CN112560329A - Data-driven robust optimization method for energy system of industrial device under uncertainty - Google Patents
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Abstract
The invention relates to the field of robust optimization of industrial devices, in particular to a data-driven robust optimization method of an energy system of an industrial device under uncertainty. The invention provides a data-driven robust optimization method for an energy system of an industrial device under uncertainty, which comprises the following steps: s1, establishing an equipment model by using the equipment characteristics; s2, performing regression to obtain the efficiency of the equipment and obtain the normal operation range of the variable based on the process history operation database; s3, establishing a deterministic optimization model by combining process energy user demand constraint, steam turbine network constraint and variable variation range and taking the lowest process energy consumption as a target; s4, establishing an uncertain parameter set by adopting a generalized cross kernel algorithm; and S5, establishing a data-driven robust optimization model based on the uncertain process function user demand constraint and in combination with the certainty optimization model. The invention ensures the feasibility of the optimization result under the condition of reducing the energy consumption of the device by using the energy system under the robust optimization uncertainty.
Description
Technical Field
The invention relates to the field of robust optimization of industrial devices, in particular to a data-driven robust optimization method of an energy system of an industrial device under uncertainty.
Background
Energy conservation and emission reduction are important tasks for the development of China all the time, the energy consumption of petroleum and chemical industries accounts for 9 percent of the total national energy consumption and 13 percent of the national industrial consumption, and the energy conservation and emission reduction method is a key field for energy conservation and consumption reduction.
The energy system transmits and converts various energy media, is an important component of large-scale industrial equipment, and mainly has the following problems:
the instrument system is not sound and the metering is not accurate;
the pipe network is huge and complex, and is difficult to schedule and manage;
the steam loss rate is too high, and the energy waste is large;
each energy medium is optimized independently, and the overall energy consumption is difficult to balance;
and the deterministic optimization is unstable and easily deviates from the optimal solution.
Therefore, the multi-energy medium coupling modeling and optimization has great potential in reducing the overall energy consumption, and the optimization under uncertainty realizes the balance between the optimization degree and the robustness.
A data-driven robust optimization method based on an equipment model, energy user requirements, system balance and an uncertain set is an important method for realizing energy conservation and consumption reduction in a chemical production process.
In robust optimization, the conservative degree of an optimization model has an important influence on a system solution result, so that the optimization degree and the robustness are balanced when a regularization parameter is selected, and a target is optimized under the condition of ensuring the robustness of an optimization result.
Ethylene is one of the most important petrochemicals, and its production level is a major marker for the development of petrochemical in a country or region.
The energy system of an ethylene plant is relatively complex, fig. 1 discloses a schematic structural diagram of an energy system of an industrial plant, and as shown in fig. 1, the energy system of a certain ethylene plant mainly comprises two boilers BO, a waste heat recovery system WHRS and a steam system.
The steam system consists of 4 main levels of steam turbine ST of the steam pipe network:
the system comprises an ultrahigh pressure steam pipe network (a pumping condensing turbine), a high pressure steam pipe network (a pumping condensing turbine, a full condensing turbine and two back pressure turbines), a medium pressure steam pipe network (two back pressure turbines), a low pressure steam pipe network, eight cooling towers CT provided with a motor MT, a circulating water tank SINK and four water pumps PU.
Wherein, it includes four kinds of energy media to have related to: fuel, steam, electricity and water are mutually related and influenced, and the enthalpy value of steam in each stage of pipe network is constantly changed, so that the multi-energy medium coupling modeling and optimization and the data-driven robust optimization have important significance for realizing the national energy conservation and emission reduction goal of ethylene production enterprises.
Disclosure of Invention
The invention aims to provide a data-driven robust optimization method for an industrial device energy system under uncertainty, and solves the problem that the optimization result and the conservative degree of the industrial device energy system in the prior art are difficult to balance.
In order to achieve the above object, the present invention provides a data-driven robust optimization method for an energy system of an industrial device under uncertainty, comprising the following steps:
s1, establishing an equipment model by utilizing the equipment characteristics, wherein the equipment characteristics are the mass and energy balance and the thermodynamic characteristics of the equipment, and the equipment model is a basic model of a boiler, a steam turbine, a temperature and pressure reducer and a cooling tower;
s2, obtaining the efficiency of the equipment and obtaining the normal operation range of the variable through regression based on the process historical operation database;
s3, based on the obtained basic model and equipment efficiency, establishing a deterministic optimization model by combining process function user demand constraint, steam turbine network constraint and variable variation range and taking the lowest process energy consumption as a target;
s4, establishing an uncertain parameter set by adopting a generalized cross-kernel algorithm based on the obtained equipment efficiency, wherein the uncertain parameter set comprises the steam admission and the enthalpy value of extracted steam of each steam turbine;
and S5, obtaining process function user demand constraint under uncertainty based on the uncertain parameter set, and establishing a data-driven robust optimization model by combining with the certainty optimization model to realize robust optimization of the energy system.
