CN110601185A - Unified power flow model and random matrix-based comprehensive energy system weak point identification method - Google Patents
Unified power flow model and random matrix-based comprehensive energy system weak point identification method Download PDFInfo
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Abstract
The invention discloses a method for identifying weak points of a comprehensive energy system based on a unified power flow model and a random matrix, which comprises the following steps of: (1) establishing a unified power flow model of the comprehensive energy system; (2) selecting flow data and establishing a random matrix; (3) normalizing the preprocessed random matrix; (4) recognizing a system abnormal state; (5) and identifying the weak point of the system. The method of the present invention may be used. According to the method, the random matrix theory is introduced into the weak identification of the comprehensive energy system, the system operation state is analyzed in a data-driven mode, the identification of the physical structure of the comprehensive energy system is not needed, the modeling process of the comprehensive energy system is avoided, the complexity of the physical structure and the modeling process of the comprehensive energy system is overcome, and the accuracy and the rapidity of the system state identification and the weak point identification are improved.
Description
Technical Field
The invention relates to the technical field of identification of weak links of an integrated energy system, in particular to a method for identifying weak points of the integrated energy system based on a unified power flow model and a random matrix.
Background
With the increasing scarcity of fossil energy and the deterioration of the environment, the integrated planning design and the operation optimization of various energy sources such as electricity, heat, gas and the like are realized by using a comprehensive energy system, the comprehensive utilization efficiency of the energy sources is improved, and the comprehensive energy system becomes a necessary way for the revolution of the energy field of the human society. However, due to the tight coupling of various energy systems, the IES (integrated energy system) needs to consider the transmission rate of the lines or pipes of different energy systems, the interconversion between different energy sources, and the energy supply efficiency. Compared with single system energy, the comprehensive energy system has more complex physical structure and more difficult model construction, thereby making the weak analysis of the comprehensive energy system more difficult. Therefore, the method has important theoretical and application research value for rapidly and effectively identifying IES weak points.
In the prior art, weak identification of a single power system mainly comprises methods such as a power flow entropy, a complex network theory and an information entropy. The power flow entropy is combined with the entropy theory, and the imbalance of the power distribution of the system is quantitatively analyzed; the complex theory is based on a system structure, and a network cascading failure model can be constructed. The methods analyze the system operation state based on the system physical structure. The method mainly comprises sensitivity analysis, importance degree, reliability tracking and the like for weak identification of a single thermodynamic system and a single natural gas system. Sensitivity coefficient is analyzed and calculated through sensitivity and is used as a system weakness index; and reliability tracking is used for performing unreliable distribution on system elements based on the minimum cut set and judging the weakness of the elements. In the methods, reliability calculation and analysis are carried out on each level of the pipe network system, and the weaknesses of the system and elements can be evaluated.
The inventor of the present application finds that the method of the prior art has at least the following technical problems in the process of implementing the present invention:
for weak identification of an integrated energy system, due to the complex system structure and the difficulty in model construction, research on IES weak analysis in the prior art is only in a preliminary exploration stage. At present, the power flow data can be utilized to calculate the node weakness index, and preliminary research is carried out on the energy system containing the electricity-gas coupling. The method shows that weak identification of the system is feasible from the data analysis perspective, but for a large-scale system or a system with more energy coupling, the method has a complex power flow model, and quick response is still difficult to realize.
Therefore, the method in the prior art has the technical problems of complex model and slow response speed.
Disclosure of Invention
In view of the above, the invention provides a method for identifying weak points of an integrated energy system based on a unified power flow model and a random matrix, which is used for solving or at least partially solving the technical problems of complex model and slow response speed existing in the method in the prior art.
In order to solve the technical problem, the invention provides a method for identifying weak points of a comprehensive energy system based on a unified power flow model and a random matrix, which comprises the following steps:
step S1: respectively constructing an electric system model, a thermal system model and a gas system model, and establishing a unified power flow model of the comprehensive energy system after adding a coupling element model, wherein the unified power flow model of the comprehensive energy system comprises an initial value of unbalance amount and is used for representing the running state of the comprehensive energy system;
step S2: historical data and real-time data of an unbalance initial value in a unified power flow model of the comprehensive energy system are collected, and a random matrix is constructed by utilizing a real-time separation window technology;
step S3: carrying out standardized preprocessing on all data in the random matrix;
step S4: calculating the M-P rate and the ring rate of the random matrix, and identifying the abnormal state of the comprehensive energy system based on the M-P rate and the ring rate;
step S5: and copying data corresponding to the node to be analyzed in the random matrix, constructing an amplification matrix, calculating the average spectrum radius MSR of the amplification matrix, wherein the MSR is used for representing the statistical characteristic of the characteristic value, and identifying the weak points of the comprehensive energy system according to the distribution condition of the average spectrum radius and the abnormal state identified in the step S4.
