Comprehensive modernization of the steam turbine PT-80/100-130/13
The purpose of the modernization is to increase the electrical and heating power of the turbine with an increase in the efficiency of the turbine plant. Modernization in the scope of the main option consists in installing HPC honeycomb shroud seals and replacing the medium pressure flow path with the manufacture of a new LP rotor in order to increase the throughput of the HPP to 383 t/h. At the same time, the range of pressure regulation in the production extraction is maintained, the maximum steam flow to the condenser does not change.
Replaceable units when upgrading the turbine unit in the scope of the basic option:
- Installation of honeycomb shroud seals 1-17 HPC stages;
- Guide apparatus TsSND;
- Saddles of the RC ChSD with a larger flow area with the completion of the steam boxes of the upper half of the ChSD body for the installation of new covers;
- SD control valves and cam-distributing device;
- Diaphragms of 19-27 stages of TsSND, equipped with over-shroud honeycomb seals and sealing rings with twisted springs;
- SND rotor with installed new working blades of 18-27 stages of TsSND with integrally milled bandages;
- Diaphragm holders No. 1, 2, 3;
- Front end seal cage and o-rings with coil springs;
- Attached discs 28, 29, 30 steps are stored in accordance with existing structure, which allows you to reduce the cost of upgrading (provided that old attachment discs are used).
As a result of modernization according to the main option, the following is achieved:
- Increasing the maximum electric power of the turbine up to 110 MW and the power of heat extraction up to 168.1 Gcal/h due to the reduction of industrial extraction.
- Ensuring reliable and maneuverable operation of the turbine plant in all operating modes, including at the lowest possible pressures in industrial and heat extraction.
- Increasing the efficiency of the turbine plant;
- Ensuring the stability of the achieved technical and economic indicators during the overhaul period.
The effect of modernization in the scope of the main offer:
| Turbine unit modes | Electric power, MW | Steam consumption for heating, t/h | Steam consumption for production, t/h |
Condensing | |||
Nominal | |||
Max Power | |||
With maximum | |||
Increasing the efficiency of the CHSD | |||
Increasing the efficiency of the HPC | |||
Additional offers (options) for modernization
- Modernization of the casing of the HPC control stage with the installation of over-shroud honeycomb seals
- Installing diaphragms of the last stages with a tangential bulk
- Highly hermetic seals for HPC control valve stems
The effect of modernization by additional options
№ | Name | Effect |
Modernization of the casing of the HPC control stage with the installation of over-shroud honeycomb seals | Power increase by 0.21-0.24 MW |
|
Installing diaphragms of the last stages with a tangential bulk | Condensing mode: |
|
Rotary diaphragm seal | Increasing the efficiency of the turbine plant when operating in the mode with a fully closed rotary diaphragm 7 Gcal/h |
|
Replacement of shroud seals of HPC and HPC with honeycomb ones | Increasing the efficiency of cylinders (high pressure cylinder by 1.2-1.4%, TsSND by 1%); |
|
Replacement of HPC control valves | Power increase by 0.02-0.11 MW |
|
Installation of LPC honeycomb end seals | Elimination of air suction through the end seals |
Introduction
For large plants of all industries with high heat consumption, the optimal system of energy supply is from a district or industrial CHP.
The process of generating electricity at CHP is characterized by increased thermal efficiency and higher energy indicators compared to condensing power plants. This is due to the fact that the waste heat of the turbine, which is diverted to a cold source (heat receiver at external consumer) is used in it.
In the work, the calculation of the thermal scheme of the power plant based on the production heat-and-power turbine PT-80/100-130/13, operating in the design mode at outdoor air temperature, is made.
The task of calculating the thermal scheme is to determine the parameters, costs and directions of the flow of the working fluid in units and units, as well as the total steam consumption, electric power and indicators of the thermal efficiency of the station.
Description of the principal thermal diagram of the PT-80/100-130/13 turbine plant
The 80 MW electric power unit consists of a drum boiler high pressureЕ-320/140, PT-80/100-130/13 turbines, generator and auxiliary equipment.
The power unit has seven selections. It is possible to carry out two-stage heating of network water in the turbine plant. There is a main and peak boiler, as well as a PVC, which turns on if the boilers cannot provide the required heating of the network water.
