How to calculate power, current and voltage: principles and examples of calculations for domestic conditions
Owners of apartments, private houses and other electrified objects are often faced with the question of determining the values of basic electrical quantities, since calculating the power based on the permissible current strength and a known voltage or solving the inverse problem is not very simple.
Direct application of the well-known Ohm's law without taking into account the characteristics of household networks and devices can lead to an incorrect result.
In this material we will understand what power is and tell you how to calculate this indicator.
The content of the article:
Basic concepts of quantities
Electrical calculations are based on well-known relationships between current (I, Ampere), voltage (U, Volt), power value (P, Watt) and resistance (R, Ohm). Practical calculations usually require knowledge of the values of the first three.
We warn you that numerical expressions of the listed values are not enough - additional characteristics are needed that reveal the power consumption mode.
Electric current strength
The calculation of the sufficient cross-section of the conductors and the rating of the circuit breaker for a specific branch of the electrical network is carried out according to the value of the maximum possible current strength for this section. This is necessary to prevent the wiring from catching fire, which often results in a fire.
Workers machine parameters and RCDs are selected according to regulatory requirements.To determine the permissible cross-section of the cores depending on the maximum possible current strength, it is necessary to use the table provided by the product manufacturer, because the cables are most often produced according to specifications, and not according to GOST.
Since the strength of the electric current can be calculated based on the power consumed by the devices and the network voltage, it is necessary to correctly determine the values of these two indicators.
Household voltage
Many apartment owners believe that the standard phase voltage for household needs is approximately 220 V. In most cases, this is true. Although GOST 29322-2014 from 10/01/2015 within the Russian Federation there was to be a transition to a 230 V system compatible with the EEC countries.
A deviation of 5% from the standard is acceptable for any period, and 10% for a period not exceeding 1 hour. Thus, according to the old rules, the voltage value can fluctuate in the range from 198 to 242 V, and according to the current GOST - from 207 to 253 V.
There are also cases when the voltage in the network for a long time is significantly lower than the standard one. This situation arises when the total power of electrical appliances connected to the branch is much higher than planned and when most of them are turned on, a “network drawdown” occurs.
This problem occurs in the area of responsibility of organizations responsible for the supply of electricity, and is associated with overloading of distribution transformers, deterioration of substations or insufficient wire cross-section.
To find out the meaning real voltage you need to periodically take measurements using a voltmeter. If the indicators fluctuate greatly, then it is necessary to use stabilizer or a more expensive converter with an electricity storage function.
Nuances in the concept of power of electrical appliances
All devices that consume electricity have such a parameter as power. The higher this indicator, the more energy the device takes from the circuit.
There are three types of power:
- Active (P). Characterizes the rate of conversion of electrical energy into another form, for example electromagnetic or thermal. It must be taken into account when calculating the irreversible costs of electricity, and therefore the cost of operating the device. Unit of measurement – W.
- Reactive (Q). Characterizes the energy that comes from the source (transformer) to the reactive elements of the consumer (capacitors, motor windings), but then almost instantly returns to the source. The unit of measurement is W or var (interpretation is reactive volt-ampere).
- Full (S). Characterizes the load that the consumer imposes on the circuit elements. It is used when calculating the cross-sectional area of the cable and choosing the rating of the machines, that is, the current strength is calculated based on the full power of all electrical appliances connected to the circuit. The unit of measurement is W or V*A (V*A – volt amperes).
All these parameters can be recalculated through the phase angle that occurs between the voltage vector and current (f):
P = S *cos(f);
Q = S *sin(f);
S2 = P2 + Q2.
Household devices in which the total power can significantly exceed the active power include refrigerators, washing machines, fluorescent and some energy-saving lamps, as well as power electronics units.
There is also such a thing as peak or starting power. The fact is that accelerating engines requires much more effort than maintaining their rotation. Therefore, when you turn on appliances such as a refrigerator or washing machine, a short-term load surge occurs on a section of the circuit.
Starting currents can be several times higher than operating currents. When calculating the required cable sections When selecting the machine’s nominal value, this should be taken into account.
To do this, you need to determine the device with the greatest difference in starting and operating power and add it to the total value. The starting currents of other devices can be ignored, since the probability of simultaneous activation of motors for different consumers is practically zero.