In one embodiment, step S1 specifically includes:
step S1.1: respectively constructing an electric system model, a thermal system model and a gas system model;
step S1.2: the method comprises the following steps of establishing a unified power flow model of the comprehensive energy system by adopting a coupling element through an electric system model, a thermal system model and a gas system model, wherein the unbalance amount delta F (x) of the unified power flow model of the comprehensive energy system is represented as follows:
wherein Δ F (χ) is an unbalance amount; delta P and delta Q are the active and reactive deviations of the electrical system; Δ Φ, Δ ph、ΔTs、ΔTrRespectively the deviation of the thermal power, the loop pressure drop, the heating temperature and the backheating temperature of the thermal system; Δ νqAnd Δ pgThe deviation of the pipeline flow and the loop pressure drop of the gas system; the superscript sp represents a known given value; subscript load represents a load node; cs、CrIs a matrix related to the supply and return network structure and the flow of the pipeline, bs、brIs a column vector related to the heat supply temperature and the heat return temperature,
the state variable χ of the comprehensive energy system is as follows:
solving the unbalance amount and the state variable of the comprehensive energy system by using a Newton Raphson method:
χ(i+1)＝χ(i)-J-1ΔF(χ)
in the formula: i is the number of iterations; j is the jacobian matrix.
In one embodiment, step S2 specifically includes:
step S2.1: the initial value of the unbalance amount of each time point forms a column vector, x (t)i)＝[x1(ti),x2(ti),...xN(ti)]T；
Step S2.2: collecting historical data and real-time data of an unbalance initial value column vector;
step S2.3: performing real-time analysis data segmentation on the basis of historical data, and constructing a random matrix X by collecting data with the length of T-1 at the ith moment and before the ith momentN×T：
XN×T＝[x(ti-T+1)...x(ti)]
Where T represents the window width.
In one embodiment, step S3 is implemented by performing normalization preprocessing on the data in the following manner:
wherein i is more than or equal to 1 and less than or equal to N; j is more than or equal to 1 and less than or equal to T; andare respectively a matrixStandard deviation and mean of (1), matrix xiStandard deviation of (a) (x)i) Is 1; mean valueIs 0.
In one embodiment, step S4 specifically includes:
step S4.1: calculating the M-P rate of the random matrix, wherein the M-P rate is used for representing the asymptotic behavior of singular values of the random matrix, and for the NxT order non-Hermitian matrix X, the sample covariance matrix of the matrixThe empirical spectral distribution of the respective covariance matrices converges to the M-P rate:
wherein f isESD(λ) is a density function of the covariance matrix SN; λ is a characteristic value;
step S4.2: calculating the ring rate of the random matrix, wherein the ring rate is used for representing the deviation of the random matrix data from the random degree, and for L non-Hermitian matricesSingular value equivalentIs the product ofThe empirical spectral density of (c) converges to:
wherein f isESD(λz) The probability density function of the matrix Z shows that the eigenvalues of Z are distributed over the complex plane with an inner circle radius of (1-c)L/2The excircle radius is in a ring with 1;
step S4.3: and for the M-P rate, judging whether the system has an abnormal state or not according to the comparison condition of the Gaussian kernel function and the M-P rate, and for the circular ring rate, judging whether the system has an abnormal state or not according to the distribution condition of the characteristic values.