In one embodiment, in step S2:
the process historical operating database includes measurable variables in all energy systems;
the regression algorithm comprises a least square method, and boiler efficiency, turbine isentropic efficiency and heat exchange efficiency of the cooling tower are obtained through regression.
In one embodiment, in step S3,
the process work user requirements are constrained by,
wherein z isstTo represent the binary variable, G, selected for the steam turbinestFor power of steam turbines, GmuFor the amount of work done by the standby motor, GuThe method comprises the steps that the work required by process work users is realized, ST is a steam turbine index, ST is a steam turbine set, U is a process work user index, U is a process work user set, MU is a standby motor index, and MU is a standby motor set;
the steam turbine network is constrained by the constraints that,
wherein the content of the first and second substances,
is the steam flow at the inlet of the temperature and pressure reducing device,
for the steam flow at the outlet of the temperature and pressure reducer, CsteamIt is the amount of steam consumed,
is the process corresponds to the steam demand, zboTo represent the binary variable selected for use by the boiler,
is the flow rate of the steam at the outlet of the boiler,
for the exhaust heat recovery system outlet steam flow, zstTo represent the binary variable selected for use in the steam turbine,
is the extracted steam flow of the steam turbine,
is the steam turbine inlet steam flow;
the variable ranges of variation are as follows,
mmin≤m≤mmax；
wherein m is a continuous decision variable, mminIs the minimum value of the continuous decision variable, mmaxIs the maximum value of the continuous decision variable.
In one embodiment, in step S3, the steam turbine network constraints include four steam level balances of extra-high pressure SS, high pressure HS, medium pressure MS, and low pressure LS.
In one embodiment, in step S3, the objective function of the deterministic optimization model is expressed as follows:
min y＝Cfuel+ζHSCHS+ζMSCMS+ζelectricityCelectricity+ζwaterCwater；
therein, ζHS、ζMS、ζelectricity、ζwaterRespectively, the parameters of converting the corresponding energy sources of high-pressure steam, medium-pressure steam, electric power and water into standard oil quantity, CfuelFor fuel consumption, CHSFor high pressure steam consumption, CMSFor medium-pressure steam consumption, CelectricityFor power consumption, CwaterIs the water consumption.
In one embodiment, the enthalpy values of the steam inlet and the steam extraction in the step S4 are calculated by using IAPWS-IF97 from the temperature and pressure of the corresponding stream in the steam condenser in the historical operation database of the process.
In one embodiment, the parameter set is not determined in step S4, and the expression is as follows:
wherein σi、
Tau is a dual-coupling parameter,
as a weighting matrix, sigma as a covariance matrix, u(i)For uncertain parameters, upsilon ═ Σi∈SVωi||W(u(i')-u(i))||1Is the intermediate variable, b is the right parameter of the original constraint, x is the decision variable, ωiIn order to be a lagrange multiplier,
is a positive n-dimensional real number set, SV is a sample point set, and i is a sample point index.
In one embodiment, in the step S5, the process work user requirement constraint under uncertainty is expressed as follows:
wherein σst,i、
τstIn order to be able to do a dual-polarization parameter,
in order to be a weighting matrix, the weighting matrix,
in order to determine the parameters of the device,
is an intermediate variable, GuAmount of work required for process work user, zstTo represent the binary variable, G, selected for the steam turbinemuIn order to reserve the work capacity of the motor,
the flow rate of the condensed steam at the outlet of the turbine,
is the enthalpy value of the turbine condensed steam,
for turbine extraction flow, omegast,iAnd the index is a Lagrangian multiplier, ST is a steam turbine index, ST is a steam turbine set, and i is a sample point index.
In an embodiment, the deterministic optimization model in step S3 and the data-driven robust optimization model in step S5 are both mixed integer nonlinear programming models, and are solved by using a Baron solver.
In an embodiment, the data drives a robust optimization model, and the corresponding expression is as follows:
wherein y is the total energy consumption.
The invention provides a data-driven robust optimization method for an energy system of an industrial device under uncertainty, which is characterized in that an uncertain set is established for uncertain parameters by utilizing a generalized cross kernel algorithm, the optimization of an actual working device can be guided, the balance between an optimization result and conservation is realized by optimizing the energy system under uncertainty through the robustness, the feasibility of the optimization result is ensured under the condition of reducing the energy consumption of the device, and the data-driven robust optimization method is suitable for the robust optimization of energy systems of various industrial devices and has wide adaptability.
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The above and other features, properties and advantages of the present invention will become more apparent from the following description of the embodiments with reference to the accompanying drawings in which like reference numerals denote like features throughout the several views, wherein:
FIG. 1 discloses a schematic diagram of an industrial plant energy system;
FIG. 2 discloses a flow chart of a method for data driven robust optimization of an industrial plant energy system under uncertainty in accordance with an embodiment of the present invention;
FIG. 3 discloses a graph of an industrial plant energy system data driven robust optimization framework under uncertainty in accordance with an embodiment of the present invention;
FIG. 4 discloses a scatter plot of uncertain parameters of an energy system according to an embodiment of the invention;
FIG. 5 is a diagram illustrating a robust optimization solution under different regularization parameters according to an embodiment of the present invention;
FIG. 6 discloses various energy consumption diagrams obtained under different regularization parameters according to an embodiment of the present invention.