Fresh steam from the boiler with a pressure of 12.8 MPa and a temperature of 555 0 C enters the turbine HPC and, after exhausting, is sent to the turbine CSD, and then to the LPC. Having worked out, the steam flows from the LPC to the condenser.
The power unit for regeneration has three high-pressure heaters (HPH) and four low-pressure heaters (LPH). The heaters are numbered from the tail of the turbine unit. The condensate of the heating steam HPH-7 is cascaded into HPH-6, into HPH-5 and then into the deaerator (6 atm). Condensate drain from LPH4, LPH3 and LPH2 is also carried out in cascade in LPH1. Then, from the LPH1, the condensate of the heating steam is sent to the CM1 (see PRT2).
The main condensate and feed water are heated sequentially in PE, SH and PS, in four low-pressure heaters (LPH), in a 0.6 MPa deaerator and in three high-pressure heaters (HPV). Steam is supplied to these heaters from three adjustable and four unregulated turbine steam extractions.
The unit for heating water in the heating network has a boiler plant, consisting of a lower (PSG-1) and an upper (PSG-2) network heaters, fed respectively with steam from the 6th and 7th selections, and PVK. Condensate from the upper and lower network heaters is supplied by drain pumps to mixers SM1 between LPH1 and LPH2 and SM2 between heaters LPH2 and LPH3.
Heating temperature feed water lies within (235-247) 0 C and depends on the initial pressure of fresh steam, the amount of subheating in HPH7.
The first steam extraction (from HPC) is used to heat feed water in HPH-7, the second steam extraction (from HPC) - to HPH-6, the third (from HPC) - to HPH-5, D6ata, for production; the fourth (from CSD) - in LPH-4, the fifth (from CSD) - in LPH-3, the sixth (from CSD) - in LPH-2, deaerator (1.2 atm), in PSG2, in PSV; the seventh (from CND) - in PND-1 and PSG1.
To make up for losses, a fence is provided in the scheme raw water. Raw water is heated in the raw water heater (RWS) to a temperature of 35 ° C, then, after passing chemical treatment, enters the deaerator 1.2 ata. To ensure heating and deaeration of additional water, the heat of steam from the sixth extraction is used.
Steam from the sealing rods in the amount of D pcs = 0.003D 0 goes to the deaerator (6 atm). Steam from the extreme seal chambers is directed to the SH, from the middle seal chambers to the PS.
Boiler blowdown - two-stage. Steam from the expander of the 1st stage goes to the deaerator (6 atm), from the expander of the 2nd stage to the deaerator (1.2 atm). Water from the expander of the 2nd stage is supplied to the network water main, to partially replenish network losses.
Figure 1. Principal thermal scheme CHPP based on TU PT-80/100-130/13
3.3.4 Steam turbine plant PT-80/100-130/13
Heating steam turbine PT-80/100-130/13 with industrial and heating steam extraction is designed for direct drive of electric generator TVF-120-2 with a rotation speed of 50 rpm and heat release for production and heating needs.
Power, MW
nominal 80
maximum 100
Rated steam parameters
pressure, MPa 12.8
temperature, 0 C 555
Consumption of extracted steam for production needs, t/h
nominal 185
maximum 300
upper 0.049-0.245
lower 0.029-0.098
Production selection pressure 1.28
Water temperature, 0 С
nutritional 249
cooling 20
Cooling water consumption, t/h 8000
The turbine has the following adjustable steam extractions:
production with an absolute pressure of (1.275 ± 0.29) MPa and two heating selections - the upper one with an absolute pressure in the range of 0.049-0.245 MPa and the lower one with a pressure in the range of 0.029-0.098 MPa. The heating extraction pressure is regulated by means of one control diaphragm installed in the upper heating extraction chamber. Regulated pressure in the heating outlets is maintained: in the upper outlet - when both heating outlets are turned on, in the lower outlet - when one lower heating outlet is turned on. Network water through the network heaters of the lower and upper stages of heating must be passed sequentially and in equal quantities. The flow of water passing through the network heaters must be controlled.
The turbine is a single-shaft two-cylinder unit. The HPC flow path has a single-row control stage and 16 pressure stages.
