CN111142381B - Control-oriented NCB type steam turbine heating system composite dynamic modeling method - Google Patents
Control-oriented NCB type steam turbine heating system composite dynamic modeling method Download PDFInfo
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Abstract
The invention discloses a control-oriented composite dynamic modeling method for a heating system of an NCB (steam turbine of the NCB) type, which comprises the steps of respectively establishing a simplified mechanism model of the NCB type steam turbine and a heating network heater of an NCB type combined heat and power supply unit based on three conservation laws, and determining the model structure, the parameter type and the quantity; the method comprises the steps that static parameters are obtained based on design data of an NCB type combined heat and power cycle unit, undetermined functions are fitted according to typical working conditions of the NCB type combined heat and power cycle unit, and dynamic parameters are identified in a closed-loop mode by adopting a particle swarm optimization algorithm based on operation data of the NCB type combined heat and power cycle unit; and verifying the accuracy of the model by using the actual operation data of the NCB type combined heat and power combined cycle unit in the back pressure mode to the extraction and condensation mode. The invention provides support for the simulation and analysis of the variable working condition running dynamic characteristics of the NCB combined heat and power combined cycle unit and the design of the control system of the NCB combined heat and power combined cycle unit.
Description
Technical Field
The invention relates to a thermal modeling method, in particular to a composite dynamic modeling method for an NCB type steam turbine and a heat supply network heater system in an NCB type combined heat and power supply combined cycle unit.
Background
At present, the unit modeling mainly comprises two methods of physical modeling and experience identification. The mechanism modeling mainly utilizes three conservation laws to analyze the interaction rule of each parameter of the unit, and can accurately reflect the dynamic/static characteristics of the system. However, the dynamic process of each device of the actual unit is very complex, when the mechanism model is established, appropriate simplification assumption needs to be carried out to omit some minor links, and parameters of some devices are unknown, so that the established mechanism model and an actual object have large errors, and the mechanism model is not beneficial to the design of the controller. Empirical identification is a method that completely depends on input and output data to determine a mathematical model of the quantitative relationship of the parameters of the system. For complex equipment such as a unit, a large number of random errors exist during operation, data needs to be processed before identification, and model precision is closely related to the quality of data processing. And the model established by experience identification has poor universality and is only suitable for running under a specific object and a specific working condition.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems that a mechanism modeling model is complex, the design of a control system is not facilitated, parameters of a system identification model have no physical meaning, the universality is poor and the like, a control-oriented composite dynamic modeling method of an NCB type steam turbine heating system is provided.
The technical scheme is as follows: in order to realize the purpose, the invention adopts the following technical scheme:
a control-oriented NCB type steam turbine heating system composite dynamic modeling method comprises the following steps:
(1) establishing a simplified mechanism model of the NCB type steam turbine heating system;
(2) obtaining static parameters based on the rated power generation working condition data of the NCB type combined heat and power cycle unit, selecting a unit typical working condition fitting undetermined function according to a thermal equilibrium diagram of the NCB type combined heat and power cycle unit, and adopting a particle swarm optimization algorithm to identify dynamic parameters in a closed loop mode based on the operation data of the NCB type combined heat and power cycle unit;
(3) and (3) dynamically verifying the accuracy of the model by utilizing the actual operation data of the NCB type combined heat and power combined cycle unit in the back pressure mode to the extraction and condensation mode.
Further, the step (1) comprises the following steps:
(11) establishing a simplified mechanism model of the heat supply network heater based on three conservation laws;
(12) establishing an NCB type steam turbine simplified mechanism model based on three conservation laws;
(13) and (4) collating the heat supply network heater simplifying mechanism model established in the step (11) and the NCB type steam turbine simplifying mechanism model established in the step (12) to obtain the NCB type steam turbine heating system simplifying mechanism model.
Further, the step (11) is specifically:
the energy equation of the water side of the heat supply network heater is as follows:
wherein M ismThe quality of circulating water in a heating network heater; cpmThe specific heat capacity of circulating water in a heating network heater is set; mjMass of a metal heat transfer pipe of a heat supply network heater; cjThe specific heat capacity of a metal heat transfer pipe of the heat supply network heater; t is tw1The temperature of the circulating water inlet of the heat supply network; t is tw2The temperature of the circulating water outlet of the heat supply network; cpThe specific heat capacity of the circulating water of the heat supply network;
the change rate of the temperature of the circulating water outlet of the heat supply network is shown; dwThe flow rate of the circulating water of the heat supply network; q1The heat transfer capacity of the heat supply network heater; τ is time;
the mass balance equation of the steam side of the heat supply network heater is as follows:
wherein D iseThe steam extraction flow of the heat supply network heater is obtained; dnDraining flow for a heat supply network heater; v' is the hydrophobic volume of the heat supply network heater; v' is the volume of the heater gas of the heat supply network; rho ', rho' are respectively the saturated water density and the saturated steam density of the heat supply network heater;
is the rate of change of mass in the heater of the heating network.