The meanings of the reference symbols in the figures are as follows:
BO is boiler, WHRS is waste heat recovery system, ST is steam turbine, U is process work user, LV is temperature and pressure reducer, MT is cooling tower equipped with motor, CT is cooling tower, SINK is circulating water pond, PU is pump.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a data-driven robust optimization method for an energy system of an industrial device under uncertainty, which is based on a chemical thermodynamic principle, process historical operating data and a steam system superstructure, establishes an uncertain set by using a support vector clustering method based on a generalized cross kernel, thereby establishing an optimization model under the certainty and the uncertainty, optimizing the super-high pressure steam (SS) amount generated by a boiler in a system, the turbine extraction steam amount, the steam flow in a temperature and pressure reducer and an equipment switch by taking the lowest energy consumption of the energy system as a target, reducing the energy consumption of the energy system of the industrial device and ensuring the feasibility of the result.
Fig. 2 discloses a flowchart of a data-driven robust optimization method for an energy system of an industrial device under uncertainty according to an embodiment of the present invention, and as shown in fig. 2, the data-driven robust optimization method for an energy system of an industrial device under uncertainty according to the present invention includes the following steps:
s1, establishing an equipment model by utilizing the equipment characteristics, wherein the equipment characteristics are the mass and energy balance and the thermodynamic characteristics of the equipment, and the equipment model is a basic model of a boiler, a steam turbine, a temperature and pressure reducer and a cooling tower;
s2, obtaining the efficiency of the equipment and the normal operation range of the variable through regression based on the process historical operation database, and obtaining the isentropic efficiency of the boiler and the turbine and the heat exchange efficiency of the cooling tower;
s3, based on the obtained basic model and equipment efficiency, establishing a deterministic optimization model by combining process function user demand constraint, steam turbine network constraint and variable variation range and taking the lowest process energy consumption as a target;
s4, determining an uncertain parameter set based on the obtained equipment efficiency, wherein the uncertain parameter set comprises the steam inlet value and the steam extraction enthalpy value of each steam turbine;
and S5, obtaining process function user demand constraint under uncertainty based on the uncertain parameter set, and establishing a data-driven robust optimization model by combining with the certainty optimization model to realize robust optimization of the energy system.
Fig. 3 discloses a data-driven robust optimization framework diagram of an industrial plant energy system under uncertainty according to an embodiment of the present invention, and each step is specifically explained in detail below with reference to fig. 3.
S1, establishing an equipment model by using the equipment characteristics, wherein the equipment characteristics are the mass and energy balance and the thermodynamic characteristics of the equipment, and the equipment model is a basic model of a boiler, a steam turbine, a temperature and pressure reducing device and a cooling tower.
And establishing a basic model of the equipment based on the equipment characteristics and the historical operation data of the process.
The main equipment involved in the energy system comprises a Boiler (BO), a Waste Heat Recovery System (WHRS), a Steam Turbine (ST), a steam condenser, a temperature and pressure reducer (LV) and a Cooling Tower (CT).
And establishing an equipment model according to the thermodynamic model.
And S2, obtaining the efficiency of the equipment and obtaining the normal operation range of the variable through regression based on the process historical operation database, and obtaining the boiler efficiency, the turbine isentropic efficiency and the heat exchange efficiency of the cooling tower.
The equipment efficiency is obtained according to the historical process operation data by adopting a least square regression method.
Typically, the amount of SS generated by the waste heat recovery system can meet most of the SS requirements of the process, with the deficient portion of SS being generated by the boiler.
The heat exchange efficiency of the boiler can be obtained by the following regression formula:
wherein the content of the first and second substances,
is the amount of fuel, eta, required by the boilerboIt is the efficiency of the boiler that is,
the amount of water required by the boiler is,
is the maximum operating load of the boiler, alphaboAnd betaboAre regression parameters.
Steam turbines are important components of energy systems, including extraction turbines, full-condensing turbines, and back-pressure turbines.
The efficiency of a steam turbine is obtained by the following regression equation.
The work of the steam turbine st can be determined by the following equation:
wherein G isstIs the work load of the steam turbine,
is the steam extraction quantity of the steam turbine,
is the amount of steam that is vaporized and condensed,
and
the enthalpy values of the steam turbine inlet steam, the steam extraction steam and the condensed steam are respectively.
The enthalpy values of the steam inlet and the steam extraction can be calculated from data in a historical process operation database, and the enthalpy value of the condensed steam is calculated from the temperature and pressure of the corresponding stream in the steam condenser by using IAPWS-IF97 (International Water and steam Property institute Industrial calculation formula 1997):
wherein the content of the first and second substances,
and STC is the steam condenser internal pressure, the steam condenser index, and the steam condenser aggregate. .
