Calculation of the cable cross-section by power and current: how to correctly calculate the wiring
The flow of current through a conductor can be compared to the flow of a river through a pipe. Incorrect calculation of the cable cross-section leads to overheating and short circuits or unjustified costs. It is very important to carry out calculations at the design stage, since the failure of hidden wiring and subsequent replacement is associated with significant costs.
The main purpose of conductors is the delivery of electrical energy to consumers in the required quantity. Since superconductors are not available under normal operating conditions, the resistance of the conductor material must be taken into account.
The calculation of the required cross-section of conductors and cables depending on the total power of consumers is based on long-term operating experience. General calculation progress:
- P = (P1+P2+..PN)*K*J;
- selection of the required section according to table 1.
P is the power of all consumers connected to the calculated branch in watts.
P1, P2, PN - power of the first consumer, second, n-th, respectively, in watts.
Table 1. The cross section of the conductors of the wires must always be selected to the nearest large side (+)
Reactive and active power of an electrical appliance
The capacities of consumers are indicated in the documents for the equipment. Usually, equipment datasheets indicate active power along with reactive power.
Devices with an active type of load convert all the received electrical energy, taking into account the efficiency, into useful work: mechanical, thermal, or any other form of it. Active load devices include incandescent lamps, heaters, electric stoves. For such devices, the calculation of power by current and voltage has the form:
P=U*I
P - power in W
U - voltage in V
I - current strength in A
With zero phase displacement, the power P=U*I always has a positive value. Such a graph of the phases of the current I and voltage U have devices with an active type of load
Devices with a reactive type of load are able to accumulate energy coming from a source, and then return it. Such an exchange occurs due to the displacement of the sinusoid of the current strength and the sinusoid of the voltage.
When there is a phase shift between the current sine wave and the voltage sine wave, the power P=U*I can be negative. A device with reactive power returns the stored energy back to the source
Reactive power devices include electric motors, electronic devices of all sizes and purposes, transformers.
Reactive power is dependent on the phase angle between the voltage and current sinusoids. The phase displacement angle is expressed in terms of cosφ. To find the total power, use the formula:
P = P p / cosφ
P p - reactive power in W
Usually, reactive power and cosφ are indicated in the passport data for the device.
Example: in the passport for the puncher, the reactive power is 1200W and cosφ = 0.7. Therefore, the total power consumption will be equal to:
P = 1200 / 0.7 = 1714W
If cosφ could not be found, for the vast majority of household electrical appliances, cosφ can be taken equal to 0.7.
Simultaneity and safety factors
K- dimensionless coefficient of simultaneity, shows how many consumers can be connected to the network at the same time. It rarely happens that all devices consume electricity at the same time. The simultaneous operation of the TV and the music center is unlikely. From established practice, K can be taken equal to 0.8. If you plan to use all consumers at the same time, K should be taken equal to 1.
J is the dimensionless safety factor. It characterizes the creation of a power reserve for future consumers. Progress does not stand still, every year new amazing and useful electrical devices are invented. Electricity consumption is expected to grow by 84% by 2050. Usually J is taken equal to from 1.5 to 2.0.
Calculation of the cross section of wires by the geometric method
In all electrical calculations, the cross-sectional area of \u200b\u200bthe conductor is taken - the cross section of the core. Measured in mm 2.
It is often necessary to learn how to correctly calculate the wire cross-section according to the conductor wire diameter. In this case, there is a simple geometric formula for a solid round wire:
S \u003d π * R 2 \u003d π * D 2 / 4, or vice versa
D = √(4*S / π)
For rectangular conductors:
S = h*m
S - core area in mm 2
R - core radius in mm
D - core diameter in mm
h, m - width and height, respectively, in mm
π is the number of pi equal to 3.14
If you purchase a stranded wire, in which one conductor consists of many twisted wires of circular cross section, then the calculation is carried out according to the formula:
S \u003d N * D 2 / 1.27
N - the number of wires in the core
Wires that have twisted strands of several wires generally have better conductivity than monolithic ones. This is due to the peculiarities of current flow through a conductor of circular cross section.
Electric current is the movement of like charges through a conductor. Charges of the same name repel each other, so the charge distribution density is shifted to the surface of the conductor.
Another advantage of stranded wires is their flexibility and mechanical resistance. Monolithic wires are cheaper and are used mainly for fixed installation.
An example of calculating the cross-section by power
Task: the total power of consumers in the kitchen is 5000W (meaning that the power of all reactive consumers is recalculated). All consumers are connected to a single-phase 220V network and are powered from one branch.
