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 a circuit alternating current, so we will consider power under 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 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.
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 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 total 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 in business; 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.
Inductive load converts energy electric current first into a magnetic field ( during half half cycle), and then converts the energy of the magnetic field into electric current 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 received 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, one should take into account nonlinear distortion sinusoids, however, are neglected in ordinary calculations.
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.
- 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.
- 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.
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 formula direct current. 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.
- AC power cannot be calculated using the formula direct current. There are three types of power in alternating current:
The most important task of equipment statistics is to measure the power of plant engines. Engine power is called its ability to perform certain work per unit of time (second). The basic unit of power is the kilowatt (kW). Since a plant's power equipment may include motors whose power is expressed in different units, the total power of all motors is expressed in kilowatts. To do this, use the following constant relationships:
Engine power can be characterized from different points of view.
Depending on the design of the engine, 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 thermal losses (from radiation) in the engine. Theoretical power can be calculated for any engines.
Power indicator(#/s) - engine power taking into account thermal, but excluding mechanical losses. Measured M.nd on the part of the engine where radiation losses end.
The third type of design capacity is effective power (G This is the actual power, taking into account thermal and mechanical losses. Measured at the engine working shaft.
Depending on the intensity of engine operation, its power can change, therefore, there are such power with load: normal (economic), maximum long and maximum short time.
Power is normal(L/^g) is the power at which the engine most economically consumes fuel and energy per unit of force, that is, it has the highest coefficient useful action(efficiency). When the load deviates up or down from normal efficiency. decreases.
Basically, in order to obtain the maximum amount of energy when operating power devices, the mode is set for them maximum load, in which the engine can operate for an indefinitely long period without damage to its condition. The power characteristic of the maximum load of most power engines is called maximum duration (Mmt()-
Maximum short-term power (No.) is the maximum load of the engine for which it can operate 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. To fully characterize the power of an engine, its power, by design and by load, should be taken into account simultaneously. As a rule, this will be the maximum continuous effective power.
To characterize engine power according to operational purpose They distinguish between connected power, installed, available, peak, reserve, average actual and average annual.
Connected capacity (Mprisd) is the power of all receivers connected to the power plant, including the power of the electric motors of someone else's current for subscribers and the electric motors of their own current.
Large power plants provide electricity to subscribers with different load schedules. For example, in the morning the energy demand for production and urban transport (trams, trolleybuses) sharply increases, but for lighting decreases; In the evening hours, the work of some enterprises stops, but the need for entertainment venues for electrical energy increases sharply. Due to the frequent connection of subscribers to the station, the connected power is usually 2-2.5 times greater than the station capacity. So, a station with a capacity of 30 thousand kW can serve subscribers whose current receiver power 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 undergoing repair and awaiting repair cannot be used, it is of great importance available power (Мяві)- the total power of all devices, minus those that are under repair or awaiting repair.
For a certain period, for example per day, month or quarter, it is important to determine the maximum load, which is called peak power of the ShA.
The difference between available and peak power is called reserve power. It consists of two parts that have different economic significance: the power of backup engines, intended to replace those that are running in the event of an accident, and the underload of engines operating during rush hour.
For many practical calculations it is determined average actual power L. It is calculated for an individual 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 engines that work together, the energy they produce must be divided by the operating time of all engines, reduced by the time they work together. Thus, the formula for the average actual power of two engines operating together in one or another combination will have the form
Example 7.1
Calculate the average actual power of two engines, of which the first worked from 6 to 16 hours and produced 630 kW x hour of energy, and the second worked from 8 to 23 hours and produced 715 kW x hour of energy.
Total amount of energy produced: 630 + 715 = 1345 kW x h.
Total engine operating time: (16-6) + (23-8) = 25 hours.
Time for the engines to work together: (16-8) = 8 hours.
In addition to the average actual power, calculate average annual power (M), which shows how many kilowatt-hours of energy are produced per hour on average per year.
To do this, the energy produced is divided by the number of lesson hours - 8760. is always less than and their ratio A^UL^ characterizes the degree of engine utilization over time over an annual period.
The enterprises have engines installed that perform various functions: primary engines produce mechanical energy, and secondary engines transform mechanical energy energy into electrical(electric generators) or electrical into mechanical and thermal (electric motors and electrical devices).
