AC power - concept, types and formulas

What is electric power

When describing electrical power in a broad sense, we are most often talking about the energy or force with which some object or action is endowed. For example, it can be defined for an explosion or a mechanism, such as an engine. This parameter is associated with force and depends on it, which is why these phenomena are often confused.

The difference is that force affects physical actions, that is, work is performed. If it is done in the specified time, then through these two parameters the power value can be calculated.

In the case of electricity, there are two types:

1. Active - turns into energy of heat, light, mechanical action, etc. It is measured in watts and calculated by the formula 1 W = 1 V x 1A. But in practice, this indicator is most often expressed in kilowatts and megawatts.
2. Reactive – load arising due to oscillations within the electromagnetic field. The unit of measurement is volt-amperes (VA), they are calculated as Q=U x I x sin angle. The latter means a phase change between current and voltage reduction.

In practice, the differences between both types are best seen using the example of heating elements and electric motors. Heating elements are assembled from a material with high resistance, so they convert all the electricity received into heat. The electric motor has parts that have inductance, that is, part of the current returns to the network and can negatively affect it, creating overloads.

In a single-phase circuit

You can understand what power indicator is in a single-phase alternating current circuit by using a current transformer. To do this, you need to use a wattmeter, which is connected through a current transformer. The readings should be multiplied by the transformer current coefficient. When measuring power at high voltage, a current transformer is needed to insulate the wattmeter and ensure the safety of the user. The parallel circuit is not connected directly, but thanks to a voltage transformer. Secondary windings with housings of measuring transformer installations must be grounded to avoid accidental insulation damage and high voltage contact with devices.

Note! To determine the parameters in the network, it is necessary to multiply the ammeter by the transformer current coefficient, and multiply the numbers obtained by the voltmeter by the transformer voltage coefficient.

In a single-phase circuit

How is power indicated?

P - electric current power is indicated (W).

In conclusion, it should be noted that total power has practical significance, as a value that describes the loads actually imposed by the consumer on the elements of the supply network (wires, cables, distribution boards, transformers, power lines), since these loads depend on the current consumed, and not from the energy actually used by the consumer. That is why this value of transformers and distribution boards is measured in volt-amperes, and not in watts.

Concept of total power. Capacity Triangle

Apparent power is a geometrically calculated value equal to the root of the sum of the squares of active and reactive powers, respectively. Denoted by the Latin letter S.

You can also calculate the total power by multiplying the voltage and current respectively.

S = U⋅I

IMPORTANT! Apparent power is measured in volt-amperes (VA).

The power triangle is a convenient representation of all the previously described calculations and relationships between active, reactive and apparent power.

The legs reflect the reactive and active components, the hypotenuse – the full power. According to the laws of geometry, the cosine of the angle φ is equal to the ratio of the active and total components, that is, it is the power factor.

Electrical appliances affecting the quality of consumption

The power factor is equal to unity when connecting lamps and heaters. It decreases to 0.7 or less when electric motors and other components with reactive components, which dominate in energy consumption, are added to the circuit.

The correct application of power definitions and calculations helps optimize the electrical network design taking into account the characteristics of the connected loads. The above information will be useful at the stage of determining the parameters of wiring and circuit breakers. The integrated use of this knowledge will increase the reliability of power supply and prevent the occurrence and development of emergency situations.

How to find out voltage by knowing current strength

To calculate the voltage, use the formulas:

U=P/I – direct current;

U=P/(I*cos(phi)) - single-phase network;

U=P/(1.73*I*cos(phi)) - three-phase network.

From the expression it can be seen that voltage is directly proportional to voltage and inversely proportional to current.

How to calculate power knowing current and voltage

The power characteristics of electrical installations are calculated using the formula:

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P=U*I - direct current;

P=U*I*cos(phi) – alternating current of a single-phase network.

P=1.73*U*I*cos(phi) - three-phase network.

The article provides simplified formulas for calculating the active power of the electrical network, which give approximate results.

To obtain accurate results, it is also necessary to take into account reactance and ordinary resistance, as well as losses.

Measurements

As shown above, some initial data can be obtained through practical measurements. The features of typical specialized devices are noted below.