Table 2. If you plan to connect additional consumers in the future, the table shows the required power of common household appliances (+)
The coefficient of simultaneity K will be taken equal to 0.8. The kitchen is a place of constant innovation, you never know, safety factor J=2.0. The total rated power will be:
P \u003d 5000 * 0.8 * 2 \u003d 8000W \u003d 8kW
Using the value of the calculated power, we are looking for the nearest value in table 1.
The closest suitable conductor cross-section for a single-phase network is a copper conductor with a cross section of 4 mm 2. Similar wire size with aluminum core 6mm 2 . For single-core wiring, the minimum diameter will be 2.3mm and 2.8mm, respectively. In the case of using a multi-core variant, the cross-section of individual cores is summed up.
Current section calculation
Calculations of the required cross-section for current and power of cables and wires will provide more accurate results. Such calculations make it possible to evaluate the overall influence of various factors on conductors, including thermal load, wire grade, gasket type, operating conditions, etc.
The entire calculation is carried out during the following steps:
- choice of power of all consumers;
- calculation of currents passing through the conductor;
- selection of a suitable cross-section according to the tables.
For this calculation option, the power of consumers in terms of current with voltage is taken without taking into account correction factors. They will be taken into account when summing the current strength.
Formulas for calculating current strength
For those who have forgotten the school physics course, we offer the basic formulas in the form of a graphic diagram as a visual cheat sheet:
The "classic wheel" clearly demonstrates the relationship of formulas and the interdependence of the characteristics of electric current
Let us write out the dependence of the current strength I on the power P and the linear voltage U:
I = P / U l
I - current strength is taken in amperes
P - power in watts
U l - linear voltage in volts.
The line voltage generally depends on the power supply source, it can be single- and three-phase. Relationship between line and phase voltage:
U l \u003d U * cosφ in the case of a single-phase voltage
U l \u003d U * √3 * cosφ in the case of a three-phase voltage
For household electrical consumers, cosφ = 1 is taken, so the linear voltage can be rewritten:
U l \u003d 220V for single-phase voltage
U l \u003d 380V for three-phase voltage
I = (I1+I2+…IN)*K*J
I - total current in amperes
I1..IN - current strength of each consumer in amperes
K is the coefficient of simultaneity.
J - safety factor.
The coefficients K and J have the same values that were used in the calculation of the apparent power.
There may be a case when a current of unequal strength flows through different phase conductors in a three-phase network. This happens when single-phase consumers and three-phase consumers are connected to a three-phase cable at the same time. For example, a three-phase machine and single-phase lighting are powered.
A natural question arises: how in such cases is the cross-section of a stranded wire calculated? The answer is simple - calculations are made on the most loaded core.
Selection of a suitable section according to the tables
The rules for the operation of electrical installations (PEU) contain a number of tables for selecting the required cross-section of the cable core.
The conductivity of a conductor depends on temperature. For metal conductors, resistance increases with increasing temperature. When a certain threshold is exceeded, the process becomes auto-sustained: the higher the resistance, the higher the temperature, the higher the resistance, etc. until the conductor burns out or causes a short circuit.
The following two tables show the cross section of the conductors depending on the currents and the laying method.
The cable differs from the wire in that all the cores of the cable, equipped with their own insulation, are twisted into a bundle and enclosed in a common insulating sheath.
Table 3. First, you need to choose the method of laying the wires, it depends on how efficiently the cooling takes place (+)
Table 4. The open method is indicated for all conductor cross-sections, however, in practice, cross-sections below 3 mm2 are not openly laid for reasons of mechanical strength (+)
When using the tables, the following coefficients are applied to the permissible continuous current:
- 0.68 if 5-6 lived;
- 0.63 if 7-9 lived;
- 0.6 if 10-12 lived.
The reduction factors are applied to the current values from the "open" column.
Zero and ground conductors are not included in the number of conductors.
According to the standards of PES, the choice of the cross section of the zero conductor according to the permissible continuous current is made as at least 50% of the phase conductor.
The following two tables show the dependence of the permissible continuous current when laying it in the ground.
Table 5. Permissible continuous current dependencies for copper cables when laying in air or ground
The current load when laying openly and when deepening into the ground differ. They are taken equal if laying in the ground is carried out using trays.
Table 6. Dependences of the permissible continuous current for aluminum cables when laying in air or ground
For the installation of temporary power supply lines (carrying if for private use), the following table applies.
