CN116629029B - Data-driven-based flow industry user flexibility assessment method and related equipment - Google Patents

Data-driven-based flow industry user flexibility assessment method and related equipment Download PDF

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CN116629029B
CN116629029B CN202310885197.0A CN202310885197A CN116629029B CN 116629029 B CN116629029 B CN 116629029B CN 202310885197 A CN202310885197 A CN 202310885197A CN 116629029 B CN116629029 B CN 116629029B
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徐宪东
单文亮
贾宏杰
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Abstract

The invention provides a flow industrial user flexibility assessment method based on data driving and related equipment, and relates to the technical field of energy information processing, wherein the method comprises the following steps: acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated; acquiring an uncertainty set by using a Dirichlet process based on historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to each type of pressure layer in a steam energy supply system respectively, and data points on each linear polyhedron are determined based on a description formula of steam enthalpy difference at two ends of one type of pressure layer, wherein the description formula is determined based on posterior distribution of steam enthalpy difference at two ends of the pressure layer; and acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertainty set into the constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of an industrial user to be evaluated. The invention can realize the flexibility evaluation of the industrial user under the influence of uncertainty.

Description

Data-driven-based flow industry user flexibility assessment method and related equipment
Technical Field
The invention relates to the technical field of energy information processing, in particular to a flow industrial user flexibility assessment method based on data driving and related equipment.
Background
The process industry users are large-electricity-consumption enterprises which are provided with own energy supply systems, the energy supply systems are usually coupled with multiple energy sources such as electricity, fuel, steam and the like, and the energy supply systems are coupled with the generation process, so that the flexibility is provided for the power system through power auxiliary services. In the process of providing auxiliary services, the process industry users need to strictly meet the requirement of bidding capacity, otherwise, service violations are subjected to punishment, so that accurate assessment of the flexibility boundary of the process industry users capable of participating in the electric auxiliary services is an important step, however, in the actual operation process of the system, a plurality of uncertain factors such as temperature and pressure change often cause steam enthalpy change, thereby influencing the output of a turbine generator and further causing the flexibility boundary to change within a certain range.
How to adopt a robust optimization method to consider uncertainty in the flexibility evaluation process and obtain the worst evaluation result of the flexibility boundary under the influence of the uncertainty, thereby avoiding possible service violation punishment is an important subject to be solved urgently at present.
Disclosure of Invention
The invention provides a flow industrial user flexibility evaluation method based on data driving and related equipment, which are used for solving the defect that the worst evaluation result of a flexibility boundary under the influence of uncertainty cannot be obtained in the prior art and realizing the flexibility evaluation under the influence of uncertainty.
The invention provides a flow industrial user flexibility assessment method based on data driving, which comprises the following steps:
acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy differences of two ends of a plurality of pressure layers;
acquiring an uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to pressure layers of each type in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
Acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertain set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an adjustable output amplitude of the power auxiliary service provided by the energy supply system;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; / >Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Indicating the normal operating point of the turbine providing the electric auxiliary service in the energy supply system.
The invention also provides a device for evaluating the flexibility of the process industrial user based on data driving, which comprises the following steps:
the system comprises a data acquisition module, a control module and a control module, wherein the data acquisition module is used for acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprise pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprise steam enthalpy difference of two ends of a plurality of pressure layers;
the uncertain set determining module is used for acquiring an uncertain set by using a Dirichlet process based on the historical steam enthalpy value data, the uncertain set comprises linear polyhedrons corresponding to pressure layers in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy value differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of steam enthalpy value differences at two ends of the pressure layer, and steam enthalpy value differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
The model solving module is used for acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertainty set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an output adjustable value of the energy supply system for providing electric auxiliary service;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Indicating the normal operating point of the turbine providing the electric auxiliary service in the energy supply system.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the method for evaluating the flexibility of the flow industrial user based on data driving when executing the program.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a data-driven-based flow industry user flexibility assessment method as described in any of the above.
According to the flow industrial user flexibility assessment method and the related equipment based on data driving, the flexibility assessment model of the energy supply system is built based on the energy supply system structure of the typical flow industrial user in advance, an uncertainty set is built by adopting a Dirichlet process based on historical steam enthalpy difference data of the energy supply system of the industrial user, the uncertainty set is an uncertainty data set capable of describing steam enthalpy uncertainty existing in the energy supply system, model optimization solving is carried out based on the uncertainty set, conservation degree of robust optimization is reduced, and flexibility assessment of the industrial user under the influence of uncertainty can be achieved.
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In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow diagram of a method for evaluating flexibility of a process industrial user based on data driving provided by the invention;
FIG. 2 is a typical configuration of an energy supply system for a process industry user;
FIG. 3 is a schematic diagram of a process for solving an objective function of a flexibility evaluation model based on a data-driven process industry user flexibility evaluation method provided by the invention;
FIG. 4 is a schematic diagram of an energy supply system based on an example of verification of a data driven process industrial user flexibility assessment method provided by the present invention;
FIG. 5 is a statistical graph of steam temperature for each pressure layer of the energy supply system for an example of verification of the data-driven process industry user flexibility assessment method provided by the present invention;
FIG. 6 is a statistical plot of vapor pressure for each pressure layer of the energy supply system for an example of verification of the data-driven process industry user flexibility assessment method provided by the present invention;
FIG. 7 is a scatter plot of uncertain data for an example verification instance based on the data driven process industry user flexibility assessment method provided by the present invention;
FIG. 8 is a schematic diagram of a polyhedron uncertainty set constructed by using deviation information in an example of verification of a data-driven process industry user flexibility assessment method provided by the invention;
FIG. 9 is a schematic diagram of an uncertainty set based on principal component analysis in a verification example of a data-driven process industry user flexibility assessment method provided by the present invention;
FIG. 10 is a schematic diagram of an uncertainty set constructed using the method of the present invention in an example of verification of the method of the present invention based on a data driven process industry user flexibility assessment method provided by the present invention;
FIG. 11 is a graph comparing turbine output boundary results obtained by the method of the present invention and the deterministic evaluation method in the verification example of the data-driven-based process industrial user flexibility evaluation method provided by the present invention;
FIG. 12 is a graph comparing results of a flexibility assessment robust optimization method employing multiple uncertainty set construction methods in a verification example of a data-driven-based process industry user flexibility assessment method provided by the present invention;
FIG. 13 is a schematic diagram of a data-driven flow industry user flexibility assessment device according to the present invention;
Fig. 14 is a schematic structural diagram of an electronic device provided by the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the actual operation of the energy supply system of the process industry user, a plurality of uncertain factors, such as the change of temperature and pressure, lead to the change of vapor enthalpy value, thus affecting the output of the turbogenerator, and further leading to the change of flexibility boundary within a certain range.
