The electrical energy of the system. Power system (power system). Electric power (electrical) system. Electric energy of the system of charges

An area of economics that encompasses resources, extraction, transformation and use different types energy.

Energy can be represented by the following interconnected blocks:

1. Natural energy resources and mining enterprises;

2. Refineries and transportation of finished fuel;

3. Generation and transmission of electrical and thermal energy;

4. Consumers of energy, raw materials and products.

A summary of the blocks:

1) Natural resources are divided into:

renewable (sun, biomass, water resources);

non-renewable (coal, oil);

2) Extractive enterprises (mines, mines, gas derricks);

3) Fuel processing enterprises (enrichment, distillation, fuel purification);

4) Fuel transportation ( Railway, tankers);

5) Generation of electrical and thermal energy (CHP, NPP, HPP);

6) Transmission of electrical and thermal energy (electrical networks, pipelines);

7) Consumers of energy, heat (power and industrial processes, heating).

A part of the energy sector, which is occupied with the problems of obtaining large amounts of electricity, transmitting it over a distance and distributing it among consumers, its development is due to electric power systems.

This is a set of interconnected power plants, electrical and thermal systems, as well as consumers of electrical and thermal energy, united by the unity of the process of production, transmission and consumption of electricity.

Electric power system: CHP - combined heat and power plant, NPP - nuclear power plant, IES - condensing power plant, 1-6 - electricity consumers of CHP

Thermal condensing power plant diagram

Electrical system (electrical system, ES)- the electrical part of the electric power system.

The circuit is shown in a single-line image, that is, one line means three phases.

Technological process in the power system

The technological process is the process of converting the primary energy resource (fossil fuel, hydropower, nuclear fuel) into the final product (electrical energy, thermal energy). The parameters and indicators of the technological process determine the efficiency of production.

The technological process is shown schematically in the figure, from which it can be seen that there are several stages of energy conversion.

Diagram of the technological process in the power system: K - boiler, T - turbine, G - generator, T - transformer, power transmission line - power lines

In boiler K, the combustion energy of the fuel is converted into heat. A boiler is a steam generator. In the turbine thermal energy converted to mechanical. In the generator mechanical energy converted to electrical. The voltage of electrical energy in the process of its transmission through power lines from the station to the consumer is transformed, which ensures the efficiency of transmission.

The efficiency of the technological process depends on all these links. Consequently, there is a complex of operational tasks associated with the operation of boilers, TPP turbines, HPP turbines, nuclear reactors, electrical equipment (generators, transformers, power lines, etc.). It is necessary to choose the composition of the operating equipment, the mode of its loading and use, and observe all restrictions.

Electrical installation- an installation in which electricity is produced, generated or consumed, distributed. Can be: open or closed (indoors).

Power station- a complex technological complex on which the energy of a natural source is converted into energy electric current or warmth.

It should be noted that power plants (especially thermal, coal-fired) are the main sources of pollution environment energy.

Electrical substation- an electrical installation designed to convert electricity from one voltage to another at the same frequency.

Power transmission (LEP)- the structure consists of elevated power transmission line substations and step-down substations (a system of wires, cables, supports) designed to transmit electricity from a source to a consumer.

Electricity of the net- a set of power lines and substations, i.e. devices connecting the power supply with.

· The potential of an electric field is a value equal to the ratio of the potential energy of a point positive charge, placed at a given point of the field, to this charge

or the potential of an electric field is a value equal to the ratio of the work of the field forces to move a point positive charge from a given point of the field to infinity to this charge:

The potential of the electric field at infinity is conventionally assumed to be zero.

Note that when moving a charge in an electric field, the work A c. C external forces is equal in modulus to work A s.p field forces and is opposite to it in sign:

A c.c. = - A c.p.

· Electric field potential created by a point charge Q on distance r from the charge,

· Potential of an electric field created by a metal carrying a charge Q sphere of radius R, on distance r from the center of the sphere:

inside the sphere ( r<R) ;

on the surface of the sphere ( r=R) ;

out of scope (r> R) .

