Physics mechanical power. What is the active and reactive power of alternating electric current? Apparent power concept

The most important task of equipment statistics is to measure the power of an enterprise's engines. Engine power called its ability to perform a certain work per unit of time (second). The basic unit of measure for power is the kilowatt (kW). Since the power equipment of an enterprise can include motors, the power of which is expressed in different units, the total power of all motors is expressed in kilowatts. To do this, use the following constant ratios:

The power of the motors can be characterized from different points of view.

Depending on the design of the engine, the power is distinguished between theoretical, indicator and effective (real).

Theoretical power(#) is determined by calculations based on the assumption that there are no mechanical losses (from friction) and heat losses (from radiation) in the engine. The theoretical power can be calculated for any engine.

Indicator power(# / sun) - engine power, taking into account thermal, but excluding mechanical losses. Measured M.nd on the engine organ where the radiation loss ends.

The third type of structural capacity is effective power (G This is the actual power, taking into account thermal and mechanical losses. Measured on the engine shaft.

Depending on the intensity of the engine's operation, its power can vary, therefore, such powers with load are distinguished: normal (economic), the longest and the shortest possible time.

Normal power(A / ^ g) is the power at which the engine uses fuel and energy most economically per unit of force, that is, it has the highest efficiency. When the load deviates up or down from the normal efficiency. decreases.

Basically, in order to obtain the maximum amount of energy during the operation of power devices, the maximum load mode is set for them, in which the engine, without prejudice to its condition, can operate for an indefinitely long period. The power characteristic of the maximum load of most power motors is called maximum long (mmt () -

Maximum short-term power (No.) is called the maximum load of the engine, during which it can work for a short time without an accident, usually no more than 30 minutes.

All three types of load power are potential, since they determine not the actual, but the possible load. For completeness of the characteristics of the power of the engine, one should simultaneously take into account its power, in terms of design and in terms of load. As a rule, this will be the maximum long-term effective power.

To characterize the power of the motors for the operational purpose distinguish between connected capacity, installed, available, peak, reserve, average actual and average annual.

Connected power (Mprd) the power of all receivers connected to the power plant is called, including the power of electric motors of someone else's current from subscribers and electric motors of their own current.

Large power plants provide electricity to subscribers with different load profiles. For example, in the morning, the demand for energy from production and urban transport (tram, trolleybus) increases sharply, but decreases for lighting; in the evening hours some enterprises stop working, but the demand of entertainment establishments for electric energy is sharply increasing. Due to the multiple-hour connection of subscribers to the station, the connected capacity is usually 2-2.5 times higher than the station's capacity. So, a station with a capacity of 30 thousand kW can serve subscribers, the capacity of current receivers of which is 60 thousand kW or more.

Power installed(l /) is the total maximum continuous effective power of the installed engines (for a power plant - the power of electric generators).

Since some of the engines under repair and awaiting repair cannot be used, it is of great importance available capacity (Mnayavі)- the total power of all devices, minus those that are under repair or awaiting it.

For a certain period, for example, per day, month or quarter, it is important to determine the maximum load, which is called peak power ША.

The difference between available and peak power is called reserve capacity. It consists of two parts that have different economic significance: the power of the standby engines, intended for the day of replacement of those that are working in the event of an accident, and the underload of the engines operating at rush hour.

For many practical calculations, it is determined average actual power L. It is calculated for a separate engine by dividing the energy generated during the period in kilowatt-hours by the actual operating time in hours, that is

To calculate the average actual power of several motors that work together, the energy they produce must be divided by the running time of all motors, reduced by the time they work together. So, the formula for the average actual power of two engines working together in one combination or another will have the form

Example 7.1

Calculate the average actual power of two motors, of which the first worked from 6 to 16 hours, and produced 630 kWh of energy, and the second worked from 8 to 23 hours, and produced 715 kWh of energy.

The total amount of energy produced: 630 + 715 = 1345 kWh.

The total running time of the engines: (16-6) + (23-8) = 25 hours.

Time of joint operation of engines: (16-8) = 8 hours.

In addition to the average actual power, calculate average annual power (M), which shows how many kilowatt hours of energy on average per year are produced during one hour.

For this, the generated energy is divided by the number of hours of the lesson-8760. always less than, and their ratio A ^ UL ^ characterizes the degree of use of the engine in time for a year.

Motors are installed in factories that perform various functions: primary motors produce mechanical energy, and secondary ones transform mechanical energy into electrical(electric generators) or electrical into mechanical and thermal (electric motors and electrical devices).