How to adopt a robust optimization method to consider uncertainty in the flexibility evaluation process and obtain the worst evaluation result of the flexibility boundary under the influence of the uncertainty, thereby avoiding possible service violation punishment is an important subject to be solved urgently at present.
The method for evaluating the flexibility of the process industrial user based on the data driving according to the present invention is described below with reference to fig. 1 to 12, and as shown in fig. 1, the method for evaluating the flexibility of the process industrial user based on the data driving according to the present invention includes the following steps:
S110, acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy difference of two ends of a plurality of pressure layers;
s120, acquiring an uncertainty set by using a Dirichlet process based on historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to each type of pressure layer in a steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type obey the same distribution;
s130, acquiring equipment operation data of an energy supply system, inputting the equipment operation data and an uncertainty set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of an industrial user to be evaluated, wherein the flexibility evaluation result reflects an output adjustable amplitude value of an electric auxiliary service provided by the energy supply system;
The operation state of the process industry users is affected by factors such as the production process and the external environment, and has larger uncertainty in the actual operation process, including changes of electric power and steam load, changes of pressure and temperature of a steam system and uncertainty of process enthalpy change caused by the changes. In the energy supply system, the key link for determining the flexibility is that the steam power generation system, the uncertainty of the steam enthalpy value can cause the output of the steam turbine generator to change randomly under the expected steam flow, and the flexibility boundary can further change within a range.
wherein , and />Respectively represent the upward and downward flexibility adjustable magnitudes of the steam turbine for the power supply system to provide the power auxiliary service;xthe steam flow of each device in the energy supply system is contained as a decision variable; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in an energy supply system;Uis an uncertainty set; /> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively; / >,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layer, between the ultrahigh pressure and the medium pressure layer, between the high pressure layer and the water, and between the medium pressure and the low pressure layer of the vapor system, respectively; />,/>Andrespectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />And the normal operating point of the steam turbine providing the power auxiliary service in the energy supply system is an operating output value of the steam turbine set by a process industry user, and the steam turbine operates according to the operating output value under the condition of no special condition. Solving the objective function to obtain the flexibility evaluation result of the industrial user to be evaluated, and evaluating the flexibilityThe result includes-> and />
A typical structure of the power supply system for the process industry user is shown in fig. 2, and mainly relates to a multi-energy network such as electricity/steam/natural gas. The system comprises a plurality of steam pressure levels of ultrahigh pressure, high pressure, medium pressure, low pressure and the like, and it is worth noting that not all energy supply systems of industrial users of the process flow comprise the steam pressure levels of ultrahigh pressure, high pressure, medium pressure and low pressure, but only have parts thereof, wherein the ultrahigh pressure, high pressure, medium pressure and low pressure can be divided according to the pressure of each pressure layer in the system, namely, the pressure layer with the lowest pressure is a low pressure layer, and then the pressure layer with the lowest pressure is a medium pressure layer, a high pressure layer and an ultrahigh pressure layer. The boiler generates ultrahigh pressure steam by burning natural gas and by-product fuel accompanying the production process. Steam meets different types of industrial production needs through a pipe network system having multiple pressure levels. The steam turbine generators are arranged between different pressure levels, so that the steam utilization rate is improved, meanwhile, a part of electricity consumption requirements are met, and the rest electricity consumption requirements are met by external network electricity purchasing. When the passing steam is lower than the production requirement, the balance of steam supply and demand can be maintained through the bypass valve, and when the produced steam exceeds the production requirement, the surplus steam is discharged through the safety valve. When the industrial user needs to provide the electric auxiliary service, the operation state of the energy supply system can be changed through the adjustment of equipment such as a boiler, a steam turbine, a valve and the like. According to the method provided by the invention, the flexibility evaluation model of the energy supply system is constructed on the basis of the energy supply system structure of the typical process industrial user in advance, the uncertainty set is established by adopting the Dirichlet process on the basis of the historical steam enthalpy difference data of the energy supply system of the industrial user, the uncertainty set is an uncertainty data set capable of describing the uncertainty of the steam enthalpy in the energy supply system, the model optimization solution is carried out on the basis of the uncertainty set, the conservation degree of robust optimization is reduced, the flexibility evaluation of the industrial user under the influence of the uncertainty can be realized, and therefore, the conservation degree is reduced on the premise of avoiding the default of auxiliary service as far as possible, the income of the process industrial user in the electric auxiliary service is improved, and the robustness and the economy of the flexibility evaluation are considered.
Specifically, in the invention, the pre-established flexibility evaluation model comprises an operation model of each piece of equipment in the energy supply system, and the piece of equipment comprises a boiler and a steam turbine.
In the process industry user energy supply system, a gas boiler is generally installed on an ultrahigh pressure layer to generate steam, and in order to improve the energy utilization rate, byproduct fuels accompanying the combustion industry production process of a recovery boiler are generally generated, and the operation characteristic models of the gas boiler and the recovery boiler can be expressed as follows:
;/>
wherein , and />The natural gas consumption of the gas boiler and the recovery boiler are respectively represented; and />Respectively representing the difference of vapor enthalpy values at two ends of the gas boiler and the recovery boiler; />Andrespectively representing the steam flow rate generated by the gas boiler and the recovery boiler; />Representation ofThe mass flow rate of the byproduct fuel; /> and />Respectively representing the efficiency of the gas boiler and the recovery boiler; /> and />The heating values of natural gas and byproduct fuel are represented, respectively.
