H The nominal voltage of the power transmission line significantly affects its technical and economic indicators. With a high rated voltage, high power transmission is possible over long distances and with lower losses. Power transmission capacity during the transition to the next stage rated voltage increases several times. At the same time, with an increase in the nominal voltage, capital investments in equipment and construction of power transmission lines increase significantly.
Rated voltages of electrical networks in Russia are established by GOST 21128 – 83 (Table 1).
table 1
Rated phase-to-phase voltages, kV,
for voltages above 1000 V in accordance with GOST 721-77 (ST SEV 779-77)
| Networks and receivers | Generators and synchronous compensators | Transformers and autotransformers | Highest operating voltage | |||
| without on-load tap-changer | with tap changer | |||||
| primary windings | secondary windings | primary windings | secondary windings | |||
| (3) * | (3,15) * | (3) and (3.15) ** | (3.15) and (3.3) | – | (3,15) | (3,6) |
| 6,3 | 6 and 6.3 ** | 6.3 and 6.6 | 6 and 6.3 ** | 6.3 and 6.6 | 7,2 | |
| 10,5 | 10 and 10.5 ** | 10.5 and 11.0 | 10 and 10.5 ** | 10.5 and 11.0 | 12,0 | |
| 21,0 | 22,0 | 20 and 21.0 ** | 22,0 | 24,0 | ||
| – | 38,5 | 35 and 36.75 | 38,5 | 40,5 | ||
| – | – | 110 and 115 | 115 and 121 | |||
| (150) * | – | – | (165) | (158) | (158) | (172) |
| – | – | 220 and 230 | 230 and 242 | |||
| – | ||||||
| – | – | |||||
| – | – | |||||
| – | – | – | – |
* The rated voltages indicated in brackets are not recommended for newly designed networks.
** For transformers and autotransformers connected directly to the generator voltage buses of power plants or to the generator terminals.
The economically feasible nominal voltage of the transmission line depends on many factors, of which the transmitted active power and distance are the most important. In the reference literature, the fields of application of electrical networks of different nominal voltages are given, built on the basis of a criterion that is unsuitable in a market economy. Therefore, the choice of the option electrical network with one or another rated voltage should be taken on the basis of other criteria, for example, the criterion of total costs (see clause 2.4). Nevertheless, the approximate values of the rated voltages can be obtained according to the previous methods (for example, according to empirical formulas and tables, taking into account the maximum transmission distance and the capacity of lines of different rated voltages).
The most commonly used are the following two empirical formulas for determining voltage U:
Or 
, (1)
where R- transmitted power, MW; l- line length, km.
The resulting voltages are used to select a standard nominal voltage, and it is not at all necessary to select a voltage always greater than that obtained by these formulas. If the difference in total costs of the compared options for the electrical network is less than 5%, preference should be given to the option of using a higher voltage. The throughput and transmission range of 35-1150 kV lines, taking into account the most commonly used wire cross-sections and the actual average length of overhead lines, are given in Table. 2.
table 2
Capacity and transmission range of 35-1150 kV lines
| Line voltage, kV | Wire section, mm 2 | Transmitted power, MW | Power line length, km | ||
| natural | at a current density of 1.1 A / mm 2 * | limiting (with efficiency = 0.9) | medium (between two adjacent substations) | ||
| 70-150 | 4-10 | ||||
| 70-240 | 13-45 | ||||
| 150-300 | 13-45 | ||||
| 240-400 | 90-150 | ||||
| 2 ´ 240-2 ´ 400 | 270-450 | ||||
| 3 ´ 300-3 ´ 400 | 620-820 | ||||
| 3 ´ 300-3 ´ 500 | 770-1300 | ||||
| 5 ´ 300-5 ´ 400 | 1500-2000 | ||||
| 8 ´ 300-8 ´ 500 | 4000-6000 | – |
* For overhead lines 750-1150 kV 0.85 A / mm 2.
Variants of the projected electrical network or its individual sections may have different rated voltages. Usually, the voltages of the head, more loaded areas are determined first. The sections of the ring network, as a rule, must be carried out for one rated voltage.
Voltages 6 and 10 kV are intended for distribution networks in cities, rural areas and industrial enterprises. The predominant voltage is 10 kV, 6 kV networks are used when enterprises have a significant load of electric motors with a rated voltage of 6 kV. The use of voltages of 3 and 20 kV for newly designed networks is not recommended.
The 35 kV voltage is used to create 6 and 10 kV power centers, mainly in rural areas. In Russia (the former USSR), two voltage systems of electrical networks (110 kV and above) have become widespread: 110–220–500 and 110 (150) –330–750 kV. The first system is used in most IES, the second, after the division of the USSR, remained only in the IES of the North-West (in IES of the Center and IES of the North Caucasus, with the main system of 110-220-500 kV, 330 kV grids also have limited distribution).
The 110 kV voltage is the most widespread for distribution networks in all UPS systems, regardless of the adopted voltage system. Networks with a voltage of 150 kV perform the same functions as networks of 110 kV, but are available only in the Kola power system and are not used for newly designed networks. The voltage of 220 kV is used to create power centers for the 110 kV network. With the development of the 500 kV network, the 220 kV networks acquired mainly distribution functions. The voltage of 330 kV is used for the backbone network of power systems and the creation of power centers for 110 kV networks. The backbone networks are carried out at a voltage of 500 or 750 kV, depending on the adopted voltage system. For the UPS, where a voltage system of 110–220–500 kV is used, the voltage of 1150 kV is taken as the next step.
