Once again about power: active, reactive, apparent (P, Q, S), as well as power factor (PF). Features of power measurement How power is determined

Power is a physical quantity that shows how much energy moves within the electrical circuit of a particular piece of equipment. What is it, in what units is it expressed, how is power measured, what devices are there for this? More on this and more below.

Power is a scalar form of a physical quantity that is equal to the rate of change with the conversion, transmission or consumption of system energy. According to a narrower concept, this is an indicator that is equal to the ratio of time spent on work to the period itself spent on work. In mechanics it is designated by the symbol N. In electrical engineering the letter P is used. You can often also see the symbol W, from the word watt.

Power

There is a difference between useful, gross and nominal in a machine engine. The useful power is the engine power, excluding the costs that are spent on the operation of all other systems. Full is the indicated power without deductions, and nominal is indicated and guaranteed by the factory.

Additional Information! It is worth noting that there is also sound power and explosive sound. In the first case, it is a scalar quantity associated with sound waves and sound energy, which is also measured in watts, and the second is associated with the energy release of TNT decompositions.

Basic concept in the tutorial

What is it measured in?

Horsepower is considered an obsolete unit of measurement. Answering clearly the question of how mechanical power is measured, it is worth noting that according to modern international indicators, the unit of power is the watt. It is worth noting that the watt is a derived unit that is related to others. It is equal to Joule per second or kilogram times meter squared divided by second. Also, a watt is a volt multiplied by an ampere.

It is important to note that a watt is divided into mega, kilo and volt ampere.

Formulas for measurement

Power is a quantity that is directly related to other indicators. Thus, it is directly related to time, force, speed, force vector and speed, force and speed modulus, torque and rotation frequency. Often, in formulas when calculating the electrical power type, the number Pi, the resistance indicator, instantaneous current with voltage in a specific section of the electrical network, active, total and reactive power are also used. A direct participant in the calculation is the amplitude with angular velocity and the initial current strength with voltage.

Electric

Electrical power is a quantity that shows the speed or transformation at which electrical energy moves. To study the instantaneous electrical power characteristic in a certain section of the circuit, it is necessary to know the value of the current and voltage of the instantaneous current and multiply these values.

To understand how much the active, total, reactive or instantaneous reactive power indicator is, you need to know the exact numbers of current amplitude, voltage amplitude, angle of current with voltage, as well as angular velocity and time, since all existing physical formulas are reduced to these parameters. The formulas also use the sine, cosine of the angle and the value 1/2.

Electric power concept

Hydraulic

The hydraulic power indicator in a hydraulic machine or hydraulic cylinder is the product of the machine pressure drop and the liquid flow rate. Typically this is the basic formulation taken from the only existing formula for the calculation.

Note! More algebraic and engineering rules can be found in the applied science of the movement of liquids and gases, namely hydraulics.

Direct and alternating current

As for direct and alternating current power, they are most often classified as the electrical variety. There is no specific concept for the two varieties, but they can be calculated based on existing algebraic settings. Thus, direct current power is the product of current and constant voltage, or twice the current and electrical resistance, which, in turn, is calculated by dividing twice the voltage by the usual resistance.

As for alternating current, this is the product of the current strength with the voltage and the cosine of the phase shift. In this case, only the active and reactive varieties can be easily counted. You can find out the full power value through the vector dependence of these indicators and area.

To measure these indicators, you can use both the above instruments and a phase meter. This device is used to calculate the reactive variety according to the state standard.

Concept of variable current power

In general, power is a quantity whose main purpose is to show the strength of a particular device and, in many cases, the speed of activity interacting with it. It can be mechanical, electrical, hydraulic and for direct current and alternating current. Measured according to the international system in watts and kilowatts. The instruments for calculating it are a voltmeter and a wattmeter. The basic formulas for independent calculations are listed above.

that is, the product of force vectors and speed of movement is power. How is it measured? According to the international SI system, the unit of measurement for this quantity is 1 Watt.

Watt and other power units

Watt means power, where one joule of work is done in one second. The last unit was named after the Englishman J. Watt, who invented and built the first steam engine. But he used another quantity - horsepower, which is still used today. One horsepower is approximately equal to 735.5 watts.