Steam turbines installed in process industry consumer energy systems are generally divided into three types: back pressure, extraction-back pressure, condensing. The extraction-back pressure type steam turbine and the condensing steam turbine can be equivalently used as a back pressure type steam turbine, and the generated energy is expressed as follows:
generating power for the steam turbine; / >The power generation efficiency of the steam turbine; />Representing steam flow through the steam turbine; />Indicating the difference in enthalpy of the steam flowing across the turbine.
The flexibility evaluation model pre-constructed in the invention also comprises an electric network power balance model, a natural gas network supply and demand balance model and a steam network supply and demand balance model.
The network power balancing model can be expressed as:;/>representing the power input by an external power grid; />Representing the electrical load of the industrial process.
The natural gas network supply and demand balance model can be expressed as:;/>is the volume of natural gas input by the external natural gas network.
The steam flow of the steam network on each pressure layer should be balanced in input and output, and the steam network supply and demand balance model can be expressed as:
wherein ,,/> and />Respectively means passing through an ultrahigh pressure layer, a high pressure layer, an ultrahigh pressure layer, a medium pressure layer and a medium pressure layerSteam flow of the back pressure turbine between the layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />,/>,/> and />Respectively representing the steam flow flowing through the bypass valve between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, the high pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing industrial production steam flow demand; / >Representing the flow of steam discharged through a relief valve mounted on the low pressure layer.
In the invention, the pre-established flexibility evaluation model also comprises constraint conditions, wherein the constraint conditions determine the feasible domain of the variable in the objective function, and the constraint conditions comprise equipment operation constraint and external purchase energy limitation. Specifically, the device operational constraints may be formulated as:
;/>
;/>
wherein , and />Respectively representing the minimum output and the maximum output of the steam turbine; />Steam flow indicative of bypass valve, +.>Representing the steam flow of the safety valve; /> and />Respectively representing the minimum steam yield and the maximum steam yield of the boiler; /> and />The maximum steam flow of the bypass valve and the relief valve are indicated, respectively.
The external purchase energy limit may be formulated as:
and />Respectively represent the lower limit of electricity purchasing to the external power gridAnd upper limit of electricity purchase; /> and />The lower limit and the upper limit of the gas purchasing to the external natural gas network are respectively indicated.
Based on the historical vapor enthalpy data, acquiring an uncertainty set by using a dirichlet procedure, including:
classifying pressure layers of an energy supply system by using a Dirichlet process based on historical steam enthalpy value data, and obtaining corresponding posterior distribution parameters of each type;
Wherein parameters in the dirichlet procedure are determined based on a variance inference; the variation deducing process is as follows:
random initialization parameters, noted as
Solving for mixing parametersApproximate distribution of posterior distribution +.>, wherein ,;/>mult stands for polynomial distribution, +.>Representing Beta distribution->Representing the distribution of n-tai-li-wei-sha>Represent the uncertainty concentrationiDistribution parameters corresponding to data tags of individual categories, < ->Is->Posterior distribution-related parameters of vapor enthalpy differences of pressure-like layers->Is a concentration parameter for controlling the data dispersion, when +.>When (I)>The method comprises the steps of carrying out a first treatment on the surface of the When->When (I)>,/>For a preset cut-off level, +.>Is constant (I)>Represent the uncertainty concentrationiData labels of the respective categories, N being the total number of data categories,/->,/>Indicate->The mean vector of the vapor enthalpy differences of the pressure-like layer,indicate->Covariance matrix of steam enthalpy difference of pressure-like layer;
lower bound of the transformation,/>Representing the desire for an approximate distribution;
solving forOrder-making
Solving for
Order theRepeat the mixing parameters->Approximate distribution of posterior distribution +.>Until the convergence condition is satisfied, parameter after the convergence condition is satisfied +.>As posterior distribution parameters of differences in vapor enthalpy values of the pressure layers of the energy supply system.
The method provided by the invention adopts the Dirichlet process to construct an uncertainty set so as to solve the objective function. Firstly preprocessing steam enthalpy value historical data, forming the steam into an enthalpy value difference form, secondly clustering the data based on a dirichlet process mixed model, then sampling the data based on a variation inference method, describing boundary characteristics of each type of data, obtaining a plurality of basic uncertainty sets in the form of convex polyhedrons, and finally taking a union set of the basic uncertainty sets as a data driving uncertainty set. The following is a detailed description.
The method is influenced by an industrial production process, steam enthalpy values of pressure layers of a steam system are related, steam enthalpy values in a section of historical events are collected, and an enthalpy value difference data set is obtained according to industrial steam system results and is used as historical steam enthalpy value data. Assume that the enthalpy difference between two ends of n devices in the energy supply system is t periodStatistics of->The enthalpy value difference history data sample set obtained in each period is +.>,/>The historical vapor enthalpy value data are the historical vapor enthalpy value data. The data set presents multi-modal, related and uncertain complex distribution characteristics, and uncertain parameters are difficult to describe by linear or nonlinear functions directly.
Wherein K represents the number of basic components in the Gaussian mixture distribution, and each component represents one type;representing the weight of the kth component; />Is the mean value +.>Covariance matrix +.>Is a multi-dimensional normal distribution of (2); i.i.d represents independent co-distribution.
The dirichlet process mixture model is a non-parametric bayesian method, which is used for clustering uncertain data by adopting the dirichlet process mixture model, and the dirichlet process is introduced on a Gaussian mixture distribution level as a weight The K value can be automatically and systematically determined, and can be adaptively increased along with the increase of the complexity of the data, so that the model complexity of the dirichlet procedure hybrid model can adapt to the complexity of uncertain data, thereby better describing the uncertainty characteristics thereof and extracting uncertain information.
The dirichlet process is a random process in a non-parametric bayesian model, forms a basic block of a dirichlet process mixture model, and is defined as: hypothesis metric spaceRandom distribution onGFollowing the dirichlet procedure, denoted +.>Then for the measure space->Any finite division of (a)The following relationship exists:
wherein Dir represents dirichlet distribution;is randomly distributedGConcentration parameters of (2); />Is the basis measure of the random distribution G.