The energy balance equation of the steam side of the heat supply network heater is as follows:
wherein, h 'and h' are respectively the saturated water enthalpy value and the saturated steam enthalpy value of the heating network heater; h iseFor heating heat supply networkThe enthalpy value of the extracted steam of the device; h isnThe hydrophobic enthalpy value of the heater of the heat supply network is shown;
the volume conservation formula of the heating network heater is as follows:
V′+V″＝const；
the mass balance equation of the steam side of the heat supply network heater, the energy balance equation of the steam side of the heat supply network heater and the volume conservation formula of the heat supply network heater are derived to obtain:
wherein const represents the heat net heater volume; cbThe heat storage coefficient of the heat supply network heater; psThe internal pressure of the heating network heater;
is the rate of change of pressure inside the heater of the heating network; k is a radical of1The pressure change coefficient of the heat supply network heater caused by the mass unbalance of the heat supply network heater;
the hydrophobic volume change rate of the heat supply network heater;
respectively the saturated water density and saturated steam density change rate caused by the internal pressure change of the heat supply network heater; the sigma D is the difference between the steam extraction flow and the drainage flow of the heat supply network heater;
assuming a zero water level at the heater centerline of the heating network, neglecting the non-linear relationship between heater water level and hydrophobic volume, the heating network heater relative water level change is calculated using the following equation:
wherein A isdThe cross section area of the zero water level position of the heat supply network heater; delta h is the relative water level change of the heating network heater; delta V' is the change of the hydrophobic volume of the heat supply network heater;
the heat transfer equation of the heat supply network heater is as follows:
wherein F is the heat exchange area of the heat supply network heater; t is tsThe saturation temperature of the working medium in the heating network heater;
the heat transfer coefficient α equation is:
wherein alpha is0The heat exchange coefficient is the heat exchange coefficient under the rated working condition; de0The steam extraction flow rate is under the rated working condition;
taking into account the internal pressure P of the heating network heatersNormally without measuring points, the medium discharge pressure P being selectedzIn place of Ps(ii) a The internal pressure of the heating network heater and the pressure of the middle exhaust have the following relations:
Ps＝UEPz；
wherein, UEThe opening of the middle exhaust steam extraction valve is determined;
according to the saturation temperature t of the heater of the heat supply networksAnd the internal pressure P of the heating network heatersThere is a one-to-one correspondence, resulting in the following equation:
ts＝f(Ps)＝f(UEPz)；
the mechanism analyzes that the value of the extraction flow of the heat supply network heater is in linear relation with the current turbine power, the main steam flow and the intermediate discharge pressure, and the simplified calculation formula of the extraction flow of the heat supply network heater is given as follows:
De＝k2Pz+k3qt+k4NE+c；
wherein q istIs a main steamingThe flow rate of steam; n is a radical ofEIs the turbine power; k is a radical of2,k3,k4Respectively, fitting coefficients, c is a constant;
the equations of the drainage flow of the heat supply network heater and the rotation speed of the drainage pump are as follows:
Dn＝f(s)；
wherein s is the rotation speed of the drainage pump.
Further, the step (12) is specifically:
main steam flow qtThe functional relationship with main steam pressure and turbine valve is as follows:
qt＝g(Pst)Ut；
wherein, UtAdjusting the opening of the steam turbine; pstIs the main steam pressure;
the enthalpy value h of the extracted steam in the normal working rangeeApproximately a fixed value C, let:
he＝C；
describing the work amount of the steam in the steam turbine as the sum of the work of the steam in the high-medium pressure cylinder and the work of the low-pressure cylinder:
wherein, TtIs the turbine time constant; k is a radical of5,k6,k7,k8Respectively increasing the gain of a steam turbine, wherein the work of a high and medium pressure cylinder of the steam turbine accounts for the work proportion of the steam turbine, the exhaust energy of the medium pressure cylinder accounts for the work proportion, and the gain of a low pressure cylinder of the steam turbine accounts for the gain; u shapeLThe opening of the steam inlet valve of the low-pressure cylinder; tau isdAfter the mode switching, the SSS clutch is engaged, and the low-pressure cylinder does work for a delay time;
the low cylinder rotor speed equation is given by:
wherein n is the rotor speed of the low pressure cylinder of the steam turbine, T0Is the time constant, N, of the rotor of the low-pressure cylinder of the steam turbineTIs the power of the low-pressure cylinder of the steam turbine, NfThe friction power consumption of the low-pressure cylinder rotor of the steam turbine is calculated according to the following formula:
NT＝k8PzUL；
wherein, JdThe rotational inertia of a rotor of a low-pressure cylinder of the steam turbine; a, B and C are coefficients, and can be obtained through an idling curve of a low-pressure cylinder rotor of the steam turbine; n is0The rated rotating speed of the low-pressure cylinder rotor is obtained.