Linear and phase relationships
Nowadays, the practice of connecting household objects to three-phase electrical networks has become widespread.
This is justified for the following reasons:
- Significant energy consumption. In this case, connecting a high-power single-phase network will be very irrational due to the large cross-section of the cable and the high material consumption of the transformer.
- Availability of devices operating on three phases. The implementation of a circuit for connecting such a device to a single-phase circuit is not very simple and is fraught with interference that occurs, for example, when starting an asynchronous motor.
There are two ways to connect three-phase devices - “star” and “triangle”.
In star-type circuits, the linear and phase currents are identical, and the linear voltage is 1.73 times greater than the phase voltage:
Il = If;
Ul = 1.73 * Uf.
This formula explains the known voltage ratio for household and low-voltage industrial networks with a frequency of 50 Hz: 220 / 380 V (according to the new GOST: 230 / 400 V).
With a triangle connection, on the contrary, the voltage is the same, and the linear currents are greater than the phase currents:
Il = 1.73 * If;
Ul = Uf.
These formulas can only be used with symmetrical phase loads. If the current consumption across the cables is different (unbalanced receiver), then calculations are carried out using the rules of vector algebra, and the resulting equalizing current is compensated by the neutral wire. However, for networks with connected household appliances, such cases are rare.
Relationship between basic quantities
The most common task faced by ordinary consumers is calculating the actual current strength. So how to correctly calculate amperage based on known voltage and power values? It is necessary to solve it by justifying the cross-sectional values of the cores and the rating of the machine, having technical information about the devices that will be powered into this circuit.
After calculating the current, cables with the smallest permissible cross-section are often selected. However, this is not always correct, since such a solution leads to significant restrictions when it is necessary to add new electrical appliances to the network.
Sometimes it is necessary to carry out reverse calculations and determine what total power can be connected to devices at a known voltage and maximum permissible current, which is limited by existing wiring.
You can solve these two problems for a single-phase circuit using a simple formula:
I = S / U;
S = U * I,
Where S – total total power of all electrical consumers.
To solve the problem of calculating current using known or calculated values of power and voltage in a three-phase circuit, you need to know the total load imposed on each phase.
Both the required cross-section of the cable cores and the minimum permissible rating of the machine are selected according to the busiest line, considering that:
S = 3 * max{S1, S2, S3}.
I = S / (U * 1.73).
The permissible power for each phase can be calculated using the following formula:
S1,2,3 I * U / 1.73,
Where I – maximum permissible current for existing wiring.
Conclusions and useful video on the topic
Calculation of current strength by power for selecting cable cross-section:
Determination of power consumption of groups of electrical appliances using the example of a private house:
You can calculate the current strength to determine wiring parameters or determine the permissible power in an existing circuit yourself. To correctly solve the problem, it is necessary to take into account the nuances that arise in practice, and not just use well-known formulas that work under “ideal” conditions.
If you have questions about the topic of the article or you can add interesting information to this material, please leave your comments in the block below.
Three-phase circuits are usually used in production, since large power is needed there. In houses and apartments, one phase is sufficient. You can make calculations, or you can just remember: for lighting, a copper wire with a cross-section of 1.5 square mm is sufficient, but for sockets it is better to take a cross-section of 2.5. This is sufficient for household appliances. But large water heaters are powered by a separate cable with a cross-section of 4 kV and connected to a separate line with its own automatic circuit breaker.
I don’t understand, if everything is so simple and standard for each apartment, then why is this information given above at all? “You can do calculations, or you can just memorize.” And how does it work? Why do them then if we already know the result. This is a very controversial statement; if I were you, I would slow down with such statements and comments, otherwise you will create problems for someone.
Good day, Sergey.
You're right - it's not that simple. Vladimir’s comment is based on information circulating on the network - they often “forget” about the “Rules for the construction of electrical installations” and talk about the cross-sections of apartment wiring as follows: “usually wires are used...” and then they talk about 1.5, 2.5 squares, which Vladimir mentioned.
The PUE, I emphasize, requires calculations, warning: if the result is less than the minimum section given in the table, the tabulated section should be used. I attached a screenshot of this requirement to my comment.