Table 7. Permissible continuous current when using portable hose cords, portable hose and mine cables, searchlight cables, flexible portable wires. Only applies to copper conductors
When cables are laid in the ground, in addition to heat dissipation properties, it is necessary to take into account the resistivity, which is reflected in the following table
Table 8. Correction factor depending on the type and resistivity of the soil for the allowable continuous current, when calculating the cross-section of cables (+)
Calculation and selection of copper conductors up to 6mm 2 or aluminum up to 10mm 2 is carried out as for continuous current. In the case of large cross sections, it is possible to apply a reduction factor:
0.875 * √T pv
T pv - the ratio of the duration of the inclusion to the duration of the cycle. The duration of the inclusion is taken from the calculation of no more than 4 minutes. In this case, the cycle should not exceed 10 minutes.
An example of calculating the cross section of a conductor by current
- three-phase woodworking machine with a power of 4000W;
- three-phase welding machine with a power of 6000W;
- household appliances in the house with a total capacity of 25000W;
The connection will be made with a five-core cable (three phase conductors, one neutral and one ground), laid in the ground.
The insulation of cable and wire products is calculated for a specific value of the operating voltage. Please note that the operating voltage specified by the manufacturer of his product must be higher than the mains voltage
Step 1. We calculate the line voltage of a three-phase connection:
U l \u003d 220 * √3 \u003d 380V
Step #2 Household appliances, a machine tool and a welding machine have reactive power, so the power of machinery and equipment will be:
P tech \u003d 25000 / 0.7 \u003d 35700W
P turn = 10000 / 0.7 = 14300W
Step #3. The current required to connect household appliances:
I those \u003d 35700 / 220 \u003d 162A
Step #4. Current required to connect equipment:
I turn = 14300 / 380 = 38A
Step #5. The required current for connecting household appliances is calculated on the basis of one phase. According to the condition of the problem, there are three phases. Therefore, the current can be distributed over the phases. For simplicity, let's assume a uniform distribution:
I those \u003d 162 / 3 \u003d 54A
Step #6 Current per phase:
I f \u003d 38 + 54 \u003d 92A
Step #7 Equipment and household appliances will not work at the same time, except for this, we will lay a margin of 1.5. After applying the correction factors:
I f \u003d 92 * 1.5 * 0.8 \u003d 110A
Step #8 Although the cable has 5 cores, only three phase cores are taken into account. According to table 8 in the column of a three-core cable in the ground, we find that a current of 115A corresponds to a core cross section of 16mm 2.
Step #9. According to table 8, we apply a correction factor depending on the characteristics of the land. For a normal type of land, the coefficient is 1.
Step #10. Optional, calculate the core diameter:
D = √(4*16 / 3.14) = 4.5mm
If the calculation was made only by power, without taking into account the features of cable laying, then the cross section of the core would be 25 mm 2. Calculating the current strength is more complicated, but sometimes it saves significant money, especially when it comes to multi-core power cables.
Voltage drop calculation
Any conductor, except superconductors, has resistance. Therefore, with a sufficient length of cable or wire, a voltage drop occurs. PES standards require that the cross section of the cable core be such that the voltage drop is not more than 5%.
First of all, this concerns low-voltage cables of small cross section. The voltage drop calculation is as follows:
R = 2*(ρ * L) / S
U pad = I * R
U% \u003d (U pad / U lin) * 100
2 - coefficient due to the fact that the current flows necessarily through two cores
R - conductor resistance, Ohm
ρ - specific resistance of the conductor, Ohm * mm 2 / m
S - conductor section, mm 2
U pad - drop voltage, V
U% - voltage drop in relation to U lin,%
Table 9. Resistivity of common metal conductors (+)
Carry Calculation Example
Those who wish to connect a household welding machine to a branch of the mains should take into account the current sieve for which the cable used is designed. It is possible that the total power of the working devices may be higher. The best option is to connect consumers to separate branches
Step 1. We calculate the resistance of the copper wire using table 9:
R \u003d 2 * (0.0175 * 20) / 1.5 \u003d 0.47 Ohm
Step #2 The strength of the current flowing through the conductor:
I \u003d 7000 / 220 \u003d 31.8A
Step #3 Voltage drop across the wire:
U pad \u003d 31.8 * 0.47 \u003d 14.95V
Step #4 Calculate the percentage of voltage drop:
U% \u003d (14.95 / 220) * 100 \u003d 6.8%
Conclusion: to connect the welding machine, a conductor with a large cross section is required.
Video materials for selecting conductors
Calculation of the conductor section according to the formulas:
Recommendations of experts on the selection of cable and wire products:
The above calculations are valid for copper and aluminum conductors for industrial use. For other types of conductors, the total heat transfer is preliminarily calculated. Based on these data, the maximum current that can flow through the conductor without causing excessive heating is calculated.