The flow part of the LPC consists of three parts:
the first (up to the upper heating outlet) has a control stage and 7 pressure stages,
the second (between the heating taps) two pressure stages,
the third - the control stage and two pressure stages.
The high pressure rotor is one-piece forged. The first ten disks of the low-pressure rotor are forged integrally with the shaft, the remaining three disks are mounted.
The steam distribution of the turbine is nozzle. At the exit from the HPC, part of the steam goes to controlled production extraction, the rest goes to the LPC. Heating extractions are carried out from the corresponding LPC chambers.
To reduce the warm-up time and improve start-up conditions, steam heating of flanges and studs and live steam supply to the HPC front seal are provided.
The turbine is equipped with a barring device that rotates the shafting of the turbine unit at a frequency of 3.4 rpm.
The turbine blade apparatus is designed to operate at a mains frequency of 50 Hz, which corresponds to a turbine rotor speed of 50 rpm (3000 rpm). Long-term operation of the turbine is allowed with a frequency deviation in the network of 49.0-50.5 Hz.
3.3.5 Steam turbine plant Р-50/60-130/13-2
The R-50/60-130/13-2 counterpressure steam turbine is designed to drive the TVF-63-2 electric generator with a rotation speed of 50 s -1 and to release steam for production needs.
The nominal values of the main parameters of the turbine are given below:
Power, MW
Rated 52.7
Maximum 60
Initial steam parameters
Pressure, MPa 12.8
Temperature, o C 555
Pressure in the exhaust pipe, MPa 1.3
The turbine has two unregulated steam extractions intended for heating feed water in high pressure heaters.
Turbine design:
The turbine is a single-cylinder unit with a single-crown control stage and 16 pressure stages. All rotor discs are forged integrally with the shaft. Steam distribution of the turbine with bypass. Fresh steam is supplied to a free-standing steam box in which an automatic shutter valve is located, from where the steam passes through bypass pipes to four control valves.
The turbine blade apparatus is designed to operate at a frequency of 3000 rpm. Long-term operation of the turbine is allowed with a frequency deviation in the network of 49.0-50.5 Hz
The turbo unit is equipped protective devices for joint shutdown of the HPH with simultaneous activation of the bypass line by giving a signal. Atmospheric diaphragm valves installed on the exhaust pipes and opening when the pressure in the pipes rises to 0.12 MPa.
3.3.6 Steam turbine plant T-110/120-130/13
The T-110/120-130/13 heating steam turbine with heating steam extraction is designed for direct drive of the TVF-120-2 electric generator with a rotation speed of 50 rpm and heat supply for heating needs.
The nominal values of the main parameters of the turbine are given below.
Power, MW
nominal 110
maximum 120
Rated steam parameters
pressure, MPa 12.8
temperature, 0 C 555
nominal 732
maximum 770
Limits of steam pressure change in controlled heating extraction, MPa
upper 0.059-0.245
lower 0.049-0.196
Water temperature, 0 С
nutritional 232
cooling 20
Cooling water consumption, t/h 16000
Vapor pressure in the condenser, kPa 5.6
The turbine has two heating extractions - lower and upper, designed for stepwise heating of network water. In case of stepwise heating of network water with steam from two heating extractions, the control maintains the set temperature of network water downstream of the upper network heater. When heating network water with one lower heating extraction, the temperature of network water is maintained behind the lower network heater.
Pressure in adjustable heating extractions can vary within the following limits:
in the upper 0.059 - 0.245 MPa with two heating extractions turned on,
at the bottom 0.049 - 0.196 MPa with the top heating off.
Turbine T-110/120-130/13 is a single-shaft unit consisting of three cylinders: high pressure cylinder, low pressure cylinder, low pressure cylinder.
The HPC is single-flow, has a two-row control stage and 8 pressure stages. The high-pressure rotor is one-piece forged.
TsSD - also single-flow, has 14 steps of pressure. The first 8 disks of the medium pressure rotor are forged integrally with the shaft, the remaining 6 are mounted. The guide vane of the first stage of the TsSD is installed in the housing, the remaining diaphragms are installed in holders.