Example 2
For the network development options selected in example 1 b, v and e(Fig. 1) select the rated voltage of the network sections. Values of active loads at power points: R 1 = 40 MW, R 2 = 30 MW and R 3 = 25 MW.
Solution. All the options under consideration are characterized by the presence of the head section of the central processor network - 1. The power flow in this section of the network (excluding power losses on others) is equal to the sum of the loads of all three power nodes, i.e. R CPU - 1 = R 1 + R 2 + R 3 = 95 MW. According to expressions (1), we obtain the voltages for this section of the network or 
and, in accordance with the recommended voltage scale (Table 1), you can take a rated voltage of 110 or 220 kV. Emergency current for this section of the network at U n = 110 kV is equal to 
And, at U n = 220 kV - 268 kA. For both voltage classes, you can use the AC ‑ 240/32 wire brand in a 110 kV network according to the permissible heating, in a 220 kV network - according to the conditions of the corona. Consider the rest of the projected network.
Section 1 - 2 is typical for all variants of the network development b, v and e(Fig. 1) and differs in them only in the level of power flow through it. For option b stresses according to expressions (1) are respectively equal to U 1 - 2 = 79.18 and U 1 - 2 = 96.08 kV, for options v and e U 1 - 2 = 92.14 and U 1 - 2 = 119.13 kV.
Section 1 - 3 is typical for two options for the development of the network - b and e. For option b stresses for this section in accordance with expressions (1) are respectively equal to U 1 - 3 = 80 and U 1 - 3 = 91.29 kV, options e–U 1 - 3 = 97.43 and U 1 - 3 = 123.61 kV.
Section 2 - 3 is typical for options v and e. The stresses for this section are U 2 - 3 = 73.7 and U 2 - 3 = 92.59 kV.
Measuring current transformer
In modern electrical installations, the voltage reaches 750 kV and above, and currents are measured in tens of kiloamperes or more. To measure them directly, very bulky and expensive electrical measuring instruments would be required. In some cases, such measurements would be completely impossible. In addition, when servicing appliances directly connected to a high voltage network, the service personnel would be exposed to a great risk of electric shock. The use of measuring current transformers expands the measurement range of conventional electrical measuring instruments and at the same time isolates them from high voltage circuits.
Measuring current transformers are used to connect ammeters, voltmeters, wattmeters, relay protection devices and electrical automatics, meters for accounting for the generation and consumption of electrical energy. The accuracy of the metering of electrical energy and the measurement of electrical parameters, the correctness and reliability of the relay protection operation depend on their work.
Measuring current transformer circuit
In the diagram:
L1-L2 primary winding
I1-I2 secondary winding
I 1 - line current;
I 2 - current flowing in the secondary winding;
The main elements of the measuring current transformer involved in the conversion of current are the primary and secondary windings, wound on the same magnetic circuit. The primary winding of the measuring current transformer is connected in series (in the section of the high voltage conductor). Measuring devices (ammeter, current winding of the meter) or relays are connected to the secondary winding. When the measuring current transformer is in operation, the secondary winding is always closed to the load.
The primary winding together with the high voltage circuit is called the primary circuit, and the external circuit receiving measurement information from the secondary winding of the measuring current transformer (i.e. the load and connecting wires) is called the secondary circuit. The circuit formed by the secondary winding and the secondary circuit connected to it is called the secondary current branch.
There is no electrical connection between the primary and secondary windings of the current transformer. They are isolated from each other for their full operating voltage. This allows the direct connection of measuring devices or relays to the secondary winding and thereby exclude the effect of high voltage applied to the primary winding on the operating personnel, since both windings are superimposed on the same magnetic circuit, they are magnetically coupled.
Main parameters and characteristics of the measuring current transformer
Measuring current transformer TNSh
Specifications:
Rated voltage 0.66 kV
Rated secondary current 5A
Rated primary current 15000A, 25000A
Rated voltage- the effective value of the line voltage at which the measuring current transformer is intended to operate, indicated in the rating table of the measuring current transformer. For domestic measuring current transformers, the following scale of rated voltages is adopted, kV;
0,66; 6; 10; 15; 20; 24; 27; 35; 110; 150; 220; 330; 500; 750; 1150
Rated primary current I 1n - indicated in the rating table of the measuring current transformer, passing through the primary winding, in which the continuous operation of the measuring current transformer is provided. For domestic measuring current transformers, the following scale of rated primary currents is adopted, A:
1; 5; 10; 15; 20; 30; 40; 50; 75; 80; 100; 150; 200; 300; 400; 500; 600; 750; 800; 1000; 1200; 1500; 2000; 3000;
4000; 5000; 6000; 8000;
10000; 12000; 14000; 16000; 18000; 20000; 25000; 28000; 32000; 35000; 40000.
In measuring current transformers intended for completing turbo- and hydrogenerators, rated current values are higher than 10,000 A may differ from the values given in this scale.
Instrument current transformers for rated primary current 15; 30; 75; 150; 300; 600; 750; 1200; 1500; 3000 and 6000 A, must allow for an unlimited long time the highest operating primary current, equal respectively 16; 32; 80; 160; 320; 630; 800; 1250; 1600; 3200 and 6300 A... Otherwise, the highest primary current is equal to the rated primary current.
Rated secondary current I 2n - indicated in the rating table of the measuring transformer current current passing through the secondary winding. The rated secondary current is assumed to be 1 or 5 A, and the current 1 A allowed only for measuring current transformers with a rated primary current up to 4000 A... By agreement with the customer, it is allowed to manufacture measuring current transformers with a rated secondary current 2 or 2.5 A
Transformer ratio of the measuring current transformer equal to the ratio of the primary current to the secondary current.
