Electric capacitor. Operating principle. Capacity. Mathematical model. Schemes. Types, types, categories, classification. Calculation of the Claus process Calculation of the main technological devices

A capacitor is an electronic device designed for accumulation and subsequent release electric charge. The performance of a capacitor is directly related to time. Without considering the change in charge over time, it is impossible to describe the operation of a capacitor.

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5 .1 Initial data

As initial data for the basic mathematical model of the scientific and industrial complex, I used tables of monthly changes in the parameters of the T-180/210-130-1 installation of the Komsomolskaya CHPP-3 for 2009 (Table 5.1).

From this data were taken:

§ pressure and temperature of steam in front of the turbine;

§ turbine net efficiency;

§ heat consumption for electricity production and hourly heat consumption;

§ vacuum in the condenser;

§ temperature of cooling water at the condenser outlet;

§ temperature difference in the condenser

§ steam flow to the condenser.

The use of data from a real turbine plant as initial data can also be considered in the future as confirmation of the adequacy of the resulting mathematical model.

Table 5.1 - Installation parameters T-180/210-130 KTETs-3 for 2009

5 .2 Basic mathematical model

The scientific and industrial complex mathematical model reflects the main processes occurring in the equipment and structures of the low-potential part of thermal power plants. It includes models of R&D equipment and structures used at real thermal power plants and included in the designs of new thermal power plants.

The main elements of the scientific and industrial complex - a turbine, condensers, water-cooling devices, circulation pumping stations and a circulation water pipeline system - are in practice implemented in the form of a number of different standard sizes of equipment and structures. Each of them is characterized by more or less numerous internal parameters, constant or changing during operation, which ultimately determine the degree of efficiency of the power plant as a whole.

When using one type of water coolers at the thermal power plant under study, the amount of heat removed in the coolers to the environment is uniquely determined by the heat transferred to the cooling water in the turbine condensers and auxiliary equipment. The temperature of the cooling water in this case is easily calculated from the characteristics of the cooler. If several coolers are used, connected in parallel or in series, the calculation of the chilled water temperature becomes significantly more complicated, since the temperature of the water behind individual coolers can differ greatly from the temperature of the water after mixing the flows from different coolers. In this case, to determine the temperature of the chilled water, iterative refinement of the water temperature behind each of the jointly operating coolers is necessary.

Mathematical models of water coolers make it possible to determine both the temperature of the cooled water and the loss of water in the coolers due to evaporation, droplet entrainment and filtration into the ground. Replenishment of water losses is carried out either continuously or during some part of the calculation period. It is assumed that additional water is supplied to the circulation path at the point where water flows from the coolers are mixed, and its effect on the temperature of the cooling water is taken into account.

Resistor

The mathematical model of the resistor (Fig. 2.1) is described by Ohm’s law:

U R =IR, or I=gU R, where g=1/R.

In the first case, the voltage drop U R across the resistor is specified, and the desired value is the current I through the resistor. In the second case, the current I is specified through a resistor, and the desired value is U R across the resistor.

nominal resistance value R N;

resistance tolerance R;

temperature coefficient TCR.

Tolerance R is the limit of resistance deviations from the nominal value that arise during the manufacturing process of resistors:

in this case, the resistances of resistors during their production can take on the following values:

If the resistance value R is less than the nominal R H , then the relative deviation R/ R H  0, otherwise R/ R H  0.

Usually the tolerance R is specified as a percentage.

Temperature coefficient TKR sets the resistance value for the current temperature T:

where T N – nominal temperature value taken equal to 27 0 C.

Thus, TKR is equal to the relative deviation of the resistance from the nominal value when the temperature changes by 1 0 C. Sometimes TKR is set in propromil (ppm) :

TKR ppm = TKR  10 6.

Capacitor

The mathematical model of the capacitor (Fig. 2.2) is written as:

or

In the first case, the given value is the voltage drop U C (t) across the capacitor, and the desired value is the current through the capacitor I(). In the second case, the given value is the current through the capacitor I(t), and the desired value is the voltage drop U C (t).

Parameters of the mathematical model:

nominal value of capacitance CH;

capacity tolerance С;

temperature coefficient TKC.

The concept of tolerance and temperature coefficient was given when describing the resistor model.

Inductor

The inductor (Fig. 2.3) is described by two mathematical models:

or

The parameters of the mathematical model are L H , L , TKL, the contents of which are similar to those considered for the resistor and capacitor.

Real models of a resistor, capacitor, and inductance are more complex than those discussed here.

