Theory and basic terms of energy saving. Active power

Power can be active or full. The question is, full of what? But, they say, by what serves us well, what does useful work for us, but also... it turns out that that’s not all. There is also a second component, which turns out to be a kind of makeweight, and it simply burns energy. It heats what is not needed, but it makes us neither hot nor cold.

This power is called reactive power. But, oddly enough, we ourselves are to blame. Or rather, our system for generating, transmitting and consuming electricity.

Power active, reactive and apparent

We use electricity using AC networks. The voltage in our networks fluctuates 50 times every second from the minimum value to the maximum. It happened that way. When an electric generator was invented, which converts mechanical motion into electricity, it turned out that perpetuum mobile, or, translated from Latin, perpetual motion, is easiest to arrange in a circle. A wheel was once invented, and since then we know that if you hang it on an axle, you can rotate it for a long, long time, but it will remain in the same place - on the axle.

Why is our network voltage variable?

And an electric generator has an axis and something rotating on it. And the result is electrical voltage. Only the generator consists of two parts: rotating, the rotor, and stationary, the stator. And both of them are involved in generating electricity. And when one part rotates around another, then inevitably the points of the surface of the rotating part either approach or move away from the points of the stationary surface. And this joint position is inevitably described by only one mathematical function - a sinusoid. A sinusoid is a projection of rotation in a circle onto one of the geometric axes. But many such axes can be built. Usually our coordinates are perpendicular to each other. And then, when a certain point rotates in a circle on one axis, the projection of rotation will be a sinusoid, and on the other - a cosine, or the same sinusoid, only shifted relative to the first by a quarter of a rotation, or by 90°.

This is something like the voltage that the electrical network brings to our apartment.

The rotation angle here is not divided into 360 degrees,
and by 24 divisions. That is, one division corresponds to 15°
6 divisions = 90°

So, the voltage in our network is sinusoidal with a frequency of 50 hertz and an amplitude of 220 volts, because it was more convenient to make generators that produce alternating voltage.

Benefit from AC voltage - system benefit

And to make the voltage constant, you need to specifically straighten it. And this can be done either directly in the generator (specially designed - then it will become a direct current generator), or sometime later. This “someday” came in very handy again, because alternating voltage can be converted by a transformer - raised or lowered. This turned out to be the second convenience of variable voltage. And by increasing it with transformers to literally EXTRAORDINARY voltages (half a million volts or more), it can be transmitted over gigantic distances via wires without gigantic losses. And this also came in handy in our big country.

So, having nevertheless brought the voltage to our apartment, lowering it to a somewhat conceivable (albeit still dangerous) value of 220 volts, they again forgot to convert it to constant. And why? The lights are on, the refrigerator is working, the TV is on. Although the TV has these constant/alternating voltages... but let’s not talk about that here.

AC Voltage Losses

And so we use an alternating voltage network.

And it contains a “payment for forgetfulness” - the reactance of our consuming networks and their reactive power. Reactance is resistance to alternating current. And the power that simply goes past our consuming electrical appliances.

Current flowing through wires creates an electric field around them. An electrostatic field attracts charges from everything that surrounds the source of the field, that is, the current. And the change in current also creates an electromagnetic field, which begins to non-contactly induce electric currents in all conductors around. So, our current sinusoid, as soon as we turn on something, is not just current, but its continuous change. There are plenty of conductors around, starting from the metal casings of the same electrical appliances, metal pipes for water supply, heating, sewerage and ending with reinforcement rods in reinforced concrete walls and ceilings. It is in all this that electricity is induced. Even the water in the toilet cistern takes part in the general fun - induction currents are also induced in it. We don’t need this kind of electricity at all; we didn’t “order” it. But it tries to heat up these conductors, which means it takes away electricity from our apartment network.

To characterize the power ratio in our AC network, draw a triangle.

S is the total power consumed by our network,
P – active power, also known as active active load,
Q – reactive power.

Total power can be measured with a wattmeter, and active power is obtained by calculating our network, in which we take into account only loads that are useful to us. Naturally, we neglect the resistance of the wires, considering them small relative to the useful resistance of electrical appliances.

Full power

S = U x I = U a x I f

That is, the “dumber” this acute angle is, the worse our internal apartment consuming network works - a lot of energy goes into losses.

What is active, reactive and apparent power

Angle j can also be called the phase shift angle between current and voltage in our network. The current is the result of applying an initial voltage of 220 volts with a frequency of 50 hertz to our network. When the load is active, the phase of the current coincides with the phase of the voltage in it. And reactive loads shift this phase by this angle.