The broken bar process gives a display construction method, i.e. a well-defined distribution G is constructed such that G meets the dirichlet procedure, the steps of which are as follows:
(1) Given a positive real numberConstructing a parameter sequence +.>, wherein
(2) Constructing a parameter sequence, wherein />ThenSatisfy +.>Thus->As a probability mass function.
(3) From the measurement space Basic measure->Sampling a parameter sequence +.>, wherein
(4) The random probability distribution G satisfying the dirichlet procedure satisfies the following expression:
wherein Beta represents Beta distribution;representing a dirac function; />Is->Probability measure of points.
In the above process, positive real numbersI.e.the concentration parameter, the size of which determines the parameter sequence +.>The rate of decay. />Smaller (less)>The faster the decay, i.e., the fewer the number of weights that are primarily active, the fewer the number of components considered in the gaussian mixture model, and conversely the greater the number of components considered. In realizing the parameter according to DP-> and />After sampling of (a) steam enthalpy difference dataset +.>The distribution obeyed by each sample in the system can be inferred and generated by a sample data dirichlet procedure mixed model, and the basic steps are as follows: first, according to->Weights for each class of uncertain dataAnd parameters->Sampling; then, according to the parameter->Determining sample->The category obeys the distribution, and the sample category +.>The method comprises the steps of carrying out a first treatment on the surface of the Finally, the sample class determines the corresponding likelihood function, sample +.>The values of (2) may be generated by sampling from the likelihood function. The dirichlet process mixture model described above can be expressed as:
in the formula ,a tag for representing an uncertain data class;Multrepresenting a polynomial distribution, dirichlet distribution asMultIs a common component of (2)A yoke prior distribution; />Representation and uncertainty data category->And (3) a relevant likelihood function.
In the above-mentioned description of the invention,and->By adopting a Gaussian conjugate model, parameter->The parameters of each component in the Gaussian mixture model are included, and the parameters are represented by mean vector +.>And covariance matrix->Composition, i.e.)>. Basic measure->Is normally inverse Weishade distribution, i.e.)>. The likelihood function takes a multivariate normal distribution, i.e. +.>. Dirichlet process mixed model constructed based on broken rod process, probability distribution of uncertain data is scattered with probability 1, the scattered further causes data clustering, the larger the scattered is, the more the data is classified, and the scattered is represented by concentration parameters->And (5) controlling. At the position ofIn the Gaussian mixture model, the number of components is unknown, and if the number of components is not set correctly, a large gap exists between the distribution of the observed data and the Gaussian mixture model of the data estimation. Because the dirichlet process hybrid model allows infinite data categories and can automatically determine the number of data clusters, the problems of over-fitting and under-fitting are avoided, and therefore, the dirichlet process hybrid model can adaptively adjust the complexity of the model according to the complexity of uncertain data, thereby capturing uncertain information more accurately.
The key to constructing a data-driven uncertainty set based on a dirichlet process mixture model is to mix parametersWeight->(by->Decision) and uncertain data class label +.>Since the above process cannot be directly sampled, the present invention employs a variance inference method to obtain an approximate posterior prediction distribution thereof. For processing infinite data categories in a dirichlet procedure mixture model, a cut-off level M is set, when ∈>When in use, let->The method comprises the steps of carrying out a first treatment on the surface of the When->When in use, let->. Thus, posterior distribution of the above parameters +.>The approximation can be derived from the following distribution:
in the formula ,;/>
in the mean field variation inference, the parameters in the above formula can be obtained by minimizing the KL divergence of the true posterior distribution and the approximate distribution, and can be expressed as a form which is easier to calculate after transformation and negation and maximization:
in the formula ,indicating the desire for an approximate distribution.
The variation deducing process adopts iterative mode to calculate, and the steps are as follows:
1) Randomly initializing process parameters, noted as
2) Solving for mixing parametersApproximate distribution of posterior distribution +.>
3) Lower bound of the transformation
For a pair ofMaximization, i.e.)>Let->。/>
For a pair ofMaximization, i.e.)>
Order theRepeating step 2) until convergence condition is satisfied to obtain parameters +. >
As shown in fig. 3, the related parameters of the posterior distribution are obtained in the manner described above, and then the uncertainty set in the method provided by the invention is constructed based on the related parameters of the posterior prediction distribution, and the posterior prediction distribution is in the form ofWherein the random vector->Future uncertainty data, namely vapor enthalpy differences, are represented, from which the number of components of the GMD and the parameters of each component can be inferred from the posterior prediction distribution. Parameter obtained based on the upper section->The posterior predicted distribution of vapor enthalpy differences is the mixed Student's t-distribution:
in the formula ,obtain the first for variation inferencekRelated parameters of the individual components.
Therefore, based on the extracted GMD component and parameter information of each type, the clustered vapor enthalpy difference data can be respectively described to form a basic uncertainty set, and the final data driving uncertainty set is the union of the basic uncertainty sets:
in the formula ,data assembly for representing difference of vapor enthalpy valueskIs the average value of (2);;/>data assembly for representing difference of vapor enthalpy valueskInverse of standard deviation of (2); />As a scaling factor, to control the size of each substantially uncertainty set, in one possible implementation, 3.5 may be taken; />For twiddle factors, for taking boundary points on ellipsoidal uncertainty sets to form linear polyhedral uncertainty sets, +. >, wherein And the step size is +.>
Solving an objective function of the flexibility assessment model, comprising:
based on a strong dual principle, converting the objective function solving problem into a convex optimization problem;
performing degradation processing on the uncertainty set to degrade the uncertainty set from a union of a plurality of polyhedral sets to a point set containing all polyhedral vertices;
and traversing the extreme points in the uncertain set to obtain the optimal solution of the convex optimization problem corresponding to the objective function.