Direct measurements

Wattmeters are produced in different modifications for ~220V and ~380V networks. Appropriate corrections are made during work operations. The probes should be connected taking into account the manufacturer's instructions and the appropriate location of the conductors.

As a rule, in device designs two coils are used with parallel and serial connection to the load. For increased accuracy, use professional instruments of the “laboratory” category.

Indirect measurements

These operations are performed using multimeters. Resistance, current and voltage are measured, after which the power is calculated.

Phase meters

These instruments measure the phase shift between several electrical parameters. With such a device, cos ϕ can be determined if the passport value is not in the accompanying documents for the equipment.

cos regulation

The negative impact of reactive components noted above is compensated for by special additions to the overall electrical circuit. Calculations are performed using the presented formulas.

How to calculate correctly

Active power, how to make the correct calculation?

The power of the electric current affects how quickly the device can complete the job. For example, an expensive heater with twice the power will heat a room faster than two cheap ones with half the power. It turns out that it is more profitable to buy a unit with more power in order to heat a cold room faster. But, at the same time, such a unit will consume significantly more energy than its cheaper counterpart.

The power consumption of all appliances in the house is also taken into account when selecting wiring for installation in the house. If you do not take this into account and subsequently connect too many devices to the network, this will cause network overload. The wiring will not be able to withstand the power of the electric current of all devices, which will lead to melting of the insulation, short circuit and self-ignition of the wiring. As a result, a fire may start, which can lead to irreparable consequences.

Single-phase sinusoidal current in electrical circuits is calculated by the formula P = U x I x cos φ, where υ and Ι. Their designation is encrypted as follows: the root mean square value of voltage and current, and φ is the phase angle between them.

For non-sinusoidal current circuits, the electrical capacitance is equal to the square root of the sum of the squares of the active and reactive performance. Active performance is characterized by the speed of the irreversible process of converting electrical energy into other types of energy. This capacitance can be calculated through the current, voltage and active component of the circuit resistance r or its conductivity g using the formula P = I(2) xr = U(2) x g.

Reactive Power

It should be noted that:

• The resistor consumes active power and releases it in the form of heat and light.
• inductance consumes reactive power and releases it in the form of a magnetic field.
• The capacitor consumes reactive power and releases it in the form of an electric field.

In any electrical circuit of both sinusoidal and non-sinusoidal current, the active capacity of the entire circuit is equal to the sum of the active powers of the individual parts of the circuit; for three-phase circuits, the electrical capacity is defined as the sum of the throughput of the individual phases. With the total performance S, the active one is related by the relation P = S x cos φ.

In the theory of long lines (the analysis of electromagnetic processes in a transmission line, the length of which is comparable to the length of the electromagnetic wave), the complete analogue of active power is transmitted power, which is defined as the difference between the incident power and the reflected performance.

How to find reactive apparent power through active power? This performance, which characterizes the loads created in electrical devices by fluctuations in the energy of the electromagnetic field in a sinusoidal alternating current circuit, is equal to the product of the rms values ​​of voltage U and current I, multiplied by the sine of the phase angle φ between them: Q = U x I x sin φ (if the current lags behind the voltage, the phase shift is considered positive, if it is ahead, it is negative).

Reactive quantity designation

An example of calculating the power of electric current

In the end, you will be able to test your knowledge with 2 common examples.

Imagine that in the first problem you have a resistor R = 50 Ohm through which an electric current I = 0.3A flows. What electrical power is converted in this resistor?

You can find the solution by finding the appropriate formula and plugging in the given values ​​into it. That is, we get: P = I2R = 0.32 * 50 = 4.5 W

In the second problem, a resistor R is given, the electrical resistance of which is 700 Ohms. The technical description states that the maximum power of this resistor is 10 W. How high can the voltage applied to this resistor be?

To solve this problem, we select the appropriate formula: P = U2/R, from where we find Umax = Pmax * R = 700 * 10 = 83.67 V.

This means that the maximum voltage can be 83.67 V. To be on the safe side, you should choose an electrical voltage well below this limit.

What is the difference between active power and reactive power – All about electricity

The power characteristics of an installation or network are basic for most known electrical appliances. Active power (transmitted, consumed) characterizes the part of the total power that is transmitted over a certain period of alternating current frequency.