The temperature and pressure reducing device is used for balancing a steam turbine network, and low-grade steam is obtained through temperature and pressure reduction, wherein the energy balance is as follows:
wherein the content of the first and second substances,
for the inlet steam enthalpy of the temperature and pressure reducer, Hlv,waterIs the enthalpy value of water at the inlet of the temperature and pressure reducer,
is the enthalpy value of the steam at the outlet of the temperature and pressure reducing device,
the flow rate of steam at the inlet of the temperature and pressure reducer is LV, the LV is a temperature and pressure reducer set.
The process return water is cooled by a cooling tower with a counter-flow motor, wherein the motor is of a determined load type. Due to the difference in humidity between the inside and outside of the cooling tower, part of the water will evaporate resulting in water loss. In addition, the circulating water tank has a continuous sewage draining device, so that fresh water needs to be continuously added to maintain the water balance of the whole system.
The heat exchange in the cooling tower mainly comprises air heat exchange quantity and moisture evaporation heat exchange quantity.
Air heat exchange quantity Qct,airThe corresponding expression is:
wherein M isct,airTo be the moisture of the airAmount of evaporation, Mct,vaporIs the evaporation capacity of the water in the cooling tower,
in order to realize the heat capacity of the air at the outlet of the cooling tower,
is the heat capacity of the air at the inlet of the cooling tower,
and
is the inlet and outlet air temperature, CT is the cooling tower index, and CT is the cooling tower set.
Heat transfer capacity Q of water evaporationct,vaporThe corresponding expression is:
wherein M isct,vaporIs the amount of water evaporated in the cooling tower, rwaterIs the latent heat of evaporation of water.
Heat Q of total return water taken away in cooling systemwaterComprises the following steps:
wherein z isctIs a binary variable, η, representing whether the cooling tower is selected or notctThe heat exchange efficiency of the cooling tower is improved.
Heat exchange efficiency eta of cooling towerctComprises the following steps:
wherein epsilonct，φct，
And gammactIs a regression parameter, TcwIn order to cool the temperature of the water,
the temperature of the air at the inlet is,
the flow rate of the water inlet of the cooling tower,
the maximum load of the cooling tower.
Temperature T of cooling watercwAnd the amount M of fresh water to be addedcfwThe corresponding expression is:
Mcfw＝∑zctMct,vapor+Mblw (10)
wherein, TrwTo the return water temperature, QwaterFor the heat cp of the cooling tower water being carried awaywaterIs the heat capacity of water, zctTo represent the binary variable selected for the cooling tower, Mct,vaporThe amount of water evaporated in the cooling tower, MblwThe flow of sewage is adopted.
And S3, establishing a deterministic optimization model with the aim of lowest process energy consumption based on the obtained basic model and heat exchange efficiency by combining process function user demand constraint, steam turbine network constraint and variable variation range.
The requirements of the process work user can be met by the corresponding steam turbine ST or the motor MT, and the constraint expression to be met is as follows:
wherein z isstTo indicate whether the steam turbine isSelected binary variable, GstFor power of steam turbines, GmuFor the amount of work done by the standby motor, GuThe method comprises the steps of obtaining a required work amount for a process work user, wherein ST is a steam turbine index, ST is a steam turbine set, U is a process work user index, U is a process work user set, MU is a standby motor index, and MU is a standby motor set.
The steam turbine network constraint refers to four steam level balances of SS (515 ℃, 11.5MPa), HS (390 ℃, 4.2MPa), MS (290 ℃, 1.6MPa) and LS (210 ℃, 0.35 MPa).
For each grade of steam network, the amount of steam needs to be balanced, and the constraint expression of the steam turbine network is as follows:
wherein the content of the first and second substances,
is the steam flow at the inlet of the temperature and pressure reducing device,
for the steam flow at the outlet of the temperature and pressure reducer, CsteamIt is the amount of steam consumed,
is the process corresponds to the steam demand, zboTo represent the binary variable selected for use by the boiler,
is the flow rate of the steam at the outlet of the boiler,
for the exhaust heat recovery system outlet steam flow, zstTo represent the binary variable selected for use in the steam turbine,
for extracting steam from steam turbinesThe amount of the compound (A) is,
is the steam turbine inlet steam flow.
All continuous decision variables in the process should be satisfied within the normal operating range:
mmin≤m≤mmax (13)
wherein m is a continuous decision variable, mminIs the minimum value of the continuous decision variable, mmaxIs the maximum value of the continuous decision variable.
The continuous decision variables include: the flow of the ultrahigh pressure steam generated in the boiler, the extraction and purge gas flows of the extraction condensing turbine, and the water flow of each cooling tower.
The fuel consumption in the energy system mainly comprises a boiler and a waste heat recovery system, and the power consumption mainly comprises a motor corresponding to a process user and a motor corresponding to a cooling tower.