Firstly, based on a strong dual principle, the max problem of an inner layer in the min-max problem of a robust optimization model is converted into the min problem, and the min problems of an outer layer are combined, so that uncertainty is eliminated, and a convex optimization model is formed; second, since the established data-driven uncertainty set is a convex polygon set, the uncertainty set can be retired from the union of multiple polygon sets to a point set containing all the polygon vertices and the solution traversed. The model transformation can be represented by the following formula:
in the formula, the arrow indicatesyRepresenting the dual variables corresponding to the constraint conditions;,/> and />Representing coefficient vectors associated with the uncertainty variables, respectively; />Representing a matrix of coefficients associated with the uncertainty variable.
According to the strong dual principle, it can be transformed into the following form:
in the formula, the inequality constraint defines a decision variableyIs expressed as a polyhedral feasible set of
Due to bilinear structure of objective function in the above methodVariable(s)yThe optimal solution of (2) will be polyhedron +.>Is a boundary between the two points. Similarly, uncertainty variablesuThe optimal solution will be an uncertainty setUIs a boundary between the two points. Thus, as shown in FIG. 3, the uncertainty set is degenerated from the union of multiple polygon sets to a point set containing all the extreme points of the polyhedron, and the variable is obtained by traversing all the extreme points of the uncertainty setyThe bilinear optimization problem is converted into a convex optimization problem which is easy to solve, and therefore the flexibility evaluation result is obtained through solving.
The method provided by the invention can accurately simulate the operation of an actual system based on a mathematical model of a process industrial user energy supply system, provides a precondition for flexibility evaluation, adopts a robust optimization method to treat uncertainty in the flexibility evaluation process, considers the most conservative condition, thereby avoiding the possible electric auxiliary service default phenomenon, constructs an uncertainty set based on a dirichlet process hybrid model, can consider the area with the most dense uncertain data distribution, eliminates the data sparse area, reduces the conservation on the premise of ensuring the robustness, and further improves the economy of participating in electric auxiliary service.
In order to verify the effectiveness of the method provided by the invention, a pulp and paper mill is taken as an example for research and verification. As shown in fig. 4, the paper mill power supply system comprises an electric power/natural gas/steam network, wherein the steam system is composed of three pressure layers, the high pressure layer is about 71Bar, the middle pressure layer is about 12Bar, the low pressure layer is about 3.5Bar, and the steam pressure and the temperature of each grade can fluctuate with the pulping and papermaking process to different degrees. The high pressure layer is provided with a gas boiler and a recovery boiler, the recovery boiler burns natural gas and byproduct fuel, namely black liquor, to generate steam, and the gas boiler is used for tracking the change of industrial steam load. In addition, the high-pressure layer is also provided with a steam extraction-back pressure steam turbine which is respectively connected with the medium-pressure layer and the low-pressure layer, and the electricity purchasing quantity of the external power grid is used for balancing the mismatch between the generated energy of the IIES self-provided steam turbine and the industrial production power demand. Two bypass valves are installed between the different pressure layers, and the bypass valves are started when the turbine is not running or the steam demand exceeds the steam flow of the circulating turbine. A safety valve is arranged on the low-pressure layer and is used for discharging steam which is generated by the boiler and exceeds the steam demand. The detailed parameters of the paper mill energy supply system are shown in table 1. The three pressure layer steam temperature and pressure data for the paper mill are shown in fig. 5 and 6.
TABLE 1
In order to analyze the performance of the data-driven uncertainty set provided by the invention, the conventional polyhedron set, the uncertainty set based on principal component analysis and the uncertainty set constructed by the method of the invention are respectively used for describing the uncertainty data, and the uncertainty data and the uncertainty set constructed by each method are compared with the uncertainty set constructed by the method shown in fig. 7-10.
Fig. 7 shows a scatter plot of uncertainty data, and it can be seen that the data set thus constructed has significant correlation, asymmetry and multi-modal. Fig. 8 shows a polyhedral uncertainty set, which uses only deviation information of uncertainty data, and has difficulty in characterizing correlation and multimodality of uncertainty parameters, and the size of the uncertainty set is adjusted by a predetermined parameter. Fig. 9 illustrates an uncertainty set based on principal component analysis that captures the correlation of vapor enthalpy values at different pressure levels, however, this approach treats all uncertainty data as coming from the same random distribution and does not easily reflect the multi-modal characteristics of uncertainty data. Fig. 10 illustrates an uncertainty set constructed based on a dirichlet procedure mixture model, consisting of four basic uncertainty sets, presented as a set of polyhedrons associated with each basic distribution mean and variance. It can be derived from the graph that the set of polyhedrons uncertainty and the set of uncertainty based on principal component analysis include a large amount of unnecessary space outside the main dispersion area of the uncertainty data, thus increasing the conservation of robust optimization. In contrast, the data-driven uncertainty set provided by the invention can better capture the most frequent region of uncertain data distribution, simultaneously eliminates a large amount of data sparse space, and effectively reduces the conservation of robust optimization. In addition, the uncertainty set formed by the data driving method based on the dirichlet process mixed model is a union set of a plurality of convex polyhedron sets, and the uncertainty set still has a linear structure, so that the calculation efficiency can be effectively improved.
The uncertainty sets are applied to robust optimization of flexibility evaluation, and the flexibility evaluation results under different methods are respectively solved and compared with the certainty evaluation results to analyze the effect of the method.
The deterministic evaluation method and the turbine output boundary obtained by the robust optimization method provided by the invention are shown in fig. 11. The flexibility boundary obtained by the method is smaller than that of the deterministic optimization method in the whole, and the problem that the uncertainty is conservative is considered in the whole simulation period, so that the auxiliary service violation punishment caused by overestimation of the flexibility capability of an industrial user can be avoided.
The result of the flexibility evaluation robust optimization based on the various uncertainty set construction methods is shown in fig. 12, wherein the boundaries of the flexibility based on the polygon uncertainty set, the uncertainty set based on principal component analysis, and the method of the present invention are gradually expanded, indicating that although there is some conservation in the robust optimization, the conservation can be reduced as much as possible by the appropriate uncertainty set construction method. The data-driven uncertainty set provided by the invention avoids the high conservation of the traditional robust optimization method, and can avoid underestimation of the flexibility of industrial users to obtain more potential profits. Meanwhile, the fact that the up-regulation boundary is greatly influenced by uncertainty and the down-regulation boundary is not greatly changed is seen, because when the down-regulation is carried out, the most conservative condition of the adjustable boundary of the steam turbine occurs when the steam enthalpy value difference is large, the data of the part with the large steam enthalpy value difference are relatively dense, and the part of the area is better captured by three uncertain set construction methods, so that the calculation results of the three methods are close to be consistent.