As a matter of fact, the angle characterizes the degree of efficiency of our energy consumption. And we must try to reduce it. Then S will approach P.

It’s just more convenient to operate not with the angle, but with the cosine of the angle. This is precisely the ratio of the two powers:

The cosine of an angle approaches one as the angle approaches zero. That is, the sharper the angle j, the better and more efficient the electrical consuming network works. In practice, if you achieve a cosine phi value (and it can be expressed as a percentage) of the order of 70–90%, then this is already considered good.

Another relationship that connects active power and reactive power is often used:

From the current and voltage diagram you can find expressions for powers: active, reactive and total.

If the more familiar active power is measured in watts, then the total power is measured in volt-amperes (var). A watt from a var can be calculated by multiplying by cosine phi.

What is reactive power

Reactive power can be inductive or capacitive. They behave differently in an electrical circuit. At direct current, inductance is simply a piece of wire that has some very small resistance. A constant voltage capacitor is just an open circuit.

And when we connect them to the circuit, apply voltage to them, during the transition process they also behave in exactly the opposite way. The capacitor is charged, and the resulting current is initially large, then, as charging proceeds, small, decreasing to zero.

In an inductance, a coil with a wire, the resulting magnetic field after switching on at the very beginning strongly interferes with the passage of current, and it is small at first, then increases to its stationary value, determined by the active elements of the circuit.

Capacitors thus contribute to the change in current in the circuit, while inductances prevent the change in current.

Inductive and capacitive components of network resistance

Thus, reactive elements have their own types of resistance - capacitive and inductive. This is related to the total resistance, including active and reactive components, by the following formula:

Z – total resistance,

R – active resistance,

X – reactance.

In turn, reactance consists of two parts:

X L – inductive and X C – capacitive.

From this we see that their contribution to the reactive component is different.

Everything that is inductive in the network increases the reactance of the network, everything that is capacitive in the network reduces the reactance.

Electrical appliances that affect the quality of consumption

If all the devices in our network were like light bulbs, that is, they were purely active loads, there would be no problems. If there were an active consuming network, one continuous active load, and, as they say, in an open field - there was nothing around, then everything would be easily calculated according to Ohm's and Kirchhoff's laws, and it would be fair - as much as you consumed, you paid for as much. But having a mysterious conductive “infrastructure” around us, and in the network itself there are many unaccounted capacitances and inductances, we receive, in addition to what is useful to us, also a reactive load that is unnecessary for us.

How to get rid of it? When the electrical consuming network has already been created, measures can be taken to reduce the reactive component. Compensation is based on the “antagonism” of inductances and capacitances.

That is, in an existing network, you should measure its components, and then come up with compensation.

A particularly good effect from such measures is achieved in large consuming networks. For example, at the level of a factory workshop with a large number of constantly operating equipment.

To compensate for the reactive component, special reactive power compensators (RPCs) are used, which contain capacitors in their design that change the total phase shift in the network for the better.

The use of synchronous AC motors in networks is also encouraged, since they are able to compensate for reactive power. The principle is simple: in the network they are able to operate in motor mode, and when a “blockage” of electricity is observed during a phase shift (the language no longer finds other words), they are able to compensate for this by “moonlighting” in the network in generator mode.

For power engineers at enterprises and large shopping centers, there is no doubt about the existence of reactive energy. Monthly bills and very real money that goes into payment reactive electricity, convince of the reality of its existence. But some electrical engineers seriously, with mathematical calculations, prove that this type of electricity is fiction, that the division of electrical energy into active and reactive components is artificial.

Let's try and understand this issue, especially since the creators are speculating on ignorance of the differences between different types of electricity. Promising huge percentages, they knowingly or unknowingly replace one type of electrical energy with another.

Let's start with the concepts of active and reactive electricity. Without going into the jungle of electrical engineering formulas, we can determine active energy as that which does work: heats food on electric stoves, illuminates your room, cools the air using an air conditioner. And reactive electricity creates the necessary conditions for performing such work. There will be no reactive energy, and the motors will not be able to rotate, the refrigerator will not work. A voltage of 220 Volts will not be supplied to your premises, since not a single power transformer operates without consuming reactive electricity.

If current and voltage signals are simultaneously observed on an oscilloscope, then these two sinusoids always have a shift relative to each other by an amount called phase angle. This shift characterizes the contribution of reactive energy to the total energy consumed by the load. By measuring only the current in the load, it is impossible to isolate the reactive part of the energy.

