What is reactive power? Reactive power compensation. Calculation of reactive power. Active and reactive energy - Homeowners Association Horizon Perm

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

Definition

Only alternating current can have active and reactive power, since the network characteristics (current and voltage) of direct current are always equal. The unit of measurement for active power is Watt, while reactive power is measured in reactive voltampere and kiloVAR (kVAR). It is worth noting that both full and active characteristics can be measured in kW and kVA, this depends on the parameters of the specific device and network. In industrial circuits it is most often measured in kilowatts.

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

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

Reactive component designation:

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

Calculation

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

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

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

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

S = U * I * cos φ.

A very important factor is that this electrical quantity can be either positive or negative. It depends on what characteristics cos φ has. If the phase shift angle of a sinusoidal current is in the range from 0 to 90 degrees, then the active power is positive, if from 0 to -90, then it is negative. The rule is valid only for synchronous (sinusoidal) current (used to operate an asynchronous motor or machine tool equipment).

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

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

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

Q L = U L I = I 2 x L

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

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

S = √P 2 + Q 2 , and all this equals U*I.

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

Inductance resistance: x L = ωL = 2πfL,

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

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

If there is an active reactive component in the network, the power factor must be calculated. This quantity has no units of measurement; it characterizes a specific current consumer if the electrical system contains reactive elements. Using this indicator, it becomes clear in which direction and how the energy shifts relative to the network voltage. To do this you will need a voltage triangle diagram:

For example, if there is a capacitor, the coefficient formula has the following form:

cos φ = r/z = P/S

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

Compensation

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

Q = QL – QC = ULI – UCI

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

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

In some cases, specialists do not use full-fledged UPSs, but special compensating capacitors. They are suitable for household use, available and sold in every electrical store. To calculate the planned and received savings, you can use all of the above formulas.

Active power (P)

In other words, active power can be called: actual, real, useful, real power. In a DC circuit, the power supplying a DC load is defined as the simple product of the voltage across the load and the current flowing, that is

because in a DC circuit there is no concept of phase angle between current and voltage. In other words, there is no power factor in a DC circuit.

But with sinusoidal signals, that is, in alternating current circuits, the situation is more complicated due to the presence of a phase difference between current and voltage. Therefore, the average power (active power) that actually powers the load is given by:

In an alternating current circuit, if it is purely active (resistive), the formula for power is the same as for direct current: P = U I.

Formulas for active power

P = U I - in DC circuits

P = U I cosθ - in single-phase AC circuits

P = √3 U L I L cosθ - in three-phase AC circuits

P = 3 U Ph I Ph cosθ

P = √ (S 2 – Q 2) or

P =√ (VA 2 – var 2) or

Active power = √ (Apparent power 2 – Reactive power 2) or

kW = √ (kVA 2 – kvar 2)

Reactive power (Q)

It could also be called useless or wattless power.

Power that constantly flows back and forth between source and load is known as reactive (Q).

Reactive power is power that is consumed and then returned by the load due to its reactive properties. The unit of active power is the watt, 1 W = 1 V x 1 A. Reactive power energy is first stored and then released as a magnetic field or electric field in the case of an inductor or a capacitor respectively.

Reactive power is defined as

and can be positive (+Ue) for an inductive load and negative (-Ue) for a capacitive load.

The unit of reactive power is the reactive volt-ampere (var): 1 var = 1 V x 1 A. In simple terms, a unit of reactive power determines the magnitude of the magnetic or electric field produced by 1 V x 1 A.

Formulas for reactive power

Reactive power = √ (Apparent power 2 – Active power 2)

var =√ (VA 2 – P 2)

kvar = √ (kVA 2 – kW 2)

Apparent power (S)

Apparent power is the product of voltage and current, ignoring the phase angle between them. All power in the AC network (dissipated and absorbed/returned) is total power.

The combination of reactive and active power is called apparent power. The product of the effective value of voltage and the effective value of current in an alternating current circuit is called apparent power.

