CN114492916A - Uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization - Google Patents

Uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization Download PDF

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CN114492916A
CN114492916A CN202111463269.XA CN202111463269A CN114492916A CN 114492916 A CN114492916 A CN 114492916A CN 202111463269 A CN202111463269 A CN 202111463269A CN 114492916 A CN114492916 A CN 114492916A
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李勇
钟俊杰
曹一家
谭益
刘敏
彭衍建
乔学博
段义隆
李磊
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Hunan University
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Abstract

The embodiment of the invention provides an uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization, wherein an uncertain quantity error sample set is generated, and a mean value and covariance matrix of the sample set are solved; and finding information such as correlation, eigenvalue and eigenvector of the sample by using PCA. Such as eigenvalues and eigenvectors will be used to determine the semi-axis length and axial direction of the inner ellipsoid; dividing a sample set area into k intervals, and establishing a high-dimensional ellipsoid area; constructing k convex hulls from the point set of k intervals based on a Quickhull convex hull algorithm, and finally establishing an uncertain set based on the multi-interval convex hull. Based on the uncertain set of the multi-interval convex hull, the relevance among the uncertain quantities is considered, and through setting a plurality of proper intervals, the scene with low probability in practice is avoided, and the conservative degree of robust optimization is reduced.

Description

Uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization
Technical Field
The embodiment of the invention relates to the technical field of comprehensive energy microgrid, in particular to an uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization.
Background
With the increasing severity of the problems of energy shortage, environmental pollution and the like, the search for a low-carbon and green development mode becomes an urgent need of the human society. The proposal of concepts such as energy internet and comprehensive energy system provides an important direction for energy development. In order to carry out overall planning and scheduling on a heterogeneous energy network, students provide an integrated energy microgrid uniform planning and scheduling model based on an energy concentrator. The comprehensive energy microgrid can be used for carrying out cooperative conversion, transmission, storage and the like on energy in various forms such as electricity, heat, cold, gas and the like, so that the energy utilization rate is greatly improved.
With the development from a single energy system to a multi-energy-coupled comprehensive energy microgrid, uncertainty factors such as multi-energy load levels faced by the comprehensive energy microgrid are also increased, and the uncertainty seriously affects the economic operation and safety level of the comprehensive energy microgrid. Robust optimization is a classic method of dealing with uncertainty in the optimization model. The uncertainty parameter xi is described in the form of an uncertainty set U, and as long as the uncertainty parameter xi is within the range of the uncertainty set U, the obtained optimal solution can meet the constraint condition. Therefore, the robust optimization is suitable for the condition that the uncertain parameter distribution is unknown or the historical data is less, the optimization result has good robustness, and the obtained optimal solution has low sensitivity to parameter change.
As a core of robust optimization, the construction of an uncertain set largely determines the conservative degree of the robust optimization. Currently, box-based robust-budget-considered uncertain sets (BBUS) are widely used. But the uncertain set ignores the distribution characteristics of the uncertain parameters and makes the optimization result too conservative. The uncertainty set based on ellipsoids is less conservative than BBUS. However, the quadratic form of the high-dimensional ellipsoid is transformed into a second-order cone plan when robust peer-to-peer conversion is performed, so that the calculation difficulty is increased. Further, a convex hull based data drive uncertainty set has been proposed in recent years. Compared with BBUS and an ellipse uncertain set, the convex hull uncertain set can adaptively adjust the polyhedron set according to historical data so as to reduce the conservative degree. However, the single-interval conjugal hull uncertainty sets (scuus) considered only in the above-mentioned single interval make the worst case be the pole of the outermost convex hull, and these extreme cases only occur with a small probability in practice, so that the scheduling scheme is still conservative. Therefore, it is more practical to construct an uncertainty set (MCHUS) that considers a multi-interval convex hull and that is likely to occur inside a polyhedral convex hull in an optimization cycle in consideration of uncertainty.
Disclosure of Invention
The embodiment of the invention provides an uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization, and provides an uncertain set based on a multi-interval convex hull by dividing a plurality of intervals and constructing convex hulls of corresponding intervals by combining a principal component analysis method and a Quickhull convex hull algorithm. The uncertain set can capture the distribution characteristics and the correlation of historical data in a self-adaptive manner, the accuracy of the uncertain set is improved, and the conservative degree of robust optimization is reduced.