Two quantities are used in the calculation of instrument current transformers: the actual transformation ratio n and nominal transformation ratio n n... The actual transformation ratio n is understood as the ratio of the actual primary current to the actual secondary current. The nominal transformation ratio nн is understood as the ratio of the nominal primary current to the nominal secondary current.
Resistance of the measuring current transformer to mechanical and thermal influences characterized by a current of electrodynamic resistance and a current of thermal resistance.
The main features of power systems are as follows.
Electricity is practically not accumulated. Production, transformation, distribution and consumption occur simultaneously and almost instantaneously. Therefore, all elements of the power system are interconnected by the unity of the regime. In the power system at each moment of time of the steady state, the balance is maintained for the active and reactive power... It is impossible to generate electricity without a consumer: how much electricity is generated in this moment, so much of it is given to the consumer minus losses. Repairs, accidents, etc. lead to a decrease in the amount of electricity supplied to the consumer (in the absence of a reserve), and, as a consequence, to underutilization of the installed equipment of the power system.
The relative speed of the processes (transient): wave processes - () s, off and on - s, short circuits - () s, swinging - (1-10) s. High rates of transient processes in power systems necessitate the use of automation in a wide range up to complete automation of the process of production and consumption of electricity and the exclusion of the possibility of personnel intervention.
The power system is connected to all branches of industry and transport, characterized by a wide variety of power receivers.
The development of the energy sector must outpace the growth in electricity consumption, otherwise it is impossible to create power reserves. The energy sector should develop evenly, without disproportions of individual elements.
Benefits of combining power plants into a power system
When power plants are combined into an energy system, the following is achieved:
decrease in the total reserve of power;
decrease in the total maximum load;
mutual assistance in the event of unequal seasonal changes in the capacity of power plants;
mutual assistance in case of unequal seasonal changes in consumer loads;
mutual assistance during repairs;
improving the capacity utilization of each power plant;
increasing the reliability of power supply to consumers;
the possibility of increasing the unit capacity of units and power plants;
possibility a single center management;
improving the conditions for the automation of the process of production and distribution of electricity.
Electrical installations. Nominal data of installations
Electrical installations (PUE, I.13) - installations in which electricity is produced, converted, distributed and consumed. They are divided into electrical installations with voltages up to 1000 V and over 1000 V.
The nominal (PUE, I.124) current, voltage, power, power factor, etc. of an electrical installation are passport data (in practice, this is the data at which the operation of an electrical installation is most economical).
Rated voltages
The scale of rated voltage lines in kilovolts of electrical installations of three-phase alternating current with a frequency of 50 Hz is given in table. 1.
Table 1
Scale of rated voltage of electrical installations, kV
|
Electrical receivers |
Generator |
Transformer |
|
|
primary winding |
secondary winding |
||
Scales of rated voltages of generators and secondary windings of transformers are selected 5-10% higher than rated voltages of consumers, power lines, primary windings of transformers in order to facilitate maintaining the rated voltage of consumers.
The rated voltage of the consumer () is taken as the reference base, then the rated voltage of the generator, the secondary winding of the transformer. With the help of rationally selected rated voltages and transformation ratios, it is possible to compensate for the voltage drop in the power transmission (,,) and maintain the rated voltage at the consumer.
The maximum permissible operating voltages exceed the rated ones by 15% (), 10% () and 5% ().
Maximum voltage scale, kV: 3.6; 6.9; 11.5; 23; 40.5; 126; 172; 252; 525; 787; 1207.5.
The change in the transformation ratio is achieved by changing the number of turns (taps) on one of the windings, for example, with and,
This expression means that the number of turns on the high voltage side changes from to, while changing from one to another (Fig. 1.4):
Review the information on transformers given in the electrical manuals and determine the limits and steps for regulating the transformation ratios.
As you know, the scale of rated voltages of electrical networks is over 1000 V general purpose alternating current is determined according to GOST 721-77 and recommends the following voltages for newly designed networks:
6, 10, 35, 110, 220, 330, 500, 750, 1150 kV.
When choosing a voltage, it is necessary to take into account the existing voltage systems in the European part of Russia 110 (150) / 330/750 kV and in the Urals and Siberia - 110/220/500/1150 kV.
Pre-selection of voltage can be made according to the empirical formula of G.A. Illarionova:
where is the length of the line, km; - power transmitted along the circuit, MW.
This formula gives satisfactory results for the full scale of rated AC voltages in the range 35–1150 kV.
There are other empirical formulas for choosing the nominal voltage. The scope of their application is limited by some conditions presented below (Table 2.4).
Table 2.4
Formulas for selecting rated transmission voltage
The areas of application of standard rated voltages depending on the power and transmission distance are shown in Figure 2.16 and Table 2.5.
