Natural sources from which energy is drawn for its preparation in the necessary types for various technological processes are called energy resources. The following types of basic energy resources are distinguished: a chemical energy of fuel; b atomic energy; in water energy that is hydraulic; g radiation energy from the sun; d wind energy. e energy of ebb and flow; f geothermal energy. Primary source of energy or energy resource coal gas oil uranium concentrate hydropower solar...

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Lecture No. 1.

Basic definitions

Energy system (energy system)consists of power plants, electrical networks and electricity consumers, interconnected and connected by the commonality of the mode and the general management of this mode.

Electrical power (electrical) systemthis is 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 networkthis is 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 from one voltage or frequency to another voltage or frequency.

Characteristics of power systems

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

Equality of consumed and generated power

The voltage in different network nodes is not the same

Benefits of grid interconnection

Increasing the reliability of power supply

Increasing the stability of power systems

Improving the technical and economic indicators of energy systems

Stable power quality

Reducing the required power reserve

Loading conditions for units are improved by leveling the load curve and reducing the maximum load of the power system.

There is an opportunity for more complete use of the generating capacities of electric power plants, due to the difference in their geographical location by latitude and longitude.

Operational control of power systems is carried out by their dispatch services, which, based on appropriate calculations, establish the optimal operating mode of power plants and networks of various voltages.

Energy sources

There are renewable and non-renewable energy sources.

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

The following types of basic energy resources are distinguished:

a) chemical energy of the fuel;

b) nuclear energy;

c) water energy (that is, hydraulic);

d) solar radiation energy;

e) wind energy.

f) tidal energy;

g) geothermal energy.

The primary source of energy 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 (a product of oil refining). When they are burned, the chemical energy of the fuel is converted into thermal energy.

Power plants that convert the thermal energy obtained by burning fuel into mechanical energy, and the latter into electrical energy, are called thermal power plants (TES).

Power plants operating at the highest possible load for a significant part of the year are called base-load power plants, power plants used only during part of the year to cover the “peak” load are called peaking power plants.

ES classification:

1. TPP (KPP, CHPP, GTS, PGPP)
2. NPPs (1-circuit, 2-circuit, 3-circuit)
3. Hydroelectric power stations (dam, diversion)

Electrical part of the ES

Electric power stations (ES) are complex technological complexes with total number main and auxiliary equipment. The main equipment is used for the production, conversion, transmission and distribution of electricity, auxiliary for performing auxiliary functions (measurement, signaling, control, protection and automation, etc.). We will show the mutual connection of various equipment on a simplified circuit diagram of an electrical system with generator voltage busbars (see Fig. 1).

Rice. 1

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

1. Q switches for turning on and off the circuit in normal and emergency modes.

2. QS disconnectors to relieve voltage from de-energized parts of an electrical installation and to create a visible circuit break necessary for repair work. Disconnectors, as a rule, are repair, rather than operational elements.

3. Prefabricated busbars for receiving electricity from sources and distributing it between consumers.

4. Relay protection devices 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 automatically switching on or switching circuits and devices, as well as for automatically regulating the operating modes of electrical installation elements.

6. Measuring instruments IP for monitoring the operation of the main equipment of the power plant and the quality of energy, as well as for accounting for generated and supplied electricity.

7. Current transformers TA and voltage TV.

Security questions:

1. Give a definition of the energy system and all the elements included in it.
2. Basic parameters of electricity.
3. What energy sources are natural sources?
4. Which power plants are called thermal?
5. What methods of electricity production are traditional?
6. What methods of generating electricity are considered non-traditional?
7. List the types of renewable energy sources?
8. List the types of non-renewable energy sources?
9. What types of power plants are classified as thermal power plants?
10. Name the technical and economic advantages of interconnecting energy systems.
11. Which power plants are called base-loading and which are peaking?
12. What are the requirements for energy systems?
13. List the main purposes of automation devices, current and voltage transformers, and switches.
14. List the main purposes of disconnectors, relay protection devices and busbars. What is the purpose of a current limiting reactor?

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Energy approach to interaction. Energy approach to interaction electric charges is, as we will see, very fruitful in its practical applications, and in addition, it opens up the possibility of taking a different look at the electric field itself as a physical reality.