Thus, in addition to Watts, power is measured in metric horsepower. And for a very small value, Erg is also used, equal to ten to the minus seventh power of Watt. It is also possible to measure in one unit of mass/force/meters per second, which is equal to 9.81 Watts.

Engine power

This value is one of the most important in any motor, which comes in a wide range of power. For example, an electric razor has hundredths of a kilowatt, and a spaceship rocket has millions.

Different loads require different power to maintain a certain speed. For example, a car will become heavier if more cargo is placed in it. Then the friction force on the road will increase. Therefore, to maintain the same speed as in an unloaded state, more power will be required. Accordingly, the engine will consume more fuel. All drivers know this fact.

But at high speeds, the inertia of the machine is also important, which is directly proportional to its mass. Experienced drivers who know about this fact find when driving best combination fuel and speed so that less gasoline is consumed.

Current power

How is current power measured? In the same SI unit. It can be measured by direct or indirect methods.

The first method is implemented using a wattmeter, which consumes significant energy and heavily loads the current source. It can be used to measure ten watts or more. The indirect method is used when it is necessary to measure small values. The instruments for this are an ammeter and a voltmeter connected to the consumer. The formula in this case will look like this:

With a known load resistance, we measure the current flowing through it and find the power as follows:

P = I 2 ∙ R n.

Using the formula P = I 2 /R n, the current power can also be calculated.

How it is measured in a three-phase current network is also no secret. For this, an already familiar device is used - a wattmeter. Moreover, the problem of how electrical power is measured can be solved using one, two or even three devices. For example, a four-wire installation would require three devices. And for a three-wire with an asymmetric load - two.

Power- a physical quantity equal to the ratio of work done to a certain period of time.

There is a concept of average power over a certain period of time Δt. Average power is calculated using this formula: N = ΔA / Δt, instantaneous power according to the following formula: N=dA/dt. These formulas have a rather generalized form, since the concept of power is present in several branches of physics - mechanics and electrophysics. Although the basic principles for calculating power remain approximately the same as in the general formula.

Power is measured in watts. Watt is a unit of power equal to joule divided by second. In addition to the watt, there are other units for measuring power: horsepower, erg per second, mass-force-meter per second.

• • One metric horsepower equal to 735 watts, English - 745 watts.
  • Erg- a very small unit of measurement, one erg is equal to ten to the minus seventh power of watts.
  • One mass-force-meter per second equal to 9.81 watts.

Measuring instruments

Measuring instruments for measuring power are mainly used in electrophysics, since in mechanics, knowing a certain set of parameters (speed and force), you can independently calculate the power. But in the same way, in electrophysics you can calculate power using parameters, but in fact, in everyday life we ​​simply do not use measuring instruments to record mechanical power. Since most often these parameters for certain mechanisms are designated as such. As for electronics, the main device is a wattmeter, used in everyday life in a conventional electric meter.

Wattmeters can be divided into several types according to frequencies:

• • Low frequency
  • Radio frequency
  • Optical

Wattmeters can be either analog or digital. Low-frequency (LF) ones contain two inductance coils, are both digital and analogue, and are used in industry and everyday life as part of conventional electricity meters. Radio frequency wattmeters are divided into two groups: absorbed power and transmitted power. The difference lies in the way the wattmeter is connected to the network; those passing through are connected in parallel to the network, which is absorbed at the end of the network as an additional load. Optical wattmeters are used to determine the power of light fluxes and laser beams. They are mainly used in various industries and laboratories.

Mechanical power

Power in mechanics directly depends on the force and the work that this force performs. Work is a quantity that characterizes the force applied to a body, under the influence of which the body travels a certain distance. Power is calculated by the scalar product of the velocity vector and the force vector: P = F * v = F * v * cos a (force multiplied by the velocity vector and the angle between the force and velocity vector (cosine alpha)).

You can also calculate the power of the rotational movement of the body. P=M* w= π * M * n / 30. Power is equal to (M) torque multiplied by (w) angular velocity or pi (n) multiplied by torque (M) and (n) rotational speed divided by 30.