LPC - double-flow, has two stages in each stream of left and right rotation (one control and one pressure stage). The length of the working blade of the last stage is 550 mm, the average diameter of the impeller of this stage is 1915 mm. The low pressure rotor has 4 mounted discs.
In order to facilitate the start-up of the turbine from a hot state and increase its maneuverability during operation under load, the temperature of the steam supplied to the penultimate chamber of the HPC front seal is increased by mixing hot steam from the control valve stems or from the main steam pipeline. From the last compartments of the seals, the vapor-air mixture is sucked off by the suction ejector from the seals.
To reduce the heating time and improve the conditions for starting the turbine, steam heating of the HPC flanges and studs is provided.
The turbine blade apparatus is designed to operate at a mains frequency of 50 Hz, which corresponds to a turbine rotor speed of 50 rpm (3000 rpm).
Long-term operation of the turbine is allowed with a frequency deviation in the network of 49.0-50.5 Hz. In emergency situations for the system, short-term operation of the turbine is allowed at a network frequency below 49 Hz, but not below 46.5 Hz (the time is specified in the technical specifications).
Information about the work "Modernization of the Almaty CHP-2 by changing the water-chemical regime of the make-up water treatment system in order to increase the temperature of the network water to 140-145 C"
- tutorial
Preface to the first part
Modeling steam turbines is a daily task for hundreds of people in our country. Instead of a word model it is customary to say flow characteristic. The consumption characteristics of steam turbines are used in solving such problems as calculating the specific consumption of standard fuel for electricity and heat produced by CHPs; optimization of CHPP operation; planning and maintenance of CHP modes.
I have developed new flow characteristic of a steam turbine is the linearized flow characteristic of the steam turbine. The developed flow characteristic is convenient and effective in solving these problems. However, to date, it has been described only in two scientific papers:
- Optimization of CHP operation in the conditions of the wholesale electricity and power market in Russia;
- Computational Methods for Determination of Specific Consumptions of Equivalent Fuel of Thermal Power Plant for Electricity and Thermal Energy Supplied in Combined Generation Mode.
And now in my blog I would like:
- firstly, to answer the main questions about the new flow characteristic in a simple and accessible language (see Linearized flow characteristic of a steam turbine. Part 1. Basic questions);
- secondly, to provide an example of constructing a new consumption characteristic, which will help to understand both the construction method and the properties of the characteristic (see below);
- thirdly, to refute two well-known statements regarding the operating modes of a steam turbine (see Linearized flow characteristic of a steam turbine. Part 3. Debunking myths about the operation of a steam turbine).
1. Initial data
The initial data for constructing a linearized flow characteristic can be
- actual power values Q 0 , N, Q p, Q t measured during the operation of the steam turbine,
- nomograms q t gross from normative and technical documentation.
In cases where the actual values of Q 0 , N, Q p, Q t are not available, it is possible to process nomograms q t gross. These, in turn, were derived from measurements. Read more about testing turbines in Gorshtein V.M. and etc. Methods for optimizing power system modes.
2. Algorithm for constructing a linearized flow characteristic
The construction algorithm consists of three steps.
- Translation of nomograms or measurement results into tabular form.
- Linearization of the flow characteristics of a steam turbine.
- Determination of the boundaries of the control range of the steam turbine.
When working with nomograms q t gross, the first step is carried out quickly. Such work is called digitization(digitization). Digitizing 9 nomograms for the current example took me about 40 minutes.
The second and third steps require the application of math packages. I love and have been using MATLAB for many years. My example of constructing a linearized flow characteristic is made in it. An example can be downloaded from the link, run and independently understand the method of constructing a linearized flow characteristic.
The flow characteristic for the considered turbine was built for the following fixed values of the mode parameters:
- single stage operation,
- medium pressure steam pressure = 13 kgf/cm2,
- low pressure steam pressure = 1 kgf/cm2.
1) Nomograms of specific consumption q t gross for electricity generation (marked red dots are digitized - transferred to the table):
- PT80_qt_Qm_eq_0_digit.png,
- PT80_qt_Qm_eq_100_digit.png,
- PT80_qt_Qm_eq_120_digit.png,
- PT80_qt_Qm_eq_140_digit.png,
- PT80_qt_Qm_eq_150_digit.png,
- PT80_qt_Qm_eq_20_digit.png,
- PT80_qt_Qm_eq_40_digit.png,
- PT80_qt_Qm_eq_60_digit.png,
- PT80_qt_Qm_eq_80_digit.png.