Water is mainly used for SS generation in boilers and waste heat recovery systems, for balancing the water quantity and in desuperheaters.
The steam consumption includes outsourced high pressure steam and medium pressure steam.
The optimization goal of the deterministic optimization model is to minimize the total energy consumption after weighting of various energy sources, and the expression of the objective function is as follows:
min y＝Cfuel+ζHSCHS+ζMSCMS+ζelectricityCelectricity+ζwaterCwater (14)
therein, ζHS、ζMS、ζelectricity、ζwaterRespectively, the parameters of converting the corresponding energy sources of high-pressure steam, medium-pressure steam, electric power and water into standard oil quantity, CfuelFor fuel consumption, CHSFor high pressure steam consumption, CMSFor medium-pressure steam consumption, CelectricityFor power consumption, CwaterIs the water consumption.
In this embodiment, ζHS＝0.08kg/kg，ζMS＝0.066kg/kg，ζelectricity＝0.00023kg/Mw， ζwater＝0.00017kg/t。
And establishing a deterministic optimization model based on the established equipment model, the system balance constraint and the requirement constraint of the process work user.
The deterministic optimization model is shown in equation 15, which is a Mixed-Integer Nonlinear Programming (MINLP) problem.
Wherein y is total energy consumption;
mass and energy constraints, corresponding to equations 1-10;
process work user demand constraints, corresponding to equation 11;
steam network balance constraints, corresponding to equation 12;
the variable range constraint corresponds to equation 13.
And S4, determining an uncertain parameter set based on the obtained equipment efficiency, wherein the uncertain parameter set comprises the enthalpy values of the steam inlet and the steam extraction of each steam turbine.
In deterministic optimization, the temperature and pressure of each steam stage are considered constant, i.e., the enthalpy of the two feeds is considered the same for both turbines for the inlet steam and the high pressure steam.
However, in the actual industry, there is a certain distance between the turbines, and the steam has pressure and temperature losses in the pipe network, that is, the enthalpy of the steam actually varies. However, these variations cannot be measured in time, resulting in deviations of the actual values from the ideal values, and therefore the result of deterministic optimization may not be optimal or even feasible in practical situations.
According to the method, the enthalpy value of each steam stream is calculated by utilizing the process duration operation data, and an uncertain set is established by adopting a generalized cross kernel SVC.
The uncertain parameters are all steam turbine steam inlet and extraction enthalpy values, and are calculated according to IAPWS-IF97 by the temperature and pressure of the steam in the process history database.
SVC is widely used to estimate the support of unknown probability distribution from random data samples, and generalized cross-kernel SVC captures the relationship between uncertain parameters through a weight matrix based on a covariance matrix.
The SVC describes a large number of data points in the form of a closed sphere of minimal volume:
wherein p is the center of the interval with radius R, u(i)Is the ith sample, and N is the number of samples.
By adding relaxation variables and introducing lagrange multipliers, equation 16 can be rewritten as a strict quadratic programming dual problem:
wherein the kernel function K (u)(i),u(j))＝ψ(u(i))Tψ(u(j))；
u(i)For the ith uncertain parameter, u(j)For the jth uncertain parameter, ωi、ωjFor lagrange multipliers, N is the number of samples and κ is the positive regularization parameter.
Only having positive omegaiSample u of(i)It points to the center p, i.e. the support vector.
Wherein the boundary support vector | | ψ (u)(i))-p||2＝R2Exactly on the boundary of the sphere, and | | | | ψ (u)(i))-p||2＞R2Is an outlier, forming the following expression:
the radius may be represented by the distance of the center to any boundary support vector, so the expression for the normal data set can be written as:
the weighted kernel function is:
wherein, the weighting matrix W ═ Σ-1/2And Σ is a covariance matrix.
Since K (u, u) is constant, define
U (D) may be expressed as:
the worst-case constraint (equation 23) can be transformed into a dual-form uncertainty parameter set (equation 24) by introducing lagrange multipliers:
wherein σi、
Tau is a dual-coupling parameter,
as a weighting matrix, sigma as a covariance matrix, u(i)For uncertain parameters, upsilon ═ Σi∈SVωi||W(u(i')-u(i))||1Is the intermediate variable, b is the right parameter of the original constraint, x is the decision variable, ωiIn order to be a lagrange multiplier,
is a positive n-dimensional real number set, SV is a sample point set, and i is a sample point index.
And S5, obtaining process function user demand constraint under uncertainty based on the uncertain parameter set, and establishing a data-driven robust optimization model by combining with the certainty optimization model to realize robust optimization of the energy system.
In this embodiment, the process power user demand constraint includes the turbine inlet steam enthalpy value with the uncertain parameter
And enthalpy of extraction
An uncertain vector of
Thus, the process function user requirement constraint under uncertainty is expressed as follows:
wherein σst,i、
τstIn order to be able to do a dual-polarization parameter,
in order to be a weighting matrix, the weighting matrix,
in order to determine the parameters of the device,
is an intermediate variable, GuAmount of work required for process work user, zstTo represent the binary variable, G, selected for the steam turbinemuIn order to reserve the work capacity of the motor,
the flow rate of the condensed steam at the outlet of the turbine,
is the enthalpy value of the turbine condensed steam,
for turbine extraction flow, omegast,iAnd the index is a Lagrangian multiplier, ST is a steam turbine index, ST is a steam turbine set, and i is a sample point index.