In all formulas given for the potential of a charged sphere, e is the dielectric constant of a homogeneous unlimited dielectric surrounding the sphere.

· The potential of the electric field generated by the system P point charges, at a given point in accordance with the principle of superposition of electric fields is equal to the algebraic sum of potentials j 1, j 2, ... , j n generated by individual point charges Q 1, Q 2, ..., Q n:

· Energy W interaction of the system of point charges Q 1, Q 2, ..., Q n is determined by the work that this system of charges can perform when they move away from each other to infinity, and is expressed by the formula

where is the potential of the field created by all P- 1 charges (excluding i th) at the point where the charge is located Q i.

· The potential is related to the electric field strength by the relation

In the case of an electric field with spherical symmetry, this relationship is expressed by the formula

or in scalar form

and in the case of a homogeneous field, that is, a field whose strength at each point is the same both in magnitude and in direction

where j 1 and j 2- potentials of points of two equipotential surfaces; d - the distance between these surfaces along the electric line of force.

· The work done electric field when moving a point charge Q from one point of the field with the potential j 1, to another one with potential j 2

A=Q ∙(j 1 - j 2), or

where E l - the projection of the tension vector on the direction of movement; dl - moving.

In the case of a uniform field, the last formula takes the form

A = Q ∙ E ∙ l ∙ cosa,

where l- moving; a- the angle between the directions of the vector and displacement.

A dipole is a system of two point electric charges equal in size and opposite in sign, distance l between which there is much less distance r from the center of the dipole to the observation points.

Vector drawn from negative charge a dipole to its positive charge is called the arm of the dipole.

Charge product | Q| a dipole on its shoulder is called the electric moment of the dipole:

Dipole field strength

where R- the electric moment of the dipole; r- the modulus of the radius vector, drawn from the center of the dipole to the point, the field strength in which we are interested; α is the angle between the radius vector and the arm of the dipole.

Potential of the dipole field

Mechanical moment acting on a dipole with an electric moment, placed in a uniform electric field with strength

or M = p ∙ E ∙ sin,

where α is the angle between the directions of the vectors and.

In an inhomogeneous electric field, in addition to a mechanical moment (a pair of forces), a certain force acts on the dipole. In the case of a field with symmetry about the axis X, the force is expressed by the ratio

where is the partial derivative of the field strength, which characterizes the degree of field inhomogeneity in the direction of the axis X.

With strength F x is positive. This means that under the action of its action the dipole is drawn into the region of the strong field.

Potential energy of a dipole in an electric field

An energetic approach to interaction. The energy approach to the interaction of electric charges is, as we will see, very fruitful in its practical applications, and in addition, it opens up the possibility of looking differently at the electric field itself as a physical reality.

First of all, we will find out how you can come to the concept of the interaction energy of a system of charges.

1. First, consider a system of two point charges 1 and 2. Let us find the algebraic sum of the elementary work of the forces F, and F2, with which these charges interact. Let in some K-frame of reference in the time cU the charges have made displacements dl, and dl 2. Then the corresponding work of these forces

6Л, 2 = F, dl, + F2 dl2.

Considering that F2 = - F, (according to Newton's third law), we rewrite the previous expression: Mlj, = F, (dl1-dy.

The value in brackets is the movement of charge 1 relative to charge 2. More precisely, it is the movement of charge / in / ("- a frame of reference rigidly connected with charge 2 and moving along with it translationally relative to the original / (- system. Indeed, the movement dl, charge 1 in / (- the system can be represented as displacement dl2 / ("- system plus displacement dl, charge / relative to this / (" - system: dl, = dl2 + dl,. Hence dl, - dl2 = dl " , and

So, it turns out that the sum of elementary work in an arbitrary / (- frame of reference is always equal to the elementary work performed by a force acting on one charge, in a frame of reference where the other charge is at rest. - reference systems.