First of all, we will find out how we 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’s find the algebraic sum of the elementary works of forces F and F2 with which these charges interact. Let in some K-frame of reference during the time cU the charges have made movements dl, and dl 2. Then the corresponding work of these forces

6L, 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 parentheses is the movement of charge 1 relative to charge 2. More precisely, this is the movement of charge / in the /("-frame of reference, rigidly connected with charge 2 and moving with it translationally with respect to the original /(-system. Indeed, movement dl, charge 1 in the /(-system can be represented as the displacement dl2 of the /("-system plus the 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 /(-reference frame is always equal to the elementary work performed by the force acting on one charge in a reference frame where the other charge is at rest. In other words, the work 6L12 does not depend on the choice of the initial /( -reference systems.

The force F„ acting on the charge / from the side of charge 2 is conservative (as the 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 pair of charges under consideration:

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

2. Now let's move on 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 that all interaction forces do during elementary movements of all charges can be represented as the sum of the work of all three pairs of interactions, i.e. 6A = 6A (2 + 6A, 3 + 6A 2 3. But for each pair of interactions, as soon as what was shown is 6L ik = - d Wik, therefore

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

W «= wa + Wtз + w23.

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

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

Similar reasoning is obviously valid for a system of any number of charges. This means that we can say that each configuration of an arbitrary system of charges has its own energy value W and the work of all interaction forces when changing this configuration is equal to the decrease in energy W:

bl = -ag. (4.1)

Energy of interaction. Let's find an expression for the energy W. First, consider again a system of three point charges, for which we showed that W = - W12+ ^13+ ^23- Let's transform this sum as follows. Let us represent each term Wik in a 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 ith charge with the remaining charges. Therefore, the last expression can be rewritten as follows:

Generalization of arbitrary

The resulting expression for the system from the number of charges is obvious, because it is clear that the arguments carried out are completely independent of the number of charges making up the system. So, the interaction energy of a system of point charges

Keeping 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 edge a (Fig. 4.1). Find the interaction energy of the charges of this system.

The interaction energy of each pair of charges here is the same and equals = 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 issue 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, decomposing the system of charges into a set of elementary charges dq = p 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 with volume dV. A similar expression can be written for the distribution of charges, for example, over a surface; To do this, it is enough to replace p by o and dV by dS in formula (4.4).

One might mistakenly think (and this often leads to misunderstandings) that expression (4.4) is only a modified expression (4.3), corresponding to replacing the idea of ​​point charges with the idea of ​​a continuously distributed charge. In reality this is not so - both expressions differ in their content. The origin of this difference is in the different meaning of the potential φ included in both expressions, which is best explained with the following example.

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

According to formula (4.3)

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

finding a charge has a similar meaning

and potential f2.

According to formula (4.4), we must divide 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 the other ball, but also by the charge elements 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 of the charge elements of the first ball with each other; W2 - the same, but for the second ball; Wi2 is the energy of interaction between the charge elements of the first ball and 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 charge-charge interaction q2.

Thus, we see that calculating the energy W using formula (4.3) gives only Wl2, and calculating using 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 the source gross mistakes.

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

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

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

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

Note that when a charge moves in an electric field, the work A v.s external forces are equal in magnitude to work A s.p field strength and opposite in sign:

A v.s = – A s.p.

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

· Electric field potential created by a metal that carries a charge Q sphere with radius R, at a distance r from the center of the sphere:

inside the sphere ( r<R) ;

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

outside the sphere (r>R) .

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

· Electric field potential created by the system n 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, created by individual point charges Q 1, Q 2, ..., Qn:

· Energy W interaction of a system of point charges Q 1, Q 2, ..., Qn is determined by the work that this system of charges can do when moving them relative to each other to infinity, and is expressed by the formula

where is the potential of the field created by all p– 1 charges (except i th) at the point where the charge is located Qi.

· 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, i.e. 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 field line.

· Work done by an electric field when moving a point charge Q from one point of the field having potential j 1, to another with potential j 2

A=Q∙(j 1 – j 2), or

Where E l - projection of the tension vector onto the direction of movement; dl- movement.

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

A=Q∙E∙l∙cosa,

Where l- movement; a- the angle between the vector and displacement directions.

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

The vector drawn from the negative charge of the dipole to its positive charge is called the arm of the dipole.

Product of charge | Q| dipole on its arm is called the electric moment of the dipole:

Dipole field strength

Where r- electric dipole moment; r- module of the radius vector drawn from the center of the dipole to the point at which the field strength interests us; α is the angle between the radius vector and the dipole arm.