In one embodiment, step S5 specifically includes:
step S5.1: copying data corresponding to the node to be analyzed in the random matrix for k times, so that the relevance between the node to be analyzed and the original data matrix is enhanced, and an augmented matrix of the original data matrix is obtained
Wherein the content of the first and second substances,to representData corresponding to the row where the node to be analyzed is located; the upper corner mark k is the number of copies;random noise, mean 0 and variance 1;
step S5.2: calculating the average spectrum radius MSR of the augmentation matrix, wherein the MSR is used for representing the statistical characteristics of the characteristic values, specifically the average value r of all the characteristic values on the complex plane from the central pointMSR：
Wherein λ isiN is a matrix eigenvalue;
step S5.3: the distribution condition of MSR is digitalized by adopting an entropy theory, and the entropy is used for measuring the disorder degree of a system and is defined as:
wherein C is a constant; l is the number of states; p (omega)i) (i 1.., l) is a state occurrence probability;
calculating an evaluation value S of each node by combining the distribution condition of the MSR and the abnormal state identified in the step S4 to obtain a weak point identification result;
wherein M is a weight factor; c is a constant, the S value represents the influence degree of the node on the system, and the larger the S value is, the higher the weak degree of the node is.
One or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:
the invention provides a method for identifying weak points of a comprehensive energy system based on a unified power flow model and a random matrix, which comprises the steps of firstly, respectively constructing an electric system model, a thermal system model and a gas system model, and establishing a unified power flow model of the comprehensive energy system after adding a coupling element model; then, acquiring historical data and real-time data of an unbalance initial value in the unified power flow model of the comprehensive energy system, and constructing a random matrix by using a real-time separation window technology; then, carrying out standardized preprocessing on all data in the random matrix; then, calculating the M-P rate and the ring rate of the random matrix, and identifying the abnormal state of the comprehensive energy system based on the M-P rate and the ring rate; and finally, copying data corresponding to the node to be analyzed in the random matrix, constructing an amplification matrix, calculating the average spectrum radius MSR of the amplification matrix, wherein the MSR is used for representing the statistical characteristic of the characteristic value, and identifying the weak point of the comprehensive energy system according to the distribution condition of the average spectrum radius and the abnormal state identified in the step S4.
According to the method, the random matrix theory is introduced into the weak identification of the comprehensive energy system, the system operation state is analyzed in a data-driven mode, the physical structure of the comprehensive energy system does not need to be identified, the modeling process of the comprehensive energy system is avoided, the physical structure of the system does not need to be considered, the model is simple to construct, and the quick response of the weak identification of the complex system can be realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is an overall flow diagram of a comprehensive energy system vulnerability identification method based on a unified power flow model and a random matrix according to the present invention;
FIG. 2 is a schematic diagram of an integrated energy system according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an exemplary model of an integrated energy system according to an embodiment of the invention;
FIG. 4 is a diagram illustrating the M-P ratio of the initial state of the system in accordance with an embodiment of the present invention;
FIG. 5 is a graph illustrating a ring rate of an initial state of a system according to an embodiment of the present invention;
FIG. 6 is a graph of M-P rate at which system load begins to increase gradually, in accordance with an embodiment of the present invention;
FIG. 7 is a graph illustrating the ring rate at which system load begins to increase in accordance with an embodiment of the present invention;
FIG. 8 is a graph illustrating the M-P rate of system near crash in an embodiment of the present invention;
FIG. 9 is a graph illustrating the ring rate for system near crash in accordance with an embodiment of the present invention;
FIG. 10 is a MSR of thermal node 1 in an embodiment of the present invention;
FIG. 11 is a MSR of the hot node 9 in an embodiment of the present invention;
FIG. 12 is a graph illustrating the ring ratio of the electrical node 10 in an embodiment of the present invention;
FIG. 13 is a graph of the ring ratio of the electrical node 4 in an embodiment of the present invention;
FIG. 14 is a graph showing the ring ratio of the gas node 5 in the embodiment of the present invention;
FIG. 15 is a graph showing the ring ratio of the thermal node 9 in the embodiment of the present invention;
Detailed Description
The invention aims to provide an electric-heat-gas comprehensive energy system weak point identification method based on a unified power flow model and a random matrix, which is used for identifying a system without a physical structure in a data driving angle, avoiding a system modeling process, providing a new idea for comprehensive energy system weak point identification, simplifying a modeling process and improving the accuracy and rapidity of system state identification and weak point identification.
In order to achieve the above purpose, the main concept of the invention is as follows:
the random matrix theory is a big data analysis method with high universality. The invention introduces a random matrix theory into the comprehensive energy system from the data driving angle, provides a method for identifying weak points of the comprehensive energy system based on a unified power flow model, and verifies the effectiveness of the method by improved comprehensive energy system example simulation. The method does not need to consider the physical structure of the system, has simple model construction, and can realize quick response to the identification of the weak points of the complex system.