Table 2.5
Power transmission capacity 110-1150 kV
| U nom, kV | F, mm 2 | Natural power, MW, at characteristic impedance, Ohm | Maximum transmitted power per circuit, MW | Greatest transmission length, km | ||
| 400 | 300–314 | 250–275 | ||||
| 70-240 | – | – | 25-50 | 50-150 | ||
| 240-400 | – | 100-200 | 150-250 | |||
| 2 × 240-2 × 400 | – | 300-400 | 200-300 | |||
| 3 × 330-3 × 500 | – | 700-900 | 800-1200 | |||
| 5 × 240-5 × 400 | – | – | 1800-2200 | 1200-2000 | ||
| 8 × 300-8 × 500 | – | – | 4000-6000 | 2500-3000 |
Today, two systems that have developed in Russia have a nominal voltage step inside each of approximately equal to 2 and a difference in transmitted power for adjacent voltages by 4 ÷ 6 times. This leads to the fact that when transmitting a certain power, at low voltage several circuits will be required, and at high voltage the line will be underloaded. In this regard, when choosing a voltage, it is possible to use the neighboring PUE U nom, but with an increased splitting radius.
Rice. 2.16. Areas of application of electrical networks of different rated voltages. The boundaries of equal efficiency are indicated: 1 –1150 and 500 kV; 2 - 500 and 220 kV; 3 - 220 and 110 kV; 4 - 110 and 35 kV; 5 - 750 and 330 kV; 6 - 330 and 150 kV; 7 - 150 and 35 kV
Configuration
When choosing schemes for the development of electrical networks, the following techniques can be used:
a) reconstruction of the main transmission by adding a second circuit, sometimes at a higher voltage;
b) the appearance of new circular lines;
v) deep insertion at a higher voltage.
Of course, the final choice of voltage and configuration should be based on technical and economic calculations.
Section selection
When choosing a cross-section, it is necessary to take into account the corona phenomenon, which determines the minimum allowable cross-section for each rated voltage.
The maximum allowable cross-section for power transmission lines depends on the rated voltage and is determined by the rational ratio of the consumption of non-ferrous and ferrous metal in the line structure.
The cross-section is selected according to the economic current density or economic intervals. Economic density is determined by the minimum costs in power lines and depends on the type of line, wire material, load schedule.
2.8.2. Economic intervals
The use of economic intervals makes it possible to exclude discrete sections and rated powers of transformers from the number of variables. With the help of economic intervals, it is possible to represent costs as a function of only the transmitted power. When choosing the structure of generating capacities, the costs of power transmission lines can be presented in the form. When planning the development of the network, a more accurate approximation can be used in the form 
or 
, but they all have a gap at. As a continuous function, an approximation of the form 
, according to which at costs 
can be reduced by choosing ε.
When choosing economic intervals for transformers, costs are taken into account by the following formula:
where is the cost of the th transformer; - operating time of the transformer;
- the cost of lost energy, determined by the cost of basic ES;
- cost determined by costs at peak stations.
Usually, but often taken 
.
From the condition 
the upper limit of the economic interval of a transformer with a rated power is determined.
2.8.3. Mathematical model of network development planning
The formation of the model begins with drawing up a calculation scheme, which shows the existing nodes and branches, new nodes and possible additional traces of lines connecting objects into the system. It should also take into account those lines that were found as a result of the analysis of the model for the choice of the structure of generating capacities. The design scheme should be reasonably redundant and include additional lines so as not to miss possible optimal connections.
For the nodes, the predicted loads and powers of the input units must be specified. Thus, the design model will have design nodes, including existing ones; those. node index 
... The number of branches in the design scheme, of which - existing.
Streams can be taken as unknowns active power by branches 
.
As an objective function, we will consider the costs in existing lines, proportional to energy losses, and in new lines, determined in accordance with the adopted approximating expressions for costs:
, (2.35)
where 
.
The unknown power flows along the branches are subject to the power balance condition at the nodes, which can be written in matrix form:
.
- a rectangular matrix of nodes-branches connections, and its elements for a node and a branch s are denoted and can take values equal to 1 if the branch leaves the node; +1 if the branch is included in a node and 0 if it is not associated with a node.
Let's compose the balance equation for the node (Fig.2.19):
In general, the balance equation for any node can be written:
.
Thus, the problem of choosing the optimal network scheme is to find the minimum of some nonlinear function 
subject to the linear equality constraint 
.
The network development planning problem formulated in this way is reduced to a nonlinear programming problem. This problem usually has one extreme. To solve it, the previously considered nonlinear programming methods can be used.
2.8.4. Applying gradient methods
As you know, the basic equation of the gradient method is:
. (2.36)
Consider an example in which you need to select a network to power only one node (Fig. 2.20). We assume that the costs are represented by quadratic dependencies. As a starting point, we take R 0 =(0,NS).
Taking into account the constraints, the movement to the minimum should be carried out along the projection of the gradient onto the constraint surface, i.e. along the vector V. Vector V can be obtained by eliminating constraints from components perpendicular to the surface. These components form the gradient of the constraints. Thus, the vector V defined by the expression
. (2.37)
To determine the undefined factors that form the vector V, the condition of equality to zero is used dot product:
. (2.38)
From this condition, taking the gradient equal for the linear constraint, we can find. Indeed, from the transformation
you can get the following matrix expression for the factors
. (2.40)
Components of the vector of factors λ allow you to determine all the components of the vector V
,
and use them in the gradient method procedure
.
However, it is easier to find the projection of the gradient if expression (2.40) is substituted in (2.37) and a simple transformation
where NS=
- design matrix.
The iterative process continues until the condition of the required accuracy for all components is satisfied.