Further, the simplified mechanism model of the heating system of the NCB turbine established in step (13) is as follows:
wherein, the input variables in the established simplified mechanism model of the NCB type steam turbine heating system are as follows: main steam pressure PstOpening U of steam turbine governortOpening U of steam inlet valve of low-pressure cylinderLOpening U of medium exhaust steam extraction valveERotation speed S of drainage pump and circulating water flow D of heat supply networkwTemperature t of circulating water inlet of heat supply networkw1(ii) a The intermediate state variables are: outlet temperature t of circulating water of heat supply networkw2Middle exhaust pressure PzThe drainage volume V' of the heating network heater and the power N of the steam turbineEHeat transfer capacity Q of heat supply network heater1Rotating speed n of a rotor of a low-pressure cylinder of the steam turbine; the model output variables are: middle exhaust pressure PzTemperature t of circulating water outlet of heat supply networkw2Power N of the steam turbineEWater level h of heat supply network heater and steam extraction flow D of heat supply network heatereDrainage flow rate of heat supply network heater Dn(ii) a The static parameters of the model are a, k5,k6,k7,k8,Cp(ii) a The fitting function to be determined is De＝k2Pz+k3qt+k4NE+c，ts＝f(Ps)＝f(UEPz)，qt＝g(Pst)Ut(ii) a The model dynamic parameters are: cb，Tt,τb,b。
Further, the step (2) comprises the following steps:
(21) and (3) solving static parameters:
the static parameters of the model are obtained through the rated power generation working condition of the NCB type combined heat and power cycle unit, wherein k is5For the gain of the steam turbine, the calculation formula is as follows:
k6taking the pure condensing working condition design value of the steam turbine for the working ratio of the high and medium pressure cylinders of the steam turbine to the working ratio of the steam turbine: k is a radical of6＝0.535；
k7The exhaust steam of the intermediate pressure cylinder brings out energy accounting for the work-doing proportion: k is a radical of7＝0.51；
k8For the low pressure cylinder gain, the calculation formula is:
the static parameter a takes different values according to different medium discharge pressures; the constant pressure specific heat capacity of the circulating water is taken according to the temperature;
(22) and (3) obtaining a function to be determined:
based on a thermodynamic equilibrium diagram of an NCB type combined heat and power supply combined cycle unit, the extraction flow D of a heat supply network heater under a plurality of groups of typical loads from low load to high load is selectedeMiddle exhaust pressure PzMain steam flow qtPower N of the steam turbineEMain steam pressure PstOpening U of steam turbine governortFitting the data to be determined by least squaresFunction De＝k2Pz+k3qt+k4NE+c，qt＝g(Pst)UtUndetermined function ts＝f(Ps)＝f(UEPz) Obtaining the model precision within the range of improving the large load variation through water and water vapor calculation software;
(23) and (3) solving dynamic parameters:
the model dynamic parameters include: heat storage coefficient of heating network heater CbInertia time T of steam turbinetAnd after the SSS clutch is engaged after the mode switching, the low-pressure cylinder does work and delays the time taudPressure-induced hydrophobic volume change coefficient b; the inertia time of the steam turbine is calculated according to overspeed protection experiment data of the steam turbine, taudObtained from the experience of a field engineer; and solving the identification problem of the dynamic parameter b by adopting a Particle Swarm Optimization (PSO).
Further, the step (23) comprises the steps of:
(231) initialization: setting parameter motion range and learning factor c1,c2Maximum evolution generation G, current evolution generation kg, population size, ith particle position Xi，XiRepresenting a dynamic parameter b, speed Vi(ii) a Randomly generating size particles, and randomly generating a position matrix and a speed matrix of the initial population;
(232) setting an optimizing objective function:
wherein h isiIs the water level value of the heater of the actual operation heat supply network,
is a model to calculate the water level value of the heater of the heat supply network, hi0Is a water level set value of a heat supply network heater;
(233) individual evaluation: according to the formula
And
calculating the water level value of the model heat supply network heater and then calculating the initial adaptive value J (X) of each particle in the populationi) And calculating the optimal position of the population;
(234) updating the speed and the position of the particles to generate a new population, and carrying out border crossing inspection on the speed and the position of the particles; in order to avoid the algorithm from falling into the local optimal solution, a local self-adaptive mutation operator is added for adjustment;
wherein, Vi kg,
Respectively, the ith particle velocity and position, Vi kg+1，
(ii) the ith particle velocity and position for the kg +1 th generation; omega is the inertial weight, c1Is a local learning factor, c2Is a global learning factor, r1,r2Is [0,1 ]]A random number is added to the random number,
is the extreme value of the kg generation individuals,
is the kg-th generation global extreme value;
(235) comparing the current fitness value J (X) of the particlesi) And self-history optimal value piIf J (X)i) Is superior to piThen J (X)i) Value assignment piAnd updating the particle position;
(236) comparing the current fitness value J (X) of the particlesi) And population optimum BestS if J (X)i) Is superior to BestS in that J (X)i) Giving the value to BestS, and updating the global optimal value of the population;
(237) and (4) when the optimization reaches the maximum evolution algebra or the evaluation value is smaller than the given precision, ending the optimization, wherein the BestS value is the dynamic parameter b to be solved, otherwise, kg is kg +1, and going to the step (234).
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
the invention adopts a composite modeling method to establish a working condition-variable simplified nonlinear model of the NCB type steam turbine and the heat supply network heater of the NCB type combined heat and power supply unit, integrates the advantages of mechanism modeling and system identification, has clear physical meaning of parameters, simple structure, convenient further control system design and high model precision, and considers the nonlinear dynamic characteristics of each main link of the system.
Drawings
FIG. 1 is a flow chart of a composite dynamic modeling of a heating system of an NCB steam turbine according to an embodiment of the present invention;
fig. 2 is a comparison graph of the output result of the NCB-type steam turbine heating system model and the actual data of the NCB-type cogeneration combined cycle unit in the back pressure mode to the extraction condensing mode according to an embodiment of the present invention.
Detailed Description
The invention is described in detail with reference to the accompanying drawings and specific embodiments, and the modeling process and the accuracy of the established model can be understood through the accompanying drawings.
The embodiment relates to an NCB type combined heat and power cycle unit, wherein a steam turbine is a domestic NCB (N: straight condensing type; C: steam extraction type; B: back pressure type) type, a heat supply network heater is a U-shaped pipe horizontal heat supply network heater with the model number of HB 2000-2.5/0.6-1654-QS/W.
As shown in fig. 1, a control-oriented NCB steam turbine heating system composite dynamic modeling method includes the following steps:
step 1, establishing a simplified mechanism model of a NCB type steam turbine heating system
Respectively establishing an NCB type steam turbine and heat supply network heater simplifying mechanism model based on three conservation laws, and determining a model structure, parameter types and quantity; the method specifically comprises the following steps:
(11) simplified mechanism model of heat supply network heater
The energy equation of the water side of the heat supply network heater is as follows:
wherein M ismThe quality of circulating water in a heating network heater; cpmThe specific heat capacity of circulating water in a heating network heater is set; mjMass of a metal heat transfer pipe of a heat supply network heater; cjThe specific heat capacity of a metal heat transfer pipe of the heat supply network heater; t is tw1The temperature of the circulating water inlet of the heat supply network; t is tw2The temperature of the circulating water outlet of the heat supply network; cpThe specific heat capacity of the circulating water of the heat supply network;
the change rate of the temperature of the circulating water outlet of the heat supply network is shown; dwThe flow rate of the circulating water of the heat supply network; q1The heat transfer capacity of the heat supply network heater; τ is the simulation time.