If, to determine the total capacity of the enterprise, we add up the power of the primary and secondary engines, then a repeated counting will be allowed; in addition, the calculation of the total capacity should include only the capacity that is used in the production process. Consequently, the power of the motors installed at the power station of the enterprise, the energy of which is supplied to the side, should not be taken into account when determining the energy capacity of a particular enterprise, since it will be taken into account at the enterprises - energy consumers.

Rice. 7.1. v

From fig. 7.1 it can be seen that prime movers can directly drive working machines or transmit mechanical energy to electric generators to transform it into electrical energy; Electricity from own electric generators can be used both to power electric motors and electric devices of its own and mixed current, and to meet the economic needs of the enterprise. Some of the electricity can be supplied to the side. At the same time, the energy received from the outside ensures the operation of electric motors and electric devices of foreign and mixed current. The power of direct-acting prime movers and the power of transport engines are taken into account independently. Having summed up the powers of the primary and secondary motors, we will allow a double counting. Therefore, the calculation formula is applied energy capacity of the enterprise, which completely excludes repeated counting:

The total power of prime movers №) also takes into account the power of direct-acting motors and those used in factory transport.

Formula 7.3 not only eliminates power over counting, but also differentiates between mechanical and electrical power.

The power of the mechanical drive is equal to the difference between the power of all the primary motors of the enterprise and the power of that part of them that serves the electric generators (Mpd-M ^^^^). This the difference is in the power of the prime movers directly connected to the working machines (using a transmission or a gear system).

The power of an electric drive is defined as the sum of the powers of electric motors and electric devices, that is, secondary motors that directly serve the production process.

Sometimes, when calculating the energy capacity of an enterprise, the power of the prime movers serving electric generators Gp.d. observ.el.gen)> unknown. To determine it, you need to multiply the power of electric generators by a factor of 1.04. The origin of this coefficient is as follows: the average efficiency of electric generators is taken to be 0.96, which means that the power of the prime movers that serve them can be obtained by dividing the power of the prime movers by 0.96 or multiplying by_ = 1.04. 0.96

For determining the amount of energy consumed by the enterprise, use a formula similar to that used to calculate the total power:

Example 7.2

Calculate the potential and average actual capacity of the enterprise, knowing that the enterprise has worked 200 hours and a little his the disposal of the following power equipment:

^^ = 400 + 50 + 350 0.736 + 100 0.736 - 250-1.04 + 220 + 600 = І34І, 2l5zh.

To calculate If it is necessary to determine the energy consumed by the enterprise:

Yeschypr = 80000 + 42000 o 0.736 + 10000 - 0.736 - 48000 o 1.04 + 42000 + 90000 = 200352 kW.

All of us are faced with electrical appliances every day, it seems that without them our life stops. And each of them has a specified capacity 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 mains operate in an alternating current circuit, so we will consider power in these conditions. However, first, let's give a general definition of the concept.

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

In a narrower sense, electrical power is said to be the ratio of work performed over a given period of time to that period of time.

If we rephrase 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 a conventional incandescent lamp. The rate at which a light bulb converts consumed electricity into heat and light will be its power. Accordingly, the higher the initially this indicator of the light bulb, the more it will consume energy, and the more light it will give.

Since in this case, there is not only the process of converting electricity into some other ( light, heat, 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 the power in an alternating current circuit, it is customary to distinguish active, reactive and total components.

Active power concept

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

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

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

IMPORTANT! The formula described earlier is suitable for calculating circuits with, however, powerful units usually use a 380V network. 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, it is energy that goes from the power source to the consumer, and then returns back to the network.

It is naturally impossible to use this component in business, moreover, it largely harms the power supply network, therefore they usually try to compensate for it.

This value is designated by the Latin letter Q.

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

Calculated by 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 angle between voltage and current.

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

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 give it to the network.

An inductive load converts the energy of an electric current first into a magnetic field ( for half a half period), and then converts the energy of the magnetic field into an electric current and transfers it to the network. An example is asynchronous motors, rectifiers, transformers, electromagnets.

IMPORTANT! When operating an inductive load, the current curve always lags behind 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, take place for half a half-period each. Examples are capacitors, batteries, synchronous motors.

IMPORTANT! During the operation of the 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 factor shows the presence of a reactive part and the value of the resulting active part relative to the total power.

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

NOTE! For a more accurate calculation, the harmonic distortion of the sinusoid should be taken into account, however, in normal calculations they are neglected.

The value of this coefficient can vary from 0 to 1 ( if the calculation is in percent, then from 0% to 100%). It is not difficult to understand from the calculation formula that the greater its value, the greater the active component, and therefore the better the performance of the device.

Full power concept. Power triangle

Apparent power is a geometrically calculated value equal to the root of the sum of the squares of the active and reactive power, respectively. It is designated 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 previously described calculations and the relationship 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 indicated formulas and the power triangle. Let's take a look at the most common problem in practice.