2) Digitization result(each csv file has a corresponding png file):
- PT-80_Qm_eq_0.csv,
- PT-80_Qm_eq_100.csv,
- PT-80_Qm_eq_120.csv,
- PT-80_Qm_eq_140.csv,
- PT-80_Qm_eq_150.csv,
- PT-80_Qm_eq_20.csv,
- PT-80_Qm_eq_40.csv,
- PT-80_Qm_eq_60.csv,
- PT-80_Qm_eq_80.csv.
3) MATLAB script with calculations and plotting graphs:
- PT_80_linear_characteristic_curve.m
4) The result of digitizing nomograms and the result of constructing a linearized flow characteristic in tabular form:
- PT_80_linear_characteristic_curve.xlsx.
Step 1. Translation of nomograms or measurement results into a tabular form
1. Processing of initial data
The initial data for our example are nomograms q t gross.
A special tool is needed to digitize many nomograms. I have used the web application many times for this purpose. The application is simple, convenient, but does not have sufficient flexibility to automate the process. Some of the work has to be done by hand.
At this step, it is important to digitize the extreme points of the nomograms that set the boundaries of the control range of the steam turbine.
The job was to mark the points of the consumption characteristic in each png file using the application, download the resulting csv and collect all the data in one table. The result of digitization can be found in the file PT-80-linear-characteristic-curve.xlsx, sheet "PT-80", table "Initial data".
2. Reduction of units of measurement to units of power
$$display$$\begin(equation) Q_0 = \frac (q_T \cdot N) (1000) + Q_P + Q_T \qquad (1) \end(equation)$$display$$
and we bring all the initial values to MW. The calculations were carried out using MS Excel.
The resulting table "Initial data (power units)" is the result of the first step of the algorithm.
Step 2. Linearization of the flow characteristic of the steam turbine
1. Checking the work of MATLAB
At this step, you need to install and open MATLAB version 7.3 or higher (this is old version, current 8.0). In MATLAB, open the PT_80_linear_characteristic_curve.m file, run it and make sure it works. Everything works correctly if, as a result of running the script in command line you see the following message:
Values are read from file PT_80_linear_characteristic_curve.xlsx in 1 sec. = 37
If you have any errors, then figure it out on your own how to fix them.
2. Calculations
All calculations are implemented in the PT_80_linear_characteristic_curve.m file. Let's consider it in parts.
1) Specify the name of the source file, sheet, range of cells containing the table “Initial data (capacity units)” obtained at the previous step.
XLSFileName = "PT_80_linear_characteristic_curve.xlsx"; XLSSheetName = "PT-80"; XLSRange="F3:I334";
2) We consider the initial data in MATLAB.
sourceData = xlsread(XLSFileName, XLSSheetName, XLSRange); N = sourceData(:,1); Qm = sourceData(:,2); Ql = sourceData(:,3); Q0 = sourceData(:,4); fprintf("Values read from file %s in %1.0f seconds\n", XLSFileName, toc);
We use the variable Qm for the flow rate of medium pressure steam Q p, index m from middle- average; similarly, we use the variable Ql for the flow rate of low-pressure steam Q n , the index l from low- short.
3) Let's define coefficients α i .
Recall the general formula for the flow characteristic
$$display$$\begin(equation) Q_0 = f(N, Q_P, Q_T) \qquad (2) \end(equation)$$display$$
and specify independent (x_digit) and dependent (y_digit) variables.
x_digit = ; % electricity N, industrial steam Qp, heating steam Qt, unit vector y_digit = Q0; % consumption of live steam Q0
If you don’t understand why there is a unit vector (last column) in the x_digit matrix, then read the materials on linear regression. On the topic of regression analysis, I recommend the book Draper N., Smith H. Applied regression analysis. New York: Wiley, In press, 1981. 693 p. (available in Russian).