If, to determine the total power of an enterprise, the power of the primary and secondary engines is added, then a repeated count will be allowed; In addition, the total power calculation should only include the power that is used in the production process. Consequently, the power of the engines 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 certain enterprise, since it will be taken into account at the enterprises that consume energy.
Rice. 7.1. V
From Fig. 7.1 shows that prime movers can directly drive working machines or transmit mechanical energy to electric generators to transform it into electrical energy; The electricity from your own electric generators can be used both to power electric motors and electric devices of your own and mixed current, and to meet the economic needs of the enterprise. Part of the electricity can be released to the side. At the same time, energy received from outside ensures the operation of electric motors and electric devices of foreign and mixed current. The power of direct primary engines and the power of transport engines are taken into account independently. By summing the powers of the primary and secondary engines, we will allow double counting. Therefore, the calculation formula is applied energy capacity of the enterprise, which completely eliminates double counting:
The total power of prime movers No.) also takes into account the power of direct-acting motors and those used in factory vehicles.
Formula 7.3 not only eliminates the repeated calculation of power, but also distinguishes between the power of a mechanical and electric drive.
The power of the mechanical drive is equal to the difference between the power of all primary engines of the enterprise and the power of that part of them that serves electric generators (Mpd-M^^^^). This the difference is the power of the prime movers directly connected to the working machines (using a transmission or gear system).
The power of an electric drive is defined as the sum of the powers of electric motors and electrical devices, that is, secondary engines that directly serve the production process.
Sometimes, when calculating the energy power of an enterprise, the power of the primary engines servicing electric generators Gp.d.obs.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 worked for 200 hours and little his The following power equipment is at our disposal:
^^=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:
Yeschipr = 80000 + 42000 o 0.736+10000 - 0.736 - 48000 o 1.04 + 42000 + 90000 = 200352 kW.
Power- a physical quantity equal in the general case to the rate of change, transformation, transmission or consumption of system energy. In a narrower sense, power is equal to the ratio of the work performed in a certain period of time to this period of time.
Distinguish between average power over a period of time
and instantaneous power in this moment time:
The integral of instantaneous power over a period of time is equal to the total transferred energy during this time:
Units. The International System of Units (SI) unit of power is the watt, equal to one joule divided by a second. mechanical work power electrical
Another common, but now outdated, unit of power measurement is horsepower. In its recommendations, the International Organization of Legal Metrology (OIML) lists horsepower as a unit of measurement “which should be phased out as soon as possible where it is currently used and which should not be introduced if it is not in use.”
Relationships between power units (see Appendix 9).
Mechanical power. If a force acts on a moving body, then this force does work. Power in this case is equal to the scalar product of the force vector and the velocity vector with which the body moves:
Where F- force, v- speed, - angle between the vector of speed and force.
A special case of power during rotational motion:
M- torque, - angular velocity, - pi, n- rotation speed (revolutions per minute, rpm).
Electric power
Mechanical power. Power characterizes the speed at which work is done.
Power (N) is a physical quantity equal to the ratio of work A to the time period t during which this work was performed.
Power shows how much work is done per unit of time.
In the International System (SI), the unit of power is called the Watt (W) in honor of the English inventor James Watt (Watt), who built the first steam engine.
[N]= W = J/s
- 1 W = 1 J / 1s
- 1 Watt is equal to the power of a force that does 1 J of work in 1 second or when a load weighing 100 g is raised to a height of 1 m in 1 second.
James Watt himself (1736-1819) used another unit of power - horsepower (1 hp), which he introduced in order to compare the performance of a steam engine and a horse.
1hp = 735 W.
However, the power of one average horse is about 1/2 hp, although horses are different.
“Living engines” can briefly increase their power several times.
A horse can increase its power when running and jumping up to tenfold or more.
Making a jump to a height of 1 m, a horse weighing 500 kg develops a power equal to 5,000 W = 6.8 hp.
It is believed that the average power of a person during quiet walking is approximately 0.1 hp. i.e. 70-90W.
When running and jumping, a person can develop power many times greater.
It turns out that the most powerful source of mechanical energy is a firearm!
Using a cannon, you can throw a cannonball weighing 900 kg at a speed of 500 m/s, developing about 110,000,000 J of work in 0.01 seconds. This work is equivalent to lifting 75 tons of cargo to the top of the Cheops pyramid (height 150 m).
The power of the cannon shot will be 11,000,000,000 W = 15,000,000 hp.