Considering that reactive energy does not do work, it can be generated at the point of consumption. Capacitors are used for this. The fact is that coils and capacitors consume different types of reactive energy: inductive and capacitive, respectively. They shift the current versus voltage curve in opposite directions.

Due to these circumstances a capacitor can be considered a consumer of capacitive energy or a generator of inductive energy. For a motor that consumes inductive energy, a nearby capacitor can become a source of energy. Such reversibility is possible only for reactive circuit elements that do not perform work. For active energy, such reversibility does not exist: its generation is associated with fuel consumption. After all, before you can do work, you need to expend energy.

In domestic conditions, power transmission organizations do not charge a fee for reactive energy, and a household meter only counts the active component of electrical energy. The situation is completely different in large enterprises: a large number of electric motors, welding machines and transformers, which require reactive energy to operate, create additional load on power lines. At the same time, the current and heat losses of the active energy increase.

In these cases, reactive energy consumption is taken into account by the meter and paid separately. The cost of reactive electricity is less than the cost of active electricity, but for large volumes of consumption, payments can be very significant. In addition, fines are imposed for the consumption of reactive energy in excess of the specified values. Therefore, it becomes economically profitable for such enterprises to generate such energy at the place of its consumption.

For this, either individual capacitors or automatic compensation units are used, which monitor consumption volumes and connect or disconnect capacitor banks. Modern compensation systems allow you to significantly reduce the consumption of reactive energy from the external network.

Returning to the question in the title of the article, we can answer it in the affirmative. Reactive energy exists. Without it, the operation of electrical installations in which a magnetic field is created is impossible. Without performing visible work, it is, nevertheless, a necessary condition for the performance of work performed by active electrical energy.

WHAT IS TOTAL, ACTIVE AND REACTIVE POWER? FROM COMPLEX TO SIMPLE.

In everyday life, almost everyone comes across the concept of “electrical power”, “power consumption” or “how much electricity does this thing consume”. In this collection, we will explain the concept of electrical power of alternating current for technically savvy specialists and show in the picture the electrical power in the form of “how much electricity does this thing consume” for people with a humanitarian mindset :-). We reveal the most practical and applicable concept of electrical power and deliberately avoid describing differential expressions of electrical power.

WHAT IS AC POWER?

In AC circuits, the formula for DC power can only be used to calculate instantaneous power, which varies greatly over time and is useless for practical calculations. Direct calculation of average power requires integration over time. To calculate power in circuits where voltage and current vary periodically, average power can be calculated by integrating the instantaneous power over the period. In practice, the greatest importance is the calculation of power in circuits of alternating sinusoidal voltage and current.

In order to connect the concepts of total, active, reactive power and power factor, it is convenient to turn to the theory of complex numbers. We can assume that the power in an alternating current circuit is expressed by a complex number such that the active power is its real part, the reactive power is the imaginary part, the apparent power is the modulus, and the angle φ (phase shift) is the argument. For such a model, all the relations written below turn out to be valid.

Active power (Real Power)

The unit of measurement is watt (Russian designation: W, kilowatt - kW; international: watt -W, ​​kilowatt - kW).

The average value of instantaneous power over a period T is called active power, and

expressed by the formula:

In single-phase sinusoidal current circuits, where υ and Ι are the rms values ​​of voltage and current, and φ is the phase shift angle between them.

For non-sinusoidal current circuits, the electric power is equal to the sum of the corresponding average powers of the individual harmonics. Active power characterizes the rate of irreversible conversion of electrical energy into other types of energy (thermal and electromagnetic). Active power can also be expressed in terms of current, voltage and the active component of the circuit resistance r or its conductivity g according to the formula. In any electrical circuit of both sinusoidal and non-sinusoidal current, the active power of the entire circuit is equal to the sum of the active powers of the individual parts of the circuit; for three-phase circuits, the electrical power is defined as the sum of the powers of the individual phases. With the total power S, the active one is related by the relation.

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

Reactive Power

The unit of measurement is reactive volt-ampere (Russian designation: var, kVAR; international: var).

Reactive power is a quantity characterizing the loads created in electrical devices by fluctuations in the energy of the electromagnetic field in a sinusoidal alternating current circuit, equal to the product of the rms values ​​of voltage U and current I, multiplied by the sine of the phase angle φ between them:

(if the current lags behind the voltage, the phase shift is considered positive, if it leads, it is considered negative). Reactive power is related to total power S and active power P by the ratio: .