The mass balance equation of the steam side of the heat supply network heater is as follows:
wherein D iseThe steam extraction flow of the heat supply network heater is obtained; dnDraining flow for a heat supply network heater; v' is the hydrophobic volume of the heat supply network heater; v' is the volume of the heater gas of the heat supply network; rho ', rho' are respectively the saturated water density and the saturated steam density of the heat supply network heater;
is the rate of change of mass in the heater of the heating network.
The energy balance equation of the steam side of the heat supply network heater is as follows:
wherein, h 'and h' are respectively the saturated water enthalpy value and the saturated steam enthalpy value of the heating network heater; h iseThe enthalpy value of the extracted steam of the heating network heater is obtained; h isnThe hydrophobic enthalpy value of the heater of the heat supply network is shown;
the volume conservation formula of the heating network heater is as follows:
V′+V″＝const (4)；
where const represents the heat net heater volume.
Derived from equations (2) - (4):
wherein, CbThe heat storage coefficient of the heat supply network heater; psThe internal pressure of the heating network heater;
is the rate of change of pressure inside the heater of the heating network; k is a radical of1The pressure change coefficient of the heat supply network heater caused by the mass unbalance of the heat supply network heater;
the hydrophobic volume change rate of the heat supply network heater;
respectively the saturated water density and saturated steam density change rate caused by the internal pressure change of the heat supply network heater; and sigma D is the difference between the extraction flow and the drainage flow of the heat supply network heater.
Assuming a zero water level at the heater centerline of the heating network, neglecting the non-linear relationship between heater water level and hydrophobic volume, the heating network heater relative water level change is calculated using the following equation:
wherein A isdThe cross section area of the zero water level position of the heat supply network heater; delta h is the relative water level change of the heating network heater; Δ V' is the change in hydrophobic volume of the heater grid.
The heat transfer equation of the heat supply network heater is as follows:
wherein F is the heat exchange area of the heat supply network heater; t is tsThe saturation temperature of the working medium in the heating network heater;
the heat transfer coefficient α equation is:
wherein alpha is0The heat exchange coefficient is the heat exchange coefficient under the rated working condition; de0The steam extraction flow rate is under the rated working condition.
Taking into account the internal pressure P of the heating network heatersNormally without measuring points, the medium discharge pressure P being selectedzIn place of Ps. The internal pressure of the heating network heater and the pressure of the middle exhaust have the following relations:
Ps＝UEPz (10)；
wherein, UEThe opening of the middle exhaust steam extraction valve.
According to the saturation temperature t of the heater of the heat supply networksAnd the internal pressure P of the heating network heatersThere is a one-to-one correspondence, resulting in the following equation:
ts＝f(Ps)＝f(UEPz) (11)；
the extraction flow of the heat supply network heater is one of important parameters for determining the operation range of the unit, but no measurement point for the extraction flow of the heat supply network heater is arranged on the site, and an empirical calculation formula for the extraction flow of the heat supply network heater is established by adopting a data fitting coefficient method. The mechanism analyzes that the value of the extraction flow of the heat supply network heater is in linear relation with the current turbine power, the main steam flow and the intermediate discharge pressure, and the simplified calculation formula of the extraction flow of the heat supply network heater is given as follows:
De＝k2Pz+k3qt+k4NE+c (12)；
wherein q istIs the main steam flow; n is a radical ofEIs the turbine power. k is a radical of2,k3,k4Respectively, fitting coefficients, c is a constant, and can be fitted through typical working condition data.
The equations of the drainage flow of the heat supply network heater and the rotation speed of the drainage pump are as follows:
Dn＝f(s) (13)；
wherein s is the rotation speed of the drainage pump.
(12) Establishing simplified mechanism model of NCB type steam turbine
Main steam flow qtThe functional relationship with main steam pressure and turbine valve is as follows:
qt＝g(Pst)Ut (14)；
wherein, UtAdjusting the opening of the steam turbine; pstIs the main steam pressure.
The enthalpy value h of the extracted steam in the normal working rangeeApproximately a fixed value C, let:
he＝C (15)；
describing the work amount of the steam in the steam turbine as the sum of the work of the steam in the high-medium pressure cylinder and the work of the low-pressure cylinder:
wherein, TtIs steamA turbine time constant; k is a radical of5,k6,k7,k8Respectively increasing the gain of a steam turbine, wherein the work of a high and medium pressure cylinder of the steam turbine accounts for the work proportion of the steam turbine, the exhaust energy of the medium pressure cylinder accounts for the work proportion, and the gain of a low pressure cylinder of the steam turbine accounts for the gain; u shapeLThe opening of the steam inlet valve of the low-pressure cylinder; tau isdThe work delay time of the low-pressure cylinder is obtained after the SSS clutch is engaged after the mode switching.
The low cylinder rotor speed equation is given by:
wherein n is the rotor speed of the low pressure cylinder of the steam turbine, T0Is the time constant, N, of the rotor of the low-pressure cylinder of the steam turbineTIs the power of the low-pressure cylinder of the steam turbine, NfThe friction power consumption of the low-pressure cylinder rotor of the steam turbine is calculated according to the following formula:
NT＝k8PzUL (19)；
wherein, JdThe rotational inertia of a rotor of a low-pressure cylinder of the steam turbine; a, B and C are coefficients, and can be obtained through an idling curve of a low-pressure cylinder rotor of the steam turbine; n is0The rated rotating speed of the low-pressure cylinder rotor is obtained.