Steam turbine linearized flow characteristic equation
$$display$$\begin(equation) Q_0 = \alpha_N \cdot N + \alpha_P \cdot Q_P + \alpha_T \cdot Q_T + \alpha_0 \qquad (3) \end(equation)$$display$$
is a multiple linear regression model. The coefficients α i will be determined using "the great good of civilization"- the method of least squares. Separately, I note that the method of least squares was developed by Gauss in 1795.
In MATLAB, this is done in one line.
A = regress(y_digit, x_digit); fprintf("Coefficients: a(N) = %4.3f, a(Qp) = %4.3f, a(Qt) = %4.3f, a0 = %4.3f\n",... A);
Variable A contains the desired coefficients (see message at the MATLAB command line).
Thus, the resulting linearized flow characteristic of the steam turbine PT-80 has the form
$$display$$\begin(equation) Q_0 = 2.317 \cdot N + 0.621 \cdot Q_P + 0.255 \cdot Q_T + 33.874 \qquad (4) \end(equation)$$display$$
4) Let us estimate the linearization error of the obtained flow characteristic.
y_model = x_digit * A; err = abs(y_model - y_digit) ./ y_digit; fprintf("Mean error = %1.3f, (%4.2f%%)\n\n", mean(err), mean(err)*100);
Linearization error is 0.57%(see message at MATLAB command line).
To assess the convenience of using the linearized flow characteristic of a steam turbine, we solve the problem of calculating the flow rate of high pressure steam Q 0 at known values loads N, Q p, Q t.
Let N = 82.3 MW, Q p = 55.5 MW, Q t = 62.4 MW, then
$$display$$\begin(equation) Q_0 = 2.317 \cdot 82.3 + 0.621 \cdot 55.5 + 0.255 \cdot 62.4 + 33.874 = 274.9 \qquad (5) \end(equation)$$ display$$
Let me remind you that the average calculation error is 0.57%.
Let us return to the question, why is the linearized flow characteristic of a steam turbine fundamentally more convenient than the nomograms of the specific flow rate q t gross for power generation? To understand the fundamental difference in practice, solve two problems.
- Calculate Q 0 to the specified accuracy using the nomograms and your eyes.
- Automate the process of calculating Q 0 using nomograms.
Obviously, in the first problem, determining the values of q t gross by eye is fraught with gross errors.
The second task is cumbersome to automate. Because the q values are grossly non-linear, then for such automation the number of digitized points is ten times greater than in the current example. One digitization is not enough, it is also necessary to implement an algorithm interpolation(finding values between points) non-linear gross values.
Step 3. Determining the boundaries of the control range of the steam turbine
1. Calculations
To calculate the adjustment range, we use another "Blessing of Civilization"- by the convex hull method, convex hull.
In MATLAB, this is done as follows.
indexCH = convhull(N, Qm, Ql, "simplify", true); index = unique(indexCH); regRange = ; regRangeQ0 = * A; fprintf("Number of border points of the adjustment range = %d\n\n", size(index,1));
The convhull() method defines limit points of the adjustment range, given by the values of the variables N, Qm, Ql. The indexCH variable contains the vertices of triangles built using Delaunay triangulation. The regRange variable contains the limit points of the adjustment range; variable regRangeQ0 — high-pressure steam flow rates for the boundary points of the control range.
The calculation result can be found in the file PT_80_linear_characteristic_curve.xlsx, sheet "PT-80-result", table "Boundaries of the adjustment range".
The linearized flow characteristic is built. It is a formula and 37 points that define the boundaries (shell) of the adjustment range in the corresponding table.
2. Verification
When automating the calculation processes Q 0, it is necessary to check whether a certain point with the values N, Q p, Q t is inside the adjustment range or outside it (the mode is technically not realizable). In MATLAB, this can be done in the following way.
We set the values of N, Q n, Q t, which we want to check.
n=75; qm = 120; ql = 50;
We check.
in1 = inpolygon(n, qm, regRange(:,1),regRange(:,2)); in2 = inpolygon(qm, ql, regRange(:,2),regRange(:,3)); in = in1 && in2; if in fprintf("Point N = %3.2f MW, Qp = %3.2f MW, Qt = %3.2f MW is within the control range\n", n, qm, ql); else fprintf("Point N = %3.2f MW, Qp = %3.2f MW, Qt = %3.2f MW is outside the control range (technically unattainable)\n", n, qm, ql); end
Verification is carried out in two steps:
- the variable in1 shows whether the values N, Q p got inside the projection of the shell on the axes N, Q p;
- similarly, the variable in2 shows whether the values Q p, Q t fell inside the projection of the shell on the axes Q p, Q t.