The physical meaning of reactive power is energy pumped from the source to the reactive elements of the receiver (inductors, capacitors, motor windings), and then returned by these elements back to the source during one oscillation period, referred to this period.

It should be noted that the value of sin φ for values ​​of φ from 0 to plus 90° is a positive value. The value of sin φ for values ​​of φ from 0 to minus 90° is a negative value. According to the formula

reactive power can be either a positive value (if the load is active-inductive in nature) or negative (if the load is active-capacitive in nature). This circumstance emphasizes the fact that reactive power does not participate in the operation of electric current. When a device has positive reactive power, it is customary to say that it consumes it, and when it produces negative power, it produces, but this is purely a convention due to the fact that most power-consuming devices (for example, asynchronous motors), as well as purely active loads, are connected through a transformer, are active-inductive.

The use of modern electrical measuring transducers on microprocessor technology allows for a more accurate assessment of the amount of energy returned from an inductive and capacitive load to an alternating voltage source.

Power can be either a positive value (if the load is active-inductive in nature) or negative (if the load is active-capacitive in nature). This circumstance emphasizes the fact that reactive power does not participate in the operation of electric current. When a device has positive reactive power, it is customary to say that it consumes it, and when it produces negative power, it produces, but this is purely a convention due to the fact that most power-consuming devices (for example, asynchronous motors), as well as purely active loads, are connected through a transformer, are active-inductive.

Synchronous generators installed in power plants can both produce and consume reactive power depending on the magnitude of the excitation current flowing in the generator rotor winding. Due to this feature of synchronous electrical machines, the specified network voltage level is regulated. To eliminate overloads and increase the power factor of electrical installations, reactive power compensation is carried out.

The use of modern electrical measuring transducers on microprocessor technology allows for a more accurate assessment of the amount of energy returned from inductive and capacitive loads to an alternating voltage source

Apparent Power

The unit of total electrical power is volt-ampere (Russian designation: VA, VA, kVA-kilo-volt-ampere; international: V A, kVA).

Total power is a value equal to the product of the effective values ​​of the periodic electric current I in the circuit and the voltage U at its terminals: ; The ratio of total power with active and reactive powers is expressed as follows: where P is active power, Q is reactive power (with an inductive load Q›0, and with a capacitive load Q‹0).

The vector relationship between total, active and reactive power is expressed by the formula:

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

All of the above formulaic and textual descriptions of total, reactive and active powers are visually and intuitively clear in the following figure:-)

Specialists of the NTS-group company (TM Elektrokaprizam-NET) have extensive experience in selecting specialized equipment for building systems for providing vital facilities with uninterrupted power supply. We are able to take into account as efficiently as possible many electrical and operational parameters, which allow us to choose an economically feasible option for building an uninterruptible power supply system using fuel power plants, and other related equipment.

© The material was prepared by specialists of the NTS-group company (TM Elektrokaprizam-NET) using information from open sources, incl. from the free encyclopedia Wikipedia https://ru.wikipedia.org

Apartments and private houses have one electric meter, which is used to calculate payments for consumed energy. It is simply believed that only its active component is used in everyday life, although this is not entirely true. Modern homes are full of devices whose circuits contain phase-shifting elements. However, the reactive power consumed by household appliances is incomparably less than that of industrial enterprises, so it is traditionally neglected when calculating payments.

Inductive and capacitive load

If you take an ordinary heating device or light bulb, then the power indicated in the corresponding inscription on the bulb or nameplate will correspond to the product of the current passing through this device and the network voltage (for us it is 220 Volts). The situation changes if the device contains a transformer, other elements containing capacitors. These parts have special properties; the graph of the current flowing in them lags behind or advances the sinusoid of the supply voltage - in other words, a phase shift occurs. An ideal capacitive load shifts the vector by -90 degrees, and an inductive load shifts it by +90 degrees. Power in this case becomes the result of not only the product of current and voltage; a certain correction factor is added. What does this lead to?

Geometric reflection of the process

From the school geometry course, everyone knows that the hypotenuse is longer than any of the legs in a right triangle. If active, reactive and apparent power form its sides, then the currents consumed by the coil and capacitor will be at right angles to the resistive component, but with directions in opposite directions. When adding (or, if you like, subtracting, they are of opposite signs) quantities, the total vector, that is, the total reactive power, depending on what character of the load predominates in the circuit, will be directed up or down. By its direction one can judge which character of the load predominates.