Based on the obtained uncertain set, the data-driven robust optimization model is an MINLP model, and the expression is as follows:
wherein y is the total energy consumption.
Mass and energy constraints, corresponding to equations 1-10;
process work user demand constraints, corresponding to equation 25;
steam network balance constraints, corresponding to equation 12;
the variable range constraint corresponds to equation 13.
After the establishment of the energy system deterministic optimization model and the data-driven robust optimization model is completed, programming is carried out in GAMS 24.7.4, and a BARON (16.8.24) solver is selected for solving.
The GAMS is a piece of general commercial numerical analysis software, is suitable for solving linear, nonlinear and mixed integer optimization problems, is modeled in a highly concise and natural way, and facilitates rapid modification of formulas, conversion of solvers and sensitivity analysis.
The BARON (Branch-And-Reduce Optimization Navigator) is a solver for solving nonlinear programming (NLP) And MINLP model global optimal solutions, And is a Branch-And-bound type algorithm, which is enhanced by various constraint propagation, interval analysis And dual techniques to Reduce the range of variables in the algorithm process And to construct strict slack by expanding feasible regions And/or underestimating objective functions.
The invention provides a data-driven robust optimization method of an energy system of an industrial device under uncertainty, which adopts a hybrid modeling method, establishes an equipment model according to equipment characteristics and process historical operating data, converts a deterministic optimization model into a mixed integer nonlinear programming (MINLP) model on the basis of mass and energy conservation, turbine work-doing constraint, steam pipe network balance constraint and process variable variation range constraint in the process, and adopts GAMS to solve.
In consideration of uncertainty in the operation process, an uncertain set is established by a Support Vector Clustering (SVC) method based on a generalized cross kernel, turbine work constraint is rewritten into an uncertain form, an original deterministic optimization model can be written into a robust optimization model under uncertainty, optimization of an energy system under uncertainty is achieved, and feasibility of an optimization result is guaranteed.
Taking the industrial device energy system shown in fig. 1 as an example, the data-driven robust optimization method for the industrial device energy system under uncertainty provided by the present invention is adopted for optimization, wherein four energy mediums are designed, which are fuel, steam, electricity and water.
Waste heat recovery systems typically consume fuel and water to produce ultra-high pressure steam that can meet most of the demand, and boilers are used to supplement the deficit.
Steam turbine networks involve ultra-high pressure steam, medium pressure steam, and low pressure steam, with multiple turbines used to generate steam as a process heat exchange medium and to drive process work users.
The process steam requirements were 21,727kg/h HS, 55,176kg/h MS and 1466kg/h LS.
The process power user may select either a turbine drive or a backup motor drive.
The temperature and pressure reducing device is used for balancing a steam pipe network.
The cooling tower is used for cooling return water in the system, and the cooling water is collected in a circulating water tank and is electrically pumped to each water-consuming device.
The lowest energy consumption of the energy system is taken as an optimization target, decision variables are shown in a table 1, and turbine description is shown in a table 2.
TABLE 1 decision variables
TABLE 2 turbine description
In this embodiment, 1000 sets of samples are extracted from the historical operating database of the process, and a point is taken every 5 hours, and the data of the year may contain most of typical operating conditions.
The enthalpy values of the inlet and extraction are calculated by IAPWS-IF97 based on the temperature and pressure in the process history database, eliminating outliers by estimating the normal operating range.
Two-dimensional scatter plots of uncertain parameters of turbines st1-st7 are shown in FIG. 4. FIG. 4 discloses a scatter plot of uncertain parameters of an energy system according to an embodiment of the present invention. As can be seen from FIG. 4, the distribution of parameters is not uniform, and is a multi-modal, correlated and asymmetric uncertain parameter set, and it is difficult to model parameters under all conditions with linear or non-linear functions.
The range of variation of each uncertain parameter is shown in table 3.
TABLE 3 uncertain parameter ranges
After the energy system certainty and robust optimization model establishment is completed, programming is performed in GAMS 24.7.4, and a BARON (16.8.24) solver is selected for solving.
The regularization parameter k is set to 0.02, the problem scale and optimization results of deterministic and robust optimization are shown in table 4, and the decision variables before and after optimization are shown in table 5.
TABLE 4 problem Scale for deterministic and robust optimization and optimization results
TABLE 5 decision variables before and after optimization
The total energy consumption of the deterministically optimized energy system is 15,148.84 kilograms standard oil per hour (kg oil/h), and the total energy consumption of the robustly optimized energy system is 16,209.81kg oil/h which is far greater than that of the former.