Only alternating current can have active and reactive power, since the network characteristics (current and voltage) of direct current are always equal.

The unit of measurement for active power is Watt, while reactive power is measured by reactive voltampere and kiloVAR (kVAR).

It is worth noting that both full and active characteristics can be measured in kW and kVA, this depends on the parameters of the specific device and network. In industrial circuits it is most often measured in kilowatts.

Energy ratio

Electrical engineering uses the active component to measure the energy transfer of individual electrical devices. Let's look at how much power some of them consume:

Based on everything said above, active power is a positive characteristic of a specific electrical circuit, which is one of the main parameters for selecting electrical appliances and controlling electricity consumption.

Active component generation

Reactive component designation:

This is a nominal value that characterizes the loads in electrical devices using EMF fluctuations and losses during operation of the device. In other words, the transmitted energy goes to a specific reactive converter (this is a capacitor, diode bridge, etc.) and is manifested only if the system includes this component.

To find out the active power indicator, you need to know the total power; the following formula is used to calculate it:

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S = UI, where U is the network voltage and I is the network current.

The same calculation is performed when calculating the energy transfer level of the coil with a symmetrical connection. The diagram looks like this:

Symmetrical load diagram

The calculation of active power takes into account the phase angle or coefficient (cos φ), then:

S = U * I * cos φ.

A very important factor is that this electrical quantity can be either positive or negative. It depends on what characteristics cos φ has.

If the phase shift angle of a sinusoidal current is in the range from 0 to 90 degrees, then the active power is positive, if from 0 to -90, then it is negative.

The rule is valid only for synchronous (sinusoidal) current (used to operate an asynchronous motor or machine tool equipment).

Also, one of the characteristic features of this characteristic is that in a three-phase circuit (for example, a transformer or generator), the active indicator is completely generated at the output.

Three-phase network calculation

Maximum and active power is denoted by P, reactive power by Q.

Due to the fact that reactive is determined by the movement and energy of the magnetic field, its formula (taking into account the phase shift angle) has the following form:

QL = ULI = I2xL

For non-sinusoidal current it is very difficult to select standard network parameters. To determine the required characteristics for the purpose of calculating active and reactive power, various measuring devices are used. This is a voltmeter, ammeter and others. Based on the load level, the desired formula is selected.

Due to the fact that the reactive and active characteristics are related to the total power, their relationship (balance) is as follows:

S = √P2 + Q2, and all this equals U*I.

But if the current passes directly through the reactance. There are no losses in the network. This is determined by the inductive inductive component - C and resistance - L. These indicators are calculated using the formulas:

Inductance resistance: xL = ωL = 2πfL,

Capacitance resistance: xc = 1/(ωC) = 1/(2πfC).

To determine the ratio of active and reactive power, a special coefficient is used. This is a very important parameter by which you can determine what part of the energy is used for other purposes or is “lost” during operation of the device.

If there is an active reactive component in the network, the power factor must be calculated.

This quantity has no units of measurement; it characterizes a specific current consumer if the electrical system contains reactive elements.

Using this indicator, it becomes clear in which direction and how the energy shifts relative to the network voltage. To do this you will need a voltage triangle diagram:

Stress Triangle Diagram

For example, if there is a capacitor, the coefficient formula is as follows:

cos φ = r/z = P/S

To obtain the most accurate results, it is recommended not to round the data obtained.

Considering that when the currents resonate, the reactive power is 0:

Q = QL – QC = ULI – UCI

In order to improve the quality of operation of a particular device, special devices are used to minimize the impact of losses on the network. In particular, this is a UPS. This device does not require electrical consumers with a built-in battery (for example, laptops or portable devices), but for most others an uninterruptible power supply is necessary.

When installing such a source, you can not only determine the negative consequences of losses, but also reduce the cost of paying for electricity. Experts have proven that on average, a UPS will help save from 20% to 50%. Why is this happening:

1. The load on power transformers is significantly reduced;
2. The wires heat up less, this not only has a positive effect on their operation, but also increases safety;
3. Signaling and radio devices have reduced interference;
4. Harmonics in the electrical network are reduced by an order of magnitude.