Reactive power when added vectorially with the active component will give the full amount of power consumed. It is graphically depicted as the hypotenuse of the power triangle. The more flat this line is in relation to the x-axis, the better.

Cosine phi

Theory and practice

All theoretical calculations have greater value the more applicable they are in practice. The picture at any developed industrial enterprise is as follows: most of the electricity is consumed by motors (synchronous, asynchronous, single-phase, three-phase) and other machines. But there are also transformers. The conclusion is simple: in real production conditions, inductive reactive power predominates. It should be noted that enterprises install not one electricity meter, as in houses and apartments, but two, one of which is active, and the other - it’s easy to guess which one. And the relevant authorities mercilessly fine for excessive consumption of energy “driven” through power lines in vain, so the administration is vitally interested in calculating reactive power and taking measures to reduce it. It is clear that it is impossible to solve this problem without electrical capacitance.

Compensation according to theory

The calculation is made using the formula:

• C = 1 / (2πFX), where X is the total reactance of all devices connected to the network; F - supply voltage frequency (we have 50 Hz);

It seems like - what could be simpler? Multiply “X” and “pi” by 50 and divide. However, everything is somewhat more complicated.

What about in practice?

The formula is not complicated, but defining and calculating X is not so easy. To do this, you need to take all the data about the devices, find out their reactance, and in vector form, and then... In fact, no one does this, except for students in laboratory work.

Reactive power can be determined in another way, using a special device - a phase meter, indicating the cosine phi, or by comparing the readings of a wattmeter, ammeter and voltmeter.

The matter is complicated by the fact that in the conditions of a real production process the load value is constantly changing, since some machines are turned on during operation, while others, on the contrary, are disconnected from the network, as required by technological regulations. Accordingly, ongoing measures to monitor the situation are necessary. During night shifts, lighting is on; in winter, the air in the workshops can be heated, and in summer it can be cooled. One way or another, reactive power compensation is carried out on the basis of theoretical calculations with a large share of practical measurements of cos φ.

Connecting and disconnecting capacitors

The simplest and most obvious way to solve the problem is to place a special worker near the phase meter who would turn on or off the required number of capacitors, achieving the minimum deviation of the needle from unity. This is what they did at first, but practice has shown that the notorious human factor does not always allow one to achieve the desired effect. In any case, compensation for reactive power, which is most often inductive in nature, is carried out by connecting an electrical capacitance of the appropriate size, but it is better to do this in automatic mode, otherwise a careless employee may subject his or her enterprise to a large fine. Again, this work cannot be called skilled; it is quite amenable to automation. The simplest circuit includes an optical electron pair of a light emitter and a light receiver. The arrow has crossed the minimum value, which means you need to add capacity.

Automation and intelligent algorithms

Currently, there are systems that allow you to reliably keep cos φ in the range from 0.9 to 1. Since the capacitors are connected discretely in them, it is impossible to achieve an ideal result, but the economic effect of the automatic reactive power compensator still gives a very good one. The operation of this device is based on intelligent algorithms that ensure operation immediately after switching on, most often even without additional settings. Technological advances in computer technology make it possible to achieve uniform connection of all stages of capacitor banks in order to avoid premature failure of one or two of them. Response times are also minimized, and additional chokes reduce the magnitude of voltage drop during transients. A modern power plant has an appropriate ergonomic layout, which creates conditions for the operator to quickly assess the situation, and in the event of an accident or failure, he will receive an immediate alarm signal. The price of such a cabinet is considerable, but it is worth paying for it, it brings benefits.

Compensator device

A conventional power factor compensator is a standard sized metal cabinet with a monitoring and control panel on the front panel, which is usually openable. At the bottom of it there are sets of capacitors (batteries). This arrangement is due to a simple consideration: the electrical containers are quite heavy, and it is quite logical to strive to make the structure more stable. In the upper part, at the operator’s eye level, there are the necessary control devices, including a phase indicator, with which you can judge the value of the power factor. There are also various indications, including emergency ones, controls (on and off, switching to manual mode, etc.). The comparison of readings from measuring sensors and the development of control actions (connecting capacitors of the required value) are assessed by a circuit based on a microprocessor. Actuators operate quickly and silently; they are usually built on powerful thyristors.