If both variables are equal to 1 (true), then the desired point is inside the shell that specifies the control range of the steam turbine.
Illustration of the resulting linearized flow characteristic of a steam turbine
Most "the bounty of civilization" we got in terms of illustrating the results of calculations.
It must first be said that the space in which we build graphs, i.e. the space with axes x - N, y - Q t, z - Q 0, w - Q p, is called regime space(see Optimization of CHP operation in the conditions of the wholesale electricity and power market in Russia
). Each point of this space determines a certain mode of operation of the steam turbine. mode can be
- technically feasible if the point is inside the shell that defines the adjustment range,
- technically unrealizable if the point is outside this shell.
If we talk about the condensation mode of operation of the steam turbine (Q p \u003d 0, Q t \u003d 0), then linearized flow characteristic represents line segment. If we talk about a T-type turbine, then the linearized flow characteristic is flat polygon in 3D mode space with axes x - N, y - Q t, z - Q 0, which is easy to visualize. For a PT-type turbine, the visualization is the most difficult, since the linearized flow characteristic of such a turbine is flat polygon in four dimensions(for explanations and examples, see Optimizing the operation of CHP plants in the conditions of the Russian wholesale electricity and capacity market, section Turbine Flow Linearization).
1. Illustration of the obtained linearized flow characteristic of a steam turbine
Let's build the values of the table "Initial data (power units)" in the regime space.
Rice. 3. Initial points of the flow characteristics in the regime space with axes x - N, y - Q t, z - Q 0
Since we cannot build a dependence in four-dimensional space, we have not yet reached such a blessing of civilization, we operate with the values of Q p as follows: we exclude them (Fig. 3), we fix them (Fig. 4) (see the plotting code in MATLAB).
We fix the value of Q p = 40 MW and construct the initial points and a linearized flow characteristic.
Rice. 4. Flow characteristic reference points (blue dots), linearized flow characteristic (green flat polygon)
Let us return to the formula of the linearized flow characteristic (4) that we obtained. If we fix Q p \u003d 40 MW MW, then the formula will look like
$$display$$\begin(equation) Q_0 = 2.317 \cdot N + 0.255 \cdot Q_T + 58.714 \qquad (6) \end(equation)$$display$$
This model defines a flat polygon in three-dimensional space with axes x - N, y - Q t, z - Q 0 by analogy with a T-type turbine (we see it in Fig. 4).
Many years ago, when developing nomograms q t gross, they made a fundamental mistake at the stage of analyzing the initial data. Instead of applying the least squares method and constructing a linearized flow characteristic of a steam turbine, for some unknown reason, a primitive calculation was made:
$$display$$\begin(equation) Q_0(N) = Q_e = Q_0 - Q_T - Q_P \qquad (7) \end(equation)$$display$$
Subtracted from the flow rate of high-pressure steam Q 0 steam costs Q t, Q p and attributed the resulting difference Q 0 (N) \u003d Q e to power generation. The resulting value Q 0 (N) \u003d Q e was divided by N and converted to kcal / kWh, obtaining specific consumption q t gross. This calculation does not comply with the laws of thermodynamics.
Dear readers, maybe you are the one who knows the unknown reason? Share it!
2. Illustration of the steam turbine control range
Let's look at the shell of the adjustment range in the mode space. The starting points for its construction are shown in fig. 5. These are the same points that we see in fig. 3, but the parameter Q 0 is now excluded.
Rice. 5. Initial points of the flow characteristic in the regime space with axes x - N, y - Q p, z - Q t
The set of points in fig. 5 is convex. Using the convexhull() function, we have determined the points that define the outer shell of this set.
Delaunay triangulation(a set of connected triangles) allows us to construct a shell of the adjustment range. The vertices of the triangles are the boundary values of the control range of the PT-80 steam turbine we are considering.