(13) The heat supply network heater simplifying mechanism model established in the step (11) and the NCB type steam turbine simplifying mechanism model established in the step (12) are summarized to obtain a heat supply unit model with seven inputs and six outputs, namely the NCB type steam turbine heat supply system simplifying mechanism model is as follows:
wherein, the input variables in the established simplified mechanism model of the NCB type steam turbine heating system are as follows: main steam pressure PstOpening U of steam turbine governortOpening U of steam inlet valve of low-pressure cylinderLOpening U of medium exhaust steam extraction valveEThe rotation speed of the drainage pump s and the circulating water flow D of the heat supply networkwTemperature t of circulating water inlet of heat supply networkw1. The intermediate state variables are: outlet temperature t of circulating water of heat supply networkw2Middle exhaust pressure PzThe drainage volume V' of the heating network heater and the power N of the steam turbineEHeat transfer capacity Q of heat supply network heater1And the rotor speed n of the low-pressure cylinder of the steam turbine. The model output variables are: middle exhaust pressure PzTemperature t of circulating water outlet of heat supply networkw2Power N of the steam turbineEWater level h of heat supply network heater and steam extraction flow D of heat supply network heatereDrainage flow rate of heat supply network heater Dn. The static parameters in the formula (21) are a, k5,k6,k7,k8,Cp(ii) a The fitting function to be determined is De＝k2Pz+k3qt+k4NE+c，ts＝f(Ps)＝f(UEPz)，qt＝g(Pst)Ut(ii) a The dynamic parameters are: cb，Tt,τb,b。
Step 2, obtaining static parameters based on the rated power generation working condition data of the NCB type combined heat and power cycle unit, selecting a typical working condition fitting undetermined function of the NCB type combined heat and power cycle unit according to a thermodynamic equilibrium diagram, and identifying dynamic parameters in a closed loop mode by adopting a particle swarm optimization algorithm based on the operation data of the NCB type combined heat and power cycle unit; the method comprises the following steps:
(21) and (3) solving static parameters:
the static parameters of the simplified mechanism model of the NCB type steam turbine heating system can be obtained through the rated power generation working condition (THA) of the unit, and the design data of the rated power generation working condition of the NCB type combined heat and power cycle unit is shown in a table 1:
TABLE 1 NCB-TYPE CONDENSED GENERATION CONDITION CONDITIONING CONDITION DESIGN DATA FOR COMBINED CYCLE UNIT
Wherein k is5For the gain of the steam turbine, the calculation formula is as follows:
NE,THAturbine power P for rated power generation working condition of NCB type combined heat and power supply combined cycle unit1,THAThe primary pressure of the turbine under the rated power generation condition of the NCB type combined heat and power cycle unit.
k6Taking the pure condensing working condition design value of the steam turbine for the working ratio of the high and medium pressure cylinders of the steam turbine to the working ratio of the steam turbine: k is a radical of6＝0.535。
k7The exhaust steam of the intermediate pressure cylinder brings out energy accounting for the work-doing proportion: k is a radical of7＝0.51。
k8For the low pressure cylinder gain, the calculation formula is:
Pz,THAthe pressure is discharged under the rated power generation working condition of the NCB type combined heat and power cycle unit.
The values of the static parameter a at different medium discharge pressures are shown in table 2:
TABLE 2 relationship of parameter a to Medium exhaust pressure
Take a as 0.001065.
The relationship between the specific heat capacity and the temperature of the circulating water of the heat supply network is shown in the table 3:
TABLE 3 relationship between specific heat capacity at constant pressure and temperature
The specific heat capacity of the circulating water of the heat supply network is 4.25.
(22) Undetermined function solving
Based on a thermodynamic equilibrium diagram of an NCB type combined heat and power supply combined cycle unit, the extraction flow D of a heat supply network heater under a plurality of groups of typical loads from low load to high load is selectedeMiddle exhaust pressure PzMain steam flow qtPower N of the steam turbineEMain steam pressure PstOpening U of steam turbine governortData, fitting the undetermined function D by least square methode＝k2Pz+k3qt+k4NE+c，qt＝g(Pst)UtUndetermined function ts＝f(Ps)＝f(UEPz) The model accuracy in the large load variation range is improved by water and water vapor calculation software.
In this embodiment, typical operating point data of the NCB combined heat and power cycle unit is shown in table 4:
TABLE 4 typical operating point data for NCB combined heat and power cycle
The model of the extraction flow of the heating network heater is fitted by the least square method as follows:
De＝-500Pz+5.7124qt-2.2523NE-20 (24)；
the relationship between the internal pressure and saturation temperature of the heating network heater within the normal working condition range is shown in table 5:
TABLE 5 saturation temperature and saturation pressure
After least square fitting, the following can be obtained:
ts＝96Ps+103＝96UEPz+103 (25)；
the extraction enthalpy values at different medium exhaust pressures are shown in table 6:
TABLE 6 extraction enthalpy values for different medium exhaust pressures
From table 6, it can be known that the change of the extraction enthalpy value is not large with the change of the medium discharge pressure, and the relative maximum change amount is:
the extraction enthalpy can therefore take a fixed value: h ise＝3090。
The main steam flow versus main steam pressure relationship is shown in table 7:
TABLE 7 Main steam flow and Main steam pressure
The following can be obtained through least square fitting:
qt＝(13.26*Pst-19.57)Ut (27)；
(23) dynamic parameter determination
The model dynamic parameters include: heat storage coefficient of heating network heater CbTime constant T of steam turbinetAnd after the SSS clutch is engaged after the mode switching, the low-pressure cylinder does work and delays the time taubThe heat supply network heater pressure causes the heat supply network heater hydrophobic volume change coefficient b. The time constant of the steam turbine is calculated according to overspeed protection experimental data of the steam turbine, taubMay be obtained from the experience of a field engineer. When an uncertain and nonlinear system is identified, the intelligent algorithm has advantages, and the Particle Swarm Optimization (PSO) is adopted to solve the problem of identifying the dynamic parameter b.