The force of tension in a person's muscles is approximately equal to the force of gravity acting on him.
this formula is valid for uniform motion with constant speed and in the case of variable motion for average speed.
From these formulas it is clear that at constant engine power, the speed of movement is inversely proportional to the traction force and vice versa.
This is the basis for the operating principle of the gearbox (gearbox) of various vehicles.
Electric power. Electrical power is a physical quantity that characterizes the speed of transmission or conversion of electrical energy. When studying AC networks, in addition to instantaneous power corresponding to the general physical definition, the concepts of active power are also introduced, equal to the average value of instantaneous power over a period, reactive power, which corresponds to energy circulating without dissipation from the source to the consumer and back, and total power, calculated as the product of the effective values of current and voltage without taking into account the phase shift.
U is the work performed when moving one coulomb, and the current I is the number of coulombs passing in 1 second. Therefore, the product of current and voltage shows the total work done in 1 second, that is, electrical power or electric current power.
Analyzing the above formula, we can draw a very simple conclusion: since the electrical power “P” equally depends on the current “I” and on the voltage “U”, then, therefore, the same electrical power can be obtained either with a high current and a low current voltage, or, conversely, at high voltage and low current (This is used when transmitting electricity over long distances from power plants to places of consumption, through transformer conversion at step-up and step-down power substations).
Active electrical power (this is power that is irrevocably converted into other types of energy - thermal, light, mechanical, etc.) has its own unit of measurement - W (Watt). It is equal to 1 volt times 1 ampere. In everyday life and in production, it is more convenient to measure power in kW (kilowatts, 1 kW = 1000 W). Power plants already use larger units - mW (megawatts, 1 mW = 1000 kW = 1,000,000 W).
Reactive electrical power is a quantity that characterizes this type electrical load, which are created in devices (electrical equipment) by energy fluctuations (inductive and capacitive) of the electromagnetic field. For conventional alternating current, it is equal to the product of the operating current I and the voltage drop U by the sine of the phase angle between them:
Q = U*I*sin(angle).
Reactive power has its own unit of measurement called VAR (volt-ampere reactive). Denoted by the letter "Q".
Power density. Specific power is the ratio of engine power to its mass or other parameter.
Vehicle power density. In relation to cars, specific power is called maximum power motor, related to the entire mass of the car. The power of a piston engine divided by the displacement of the engine is called liter power. For example, the liter power of gasoline engines is 30...45 kW/l, and for diesel engines without turbocharging - 10...15 kW/l.
An increase in the specific power of the engine ultimately leads to a reduction in fuel consumption, since there is no need to transport a heavy engine. This is achieved through light alloys, improved design and boosting (increasing speed and compression ratio, using turbocharging, etc.). But this dependence is not always observed. In particular, heavier diesel engines can be more economical, as the efficiency of a modern turbocharged diesel reaches up to 50%
In the literature, using this term, the inverse value kg/hp is often given. or kg/kW.
Specific power of tanks. The power, reliability and other parameters of tank engines were constantly growing and improving. If in the early models they were content with essentially automobile engines, then with the increase in the mass of tanks in the 1920s-1940s. Adapted aircraft engines, and later specially designed tank diesel (multi-fuel) engines, became widespread. To ensure acceptable driving performance of a tank, its specific power (the ratio of engine power to the combat weight of the tank) must be at least 18-20 hp. With. /T. Specific power of some modern tanks (see Appendix 10).
Active power. Active power is the average value of instantaneous alternating current power over a period:
Active power is a quantity that characterizes the process of converting electricity into some other type of energy. In other words, electrical power, as it were, shows the rate of electricity consumption. This is the power for which we pay money, which is counted by the meter.
Active power can be determined using the following formula:
The power characteristics of the load can be accurately specified by one single parameter (active power in W) only for the case of direct current, since in a direct current circuit there is only one type of resistance - active resistance.
The power characteristics of the load for the case of alternating current cannot be accurately specified by one single parameter, since there are two different types resistance - active and reactive. Therefore, only two parameters: active power and reactive power accurately characterize the load.
The operating principles of active and reactive resistance are completely different. Active resistance - irreversibly converts electrical energy into other types of energy (thermal, light, etc.) - examples: incandescent lamp, electric heater.
Reactance - alternately stores energy and then releases it back into the network - examples: capacitor, inductor.
Active power (dissipated through active resistance) is measured in watts, and reactive power (circulating through reactance) is measured in vars; Also, to characterize the load power, two more parameters are used: apparent power and power factor. All these 4 parameters:
Active power: designation P, unit: Watt.