It is the product of voltage and current values ​​without taking into account the phase angle. The unit of apparent power (S) is VA, 1 VA = 1 V x 1 A. If the circuit is purely active, the apparent power is equal to the active power, and in an inductive or capacitive circuit (with reactance present), the apparent power is greater than the active power.

Formula for Full Power

Apparent power = √ (Active power 2 + Reactive power 2)

kUA = √(kW 2 + kUAR 2)

It should be noted that:

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

Instantaneous power p 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) for 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 watt, but 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 relationships 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.

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On the one hand, the work of current can be easily calculated by knowing the current strength, voltage and load resistance. Painfully familiar formulas from a school physics course look like this.

Rice. 1. Formulas

And there is not a word about the reactive component.

On the other hand, a number of physical processes actually impose their own characteristics on these calculations. We are talking about reactive energy. Problems with understanding reactive processes come with electricity bills in large enterprises, because in household networks we pay only for active energy (the amount of reactive energy consumption is so small that they are simply neglected).

Definitions

To understand the essence of physical processes, let's start with definitions.

Active electricity- This is completely converted energy supplied to the circuit from the power source. Conversion can occur into heat or into another type of energy, but the essence remains the same - the received energy does not return back to the source.

An example of how active energy works: current passing through a resistance element converts part of the energy into heating. This perfect work of current is active.

Reactive power is the energy returned back to the current source. That is, the current previously received and taken into account by the meter, without completing the work, is returned. Among other things, the current makes a jump (the load increases greatly for a short time).

It's difficult to understand the process without examples.

The most obvious one is the operation of a capacitor. The capacitor itself does not convert electricity into useful work; it accumulates it and releases it. Of course, if part of the energy is still spent on heating the element, then it can be considered active. The reactive one looks like this:

1. When the capacitor is powered with alternating voltage, along with the increase in U, the charge of the capacitor also increases.

2. At the moment the voltage drop begins (the second quarter cycle on a sine wave), the voltage on the capacitor turns out to be higher than that of the source. And so the capacitor begins to discharge, giving energy back to the power circuit (current flows in the opposite direction).

3. In the next two quarter periods the situation is completely repeated, only the voltage changes to the opposite.

Due to the fact that the capacitor itself does not do any work, the received voltage reaches its maximum amplitude value (that is, √2=1.414 times more than the current 220V, or 220·1.414=311V).

When working with inductive elements (coils, transformers, electric motors, etc.) the situation is similar. The indicator graph can be seen in the image below.

Rice. 2. Indicator charts

Due to the fact that modern household appliances consist of many different elements with and without a “reactive” power effect, the reactive current, flowing in the opposite direction, does very real work on heating the active elements. Thus, the reactive power of a circuit is essentially expressed in collateral losses and voltage surges.

It is very difficult to separate one power indicator from another when calculating. And a high-quality and efficient metering system is expensive, which, in fact, led to the refusal to measure the volume of reactive current consumption in everyday life.

In large commercial facilities, on the contrary, the volume of reactive energy consumption is much greater (due to the abundance of power equipment supplied with powerful electric motors, transformers and other elements that generate reactive current), so separate metering is introduced for them.

How is active and reactive electricity calculated?

Most manufacturers of electricity meters for enterprises implement a simple algorithm.

Q=(S 2 - P 2) 1/2

Here, the active power P is subtracted from the total power S (in an easy-to-understand form).

Thus, the manufacturer does not have to organize completely separate accounting.

What is cosϕ (cosine phi)

To numerically express the ratio of active and reactive powers, a special coefficient is used - cosine phi.

It is calculated using the formula.

cosϕ = P act /P total

Where total power is the sum of active and reactive.

The same coefficient is indicated on the nameplates of power tools equipped with motors. In this case, cosϕ is used to estimate the peak power consumption. For example, the rated power of the device is 600 W, and cosϕ = 0.7 (the average for the vast majority of power tools), then the peak power required to start the electric motor will be considered as Pnomin / cosϕ, = 600 W / 0.7 = 857 VA ( reactive power is expressed in volt-amperes).