Approximate calculation of capacitor banks

In relatively small enterprises, the reactive power of a circuit can be approximately estimated by the number of connected devices, taking into account their phase-shifting characteristics. Thus, an ordinary asynchronous electric motor (the main “hard worker” of factories and factories) with a load equal to half of it has a cos φ equal to 0.73, and a fluorescent lamp - 0.5. The resistance welding machine parameter ranges from 0.8 to 0.9, the arc furnace operates with a cosine φ equal to 0.8. The tables, available to almost every chief power engineer, contain information about almost all types of industrial equipment, and the preliminary installation of reactive power compensation can be done using them. However, such data only serves as a basis from which adjustments must be made by adding or removing capacitor banks.

Nationwide

One may get the impression that the state has entrusted all concerns about the parameters of electrical networks and the uniformity of the load on them to factories, factories and other industrial enterprises. This is wrong. The country's energy system controls phase shifts on a national and regional scale, right at the exit of its special product from power plants. Another question is that compensation for the reactive component is carried out not by connecting capacitor banks, but by another method. To ensure the quality of energy supplied to consumers, the bias current in the rotor windings is regulated, which is not a big problem in synchronous generators.

Instantaneous power p an arbitrary section of the circuit, the voltage and current of which vary according to the law u=U m sin( t), i = I m sin( t–), looks like

p=ui=U m sin( t)I m sin( t– )= U m I m/2 =

= Ui cos - UI cos(2 t-) = (UI cos – UI cos cos2 t)– UI sin sin2 t. (1)

AC circuit active power P defined as the average instantaneous power p(t) during the period:

since the average value of the harmonic function over the period is 0.

It follows from this that the average power over a period depends on the phase angle between voltage and current and is not equal to zero if a section of the circuit has active resistance. The latter explains its name  active power. Let us emphasize once again that in active resistance there is an irreversible conversion of electrical energy into other types of energy, for example into thermal energy. Active power can be defined as the average rate of energy input into a section of a circuit over a period. Active power is measured in watts (W).

Reactive power

When calculating electrical circuits, the so-called reactive power. It characterizes the processes of energy exchange between reactive elements of the circuit and energy sources and is numerically equal to the amplitude of the variable component of the instantaneous power of the circuit. In accordance with this, reactive power can be determined from (1) as

Q = UI sin.

Depending on the sign of the angle , reactive power can be positive or negative. The unit of reactive power, in order to distinguish it from the unit of active power, is called not a watt, but a volt-ampere reactivevar. The reactive powers of inductive and capacitive elements are equal to the amplitudes of their instantaneous powers p L and p C. Taking into account the resistances of these elements, the reactive powers of the inductor and capacitor are equal Q L= UI=x L I 2 and Q C= UI=x C I 2, respectively.

The resulting reactive power of a branched electrical circuit is found as the algebraic sum of the reactive powers of the circuit elements, taking into account their nature (inductive or capacitive): Q=Q L – Q S. Here Q L is the total reactive power of all inductive elements of the circuit, and Q C represents the total reactive power of all capacitive elements in the circuit.

Full power

In addition to active and reactive powers, a sinusoidal current circuit is characterized by total power, denoted by the letter S. The total power of a section is understood as the maximum possible active power at a given voltage U and current I. It is obvious that the maximum active power is obtained at cos = 1, i.e. in the absence of a phase shift between voltage and current:

S = UI

The need to introduce this power is explained by the fact that when designing electrical devices, apparatus, networks, etc., they are designed for a certain rated voltage U rated and defined rated current I nom and their work U nom I nom = S nom gives the maximum possible power of this device (the total power S nom is indicated in the passport of most AC electrical devices.). To distinguish total power from other powers, its unit of measurement is called volt-ampere and is abbreviated as VA. The total power is numerically equal to the amplitude of the variable component of the instantaneous power.

From the above relations you can find the relationship between different powers:

P = S cos, Q= S sin, S= UI=

and express the phase angle through active and reactive power:

.

Let's consider a simple technique that allows you to find the active and reactive power of a circuit section using complex voltage and current. It consists in taking the product of the complex stress and current , complex conjugate current the section of the circuit under consideration. The operation of complex conjugation consists of changing the sign to the opposite one in front of the imaginary part of a complex number or changing the sign of the phase of a complex number if the number is represented in exponential form. As a result, we obtain a quantity called full integrated power and is designated . If
, then for the total complex power we obtain:

From this it can be seen that active and reactive power represent the real and imaginary parts of the total complex power, respectively. To make it easier to memorize all formulas related to capacities, in Fig. 7, b(p. 38) a power triangle has been constructed.