Reactive power: designation Q, unit of measurement: VAR (Volt Ampere reactive).
Apparent power: designation S, unit: VA (Volt Ampere).
Power factor: designation k or cosФ, unit of measurement: dimensionless quantity.
These parameters are related by the following relations:
S*S=P*P+Q*Q, cosФ=k=P/S.
CosФ is also called power factor.
Therefore, in electrical engineering, any two of these parameters are specified to characterize power, since the rest can be found from these two.
It's the same with power supplies. Their power (load capacity) is characterized by one parameter for DC power supplies - active power (W), and two parameters for sources. AC power supply. Typically these two parameters are apparent power (VA) and active power (W).
Most office and household appliances, active (no or little reactance), therefore their power is indicated in Watts. In this case, when calculating the load, the UPS power value in Watts is used. If the load is computers with power supplies (PSUs) without input power factor correction (APFC), laser printer, refrigerator, air conditioner, electric motor (for example, a submersible pump or a motor as part of a machine), fluorescent ballast lamps, etc. - all outputs are used in the calculation. UPS data: kVA, kW, overload characteristics, etc.
Reactive power. Reactive power, methods and types (means) of reactive power compensation.
Reactive power is the part of the total power expended on electromagnetic processes in a load that has capacitive and inductive components. Doesn't perform useful work, causes additional heating of the conductors and requires the use of an energy source of increased power.
Reactive power refers to technical losses in electrical networks according to Order of the Ministry of Industry and Energy of the Russian Federation No. 267 dated October 4, 2005.
Under normal operating conditions, all consumers of electrical energy whose mode is accompanied by the constant occurrence of electromagnetic fields (electric motors, welding equipment, fluorescent lamps and much more) load the network with both active and reactive components of the total power consumption. This reactive component of power (hereinafter referred to as reactive power) is necessary for the operation of equipment containing significant inductances and at the same time can be considered as an unwanted additional load on the network.
With significant consumption of reactive power, the voltage in the network decreases. In power systems that are deficient in active power, the voltage level is usually lower than the nominal one. Insufficient active power to complete the balance is transferred to such systems from neighboring power systems that have excess generated power. Typically, power systems are deficient in active power and deficient in reactive power. However, it is more efficient not to transfer the missing reactive power from neighboring power systems, but to generate it in compensating devices installed in the given power system. Unlike active power, reactive power can be generated not only by generators, but also by compensating devices - capacitors, synchronous compensators or static reactive power sources, which can be installed at substations of the electrical network.
Reactive power compensation, currently, is an important factor in solving the issue of energy saving and reducing loads on the power grid. According to estimates of domestic and leading foreign experts, the share of energy resources, and in particular electricity, occupies a significant amount in the cost of production. This is a strong enough argument to seriously approach the analysis and audit of an enterprise’s energy consumption, the development of a methodology and the search for means to compensate for reactive power.
Reactive power compensation. Reactive power compensation means. The inductive reactive load created by electrical consumers can be counteracted with a capacitive load by connecting a precisely sized capacitor. This reduces the reactive power consumed from the network and is called power factor correction or reactive power compensation.
Advantages of using capacitor units as a means of reactive power compensation:
- · low specific losses of active power (the own losses of modern low-voltage cosine capacitors do not exceed 0.5 W per 1000 VAr);
- · no rotating parts;
- · simple installation and operation (no foundation required);
- · relatively low capital investments;
- · the ability to select any required compensation power;
- · Possibility of installation and connection at any point in the electrical network;
- · no noise during operation;
- · low operating costs.
Depending on the connection of the capacitor unit, the following types of compensation are possible:
- 1. Individual or constant compensation, in which inductive reactive power is compensated directly at the point of its occurrence, which leads to unloading of the supply wires (for individual consumers operating in continuous mode with constant or relatively high power - asynchronous motors, transformers, welding machines, discharge lamps, etc.).
- 2. Group compensation, in which, similar to individual compensation for several simultaneously operating inductive consumers, a common constant capacitor is connected (for electric motors located close to each other, groups of discharge lamps). Here the supply line is also unloaded, but only before distribution to individual consumers.