The method specifically comprises the following steps: (1) establishing a unified power flow model of the comprehensive energy system; (2) selecting flow data and establishing a random matrix; (3) normalizing the preprocessed random matrix; (4) recognizing a system abnormal state; (5) identifying a system weak point; according to the method, the random matrix theory is introduced into the weak identification of the comprehensive energy system, the system operation state is analyzed in a data-driven mode, the physical structure of the comprehensive energy system does not need to be identified, the modeling process of the comprehensive energy system is avoided, and a new thought is provided for the weak identification of the comprehensive energy system.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment provides a method for identifying weak points of an integrated energy system based on a unified power flow model and a random matrix, please refer to fig. 1, and the method includes:
step S1: and respectively constructing an electric system model, a thermal system model and a gas system model, adding a coupling element model, and then establishing a unified power flow model of the comprehensive energy system, wherein the unified power flow model of the comprehensive energy system comprises an initial value of unbalance for representing the running state of the comprehensive energy system.
In one embodiment, step S1 specifically includes:
step S1.1: respectively constructing an electric system model, a thermal system model and a gas system model;
step S1.2: the method comprises the following steps of establishing a unified power flow model of the comprehensive energy system by adopting a coupling element through an electric system model, a thermal system model and a gas system model, wherein the unbalance amount delta F (x) of the unified power flow model of the comprehensive energy system is represented as follows:
wherein Δ F (χ) is an unbalance amount; delta P and delta Q are the active and reactive deviations of the electrical system; Δ Φ, Δ ph、ΔTs、ΔTrRespectively the deviation of the thermal power, the loop pressure drop, the heating temperature and the backheating temperature of the thermal system; Δ νqAnd Δ pgThe deviation of the pipeline flow and the loop pressure drop of the gas system; the superscript sp represents a known given value; subscript load represents a load node; cs、CrIs a matrix related to the supply and return network structure and the flow of the pipeline, bs、brIs a column vector related to the heat supply temperature and the heat return temperature,
the state variable χ of the comprehensive energy system is as follows:
solving the unbalance amount and the state variable of the comprehensive energy system by using a Newton Raphson method:
χ(i+1)＝χ(i)-J-1ΔF(χ)
in the formula: i is the number of iterations; j is the jacobian matrix.
In a specific implementation process, each model is constructed in the following manner:
1. construction of a model of an electric power system
In a traditional power system power flow model, the power of a node is expressed as:
in the formula: n is a radical ofeIs the number of nodes; v is the node voltage; i is a node current; y is a node admittance matrix; s is complex power; p is active power; and Q is reactive power.
2. Construction of thermodynamic system model
1) Hydraulic model
The nodes satisfy the flow continuity equation:
in the formula: a. thehIs a node-branch incidence matrix;for each pipeline flow;and flow out for each node.
Each loop satisfies the loop pressure equation:
Bhhf＝0
in the formula: b ishIs a loop-branch correlation matrix; h isfIs the head loss vector.
The relationship between each pipeline flow and head loss is:
in the formula: khIs a pipeline resistance coefficient matrix.
2) Thermal model
The thermal model being used to determine each nodeAnd (3) temperature. Each thermal load node has: temperature T of heat supplysOutput temperature ToTemperature of heat regeneration Tr. The thermal power phi of each node is as follows:
in the formula: cpIs the specific heat of water. And (3) expressing the relation of the temperature of the beginning end and the end of the pipeline by adopting a temperature drop equation:
in the formula: l ishIs the length of the pipeline; t isstartAnd TendThe temperatures of the starting and end nodes of the pipeline; t isaIs ambient temperature; lambda [ alpha ]hIs the heat transfer coefficient of the pipe. The relationship between the hot water mixing at the node before and after is:
in the formula:TinandToutrespectively the flow rate and temperature of the hot water in the inflow and outflow pipes.
3. Natural gas system model
The natural gas model is similar to the thermodynamic network hydraulic model and meets the flow continuity equation:
Agνg＝νq
in the formula: a. thegIs a node-branch incidence matrix; v isgThe gas flow rate of each pipeline; v isqThe gas flow is discharged for each node. The loop pressure equation is expressed as:
BgΔp＝0
in the formula: b isgIs a loop-branchA correlation matrix; Δ p is the duct pressure drop vector. The relationship between gas flow and line pressure drop is:
in the formula: kgThe index k is related to the air network pressure level for the pipeline drag coefficient.