 Rice. 2.21 | The block diagram of the algorithm with the choice of the optimal step is shown in Figure 2.21. Purpose of the blocks: 1. Formation of the calculation scheme. 2. Determination of the type of functions for calculating costs and their derivatives for all branches. 3. Formation of the matrix of incidents M. 4. Determination of the gradient projection matrix A. 5. Initial approximation of flows Р = Р0. 6. Calculation of the gradient at point P. 7. Determination of the projection V gradient. 8. Checking the termination condition. 9. Organization of a trial step P 1 = P- V t 0 /. 10. Calculation of gradient and projection V 1 at the end of the step. 11. Determination of the optimal step  ... 12. Working step. 13. Output of results |
Example 2.3... Determine the optimal flows in the branches of the network, the design scheme of which is shown in Figure 2.22.
The iterative calculation begins with the adoption of the initial approximation P 0, determining the magnitude of the gradient and its projection onto the surface of constraints
Then a test step is made in the direction of the projection. t 0 = 0.1 and flows are determined by branches R 1 at the end of this step, the gradient and its projection
After that, you can determine the step close to the optimal
and perform a working step from the starting point P in the direction of the projection
After that, in accordance with the algorithm, we return to block 6, where the gradient and its projection are calculated again
Checking the condition in block 8 determines the completion of the iterative process.
The found flows can be used to select the cross-section of the power transmission line.
The fast convergence of the process is explained by the quadratic nature of the objective function, which has a linear gradient and the optimal step found from two points leads to an exact solution.
The disadvantage of this method is the large dimension of the problem, which is determined by the number of branches of the computational scheme.
2.8.5. Coordinate Optimization Method
In the design scheme, as a rule, the minimum is the number of contours, defined as the difference in the number of branches and nodes. Therefore, when optimizing as unknowns, it is advisable to use the contour powers and apply the coordinate search method. The advantage of this method is that at each step of optimization of the objective function 
only one variable is selected while the rest are fixed. The found value is fixed, and then proceeds to optimization of the next variable, etc.
Consider the balance constraint. All flows along the branches can be divided into two components:
,
where are the flows in the tree, the branches of which connect all nodes with the balancing one without the formation of contours;
–Flows in chords, ie in the branches forming the outlines.
The main constraint can be thought of as divided into block matrices, as shown in Figure 2.23.
The flows in the branches of the tree are uniquely determined by the flows in the chords, which follows from the relations obtained on the basis of operations with block matrices and presented below:
(2.42)
As an initial approximation, you can take:
Then streams in trees:
.
Different branches of the original scheme can be selected as chords, complementing the selected tree with the formation of contours. The number of combinations is determined by the possible number of trees calculated using the Trent determinant generated for independent nodes:
, (2.43)
where is the number of branches associated with the node; - the number of branches connecting the nodes and.
Example 2.4. Determine the number of trees for the circuit
 |  |
Contour optimization is carried out according to the following algorithm.
1) A calculation scheme is drawn up.
2) Determines the dependencies for cost accounting in the line of the calculation scheme. For this, any approximating functions can be used up to the exact lower envelope of costs in new lines.
3) Chords are selected and numbered, for which the initial approximation of flows is taken, and flows in the branches of the tree are counted.
4) A chord cycle is organized, in which the following operations are performed sequentially:
- for the current chord, the contour that it closes is visible;
- on the basis of the received flow in the chord, flows in the branches of the contour are determined;
- by flows in the branches of the circuit, the costs in each branch and the total costs in all branches of the circuit are considered;
- sequentially changing the value of the fluxes of the chord in the direction of increasing or decreasing, while new flows in the branches of the contour and new costs are determined, which are compared with the previous ones until the minimum is found.
Thus, optimization is carried out. If the costs are calculated by approximation, then it is possible to consider such flows in the chord at which a branch with zero power appears in the loop, which provides a minimum of costs. After that, the current chord is transferred to this branch.
5) After exiting the cycle, the new position of the chords is compared with the previous one. If it does not match, then the next optimization cycle is carried out. If there is a match, the calculation ends. Usually two to three cycles are sufficient.
Example 2.5. Choose the optimal plan for the development of the 220 kV network, which is shown in Figure 2.25-a.
For the network under consideration, the development is associated with an increase in loads and the connection of a new substation. The dotted line shows the possible routes of power transmission lines. Figure 2.25-b shows the cost curves for existing and new power lines and their linear approximations.
The table contains expressions for determining the costs for each branch of the calculation scheme, taking into account the length.
Table 2.6
| Line | Expenses |
| 0-1 | |
| 1-2 |  |
| 2-3 |  |
| 0-3 |
In the design scheme, there is only 1 contour and we will take section 2-3 as the initial position of the chord. Select all branches of the contour for calculating costs. The iterative process is shown in Table 2.7:
Table 2.7
| 0-1 | ||||||
| 1-2 | ||||||
| 2-3 | ||||||
| 0-3 | ||||||
In the initial position of the chord, the costs amounted to 812 thousand rubles. Moving the chord to an adjacent position changed flows and reduced costs. Further movement in the same direction was no longer profitable.
As a result of optimization, a tree is found that corresponds to the minimum cost.
For a network of any complexity, the iterative process converges quickly enough. In this case, special fast algorithms can be used, which are used for open circuits. They are based on the "second address mappings" method.
The tree found as a result of optimization determines the basis of the developing network, which can be supplemented taking into account the requirements of reliability and quality of the regime.
Let us consider the essence of the second address mapping method, which can be used when choosing the optimal tree for a developing network. Consider an open circuit (Fig. 2.26), through which the load from the power center is supplied to several consumers. For given nodal loads, for example, current, the current of each branch is determined by a simple summation of the currents of those nodes that pass through this branch. If the network scheme is specified by pairs of nodes for each branch strictly in the direction from the CPU, which is quite natural, then serial number the start node of a branch in the list (array) of end nodes will allow you to easily organize a passage from any node to the CPU, which must have a special number, for example, negative, to complete the path. The numbers found in this way for each branch are called "second addresses".