Thus, models of even the simplest components can be quite complex if a high degree of adequacy of the parameters of a physical object and its mathematical model is required.

Double winding transformer

The transformer (Fig. 2.4) can be represented in the form of the following mathematical model:

where L 1, L 2 are the inductances of the windings,

M 12 – mutual inductance.

The model parameters are the values ​​of L 1, L 2 and the coupling coefficient

The value of K SV ranges from zero to one. The value K SV =1 indicates the presence of a rigid connection between the windings, which is typical for matching and power transformers and for output transformers of amplifiers. K value NE<1 говорит о наличии в трансформаторе индуктивности рассеяния, что приводит к уменьшению коэффициента передачи на высоких частотах. Такие трансформаторы используются в резонансных контурах фильтров.

Sometimes the following parameters are specified:

In addition to the listed parameters, you need to indicate the method of switching on the windings - consonant or counter.

Zubov D.I. 1 Suvorov D.M. 2

1 ORCID: 0000-0002-8501-0608, Graduate Student; 2 ORCID: 0000-0001-7415-3868, Candidate of Technical Sciences, Associate Professor, Vyatka State University (VyatSU)

DEVELOPMENT OF A MATHEMATICAL MODEL OF STEAM TURBINE T-63/76-8.8 AND ITS VERIFICATION FOR CALCULATION OF MODES WITH SINGLE-STAGE HEATING OF NETWORK WATER

Annotation

The relevance of creating reliable mathematical models of equipment involved in the generation of electrical and thermal energy is determined in order to optimize their operating modes. The main methods and results of development and verification of the mathematical model of the T-63/76-8.8 steam turbine are presented.

Key words: mathematical modeling, steam turbines, combined-cycle plants, district heating, energy.

Zubov D.I. 1, Suvorov D.M. 2

1 ORCID: 0000-0002-8501-0608, postgraduate student; 2 ORCID: 0000-0001-7415-3868, PhD in Engineering, associate professor, Vyatka State University

DEVELOPMENT OF MATHEMATICAL MODEL OF THE STEAM TURBINE T-63/76-8.8 AND ITS VERIFICATION FOR CALCULATION REGIMES WITH SINGLE STAGE HEATING OF DELIVERY WATER

Abstract

The article defines the relevance of creating reliable mathematical models of the equipment involved in the generation of electricity and heat energy for the purpose of optimization of their work. The article presents the basic methods and results of the development and verification of a mathematical model of the steam turbine T-63/76-8,8.

Keywords: mathematical modeling, steam turbines, combined-cycle plants, district heating, energetics.

In the context of a shortage of investment resources in the Russian energy sector, areas of research related to identifying reserves for increasing the efficiency of already operating turbine units are becoming a priority. Market mechanisms in the energy sector force us to especially carefully evaluate the existing production capabilities of industry enterprises and, on this basis, provide favorable financial and economic conditions for the participation of thermal power plants in the electricity (capacity) market.

One of the possible ways to save energy at thermal power plants is the development, research and implementation of optimal variable operating modes and improved thermal schemes, including by ensuring maximum electricity generation from thermal consumption, optimal ways to obtain additional power and optimization of operating modes of both individual turbine units and thermal power plants generally .

Typically, the development of turbine operating modes and assessment of their efficiency is carried out by plant personnel using standard energy characteristics that were compiled during testing of the prototype turbine samples. However, over 40-50 years of operation, the internal characteristics of the turbine compartments, the composition of the equipment and the thermal design of the turbine unit inevitably change, which requires regular review and adjustment of the characteristics.

Thus, to optimize and accurately calculate the operating modes of turbine units, mathematical models must be used that include adequate flow and power characteristics of all turbine compartments, starting from the control stage and ending with the low pressure part (LPP). It should be noted that when constructing factory diagrams of heating turbine modes, the indicated adequate characteristics of the compartments were not used; these characteristics themselves were approximated by linear dependencies, and for this and other reasons, the use of these diagrams to optimize modes and determine the energy effect can lead to significant errors.

After the commissioning of the PGU-220 unit at the Kirov CHPP-3 in 2014, the task arose of optimizing its operating modes, in particular, maximizing the generation of electrical power while maintaining a given temperature schedule. Taking into account the reasons mentioned above, as well as the incompleteness of the regulatory characteristics provided by the plant, it was decided to create a mathematical model of the PGU-220 unit of the Kirov CHPP-3, which will allow solving this problem. The mathematical model should make it possible to calculate with high accuracy the operating modes of the unit, which consists of one gas turbine unit GTE-160, waste heat boiler type E-236/40.2-9.15/1.5-515/298-19.3 and one steam turbine unit T-63/76-8.8. The schematic diagram of the power unit is shown in Figure 1.