Specifically, the model constructed by the invention comprises a power system power flow model, a hydraulic power and thermal power flow model in a thermal system and a natural gas system power flow model.
The coupling element is equipment for realizing conversion among different energy sources, and comprises a combined heat and power generation (CHP), a gas-fired boiler, an electric boiler and the like, wherein the combined heat and power generation (CHP) can utilize high-grade energy of gas for power generation, low-grade energy for heat supply and cold supply, the energy utilization efficiency can reach more than 80 percent, and the coupling element is an operation mode with the most commercial prospect in the current comprehensive energy system;
in the formula: pCHPAnd phiCHPElectric power and thermal power output by the CHP unit; finThe gas consumption is; c. CmThe thermoelectric proportionality coefficient of the CHP unit; etaeThe power generation efficiency of the CHP unit.
Step S2: historical data and real-time data of the initial unbalance value in the unified power flow model of the comprehensive energy system are collected, and a random matrix is constructed by utilizing a real-time separation window technology.
In one embodiment, step S2 specifically includes:
step S2.1: the initial value of the unbalance amount of each time point forms a column vector, x (t)i)＝[x1(ti),x2(ti),...xN(ti)]T；
Step S2.2: collecting historical data and real-time data of an unbalance initial value column vector;
step S2.3: performing real-time analysis data segmentation on the basis of historical data, and constructing a random matrix X by collecting data with the length of T-1 at the ith moment and before the ith momentN×T：
XN×T＝[x(ti-T+1)...x(ti)]
Where T represents the window width.
Specifically, the acquired historical data and real-time data are retained, and Gaussian white noise is added to simulate the data acquired by actual operation to construct a matrix X:
X＝[x(t1),x(t2),...x(ti)...]
and then, carrying out data segmentation by adopting a real-time separation window technology, collecting data with the length of T-1 at the ith moment and before the ith moment, and jointly constructing a random matrix.
Step S3: all data in the random matrix is subjected to a normalization pre-processing.
Specifically, by performing the normalization preprocessing on the random matrix, including the de-dimensionalization and numerical normalization on all data in the matrix, each index can be made comparable.
In one embodiment, step S3 is implemented by performing normalization preprocessing on the data in the following manner:
wherein i is more than or equal to 1 and less than or equal to N; j is more than or equal to 1 and less than or equal to T; andare respectively a matrixStandard deviation and mean ofMatrix xiStandard deviation of (a) (x)i) Is 1; mean valueIs 0.
Step S4: and calculating the M-P rate and the ring rate of the random matrix, and identifying the abnormal state of the comprehensive energy system based on the M-P rate and the ring rate.
In one embodiment, step S4 specifically includes:
step S4.1: calculating the M-P rate of the random matrix, wherein the M-P rate is used for representing the asymptotic behavior of singular values of the random matrix, and for the NxT order non-Hermitian matrix X, the sample covariance matrix of the matrixThe empirical spectral distribution of the respective covariance matrices converges to the M-P rate:
wherein f isESD(λ) is a density function of the covariance matrix SN; λ is a characteristic value;
step S4.2: calculating the ring rate of the random matrix, wherein the ring rate is used for representing the deviation of the random matrix data from the random degree, and for L non-Hermitian matricesSingular value equivalentIs the product ofThe empirical spectral density of (c) converges to:
wherein f isESD(λz) The probability density function of the matrix Z shows that the eigenvalues of Z are distributed over the complex plane with an inner circle radius of (1-c)L/2The excircle radius is in a ring with 1;
step S4.3: and for the M-P rate, judging whether the system has an abnormal state or not according to the comparison condition of the Gaussian kernel function and the M-P rate, and for the circular ring rate, judging whether the system has an abnormal state or not according to the distribution condition of the characteristic values.
Specifically, in step S4.1, for the N × T order non-Hermitian matrix X, when N, T → ∞ and the scaling factor c ═ N/te ∈ (0, 1)]The sample covariance matrix of the matrixWhen the elements in the matrix X are independent and distributed in the same way and are random variables, the mean value mu is 0 and the variance sigma is satisfied2When < ∞, the empirical spectral distribution of the corresponding covariance matrix converges on the M-P rate.
In step S4.2, L non-Hermitian matricesSingular value equivalent thereofIs the product ofThe empirical spectral density of Z converges to the ring rate.