Dipole field potential

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

or M=p∙E∙ sin,

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

In a non-uniform electric field, in addition to the mechanical moment (a pair of forces), some force also acts on the dipole. In the case of a field that is symmetric about the axis X,strength is expressed by the ratio

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

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

Potential energy of a dipole in an electric field

Electrical energy of a system of charges.

Field work during dielectric polarization.

Electric field energy.

Like all matter, an electric field has energy. Energy is a function of state, and the state of the field is given by strength. Whence it follows that the energy of the electric field is an unambiguous function of intensity. Since, it is extremely important to introduce the concept of energy concentration in the field. A measure of the field energy concentration is its density:

Let's find an expression for. For this purpose, let us consider the field of a flat capacitor, considering it uniform everywhere. An electric field in any capacitor arises during the process of charging, which can be represented as the transfer of charges from one plate to another (see figure). The elementary work spent on charge transfer is equal to:

where and the complete work:

which goes to increase the field energy:

Considering that (there was no electric field), for the energy of the electric field of the capacitor we obtain:

In the case of a parallel plate capacitor:

since, - the volume of the capacitor is equal to the volume of the field. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, the energy density of the electric field is equal to:

This formula is valid only in the case of an isotropic dielectric.

The energy density of the electric field is proportional to the square of the intensity. This formula, although obtained for a uniform field, is true for any electric field. In general, the field energy can be calculated using the formula:

The expression includes dielectric constant. This means that in a dielectric the energy density is greater than in a vacuum. This is due to the fact that when a field is created in the dielectric, additional work is performed associated with the polarization of the dielectric. Let us substitute the value of the electrical induction vector into the expression for energy density:

The first term is associated with the field energy in vacuum, the second – with the work expended on the polarization of a unit volume of the dielectric.

The elementary work spent by the field on the increment of the polarization vector is equal to.

The work of polarization per unit volume of a dielectric is equal to:

since that is what needed to be proven.

Let's 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 associated with the electric fields of charges and, respectively, and the second term reflects the electrical energy associated with the interaction of charges:

The self-energy of charges is positive, and the interaction energy can be either positive or negative.

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

which can be represented as the sum:

where is the charge field potential at the location of the charge, and is the charge field potential at the location of the charge.

Generalizing the result obtained to a system of an arbitrary number of charges, we obtain:

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

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

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

Work done by an electric field to move a charge

Work concept A electric field E by charge movement Q is introduced in full accordance with the definition of mechanical work:

Where - potential difference (the term voltage is also used)

Many problems consider continuous charge transfer over a period of time between points with a given potential difference U(t), in this case the formula for the work should be rewritten as follows:

where is the current strength

Electric current power in the circuit

Power W electric current for a section of a circuit is determined in the usual way, as a derivative of work A in time, that is, by the expression:

This is the most general expression for power in an electrical circuit.

Taking into account Ohm's law:

Electrical power released at the resistance R can be expressed in terms of current: ,

Accordingly, work (heat released) is the integral of power over time:

Energy of electric and magnetic fields

For electric and magnetic fields, their energy is proportional to the square of the field strength. It should be noted that, strictly speaking, the term electromagnetic field energy is not entirely correct. Calculating the total energy of the electric field of even one electron leads to a value equal to infinity, since the corresponding integral (see below) diverges. The infinite energy of the field of a completely finite electron is one of the theoretical problems of classical electrodynamics. Instead, in physics they usually use the concept electromagnetic field energy density(at a certain point in space). The total energy of the field is equal to the integral of the energy density over the entire space.

The energy density of the electromagnetic field is the sum of the energy densities of the electric and magnetic fields.

In the SI system:

Where E- electric field strength, H- magnetic field strength, - electric constant, and - magnetic constant. Sometimes for the constants and - the terms dielectric constant and magnetic permeability of vacuum are used - which are extremely unfortunate and are now almost never used.

Electromagnetic field energy flows

For an electromagnetic wave, the energy flux density is determined by the Poynting vector S(in the Russian scientific tradition - the Umov-Poynting vector).

In the SI system the Poynting vector is equal to: ,

The vector product of the electric and magnetic field strengths, and is directed perpendicular to the vectors E And H. This naturally agrees with the transverse property of electromagnetic waves.

At the same time, the formula for the energy flux density can be generalized for the case of stationary electric and magnetic fields, and has exactly the same form: .

The very fact of the existence of energy flows in constant electric and magnetic fields, at first glance, looks very strange, but this does not lead to any paradoxes; Moreover, such flows are detected in experiment.