At the first stage, the problem of creating and verifying a mathematical model of a steam turbine unit as part of the PGU-220 is solved. The model is built on the basis of calculation of its thermal circuit using the flow and power characteristics of its compartments. Since the factory characteristics of the turbine unit did not contain data on the efficiency values ​​of the turbine compartments, which is necessary when constructing their characteristics, it was decided to, as a first approximation, determine the missing indicators using the data factory calculation.

For this purpose, the turbine was conventionally divided into several sections: to the section for mixing high and low pressure steam, from the mixing section to the upper heating extraction (UHE), from the upper to the lower heating extraction (LTO), from the lower heating extraction to the condenser. For the first three compartments, the relative internal efficiency varies in the range of 0.755-0.774, and for the last, namely the compartment between the lower heating extraction and the condenser, it varies depending on the volumetric flow rate of steam into the condenser (in this case, the volumetric flow rate of steam into the condenser was determined based on the mass steam flow and density by pressure and degree of dryness). Based on the factory data, the dependence presented in Figure 2 was obtained, which is further used in the model (a curve approximating the experimental points).

Figure 2. Dependence of the efficiency of the compartment between the LHE and the condenser on the volumetric flow rate of steam into the condenser

If you have a known temperature graph of the heat supply source, it is possible to determine the temperature of the network water after the upper network heater, and then, given the temperature pressure of the heater and the pressure loss in the steam line, determine the pressure in the WHE. But using this method, it is impossible to determine the temperature of the network water after the lower network heater with two-stage heating, which is necessary to determine the steam pressure in the LHE. To solve this problem, in the course of an experiment organized according to the current methodology, the throughput coefficient of the intermediate compartment (between the WTO and the LTO) was obtained, which is determined by the formula resulting from the well-known Stodola-Flügel equation:

Where

k by– throughput coefficient of the intermediate compartment, t/(h∙bar);

G by– steam consumption through the intermediate compartment, t/h;

p in– pressure in the upper heating outlet, bar;

p n– pressure in the lower heating outlet, bar.

As can be seen from the diagram presented in Figure 1, the T-63/76-8.8 turbine does not have regenerative steam extraction, since the entire regeneration system is replaced by a gas condensate heater located in the tail part of the waste heat boiler. In addition, during the experiments, the upper heating exhaust of the turbine was turned off due to production needs. Thus, the steam flow through the intermediate compartment could, with some assumptions, be taken as the sum of the steam flow into the high and low pressure circuit of the turbine:

Where

G vd– steam flow into the turbine high-pressure circuit, t/h;

G nd– steam flow into the low pressure circuit of the turbine, t/h.

The results of the tests are presented in Table 1.

The value of the intermediate compartment throughput coefficient obtained in various experiments varies within 0.5%, which indicates that the measurements and calculations were carried out with an accuracy sufficient for further construction of the model.

Table 1. Determination of the throughput of the intermediate compartment

When constructing the model, the following assumptions were also made, corresponding to the factory calculation data:

• if the volumetric flow rate in the low pressure pump is greater than the calculated one, it is considered that the efficiency of the last section of the steam turbine is 0.7;
• network water pressure at the heater inlet is 1.31 MPa;
• network water pressure at the outlet of the heater is 1.26 MPa;
• return network water pressure 0.5 MPa.

Based on the design and operational documentation for PGU-220, as well as data obtained during testing, a model of the heating part of the unit was created at VyatGU. Currently, the model is used to calculate turbine operating modes for single-stage heating.

The value of the throughput coefficient of the intermediate compartment, determined experimentally, was used to verify the turbine model for single-stage heating. The results of model verification, namely the difference between the actual (based on measurement results) and calculated (based on the model) electrical load obtained at an equal heating load, are presented in Table 2.

Table 2. Comparison of calculated and experimental data for single-stage heating of network water.

The comparison shows that as the load on the gas turbine unit decreases, the discrepancy between the calculated and experimental data increases. This may be influenced by the following factors: unaccounted for leaks through end seals and in other elements; changes in the volumetric flow rate of steam in the turbine compartments, which does not allow determining their exact efficiency; inaccuracy of measuring instruments.