Initial value of Δ F due to unbalance amount(0)The (χ) data is real, and the eigenvalue of the real field needs to be mapped to the complex field, i.e. singular processing is performed. The invention adopts unitary matrix U to obtainSingular value equivalence matrix ofU is a unitary matrix satisfying Haar distribution, and is knownFor L such matrices, consider their productAnd carrying out standardization treatment:
in the formula: z is a radical ofi＝(zi1,zi2,…,ziN)；σ(zi) Is a matrix ziStandard deviation of (d);
in a specific implementation process, in step S4.3, for the M-P rate, the gaussian kernel function is used in this embodiment to compare with the M-P rate, where the gaussian kernel function is to perform non-parameter estimation on the feature value distribution:
in the formula: f. ofn(x) Is a nonparametric function; h is a broadband parameter; k (.) is a kernel function.
If the two curves are well matched, the system is stable, and if the two curves are greatly different, the system has an abnormal condition. The gaussian kernel function can map data to an infinite dimension, being some sort of scalar function that is radially symmetric.
For the ring rate, drawing the characteristic values on a complex plane, and if all the characteristic values are in the ring, stabilizing the system; statistical errors are considered if only a few eigenvalues (less than 2.5%) fall outside the circle. Conversely, when a preset number of feature values fall within the inner loop, it can be determined that the system is abnormal.
Step S5: and copying data corresponding to the node to be analyzed in the random matrix, constructing an amplification matrix, calculating the average spectrum radius MSR of the amplification matrix, wherein the MSR is used for representing the statistical characteristic of the characteristic value, and identifying the weak points of the comprehensive energy system according to the distribution condition of the average spectrum radius and the abnormal state identified in the step S4.
Specifically, step S5 is to utilize MSR and an augmentation matrix in the random matrix, and combine entropy theory to effectively identify weak points of the integrated energy system.
In one embodiment, step S5 specifically includes:
step S5.1: copying data corresponding to the node to be analyzed in the random matrix for k times, so that the relevance between the node to be analyzed and the original data matrix is enhanced, and an augmented matrix of the original data matrix is obtained
Wherein the content of the first and second substances,to representData corresponding to the row where the node to be analyzed is located; the upper corner mark k is the number of copies;random noise, mean 0 and variance 1;
step S5.2: calculating the average spectrum radius MSR of the augmentation matrix, wherein the MSR is used for representing the statistical characteristics of the characteristic values, specifically the average value r of all the characteristic values on the complex plane from the central pointMSR：
Wherein λ isi(i ═ 1,2, … N) is a matrix eigenvalue;
step S5.3: the distribution condition of MSR is digitalized by adopting an entropy theory, and the entropy is used for measuring the disorder degree of a system and is defined as:
wherein C is a constant; l is the number of states; p (omega)i) (i ═ 1, …, l) is the probability of state occurrence;
calculating an evaluation value S of each node by combining the distribution condition of the MSR and the abnormal state identified in the step S4 to obtain a weak point identification result;
wherein M is a weight factor; c is a constant, the S value represents the influence degree of the node on the system, and the larger the S value is, the higher the weak degree of the node is.
Specifically, the MSR result is biased to the data characteristic of the node by the aid of the augmentation matrix, and the distribution situation of the MSR is digitized by the aid of entropy theory. Entropy is used to measure the degree of disorder of a system. Then selecting MSR fluctuation value of the nodeAs the amount of state,andthe MSR values of the ith augmented matrix in normal and abnormal states, respectively. For omegaiAnd (3) carrying out normalization treatment:
wherein, muiThe probability value of the MSR of the ith node is obtained; n ishFor number of rows of matrix。
Then, an evaluation value S of each node is calculated, and since each node may have different degrees of influence on the system, the weakness of each node may use MSR to calculate a weight factor:
the S value represents the influence degree of the node on the system, the larger the S value is, the more disordered the MSR value distribution is, the larger the influence of the node state change on the system state is, and the higher the node weakness degree is.
The technical scheme of the invention is further specifically described below by combining the specific examples and the attached drawings.