Force F „acting on the charge / from the side of charge 2, conservative (as a central force). Therefore, the work of this force on displacement dl can be represented as a decrease in the potential energy of charge 1 in the field of charge 2 or as a decrease in the potential energy of interaction of the considered pair of charges:

where 2 is a value that depends only on the distance between these charges.

2. Now we turn to a system of three point charges (the result obtained for this case can be easily generalized to a system of an arbitrary number of charges). The work done by all forces of interaction during elementary displacements of all charges can be represented as the sum of the work of all three pairs of interactions, ie 6L = 6L (2 + 6L, 3 + 6L 2 3. But for each pair of interactions, as soon as which was shown, ik = - d Wik, therefore

where W is the interaction energy of a given system of charges,

W «= wa + Wtz + w23.

Each term of this sum depends on the distance between the corresponding charges, so the energy W

a given system of charges is a function of its configuration.

Similar reasoning is obviously valid for a system of any number of charges. Hence, it can be argued that each configuration of an arbitrary system of charges has its own energy value W and the work of all interaction forces when this configuration changes is equal to the loss of energy W:

bl = -ag. (4.1)

Energy of interaction. Let us find an expression for the energy W. First, consider again a system of three point charges, for which we have shown that W = - W12 + ^ 13 + ^ 23- We transform this sum as follows. We represent each term Wik in symmetric form: Wik =] / 2 (Wlk + Wk), since Wik = Wk, Then

Let's group members with the same first indices:

Each sum in parentheses is the energy Wt of interaction of the i-th charge with the rest of the charges. Therefore, the last expression can be rewritten as follows:

Generalization of an arbitrary

the obtained expression for a system of the number of charges is obvious, because it is clear that the above reasoning is completely independent of the number of charges that make up the system. So, the interaction energy of the system of point charges

Bearing in mind that Wt =<7,9, где qt - i-й заряд системы; ф,- потенциал, создаваемый в месте нахождения г-го заряда всеми остальными зарядами системы, получим окончательное выражение для энергии взаимодействия системы точечных зарядов:

Example. Four identical point charges q are located at the vertices of a tetrahedron with an edge a (Fig. 4.1). Find the interaction energy of the charges of this system.

The interaction energy of each pair of charges is here the same and equal to = q2 / Ale0a. There are six such interacting pairs in total, as can be seen from the figure, therefore the interaction energy of all point charges of a given system

W = 6 #, = 6<72/4яе0а.

Another approach to solving this problem is based on the use of formula (4.3). The potential φ at the location of one of the charges, due to the field of all other charges, is equal to φ = 3<7/4яе0а. Поэтому

Total energy of interaction. If the charges are distributed continuously, then, expanding the system of charges into a set of elementary charges dq = р dV and passing from summation in (4.3) to integration, we obtain

where f is the potential created by all charges of the system in an element of volume dV. A similar expression can be written for the distribution of charges, for example, over a surface; for this it is sufficient to replace p by o and dV by dS in formula (4.4).

One may mistakenly think (and this often leads to misunderstandings) that expression (4.4) is only a modified expression (4.3), corresponding to the replacement of the concept of point charges by the concept of a continuously distributed charge. In reality, this is not the case - both expressions differ in their content. The origin of this difference is in a different sense of the potential φ included in both expressions, which is best explained by the following example.

Let the system consist of two balls having charges q and q2 "The distance between the balls is much larger than their sizes, so the charges ql and q2 can be considered pointwise. Let us find the energy W of this system using both formulas.

According to formula (4.3)

W = "AUitPi +2> where, φ [is the potential created by the charge q2 at the place

finding a charge has a similar meaning

and potential f2.