In the deterministic optimization, the steam turbine steam inlet enthalpy parameter and the steam extraction enthalpy parameter are considered as constants, while the worst case is considered in the robust optimization, so the optimization result is poor.
Due to the introduced auxiliary variables and the Lagrange multiplier, the problem scale of the robust optimization is far larger than that of the deterministic optimization model, so that the robust optimization needs longer calculation time.
To avoid accidental errors, the possible optimal solutions for robust optimization are also listed in the table, whose values are also much larger than the result of deterministic optimization.
Deterministic optimization has primarily reduced the SS produced by the boiler compared to current conditions, where the SS produced by the waste heat recovery system can meet most of the demand.
The steam turbine st1 has an increased extraction and a reduced condensation, whereas the steam turbine st2 has a lower HS consumption than the turbine st 3.
In the robust optimization, the steam extraction amount of the turbine st2 is smaller, and the steam consumption of the turbine st3 is larger. The desuperheater causes a loss of energy and therefore in practice the amount of steam entering the desuperheater should be as small as possible.
In this embodiment, the waste heat recovery system generates too much SS, so the excess is used for downgrading to HS.
The requirement of 1364kg/h LS is met by MS degradation.
In both deterministic and robust optimization, all process work users select a backup motor drive.
In a deterministic optimization, one cooling tower and one pump are shut down, and in a robust optimization, two pumps are shut down, compared to the current operating conditions.
The degree of conservation of the robust optimization in this embodiment can be adjusted by the regularization parameter, setting k to 0.001, 0.005, 0.01, 0.02, 0.04.
Fig. 5 discloses a schematic diagram of a robust optimization solution result under different regularization parameters according to an embodiment of the present invention, and fig. 6 discloses a schematic diagram of various energy consumptions obtained under different regularization parameters according to an embodiment of the present invention, as shown in fig. 5 and fig. 6, as κ increases, an uncertainty set is smaller, and a conservative degree of an optimization result is lower. The fuel consumption remained the same and was equal to 26,051kg/h of waste heat recovery system consumption.
The HS delivery increases slightly with increasing κ, while LS delivery reaches a critical value when κ is 0.005.
The consumption of both energy sources does not vary much, since the uncertain parameters have a small influence on the consumption of electricity and water.
Due to the uncertainty of the actual plant, a solution for deterministic optimization may be optimal in the current case, but not feasible in the next case.
While the robust optimization results are generally worse than the deterministic optimization results, the actual case is better than the worst case, and therefore the solution is also better than the robust optimization results. Robust optimization ensures that knowledge is feasible under any possible operating condition, achieving a tradeoff between optimization and robustness.
The results are combined to prove the high efficiency and the reliability of the data-driven robust optimization model provided by the invention.
The invention provides a data-driven robust optimization method for an energy system of an industrial device under uncertainty, which is characterized in that an uncertain set is established for uncertain parameters by utilizing a generalized cross kernel algorithm, the optimization of an actual working device can be guided, the balance between an optimization result and conservation is realized by optimizing the energy system under uncertainty through the robustness, the feasibility of the optimization result is ensured under the condition of reducing the energy consumption of the device, and the data-driven robust optimization method is suitable for the robust optimization of energy systems of various industrial devices and has wide adaptability.
While, for purposes of simplicity of explanation, the methodologies are shown and described as a series of acts, it is to be understood and appreciated that the methodologies are not limited by the order of acts, as some acts may, in accordance with one or more embodiments, occur in different orders and/or concurrently with other acts from that shown and described herein or not shown and described herein, as would be understood by one skilled in the art.
As used in this application and the appended claims, the terms "a," "an," "the," and/or "the" are not intended to be inclusive in the singular, but rather are intended to be inclusive in the plural unless the context clearly dictates otherwise. In general, the terms "comprises" and "comprising" merely indicate that steps and elements are included which are explicitly identified, that the steps and elements do not form an exclusive list, and that a method or apparatus may include other steps or elements.
The embodiments described above are provided to enable persons skilled in the art to make or use the invention and it is to be understood that modifications or variations may be made to the embodiments described above without departing from the inventive concept of the present invention, and therefore the scope of protection of the present invention is not limited by the embodiments described above but should be accorded the widest scope consistent with the innovative features set forth in the claims.
Claims (10)
1. A data-driven robust optimization method for an energy system of an industrial device under uncertainty is characterized by comprising the following steps:
s1, establishing an equipment model by utilizing the equipment characteristics, wherein the equipment characteristics are the mass and energy balance and the thermodynamic characteristics of the equipment, and the equipment model is a basic model of a boiler, a steam turbine, a temperature and pressure reducer and a cooling tower;
s2, performing regression to obtain the efficiency of the equipment and obtain the normal operation range of the variable based on the process history operation database;
s3, based on the obtained basic model and equipment efficiency, establishing a deterministic optimization model by combining process function user demand constraint, steam turbine network constraint and variable variation range and taking the lowest process energy consumption as a target;
s4, establishing an uncertain parameter set by adopting a generalized cross-kernel algorithm based on the obtained equipment efficiency, wherein the uncertain parameter set comprises the enthalpy values of the steam admission and the steam extraction of each steam turbine;
and S5, obtaining process function user demand constraint under uncertainty based on the uncertainty parameter set, and establishing a data-driven robust optimization model by combining with the certainty optimization model to realize robust optimization of the energy system.