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

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

How cosφ is measured in practice

The value of the cosφ coefficient is usually indicated on the tags of electrical appliances, however, if it is necessary to measure it in practice, they use a specialized device - a phase meter. Also, a digital wattmeter can easily cope with this task.

If the resulting cosφ is low enough, it can be practically compensated. This is done mainly by including additional devices in the chain.

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 induction motor, for example an inductive load, a capacitor is connected in parallel. An electromagnet is connected to compensate for the synchronous motor.
2. If it is necessary to correct nonlinearity problems, a passive cosφ corrector is introduced into the circuit, for example, it can be a high inductance choke 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 technology, but also for each of us.

Back in the 18th century, power began to be counted in horsepower. Until now, this physical quantity is used to denote the strength of the motors. Next to the power indicator of the internal combustion engine in watts, the value in hp continues to be written.

Power as a physical quantity, power formula

A value that shows how quickly the conversion, translation or consumption of energy in any system occurs - power. For the characteristics of the energy conditions, it is important how quickly the process is carried out. The work carried out per unit of time is called power:

• What about work;
• t is time.

Mechanical power and electrical power can be taken into account separately.

To get an answer to the question: how the mechanical power is measured, consider the action of the force on a moving body. The force does the work, the power in this case is determined by the formula:

• F - strength;
• v is the speed.

During rotational motion, this value is determined taking into account the moment of force and the frequency of rotation, "rpm."

The relationship between electric current and power

In electrical engineering, work will be U - the voltage that moves 1 coulomb, the number of coulombs moved per unit time is the current (I). Electric current power or electrical power P is obtained by multiplying current by voltage:

This is a complete job done in 1 second. The dependence is direct here. By changing the current or voltage, the power consumed by the device is changed.

The same value of P is achieved by varying one of the two values.

Determination of the unit of measure for current power

The unit for measuring current power is named after James Watt, a Scottish mechanical engineer. 1 W is the power that a current of 1 A produces at a potential difference of 1 V.

For example, a source at a voltage of 3.5 V creates a current of 0.2 A in the circuit, then the current power will turn out:

P = U * I = 3.5 * 0.2 = 0.7 W.

Attention! In mechanics, power is usually represented by the letter N, in electrical engineering - by the letter P. How are n and P measured? Regardless of the designation, it is one quantity, and it is measured in watts "W".

Watt and other power units

Talking about what the power is measured in, you need to know what it is about. A watt is a value corresponding to 1 J / s. It is accepted in the International System of Units. In what units is power measured? The branch of science of astrophysics works with a unit called erg / s. Erg is a very small value, equal to 10-7 W.

Another, still widespread, unit from this series is "horsepower". In 1789, James Watt calculated that a 75 kg load from a mine could be pulled by one horse and done at a speed of 1 m / s. Based on the calculation of such labor intensity, the power of the engines can be measured with this value in the ratio:

1 h.p. = 0.74 kW.

Interesting. The Americans and the British believe that 1 hp. = 745.7 watts, and Russians - 735.5 watts. It makes no sense to argue who is right and who is not, since this measure is non-systemic and should not be used. The International Organization of Legal Metrology recommends that it be removed from circulation.

In Russia, when calculating a CASCO or OSAGO policy, these data of the power unit of the car are used.

The formula for the relationship between power, voltage and current

In electrical engineering, work is considered as a certain amount of energy given off by a power source to operate an electrical appliance over a period of time. Therefore, electrical power is a quantity that describes the speed of transformation or transmission of electricity. Its formula for direct current looks like this:

• U - voltage, V;
• I - current strength, A.

For some cases, using the Ohm's law formula, the power can be calculated by substituting the resistance value:

P = I * 2 * R, where:

• I - current strength, A;
• R - resistance, Ohm.

In the case of calculating the power of AC circuits, you will have to face three types:

• its active formula: P = U * I * cos ϕ, where is the phase angle coefficient;
• reactive is calculated: Q = U * I * sin ϕ;
• full is presented in the form: S = √P2 + Q2, where P is active, and Q2 is reactive.

Calculations for single-phase and three-phase AC circuits are performed according to different formulas.

Important! Electricity consumers in enterprises are mostly induction motors, transformers and other inductive receivers. During operation, they use reactive power, and that, flowing along power lines, leads the transmission line to an additional load. To improve the quality of energy, reactive energy compensation is used in the form of capacitor units.