According to formula (4.4), we must break the charge of each ball into infinitesimal elements p AV and multiply each of them by the potential φ, created not only by the charges of another ball, but also by the elements of the charge of this ball. It is clear that the result will be completely different, namely:

W = Wt + W2 + Wt2, (4.5)

where Wt is the energy of interaction with each other of the charge elements of the first ball; W2 - the same, but for the second ball; Wi2 is the interaction energy of the charge elements of the first ball with the charge elements of the second ball. The energies W, and W2 are called the intrinsic energies of the charges qx and q2, and W12 is the energy of interaction of the charge with the charge q2.

Thus, we see that the calculation of the energy W according to the formula (4.3) gives only Wl2, and the calculation according to the formula (4.4) gives the total interaction energy: in addition to W (2, also the own energies IF, and W2. Ignoring this circumstance is often a source gross mistakes.

We will return to this issue in § 4.4, and now we will obtain several important results using formula (4.4).

Natural natural sources from which energy is drawn to prepare it in the required forms for various technological processes are called energy resources. There are the following types of main energy resources: a chemical energy of the fuel; b atomic energy; into water energy, that is, hydraulic; d solar radiation energy; q wind energy. e energy of ebb and flow; Well geothermal energy. Primary energy source or energy resource coal gas oil uranium concentrate hydropower solar ...

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Lecture number 1.

Basic definitions

Power system (power system)consists of power plants, power grids and electricity consumers, interconnected and connected by a common mode and general management of this mode.

Electric power (electrical) systemIs a set of electrical parts of a power plant, electrical networks and electricity consumers, i.e. it is part of the energy system, with the exception of heating networks and heat consumers.

Electrical networkIs a set of electrical installations for the distribution of electrical energy, consisting of substations, switchgears, overhead and cable power lines.

Electrical substationsIs an electrical installation designed to convert electricity of one voltage or frequency to another voltage or frequency.

Power system characteristics

The frequency at all points of electrically connected networks is the same

Equality of consumed and generated capacities

The voltage in different network nodes is not the same

Benefits of power interconnection

Improving the reliability of power supply

Improving the stability of power systems

Improvement of technical and economic indicators of power systems

Stable power quality

Reducing the required power reserve

The loading conditions of the units are improved due to the equalization of the load curve and the reduction of the maximum load of the power system.

The possibility of a more complete use of the generating capacities of electric power plants appears, due to the difference in their geographical position in latitude and longitude.

The operational management of power systems is carried out by their dispatching services, which, on the basis of appropriate calculations, establish the optimal operating mode for power plants and networks of various voltages.

Energy sources

There are renewable and non-renewable energy sources.

Natural (natural) sources from which energy is drawn to prepare it in the required forms for various technological processes are called energy resources.

There are the following types of main energy resources:

a) chemical energy of the fuel;

b) atomic energy;

c) water energy (i.e. hydraulic);

d) the energy of the sun's radiation;

e) wind energy.

f) the energy of the ebb and flow;

g) geothermal energy.

The primary energy source or energy resource (coal, gas, oil, uranium concentrate, hydropower, solar energy, etc.) enters one or another energy converter, the output of which is either electrical energy, or electrical and thermal energy. If thermal energy is not generated, then it is necessary to use an additional energy converter from electrical to thermal (dotted lines in Fig. 1.1).

The largest part of the electrical energy consumed in our country is obtained by burning fuels extracted from the bowels of the earth - coal, gas, fuel oil (oil refined product). When they are burned, the chemical energy of the fuels is converted into heat.

Power plants that convert thermal energy resulting from fuel combustion into mechanical energy, and this latter into electrical energy, are called thermal power plants (TPP).

Power plants that operate at the highest possible load for a significant part of the year are called base power plants, power plants that are used only during part of the year to cover the "peak" load are called peak power plants.

ES classification:

TPP (IES, TPP, GTS, PGPP)
NPP (1-circuit, 2-circuit, 3-circuit)
HPPs (dam, diversion)

Electrical part of the ES

Power plants (ES) are complex technological complexes with a total number of main and auxiliary equipment. The main equipment is used for the production, transformation, transmission and distribution of electricity, the auxiliary equipment is used to perform auxiliary functions (measurement, signaling, control, protection and automation, etc.). We will show the interconnection of various equipment on a simplified schematic diagram of an ES with busbars of generator voltage (see Fig. 1).