The earliest PSO is a random search algorithm based on group cooperation developed by simulating foraging behavior of bird groups, belongs to one of evolutionary algorithms, and is used for searching an optimal solution through iteration starting from a random solution. In each iteration, the particle updates its position by tracking two extreme values. The first extreme is the optimal solution found by the particle itself, this extreme is called the individual extreme. The other extreme is the best solution currently found by the whole population, and this extreme is called the global extreme.
Based on the actual data of the backpressure state-to-extraction-condensation state of the unit and combined with formulas (1), (5), (6) and (12), the dynamic parameter b which is difficult to directly determine is identified in a closed loop mode by adopting a particle swarm optimization algorithm, and the method comprises the following steps:
(231) initialization: setting parameter motion range and learning factor c1,c2Maximum evolution generation G, current evolution generation kg, population size, ith particle position Xi，XiRepresenting a dynamic parameter b, speed Vi. Size particles are randomly generated, and a position matrix and a velocity matrix of the initial population are randomly generated.
(232) Setting an optimizing objective function:
wherein J is an identification error objective function, m is the quantity of water level samples of the heat supply network heater in the identification process, and hiIs the water level value of the heater of the actual operation heat supply network,
is a model to calculate the water level value of the heater of the heat supply network, hi0Is the water level set value of the heating network heater.
(233) Individual evaluation: calculating model heat supply network heater according to formulas (6) and (7)The water level value is then calculated for each particle in the population as an initial fitness value J (X)i) And solving the optimal position of the population.
(234) And updating the speed and the position of the particles, generating a new population, and checking the speed and the position of the particles by crossing the boundary. In order to avoid the algorithm from falling into the local optimal solution, a local self-adaptive mutation operator is added for adjustment.
Wherein, Vi kg,
Respectively, the ith particle velocity and position, Vi kg+1，
(ii) the ith particle velocity and position for the kg +1 th generation; omega is the inertial weight, c1Is a local learning factor, c2Is a global learning factor, r1,r2Is [0,1 ]]A random number is added to the random number,
is the extreme value of the kg generation individuals,
is the kg-th generation global extremum.
(235) Comparing the current fitness value J (X) of the particlesi) And self-history optimal value piIf J (X)i) Is superior to piThen J (X)i) Value assignment piAnd updates the particle position.
(236) Comparing the current fitness value J (X) of the particlesi) And population optimum BestS if J (X)i) Is superior to BestS in that J (X)i) And assigning the value to BestS, and updating the global optimal value of the population.
(237) And (4) when the optimization reaches the maximum evolution algebra or the evaluation value is smaller than the given precision, ending the optimization, wherein the BestS value is the dynamic parameter b to be solved, otherwise, kg is kg +1, and going to the step (234).
In the embodiment of the invention, the particle motion speed range of the particle swarm algorithm [ -1000,10000], learning factors are respectively 1.3 and 1.7, the inertia weights are 0.1 and 0.9, the maximum iteration frequency is 50, the number of the initialized population individuals is 50, and the identification error function is as follows:
the recognition result is b-7807.
Step 3, utilizing the actual operation data of the NCB type combined heat and power cycle unit in a back pressure mode conversion condensation mode to dynamically verify the accuracy of the model; the method specifically comprises the following steps:
and (4) building a simulation model on a computer according to the built NCB type steam turbine heating system composite dynamic model for numerical simulation. Fig. 2(a) - (d) are model simulation output results obtained according to input signals of switching from the actual back pressure mode to the extraction and condensation mode of the actual NCB combined heat and power cycle unit, and for comparison, the graphs simultaneously show actual data of the turbine power, the intermediate discharge pressure, the drainage flow and the outlet temperature of the heat supply network heater. The result shows that the model parameter variation trend of the modeling method provided by the invention accords with the actual operation data, and the relative error of the model is less than 3%.