The data-driven process industrial user flexibility evaluation device provided by the invention is described below, and the data-driven process industrial user flexibility evaluation device and the data-driven process industrial user flexibility evaluation method described below can be correspondingly referred to each other. As shown in fig. 13, the data-driven flow industrial user flexibility evaluation device includes:
a data acquisition module 1310, configured to acquire historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, where the energy supply system includes a steam energy supply system, the historical steam enthalpy data includes pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period includes steam enthalpy differences of two ends of a plurality of pressure layers;
an uncertainty set determining module 1320, configured to obtain an uncertainty set by using a dirichlet procedure based on the historical vapor enthalpy value data, where the uncertainty set includes linear polyhedrons corresponding to pressure layers of each type in the vapor energy supply system, and each data point on each linear polyhedron is determined based on a description formula of vapor enthalpy value differences at two ends of one type of pressure layer, where the description formula is determined based on a posterior distribution of vapor enthalpy value differences at two ends of the pressure layer, and vapor enthalpy value differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
The model solving module 1330 is configured to obtain device operation data of the energy supply system, input the device operation data and the uncertainty set into a constructed flexibility evaluation model, so as to solve an objective function of the flexibility evaluation model, and obtain a flexibility evaluation result of the industrial user to be evaluated, where the flexibility evaluation result reflects an output adjustable value of the energy supply system for providing an electric auxiliary service;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system; ,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Indicating the normal operating point of the turbine providing the electric auxiliary service in the energy supply system. />
Fig. 14 illustrates a physical structure diagram of an electronic device, as shown in fig. 14, which may include: processor 1410, communication interface (Communications Interface) 1420, memory 1430 and communication bus 1440, wherein processor 1410, communication interface 1420 and memory 1430 communicate with each other via communication bus 1440. Processor 1410 can invoke logic instructions in memory 1430 to perform a data-driven process industry user flexibility assessment method comprising:
acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy differences of two ends of a plurality of pressure layers;
Acquiring an uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to pressure layers of each type in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertain set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an adjustable output amplitude of the power auxiliary service provided by the energy supply system;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; / >A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Indicating the normal operating point of the turbine providing the electric auxiliary service in the energy supply system.
In addition, the logic instructions in the memory 1430 described above may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product, the computer program product comprising a computer program, the computer program being storable on a non-transitory computer readable storage medium, the computer program, when executed by a processor, being capable of performing the method for evaluating the flexibility of a process industry user based on data driving provided by the above methods, the method comprising: acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy differences of two ends of a plurality of pressure layers;
acquiring an uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to pressure layers of each type in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
Acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertain set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an adjustable output amplitude of the power auxiliary service provided by the energy supply system;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system; />,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; / >Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Indicating the normal operating point of the turbine providing the electric auxiliary service in the energy supply system.
In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the data-driven based flow industry user flexibility assessment method provided by the methods above, the method comprising: acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy differences of two ends of a plurality of pressure layers;
acquiring an uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to pressure layers of each type in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
Acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertain set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an adjustable output amplitude of the power auxiliary service provided by the energy supply system;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />Feasible for decision variablesA domain;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; / >Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Representing the energy supply systemA normal operating point of a steam turbine providing electric auxiliary services.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (5)

1. A method for assessing flexibility of a process industrial user based on data driving, comprising:
acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, wherein the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprises pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprises steam enthalpy differences of two ends of a plurality of pressure layers;
acquiring an uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data, wherein the uncertainty set comprises linear polyhedrons corresponding to pressure layers of each type in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of the steam enthalpy differences at two ends of the pressure layer, and the steam enthalpy differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
Acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertain set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an adjustable output amplitude of the power auxiliary service provided by the energy supply system;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively, between the ultra-high pressure layer and the high pressure layer, the ultra-high pressure layer and the medium pressure layer, and between the medium pressure layer and the low pressure layer Steam flow of the back pressure turbine; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Representing a normal operating point of a turbine providing an electric auxiliary service in the energy supply system;
the flexibility evaluation model comprises an operation model of each piece of sub-equipment in the energy supply system; the sub-equipment comprises a boiler and a steam turbine; the operational model of the sub-device is formulated as:
;/>
wherein , and />The natural gas consumption of the gas boiler and the recovery boiler are respectively represented; />Andrespectively representing the difference of vapor enthalpy values at two ends of the gas boiler and the recovery boiler; /> and />Respectively representing the steam flow rate generated by the gas boiler and the recovery boiler; />Indicating the mass flow rate of the byproduct fuel; />Andrespectively representing the efficiency of the gas boiler and the recovery boiler; /> and />Respectively representing the heat values of natural gas and byproduct fuel; />Generating power for the steam turbine; />The power generation efficiency of the steam turbine; />Representing steam flow through the steam turbine; />Representing the difference in enthalpy of steam flowing across the turbine;
