Energy through current and voltage. Electrical power

DC power

Since the current and voltage values ​​are constant and equal to the instantaneous values ​​at any time, the power can be calculated using the formula:

For passive linear circuit, in which it is observed Ohm's law, we can write:

If the circuit contains a source EMF, then given by it or absorbed on it electrical power is equal to:

If the current inside the EMF is opposite to the potential gradient (flows inside the EMF from plus to minus), then the power is absorbed by the EMF source from the network (for example, during operation electric motor or charge battery), if codirectional (flows inside the EMF from minus to plus), then it is given by the source to the network (say, during operation galvanic battery or generator). When taking into account internal resistance EMF source The power released on it is added to the absorbed or subtracted from the output.

AC power

In an alternating electric field, the formula for power is DC turns out to be inapplicable. In practice highest value has a power calculation 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 theory complex numbers. We can assume that the power in the circuit AC 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 module, 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

Average for the period T the value of instantaneous power is called active power: In single-phase sinusoidal current circuits where U And I - rms voltage and current , φ - phase 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 active component of 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 electrical power is defined as the sum of the powers of the individual phases. With full power S active is related by the relation

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

Re measuring transducers active power, using the formula Q = UI sin φ are simpler and much cheaper than microprocessor-based measuring transducers.

Full power

Unit of total electrical power - volt-ampere(V A, VA)

Apparent power - a value equal to the product of the effective values ​​of the periodic electric current I in circuit and voltage U on its clamps: S = UI; is related to active and reactive powers by the relation: where R- active power, Q- reactive power (with inductive load Q> 0, and with capacitive 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 power rating of transformers and distribution boards is measured in volt-amperes rather than watts.

Complex power

Availability nonlinear distortion current in a circuit means a violation of the proportionality between the instantaneous values ​​of voltage and current caused by the nonlinearity of the load, for example, when the load is reactive or pulsed in nature. With a linear load, the current in the circuit is proportional to the instantaneous voltage, all power consumed is active. With a nonlinear load, the apparent (total) power in the circuit increases due to the power of nonlinear current distortions, which does not participate in the performance of work. The power of nonlinear distortions is not active and includes both reactive power and the power of other current distortions. This physical quantity has the dimension of power, so VA (volt-ampere) or VAR (volt-ampere reactive) can be used as a unit of measurement for inactive power. It is not advisable to use W (watt) so that inactive power is not confused with active power.

Relationship between inactive, active and full power

Let us denote the amount of inactive power N. Through i let us denote the current vector by u- voltage vector. Letters I And U we will denote the corresponding effective values:

Let's imagine the current vector i as the sum of two orthogonal components i a And i p, which we will call active and passive, respectively. Since only the current component collinear to the voltage is involved in the work, we will require that the active component be collinear to the voltage, that is i a = λ u, where λ is some constant, and the passive one is orthogonal, that is, we have

Let's write down the expression for active power P, scalarly multiplying the last equality by u :

From here we find

The expression for the amount of inactive power has the form where S = U I- full power.

For full power circuit, a representation similar to the expression for a circuit with harmonic current and voltage is valid, only instead of reactive power, inactive power is used:

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Electric current power concept

Electric current power

Before talking about electrical power, we should define the concept of power in in a general sense. Typically, when people talk about power, they mean some kind of force that an object has (a powerful electric motor) or an action (a powerful explosion).

But, as we know from school physics, force and power are different concepts, although they have a relationship.

Initially, power (N) is a characteristic related to a certain event (action), and if it is tied to a certain object, then the concept of power is also conditionally correlated with it. Any physical action involves the use of force. The force (F), with the help of which a certain path (S) was traveled, will be equal to the work done (A). And the work done for certain time(t), and will be equal to power.

Power is a physical quantity that is equal to the ratio of the work performed over a certain period of time to the same period of time. Since work is a measure of energy change, we can also say this: power is the rate of energy conversion of the system.

Having understood the concept of mechanical power, we can move on to considering electrical power (electric power). As you should know, U is the work done when moving 1 coulomb, and the current I is the number of coulombs passing in 1 sec. Therefore, the product of current and voltage shows full time job, performed 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 low voltage, or, vice versa , at high voltage and low current (this is used when transmitting electricity over remote distances from power plants to places of consumption by 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 the product of 1 V times 1 A. 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 of electrical load that is 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.

Using an example, active and reactive electrical power can be expressed as follows: given is an electrical device that has heating elements and an electric motor. Heating elements are usually made of high resistance material. When an electric current passes through a heating element spiral electrical energy completely converted into heat. This example is typical of active electrical power.