- 3. Centralized compensation, in which a certain number of capacitors are connected to the main or group distribution cabinet. Such compensation is usually used in large electrical systems with variable loads. Such a capacitor installation is controlled by an electronic regulator - a controller that constantly analyzes the consumption of reactive power from the network. Such regulators turn on or off capacitors, with the help of which the instantaneous reactive power of the total load is compensated and, thus, the total power consumed from the network is reduced.
Back in the 18th century, power began to be measured in horsepower. Until now, this physical quantity is used to indicate the power of engines. Next to the power indicator of the internal combustion engine in watts, they continue to write the value in hp.
Power as a physical quantity, power formula
A value that shows how quickly energy is converted, transmitted, or consumed in a system—power. It is important to characterize the energy conditions how quickly the process is performed. The work performed per unit of time is called power:
- What about work;
- t – time.
Mechanical power and electrical power can be taken into account separately.
To get an answer to the question: how is mechanical power measured, consider the effect of force on a moving body. Force does work, power in this case is determined by the formula:
- F – force;
- v – speed.
During rotational motion, this value is determined taking into account the moment of force and rotational speed, “rpm.”
Relationship between electric current and power
In electrical engineering, the 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 the current by the voltage:
This is a complete job done in 1 second. The dependence here is direct. By changing the current or voltage, the power consumed by the device is changed.
The same P value is achieved by varying one of two values.
Definition of current power unit
The unit for measuring current power is named after James Watt, a Scottish mechanical engineer. 1 W is the power generated by a current of 1 A at a potential difference of 1 V.
For example, a source with a voltage of 3.5 V creates a current of 0.2 A in the circuit, then the current power will be:
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
When talking about how power is measured, you need to know what we are talking about. Watt is a value corresponding to 1 J/s. It is adopted in the International System of Units. In what other units is power measured? The branch of science astrophysics works with a unit called erg/s. Erg is a very small value, equal to 10-7 W.
Another, still common, unit from this series is “horsepower”. In 1789, James Watt calculated that a 75 kg load could be pulled from a shaft by one horse at a speed of 1 m/s. Based on the calculation of such labor intensity, the engine power can be measured by this value in the ratio:
1 hp = 0.74 kW.
Interesting. Americans and British believe that 1 hp. = 745.7 W, and Russians – 735.5 W. There is no point in arguing who is right and who is wrong, since this is an extra-systemic measure and should not be used. The International Organization of Legal Metrology recommends its withdrawal from circulation.
In Russia, when calculating a CASCO or OSAGO policy, these data from the car’s power unit are used.
Formula for the relationship between power, voltage and current
In electrical engineering, work is considered as a certain amount of energy supplied by a power source to the operation of an electrical device 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, power can be calculated by substituting the resistance value:
P = I*2*R, Where:
- I – current strength, A;
- R – resistance, Ohm.
When calculating the power of AC circuits, you will have to deal with three types:
- its active formula: P = U*I*cos ϕ, where is the phase shift angle coefficient;
- reactive is calculated: Q = U*I*sin ϕ ;
- the complete one 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 using different formulas.
Important! Consumers of electricity in enterprises are mostly asynchronous motors, transformers and other inductive receivers. During operation, they use reactive power, which, flowing through power lines, leads to additional load on power lines. To improve energy quality, reactive energy compensation is used in the form of capacitor units.
Instruments for measuring electrical power
A wattmeter allows you to measure power. It has two windings. One is connected to the circuit in series, like an ammeter, the second in parallel, like a voltmeter. In electrical power installations, wattmeters measure values in kilowatt-hour “kW*h.” Measurements require not only electrical energy, but also laser energy. Devices capable of measuring this indicator are manufactured in both stationary and portable versions. With their help, the level of laser radiation from equipment using this type of energy is assessed. One of the portable meters is LP1, made by a Japanese manufacturer. LP1 allows you to directly determine the intensity of light radiation, for example, in a visual spot optical devices DVD players.
Power in household electrical appliances
To heat the metal filament of a light bulb, 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,” this means that in 1 hour it consumes 40 W from the AC network. Knowing the number of light bulbs and parameters, they calculate how much energy is spent on lighting rooms per month.
How to convert watts
Since watt– the value is small, in everyday life they operate in kilowatts, they use a system for converting quantities:
- 1 W = 0.001 kW;
- 10 W = 0.01 kW;
- 100 W = 0.1 kW;
- 1000 W = 1 kW.
Power of some electrical appliances, W
Average electricity consumption values for household devices:
- stoves – 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 body. The exact values for consumer information are defined there.
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