At this stage of development, the mathematical model can be called satisfactory, since the accuracy of the calculated data in comparison with the experimental data is quite high when working with a fresh steam flow rate close to the nominal one. This allows, on its basis, to carry out calculations in order to optimize the heating modes of operation of CCGT and CHP plants as a whole, especially when operating according to the thermal and electrical schedules at the maximum or close to it steam flow to the steam turbine. At the next stage of development, it is planned to debug and verify the model when working with two-stage heating of network water, as well as collecting and analyzing data to replace the standard factory energy characteristics of the flow part with characteristics that are significantly closer to the actual ones.

Literature

1. Tatarinova N.V., Efros E.I., Sushikh V.M. Results of calculations using mathematical models of variable operating modes of cogeneration steam turbine units under real operating conditions // Perspectives of Science. – 2014. – No. 3. – pp. 98-103.
2. Rules for the technical operation of power plants and networks of the Russian Federation. – M.: Publishing House NC ENAS, 2004. – 264 p.
3. Suvorov D.M. On simplified approaches to assessing the energy efficiency of district heating // Electric Stations. – 2013. – No. 2. – P. 2-10.
4. Cogeneration steam turbines: increasing efficiency and reliability / Simoyu L.L., Efros E.I., Gutorov V.F., Lagun V.P. St. Petersburg: Energotekh, 2001.
5. Sakharov A.M. Thermal tests of steam turbines. – M.: Energoatomizdat, 1990. – 238 p.
6. Variable operating mode of steam turbines / Samoilovich G.S., Troyanovsky B.M. M.: State Energy Publishing House, 1955. – 280 pp.: ill.

References

1. Tatarinova N.V., Jefros E.I., Sushhih V.M. Rezul’taty raschjota na matematicheskih modeljah peremennyh rezhimov raboty teplofikacionnyh paroturbinnyh ustanovok v real’nyh uslovijah jekspluatacii // Perspektivy nauki. – 2014. – No. 3. – P. 98-103.
2. Pravila tehnicheskoj jekspluatacii jelektricheskih stancij i setej Rossijskoj Federacii. – M.: Izd-vo NC JeNAS, 2004. – 264 p.
3. Suvorov D.M. Ob uproshhjonnyh podhodah pri ocenke jenergeticheskoj jeffektivnosti teplofikacii // Jelektricheskie stancii. – 2013. – No. 2. – P. 2-10.
4. Teplofikacionnye parovye turbiny: povyshenie jekonomichnosti i nadjozhnosti / Simoju L.L., Jefros E.I., Gutorov V.F., Lagun V.P. SPb.:Jenergoteh, 2001.
5. Sakharov A.M. Teplovye ispytanija parovyh turbine. – M.:Jenergoatomizdat, 1990. – 238 p.
6. Peremennyj rezhim raboty parovyh turbin / Samojlovich G.S., Trojanovskij B.M. M.: Gosudarstvennoe Jenergeticheskoe Izdatel’stvo, 1955. – 280p.

When studying the dynamics of turbine control, the change in pressure pg in the condenser is usually not taken into account, assuming lg = kr £ 1pl = 0. However, in a number of cases the validity of this assumption is not obvious. Thus, during emergency control of heating turbines, opening the rotary diaphragm can quickly increase the steam flow through the LPC. But at low flow rates of circulating water, characteristic of conditions of high thermal loads of the turbine, condensation of this additional steam can proceed slowly, which will lead to an increase in pressure in the condenser and a decrease in power gain. A model that does not take into account the processes in the capacitor will give an overestimated efficiency of the noted method of increasing injectivity compared to the actual one. The need to take into account processes in the condenser also arises when using a condenser or its special compartment as the first stage of heating network water in heating turbines, as well as when regulating heating turbines operating at high thermal loads using the method of sliding back pressure in the condenser and in a number of other cases.
The condenser is a surface-type heat exchanger, and the above principles of mathematical modeling of surface heaters are fully applicable to it. Just as for them, for a capacitor one should write down the equations of the water path either assuming the parameters are distributed [equations (2.27) - (2.33)], or approximately taking into account the distribution of parameters by dividing the path into a number of sections with lumped parameters [equations (2.34) - ( 2.37)]. These equations must be supplemented with equations (2.38)–(2.40) for heat accumulation in the metal and equations for the vapor space. When modeling the latter, one should take into account the presence in the steam space, along with steam, of a certain amount of air due to its influx through leaks in the vacuum part of the turbine unit. The fact that the air does not condense determines the dependence of the pressure change processes in the condenser on its concentration. The latter is determined both by the amount of inflow and by the operation of the ejectors, pumping air out of the condenser along with part of the steam. Therefore, the mathematical model of the vapor space should, in essence, be a model of the “condenser vapor space - ejectors” system.