Application of reactive power compensators

To encourage consumers to operate the power grid without reactive load, electricity suppliers introduce an additional paid tariff for reactive power, but payment is charged only if the average monthly consumption exceeds a certain coefficient, for example, if the ratio of total and active power is over 0.9, the bill for payment for reactive power is not exhibited.

In order to reduce costs, enterprises install special equipment - compensators. They can be of two types (according to the principle of operation):

• Capacitive;
• Inductive.

Reactive power is the part of electrical energy returned by the load to the source. The phenomenon of a situation occurring is considered harmful.

Occurrence of reactive power

Let's say the circuit contains a DC power supply and an ideal inductance. Turning on the circuit generates a transient process. The voltage tends to reach the nominal value; the growth is actively hampered by the inductance’s own flux linkage. Each turn of the wire is bent in a circular path. The resulting magnetic field will cross the adjacent segment. If the turns are located one after the other, the nature of the interaction will increase. This is called intrinsic flux linkage.

The nature of the process is as follows: the induced EMF prevents changes in the field. The current tries to grow rapidly, the flux linkage pulls back. Instead of a step we see a smoothed protrusion. The energy of the magnetic field is spent to interfere with the process that created it. The case of reactive power occurrence. The phase differs from the beneficial one and is harmful. Ideal: the direction of the vector is perpendicular to the active component. It is assumed that the wire resistance is zero (a fantastic scenario).

When the circuit is turned off, the process will be repeated in reverse order. The current tends to instantly drop to zero; energy is stored in the magnetic field. If the inductance disappears, the transition will take place suddenly, flux linkage gives the process a different coloring:

1. A decrease in current causes a decrease in the magnetic field strength.
2. The effect produced induces the back-EMF of the turns.
3. As a result, after the power source is turned off, the current continues to exist, gradually attenuating.

Graphs of voltage, current, power

Reactive power is a certain link of inertia, constantly lagging and interfering. The first question is: why then are inductors needed? Oh, they have plenty of useful qualities. Benefit makes you put up with reactive power. A common positive effect is the operation of electric motors. Energy transfer occurs through magnetic flux. Between the turns of one coil, as shown above. A permanent magnet, a choke, and everything capable of being captured by an induction vector are subject to interaction.

The cases cannot be called comprehensive in a descriptive sense. Sometimes clutch flow is used in the form shown as an example. The principle is used by ballasts of gas-discharge lamps. The inductor is equipped with a myriad of turns: turning off the voltage does not cause a smooth decrease in current, but a surge of large amplitude of the opposite polarity. The inductance is great: the response is truly amazing. Exceeds the original 230 volts by an order of magnitude. It is enough for a spark to appear and the light bulb to light up.

Reactive power and capacitors

Reactive power is stored by magnetic field energy by inductances. What about the capacitor? Acts as a source of the reactive component. Let us supplement the review with the theory of vector addition. The average reader will understand. Oscillatory processes are often used in the physics of electrical networks. The well-known 220 volts (now accepted 230) in a 50 Hz outlet. A sine wave whose amplitude is 315 volts. When analyzing circuits, it is convenient to represent them as a clockwise rotating vector.

Graphical circuit analysis

The calculation is simplified and the engineering representation of reactive power can be clarified. The current phase angle is considered equal to zero and is plotted to the right along the abscissa axis (see figure). The reactive energy of the inductance is in phase with the UL voltage and is 90 degrees ahead of the current. Ideal case. Practitioners have to take winding resistance into account. Part of the power will be reactive in inductance (see figure). The angle between projections is important. The value is called power factor. What does this mean in practice? Before answering the question, let's consider the concept of a resistance triangle.

Resistance triangle and power factor

To make it easier to analyze electrical circuits, physicists suggest using a resistance triangle. The active part is deposited, like a current, to the right of the abscissa axis. We agreed to direct the inductance up and the capacitance down. When calculating the total resistance of the circuit, we subtract the values. A combined case has been excluded. There are two options available: positive or negative reactance.