As shown in fig. 1, a method for identifying weak points of an electric-thermal-gas integrated energy system based on a unified power flow model and a random matrix comprises the following steps:
step 1, independently constructing a power system 13 node power flow model, a thermal system 13 node power flow model and a gas system 7 node power flow model, adding 2 CHP units as coupling element models of coupling elements, and jointly establishing a unified power flow model of the 33-node comprehensive energy system. FIG. 2 is a schematic diagram of an integrated energy system, and FIG. 3 is a schematic diagram of an exemplary model of the integrated energy system;
and 2, acquiring data of the unbalance initial value in the unified power flow model of the comprehensive energy system. The system state is changed by continuously changing the system load, so that the initial value of the unbalance is continuously refreshed, and historical data and real-time data are accumulated. The data are sequenced in time sequence, and the node characteristics in the integrated energy system have spatial characteristics, so that a data source with space-time characteristics is formed. Decomposing a data source into random matrixes by using a real-time separation window technology;
step 3, performing standardization preprocessing on all data in the random matrix, namely de-dimensionalization and numerical value normalization;
and 4, changing the system state by changing the system load, calculating the M-P rate and the ring rate, and analyzing the process that the characteristic value distribution of the M-P rate curve and the ring rate changes along with the change of the system state.
Fig. 4 is an M-P rate of an initial state of the system, fig. 5 is a circular rate of the initial state of the system, fig. 6 is an M-P rate when a system load starts to increase gradually, and fig. 7 is a circular rate when a system load starts to increase gradually. FIG. 8 is the M-P rate at which the system approaches collapse, and FIG. 9 is the torus rate at which the system approaches collapse.
For the M-P rate, the Gaussian kernel function is compared thereto. If the two are well matched, the system is stable, and if the difference between the two is large, the system has an abnormal condition. For the ring rate, if all the characteristic values are in the ring, the system is stable; when a considerable number of characteristic values fall into the inner ring, the system can be judged to be abnormal;
and 5, changing the load of a certain node, respectively constructing an augmentation matrix taking each node as a key observation object, calculating the MSR of the augmentation matrix, and analyzing the influence of the change of the certain node on the system. FIG. 10 is the MSR of hot node 1, and FIG. 11 is the MSR of hot node 9;
and calculating weak values of all nodes in the comprehensive energy system by combining an entropy theory and sequencing the weak values. The invention verifies the weak point sequencing through the ring rate, namely changes the load of a certain node, observes the ring rate of the system at the same time, and verifies and shows the effectiveness of the method. FIG. 12 is the ring ratio for electrical node 10, FIG. 13 is the ring ratio for electrical node 4, FIG. 14 is the ring ratio for air node 5, and FIG. 15 is the ring ratio for hot node 9;
the invention introduces a random matrix theory into the comprehensive energy system from the data driving angle, provides a method for identifying weak points of the comprehensive energy system based on a unified power flow model, and verifies the effectiveness of the method by improved comprehensive energy system example simulation. The method does not need to consider the physical structure of the system, has simple model construction, and can realize quick response to the identification of the weak points of the complex system.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the embodiments of the present invention without departing from the spirit or scope of the embodiments of the invention. Thus, if such modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to encompass such modifications and variations.
Claims (6)
1. A method for identifying weak points of a comprehensive energy system based on a unified power flow model and a random matrix is characterized by comprising the following steps:
step S1: respectively constructing an electric system model, a thermal system model and a gas system model, and establishing a unified power flow model of the comprehensive energy system after adding a coupling element model, wherein the unified power flow model of the comprehensive energy system comprises an initial value of unbalance amount and is used for representing the running state of the comprehensive energy system;
step S2: historical data and real-time data of an unbalance initial value in a unified power flow model of the comprehensive energy system are collected, and a random matrix is constructed by utilizing a real-time separation window technology;
step S3: carrying out standardized preprocessing on all data in the random matrix;
step S4: calculating the M-P rate and the ring rate of the random matrix, and identifying the abnormal state of the comprehensive energy system based on the M-P rate and the ring rate;
step S5: and copying data corresponding to the node to be analyzed in the random matrix, constructing an amplification matrix, calculating the average spectrum radius MSR of the amplification matrix, wherein the MSR is used for representing the statistical characteristic of the characteristic value, and identifying the weak points of the comprehensive energy system according to the distribution condition of the average spectrum radius and the abnormal state identified in the step S4.