Rice. 6. The shell of the adjustment range, represented by many triangles
When we checked a certain point for falling inside the adjustment range, we checked whether this point lies inside or outside the resulting shell.
All graphs presented above were built using MATLAB tools (see PT_80_linear_characteristic_curve.m).
Perspective tasks related to the analysis of the operation of a steam turbine using a linearized flow characteristic
If you are doing a diploma or dissertation, then I can offer you several tasks, the scientific novelty of which you can easily prove to the whole world. In addition, you will do an excellent and useful job.
Task 1
Show how a flat polygon changes with a change in low-pressure steam pressure Qt.
Task 2
Show how the flat polygon changes as the pressure in the condenser changes.
Task 3
Check if the coefficients of the linearized flow characteristic can be represented as functions additional options mode, namely:
$$display$$\begin(equation) \alpha_N = f(p_(0),...); \\ \alpha_P = f(p_(P),...); \\ \alpha_T = f(p_(T),...); \\ \alpha_0 = f(p_(2),...). \end(equation)$$display$$
Here p 0 is the high pressure steam pressure, p p is the medium pressure steam pressure, p t is the low pressure steam pressure, p 2 is the exhaust steam pressure in the condenser, all units are kgf / cm2.
Justify the result.
Links
Chuchueva I.A., Inkina N.E. Optimization of CHP operation in the conditions of the wholesale market of electricity and power in Russia. N.E. Bauman. 2015. No. 8. S. 195-238.
- Section 1. Meaningful formulation of the problem of optimizing the operation of CHPPs in Russia
- Section 2. Linearization of the flow characteristic of the turbine
Heating steam turbine PT-80/100-130/13 with industrial and heating steam extraction is designed for direct drive of electric generator TVF-120-2 with a rotation speed of 50 rpm and heat release for production and heating needs.
The nominal values of the main parameters of the turbine are given below.
Power, MW
nominal 80
maximum 100
Rated steam parameters
pressure, MPa 12.8
temperature, 0 C 555
Consumption of extracted steam for production needs, t/h
nominal 185
maximum 300
Limits of steam pressure change in controlled heating extraction, MPa
upper 0.049-0.245
lower 0.029-0.098
Production selection pressure 1.28
Water temperature, 0 С
nutritional 249
cooling 20
Cooling water consumption, t/h 8000
The turbine has the following adjustable steam extractions:
production with an absolute pressure (1.275 0.29) MPa and two heating selections - the upper one with an absolute pressure in the range of 0.049-0.245 MPa and the lower one with a pressure in the range of 0.029-0.098 MPa. The heating extraction pressure is regulated by means of one control diaphragm installed in the upper heating extraction chamber. Regulated pressure in the heating outlets is maintained: in the upper outlet - when both heating outlets are turned on, in the lower outlet - when one lower heating outlet is turned on. Network water through the network heaters of the lower and upper stages of heating must be passed sequentially and in equal quantities. The flow of water passing through the network heaters must be controlled.
The turbine is a single-shaft two-cylinder unit. The HPC flow path has a single-row control stage and 16 pressure stages.
The flow part of the LPC consists of three parts:
the first (up to the upper heating outlet) has a control stage and 7 pressure stages,
the second (between the heating taps) two pressure stages,
the third - the control stage and two pressure stages.
The high pressure rotor is one-piece forged. The first ten disks of the low-pressure rotor are forged integrally with the shaft, the remaining three disks are mounted.
The steam distribution of the turbine is nozzle. At the exit from the HPC, part of the steam goes to controlled production extraction, the rest goes to the LPC. Heating extractions are carried out from the corresponding LPC chambers.
To reduce the warm-up time and improve start-up conditions, steam heating of flanges and studs and live steam supply to the HPC front seal are provided.
The turbine is equipped with a barring device that rotates the shafting of the turbine unit at a frequency of 3.4 rpm.
The turbine blade apparatus is designed to operate at a mains frequency of 50 Hz, which corresponds to a turbine rotor speed of 50 rpm (3000 rpm). Long-term operation of the turbine is allowed with a frequency deviation in the network of 49.0-50.5 Hz.
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