the flexibility evaluation model also comprises an electric network power balance model, a natural gas network supply and demand balance model and a steam network supply and demand balance model;
The electric network power balance model is expressed as follows:
the natural gas network supply and demand balance model is expressed as follows:
the steam network supply and demand balance model is expressed as follows:
wherein ,representing the power input by an external power grid; />Representing the electrical load of the industrial process; />Is the volume of natural gas input by the external natural gas network; />,/>,/> and />Respectively representing the steam flow flowing through the bypass valve between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, the high pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing industrial production steam flow demand; />Representing the flow of steam discharged through a relief valve mounted on the low pressure layer;
the flexibility evaluation model comprises constraint conditions, wherein the constraint conditions correspond to the decision variable feasible domains; the constraint conditions include:
;/>
;/>
wherein , and />Respectively representing the minimum output and the maximum output of the steam turbine; /> and />Respectively representing the minimum steam yield and the maximum steam yield of the boiler; />Steam flow indicative of bypass valve, +.>Representing the steam flow of the safety valve; /> and />Maximum steam flow of the bypass valve and the safety valve are respectively represented; /> and />Respectively representing a lower electricity purchasing limit and an upper electricity purchasing limit of an external power grid; / > and />Respectively representing the lower limit and the upper limit of the gas purchasing to the external natural gas network;
the acquiring the uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data comprises:
classifying pressure layers of the energy supply system by using a dirichlet allocation process based on the historical steam enthalpy data, and obtaining posterior distribution parameters corresponding to each type;
wherein parameters in the dirichlet procedure are determined based on a variance inference; the variation deducing process is as follows:
random initialization parameters, noted as
Solving for mixing parametersApproximate distribution of posterior distribution +.>, wherein ,;/>mult stands for polynomial distribution, +.>Representing Beta distribution->Representing the distribution of n-tai-li-wei-sha>Representing the uncertainty setiDistribution parameters corresponding to data tags of individual categories, < ->Is->Posterior distribution-related parameters of vapor enthalpy differences of pressure-like layers->Is a concentration parameter for controlling the data dispersion, when +.>When (I)>The method comprises the steps of carrying out a first treatment on the surface of the When->In the time-course of which the first and second contact surfaces,,/>for a preset cut-off level, +.>Is constant (I)>Representing the uncertainty setiData tags of the respective categories, N being the number of data categories, ">,/>Indicate->Mean vector of vapor enthalpy differences of pressure-like layer, +. >Indicate->Covariance matrix of steam enthalpy difference of pressure-like layer;
lower bound of the transformation,/>Representing the desire for an approximate distribution ∈>Representing the difference in vapor enthalpy;
solving forOrder-making
Solving for
Order theRepeat the mixing parameters->Approximate distribution of posterior distribution +.>Until the convergence condition is satisfied, parameter after the convergence condition is satisfied +.>A posterior distribution parameter of vapor enthalpy difference as a pressure layer of the energy supply system;
the uncertainty set is formulated as:
wherein ,representing the average value of steam enthalpy difference of a kth pressure layer in the steam enthalpy difference data;;/>inverse of standard deviation representing vapor enthalpy difference of the kth pressure layer; />Is a scale factor used to control the size of each substantially uncertain set; />For a twiddle factor, to take boundary points on an ellipsoid uncertainty set to form a linear polyhedral uncertainty set,, wherein />And the step length is,/>Is the difference in vapor enthalpy.
2. The data driven process industry user flexibility assessment method of claim 1, wherein said solving the objective function of the flexibility assessment model comprises:
based on a strong dual principle, converting the objective function solving problem into a convex optimization problem;
Performing degradation processing on the uncertainty set to degrade the uncertainty set from a union of a plurality of polyhedral sets to a point set containing all polyhedral vertices;
and traversing the extreme points in the uncertain set to obtain the optimal solution of the convex optimization problem corresponding to the objective function.
3. A data-driven process industry user flexibility assessment device, comprising:
the system comprises a data acquisition module, a control module and a control module, wherein the data acquisition module is used for acquiring historical steam enthalpy data of an energy supply system of an industrial user to be evaluated, the energy supply system comprises a steam energy supply system, the historical steam enthalpy data comprise pressure layer steam enthalpy difference data of a plurality of time periods in the steam energy supply system, and the pressure layer steam enthalpy difference data of each time period comprise steam enthalpy difference of two ends of a plurality of pressure layers;
the uncertain set determining module is used for acquiring an uncertain set by using a Dirichlet process based on the historical steam enthalpy value data, the uncertain set comprises linear polyhedrons corresponding to pressure layers in the steam energy supply system respectively, data points on each linear polyhedron are determined based on a description formula of steam enthalpy value differences at two ends of one type of pressure layer, the description formula is determined based on posterior distribution of steam enthalpy value differences at two ends of the pressure layer, and steam enthalpy value differences at two ends of the pressure layer belonging to the same type of pressure layer obey the same distribution;
The model solving module is used for acquiring equipment operation data of the energy supply system, inputting the equipment operation data and the uncertainty set into a constructed flexibility evaluation model to solve an objective function of the flexibility evaluation model, and obtaining a flexibility evaluation result of the industrial user to be evaluated, wherein the flexibility evaluation result reflects an output adjustable value of the energy supply system for providing electric auxiliary service;
wherein, the objective function of the flexibility evaluation model is:
wherein , and />The upward and downward flexibility adjustable magnitudes of the steam turbine respectively representing the power auxiliary service provided by the power supply system;xas decision variables, the steam flow of each device in the energy supply system is contained; />A feasible domain for decision variables;uthe method is an uncertain variable and comprises enthalpy value differences at two ends of each pressure layer in the energy supply system;Ufor the uncertainty set; />,/> and />The efficiency of the steam extraction-back pressure type steam turbine, the condensing type steam turbine and the back pressure type steam turbine are respectively;,/>,/> and />Vapor enthalpy differences between the ultrahigh pressure and the high pressure layers, between the ultrahigh pressure and the medium pressure layers, between the high pressure layer and the water, and between the medium pressure and the low pressure layers of the vapor energy supply system;,/> and />Respectively representing the steam flow flowing through the back pressure turbine between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing the flow of steam through a condensing turbine mounted on a high pressure layer; />Representing a normal operating point of a turbine providing an electric auxiliary service in the energy supply system;