Claims (1)
1. A control-oriented NCB type steam turbine heating system composite dynamic modeling method is characterized by comprising the following steps:
(1) establishing a simplified mechanism model of the NCB type steam turbine heating system; the method comprises the following steps:
(11) establishing a simplified mechanism model of the heat supply network heater based on three conservation laws;
the method specifically comprises the following steps:
the energy equation of the water side of the heat supply network heater is as follows:
wherein M ismThe quality of circulating water in a heating network heater; cpmThe specific heat capacity of circulating water in a heating network heater is set; mjMass of a metal heat transfer pipe of a heat supply network heater; cjThe specific heat capacity of a metal heat transfer pipe of the heat supply network heater; t is tw1The temperature of the circulating water inlet of the heat supply network; t is tw2The temperature of the circulating water outlet of the heat supply network; cpThe specific heat capacity of the circulating water of the heat supply network;
the change rate of the temperature of the circulating water outlet of the heat supply network is shown; dwThe flow rate of the circulating water of the heat supply network; q1The heat transfer capacity of the heat supply network heater; τ is time;
the mass balance equation of the steam side of the heat supply network heater is as follows:
wherein D iseThe steam extraction flow of the heat supply network heater is obtained; dnDraining flow for a heat supply network heater; v' is the hydrophobic volume of the heat supply network heater; v' is the volume of the heater gas of the heat supply network; rho ', rho' are respectively the saturated water density and the saturated steam density of the heat supply network heater;
is the rate of change of mass in the heater of the heating network;
the energy balance equation of the steam side of the heat supply network heater is as follows:
wherein, h 'and h' are respectively the saturated water enthalpy value and the saturated steam enthalpy value of the heating network heater;hethe enthalpy value of the extracted steam of the heating network heater is obtained; h isnThe hydrophobic enthalpy value of the heater of the heat supply network is shown;
the volume conservation formula of the heating network heater is as follows:
V′+V″＝const；
the mass balance equation of the steam side of the heat supply network heater, the energy balance equation of the steam side of the heat supply network heater and the volume conservation formula of the heat supply network heater are derived to obtain:
wherein const represents the heat net heater volume; cbThe heat storage coefficient of the heat supply network heater; psThe internal pressure of the heating network heater;
is the rate of change of pressure inside the heater of the heating network; k is a radical of1The pressure change coefficient of the heat supply network heater caused by the mass unbalance of the heat supply network heater;
the hydrophobic volume change rate of the heat supply network heater;
respectively the saturated water density and saturated steam density change rate caused by the internal pressure change of the heat supply network heater; the sigma D is the difference between the steam extraction flow and the drainage flow of the heat supply network heater;
assuming a zero water level at the heater centerline of the heating network, neglecting the non-linear relationship between heater water level and hydrophobic volume, the heating network heater relative water level change is calculated using the following equation:
wherein A isdThe cross section area of the zero water level position of the heat supply network heater; delta h is the relative water level change of the heating network heater; delta V' is the change of the hydrophobic volume of the heat supply network heater;
the heat transfer equation of the heat supply network heater is as follows:
wherein F is the heat exchange area of the heat supply network heater; t is tsThe saturation temperature of the working medium in the heating network heater;
the heat transfer coefficient α equation is:
wherein alpha is0The heat exchange coefficient is the heat exchange coefficient under the rated working condition; de0The steam extraction flow rate is under the rated working condition;
taking into account the internal pressure P of the heating network heatersNormally without measuring points, the medium discharge pressure P being selectedzIn place of Ps(ii) a The internal pressure of the heating network heater and the pressure of the middle exhaust have the following relations:
Ps＝UEPz；
wherein, UEThe opening of the middle exhaust steam extraction valve is determined;
according to the saturation temperature t of the working medium in the heating network heatersAnd the internal pressure P of the heating network heatersThere is a one-to-one correspondence, resulting in the following equation:
ts＝f(Ps)＝f(UEPz)；
the mechanism analyzes that the value of the extraction flow of the heat supply network heater is in linear relation with the current turbine power, the main steam flow and the intermediate discharge pressure, and the simplified calculation formula of the extraction flow of the heat supply network heater is given as follows:
De＝k2Pz+k3qt+k4NE+c；
wherein q istIs the main steam flow; n is a radical ofEIs the turbine power; k is a radical of2,k3,k4Respectively, fitting coefficients, c is a constant;
the equations of the drainage flow of the heat supply network heater and the rotation speed of the drainage pump are as follows:
Dn＝f(s)；
wherein s is the rotation speed of the drainage pump;
(12) establishing an NCB type steam turbine simplified mechanism model based on three conservation laws;
the method specifically comprises the following steps:
main steam flow qtThe functional relationship with main steam pressure and turbine valve is as follows:
qt＝g(Pst)Ut；
wherein, UtIs the opening degree of the valve of the steam turbine; pstIs the main steam pressure;
the steam extraction enthalpy value h of the heating network heater in the normal working rangeeApproximately a fixed value C, let:
he＝C；
describing the work amount of the steam in the steam turbine as the sum of the work of the steam in the high-medium pressure cylinder and the work of the low-pressure cylinder:
wherein, TtIs the turbine time constant; k is a radical of5,k6,k7,k8Respectively increasing the gain of a steam turbine, wherein the work of a high and medium pressure cylinder of the steam turbine accounts for the work proportion of the steam turbine, the exhaust energy of the medium pressure cylinder accounts for the work proportion, and the gain of a low pressure cylinder of the steam turbine accounts for the gain; u shapeLThe opening of the steam inlet valve of the low-pressure cylinder; tau isdAfter the mode switching, the SSS clutch is engaged, and the low-pressure cylinder does work for a delay time;
the low cylinder rotor speed equation is given by:
wherein n is the rotor speed of the low pressure cylinder of the steam turbine, T0Is the time constant, N, of the rotor of the low-pressure cylinder of the steam turbineTIs the power of the low-pressure cylinder of the steam turbine, NfThe friction power consumption of the low-pressure cylinder rotor of the steam turbine is calculated according to the following formula:
NT＝k8PzUL；
wherein, JdThe rotational inertia of a rotor of a low-pressure cylinder of the steam turbine; a, B and C are coefficients, and can be obtained through an idling curve of a low-pressure cylinder rotor of the steam turbine; n is0The rated rotating speed of the low-pressure cylinder rotor is set;