The electric motor of this device has a copper winding inside. It represents inductance. And as we know, inductance has the effect of self-induction, and this contributes to the partial return of electricity back to the network. This energy has some offset in current and voltage values, which causes negative influence to the power grid (further overloading it).

Capacitance (capacitors) also has similar abilities. It is capable of accumulating charge and releasing it back. The difference between capacitance and inductance lies in the opposite displacement of the values ​​of current and voltage relative to each other. This energy of capacitance and inductance (phase-shifted relative to the value of the supply network) will, in fact, be reactive electrical power.

That is different types energy. In this article we will consider and study such physical concepts as electric current power.

Current power formulas

By current power, as in mechanics, we mean the work that is performed per unit of time. A physical formula will help you calculate power, knowing the work performed by electric current over a certain period of time.

Current, voltage, power in electrostatics are related by equality, which can be derived from the formula A = UIt. It determines the work that is performed electric current:

P = A/t = UIt/t = UI
Thus, the formula for direct current power at any section of the circuit is expressed as the product of the current and the voltage between the ends of the section.

Power units

1 W (watt) - current power of 1 A (ampere) in a conductor, between the ends of which a voltage of 1 V (volt) is maintained.

A device for measuring the power of electric current is called a wattmeter. Also, the current power formula allows you to determine power using a voltmeter and ammeter.

An off-system unit of power is kW (kilowatt), GW (gigawatt), mW (milliwatt), etc. Related to this are some off-system units of work that are often used in everyday life, for example (kilowatt hour). Because 1kW = 10 3 W, and 1h = 3600s, That

1kW · h = 10 3 W 3600 s = 3.6 10 6 W s = 3.6 10 6 J.

Ohm's law and power

Using Ohm's law, current power formula P=UI is written in this form:

P = UI = U 2 /R = I 2 /R
So, the power released on the conductors is directly proportional to the current flowing through the conductor and the voltage at its ends.

Actual and rated power

When measuring power in a consumer, the current power formula allows you to determine its actual value, that is, the one that is actually released in at the moment time on the consumer.

The power ratings are also noted in the data sheets of various electrical appliances. It is called nominal. The passport of an electrical device usually indicates not only the rated power, but also the voltage for which it is designed. However, the voltage in the network may differ slightly from that indicated in the passport, for example, it may increase. As the voltage increases, the current in the network increases, and therefore the current power in the consumer. That is, the actual and rated power of the device may differ. Maximum actual power electrical device more than nominal. This is done in order to prevent the device from failure due to minor changes in the voltage in the network.

If the circuit consists of several consumers, then, when calculating their actual power, it should be remembered that for any connection of consumers, the total power in the entire circuit is equal to the sum of the powers of individual consumers.

Efficiency of an electrical appliance

As you know, ideal machines and mechanisms do not exist (that is, those that would completely convert one type of energy into another or generate energy). During operation of the device, part of the expended energy is necessarily spent on overcoming unwanted resistance forces or is simply “dissipated” into the environment. Thus, only part of the energy we expend goes to perform useful work, for which the device was created.

In other words, efficiency shows how efficiently the work expended is used when it is performed, for example, by an electrical appliance.

Efficiency (denoted by the Greek letter η (“this”)) is a physical quantity that characterizes the efficiency of an electrical device and shows what part of the useful work is expended.

Efficiency is determined (as in mechanics) by the formula:

η = A P /A Z ·100%

If the power of the electric current is known, the formulas for determining the CFC will look like this:

η = P P /P Z ·100%

Before determining the efficiency of some device, it is necessary to determine what is useful work(what the device is made for), and what is the work expended (the work being done or how much energy is expended to do useful work).

Task

An ordinary electric lamp has a power of 60 W and an operating voltage of 220 V. What work does the electric current do in the lamp, and how much do you pay for electricity during the month, at a tariff of T = 28 rubles, using the lamp for 3 hours every day?
What is the current strength in the lamp and the resistance of its coil in working condition?

Solution:

1. To solve this problem:
a) calculate the operating time of the lamp during the month;
b) calculate the work done by the current in the lamp;
c) calculate the monthly fee at the rate of 28 rubles;
d) calculate the current in the lamp;
e) calculate the resistance of the lamp spiral in operating condition.

2. We calculate the work done by the current using the formula:

A = P t

The current strength in the lamp can be calculated using the current power formula:

P = UI;
I = P/U.

The resistance of the lamp coil in operating condition from Ohm’s law is equal to:

[A] = Wh;

[I] = 1B 1A/1B = 1A;

[R] = 1V/1A = 1Ohm.

4. Calculations:

t = 30 days · 3 hours = 90 hours;
A = 60·90 = 5400 Wh = 5.4 kWh;
I = 60/220 = 0.3 A;
R = 220/0.3 = 733 Ohm;
B = 5.4 kWh 28 kW / kWh = 151 rub.