Table 2.8
| No. pp | UN | Of the Criminal Code | THAT | UN2 | Branch current (TB) |
| -10 | -10 | 10+4+6+8+5=33 | |||
| 5+4+8=17 | |||||
The table shows the initial data and the stages of calculating the branch currents. The array designations are here: UN - nodes of the beginning, UK - nodes of the end of branches, ТУ - currents of nodes, TV - currents of branches, UN2 - second address mappings.
When analyzing the table, you should pay attention to the fact that when correctly given configuration network, each node number in the UC array can be found in the UC array. As already noted, its place, i.e. the sequence number in this array is called the second address mapping.
Found addresses can be used to determine branch currents, power flows, losses, i.e. to calculate the mode. Consider the procedure for determining the currents along the branches. Here, first, all elements of the DU array are rewritten into the TV array, and then the currents of all nodes, starting from the last one, are superimposed by summation on the currents of the branches through which the node is powered from the power point in accordance with the second addresses.
The calculation of the power flow distribution, taking into account the power and voltage losses is carried out in a similar way.
Consider two algorithms used in the analysis of open circuits.
Figure 2.27 shows a block diagram of the algorithm for determining the second addresses, and Figure 2.28 shows a block diagram of the algorithm for calculating current distribution.
In the contour optimization algorithm of the developing network, the chords are combined into a separate array, where the second addresses for both nodes of the open branch are formed. In the optimization cycle, for each chord, a feeding node is determined, which acts as a CPU and limits the movement of the chord position in the process of one-dimensional optimization.
2.8.6. Branch and Boundary Method (MBB) for choosing the optimal
distribution network
Distribution networks are usually operated in open circuits. Basis for selection new network is the search for the lowest cost tree. The number of possible trees is enormous and is determined by the Trent determinant. The optimal tree can be found by calculating the cost for each tree from the entire set of possible trees. But such a review of all combinations is not realistic even with modern computers.
The essence of the branch-and-bound method consists in dividing the entire set of possible designs into subsets, followed by a simplified assessment of the effectiveness of each and discarding (excluding from further analysis) unpromising subsets. In fact, this is a combinatorial method, but with a purposeful enumeration of options. The method first appeared in 1960 to solve a linear integer programming problem, but went unnoticed, and only in 1963 was it effectively used to solve the problem of a traveling salesman who must go around all commercial points along the shortest path. A similar problem is solved by orienteering athletes.
The original set and all current ones are divided into disjoint subsets, where is the partition number, is the ordinal number of the subset at the partition stage (Fig. 2.29).
For the original set, there is an unknown minimum-cost plan
, (2.44)
where is the exact lower cost bound, which is unknown;
Is the exact lower cost bound that also exists for.
We believe that there is a possibility for a fairly simple determination of some external cost estimate for this subset, for which the condition is satisfied. This estimate can be used to identify “expensive” subsets that can be excluded from further subdivision. To improve reliability in competitive subsets, internal estimates are also considered, for which. External and internal assessments are shown in Figure 2.30.
Perspective subsets are divided similarly. The branching process continues until several options (2 ÷ 4) remain in the subset, or the external and internal estimates =.
Consider the application of the idea of the branch-and-bound method to the problem of finding a new distribution network with a linear approximation of costs in the branch of the calculation scheme
SECTION 1.
GENERAL INFORMATION ABOUT ELECTRICAL INSTALLATIONS
LECTURE 1.
TOPIC 1.1–1.3 (2 hours).
Plan
1.1. Introduction. Brief historical information about the development of the electric power industry.
1.2. Legend, neutral grounding system. Standard scale of powers and voltages.
1.3. The main types of stations: CHP, IES, HPP, NPP, GTU, CCGT. Renewable energy sources: GeoPP, WPP, PES, etc.
Introduction. Brief historical background of development
Electricity
The country's fuel and energy complex covers the receipt, transmission, transformation and use of various types of energy and energy resources.
Power engineering- leading component energy, providing electrification of the country's economy on the basis of rational production and distribution of electricity.
The bulk of electricity is generated by large power plants. Power plants are interconnected with each other and with high-voltage consumers power lines(Power lines) and form electrical systems.
The beginning of the use of electricity was laid by the discovery of the electric arc by V.V. Petrov (1802), the invention of the electric arc candle by P.N. Yablochkov (1876) and A.N. Lodygin of the incandescent lamp (1873–1874).
The industrial use of electricity began with the creation of B. S. Jacobi of the first practically applicable electric motor with rotary motion (1834–1837) and the invention of electroplating (1838). In 1882 N. N. Benardos discovered a method for electric welding of metals.
The first central direct current power plants with a capacity of several dozen, and later several hundred kilowatts were built in the 80s and early 90s of the XIX century. in Moscow, St. Petersburg, Tsarskoe Selo (now Pushkin) and a number of other cities. These power plants had almost no power load, and only since 1892, when an electric tram was launched in Kiev (the first tram in Russia), there is some power load at DC stations.
The low voltage of DC stations (110–220 V) limited their range, and thus their power. The invention of the power transformer (P.N. Yablochkov, 1876) opened up the possibility of using high voltage alternating current and significantly increased the range of power plants.
The first central power plants of single-phase alternating current with a voltage of 2–2.4 kV were built in Odessa (1887), Tsarskoe Selo (1890), Petersburg (1894) and a number of other cities.