the flexibility evaluation model comprises an operation model of each piece of sub-equipment in the energy supply system; the sub-equipment comprises a boiler and a steam turbine; the operational model of the sub-device is formulated as:
;/>
wherein , and />The natural gas consumption of the gas boiler and the recovery boiler are respectively represented; />Andrespectively representing the difference of vapor enthalpy values at two ends of the gas boiler and the recovery boiler; /> and />Respectively representing the steam flow rate generated by the gas boiler and the recovery boiler; />Indicating the mass flow rate of the byproduct fuel; />Andrespectively representing the efficiency of the gas boiler and the recovery boiler; /> and />Respectively representing the heat values of natural gas and byproduct fuel; />Generating power for the steam turbine; />The power generation efficiency of the steam turbine; />Representing steam flow through the steam turbine; />Representing the difference in enthalpy of steam flowing across the turbine;
the flexibility evaluation model also comprises an electric network power balance model, a natural gas network supply and demand balance model and a steam network supply and demand balance model;
The electric network power balance model is expressed as follows:
the natural gas network supply and demand balance model is expressed as follows:
the steam network supply and demand balance model is expressed as follows:
wherein ,representing the power input by an external power grid; />Representing the electrical load of the industrial process; />Is the volume of natural gas input by the external natural gas network; />,/>,/> and />Respectively representing the steam flow flowing through the bypass valve between the ultrahigh pressure layer and the high pressure layer, the ultrahigh pressure layer and the medium pressure layer, the high pressure layer and the medium pressure layer, and the medium pressure layer and the low pressure layer; />Representing industrial production steam flow demand; />Representing the flow of steam discharged through a relief valve mounted on the low pressure layer;
the flexibility evaluation model comprises constraint conditions, wherein the constraint conditions correspond to the decision variable feasible domains; the constraint conditions include:
;/>
;/>
wherein , and />Respectively representing the minimum output and the maximum output of the steam turbine; /> and />Respectively representing the minimum steam yield and the maximum steam yield of the boiler; />Steam flow indicative of bypass valve, +.>Representing the steam flow of the safety valve; /> and />Maximum steam flow of the bypass valve and the safety valve are respectively represented; /> and />Respectively representing a lower electricity purchasing limit and an upper electricity purchasing limit of an external power grid; / > and />Respectively representing the lower limit and the upper limit of the gas purchasing to the external natural gas network;
the acquiring the uncertainty set by using a dirichlet procedure based on the historical steam enthalpy data comprises:
classifying pressure layers of the energy supply system by using a dirichlet allocation process based on the historical steam enthalpy data, and obtaining posterior distribution parameters corresponding to each type;
wherein parameters in the dirichlet procedure are determined based on a variance inference; the variation deducing process is as follows:
random initialization parameters, noted as
Solving for mixing parametersApproximate distribution of posterior distribution +.>, wherein ,;/>mult stands for polynomial distribution, +.>Representing Beta distribution->Representing the distribution of n-tai-li-wei-sha>Representing the uncertainty setiDistribution parameters corresponding to data tags of individual categories, < ->Is->Posterior distribution-related parameters of vapor enthalpy differences of pressure-like layers->Is a concentration parameter for controlling the data dispersion, when +.>When (I)>The method comprises the steps of carrying out a first treatment on the surface of the When->In the time-course of which the first and second contact surfaces,,/>for a preset cut-off level, +.>Is constant (I)>Representing the uncertainty setiData tags of the respective categories, N being the number of data categories, ">,/>Indicate->Mean vector of vapor enthalpy differences of pressure-like layer, +. >Indicate->Covariance matrix of steam enthalpy difference of pressure-like layer;
lower bound of the transformation,/>Representing the desire for an approximate distribution ∈>Representing the difference in vapor enthalpy;
solving forOrder-making
Solving for
Order theRepeat the mixing parameters->Approximate distribution of posterior distribution +.>Until the convergence condition is satisfied, parameter after the convergence condition is satisfied +.>A posterior distribution parameter of vapor enthalpy difference as a pressure layer of the energy supply system;
the uncertainty set is formulated as:
wherein ,representing the average value of steam enthalpy difference of a kth pressure layer in the steam enthalpy difference data;;/>inverse of standard deviation representing vapor enthalpy difference of the kth pressure layer; />Is a scale factor used to control the size of each substantially uncertain set; />For a twiddle factor, to take boundary points on an ellipsoid uncertainty set to form a linear polyhedral uncertainty set,, wherein />And the step length is,/>Is the difference in vapor enthalpy.
4. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the data-driven flow-based industrial user flexibility assessment method according to any one of claims 1 to 2 when executing the program.
5. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the data-driven based flow industry user flexibility assessment method according to any one of claims 1 to 2.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112054554A (en) * 2020-08-18 2020-12-08 国网山东省电力公司临沂供电公司 Non-parameter statistics-based adaptive distribution robust unit combination method and system
CN112560329A (en) * 2020-11-19 2021-03-26 华东理工大学 Data-driven robust optimization method for energy system of industrial device under uncertainty
CN114638727A (en) * 2022-03-14 2022-06-17 天津大学 Adjustable robust monitoring method for process industry flexibility considering production uncertainty
CN115965156A (en) * 2023-01-29 2023-04-14 华东理工大学 Scheduling method and scheduling device of energy system
WO2023082697A1 (en) * 2021-11-15 2023-05-19 中国电力科学研究院有限公司 Coordination and optimization method and system for comprehensive electric-thermal energy system, and device, medium and program

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20210103814A1 (en) * 2019-10-06 2021-04-08 Massachusetts Institute Of Technology Information Robust Dirichlet Networks for Predictive Uncertainty Estimation

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112054554A (en) * 2020-08-18 2020-12-08 国网山东省电力公司临沂供电公司 Non-parameter statistics-based adaptive distribution robust unit combination method and system
CN112560329A (en) * 2020-11-19 2021-03-26 华东理工大学 Data-driven robust optimization method for energy system of industrial device under uncertainty
WO2023082697A1 (en) * 2021-11-15 2023-05-19 中国电力科学研究院有限公司 Coordination and optimization method and system for comprehensive electric-thermal energy system, and device, medium and program
CN114638727A (en) * 2022-03-14 2022-06-17 天津大学 Adjustable robust monitoring method for process industry flexibility considering production uncertainty
CN115965156A (en) * 2023-01-29 2023-04-14 华东理工大学 Scheduling method and scheduling device of energy system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
"Multi-scenario data-driven robust optimisation for industrial steam power systems under uncertainty";Yulin Hana, el.;《Energy》;全文 *
"基于可调鲁棒优化的工业园区供能***自发电 灵活性评估";单文亮 等;《高电压技术》;全文 *

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