Power in electrophysics

In electrophysics, power characterizes the rate of transmission or conversion of electricity. There are the following types of power:

• • Instantaneous electrical power. Since power is work done in a certain time, and the charge moves along a certain section of the conductor, we have the formula: P(a-b) = A / Δt. A-B characterizes the area through which the charge passes. A is the work of the charge or charges, Δt is the time it takes the charge or charges to travel through the section (A-B). Using the same formula, other power values ​​are calculated for different situations when you need to measure instantaneous power on a section of conductor.

• • You can also calculate the power of a constant flow: P = I * U = I^2 * R = U^2 / R.

• • AC power cannot be calculated using the DC formula. There are three types of power in alternating current:
    • Active power (P), which is equal to P = U * I * cos f . Where U and I are the current current parameters, and f (phi) is the shift angle between the phases. This formula is given as an example for single-phase sinusoidal current.
    • Reactive power (Q) characterizes the loads created in devices by oscillations of electrical single-phase sinusoidal alternating current. Q = U * I * sin f . The unit of measurement is reactive volt-ampere (var).
    • Apparent power (S) is equal to the root of the squares of active and reactive power. It is measured in volt-amperes.
    • Inactive power is a characteristic of passive power present in circuits with alternating sinusoidal current. Equal to the square root of the sum of the squares of reactive power and harmonic power. In the absence of higher harmonic power, it is equal to the reactive power module.

If you need to bring power units into one system, you will need our power conversion - online converter. And below you can read how power is measured.

Power is a physical quantity equal to the ratio of work performed over a certain period of time to this period of time.

How is power measured?

The units of power that are known to every schoolchild and are accepted in the international community are watts. Named in honor of the scientist J. Watt. They are designated by the Latin W or vt.

1 Watt is a unit of power that produces 1 joule of work per second. A watt is equal to the power of a current, the strength of which is 1 ampere, and the voltage is 1 volt. In technology, megawatts and kilowatts are usually used. 1 kilowatt is equal to 1000 watts.
Power is also measured in ergs per second. 1 erg per second. Equal to 10 to the minus seventh power of watt. Accordingly, 1 watt is equal to 10 to the seventh power erg/sec.

And the unit of measurement of power is considered to be the non-system “horsepower”. It was introduced into circulation back in the eighteenth century and continues to be used in the automotive industry. It is designated as follows:

• L.S. (in Russian),
• HP (in English).
• PS (in German),
• CV (in French).

When converting power, remember that there is incredible confusion in the RuNet when converting horsepower to watts. In Russia, CIS countries and some other countries 1 hp. equals 735.5 watts. In England and America, 1 hp equals 745.7 watts.

Hello! To calculate a physical quantity called power, they use the formula where the physical quantity - work - is divided by the time during which this work was performed.

She looks like this:

P, W, N=A/t, (W=J/s).

Depending on the textbooks and sections of physics, power in the formula can be denoted by the letters P, W or N.

Most often, power is used in such branches of physics and science as mechanics, electrodynamics and electrical engineering. In each case, power has its own formula for calculation. It is also different for alternating and direct current. Wattmeters are used to measure power.

Now you know that power is measured in watts. In English, watt is watt, the international designation is W, the Russian abbreviation is W. This is important to remember, because all household appliances have this parameter.

Power is a scalar quantity, it is not a vector, unlike force, which can have a direction. In mechanics, the general form of the power formula can be written as follows:

P=F*s/t, where F=A*s,

From the formulas you can see how instead of A we substitute the force F multiplied by the path s. As a result, power in mechanics can be written as force multiplied by speed. For example, a car having a certain power is forced to reduce speed when driving uphill, since this requires more force.

The average human power is taken to be 70-80 W. The power of cars, airplanes, ships, rockets and industrial plants is often measured in horsepower. Horsepower was used long before watts were introduced. One horsepower is equal to 745.7 W. Moreover, in Russia it is accepted that l. With. equal to 735.5 W.

If you are suddenly asked by chance 20 years later in an interview among passers-by about power, and you remember that power is the ratio of work A performed per unit time t. If you can say so, pleasantly surprise the crowd. Indeed, in this definition, the main thing to remember is that the divisor here is work A, and the divider is time t. As a result, having work and time, and dividing the first by the second, we get the long-awaited power.