To obtain capacitive/inductive reactance, the parameters of the circuit elements are multiplied by a coefficient denoted by the Greek letter “omega”. Circular frequency is the product of the network frequency and twice the number Pi (3.14). Let us point out one more note about finding reactances. If the inductance is simply multiplied by the specified coefficient, the reciprocal of the product is taken for the capacitances. It is clear from the figure, which shows the indicated relationships that help calculate voltages. After multiplication, we take the algebraic sum of inductive and capacitive reactances. The former are considered positive quantities, the latter – negative.

Formulas of reactive components

Two components of resistance - active and imaginary - are projections of the total resistance vector on the abscissa and ordinate axes. Angles are preserved when abstractions are transferred to powers. The active one is plotted along the abscissa axis, the reactive one along the ordinate axis. Capacitances and inductances are the fundamental cause of negative effects in the network. It was shown above: without reactive elements, it becomes impossible to build electrical devices.

The power factor is usually called the cosine of the angle between the total resistance vector and the horizontal axis. Such an important parameter is attributed to the fact that the useful part of the source energy is a share of total waste. The share is calculated by multiplying the total power by the coefficient. If the voltage and current vectors coincide, the cosine of the angle is equal to one. Power is lost by the load, dissipated by heat.

Believe what is said! The average power of a period when connected to a source of pure reactance is zero. Half the time the inductance receives energy, the other half it releases. The motor winding is indicated in the diagrams by adding an EMF source that describes the transfer of energy to the shaft.

Practical interpretation of power factor

Many people notice a discrepancy in the case of practical consideration of reactive power. To reduce the coefficient, it is recommended to include large capacitors in parallel with the motor windings. The inductive reactance balances the capacitive reactance, the current is again in phase with the voltage. It's difficult to understand for this reason:

1. Let's say the primary winding of a transformer is connected to an alternating voltage source.
2. Ideally, active resistance is zero. Power must be reactive. But this is bad: they tend to make the angle between voltage and current zero!

But! The oscillatory process is indifferent to the operation of motors and transformers. The theory of reactive power assumes that all energy oscillates. Until the last drop. In a transformer or motor, an active “leakage” of energy occurs from the field to perform work and induce current in the secondary winding. Energy cannot circulate between source and consumer.

In a real chain, the process of coordinating individual sections makes it difficult. To be on the safe side, suppliers require that capacitors be installed in parallel with the motor winding so that the energy circulates in the local segment and does not escape outside, heating the connecting wires. It is important to avoid overcompensation. If the capacitors are too large, the battery will cause the power factor to increase.

As for the phase shift, it occurs on the secondary winding of the substation transformer. That's not the role. The engine is running, some of the energy is not converted into useful work and is reflected back. The result is a power factor. The participating component of inductance is a technological, structural defect. The part that is not useful. We will compensate by adding capacitor units.

The correct matching is checked based on the fact that there is no phase shift between the voltage and current of a running electric motor. Excess energy circulates between the excess inductance of the windings and the installed capacitor unit. The goal of the event was achieved - to avoid heating the conductors of the network supplying the device.

What do they offer under the guise of saving energy?

The network offers to buy energy saving devices. Reactive power compensators. It is important not to go too far. Let’s say that the compensator would look appropriate next to the included refrigerator compressor, the collector motor of a vacuum cleaner, burdening the apartment with measures when incandescent light bulbs are working is a dubious undertaking. Before installation, take the trouble to find out the phase shift between voltage and current, according to the information, correctly calculate the volume of the capacitor block. Otherwise, attempts to save in this way will fail, unless by chance you manage to point your finger at the sky and hit the mark.

The second aspect of reactive power compensation is metering. Made for large enterprises where there are powerful motors that create large phase angles. Special meters are being introduced to account for reactive power, paid according to the tariff. To calculate the payment coefficient, an assessment of heat losses of wires, deterioration of the operating conditions of the cable network, and some other factors are used.

Prospects for further study of reactive energy as a phenomenon

Reactive power is a phenomenon of energy reflection. Ideal chains of phenomena are deprived. Reactive power manifests itself as released heat at the active resistance of cable lines and distorts the sinusoidal waveform. A separate topic of conversation. If there are deviations from the norm, the motors do not operate so smoothly and the transformers are hindered.