An integrated energy system interval probability energy flow calculation method and system

Abstract

The application discloses a kind of comprehensive energy system interval probability energy flow calculation method and system, the method includes: establishing interval variable model and random variable model;Respectively to random variable model and interval variable model sampling, obtain multidimensional random variable and multidimensional interval variable;Through the HL-MEF agent model of double-layer agent model upper layer calculation determines performance flow, according to the calculation result, output energy flow upper and lower boundary value;According to multidimensional random variable, energy flow upper and lower boundary training the sPCE agent model of double-layer agent model lower layer;Large-scale random variable is regenerated and input to the sPCE agent model of training completion, and the upper and lower boundary values of interval probability energy flow are output.The application designs double-layer agent structure, through the multi-energy flow calculation model based on heterogeneous learner of upper layer, reduces the online sampling burden of lower layer training sPCE agent model, and through sPCE agent model, reduces a large amount of repeated calculation of determining performance flow.

Description

Technical Field

[0001] This invention relates to the field of uncertain energy flow calculation technology, and in particular to a method and system for calculating the interval probability energy flow of a comprehensive energy system. Background Technology

[0002] With the rapid development of renewable energy, the proportion of high-renewable energy in integrated energy systems (IES) has significantly increased. To ensure the normal operation and control of integrated energy systems, it is necessary to predict the IES status (such as bus voltage, water temperature, and gas pressure) through uncertain energy flow analysis, providing key information for decision-makers and automatic control devices.

[0003] Deterministic performance flow computation aims to solve for the operating state of a system under a given condition based on known information. Uncertainty energy flow computation, building upon deterministic performance flow computation, aims to obtain the distribution characteristics of system state variables based on the influence of uncertain factors. In recent years, uncertainty energy flows have generally been classified into three categories: probabilistic energy flow (PEF), interval energy flow (IEF), and interval-probabilistic energy flow (IPEF). PEF represents the input as a probability density function (PDF) or cumulative distribution function (CDF) and obtains system state variables in PDF or CDF form, thus representing the system's uncertainty. IEF models the input and output variables using interval form. Due to the inaccuracy, dispersion, fluctuation, incompleteness, or ambiguity of data obtained from integrated energy systems (IES), currently only limited information about CDF or PDF can be obtained. In this context, IPEF can use both accurate data (modeled as PDF or CDF) and inaccurate data (modeled as intervals) as input to form a probability box (p-box) defined by upper and lower boundaries. Although IPEF is closely related to PEF and IEF, it is essentially a new mathematical problem, not a simple combination of the two. Currently, despite much research on IEF and PEF, addressing the computational challenges of IPEF remains an important research direction.

[0004] Integrated electrothermal-gas (IGG) systems (i.e., comprehensive energy systems) involve a significant number of uncertainties, such as gas / water supply conditions, pipeline / power line properties, equipment efficiency, and the surrounding environment. Because data varies in actual engineering projects, the mathematical descriptions of these uncertainties differ. Therefore, IPEF analysis within the IES context is crucial, providing an objective model of the uncertainties rather than ignoring important information and drawing hasty conclusions.

[0005] Interval probabilistic energy flow (IPEF) calculations can quantify the uncertainties of integrated energy systems. The main challenge of this calculation method lies in improving the traditional two-layer calculation framework for calculating the boundaries of relevant variables. Without high-performance computing equipment, the two-layer calculation task is difficult to complete. Currently, this problem is addressed mainly in two ways: (1) improving the computational efficiency of p-boxes; (2) establishing an effective model to replace the numerical model in the two-layer framework.

[0006] To address problem (1), efficient computational methods have been proposed, such as introducing interval arithmetic (IA) and affine arithmetic (AA) methods to solve the electrothermal IPEF problem. However, the IES model exhibits nonlinearity, which severely limits the application of the above methods. Using these methods easily leads to a dilemma where accuracy, efficiency, and applicability are difficult to balance.

[0007] To address problem (2), current methods combine dimensionality reduction techniques with sparse polynomialchaos expansion (sPCE) to construct surrogate models for handling IPEF problems in electrically coupled systems. While surrogate models offer good flexibility and high computational efficiency, training them requires a large number of online samples, incurring additional computational burdens and limiting their application in IPEF analysis. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a method and system for calculating the inter-regional probabilistic energy flow of an integrated energy system. Based on a designed dual-level surrogate structure (DLSS), the method uses a heterogeneous-learner-based multiple energy flow (HL-MEF) calculation model as the upper-level surrogate structure of the DLSS. This reduces the online sampling burden of training the lower-level sPCE surrogate model. By using the sPCE surrogate model as the lower-level surrogate structure, the method reduces the repetitive calculation of a large number of deterministic performance flows, providing a fast and accurate solution to the IPEF problem. This achieves a high level of balance between computational accuracy, efficiency, and applicability in solving the IPEF problem.

[0009] Firstly, this disclosure provides a method for calculating the probabilistic energy flow of an integrated energy system.

[0010] A method for calculating the probabilistic energy flow of an integrated energy system includes:

[0011] Based on the integrated energy system, establish interval variable models and random variable models;

[0012] By sampling the random variable model and the interval variable model respectively, multidimensional random variables and multidimensional interval variables are obtained;

[0013] Based on multidimensional random variables and multidimensional interval variables, deterministic performance flow calculation is performed through the HL-MEF proxy model in the upper layer of the two-layer proxy model. Based on the deterministic performance flow calculation results, the upper and lower boundary values ​​of energy flow are output.

[0014] The lower layer of the two-layer proxy model, sPCE proxy model, is trained based on multidimensional random variables and upper and lower boundaries of energy flow.

[0015] The large-scale random variables regenerated based on the random variable model are used as inputs to the trained sPCE surrogate model, and the upper and lower boundary values ​​of the interval probability energy flow are output.

[0016] Further technical solutions also include:

[0017] Based on the upper and lower boundary values ​​of the interval probability energy flow, a probability box p-box is constructed.

[0018] A further technical solution involves sampling the random variable model and the interval variable model respectively to obtain multidimensional random variables and multidimensional interval variables, including:

[0019] Based on random variable models and interval variable models, a large amount of data is generated through a two-level Monte Carlo simulation method.

[0020] The generated large amount of data is sampled, including: at the upper level, simple random sampling is performed on the interval variables generated by the interval variable model to obtain multidimensional interval variables; at the lower level, the random variable data generated by the random variable model is sampled using the Latin hypersolution method to obtain multidimensional random variables.

[0021] A further technical solution, the method for constructing the HL-MEF proxy model includes:

[0022] Select the characteristic variables of the integrated electric, heat and gas energy system, take the state variables corresponding to the characteristic variables as the target values, and use a variety of data-driven methods to train a multi-energy flow calculation model based on a single learner.

[0023] By comparing the computational models generated during training, the high-performance computational models are selected for integration to generate a multi-energy flow computational model based on multiple learners, namely the HL-MEF surrogate model.

[0024] In a further technical solution, the characteristic variables are the power at the node and other uncertainties. The power at the node is the power obtained by subtracting the power generated by the photovoltaic panel and the solar thermal equipment from the load power of the power system, thermal system and gas system at the node. The other uncertainties at the node are the gas temperature and gas density.

[0025] The target values ​​include power system parameters, thermal system parameters, and gas system parameters; the power system parameters include voltage amplitude and voltage phase angle; the thermal system parameters include supply temperature, return temperature, and pipeline flow rate; and the gas system parameters include node gas pressure and natural gas flow rate.

[0026] A further technical solution is that the training process of the HL-MEF model includes:

[0027] Obtain the feature variable vector and target value of the integrated electric, thermal, and gas energy system, and divide it into the original training set and the original test set;

[0028] K-fold cross-validation is used to preprocess the original training set;

[0029] Based on the preprocessed original training set, the base learner is trained, and the trained base learner is validated using the original test set.

[0030] Based on the original training set and the original test set, use the trained base learners to generate meta-training set and meta-test set for the meta-learners;

[0031] Based on the meta-training set, train the meta-learner and use the meta-test set to verify the trained meta-learner.

[0032] By combining the trained base learner and meta learner, a multi-energy flow computation model based on heterogeneous learners is output.

[0033] Secondly, this disclosure provides a system for calculating the probabilistic energy flow of an integrated energy system.

[0034] A comprehensive energy system interval probabilistic energy flow calculation system, comprising:

[0035] The model building module is used to establish interval variable models and random variable models based on the integrated energy system;

[0036] The data acquisition module is used to sample the random variable model and the interval variable model respectively to obtain multidimensional random variables and multidimensional interval variables;

[0037] The deterministic performance flow calculation module is used to perform deterministic performance flow calculation based on multidimensional random variables and multidimensional interval variables, through the HL-MEF proxy model in the upper layer of the two-layer proxy model, and output the upper and lower boundary values ​​of energy flow based on the deterministic performance flow calculation results.

[0038] The lower-layer proxy model training module is used to train the lower-layer sPCE proxy model of the two-layer proxy model based on multidimensional random variables and the upper and lower boundaries of energy flow.

[0039] The interval probability energy flow calculation module is used to take large-scale random variables regenerated based on the random variable model as input, input them into the trained sPCE surrogate model, and output the upper and lower boundary values ​​of the interval probability energy flow.

[0040] Further technical solutions also include:

[0041] The probability box building module is used to construct a probability box (p-box) based on the upper and lower boundary values ​​of the interval probability energy flow.

[0042] Thirdly, this disclosure also provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method described in the first aspect.

[0043] Fourthly, this disclosure also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps of the method described in the first aspect.

[0044] The above one or more technical solutions have the following beneficial effects:

[0045] 1. This invention provides a method and system for calculating the interval probabilistic energy flow of an integrated energy system, and discloses a two-layer proxy structure DLSS, which is applicable to integrated electric, heat and gas energy systems. It reduces the repetitive calculation of a large number of deterministic performance flows, provides a fast and accurate solution to the IPEF problem, and achieves a high level of balance between calculation accuracy, efficiency and applicability.

[0046] 2. This invention proposes a multi-energy flow computation model based on heterogeneous learners, which can be used as an upper-layer proxy structure of DLSS to reduce the online sampling burden of training the lower-layer sPCE proxy model; moreover, when it is used independently as a deterministic MEF solver, it supports fast non-iterative computation and can be used to complete tasks with limited computation time; at the same time, the model integrates multiple base learners, which can better fit different features in MEF and obtain more accurate results. Attached Figure Description

[0047] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0048] Figure 1 This is an overall flowchart of the integrated energy system interval probabilistic energy flow calculation method described in this embodiment of the invention;

[0049] Figure 2 This is a flowchart of the HL-MEF model training process in Embodiment 1 of the present invention;

[0050] Figure 3 This is a topology diagram of the UoM campus integrated energy system in Embodiment 1 of the present invention;

[0051] Figure 4 This is a schematic diagram showing the degree of difference between different base learners in Embodiment 1 of the present invention;

[0052] Figure 5 This is a schematic diagram illustrating the difference in precision between the upper and lower boundaries of the output variables of the two methods, DLMCS-HL and DLSS, in Embodiment 1 of the present invention.

[0053] Figure 6 This is a schematic diagram of the probability boxes corresponding to the eight different variables calculated in Embodiment 1 of the present invention. Detailed Implementation

[0054] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0056] Example 1

[0057] To address the IPEF problem in Integrated Energy Systems (IES), this embodiment provides a method for calculating interval probabilistic energy flow in IES based on a dual-level surrogate structure (DLSS). The upper layer of this surrogate structure is a heterogeneous-learner-based multiple energy flow (HL-MEF) computation model, while the lower layer is a novel sparse polynomial chaos expansion (sPCE) model. In IPEF research, the sPCE model can directly map random input variables to output boundary values, avoiding the repetitive computation of numerous deterministic multiple energy flow (MEF) calculations, thus enabling the rapid computation of probability boxes (p-boxes) defined by the upper and lower boundaries. However, training the sPCE model still requires a small sample size, significantly increasing the overall time cost. Furthermore, the sPCE surrogate model cannot be pre-trained because the required sample data, random and interval variables are dependent on current conditions and cannot be obtained from historical data. In this context, this embodiment employs the HL-MEF model as the upper-layer proxy model for DLSS, accelerating the computation of the deterministic MEF and thus significantly reducing the computational burden of online sampling. Therefore, the DLSS structure proposed in this embodiment is as follows: Figure 1 As shown, the above-mentioned integrated energy system range is roughly...

[0058] The energy flow calculation method specifically includes the following steps:

[0059] Step S1: Based on the integrated energy system, establish an interval variable model and a random variable model;

[0060] Step S2: Sample the random variable model and the interval variable model respectively to obtain multidimensional random variables and multidimensional interval variables;

[0061] Step S3: Based on the multidimensional random variables and multidimensional interval variables, perform deterministic performance flow calculation through the HL-MEF proxy model in the upper layer of the two-layer proxy model, and output the upper and lower boundary values ​​of energy flow based on the deterministic performance flow calculation results.

[0062] Step S4: Train the sPCE proxy model of the lower layer of the two-layer proxy model based on multidimensional random variables and upper and lower energy flow boundaries;

[0063] Step S5: Take the large-scale random variables regenerated based on the random variable model as input and input them into the trained sPCE surrogate model, and output the upper and lower boundary values ​​of the interval probability energy flow.

[0064] Furthermore, it also includes:

[0065] Step S6: Establish a probability box p-box based on the upper and lower boundary values ​​of the interval probability energy flow.

[0066] The algorithm described above is as follows:

[0067]

[0068] First, in step S1, uncertainty modeling is performed on the integrated energy system IES. In this embodiment, interval variables and random variables are used to represent the uncertainty in the integrated energy system IES for the next calculation.

[0069] Modeling for interval variables:

[0070] In IPEF analysis, photovoltaic panels (PV) and photothermal equipment (PT) are considered as power generation devices in the power system and heating system, respectively. The power generated and heated by these renewable energy devices is then represented by interval numbers, as shown in the formula:

[0071]

[0072] In the formula, P PV and Q PV These represent the active power and reactive power emitted by the PV, respectively; Φ PT R represents the thermal power output of the PT heating system. I A is an interval variable representing the hourly solar radiation (PV / PT) at a specific tilt angle; PV and A PT Indicates the area of ​​the PV and PT panels; r PV and r PT This represents the energy conversion efficiency of PV and PT, and this coefficient is related to inverter losses, heat losses, cable losses, shading, dust, etc.; tanθ PV This represents the power factor of the PV.

[0073] In practical natural gas systems, gas temperature and density are uncertain, which affects natural gas flow calculations and even operating conditions. The gas flow equations for low-pressure gas systems (0–75 mbar), medium-pressure gas systems (0.75–7.0 bar), and high-pressure gas systems (above 7.0 bar) are as follows:

[0074]

[0075] In the formula, T I The temperature of the natural gas is expressed as a range. f represents the density of natural gas, expressed in interval form; ij p represents the natural gas flow rate in the pipeline. i and p j The pressures for nodes i and j are respectively; T n and p n denoted as temperature and pressure under standard conditions; f is the friction coefficient of the pipe; L and D are the length and diameter of the pipe, respectively; Z is the gas compressibility coefficient.

[0076] Modeling random variables:

[0077] Assuming the loads of the electrical, thermal, and gas systems follow a Gaussian distribution, their probability density function (PDF) can be expressed as:

[0078]

[0079] In the formula, X i This is the i-th load in IES; and X i The expected value and standard deviation.

[0080] Then, in step S2, the random variable model and the interval variable model are sampled to obtain multidimensional random variables and multidimensional interval variables. Specifically, based on the random variable model and the interval variable model, a large amount of data is first generated through dual-level Monte Carlo simulation, and then sampled. In the upper level, the interval variables generated by the interval variable model are simply randomly sampled to obtain multidimensional interval variables; in the lower level, the random variables generated by the random variable model are sampled using the Latin hypercube method to obtain multidimensional random variables.

[0081] In step S3, based on multidimensional random variables and multidimensional interval variables, deterministic performance flow calculation is performed through the HL-MEF proxy model in the upper layer of the two-layer proxy model. Based on the deterministic performance flow calculation results, the upper and lower boundary values ​​of energy flow are output.

[0082] The above-mentioned HL-MEF proxy model, i.e., the multi-energy flow computation model based on heterogeneous learners, includes the following construction methods:

[0083] First, characteristic variables of the integrated electric, thermal, and gas energy system are selected, and a multi-data-driven model based on a single-learner-based multiple energy flow (SL-MEF) computation is trained using various data-driven methods.

[0084] Then, the computational models generated during training are compared, and the high-performing computational models are selected for integration to generate a multi-energy-flow HL-MEF computational model based on multiple learners, thereby obtaining a model with better performance.

[0085] The HL-MEF model established above does not require iteration during the calculation process, and its calculation speed is faster than that of solving nonlinear models using the Newton-Raphson (NR) method.

[0086] Specifically, the first step is to select feature variables. In statistical analysis, correlation detection results are often used as the selection criteria for input features. However, the criteria for selection in data-driven methods differ from those in statistical analysis. They determine feature variables based on existing fundamental theories (such as equations for calculating electrical, thermal, and gaseous energy flows).

[0087] The following equation represents the energy conservation constraint equations in the Integrated Energy System (IES):

[0088]

[0089] In the formula, h and g represent the thermal system and the gas system, respectively; the superscript sp represents the given electrical and thermal load power and natural gas flow rate for each of the electrical, thermal, and gas systems. P sp and Q sp These represent the input active power and reactive power, respectively; V represents the node voltage vector; Y represents the power system admittance matrix; C p A represents the specific heat capacity of water; h This represents the correlation matrix between nodes and branches in a thermal system. T represents the mass flow rate of each pipe; s Represents the temperature vector of the supply node; T o B represents the return flow temperature vector of the load node; h K represents the correlation matrix between loops and branches. hRepresents the vector of resistance coefficients of each pipe in the thermal system; C and c are the coefficient matrix and column vector of the solution of the heat balance equation, respectively; A g The correlation matrix representing the connections between nodes and branches in a gas system; f g This represents the gas flow vector in each pipe; B represents the natural gas flow vector from source injection or load consumption; g This represents the correlation matrix between loops and branches in the gas system; Δp represents the pressure difference between the beginning and end of the pipeline in the gas system.

[0090] Then, the state variable vector in the above equation can be represented as:

[0091]

[0092] In fact, the essence of deterministic multiple energy flow (MEF) calculation is the solution of a system of nonlinear equations to obtain the specific values ​​of the aforementioned state variables.

[0093] In this embodiment, the selected characteristic variables are the power at the node and other uncertainties. The power at the node refers to the power obtained by subtracting the power generated by the photovoltaic panel and the solar thermal equipment from the load power of the power system, heating system, and gas system at that node. The load power of the power system, heating system, and gas system is a random variable, and the power generated by the photovoltaic panel and the solar thermal equipment is an interval variable. The other uncertainties at the node refer to the gas temperature (natural gas in this embodiment) and gas density, which are also interval variables.

[0094] In this embodiment, the deterministic MEF equations are solved using the NR method to obtain the state variable vector x. This state variable vector is the target value, which includes power system parameters (voltage amplitude and voltage phase angle), thermal system parameters (supply temperature, return temperature, and pipeline flow rate), and gas system parameters (node ​​pressure and natural gas flow rate).

[0095] Based on the state variables obtained from the above calculations, a single-learner-based multiple energy flow (SL-MEF) computational model is trained using various data-driven methods. Currently, energy flow computational models trained using data-driven methods based on linear regression (LR) or neural networks (NN) have significant advantages in terms of computational accuracy and speed. Since the characteristics of energy flows (IES) are more complex than those of power systems, this embodiment selects six learners (three linear regression methods and three neural network methods) that have been successfully validated in power systems to fit the relationship between input and output quantities in IES. The selected data-driven methods are shown in Table 1 below.

[0096] Table 1. Data-driven methods used in energy flow modeling

[0097]

[0098] Then, the trained models are compared, and the high-performing model is selected for ensemble. Six SL-MEF models are tested in the IES system to evaluate their performance. In this embodiment, the mean absolute percentage errors (MAPE) of the six SL-MEF models in fitting the state variables of the electric, thermal, and gaseous systems are tested, and the results are shown in Table 2 below.

[0099] Table 2. Percentage of absolute error of SL-MEF models trained with different base learners

[0100]

[0101] As can be seen from Table 2 above:

[0102] (1) PLS is more accurate than other data-driven models in fitting variables such as voltage amplitude, voltage phase angle and natural gas pipeline flow rate; OLS is the most accurate in fitting variables such as mass flow rate; SDAE is the most accurate in fitting variables such as supply temperature, reflux temperature and gas pressure.

[0103] (2) The performance of models built by different data-driven methods is related to the type of variables, making it difficult to select the optimal data-driven method;

[0104] (3) The models established by OLS and PLS in linear regression and DNN and SDAE in neural networks complement each other.

[0105] Therefore, in order to achieve the best fitting effect, this embodiment adopts a heterogeneous learner integration strategy to combine different types of learners to construct an HL-MEF model. This model combines the advantages of linear regression-type data-driven methods and neural network-type data-driven methods, thereby improving the generalization ability of the MEF model in IES.

[0106] Specifically, this embodiment employs a heterogeneous learner ensemble strategy, which combines the advantages of multiple learners to train a high-performance MEF computation model. Depending on whether the learners are composed of the same method, ensemble learning can be categorized into Bagging, Boosting, and Stacking. In this embodiment, linear regression and neural network data-driven methods are combined; therefore, Stacking is chosen as the combination method for the heterogeneous learner ensemble model.

[0107] Stacking uses the same dataset D to train base learners, and the resulting base learners can provide training data for meta-learners. This process can lead to overfitting. To address overfitting, K-fold cross-validation is introduced into the modeling and training process of the HL-MEF model, making full use of the available data. The training process of the HL-MEF model is as follows: Figure 2 As shown, its training algorithm is as follows:

[0108]

[0109]

[0110] In the above algorithm, the parameter x in the training set or test set represents the selected feature variable, and y represents the target value. That is, the state variable vector is obtained by solving the deterministic MEF equation through the NR method.

[0111] The training process of the above HL-MEF model specifically includes the following steps:

[0112] The characteristic variables and target values ​​of the integrated electric, thermal, and gas energy system are obtained and divided into the original training set and the original test set.

[0113] K-fold cross-validation is used to preprocess the original training set;

[0114] Based on the preprocessed original training set, the base learner is trained, and the trained base learner is validated using the original test set.

[0115] Based on the original training set and the original test set, use the trained base learners to generate meta-training set and meta-test set for the meta-learners;

[0116] Based on the meta-training set, train the meta-learner and use the meta-test set to verify the trained meta-learner.

[0117] By combining the trained base learner and meta learner, a multi-energy flow computation model based on heterogeneous learners is output.

[0118] The selection of base learners and meta-learners is crucial in the above process. Regarding base learner selection: to achieve the expected performance of the HL-MEF model, high-accuracy and diverse base learners should be chosen. Selecting base learners with significant differences can maximize the advantages of stacking, thereby achieving better results. In this embodiment, the degree of difference between different base learners is quantified and analyzed by calculating the Pearson correlation coefficient of the errors of each SL-MEF model, using a two-dimensional variable... The Pearson correlation coefficient can be calculated using the following formula:

[0119]

[0120] In the formula, r xy A two-dimensional vector representing the Pearson coefficients; and They represent x respectively i and y i The average value.

[0121] Regarding meta-learner selection: To combine the outputs of base learners, choose a simple meta-learner with strong generalization ability, such as Logistic Regression (LR). Models built using this data-driven approach can achieve excellent results. Furthermore, overly complex meta-learners are unnecessary, as excessive complexity may reduce model computational performance and lead to overfitting.

[0122] Based on the constructed and trained HL-MEF surrogate model described above, it is used as the upper layer of the two-layer surrogate model. Calculations are performed using multidimensional random variables and multidimensional interval variables to obtain the deterministic performance flow calculation results, outputting the upper and lower boundary values ​​of the energy flow. Then, in step S4, the lower layer of the two-layer surrogate model, the sPCE surrogate model, is trained based on the multidimensional random variables and the upper and lower boundary values ​​of the energy flow.

[0123] Specifically, the upper-layer HL-MEF surrogate model is used to obtain random input values ​​and their corresponding output values, and the lower-layer sPCE surrogate model is trained based on this. The sPCE model describes the relationship between random input values ​​and output boundary values ​​in the form of orthogonal polynomial expansion, and using this model can reduce a large amount of repetitive computation in deterministic performance flow.

[0124] sPCE is a novel polynomial chaos expansion (PCE) method that maintains maximum accuracy while retaining only a finite number of coefficients for important expansion terms, thus avoiding high-dimensional problems. Given a random input vector of PDFs, the random output PCE function is shown below:

[0125]

[0126] In the formula, Ψ α (X) denotes a multivariate polynomial orthogonal to PDFs; α∈Nm indicates that it belongs to Ψ α Component multi-index; y α ∈R represents about Ψ α The coefficient.

[0127] Based on this, the multivariate polynomial Ψ α (X) can be expressed in the form of a product of one variable:

[0128]

[0129] In the formula, This represents a univariate orthogonal polynomial, the value of which is determined by the distribution type of the variable. In this embodiment, the input variable follows a Gaussian distribution, and its basis functions are Hermitian polynomials.

[0130] As another implementation, in practice, a truncated PCE is typically used, which is represented in a finite sum form:

[0131]

[0132] In the formula, This represents the set of selected multivariate polynomials with multiple indices. The truncation length refers to all polynomials whose length is less than or equal to that of the input variable m, where:

[0133] A m,p ={α∈N m :|α|≤p}

[0134]

[0135] For truncated polynomial chaotic series, the larger the expected value of p, the greater the impact on the approximation of Y. However, as can be seen from the above equation, P increases even faster as p increases. Retaining more terms increases the computational cost of finding correlation coefficients. For the PEF problem, the improvement in accuracy using p>3 gradually diminishes, so a second-order expansion is used in the sPCE model.

[0136] In this embodiment, the sPCE model describes the relationship between random input values ​​and output boundary values ​​in the form of an orthogonal polynomial expansion. This model is a polynomial chaotic expansion and uses the orthogonal matching pursuit projection method to obtain polynomial chaotic coefficients by utilizing the orthogonality of basis functions.

[0137] In step S4, the sPCE proxy model constructed by the lower layer of the two-layer proxy model is trained based on multidimensional random variables and the upper and lower boundaries of energy flow.

[0138] Subsequently, in steps S5 and S6, the large-scale random variables regenerated based on the random variable model are used as inputs to the trained sPCE surrogate model, outputting the upper and lower boundary values ​​of the interval probability energy flow, and establishing the probability box p-box based on the upper and lower boundary values ​​of the interval probability energy flow.

[0139] To further verify the superiority of the method described in this embodiment, the following calculation examples are used to verify and illustrate the method.

[0140] Data related to the Integrated Energy System (IES) was obtained from the publicly available data of the University of Manchester (UoM) campus integrated energy system. UoM consists of a 13-node (6.6kV) electrical system, a 36-node thermal system, and a 37-node gas system, with the following topology: Figure 3 As shown. Based on existing infrastructure and investment plans, regional combined heat and power (CHP) facilities are deployed on campus.

[0141] Input variables were randomly generated using the Monte Carlo method, followed by the Noble Normative Method (NR) to calculate the deterministic Multi-Energy Flow (MEF). The nonlinear equations in the MEF were then solved to obtain the data needed to train the HL-MEF model. Load power was set as a reference value multiplied by a random number between 0.75 and 1.25, and reactive power was set as the active power value multiplied by a random number between 0.15 and 0.25. In both SL-MEF and HL-MEF modeling, the training set consisted of 15,000 data points, and the test set consisted of 3,000 data points.

[0142] To ensure the excellent performance of the HL-MEF model, suitable base learners were selected from the six data-driven methods listed in Table 2, following the selection criterion of "accurate but different". Since the models built using LASSO and RBF performed worse than those built using other base learners, they were not further considered.

[0143] By calculating the Pearson correlation coefficients of the fitting errors of the other four base learners, the degree of difference between the different base learners is quantified and analyzed. The results are as follows: Figure 4 As shown.

[0144] Depend on Figure 4 It can be seen that learners of the same type are highly correlated. Specifically, the correlation coefficients for the OLS-PLS combination and the DNN-SDAE combination are 0.9967 and 0.8829, respectively. Therefore, it can be inferred that learners of the same category are not suitable for ensemble modeling because they have little impact on the performance improvement of the ensemble model and increase the computational cost. Figure 4 Among the four LR-NN combinations, PLS-SDAE has the lowest correlation coefficient, indicating that this combination has the greatest diversity. Considering the complementary performance of PLS ​​and SDAE as shown in Table 2, PLS-SDAE was ultimately selected as the base learner.

[0145] The base learners are PLS and SDAE. The output results of the two base learners are combined using different meta-learners, and the effects are shown in Table 3 below.

[0146] Table 3. Percentage of absolute error of HL-MEF models trained with different meta-learners

[0147]

[0148] As shown in Table 3, OLS performs best in fitting voltage amplitude, voltage phase angle, supply temperature, and natural gas flow rate; PLS performs best in fitting pipeline flow rate; and SDAE performs best in fitting return temperature and node pressure. Considering the performance of different learners, OLS was ultimately chosen as the meta-learner because this method has high accuracy in fitting variables and high interpretability.

[0149] The HL-MEF model uses PLS and SDAE as base learners, and combines the two base learners through the meta-learner OLS.

[0150] 1) UoM Example: To verify the effectiveness of the HL-MEF model, the mean absolute error (MAE) and MAPE of its fitted variables were calculated and compared with the SL-MEF models trained using PLS and SDAE, respectively. The results are shown in Table 4. Table 4 shows that the HL-MEF model achieves better accuracy in fitting different variables than each SL-MEF model.

[0151] Table 4. Accuracy Comparison of SL-MEF and HL-MEF Models (UoM Examples)

[0152]

[0153] 2) NE-CN Example: To further verify the performance of the HL-MEF model, an IES consisting of a 14-node power system, a 13-node gas system, and a 69-node thermal system in a region of Northeast China was selected for verification. Table 5 shows the performance comparison results of the models in the NE-CN example, indicating that the HL-MEF model outperforms other SL-MEF models.

[0154] Table 5. Accuracy Comparison of SL-MEF and HL-MEF Models (NE-CN Example)

[0155]

[0156]

[0157] The effectiveness of the proposed method is verified using a UOM (Unified Oscillator) example. The load of each node in the system is treated as a random variable, following a Gaussian distribution. The expected value is the baseline value of the system load, with standard deviations of 7%, 5%, and 3%, respectively. The inaccurate quantities are expressed in interval form, and their information is shown in Table 6.

[0158] Table 6 Information on Interval Variables

[0159]

[0160] To verify the performance of DLSS, the calculation results of the following four methods are compared.

[0161] 1) DLMCS-NR: This method samples 59 random variables 3000 times and 3 types of interval variables 500 times, using the standard NR method to calculate the MEF (Mean Exchange Flow Framework), resulting in a total of 3000 * 500 calculations. This is the most common method for constructing p-boxes to generate CDF boundaries, but it is computationally intensive. When there are sufficient samples, the results obtained by this method can usually be considered as standard values.

[0162] 2) DLMCS-HL: In this method, the HL-MEF model is used to replace the NR method to calculate MEF multiple times, in order to reduce the computational burden and finally output 3000*500 sets of data.

[0163] 3) NR-PCE: Since the sPCE model can directly map random input variables to output boundary values, it can be used as a lower-level surrogate model to avoid repetitive computation of a large number of deterministic MEFs. However, the sPCE model cannot be trained offline because the required sample data, random and interval variables are related to the current conditions and cannot be obtained from historical data. Therefore, training time, sampling time (1000*150 MEFs calculated using the NR method), and computation time (3000 calculations) must all be factored into the time cost, making this method less competitive.

[0164] 4) DLSS (HL-MEF & sPCE): This method uses the sPCE model as the lower-layer proxy model and the HL-MEF model as the upper-layer proxy model. The HL-MEF model provides training data for the sPCE model. The HL-MEF model is computed 1000*150 times, and the sPCE model is computed 3000 times.

[0165] Since the upper and lower boundaries of the output variable are the basic elements constituting the p-box, this embodiment uses the MAPE of the boundaries to evaluate the accuracy of the method. Table 7 shows the computation time and accuracy of the four methods mentioned above.

[0166] Table 7 Performance Comparison of IPEF Solving Methods

[0167]

[0168] Based on Table 7, the following conclusions can be drawn:

[0169] 1) DLMCS-NR: This method has the longest computation time (approximately 8.07 hours) because it requires 150,000 iterations.

[0170] 2) DLMCS-HL: This method has the highest accuracy among the three methods because the HL-MEF model has high accuracy. Compared with the DLMCS-NR method, the computation speed is greatly improved;

[0171] 3) NR-PCE: Although this method calculates the MEF solution using the NR method and uses it as training data for the sPCE model, its accuracy is lower than DLMCS-HL because it only provides a small amount of data to train the sPCE model. The NR method accounts for 99.2% of the total computation time for calculating the MEF, significantly impacting computational speed.

[0172] 4) DLSS: Because the HL-MEF and sPCE models are inherently highly accurate, the DLSS method performs well. The overall performance of DLSS is comparable to the NR-PCE method, and compared to the DLMCS-NR method, the computation time is reduced to 1.23 hours, but the accuracy is slightly lower.

[0173] Furthermore, Figure 5 The MAPE values ​​for the upper and lower boundaries of all output variables are given, detailing the accuracy differences between the DLMCS-HL and DLSS methods. Comparing the MAPE values ​​for different variables reveals that both methods perform worse in fitting gas pressure variables than in fitting other variables, consistent with the performance of the HL-MEF model in fitting gas pressure. Due to errors introduced during the sPCE modeling process, the DLSS model shows reduced accuracy in fitting variables such as mass flow rate, voltage amplitude, and voltage phase angle. The largest errors occur in variables 77 and 82, corresponding to the flow rates of pipes 27 and 31 in the thermal system, respectively. These errors are mainly influenced by two factors: firstly, the loads at the ends of the two pipes are small, resulting in smaller calculated flow baseline values ​​and thus larger calculated MAPE values; secondly, the beginnings of these two pipes are at the confluence of thermal system pipes, making it difficult to predict their flow rates.

[0174] Figure 6The p-boxes are for eight variables: supply temperature, return temperature, mass flow rate, node pressure, natural gas flow rate, voltage amplitude, voltage phase angle, and branch active power. Each p-box is composed of the maximum and minimum CDF (Conversion Factor). Using DLMCS-NR (solid line) as the standard value, it can be observed that the CDF (dashed line) obtained by DLSS is very close to the solid line. The results verify that the method described in this embodiment can obtain the p-boxes of variables while maintaining accuracy. Instead of using the DLSS model to calculate branch active / reactive power, the traditional AC branch power equation is used because the branch active / reactive power can be calculated based on voltage amplitude and voltage phase angle. Other variables in the IES can also be calculated using this method. Meanwhile, the upper and lower boundaries of the gas pressure calculated using DLSS show a slight deviation from the standard values, which is consistent with the performance of the HL-MEF model in fitting gas pressure. Due to the high-dimensional nonlinear relationship between input variables and gas pressure, the fitting effect for this variable is the worst. Under uncertainty, the p-box can be used to quickly analyze the possibility of system state variables exceeding limits, providing assistance for operators in future planning and operation.

[0175] Example 2

[0176] This embodiment provides a comprehensive energy system interval probabilistic energy flow calculation system, including:

[0177] The model building module is used to establish interval variable models and random variable models based on the integrated energy system;

[0178] The data acquisition module is used to sample the random variable model and the interval variable model respectively to obtain multidimensional random variables and multidimensional interval variables;

[0179] The deterministic performance flow calculation module is used to perform deterministic performance flow calculation based on multidimensional random variables and multidimensional interval variables, through the HL-MEF proxy model in the upper layer of the two-layer proxy model, and output the upper and lower boundary values ​​of energy flow based on the deterministic performance flow calculation results.

[0180] The lower-layer proxy model training module is used to train the lower-layer sPCE proxy model of the two-layer proxy model based on multidimensional random variables and the upper and lower boundaries of energy flow.

[0181] The interval probability energy flow calculation module is used to take large-scale random variables regenerated based on the random variable model as input, input them into the trained sPCE surrogate model, and output the upper and lower boundary values ​​of the interval probability energy flow.

[0182] Furthermore, it also includes:

[0183] The probability box building module is used to construct a probability box (p-box) based on the upper and lower boundary values ​​of the interval probability energy flow.

[0184] Example 3

[0185] This embodiment provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it completes the steps in the integrated energy system interval probability energy flow calculation method as described above.

[0186] Example 4

[0187] This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps in the integrated energy system interval probability energy flow calculation method described above.

[0188] The steps and methods involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0189] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0190] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0191] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating the probabilistic energy flow of an integrated energy system, characterized in that, include: Based on the integrated energy system, establish interval variable models and random variable models; The interval variable model is constructed as follows: In interval probabilistic energy flow analysis, photovoltaic panels (PV) and solar thermal equipment (PT) are considered as power generation devices in the power system and thermal system, respectively. The power generated by renewable energy equipment and the heat generated are represented by interval numbers, which can be expressed as: ； In the formula, and These represent the active power and reactive power emitted by the PV, respectively. This indicates the thermal power output of the PT heating system; This is an interval variable, representing the amount of solar radiation (PV / PT) at a specific tilt angle per hour; and Indicates the area of ​​the PV and PT panels; and Indicates the energy conversion efficiency of PV and PT; Indicates the power factor of PV; The random variable model is constructed as follows: assuming the loads of the electric, heat, and gas systems follow a Gaussian distribution, their probability density functions can be expressed as: ； In the formula, For the Integrated Energy System (IES) One load; and They are respectively Expected value and standard deviation; By sampling the random variable model and the interval variable model respectively, multidimensional random variables and multidimensional interval variables are obtained; Based on multidimensional random variables and multidimensional interval variables, deterministic performance flow calculation is performed through the HL-MEF proxy model in the upper layer of the two-layer proxy model. Based on the deterministic performance flow calculation results, the upper and lower boundary values ​​of energy flow are output. The method for constructing the HL-MEF proxy model includes: Select the characteristic variables of the integrated electric, heat and gas energy system, take the state variables corresponding to the characteristic variables as the target values, and use a variety of data-driven methods to train a multi-energy flow calculation model based on a single learner. Comparing the computational models generated during training, the high-performing computational models are selected for integration to generate a multi-energy flow computational model based on multiple learners, namely the HL-MEF proxy model. The lower layer of the two-layer proxy model, sPCE proxy model, is trained based on multidimensional random variables and upper and lower boundaries of energy flow. The method for constructing the sPCE proxy model includes: sPCE, as a novel polynomial chaotic expansion method, retains only a finite number of important expansion coefficients while maintaining maximum accuracy to avoid high-dimensional problems. Given a random input vector of probability density functions PDFs, the randomly output polynomial chaotic expansion PCE function is: ； In the formula, Represents a multivariate polynomial orthogonal to PDFs; Indicates belonging to Multiple indexes for components; Indicates about The coefficient; Multivariate polynomial Represented as a single-variable product: ； In the formula, This represents a univariate orthogonal polynomial, the value of which is determined by the distribution type of the variable; if the input variable follows a Gaussian distribution, its basis functions are Hermitian polynomials. Using the truncated polynomial chaotic expansion PCE, it can be represented in finite sum form: ； In the formula, This represents the set of selected multivariate polynomials with multiple indices; the truncation length refers to the length of the input variables. The length is less than or equal to All polynomials, where: ； ； For truncated polynomial chaotic series The larger the expected value, the better for approximation. The greater the impact, the more... Increase, The faster the increase, the more terms are retained, and the higher the computational cost of finding correlation coefficients. Therefore, for probabilistic energy flow problems, using... The effect of improving accuracy gradually diminishes, therefore a second-order expansion is used in the sPCE model; The sPCE model describes the relationship between random input values ​​and output boundary values ​​in the form of orthogonal polynomial expansion. The sPCE model is a polynomial chaotic expansion. The orthogonal matching pursuit projection method is used to obtain polynomial chaotic coefficients by utilizing the orthogonality of basis functions. The large-scale random variables regenerated based on the random variable model are used as inputs to the trained sPCE surrogate model, and the upper and lower boundary values ​​of the interval probability energy flow are output.

2. The method for calculating the probabilistic energy flow of an integrated energy system as described in claim 1, characterized in that, Also includes: Based on the upper and lower boundary values ​​of the interval probability energy flow, a probability box p-box is constructed.

3. The method for calculating the probabilistic energy flow of an integrated energy system as described in claim 1, characterized in that, By sampling the random variable model and the interval variable model respectively, multidimensional random variables and multidimensional interval variables are obtained, including: Based on random variable models and interval variable models, a large amount of data is first generated through a two-level Monte Carlo simulation method. The generated large amount of data is sampled, including: at the upper level, simple random sampling is performed on the interval variable data generated by the interval variable model to obtain multidimensional interval variables; at the lower level, the random variable data generated by the random variable model is sampled using the Latin hypersolution method to obtain multidimensional random variables.

4. The method for calculating the probabilistic energy flow of an integrated energy system as described in claim 1, characterized in that, The characteristic variables are the power at the node and other uncertainties. The power at the node is the power obtained by subtracting the power generated by the photovoltaic panel and solar thermal equipment from the load power of the power system, thermal system and gas system at the node. The other uncertainties at the node are the gas temperature and gas density. The target values ​​include power system parameters, thermal system parameters, and gas system parameters; the power system parameters include voltage amplitude and voltage phase angle; the thermal system parameters include supply temperature, return temperature, and pipeline flow rate; and the gas system parameters include node gas pressure and natural gas flow rate.

5. The method for calculating the probabilistic energy flow of an integrated energy system as described in claim 1, characterized in that, The training process of the HL-MEF model includes: Obtain the feature variable vector and target value of the integrated electric, thermal, and gas energy system, and divide it into the original training set and the original test set; use Folded cross-validation preprocesses the original training set; Based on the preprocessed original training set, the base learner is trained, and the trained base learner is validated using the original test set. Based on the original training set and the original test set, use the trained base learners to generate meta-training set and meta-test set for the meta-learners; Based on the meta-training set, train the meta-learner and use the meta-test set to verify the trained meta-learner. By combining the trained base learner and meta learner, a multi-energy flow computation model based on heterogeneous learners is output.

6. A system for calculating the probabilistic energy flow of an integrated energy system, characterized in that, A method for calculating the interval probabilistic energy flow of a comprehensive energy system as described in any one of claims 1-5 includes: The model building module is used to establish interval variable models and random variable models based on the integrated energy system; The data acquisition module is used to sample the random variable model and the interval variable model respectively to obtain multidimensional random variables and multidimensional interval variables; The deterministic performance flow calculation module is used to perform deterministic performance flow calculation based on multidimensional random variables and multidimensional interval variables, through the HL-MEF proxy model in the upper layer of the two-layer proxy model, and output the upper and lower boundary values ​​of energy flow based on the deterministic performance flow calculation results. The lower-layer proxy model training module is used to train the lower-layer sPCE proxy model of the two-layer proxy model based on multidimensional random variables and the upper and lower boundaries of energy flow. The interval probability energy flow calculation module is used to take large-scale random variables regenerated based on the random variable model as input, input them into the trained sPCE surrogate model, and output the upper and lower boundary values ​​of the interval probability energy flow.

7. The integrated energy system interval probabilistic energy flow calculation system as described in claim 6, characterized in that, Also includes: The probability box building module is used to construct a probability box (p-box) based on the upper and lower boundary values ​​of the interval probability energy flow.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, it completes the steps of the integrated energy system interval probabilistic energy flow calculation method as described in any one of claims 1-5.

9. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of a method for calculating the interval probabilistic energy flow of an integrated energy system as described in any one of claims 1-5.

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