The turning point in the development of power supply in general and power plants in particular was the creation in 1888-1889. the outstanding Russian engineer M.O.Dolivo-Dobrovolsky of the three-phase alternating current system. He was the first to create three-phase synchronous generators, three-phase transformers and, which is especially important, three-phase asynchronous electric motors with squirrel-cage and phase rotors.
The first three-phase power plant in Russia with a capacity of 1200 kV ∙ A was built by engineer A. N. Shchensnovich in 1893 in Novorossiysk. The station was intended for the electrification of the elevator.
Summing up the general results of the development of the electric power industry in pre-revolutionary Russia, we can say that the installed capacity of all power plants in Russia in 1913 was about 1,100 MW with the production of electricity about 2 billion kWh per year. In terms of electricity production, Russia ranked 15th in the world.
The GOELRO plan, adopted in 1920, envisaged an increase in the volume of industrial production in the country by about 2 times compared with 1913. The basis of this industrial growth was the construction of 30 district power plants in various regions of the country with a total capacity of 1750 planned for 10-15 years. MW. Electricity generation was supposed to be increased to 8.8 billion kWh per year.
The GOELRO plan was completed by January 1, 1931, that is, in 10 years. The installed capacity of power plants and electricity generation in different historical periods are shown in Table. 1.1.
Table 1.1
The end of the table. 1.1
Since the beginning of the 90s of the XX century. crisis phenomena are taking place in the fuel and energy complex. In some areas, there is a shortage of electricity. The requirements for environmental protection have increased. Russia needs a new energy policy that is flexible enough. The integrity of the electric power complex and the UES of Russia must be preserved. Support for independent energy producers focused on the use of renewable or local energy resources is important.
As a result of the reform, the following results will be achieved:
- the volume of investments in the electric power industry will increase, and as a result, the process of modernization of the industry will accelerate, its efficiency will increase;
- changes in the electric power industry will contribute to the development of related industries: suppliers of equipment, fuel, etc .;
- the average specific power consumption will decrease;
- the reliability of power supply to consumers will increase;
- there will be market, economic incentives for the independent production of electricity and the development of intersystem connections.
The Energy Strategy has determined the volume of commissioning at power plants in Russia for the period until 2020. In the optimistic scenario, they are estimated at 177 million kW, including at HPPs and PSPs - 11.2 million kW, at NPPs - 23 million kW, at TPPs - 143 million kW (Fig. 1.2). At the same time, the volume of inputs for the replacement of obsolete equipment (technical re-equipment) should amount to about 76 million kW. In a moderate version, the need for commissioning of generating capacities will amount to 121 million kW, including 70 million kW for technical re-equipment.
Taking into account the increase in exports, electricity production by 2020 will amount to 1215–1365 billion kWh. At the same time, a significant increase in electricity production is planned: at nuclear power plants - from 142 billion kWh in 2002 to 230–300 billion kWh h in 2020, at hydroelectric power plants - from 164 billion kWh in 2002 to 195-215 billion kWh in 2020.
As at the present time, in the future, the peculiarities of the territorial distribution of fuel and energy resources will determine the structure of capacities commissioning.
Legend, neutral grounding system. Standard power and voltage scale
V electrical circuits ah electrical installations, the following letter and graphic designations of some elements are taken with a single-line image (Table 1.2).
Switches (Q) are designed to turn on and off electrical connections in normal mode, as well as in case of short circuits (SC) with high currents... The switches provided in the USA are called sectional ( QB). In RU at normal work they are closed, but should automatically open in the event of a short circuit.
Disconnectors (QS) isolate (separate) for the duration of the repair, for safety reasons, electrical machines, transformers, power lines, apparatus and other elements from adjacent live parts. They are able to open electrical circuit only in the absence of current in it or at a very low current. Operations with disconnectors and switches must be carried out in a strictly defined order.
Disconnectors are placed so that any apparatus or part of the switchgear can be isolated for safe access and repair. It is also necessary to ground the area of the system to be repaired. For this, the disconnectors provide grounding knives ( QSG), with the help of which the insulated section can be grounded from both sides, i.e. connected to the grounding device. The grounding knives are equipped with separate drives. The normally earthing blades are disabled. Disconnectors are also used for switching from one SN system to another without breaking the current in the circuits.
Current limiting reactors (LR) are inductive resistances designed to limit the short-circuit current in the protected area. Depending on the point of inclusion, sectional and linear reactors are distinguished.
Instrument current transformers(TA) are designed to convert current to values convenient for measurements.
Instrument voltage transformers (TV) are intended for voltages convenient for measurements.
V schematic diagrams Instrument voltage transformers usually do not show.
Valve arresters(FV), as well as surge arresters are designed to protect the insulation of electrical equipment from atmospheric overvoltage. They should be installed near transformers or electrical devices within the station, substation, switchgear.
Examples of designations for conventional graphic and letter codes of elements of electrical circuits are given in table. 1.2.