Answer: A = 5.4 kWh; I = 0.3 A; R = 733 Ohm; B = 151 rubles.

When designing any electrical circuits power calculation is performed. Based on it, the main elements are selected and the permissible load is calculated. If the calculation for a direct current circuit is not difficult (in accordance with Ohm’s law, it is necessary to multiply the current strength by the voltage - P = U * I), then with the calculation of alternating current power it is not so simple. To explain, you will need to turn to the basics of electrical engineering, without going into detail, here is a brief summary of the main points.

Total power and its components

In AC circuits, power calculations are carried out taking into account the laws of sinusoidal changes in voltage and current. In this regard, the concept of total power (S) was introduced, which includes two components: reactive (Q) and active (P). A graphical description of these quantities can be made through the power triangle (see Fig. 1).

The active component (P) refers to the power of the payload (the irreversible conversion of electricity into heat, light, etc.). This value is measured in watts (W), at the household level it is customary to calculate in kilowatts (kW), in the industrial sector - megawatts (mW).

The reactive component (Q) describes the capacitive and inductive electrical load in the alternating current circuit, the unit of measurement of this quantity is Var.

In accordance with the graphical representation, the relationships in the power triangle can be described using elementary trigonometric identities, which makes it possible to use following formulas:

• S = √P 2 +Q 2, – for full power;
• and Q = U*I*cos⁡ φ, and P = U*I*sin φ – for the reactive and active components.

These calculations are applicable for single-phase network(for example, household 220 V), to calculate power three-phase network(380 V) it is necessary to add a multiplier to the formulas - √3 (with a symmetrical load) or sum the powers of all phases (if the load is asymmetrical).

To better understand the process of influence of the components of total power, let's consider the “pure” manifestation of the load in active, inductive and capacitive form.

Active load

Let's take a hypothetical circuit that uses a "pure" active resistance and an appropriate AC voltage source. A graphical description of the operation of such a circuit is shown in Figure 2, which displays the main parameters for a certain time range (t).

We can see that the voltage and current are synchronized in both phase and frequency, while the power has double the frequency. Note that the direction of this quantity is positive and it is constantly increasing.

Capacitive load

As can be seen in Figure 3, the graph of the characteristics of a capacitive load is slightly different from an active one.

The frequency of capacitive power oscillations is twice the frequency of the sinusoidal voltage change. As for the total value of this parameter, during one harmonic period it is equal to zero. At the same time, no increase in energy (∆W) is observed either. This result indicates that its movement occurs in both directions of the chain. That is, when the voltage increases, charge accumulates in the capacitance. When a negative half-cycle occurs, the accumulated charge is discharged into the circuit circuit.

During the process of energy accumulation in the load capacitance and subsequent discharge, no useful work is performed.

Inductive load

The graph below demonstrates the nature of a “pure” inductive load. As we can see, only the direction of the power has changed; as for the increase, it is equal to zero.

Negative effects of reactive load

In the examples above, options were considered where there was a “pure” reactive load. Impact factor active resistance was not taken into account. Under such conditions, the reactive effect is zero, which means it can be ignored. As you understand, in real conditions this is impossible. Even if hypothetically such a load existed, the resistance of the copper or aluminum conductors of the cable necessary to connect it to the power source cannot be ruled out.

The reactive component can manifest itself in the form of heating of the active components of the circuit, for example, the motor, transformer, connecting wires, power cable, etc. A certain amount of energy is spent on this, which leads to a decrease in basic characteristics.

Reactive power affects a circuit as follows:

• does not produce any useful work;
• causes serious losses and abnormal loads on electrical appliances;
• may cause a serious accident.

That is why, when making appropriate calculations for an electrical circuit, one cannot exclude the influence of inductive and capacitive loads and, if necessary, provide for the use technical systems to compensate for it.

Calculation of power consumption

In everyday life, you often have to deal with calculating power consumption, for example, to check the permissible load on the wiring before connecting a resource-intensive electrical consumer (air conditioner, boiler, electric stove, etc.). Also, such a calculation is necessary when choosing circuit breakers for the distribution board through which the apartment is connected to the power supply.

In such cases, it is not necessary to calculate power by current and voltage; it is enough to sum up the energy consumption of all devices that can be turned on at the same time. Without getting involved in calculations, you can find out this value for each device in three ways:

When making calculations, it should be taken into account that the starting power of some electrical appliances may differ significantly from the nominal one. For household devices, this parameter is almost never indicated in technical documentation, therefore, it is necessary to refer to the corresponding table, which contains the average values ​​of the starting power parameters for various devices (it is advisable to choose the maximum value).