00403 1/K
B=1.023 (assuming 185mm2 is the initial value of the most economical conductor cross-section) A=0.1133cu/m·mm* (coefficient of the variable part of the installation cost, see 5.2.2) F=9.2341 cu/W
_= (80-20) /3+20=40℃
[1602 ×9.2341 × 30.3 ×10-9 ×[1 + 1.023 + 0.00403 ×(40 - 20)]Sg=1000×www.bzxz.net
=264 mm2
Therefore, the conductor cross section can be selected as 240mm or 300mm2. The estimated B value when the conductor cross section of 185mm2 was initially selected can now be corrected. For a 300mm2 conductor, the S value is recalculated using B=1.057 to obtain 269mm2, which is also within the range of 240mm2 and 300mm2.
Using formula (11) to calculate the total cost of each conductor cross-section that may be used, CT24o=[52.2×500]+[1602×(0.140/1000)×500x9.2341]=26000+16548
-42648(cu)
CT 300=[58.99×500]+[1602×(0.114/1000)x500×9.2341]=29495+13474
=42969 (cu)
Therefore, the conductor with a cross section of 240mm2 is the more economical cross section. The cross sections and costs of other line sections are calculated in a similar way. These values are exactly the same as those obtained by the previous method in A3.1 and 1A3.2, and the cross sections and costs are summarized in the same way as those given in Table A2. A5 Calculation of A5.1 Economic Current Range Method Using a Standard Conductor Cross Section for All Line Sections of the Entire Line
First, the possible conductor cross sections must be set, and the total cost is calculated for each line section using this size according to formula (11). In order to confirm that the assumed cross section is the most economical, the total cost of the adjacent larger and smaller cross sections of the assumed cross section is calculated. In this example, it is assumed that the conductor cross section of 185mm2 is the best choice. Use 185mm2 for all line sections, then calculate the costs for 150mm2 and 240mm2 and list them in Table A4. The total cost is:
150mm2
185mm2
240mm2
312841cu
312166
324707
The above costs show that for the sake of standardization, only one conductor cross section is available and 185mm2 is the most economical choice. It can also be seen here that the change in conductor size shown in A3.1 and Figure A3 has little effect on the change in total cost. A5.2 Conductor Economic Cross Section Method
Although only one conductor cross section is selected, the current in each line section is different. Therefore, the average loss must be calculated (each section is assumed to operate at the same temperature and therefore the conductor resistance is the same). Average loss_500×1602+500×1442++500×162Maximum loss
10×500×160z
According to formula (18), the B value of 185mm2 conductor is 34
=164mm2
Therefore, it can be proved that the conductor cross-section of 150mm2 or 185mm2 is the most economical. The total cost of each conductor specification is: CT1so = 42.00 × 500 × 10 + 160 × (0.226/1000) × 500 × 10 × 9.2341 × 0.385 = 210000 + 102843
= 312843cu
CT1s = 45.96 × 500 × 10 + 1602 x (0.181/1000) × 500 × 10 × 9.2341 × 0.385 229800 + 82365
= 312165cu
Therefore, if only one conductor cross section is selected for the entire line, it can be confirmed that 185mm2 is the most economical conductor cross section. Obviously, compared with the cross section selected in Table A3, the 185mm2 conductor is suitable for transmitting the maximum load at the end of 30 years of operation in terms of thermal properties.
A6 Summary of results
The results of the calculations for the cables and conditions described in A2 are summarized as follows: Cost summary
Basis for cost calculation
Each line section adopts a current carrying capacity based on thermal considerationsEach line section adopts an economical section
The entire line section adopts the same standard section of 185mm2 as the economical sectionc
146330
202095
229800
401534
547864
290535
312165
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