Rice. one

The electricity generated by the generator is fed to the busbars of the SS and then distributed between the auxiliary needs of the MV, the generator voltage load of the NG and the power system. Individual elements in fig. 1 are intended:

1. Switches Q - for switching on and off the circuit in normal and emergency modes.

2. Disconnectors QS - to relieve voltage from de-energized parts of an electrical installation and to create a visible circuit break, which is necessary during repair work. Disconnectors, as a rule, are repair and not operational elements.

3. Busbars US - for receiving electricity from sources and distributing it among consumers.

4. Relay protection devices РЗ - for detecting the fact and location of damage in an electrical installation and for issuing a command to disconnect the damaged element.

5. Automation devices A - for automatic switching on or switching of circuits and devices, as well as for automatic regulation of operating modes of electrical installation elements.

6. Measuring devices IP - to control the operation of the main equipment of the power plant and the quality of energy, as well as to account for the generated and supplied electricity.

7. Instrument current transformers TA and TV voltages.

Control questions:

Give a definition of the energy system and all the elements included in it.
The main parameters of electricity.
What energy sources are natural sources?
What power plants are called thermal?
What are the traditional methods of generating electricity?
What methods of generating electricity are non-traditional?
List the types of renewable energy sources?
List the types of non-renewable energy sources?
What types of power plants are thermal power plants?
What are the technical and economic benefits of interconnecting energy systems?
Which power plants are called basic and which are peak power plants?
What are the requirements for energy systems?
List the main purposes of automation devices, current and voltage transformers, switches.
List the main purposes of disconnectors, relay protection devices and busbars. What is the purpose of a current-limiting reactor?

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Consider a system of two point charges (see figure) according to the principle of superposition at any point in space:

Electric field energy density

The first and third terms are related to the electric fields of charges and accordingly, and the second term reflects the electrical energy associated with the interaction of charges:

The self-energy of charges is a positive value
, and the interaction energy can be both positive and negative
.

Unlike vector the energy of the electric field is not an additive quantity. The energy of interaction can be represented by a simpler relationship. For two point charges, the interaction energy is:

which can be represented as the sum:

where
- potential of the charge field at the location of the charge , a
- potential of the charge field at the location of the charge .

Generalizing the result obtained for a system of an arbitrary number of charges, we get:

where -
system charge, - potential created at the location
charge, everyone else system charges.

If charges are distributed continuously with bulk density , the sum should be replaced by a volume integral:

where is the potential created by all charges of the system in an element of volume
... The resulting expression matches total electrical energy systems.

Examples.

Charged metal ball in a homogeneous dielectric.

Using this example, we will find out why the electric forces in a dielectric are less than in a vacuum and calculate the electric energy of such a ball.

N the field strength in the dielectric is less than the strength in vacuum in once
.

This is due to the polarization of the dielectric and the appearance at the surface of the conductor of a bound charge opposite sign of the charge of the conductor (see figure). Associated charges screen the field of free charges reducing it everywhere. The electric field strength in the dielectric is equal to the sum
, where
- field strength of free charges,
- field strength of bound charges. Considering that
, we find:

→
→

→
→
→

Dividing by the surface area of the conductor, we find the relationship between the surface density of bound charges
and surface density of free charges :

The resulting ratio is suitable for a conductor of any configuration in a homogeneous dielectric.

Let's find the energy of the electric field of the ball in the dielectric:

It is taken into account here that
, and the elementary volume, taking into account the spherical symmetry of the field, is chosen in the form of a spherical layer. - the capacity of the ball.

Since the dependence of the electric field strength inside and outside the ball on the distance to the center of the ball r is described by various functions: