Dual-stage interval state estimation method for electric-thermal integrated energy system

Abstract

The invention discloses a dual-stage interval state estimation method for an electric-thermal integrated energy system, and the method comprises the steps: analyzing the uncertainty of wind power output, and constructing a wind power output uncertainty domain ellipsoid convex model; constructing a measurement model of the electric-thermal comprehensive energy system; based on the wind power output uncertain domain ellipsoid convex model, establishing an integration form of a measurement model and a measurement model of the electric-thermal integrated energy system; based on the model in the integration form, constructing an interval estimation model of the electric-thermal integrated energy system; based on an electric-thermal integrated energy system interval estimation model, first-stage interval estimation of an electric power system and a hydraulic network is realized; according to the first-stage interval estimation data, two-stage interval estimation of the thermal network is realized based on an interval linear programming model; and outputting an IEHS state quantity interval value. The method has obvious advantages in solving performance, is high in calculation efficiency and moderate in interval estimation result width, and is more suitable for practical engineering application.

Description

Technical Field

[0001] The present invention belongs to the technical field of integrated energy systems, and in particular relates to a two-stage interval state estimation method for an electric-thermal integrated energy system. Background Art

[0002] The integrated electric-heat system (IEHS) takes the power system as the core and integrates various energy forms in the region, including thermal energy and natural gas. Through optimized scheduling and coordinated control, it can achieve the comprehensive utilization of various energy sources. Therefore, the development of an integrated energy system helps to improve energy utilization efficiency, promote the consumption of renewable energy, and increase the flexibility of the energy supply system. It is an effective way to promote energy transformation. In order to ensure the safe and stable operation of IEHS, it is necessary to perceive the operating status of the system in real time. Therefore, the study of the state estimation method of IEHS is very necessary.

[0003] The study of state estimation for electric / heat energy supply networks is one of the research hotspots of integrated energy systems, and many research results have been achieved so far. The state estimation of electric-heat integrated energy systems can be traced back to 2016, when a literature proposed an electric-heat state estimation model based on weighted square sum. Subsequently, considering the time scale differences and data communication problems between electric and thermal systems, a literature conducted research on the state estimation of distributed electric-heat integrated energy systems. Furthermore, in order to study the dynamic characteristics of the energy transmission process in the heat network, a literature considered the delay of heat medium transmission in the heat network pipeline, a literature considered the slow dynamics of the pipeline and the data sampling frequency, and a literature proposed an electric-heat-gas collaborative state estimation method based on extended Kalman filtering. Researchers also focused on the impact of bad data on the joint estimation results, and a literature proposed a robust state estimation of electric-heat integrated energy systems. Recently, a literature introduced neural network algorithms into the state estimation research of heat networks, realizing the dynamic tracking of state quantities. A literature uses deep neural network algorithms to achieve heat load prediction, thereby making up for the problem of insufficient measurement in the heat network. In the study of dynamic estimation of heating networks, some literature proposed a dynamic state estimation model with minimum information loss for linear discrete systems. This model has advantages in dealing with the uncertainty factors of measurement noise.

[0004] According to the analysis of existing research results, it can be found that the following aspects of IEHS state estimation research need to be paid more attention: on the one hand, the accuracy of heat network measurement equipment in the electric-thermal integrated energy system is low, the accuracy of measurement cannot be guaranteed, and factors such as multi-system coupling and new energy output fluctuations will greatly increase the uncertainty in the system. On the other hand, there is a lack of research on interval estimation problems in electric-thermal integrated energy systems, and there are few solutions to interval nonlinear programming problems. Summary of the invention

[0005] Purpose of the invention: In order to overcome the deficiencies in the prior art, a two-stage interval state estimation method for an electric-thermal integrated energy system is provided. The method takes into account the correlated uncertainty between adjacent wind power outputs and the uncertainty factors in the IEHS measurement, proposes an interval estimation model for the IEHS, and according to whether the measurement equation group is nonlinear, a two-stage solution is performed on the IEHS interval estimation model based on Second-Order Cone Programming (SOCP) and Interval Linear Programming (ILP), respectively. The example simulation verifies the effectiveness and advantages of the proposed method by comparing the interval estimation results and performance indicators of the existing interval estimation solution method with the auxiliary state variable-Krawczyk iteration method proposed in the present invention.

[0006] Technical solution: To achieve the above-mentioned purpose, the present invention provides a two-stage interval state estimation method for an electric-thermal integrated energy system, comprising the following steps:

[0007] S1: Analyze the uncertainty of wind power output and construct an ellipsoidal convex model of wind power output uncertainty domain;

[0008] S2: Construct a measurement model for the electric-thermal integrated energy system;

[0009] S3: Based on the convex ellipsoid model of wind power output uncertainty domain, the integrated form of the measurement model and the measurement model of the electric-thermal integrated energy system is established;

[0010] S4: Based on the integrated model, an interval estimation model of the electric-thermal integrated energy system is constructed, that is, an interval nonlinear estimation model;

[0011] S5: One-stage interval estimation of the power system and water network based on the interval estimation model of the electric-thermal integrated energy system;

[0012] S6: Based on the first-stage interval estimation data, the second-stage interval estimation of the thermal network is realized based on the interval linear programming model;

[0013] S7: Output IEHS state quantity interval value.

[0014] Furthermore, the method for analyzing the uncertainty of wind power output in step S1 is:

[0015] First, the uncertainty analysis of wind power output is carried out. The factors that affect wind power output are mainly the following aspects: random changes in wind speed, characteristics of wind farms and wind turbines, etc. The present invention takes into account that wind power output is affected by wind speed. There is a correlation between wind speeds between adjacent wind farms, so there is also a correlation uncertainty in wind power output. The ellipsoid model can be used to describe the uncertainty domain of its output; the construction of the wind power ellipsoid model also requires sample data, so the Nataf inverse method is used to generate sample data of wind speed; the relationship between wind power output power and wind speed is shown in formula (1), and formula (2) indicates that the wind speed obeys the Weibull distribution;

[0016]

[0017]

[0018] In the formula, v w represents wind speed, v ci is the cut-in wind speed, v r Indicates rated wind speed, v co is the maximum wind speed, P r Indicates the rated output power of the fan; f(v w ) represents the probability density function of wind speed, e w ,d w is a constant parameter; the wind speed sample data adopts the same method as the irradiance sample data, and the sample data of wind power output is calculated through (2), providing data for constructing the wind power output ellipsoid model.

[0019] Furthermore, the method for constructing the convex ellipsoid model of the wind power output uncertainty domain in step S1 is:

[0020] When dealing with uncertainty problems, non-probabilistic convex models do not require a large amount of data to model probability distribution and parameter estimation. Therefore, compared with probabilistic models, non-probabilistic convex models are more advantageous when data is scarce or incomplete. Common non-probabilistic convex models include box models, parallelepiped models, and ellipsoid models. The uncertainty domain constructed by the ellipsoid model is an ellipsoid convex set, and its two-dimensional image is an ellipse. Formula (3) is the mathematical model of the ellipsoid model;

[0021]

[0022] In the formula, is a positive definite matrix, a characteristic matrix of the ellipsoid, and contains the relevant information between uncertain variables; Y C represents the center of the ellipsoid, Ω EL The space represented by is bounded; among them, G ij >0, Y i and Y j Positive correlation; G ij<0, Y i and Y j Negative correlation; G ij =0, Y i and Y j Unrelated; |G ij The larger the value of |, the i and Y j The stronger the correlation;

[0023] The minimum volume method is generally used to solve the ellipsoid model. In the present invention, the minimum volume method based on semi-positive definite programming is used to solve the ellipsoid model. The solution goal of the ellipsoid model is to determine the characteristic matrix G and the ellipsoid center Y C , the solution is:

[0024] Assume that the eigenvalues ​​of G are decomposed as follows:

[0025]

[0026] Where M i represents the i-th characteristic root of the matrix G; then there exists a unique matrix The following conditions are met:

[0027]

[0028] It can be seen from this that the volume of the ellipsoid is related to (det R) -1 is proportional to, therefore, the optimization model of the minimum volume ellipsoid can be constructed as shown in formula (6); formula (6) is transformed into a convex optimization problem, and then the global optimal solution is obtained;

[0029]

[0030] Furthermore, the measurement model of the electric-thermal integrated energy system in step S2 includes the power system measurement equation, the thermal network measurement equation, the hydraulic network measurement equation and the energy coupling unit measurement equation, which are as follows:

[0031] Measurement equations for power systems

[0032] The state variables selected in the power supply network are the node phase angle and node voltage amplitude, that is, x el =[θ i ,U i ]; the node voltage amplitude, node injection power and branch power are selected for measurement, that is, Formula (7) is the noise-free power supply system measurement equation;

[0033]

[0034] Measurement equations for thermal networks

[0035] In the thermal network, the heating temperature of the node and the return water temperature of the node are selected as the state quantity, that is, x ht =[H si ,H ri ]; select the node heating temperature, node return water temperature, node injection hot water flow rate and node thermal power as the quantity measurement of the thermal network, that is, The measurement equations of the thermal network are shown in formulas (8)-(10);

[0036]

[0037]

[0038]

[0039] In the formula, C h is the specific heat capacity of the heat medium, H end Indicates the pipe end temperature, H start Indicates the temperature at the beginning of the pipe, H a is the ambient temperature. h is the heat transfer coefficient of the pipeline, L is the length of the pipeline; is the mixing temperature of node q, is the outflow traffic of the node, Indicates the temperature at the head end of the pipe where the node is located. represents the injection flow of a pipeline connected to node q;

[0040] Measurement equations for hydraulic networks

[0041] The hydraulic network and the thermal network together constitute the heating system. The pressure of the selected node in the hydraulic network is the state variable, that is, x w =[p i ]; the node pressure head, hydraulic branch flow and node injection flow were selected as the quantity measurements of the hydraulic system, that is, The measurement equations for the hydraulic network are shown below;

[0042]

[0043] In the formula, l ij is the impedance coefficient of branch ij, p j represents the pressure head of node j connected to node i; μ ij The value of reflects the direction of water flow and is as follows;

[0044]

[0045] Measurement equation of energy coupling unit

[0046] The energy coupling unit considered in the present invention plays the role of electric-thermal coupling, so it can be referred to as CHP (Combined Heat and Power). CHP types include gas turbines, internal combustion engines, and steam turbines. The system studied in the present invention operates in an isolated state. The heat energy generated by gas turbines and internal combustion engines and P CHP The relationship is:

[0047]

[0048] In the formula, Indicates the thermal power generated by CHP, P CHP represents the electrical active power generated by CHP, c CHP Indicates the thermal power output ratio; the relationship between the output thermal power and electrical power of the steam turbine is:

[0049]

[0050] In the formula, g CHP represents the heat-to-electricity output ratio of the steam turbine, P con Indicates the maximum output power of the steam turbine, F uel is the fuel power; considering that the quantity measurement of each node in IEHS also includes the measurement of CHP node, therefore, zero measurement constraint is imposed on CHP in the present invention.

[0051] Furthermore, the step S3 is specifically as follows:

[0052] Uncertainty domain of wind power output pseudo-measurement

[0053] The new energy power generation system is mainly composed of photovoltaic and wind power. In the present invention, the uncertainty domain of wind power output is set to satisfy the ellipsoid model. Therefore, the wind power output is modeled with an ellipsoid model, and the uncertainty of wind power output satisfies both positive correlation and negative correlation. An ellipsoid model as shown in formula (6) is constructed, and the ellipsoid model is solved by the minimum volume method based on the generated data sample. The new energy output satisfies the conditions shown in formula (15);

[0054]

[0055] Where X is the relevant uncertain variable of wind power output;

[0056] wp

[0057] High-precision measuring equipment interval measurement

[0058] High-precision measurement equipment mainly refers to the real-time measurement of the phasor measurement unit (PMU) of the node in the power grid, the real-time measurement of the feeder terminal unit (FTU) of the branch, the remote terminal unit (RTU) measurement equipment in the heating network, and the intelligent measurement terminal of the SCADA (Supervisory Control and Data Acquisition System). The interval quantity measurement of the power supply network mainly includes the active power and reactive power of the branch. The interval quantity measurement of the heating network mainly includes the pressure head of the node, the branch flow, the injection flow of the node, the heating temperature of the node and the return water temperature of the node, the injection flow of the node and the thermal power of the node. The above high-precision interval quantity measurement is expressed as:

[0059] [z i ]=[(1-α i )·z i , (1+α i )·z i ] (16)

[0060] In the formula, α i represents the fluctuation deviation of the node i quantity measurement, [z i ] is a high-precision interval measurement;

[0061] Measurement Model of Electric-Heat Integrated Energy System

[0062] The measurement model of the power supply network of the electric-thermal integrated energy system without noise is written as shown in formula (17);

[0063]

[0064] In the formula, h el (x el ), h w (x w ) and h ht (x ht ) represent the measurement equations of the power supply network, water network and thermal network respectively;

[0065] According to the definition of interval number: [x] is a non-empty real number set; then the system measurement vector considering uncertain factors is expressed in the form of formula (18);

[0066]

[0067] In the formula, the interval quantity measured in the power supply network is the active power of the branch [P ij ], reactive power [Q ij]; The interval quantity measurement of the heating network mainly includes the node pressure [p i ], branch flow Injection flow of the node The heating temperature of the node [H si ] and the return water temperature of the node [H ri ], the injection flow of the node and the node thermal power [Q i h ].

[0068] Furthermore, the construction method of the interval estimation model of the electric-thermal integrated energy system in step S4 is:

[0069] The set X and the set z are used to represent the state scalar set and the measurement vector set of the system respectively, as shown in the following mathematical relationship:

[0070]

[0071]

[0072] In the formula, For quantity measurement, Ω M is the set of measurements, M is the total number of measurements; referring to the interval state estimation model solution idea of ​​UBBE theory, the original optimization problem with interval constraints is split into two methods containing nonlinear interval constraints, and the interval estimation optimization objective of the electric-thermal system is written in the form of formula (21); at the same time, considering that the ellipsoid uncertainty domain variables and interval variables need to be considered in the constraints, the estimation model of the energy supply network of the electric-thermal integrated energy system is shown in formula (21):

[0073]

[0074] Furthermore, the first-stage interval estimation in step S5 is specifically as follows:

[0075] In the first-stage solution, auxiliary state variables are first introduced to linearize the system measurement equations. The linearized power and hydraulic network state estimation model satisfies the second-order cone programming (SOCP) model and can be solved by the primal-dual-interior point method. The auxiliary state variables obtained by solving the problem have a nonlinear relationship with the original state variables, forming an interval nonlinear equation group, which is solved by the Krawczy iteration method.

[0076] Furthermore, the process of solving the problem using the Krawczy iteration method in step S5 is as follows:

[0077] A1: Linearization of measurement equations

[0078] First, the auxiliary state variables are introduced to linearize the measurement equations of the power supply network and the hydraulic network; the auxiliary state variable of the power network is selected as x′ el =[[V′ i ],[O′ ij ],[M′ ij ]], the relationship between the auxiliary state variable and the original state variable is as follows;

[0079]

[0080] When the auxiliary variable is introduced, the quantity measurement is expressed as When , the measurement equation in interval number form is rewritten as follows:

[0081]

[0082] The introduced auxiliary state variables satisfy the relationship shown in formula (24). Formula (25) is relaxed to obtain the form shown in formula (25):

[0083] (o′ ij ) 2 +(M′ ij ) 2 =V′ i V′ j (twenty four)

[0084] (o′ ij ) 2 +(M′ ij ) 2 ≤V′ i V′ j (25)

[0085] A2: Auxiliary state variable solution based on second-order cone programming

[0086] The auxiliary state variable selected in the hydraulic network is x′ w =[Y′ ij ],in When the measured variable is expressed as formula (26), the relationship between the auxiliary state variable and the original state variable is shown in formula (27);

[0087]

[0088]

[0089] The measurement equations after the introduction of auxiliary state variables into the power network and the water network are integrated to obtain a simplified form as shown in formula (28); where J′ is the constant coefficient matrix of the system, and the specific elements are shown in formula (29);

[0090]

[0091]

[0092] A3: Solving the original state quantity based on interval nonlinear equations

[0093] By introducing auxiliary state variables, the nonlinear interval optimization problem of the form of formula (21) is transformed into a linear interval optimization problem as shown in formula (30). Formula (30) is also a second-order cone programming model, which is solved by the primal-dual interior point method.

[0094]

[0095] By solving the second-order cone programming model (30), the auxiliary state variable [x′] is obtained. There is a nonlinear relationship between the auxiliary state variable and the original state variable as shown in formula (31);

[0096]

[0097] Simplifying the above relationship and considering that both the auxiliary state quantity and the original state quantity are interval quantities, we get the interval nonlinear equation group shown in formula (32). We need to solve formula (32) to get the required original state quantity;

[0098]

[0099] The interval Krawczyk iteration method can be used to solve the interval nonlinear equations. The key to solving the interval Krawczyk iteration method is the interval iteration formula and the interval Krawczyk operator, as shown below;

[0100] [x] k+1 =[x] k ∩K([x] k ),k=0,1,2… (33)

[0101]

[0102] Among them, x m,k and C k Specifically, as shown in formulas (35) and (36), is a nonlinear system of equations The Jacobian matrix of is as shown in formula (37);

[0103] x m,k =Mid([x] k ) (35)

[0104]

[0105] ||ICk ·J h ([x] k )||≤||IC k-1 ·J h ([x] k-1 )|| (37)

[0106]

[0107] In formula (36), the conditions of case 1 are specifically shown in formula (37); finally, according to the required interval quantity [θ ij ] and [p ij ], and the linear relationship of formula (39), the interval estimation result of the required state variables is obtained;

[0108]

[0109] Formula (39) satisfies the interval linear equation system and can be abbreviated as A H [x]=[B], and solving it gives Through the above solution, we can get the original state quantity θ of the power network and the water network i ,U i and p i .

[0110] Furthermore, the two-stage interval estimation in step S6 is specifically as follows:

[0111] In the two-stage solution, the thermal network state estimation model is solved as an interval linear programming (ILP) problem. The present invention solves the problem by converting the ILP into a mixed integer linear programming (MILP) model. According to formula (30), the thermal network state estimation model shown in the following formula (40) can be obtained. The model is an interval linear programming model, and the constraint is an interval equality constraint.

[0112]

[0113] In the thermal network state estimation model, the quantities involved are The state variable is x ht =[H si ,H ri ]; Based on the idea of ​​Best Worst Case method (BWC), the equality constraint is replaced by the upper and lower boundary values ​​of the interval, and the interval estimation result under the "worst scenario" is obtained after combined comparison; by analyzing the state variables and quantity measurements, it can be found that the supply and return water temperature H of the equivalent measurement node si and Hri When the minimum or maximum value is taken, the state quantity should also be the minimum or maximum value. Therefore, at a certain moment, when the node supply and return water temperature selects the minimum or maximum value, it is only necessary to bring the upper and lower boundaries of the node flow and node power into the constraints for combined solution, and compare the results to obtain the state quantity interval value; the thermal network state estimation model in each group of scenarios can be regarded as a MILP model for solution to obtain the thermal network state quantity interval estimation value.

[0114] The solution process of the two-stage interval state estimation model of the electric-thermal integrated energy system proposed in the present invention is specifically as follows:

[0115] In the two-stage solution process of IEHS interval state estimation, the core problem is to solve the interval nonlinear estimation model. The present invention transforms the original IEHS interval nonlinear state estimation problem into an optimization problem for solving the upper and lower boundaries of the state quantity through the UBBE theory. And further introduces auxiliary state quantities and auxiliary quantity measurements to realize the linearization of the nonlinear measurement equations of the power system and the hydraulic network, thereby transforming the original estimation problem into a SCOP problem, and solving it through the primal-dual interior point method and the Krawczyk iteration method to obtain the interval estimation values ​​of the state variables of the power system and the hydraulic network. The above process is a one-stage solution of IEHS interval estimation. Further, on the basis of obtaining the nodes and branch flows of the hydraulic network, the calculation of the thermal network estimation model based on interval linear programming is carried out. Based on the BWC principle, the original ILP problem is transformed into a MILP problem and solved to obtain the interval estimation value of the thermal network state quantity.

[0116] Beneficial effect: Compared with the existing MCS and TKA solution methods, the interval estimation results of the ASV-KA method proposed in the present invention are moderately conservative. This is because ASV-KA transforms the original estimation model into a second-order cone programming model for solution and uses the interval Krawczyk iteration method to solve the auxiliary state variables, avoiding the construction of too many interval Krawczyk operators and the interval dichotomy caused by the expansion of the interval. ASV-KA has obvious advantages in solution performance, high computational efficiency, and moderate width of interval estimation results, which is more suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Figure 1 It is a flow chart of solving the two-stage interval state estimation model for IEHS in the present invention;

[0118] Figure 2 It is a wind power output diagram model under different wind force correlations in the present invention;

[0119] Figure 3 It is a diagram of interval estimation results of node voltage / phase angle of the power system in the present invention;

[0120] Figure 4 It is an interval estimation result diagram of the node water supply temperature, return water temperature and node pressure head of the thermal system in the present invention;

[0121] Figure 5 It is a performance parameter diagram of different solution algorithms in the present invention. DETAILED DESCRIPTION

[0122] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0123] like Figure 1 As shown, the present invention provides a two-stage interval state estimation method for an electric-thermal integrated energy system, comprising the following steps:

[0124] S1: Analyze the uncertainty of wind power output and construct an ellipsoidal convex model of wind power output uncertainty domain;

[0125] S2: Construct a measurement model for the electric-thermal integrated energy system;

[0126] S3: Based on the convex ellipsoid model of wind power output uncertainty domain, the integrated form of the measurement model and the measurement model of the electric-thermal integrated energy system is established;

[0127] S4: Based on the integrated model, an interval estimation model of the electric-thermal integrated energy system is constructed, that is, an interval nonlinear estimation model;

[0128] S5: One-stage interval estimation of the power system and water network based on the interval estimation model of the electric-thermal integrated energy system;

[0129] S6: Based on the first-stage interval estimation data, the second-stage interval estimation of the thermal network is realized based on the interval linear programming model;

[0130] S7: Output IEHS state quantity interval value.

[0131] The method for analyzing the uncertainty of wind power output in step S1 is:

[0132] First, the uncertainty analysis of wind power output is carried out. The factors that affect wind power output are mainly the following aspects: random changes in wind speed, characteristics of wind farms and wind turbines, etc. The present invention takes into account that wind power output is affected by wind speed. There is a correlation between wind speeds between adjacent wind farms, so there is also a correlation uncertainty in wind power output. The ellipsoid model can be used to describe the uncertainty domain of its output; the construction of the wind power ellipsoid model also requires sample data, so the Nataf inverse method is used to generate sample data of wind speed; the relationship between wind power output power and wind speed is shown in formula (1), and formula (2) indicates that the wind speed obeys the Weibull distribution;

[0133]

[0134]

[0135] In the formula, v w represents wind speed, v ci is the cut-in wind speed, v r Indicates rated wind speed, v co is the maximum wind speed, P r Indicates the rated output power of the fan; f(v w ) represents the probability density function of wind speed, e w ,d w is a constant parameter; the wind speed sample data adopts the same method as the irradiance sample data, and the sample data of wind power output is calculated through (2), providing data for constructing the wind power output ellipsoid model.

[0136] The construction method of the convex ellipsoid model of wind power output uncertainty domain is as follows:

[0137] When dealing with uncertainty problems, non-probabilistic convex models do not require a large amount of data to model probability distribution and parameter estimation. Therefore, compared with probabilistic models, non-probabilistic convex models are more advantageous when data is scarce or incomplete. Common non-probabilistic convex models include box models, parallelepiped models, and ellipsoid models. The uncertainty domain constructed by the ellipsoid model is an ellipsoid convex set, and its two-dimensional image is an ellipse. Formula (3) is the mathematical model of the ellipsoid model;

[0138]

[0139] In the formula, is a positive definite matrix, a characteristic matrix of the ellipsoid, and contains the relevant information between uncertain variables; Y C represents the center of the ellipsoid, Ω EL The space represented by is bounded; among them, G ij >0, Y i and Y j Positive correlation; G ij <0, Yi and Y j Negative correlation; G ij =0, Y i and Y j Unrelated; |G ij The larger the value of |, the i and Y j The stronger the correlation;

[0140] The minimum volume method is generally used to solve the ellipsoid model. In the present invention, the minimum volume method based on semi-positive definite programming is used to solve the ellipsoid model. The solution goal of the ellipsoid model is to determine the characteristic matrix G and the ellipsoid center Y C , the solution is:

[0141] Assume that the eigenvalues ​​of G are decomposed as follows:

[0142]

[0143] Where M i represents the i-th characteristic root of the matrix G; then there exists a unique matrix The following conditions are met:

[0144]

[0145] It can be seen from this that the volume of the ellipsoid is related to (det R) -1 is proportional to, therefore, the optimization model of the minimum volume ellipsoid can be constructed as shown in formula (6); formula (6) is transformed into a convex optimization problem, and then the global optimal solution is obtained;

[0146]

[0147] The measurement model of the electric-thermal integrated energy system in step S2 includes the power system measurement equation, the thermal network measurement equation, the hydraulic network measurement equation and the energy coupling unit measurement equation, which are as follows:

[0148] Measurement equations for power systems

[0149] The state variables selected in the power supply network are the node phase angle and node voltage amplitude, that is, x el =[θ i ,U i ]; the node voltage amplitude, node injection power and branch power are selected for measurement, that is, Formula (7) is the noise-free power supply system measurement equation;

[0150]

[0151] Measurement equations for thermal networks

[0152] In the thermal network, the heating temperature of the node and the return water temperature of the node are selected as the state quantity, that is, x ht =[H si ,H ri ]; select the node heating temperature, node return water temperature, node injection hot water flow rate and node thermal power as the quantity measurement of the thermal network, that is, The measurement equations of the thermal network are shown in formulas (8)-(10);

[0153]

[0154]

[0155] In the formula, C h is the specific heat capacity of the heat medium, H end Indicates the pipe end temperature, H start Indicates the temperature at the beginning of the pipe, H a is the ambient temperature. h is the heat transfer coefficient of the pipeline, L is the length of the pipeline; is the mixing temperature of node q, is the outflow traffic of the node, Indicates the temperature at the head end of the pipe where the node is located. represents the injection flow of a pipeline connected to node q;

[0156] Measurement equations for hydraulic networks

[0157] The hydraulic network and the thermal network together constitute the heating system. The pressure of the selected node in the hydraulic network is the state variable, that is, x w =[p i ]; the node pressure head, hydraulic branch flow and node injection flow were selected as the quantity measurements of the hydraulic system, that is, The measurement equations for the hydraulic network are shown below;

[0158]

[0159] In the formula, l ij is the impedance coefficient of branch ij, p j represents the pressure head of node j connected to node i; μ ij The value of reflects the direction of water flow and is as follows;

[0160]

[0161] Measurement equation of energy coupling unit

[0162] The energy coupling unit considered in the present invention plays the role of electric-thermal coupling, so it can be referred to as CHP (Combined Heat and Power). CHP types include gas turbines, internal combustion engines, and steam turbines. The system studied in the present invention operates in an isolated state. The heat energy generated by gas turbines and internal combustion engines and P CHP The relationship is:

[0163]

[0164] In the formula, Indicates the thermal power generated by CHP, P CHP represents the electrical active power generated by CHP, c CHP Indicates the thermal power output ratio; the relationship between the output thermal power and electrical power of the steam turbine is:

[0165]

[0166] In the formula, g CHP represents the heat-to-electricity output ratio of the steam turbine, P con Indicates the maximum output power of the steam turbine, F uel is the fuel power; considering that the quantity measurement of each node in IEHS also includes the measurement of CHP node, therefore, zero measurement constraint is imposed on CHP in the present invention.

[0167] Step S3 is specifically as follows:

[0168] Uncertainty domain of wind power output pseudo-measurement

[0169] The new energy power generation system is mainly composed of photovoltaic and wind power. In the present invention, the uncertainty domain of wind power output is set to satisfy the ellipsoid model. Therefore, the wind power output is modeled with an ellipsoid model, and the uncertainty of wind power output satisfies both positive correlation and negative correlation. An ellipsoid model as shown in formula (6) is constructed, and the ellipsoid model is solved by the minimum volume method based on the generated data sample. The new energy output satisfies the conditions shown in formula (15);

[0170]

[0171] Where X is the relevant uncertain variable of wind power output;

[0172] wp

[0173] High-precision measuring equipment interval measurement

[0174] High-precision measurement equipment mainly refers to the real-time measurement of the phasor measurement unit (PMU) of the node in the power grid, the real-time measurement of the feeder terminal unit (FTU) of the branch, the remote terminal unit (RTU) measurement equipment in the heating network, and the intelligent measurement terminal of the SCADA (Supervisory Control and Data Acquisition System). The interval quantity measurement of the power supply network mainly includes the active power and reactive power of the branch. The interval quantity measurement of the heating network mainly includes the pressure head of the node, the branch flow, the injection flow of the node, the heating temperature of the node and the return water temperature of the node, the injection flow of the node and the thermal power of the node. The above high-precision interval quantity measurement is expressed as:

[0175] [z i ]=[(1-α i )·z i ,(1+α i )·z i ] (16)

[0176] In the formula, α i represents the fluctuation deviation of the node i quantity measurement, [z i ] is a high-precision interval measurement;

[0177] Measurement Model of Electric-Heat Integrated Energy System

[0178] The measurement model of the power supply network of the electric-thermal integrated energy system without noise is written as shown in formula (17);

[0179]

[0180] In the formula, h el (x el ), h w (x w ) and h ht (x ht ) represent the measurement equations of the power supply network, water network and thermal network respectively;

[0181] According to the definition of interval number: [x] is a non-empty real number set; then the system measurement vector considering uncertain factors is expressed in the form of formula (18);

[0182]

[0183] In the formula, the interval quantity measured in the power supply network is the active power of the branch [P ij ], reactive power [Q ij]; The interval quantity measurement of the heating network mainly includes the node pressure [p i ], branch flow Injection flow of the node The heating temperature of the node [H si ] and the return water temperature of the node [H ri ], the injection flow of the node and the thermal power of the node

[0184] The construction method of the interval estimation model of the electric-thermal integrated energy system in step S4 is:

[0185] The set X and the set z are used to represent the state scalar set and the measurement vector set of the system respectively, as shown in the following mathematical relationship:

[0186]

[0187]

[0188] In the formula, z φ For quantity measurement, Ω M is the set of measurements, M is the total number of measurements; referring to the interval state estimation model solution idea of ​​UBBE theory, the original optimization problem with interval constraints is split into two methods containing nonlinear interval constraints, and the interval estimation optimization objective of the electric-thermal system is written in the form of formula (21); at the same time, considering that the ellipsoid uncertainty domain variables and interval variables need to be considered in the constraints, the estimation model of the energy supply network of the electric-thermal integrated energy system is shown in formula (21):

[0189]

[0190] The first-stage interval estimation in step S5 is specifically as follows:

[0191] In the first stage solution, the auxiliary state variables are first introduced to linearize the system measurement equations. The linearized power and water network state estimation model satisfies the second-order cone programming (SOCP) model and can be solved by the original dual-interior point method. The auxiliary state variables obtained by the solution have a nonlinear relationship with the original state variables, forming an interval nonlinear equation group, which is solved by the Krawczy iteration method. The solution process is:

[0192] A1: Linearization of measurement equations

[0193] First, the auxiliary state variables are introduced to linearize the measurement equations of the power supply network and the hydraulic network. The auxiliary state variables of the power network are selected as x e ' l =[[V'i ],[O' ij ],[M' ij ]], the relationship between the auxiliary state variable and the original state variable is as follows;

[0194]

[0195] When the auxiliary variable is introduced, the quantity measurement is expressed as When , the measurement equation in interval number form is rewritten as follows:

[0196]

[0197] The introduced auxiliary state variables satisfy the relationship shown in formula (24). Formula (25) is relaxed to obtain the form shown in formula (25):

[0198] (O' ij ) 2 +(M' ij ) 2 =V' i V' j (twenty four)

[0199] (O' ij ) 2 +(M' ij ) 2 ≤V' i V' j (25)

[0200] A2: Auxiliary state variable solution based on second-order cone programming

[0201] The auxiliary state variable selected in the hydraulic network is x′ w =[Y′ ij ],in When the measured variable is expressed as formula (26), the relationship between the auxiliary state variable and the original state variable is shown in formula (27);

[0202]

[0203]

[0204] The measurement equations after the introduction of auxiliary state variables into the power network and the water network are integrated to obtain a simplified form as shown in formula (28); where J′ is the constant coefficient matrix of the system, and the specific elements are shown in formula (29);

[0205]

[0206]

[0207] A3: Solving the original state quantity based on interval nonlinear equations

[0208] By introducing auxiliary state variables, the nonlinear interval optimization problem of the form of formula (21) is transformed into a linear interval optimization problem as shown in formula (30). Formula (30) is also a second-order cone programming model, which is solved by the primal-dual interior point method.

[0209]

[0210] By solving the second-order cone programming model (30), the auxiliary state variable [x′] is obtained. There is a nonlinear relationship between the auxiliary state variable and the original state variable as shown in formula (31);

[0211]

[0212] Simplifying the above relationship and considering that both the auxiliary state quantity and the original state quantity are interval quantities, we get the interval nonlinear equation group shown in formula (32). We need to solve formula (32) to get the required original state quantity;

[0213]

[0214] The interval Krawczyk iteration method can be used to solve the interval nonlinear equations. The key to solving the interval Krawczyk iteration method is the interval iteration formula and the interval Krawczyk operator, as shown below;

[0215] [x] k+1 =[x] k ∩K([x] k ),k=0,1,2... (33)

[0216]

[0217] Among them, x m,k and C k Specifically, as shown in formulas (35) and (36), is a nonlinear system of equations The Jacobian matrix of is as shown in formula (37);

[0218] x m,k =Mid([x] k ) (35)

[0219]

[0220] ||IC k ·J h ([x] k )||≤||IC k-1·J h ([x] k-1 )|| (37)

[0221]

[0222] In formula (36), the conditions of case 1 are specifically shown in formula (37); finally, according to the required interval quantity [θ ij ] and [p ij ], and the linear relationship of formula (39), the interval estimation result of the required state variables is obtained;

[0223]

[0224] Formula (39) satisfies the interval linear equation system and can be abbreviated as A H [x]=[B], and solving it gives Through the above solution, we can get the original state quantity θ of the power network and the water network i ,U i and p i .

[0225] The second-stage interval estimation in step S6 is specifically as follows:

[0226] In the two-stage solution, the thermal network state estimation model is solved as an interval linear programming (ILP) problem. The present invention solves the problem by converting the ILP into a mixed integer linear programming (MILP) model. According to formula (30), the thermal network state estimation model shown in the following formula (40) can be obtained. The model is an interval linear programming model, and the constraint is an interval equality constraint.

[0227]

[0228] In the thermal network state estimation model, the quantities involved are The state variable is x ht =[H si ,H ri ]; Based on the idea of ​​Best Worst Case method (BWC), the equality constraint is replaced by the upper and lower boundary values ​​of the interval, and the interval estimation result under the "worst scenario" is obtained after combined comparison; by analyzing the state variables and quantity measurements, it can be found that the supply and return water temperature H of the equivalent measurement node si and H riWhen the minimum or maximum value is taken, the state quantity should also be the minimum or maximum value. Therefore, at a certain moment, when the node supply and return water temperature selects the minimum or maximum value, it is only necessary to bring the upper and lower boundaries of the node flow and node power into the constraints for combined solution, and compare the results to obtain the state quantity interval value; the thermal network state estimation model in each group of scenarios can be regarded as a MILP model for solution to obtain the thermal network state quantity interval estimation value.

[0229] Reference Figure 1 The solution process of the two-stage interval state estimation model of the electric-thermal integrated energy system proposed in the present invention is as follows:

[0230] In the two-stage solution process of IEHS interval state estimation, the core problem is to solve the interval nonlinear estimation model. The present invention transforms the original IEHS interval nonlinear state estimation problem into an optimization problem for solving the upper and lower boundaries of the state quantity through the UBBE theory. And further introduces auxiliary state quantities and auxiliary quantity measurements to realize the linearization of the nonlinear measurement equations of the power system and the hydraulic network, thereby transforming the original estimation problem into a SCOP problem, and solving it through the primal-dual interior point method and the Krawczyk iteration method to obtain the interval estimation values ​​of the state variables of the power system and the hydraulic network. The above process is a one-stage solution of IEHS interval estimation. Further, on the basis of obtaining the nodes and branch flows of the hydraulic network, the calculation of the thermal network estimation model based on interval linear programming is carried out. Based on the BWC principle, the original ILP problem is transformed into a MILP problem and solved to obtain the interval estimation value of the thermal network state quantity.

[0231] In order to verify the effectiveness and effect of the method of the present invention, this embodiment applies the method of the present invention to an example, as follows:

[0232] 1. Wind power output uncertainty domain model

[0233] In this embodiment, the output of the wind turbine generator sets at the grid nodes 3 and 4 is considered to be correlated, and the parameters of the wind power generation model are given with reference to the wind resources in the southeast region of my country: d w =5.26, e w =14.39, v ci =3m / s,v r =6m / s,v co =14m / s, P r =500kW. Wind speed sample data with different correlations can be generated by using the Nataf inverse method, and then combined with the wind power output model to obtain wind turbine output sample data with different correlations. Figure 2(a) and (b) are the convex models of two wind turbine outputs when the correlation is 0.5 and -0.5, respectively, including wind turbine power generation sample data (5000), ellipsoid model and parallelepiped model.

[0234] The parameters of the convex model of wind power generation obtained by the minimum volume method are shown in Table 1. Figure 2 It can be seen that both the ellipsoid model and the parallelepiped model can contain all sample points and reflect the correlation between samples. From Table 1, it can be seen that when the wind speed correlation is positive, the characteristic matrix parameter G w12 is positive, otherwise, G w12 is a negative value, G w12 The larger the |, the greater the correlation between wind speeds. In the subsequent interval estimation calculation, the wind speed correlation is selected as 0.5.

[0235] Table 1- Parameters of minimum volume ellipsoid of wind power output under different correlations

[0236]

[0237] 2. Comparison and analysis of IEHS interval estimation results

[0238] Based on the parameter setting of the system, this embodiment respectively adopts the existing Monte Carlo sampling simulation method (MCS), the traditional Krawczyk analysis algorithm (TKA) and the auxiliary state variable Krawczyk iteration method (ASV-KA) proposed in the present invention to solve the proposed IEHS interval estimation model.

[0239] In order to verify the accuracy and effectiveness of the interval dynamic state estimation results proposed in this invention, the upper bound root mean square error of the interval estimation results after convergence is adopted. The evaluation is carried out as shown in (41). is the estimated value of the interval state of node i, x k,i is the true value of the state quantity of node i; N is the sampling period; sup is the upper bound of the estimated value. The smaller.

[0240]

[0241] “Completeness” refers to whether the result of interval state estimation can contain the true value x of the node state quantity k,i, as shown in formula (42), is the average completeness index of interval dynamic state estimation. If the completeness meets the requirements, it means that the estimation result can contain the true value of the system state quantity.

[0242]

[0243] "Conservatism" is an indicator to measure the quality of interval state estimation. The smaller the conservatism, the higher the reference value of the state estimation. However, if the conservatism is too small, the error tolerance of the interval estimation result will be lost. The present invention uses the standard Kalman filter based on Monte Carlo (MCSKF) algorithm as a reference value and defines the average conservatism index C of interval dynamic estimation. ons As shown in the following formula.

[0244]

[0245] In the formula, and They are respectively the upper and lower limits of the estimated value of node i of the interval estimation method proposed in the present invention; and x k,i They are the upper and lower limits of the interval estimation results of MCSKF as reference values.

[0246] 2.1 Analysis of interval estimation results of power system

[0247] like Figure 3 The following are the interval state estimation results of the power system node voltage and phase angle in IEHS, where Figure 3 (a) is the estimated results of the voltage interval of each node calculated by different methods. Figure 3 (b) shows the phase angle interval estimation results of each node calculated using different methods.

[0248] Through the simulation results, it can be found that the node voltage / phase angle interval solved by TKA is a superset of the state quantity interval solved by MCS and the ASV-KA method proposed in this paper, and is the most conservative; the state quantity interval obtained by the MCS method is a subset of the interval results of other methods, and is the least conservative; the state quantity interval calculated by the ASV-KA proposed in this invention is a superset of the MCS calculation interval and a subset of the TKA calculation interval, and is moderately conservative.

[0249] 2.2 Analysis of interval estimation results of thermal system

[0250] like Figure 4 The following are the interval state estimation results of the supply / return water temperature and node pressure head of the thermal system in IEHS, where Figure 4(a) is the estimated results of the water supply temperature range of each node calculated using different methods. Figure 4 (b) Estimation results of return water temperature range of each node calculated by different methods, Figure 4 (c) The estimated results of the pressure head interval of each node calculated using different methods. Figure 4 It can be seen intuitively that the system state quantity interval estimation result obtained by the ASV-KA calculation method proposed in the present invention is a superset of the result obtained by the MCS calculation method and a subset of the result obtained by the TKA calculation method, and the estimation result is moderately conservative.

[0251] 2.3 Performance comparison of different algorithms for solving interval estimation models

[0252] In order to analyze the performance of the proposed algorithm, the existing affine algorithm (AA) and TKA are used to solve the interval estimation model proposed in this paper and obtain the following Figure 5 The performance results of interval estimation solutions of three different algorithms are shown. For the convenience of representation, the performance parameters are normalized. Figure 5 (a) is the performance parameter of three different algorithms for solving the power system state estimation model. It can be seen from the figure that the interval estimation solution using AA has a smaller interval estimation width, but the calculation time is longer and the number of iterations is more. Compared with the TKA solution method, the ASV-KA solution method proposed in the present invention has more advantages in terms of calculation efficiency and estimation results. Figure 5 The performance results of the three different algorithms presented in (b) for the thermal system are consistent with those for the power system. Therefore, compared with the existing methods, the ASV-KA method proposed in the present invention has higher computational efficiency and moderately conservative interval estimation results, and is more advantageous in engineering applications.

Claims

1. A two-stage interval state estimation method for an electric-thermal integrated energy system, characterized in that: The steps include: S1: Analyze the uncertainty of wind power output and construct an ellipsoidal convex model of wind power output uncertainty domain; S2: Construct a measurement model for the electric-thermal integrated energy system; S3: Based on the convex ellipsoid model of wind power output uncertainty domain, the integrated form of the measurement model and the measurement model of the electric-thermal integrated energy system is established; S4: Based on the integrated model, an interval estimation model for the electric-thermal integrated energy system is constructed; S5: One-stage interval estimation of the power system and water network based on the interval estimation model of the electric-thermal integrated energy system; S6: Based on the first-stage interval estimation data, the second-stage interval estimation of the thermal network is realized based on the interval linear programming model; S7: Output IEHS state quantity interval value.

2. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 1, characterized in that: The method for analyzing the uncertainty of wind power output in step S1 is: The ellipsoid model is used to describe the uncertainty domain of its output; the Nataf inverse method is used to generate sample data of wind speed; the relationship between wind power output and wind speed is shown in formula (1), and formula (2) indicates that the wind speed obeys the Weibull distribution; In the formula, v w represents wind speed, v ci is the cut-in wind speed, v r Indicates rated wind speed, v co is the maximum wind speed, P r Indicates the rated output power of the fan; f(v w ) represents the probability density function of wind speed, e w ,d w is a constant parameter; the wind speed sample data adopts the same method as the irradiance sample data, and the sample data of wind power output is calculated through (2), providing data for constructing the wind power output ellipsoid model.

3. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 2, characterized in that: The method for constructing the convex ellipsoid model of the wind power output uncertainty domain in step S1 is: The uncertainty domain constructed by the ellipsoid model is the convex set of the ellipsoid, and its two-dimensional image is an ellipse. Formula (3) is the mathematical model of the ellipsoid model; In the formula, is a positive definite matrix, a characteristic matrix of the ellipsoid, and contains the relevant information between uncertain variables; Y C represents the center of the ellipsoid, Ω EL The space represented by is bounded; among them, G ij >0, Y i and Y j Positive correlation; G ij When Y i and Y j Negative correlation; G ij =0, Y i and Y j Unrelated; |G ij The larger the value of |, the i and Y j The stronger the correlation; The minimum volume method based on semi-positive programming is selected to solve the ellipsoid model; the solution goal of the ellipsoid model is to determine the characteristic matrix G and the ellipsoid center Y C , the solution is: Assume that the eigenvalues ​​of G are decomposed as follows: Where M i represents the i-th characteristic root of the matrix G; then there exists a unique matrix The following conditions are met: The optimization model for constructing the minimum volume ellipsoid is shown in formula (6); formula (6) is transformed into a convex optimization problem, and then the global optimal solution is obtained; 4. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 1, characterized in that: The measurement model of the electric-thermal integrated energy system in step S2 includes the power system measurement equation, the thermal network measurement equation, the hydraulic network measurement equation and the energy coupling unit measurement equation, which are specifically as follows: Measurement equations for power systems The state variables selected in the power supply network are the node phase angle and node voltage amplitude, that is, x el =[θ i ,U i ]; the node voltage amplitude, node injection power and branch power are selected for measurement, that is, Formula (7) is the noise-free power supply system measurement equation; Measurement equations for thermal networks In the thermal network, the heating temperature of the node and the return water temperature of the node are selected as the state quantity, that is, x ht =[H si ,H ri ]; select the node heating temperature, node return water temperature, node injection hot water flow rate and node thermal power as the quantity measurement of the thermal network, that is, The measurement equations of the thermal network are shown in formulas (8)-(10); In the formula, C h is the specific heat capacity of the heat medium, H end Indicates the pipe end temperature, H start Indicates the temperature at the beginning of the pipe, H a is the ambient temperature. h is the heat transfer coefficient of the pipeline, L is the length of the pipeline; is the mixing temperature of node q, is the outflow traffic of the node, Indicates the temperature at the head end of the pipe where the node is located. represents the injection flow of a pipeline connected to node q; Measurement equations for hydraulic networks The hydraulic network and the thermal network together constitute the heating system. The pressure of the selected node in the hydraulic network is the state variable, that is, x w =[p i ]; the node pressure head, hydraulic branch flow and node injection flow were selected as the quantity measurements of the hydraulic system, that is, The measurement equations for the hydraulic network are shown below; In the formula, l ij is the impedance coefficient of branch ij, p j represents the pressure head of node j connected to node i; μ ij The value of reflects the direction of water flow and is as follows; Measurement equation of energy coupling unit Gas turbines and internal combustion engines, which generate heat and P CHP The relationship is: In the formula, Indicates the thermal power generated by CHP, P CHP represents the electrical active power generated by CHP, c CHP Indicates the thermal power output ratio; the relationship between the output thermal power and electrical power of the steam turbine is: In the formula, g CHP represents the heat-to-electricity output ratio of the steam turbine, P con Indicates the maximum output power of the steam turbine, F uel is the fuel power; considering that the measurement of each node in IEHS also includes the measurement of CHP node, therefore, zero measurement constraint is imposed on CHP.

5. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 3, characterized in that: The step S3 is specifically as follows: Uncertainty domain of wind power output pseudo-measurement The uncertainty domain of wind power output power is set to satisfy the ellipsoid model. Therefore, the wind power output is modeled with an ellipsoid model. The uncertainty of wind power output satisfies both positive correlation and negative correlation. An ellipsoid model is constructed as shown in formula (6), and the ellipsoid model is solved by the minimum volume method based on the generated data sample. The new energy output satisfies the conditions shown in formula (15). Where X is the relevant uncertain variable of wind power output; wp High-precision measuring equipment interval measurement High-precision interval measurement is expressed as: [With i ]=[(1-α i )·With i ,(1+α i )·With i ] (16) In the formula, α i represents the fluctuation deviation of the node i quantity measurement, [z i ] is a high-precision interval measurement; Measurement Model of Electric-Heat Integrated Energy System The measurement model of the power supply network of the electric-thermal integrated energy system without noise is written as shown in formula (17); In the formula, h el (x el ), h w (x w ) and h ht (x ht ) represent the measurement equations of the power supply network, water network and thermal network respectively; According to the definition of interval number: [x] is a non-empty real number set; then the system measurement vector considering uncertain factors is expressed in the form of formula (18); In the formula, the interval quantity measured in the power supply network is the active power of the branch [P ij ], reactive power [Q ij ]; the interval quantity measurement of the heating network mainly includes the node pressure [p i ], branch flow Injection flow of the node The heating temperature of the node [H si ] and the return water temperature of the node [H ri ], the injection flow of the node and the thermal power of the node 6. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 5, characterized in that: The construction method of the interval estimation model of the electric-thermal integrated energy system in step S4 is: The set X and the set z are used to represent the state scalar set and the measurement vector set of the system respectively, as shown in the following mathematical relationship: In the formula, For quantity measurement, Ω M is the set of measurements, M is the total number of measurements; referring to the interval state estimation model solution idea of ​​UBBE theory, the original optimization problem with interval constraints is split into two methods containing nonlinear interval constraints, and the interval estimation optimization objective of the electric-thermal system is written in the form of formula (21); at the same time, considering that the ellipsoid uncertainty domain variables and interval variables need to be considered in the constraints, the estimation model of the energy supply network of the electric-thermal integrated energy system is shown in formula (21):

7. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 6, characterized in that: The first-stage interval estimation in step S5 is specifically as follows: In the first-stage solution, auxiliary state variables are first introduced to linearize the system measurement equations. The linearized power and hydraulic network state estimation model satisfies the second-order cone programming model and can be solved by the primal-dual-interior point method. The auxiliary state variables obtained by solving the problem have a nonlinear relationship with the original state variables, forming an interval nonlinear equation group, which is solved by the Krawczy iteration method.

8. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 7, characterized in that: The process of solving the problem using the Krawczy iteration method in step S5 is as follows: A1: Linearization of measurement equations First, the auxiliary state variables are introduced to linearize the measurement equations of the power supply network and the hydraulic network; the auxiliary state variable of the power network is selected as x′ el =[[V' i ],[O' ij ],[M' ij ]], the relationship between the auxiliary state variable and the original state variable is as follows; When the auxiliary variable is introduced, the quantity measurement is expressed as When , the measurement equation in interval number form is rewritten as follows: The introduced auxiliary state variables satisfy the relationship shown in formula (24). Formula (25) is relaxed to obtain the form shown in formula (25): (Oh) ij ) 2 +(M' ij ) 2 =V' i In' j (24) (Oh) ij ) 2 +(M' ij ) 2 ≤V' i In' j (25) A2: Auxiliary state variable solution based on second-order cone programming The auxiliary state variable selected in the hydraulic network is x′ w =[Y′ ij ],in When the measured variable is expressed as formula (26), the relationship between the auxiliary state variable and the original state variable is shown in formula (27); The measurement equations after the introduction of auxiliary state variables into the power network and the water network are integrated to obtain a simplified form as shown in formula (28); where J′ is the constant coefficient matrix of the system, and the specific elements are shown in formula (29); A3: Solving the original state quantity based on interval nonlinear equations By introducing auxiliary state variables, the nonlinear interval optimization problem of the form of formula (21) is transformed into a linear interval optimization problem as shown in formula (30). Formula (30) is also a second-order cone programming model, which is solved by the primal-dual interior point method. The auxiliary state variables are obtained by solving the second-order cone programming model (30) As a result, there is a nonlinear relationship between the auxiliary state variable and the original state variable as shown in formula (31); Simplifying the above relationship and considering that both the auxiliary state quantity and the original state quantity are interval quantities, we get the interval nonlinear equation group shown in formula (32). We need to solve formula (32) to get the required original state quantity; The interval Krawczyk iteration method can be used to solve the interval nonlinear equations. The key to solving the interval Krawczyk iteration method is the interval iteration formula and the interval Krawczyk operator, as shown below; [x] k+1 =[x] k ∩K([x] k ),k=0,1,2... (33) Among them, x m,k and C k Specifically, as shown in formulas (35) and (36), is a nonlinear system of equations The Jacobian matrix of is as shown in formula (37); x m,k =Mid([x] k ) (35) ||I-C k ·J a ([x] k )||≤||I-C k-1 ·J h ([x] k-1 )|| (37) In formula (36), the conditions of case 1 are specifically shown in formula (37); finally, according to the required interval quantity [θ ij ] and [p ij ], and the linear relationship of formula (39), the interval estimation result of the required state variables is obtained; Formula (39) satisfies the interval linear equation system and can be simplified as Solving it gives Through the above solution, we can get the original state quantity θ of the power network and the water network i ,U i and p i .

9. A two-stage interval state estimation method for an electric-thermal integrated energy system according to claim 7, characterized in that: The two-stage interval estimation in step S6 is specifically as follows: In the two-stage solution, the thermal network state estimation model is solved as an interval linear programming problem, which is solved by converting the ILP into a mixed integer linear programming model. According to formula (30), the thermal network state estimation model shown in the following formula (40) is obtained. The model is an interval linear programming model, and the constraints are interval equality constraints. In the thermal network state estimation model, the quantities involved are The state variable is x ht =[H si ,H ri ]; Based on the idea of ​​the best-worst method, the equality constraint is equivalently replaced by the upper and lower boundary values ​​of the interval, and the interval estimation results under the "worst scenario" are obtained after combined comparison; by analyzing the state variables and quantity measurements, it can be found that the supply and return water temperature H of the equivalent measurement node si and H ri When the minimum or maximum value is taken, the state quantity should also be the minimum or maximum value. Therefore, at a certain moment, when the node supply and return water temperature selects the minimum or maximum value, it is only necessary to bring the upper and lower boundaries of the node flow and node power into the constraints for combined solution, and compare the results to obtain the state quantity interval value; The thermal network state estimation model in each scenario can be regarded as a MILP model and solved to obtain the interval estimation value of the thermal network state quantity.

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