2. The method for uncertainty-based data-driven robust optimization of industrial plant energy systems according to claim 1, wherein in step S2:
the process historical operating database includes measurable variables in all energy systems;
the regression algorithm comprises a least square method, and boiler efficiency, turbine isentropic efficiency and heat exchange efficiency of the cooling tower are obtained through regression.
3. The method for uncertainty-based data-driven robust optimization of industrial plant energy systems according to claim 1, wherein in step S3,
the process work user requirements are constrained by,
wherein z isstTo represent the binary variable, G, selected for the steam turbinestFor the work done by the steam turbine, GmuFor the amount of work done by the standby motor, GuThe method comprises the steps that the work required by process work users is realized, ST is a steam turbine index, ST is a steam turbine set, U is a process work user index, U is a process work user set, MU is a standby motor index, and MU is a standby motor set;
the steam turbine network is constrained by the constraints that,
wherein the content of the first and second substances,
is the steam flow at the inlet of the temperature and pressure reducing device,
for reducing the steam flow at the outlet of the temperature and pressure reducer, CsteamIt is the amount of steam consumed,
is the process corresponds to the steam demand, zboTo represent whether the boiler is selected for use as a binary variable,
is the flow rate of the steam at the outlet of the boiler,
is an outlet of a waste heat recovery systemSteam flow rate, zstTo represent the binary variable selected for use in the steam turbine,
is the extracted steam flow of the steam turbine,
is the steam turbine inlet steam flow;
the variable ranges of variation are as follows,
mmin≤m≤mmax；
wherein m is a continuous decision variable, mminIs the minimum value of the continuous decision variable, mmaxIs the maximum value of the continuous decision variable.
4. The method for uncertainty industrial plant energy system data driven robust optimization of claim 1, wherein in step S3, the steam turbine network constraints include four steam level balances of extra-high pressure SS, high pressure HS, medium pressure MS, and low pressure LS.
5. The uncertainty based industrial device energy system data-driven robust optimization method of claim 4, wherein in step S3, the objective function of the deterministic optimization model is expressed as follows:
min y＝Cfuel+ζHSCHS+ζMSCMS+ζelectricityCelectricity+ζwaterCwater；
therein, ζHS、ζMS、ζelectricity、ζwaterRespectively, the parameters of converting the corresponding energy sources of high-pressure steam, medium-pressure steam, electric power and water into standard oil quantity, CfuelFor fuel consumption, CHSFor high-pressure steam consumption, CMSFor medium-pressure steam consumption, CelectricityFor power consumption, CwaterIs the water consumption.
6. The uncertain industrial plant energy system data-driven robust optimization method of claim 1, wherein the enthalpy values of the steam intake and steam extraction in the step S4 are calculated from the temperature pressure of the corresponding stream in the steam condenser in the process history operation database by IAPWS-IF 97.
7. The uncertain industrial plant energy system data-driven robust optimization method of claim 3, wherein the uncertain parameter set in step S4 is expressed as follows:
wherein σi、
Tau is a dual-coupling parameter,
as a weighting matrix, ∑ as a covariance matrix, u(i)For uncertain parameters, upsilon ═ Σi∈SVωi||W(u(i')-u(i))||1Is the intermediate variable, b is the right parameter of the original constraint, x is the decision variable, ωiIn order to be a lagrange multiplier,
is a positive n-dimensional real number set, SV is a sample point set, and i is a sample point index.
8. The uncertain industrial device energy system data-driven robust optimization method of claim 7, wherein in step S5, uncertain process work user demand constraints are expressed as follows:
wherein σst,i、
τstIn order to be able to do a dual-polarization parameter,
in order to be a weighting matrix, the weighting matrix,
in order to determine the parameters of the device,
is an intermediate variable, GuAmount of work required for process work user, zstTo represent the binary variable, G, selected for the steam turbinemuIn order to reserve the work capacity of the motor,
the flow rate of the condensed steam at the outlet of the turbine,
is the enthalpy value of the turbine condensed steam,
for turbine extraction flow, omegast,iAnd the index is a Lagrange multiplier, ST is a steam turbine index, ST is a steam turbine set, and i is a sample point index.
9. The method for uncertainty-based data-driven robust optimization of an industrial plant energy system according to claim 8, wherein the deterministic optimization model in step S3 and the data-driven robust optimization model in step S5 are both mixed integer nonlinear programming models, and are solved using a Baron solver.
10. The method for the data-driven robust optimization of the industrial device energy system under the uncertainty of claim 8, wherein the data-driven robust optimization model corresponds to the following expressions:
wherein y is the total energy consumption.
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