When choosing in stores, it is important to pay attention to the power of the device. The more powerful the kettle, the faster it will heat the water. The power of the air conditioner determines how large a space it can cool without putting extreme load on the engine. The greater the power of an electrical appliance, the more current it consumes, the more electricity it will consume, and the higher the electricity bill will be.

In general, electrical power is determined by the formula:

where I is current, U is voltage

Sometimes it is even measured in volt-amperes, written as V*A. The total power is measured in volt-amperes, and to calculate the active power you need to multiply the total power by the coefficient of performance (efficiency) of the device, then we get the active power in watts.

Often, appliances such as an air conditioner, refrigerator, or iron operate cyclically, turning on and off from the thermostat, and their average power over the total operating time can be small.

In alternating current circuits, in addition to the concept of instantaneous power, which coincides with general physical power, there are active, reactive and apparent powers. Apparent power is equal to the sum of active and reactive power.

To measure power, electronic devices are used - wattmeters. The unit of measurement, Watt, got its name in honor of the inventor of the improved steam engine, which revolutionized power plants of the time. Thanks to this invention, the development of industrial society accelerated, trains, steamships, and factories appeared that used the power of the steam engine for movement and production of products.

We have all come across the concept of power many times. For example, different cars have different engine power. Also, electrical appliances can have different power levels, even if they have the same purpose.

Power is a physical quantity that characterizes the speed of work.

Respectively, mechanical power is a physical quantity that characterizes the speed of mechanical work:

That is, power is work per unit of time.

Power in the SI system is measured in watts: [ N] = [W].

1 W is 1 J of work done in 1 s.

There are other units of power measurement, such as horsepower:

It is in horsepower that the power of a car engine is most often measured.

Let's return to the formula for power: We know the formula by which work is calculated: Therefore we can rearrange the expression for power:

Then in the formula we form the ratio of the displacement modulus to the period of time. This is, as you know, the speed:

Just note that in the resulting formula we use the velocity module, since we divided not the movement itself, but its module by time. So, power is equal to the product of the force modulus, the velocity modulus and the cosine of the angle between their directions.

This is quite logical: say, the power of the piston can be increased by increasing the force of its action. By applying more force, it will do more work in the same time, that is, it will increase power. But even if we leave the force constant and make the piston move faster, it will undoubtedly increase the work done per unit time. Consequently, the power will increase.

Examples of problem solving.

Task 1. The motorcycle's power is 80 hp. Moving along a horizontal section, a motorcyclist reaches a speed of 150 km/h. At the same time, the engine operates at 75% of its maximum power. Determine the frictional force acting on the motorcycle.

Task 2. The fighter, under the influence of a constant thrust force directed at an angle of 45° to the horizon, accelerates from 150 m/s to 570 m/s. At the same time, the vertical and horizontal speed of the fighter increases by the same amount at each moment of time. The mass of the fighter is 20 tons. If the fighter accelerates for one minute, then what is the power of its engine?

We all come across electrical appliances every day; it seems that without them our lives stop. And each of them has power indicated in the technical instructions. Today we will figure out what it is, find out the types and methods of calculation.

Electrical appliances connected to the electrical network operate in an alternating current circuit, so we will consider power under these conditions. However, first, let's give general definition concept.

Power is a physical quantity that reflects the rate of conversion or transmission of electrical energy.

In a narrower sense, they say that electrical power is the ratio of the work performed over a certain period of time to this period of time.

To paraphrase this definition less scientifically, it turns out that power is a certain amount of energy that is consumed by the consumer over a certain period of time. The simplest example is an ordinary incandescent lamp. The rate at which a light bulb converts the electricity it consumes into heat and light is its power. Accordingly, the higher this indicator is initially for a light bulb, the more energy it will consume and the more light it will give off.

Since in this case, not only the process of converting electricity into some other ( light, thermal, etc.), but also the process of oscillation of the electric and magnetic fields, a phase shift appears between the current and voltage, and this should be taken into account in further calculations.

When calculating power in an alternating current circuit, it is customary to distinguish active, reactive and apparent components.