Table 1.2
| Scheme element name | Graphic designation | Letter code |
| A. Symbols for primary circuit diagrams | ||
| The machine is electric. General designation Note... Inside the circle, it is allowed to place qualifying symbols and additional information, while the diameter of the circle, if necessary, is changed | G, M | |
| Three-phase alternating current generator, for example with a stator winding connected in a star with parallel branches | G | |
| AC motor | M | |
| DC generator (exciter) |  | GE |
| Stator winding (each phase) of an AC machine | – | |
| Excitation winding of a synchronous generator | Lg | |
| Power transformer (autotransformer). General designation Note... It is allowed to place qualifying symbols and Additional information... At the same time, it is allowed to increase the diameter of the circles | T | |
| For example, transformer and autotransformer with on-load tap-changer indicating the group of winding connections |  | T |
| Power transformer, three-winding | T | |
| Bypass switch | QO | |
| Accumulator battery | GB | |
| B. Symbols for circuits remote control, alarms, interlocks and measurements | ||
| Contacts of switching devices: - closing (a); - disconnecting (b) | ||
| Control key with a complex switching circuit | SA | |
| Push-button switch: - with a closing contact (a); - with a break contact (b) | SB SBC SBT | |
| Diode, Zener diode | VD | |
| Transistor | VT | |
| Thyristor | VS | |
| Electromechanical devices with an electromagnetic drive: - switching electromagnet; - shutdown electromagnet | YA YAC YAT | |
| Relay windings, contactors, magnetic starters in control circuits: - current relay; - voltage relay; - time relay; - intermediate relay; - blocking relay against multiple switching on; - command relay; - pressure control relay; - position relay; - command latching relay | K KA KV KT KL KBS KC KSP KQ KQQ | |
| Travel switch: | SQ SQT SQC | |
| Signal lamp: - with a green lens; - with red lens | HL HLG HLR | |
| Indicating measuring devices. General designation Note... Explanatory letters can be inscribed inside the general designation: - ammeter A - voltmeter V - wattmeter W - varmeter var - frequency meter Hz - synchroscope T | P PA PV PW PVA PF PS | |
| Recording devices. General designation. For example: - registering ammeter; - recording voltmeter; - recording frequency meter; - oscilloscope | PSA PSV PSF PO |
Generators, transformers and other electrical elements systems have neutrals, the operating mode of which (the method of working grounding) affects the technical and economic parameters and characteristics of electrical networks (insulation level, requirements for its protection against overvoltage and other abnormal modes, reliability, investment, etc.).
Electric networks, depending on the neutral mode, can be conditionally divided into four groups: ungrounded networks (with isolated neutral) - 660, 1140 V and 3-35 kV, resonant-grounded networks (networks with compensation of capacitive currents) - 3-35 kV, networks effectively grounded 110–220 kV and grounded networks - 220, 380 V and 330–1150 kV.
At small values of capacitive current single-phase earth fault I C(for generators less than 5 A, for networks up to 35 kV less than 10 A) the arc does not arise, or it goes out without re-ignition and accompanying overvoltages. The phase-to-phase voltage triangle remains unchanged, the damaged equipment and network sections remain in operation for several hours necessary to find and disconnect the place of damage, the power supply to consumers is not disturbed (positive effect). The voltages of the undamaged phases rise to the phase-to-phase value, which requires additional costs for insulation (negative effect). In general, given the low voltage class, we have a positive economic effect.
If the single-phase earth fault current exceeds the specified values, the arc is intermittent (repeated repeated arc striking), accompanied by significant overvoltages and the possibility of transition of a single-phase circuit to phase-to-phase (multiphase). Compensation of the capacitive current to earth is carried out using adjustable or unregulated arc-suppressing reactors (resistors) connected to the neutral of generators or transformers. If the arc does not occur, then the process of destruction of the insulation is slowed down.
In electrical networks with effectively grounded neutrals to fulfill the ratio of currents of single-phase and three-phase short circuits, which is desirable according to the operating conditions of electrical devices some of the transformers either earthed neutrals, or in the neutral of some transformers they include special active, reactive, complex or non-linear resistances. Single-phase short circuits are tripped by high-speed protections and circuit breakers. Exposure to overvoltages is short-term. Reduced switching overvoltages. Voltage at single phase short circuit do not exceed 1.4 normal phase voltage or 0.8 linear. The listed factors allow reducing the cost of insulation, which gives a positive economic effect.
In networks 330 kV and above earthing of neutrals of transformers is not allowed.
According to GOST 724-74 and GOST 21128-83 a scale of rated voltages of electrical networks of direct and alternating (50 Hz) currents is installed: direct current up to 1000 V - 12, 24, 36, 48, 60, 110, 220, 440 V; three-phase current up to 1000 V (phase-to-phase voltage) - 12, 24, 36, 42, 220/127, 380/220, 600/380 V, more than 1000 V - (3), 6, 10, 20, 35, 110, ( 150), 220, 330, 500, 750, 1150 kV. For turbine generators in accordance with GOST 533-85 rated voltages, kV - 3.15, 6.3, 10.5, 15.75, 18, 20, 24, rated power, MW - 2.5, 4, 6, 12, 32 , 63, 110, 160, 220, 320, 500, 800, 1000, 1200.
Rated parameters of electrical equipment- these are the parameters that determine the properties of electrical equipment: U n, I n and many others. They are appointed by the manufacturing plants. They are indicated in catalogs and reference books, on equipment shields.
Rated voltage Is the base voltage from a standardized range of voltages that determine the insulation level of the network and electrical equipment. Actual voltages at different points of the system may differ slightly from the nominal, however, they should not exceed the highest operating voltages established for continuous operation.
The rated voltage of generators, transformers, networks and receivers of electricity (electric motors, lamps, etc.) is the voltage at which they are designed for normal operation.
Table 1.3
Three-phase standard voltages
Rated voltages for generators, synchronous compensators, secondary windings power transformers taken 5-10% higher than the nominal voltages of the corresponding networks, which takes into account voltage losses when current flows through the lines.