(13) the heat supply network heater simplifying mechanism model established in the step (11) and the NCB type steam turbine simplifying mechanism model established in the step (12) are collated to obtain an NCB type steam turbine heat supply system simplifying mechanism model;
the established simplified mechanism model of the NCB type steam turbine heating system is as follows:
wherein, the input variables in the established simplified mechanism model of the NCB type steam turbine heating system are as follows: main steam pressure PstOpening degree U of steam turbine valvetOpening U of steam inlet valve of low-pressure cylinderLOpening U of medium exhaust steam extraction valveESpeed of drain pump s and flow rate of circulating water in heat supply network DwTemperature t of circulating water inlet of heat supply networkw1(ii) a The intermediate state variables are: circulating water outlet of heat supply networkTemperature tw2Middle exhaust pressure PzThe drainage volume V' of the heating network heater and the power N of the steam turbineEHeat transfer capacity Q of heat supply network heater1Rotating speed n of a rotor of a low-pressure cylinder of the steam turbine; the model output variables are: middle exhaust pressure PzTemperature t of circulating water outlet of heat supply networkw2Power N of the steam turbineEWater level h of heat supply network heater and steam extraction flow D of heat supply network heatereDrainage flow rate of heat supply network heater Dn(ii) a The static parameters of the model are a, k5,k6,k7,k8,Cp(ii) a The fitting function to be determined is De＝k2Pz+k3qt+k4NE+c，ts＝f(Ps)＝f(UEPz)，qt＝g(Pst)Ut(ii) a The model dynamic parameters are: cb，Tt,τb,b；
(2) Obtaining static parameters based on the rated power generation working condition data of the NCB type combined heat and power cycle unit, selecting a typical working condition fitting undetermined function of the NCB type combined heat and power cycle unit according to a thermodynamic equilibrium diagram, and identifying dynamic parameters in a closed loop mode by adopting a particle swarm optimization algorithm based on the operation data of the NCB type combined heat and power cycle unit;
the method comprises the following steps:
(21) and (3) solving static parameters:
the static parameters of the model are obtained through the rated power generation working condition of the NCB type combined heat and power cycle unit, wherein k is5For the gain of the steam turbine, the calculation formula is as follows:
wherein N isE,THATurbine power P for rated power generation working condition of NCB type combined heat and power supply combined cycle unit1,THAThe primary pressure of a turbine under the rated power generation working condition of the NCB type combined heat and power supply combined cycle unit;
k6taking the pure condensing working condition design value of the steam turbine for the working ratio of the high and medium pressure cylinders of the steam turbine to the working ratio of the steam turbine: k is a radical of6＝0.535；
k7The exhaust steam of the intermediate pressure cylinder brings out energy accounting for the work-doing proportion: k is a radical of7＝0.51；
k8For the low pressure cylinder gain, the calculation formula is:
wherein, Pz,THAThe discharge pressure is the discharge pressure of the NCB type combined heat and power cycle unit under the rated power generation working condition;
the static parameter a takes different values according to different medium discharge pressures; the constant pressure specific heat capacity of the circulating water is taken according to the temperature;
(22) and (3) obtaining a function to be determined:
based on a thermodynamic equilibrium diagram of an NCB type combined heat and power supply combined cycle unit, the extraction flow D of a heat supply network heater under a plurality of groups of typical loads from low load to high load is selectedeMiddle exhaust pressure PzMain steam flow qtPower N of the steam turbineEMain steam pressure PstOpening degree U of steam turbine valvetData, fitting the undetermined function D by least square methode＝k2Pz+k3qt+k4NE+c，qt＝g(Pst)UtUndetermined function ts＝f(Ps)＝f(UEPz) Obtaining the model precision within the range of improving the large load variation through water and water vapor calculation software;
(23) and (3) solving dynamic parameters:
the model dynamic parameters include: heat storage coefficient of heating network heater CbInertia time T of steam turbinetAnd after the SSS clutch is engaged after the mode switching, the low-pressure cylinder does work and delays the time taudPressure-induced hydrophobic volume change coefficient b; the inertia time of the steam turbine is calculated according to overspeed protection experiment data of the steam turbine, taudObtained from the experience of a field engineer; solving the problem of identification of the dynamic parameter b by adopting a Particle Swarm Optimization (PSO);
the method comprises the following steps:
(231) initialization: setting parameter motion range and learning factor c1,c2Maximum evolution generation G, current evolution generation kg, population size, ith particle position Xi，XiRepresenting a dynamic parameter b, speed Vi(ii) a Randomly generating size particles, and randomly generating a position matrix and a speed matrix of the initial population;
(232) setting an optimizing objective function:
wherein h isiIs the water level value of the heater of the actual operation heat supply network,
is a model to calculate the water level value of the heater of the heat supply network, hi0Is a water level set value of a heat supply network heater;
(233) individual evaluation: according to the formula
And
calculating the water level value of the model heat supply network heater and then calculating the initial adaptive value J (X) of each particle in the populationi) And calculating the optimal position of the population;
(234) updating the speed and the position of the particles to generate a new population, and carrying out border crossing inspection on the speed and the position of the particles; in order to avoid the algorithm from falling into the local optimal solution, a local self-adaptive mutation operator is added for adjustment;
wherein, Vi kg,
Respectively, the ith particle velocity and position, Vi kg+1，
(ii) the ith particle velocity and position for the kg +1 th generation; omega is the inertial weight, c1Is a local learning factor, c2Is a global learning factor, r1,r2Is [0,1 ]]A random number is added to the random number,
is the extreme value of the kg generation individuals,
is the kg-th generation global extreme value;
(235) comparing the current fitness value J (X) of the particlesi) And self-history optimal value piIf J (X)i) Is superior to piThen J (X)i) Value assignment piAnd updating the particle position;
(236) comparing the current fitness value J (X) of the particlesi) And population optimum BestS if J (X)i) Is superior to BestS in that J (X)i) Giving the value to BestS, and updating the global optimal value of the population;
(237) optimizing to reach the maximum evolution algebra, or finishing optimizing when the evaluation value is smaller than the given precision, wherein the BestS value is the dynamic parameter b, otherwise, kg is kg +1, and turning to the step (234);
(3) and (3) dynamically verifying the accuracy of the model by utilizing the actual operation data of the NCB type combined heat and power combined cycle unit in the back pressure mode to the extraction and condensation mode.
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