Concept of active power

Active “useful” power is that part of the power that directly characterizes the process of converting electrical energy into some other energy. Denoted by the Latin letter P and measured in ( W).

Calculated using the formula: P = U⋅I⋅cosφ,

where U and I are the root mean square value of the voltage and current of the circuit, respectively, cos φ is the cosine of the phase shift angle between voltage and current.

IMPORTANT! The formula described earlier is suitable for calculating circuits with, however, powerful units usually use a network with a voltage of 380V. In this case, the expression should be multiplied by the root of three or 1.73

Reactive power concept

Reactive “harmful” power is the power that is generated during the operation of electrical appliances with an inductive or capacitive load, and reflects the occurring electromagnetic oscillations. Simply put, this is energy that moves from the power source to the consumer, and then returns back to the network.

Naturally, this component cannot be used; moreover, it greatly harms the power supply network, which is why they usually try to compensate for it.

This value is denoted by the Latin letter Q.

REMEMBER! Reactive power is not measured in conventional watts ( W), and in reactive volt-amperes ( Var).

Calculated using the formula:

Q = U⋅I⋅sinφ,

where U and I are the rms value of the voltage and current of the circuit, respectively, sinφ is the sine of the phase shift angle between voltage and current.

IMPORTANT! When calculating, this value can be either positive or negative, depending on the phase movement.

Capacitive and inductive loads

The main difference between reactive ( capacitive and inductive) load – the presence, in fact, of capacitance and inductance, which tend to store energy and later release it into the network.

An inductive load converts the energy of an electric current first into a magnetic field ( during half half cycle), and then converts the energy of the magnetic field into electricity and transmits it to the network. Examples include asynchronous motors, rectifiers, transformers, and electromagnets.

IMPORTANT! When operating an inductive load, the current curve always lags the voltage curve by half a half cycle.

A capacitive load converts the energy of an electric current into an electric field, and then converts the energy of the resulting field back into an electric current. Both processes again occur for half a half cycle each. Examples are capacitors, batteries, synchronous motors.

IMPORTANT! During operation of a capacitive load, the current curve leads the voltage curve by half a half cycle.

Power factor cosφ

Power factor cosφ ( read cosine phi) is a scalar physical quantity that reflects the efficiency of electrical energy consumption. Simply put, the cosφ coefficient shows the presence of a reactive part and the magnitude of the resulting active part relative to the total power.

The cosφ coefficient is found through the ratio of active electrical power to total electrical power.

NOTE! For a more accurate calculation, nonlinear distortions of the sinusoid should be taken into account, however, in conventional calculations they are neglected.

The value of this coefficient can vary from 0 to 1 ( if the calculation is carried out as a percentage, then from 0% to 100%). From the calculation formula it is not difficult to understand that the greater its value, the greater the active component, which means the better the performance of the device.

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.

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.

How to find active, reactive and apparent power. Calculation example

All calculations are based on the previously mentioned formulas and the power triangle. Let's look at a problem that is most often encountered in practice.

Typically, electrical appliances indicate the active power and the value of the cosφ coefficient. Having this data, it is easy to calculate the reactive and total components.

To do this, divide the active power by the cosφ coefficient and obtain the product of current and voltage. This will be the full power.

How cosφ is measured in practice

The value of the cosφ coefficient is usually indicated on the labels of electrical appliances, however, if it is necessary to measure it in practice, a specialized device is used - a phase meter. A digital wattmeter can also easily handle this task.

If the resulting cosφ coefficient is low enough, then it can be practically compensated. This is accomplished mainly by including additional devices in the circuit.

1. If it is necessary to correct the reactive component, then a reactive element should be included in the circuit, acting opposite to the already functioning device. To compensate for the operation of an asynchronous motor, for example an inductive load, a capacitor is connected in parallel. An electromagnet is connected to compensate the synchronous motor.
2. If it is necessary to correct nonlinearity problems, a passive cosφ coefficient corrector is introduced into the circuit, for example, it can be a high-inductance inductor connected in series with the load.

Power is one of the most important indicators of electrical appliances, so knowing what it is and how it is calculated is useful not only for schoolchildren and people specializing in the field of technology, but also for each of us.