Instruments for measuring electrical power

A wattmeter allows you to measure the power. It has two windings. One is included in the circuit in series, like an ammeter, the second in parallel, like a voltmeter. In installations of the electric power industry, wattmeters determine values ​​in kilowatt-hours "kWh". Measurements are needed not only for electrical energy, but also for laser energy. Devices capable of measuring this indicator are manufactured both in stationary and portable versions. With their help, the level of laser radiation of equipment using this type of energy is estimated. One of the portable meters is the LP1, a Japanese manufacturer. LP1 allows direct determination of light intensity values, for example, in the visual spot of optical devices of DVD players.

Power in household electrical appliances

To heat the metal of the filament of a light bulb, to increase the temperature of the working surface of an iron or other household appliance, a certain amount of electricity is spent. Its value taken by the load per hour is considered the power consumption of this device.

Attention! If the light bulb says "40 W, 230 V", it means that in 1 hour it consumes 40 W from the AC mains. Knowing the number of bulbs and parameters, they calculate how much energy is spent on lighting rooms per month.

How to translate watts

Since watt– the value is small, in everyday life they operate with kilowatts, use the conversion system:

• 1 W = 0.001 kW;
• 10 W = 0.01 kW;
• 100 W = 0.1 kW;
• 1000 W = 1 kW.

The power of some electrical appliances, W

Average values ​​of electricity consumption of household devices:

• plates - 110006000 W;
• refrigerators - 150-600 W;
• washing machines - 1000-3000 W;
• vacuum cleaners - 1300-4000 W;
• electric kettles - 2000-3000 W.

The parameters of each household appliance are indicated in the passport, and are also indicated on the case. The exact values ​​for consumer information are defined there.

Video

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

Power is called the scalar form of a physical quantity, which is equal to the rate of change with the transformation, transfer or consumption of system energy. According to a narrower concept, this is an indicator that is equal to the ratio of the time spent on work to the period itself that is spent on work. It is denoted in mechanics by the symbol N. In electrical engineering, the letter P is used. Often you can also see the symbol W, from the word watt.

Power

Distinguishes between useful, full and rated in a machine engine. Useful is the power of the engine, excluding the costs that are spent on running all other systems. Full - the specified force without deductions, and the nominal - specified and guaranteed by the factory.

Additional Information! It is worth noting that there is also the power of sound 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 from TNT decomposition.

Basic concept in the tutorial

What is measured

The obsolete unit of measurement is horsepower. Answering clearly to the question of how mechanical power is measured, it is worth noting that according to modern international indicators, the unit of power is a 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 a meter squared divided by a second. Also, a watt is a volt times an ampere.

It is important to note that watts are divided into mega, kilo and volt amperes.

Measurement formulas

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

Electric

Electrical power is a quantity that shows how fast or transforming electrical energy moves. To study the instantaneous electrical power characteristics at 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 figures of the 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 by the fluid flow rate. As a rule, this is the basic formulation taken from the only existing calculation formula.

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

DC and AC

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

With regard to alternating current, it 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 species can be counted without hindrance. 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 serves to calculate the reactive species according to the state standard.

Variable current power concept

In general, power is a quantity, the main purpose of which is to show the power 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 with alternating current. Measured according to the international system in watts and kilowatts. The instruments for calculating it are a voltmeter, a wattmeter. The basic formulas for self-calculation are listed above.

Performed for a certain period of time, by this period of time.

Effective power, the engine power delivered to the working machine directly or through the power train. Distinguish between useful, full and nominal em. Of the engine. E. M. Of the engine is called useful minus the power consumption for driving auxiliary units or mechanisms necessary for its operation, but having a separate drive (not from the engine directly). Full e. M. - engine power without deducting the specified costs. Nominal E. m., Or simply nominal power, - E. M., guaranteed by the manufacturer for certain operating conditions. Depending on the type and purpose of the engine, electric motors are installed that are regulated by standards or technical conditions (for example, the maximum power of a marine reversible engine at a certain crankshaft speed in the case of a ship's reverse speed - the so-called reverse power, the highest power of an aircraft engine at a minimum specific fuel consumption - the so-called cruising power, etc.). E. m. Depends on the forcing (intensification) of the working process, the size and mechanical efficiency of the engine.

Units

Another common unit for measuring power is horsepower.

Power in mechanics

If a force acts on a moving body, then this force does the work. Power in this case is equal to the scalar product of the force vector by the vector of the velocity with which the body moves:

M- moment, - angular velocity, - number pi, n- rotation frequency (rpm).

Electric power

Electric power- a physical quantity characterizing the rate of transmission or conversion of electrical energy.

S - Apparent power, VA

P - Active power, W

Q - Reactive power, VAR

Power measuring instruments

Notes (edit)

see also

Links

• Influence of the form of electric current on its action. Radio magazine, number 6, 1999

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