2. The method according to claim 1, wherein step S1 specifically comprises:
step S1.1: respectively constructing an electric system model, a thermal system model and a gas system model;
step S1.2: the method comprises the following steps of establishing a unified power flow model of the comprehensive energy system by adopting a coupling element through an electric system model, a thermal system model and a gas system model, wherein the unbalance amount delta F (x) of the unified power flow model of the comprehensive energy system is represented as follows:
wherein Δ F (χ) is an unbalance amount; delta P and delta Q are the active and reactive deviations of the electrical system; Δ Φ, Δ ph、ΔTs、ΔTrRespectively the deviation of the thermal power, the loop pressure drop, the heating temperature and the backheating temperature of the thermal system; Δ νqAnd Δ pgThe deviation of the pipeline flow and the loop pressure drop of the gas system; the superscript sp represents a known given value; subscript load represents a load node; cs、CrIs a matrix related to the supply and return network structure and the flow of the pipeline, bs、brIs a column vector related to the heat supply temperature and the heat return temperature,
the state variable χ of the comprehensive energy system is as follows:
solving the unbalance amount and the state variable of the comprehensive energy system by using a Newton Raphson method:
χ(i+1)＝χ(i)-J-1ΔF(χ)
in the formula: i is the number of iterations; j is the jacobian matrix.
3. The method according to claim 1, wherein step S2 specifically comprises:
step S2.1: the initial value of the unbalance amount of each time point forms a column vector, x (t)i)＝[x1(ti),x2(ti),...xN(ti)]T；
Step S2.2: collecting historical data and real-time data of an unbalance initial value column vector;
step S2.3: in thatPerforming data segmentation of real-time analysis on the basis of historical data, and constructing a random matrix X by collecting data with the length of T-1 at the ith moment and before the ith momentN×T：
XN×T＝[x(ti-T+1)...x(ti)]
Where T represents the window width.
4. The method according to claim 1, wherein step S3 is embodied as a normalization preprocessing of the data in the following manner:
wherein i is more than or equal to 1 and less than or equal to N; j is more than or equal to 1 and less than or equal to T; andare respectively a matrixStandard deviation and mean of (1), matrix xiStandard deviation of (a) (x)i) Is 1; mean valueIs 0.
5. The method according to claim 1, wherein step S4 specifically comprises:
step S4.1: calculating the M-P rate of the random matrix, wherein the M-P rate is used for representing the asymptotic behavior of singular values of the random matrix, and for the NxT order non-Hermitian matrix X, the sample covariance matrix of the matrixThe empirical spectral distribution of the respective covariance matrices converges to the M-P rate:
wherein f isESD(λ) is a density function of the covariance matrix SN; λ is a characteristic value;
step S4.2: calculating the ring rate of the random matrix, wherein the ring rate is used for representing the deviation of the random matrix data from the random degree, and for L non-Hermitian matricesSingular value equivalentIs the product ofThe empirical spectral density of (c) converges to:
wherein the content of the first and second substances,the probability density function of the matrix Z shows that the eigenvalues of Z are distributed over the complex plane with an inner circle radius of (1-c)L/2The excircle radius is in a ring with 1;
step S4.3: and for the M-P rate, judging whether the system has an abnormal state or not according to the comparison condition of the Gaussian kernel function and the M-P rate, and for the circular ring rate, judging whether the system has the abnormal state or not according to the distribution condition of the characteristic values.
6. The method according to claim 1, wherein step S5 specifically comprises:
step S5.1: copying data corresponding to the node to be analyzed in the random matrix for k times, so that the relevance between the node to be analyzed and the original data matrix is enhanced, and an augmented matrix of the original data matrix is obtained
Wherein the content of the first and second substances,to representData corresponding to the row where the node to be analyzed is located; the upper corner mark k is the number of copies;random noise, mean 0 and variance 1;
step S5.2: calculating the average spectrum radius MSR of the augmentation matrix, wherein the MSR is used for representing the statistical characteristics of the characteristic values, specifically the average value r of all the characteristic values on the complex plane from the central pointMSR：
Wherein λ isiN is a matrix eigenvalue;
step S5.3: the distribution condition of MSR is digitalized by adopting an entropy theory, and the entropy is used for measuring the disorder degree of a system and is defined as:
wherein C is a constant; l is the number of states; p (omega)i) (i 1.., l) is a state occurrence probability;
calculating an evaluation value S of each node by combining the distribution condition of the MSR and the abnormal state identified in the step S4 to obtain a weak point identification result;
wherein M is a weight factor; c is a constant, the S value represents the influence degree of the node on the system, and the larger the S value is, the higher the weak degree of the node is.
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