In a first aspect, an embodiment of the present invention provides an indeterminate set construction method applicable to robust optimization of an integrated energy microgrid, including:
step S1, generating a sample set of uncertainty errors of the comprehensive energy microgrid, and determining a mean value and a covariance matrix of the sample set;
step S2, determining the eigenvalue and the eigen direction of the covariance matrix of the sample set based on a principal component analysis method;
step S3, determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic values, determining the half-axis direction according to the characteristic direction, and dividing the sample set into a plurality of high-dimensional ellipsoid regions;
step S4, integrating the sample points in the high-dimensional ellipsoid area into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertainty set based on the multi-interval convex hull.
Preferably, the step S1 specifically includes:
constructing a sample set of uncertainty errors based on historical error data of the comprehensive energy microgrid;
if the data quantity of the historical error data is larger than a preset data threshold, based on a data driving method, calculating a mean value and a covariance matrix according to the historical error data;
if the data volume of the historical error data is not larger than a preset data threshold, generating error distribution of uncertain quantity based on a symmetric distribution method, and calculating a mean value and a covariance matrix; the symmetric distribution method includes normal distribution, t distribution and Cauchy distribution.
Preferably, in step S1, if the edge distributions corresponding to different uncertainty errors are different, a joint distribution function of the known edges is constructed based on the gaussian function, and uncertainty error samples are generated based on the joint distribution function:
H(x1,x2,…,xm)＝C[F(x1),F(x1),…,F(xm)]
in the above formula, F (x)1),F(x1),…,F(xm) Respectively uncertainty error x1,x2,…,xmThe function C is a gaussian function; h (x)1,x2,…,xm) Is divided into corresponding associationsDistributing a function;
based on the joint distribution function H (x)1,x2,…,xm) Generating N m-dimensional uncertainty error samples u ═ { u ═1,u2,…,uNMean value of }
Figure BDA0003390229500000031
Sum covariance matrix
Figure BDA0003390229500000032
The calculation formula is as follows:
Figure BDA0003390229500000033
Figure BDA0003390229500000034
preferably, the step S2 specifically includes:
centralizing the data of the sample set to zero mean, and decomposing based on the eigenvalue to obtain the eigenvalue and eigenvector of the covariance matrix:
Figure BDA0003390229500000035
in the above formula, the first and second carbon atoms are,
Figure BDA0003390229500000036
is a covariance matrix; q is an orthogonal matrix composed of eigenvectors, and
Figure BDA0003390229500000037
λirespectively, the scaling factor in the corresponding dimension i.
Preferably, in step S3, the sample set region is divided into k partial intervals.
Preferably, in step S3, k is 3, and the first partial interval is a first high-dimensional ellipsoid region constructed with 1-fold eigenvalue σ as each half axis and the eigenvector as the direction; a second high-dimensional ellipsoid region constructed by taking a characteristic value sigma which is 2 times of that of the second part interval region as each half shaft; the third partial interval is a third high-dimensional ellipsoid region constructed for the remaining sample space of the sample set, wherein:
Figure BDA0003390229500000038
Figure BDA0003390229500000039
P1＝QΛ-1QT
Figure BDA00033902295000000310
in the above formula, Q is an orthogonal matrix composed of eigenvectors, and
Figure BDA0003390229500000041
λirespectively representing the expansion coefficients in the corresponding dimension i; c (u)1) Is a first high-dimensional ellipsoid region, C (u)2) Is a first high-dimensional ellipsoid region.
Preferably, in step S4, the uncertainty set based on the multi-interval convex hull is:
Figure BDA0003390229500000042
in the above-mentioned formula, the compound has the following structure,
Figure BDA0003390229500000043
the vertex coordinates of a kth interval are represented, wherein t represents scheduling time, s represents the number of scenes, k represents the number of convex hulls, and v represents the number of vertices of the corresponding interval;
Figure BDA0003390229500000044
in micro-grids respectively representing comprehensive energy resourcesElectrical load, thermal load, cold load; ξ denotes the set of polyenergetic loads,
Figure BDA0003390229500000045
representing a predicted value of the multi-energy load;
Figure BDA0003390229500000046
the method comprises the steps that binary variables are used for representing whether a v-th vertex of a k-th interval is taken at t moment in an s scene, if the value is 1, the implementation of the uncertainty quantity is represented, otherwise, the implementation is not achieved when the value is 0; gamma-shapedξAn uncertainty budget for the entire scheduling period;
Figure BDA0003390229500000047
an uncertain budget for the kth interval;
Figure BDA0003390229500000048
and obtaining the probability of the corresponding interval by calculating the proportion of the error samples to the total number of the error samples in the corresponding interval.
In a second aspect, an embodiment of the present invention provides an indeterminate set constructing system suitable for robust optimization of an integrated energy microgrid, including:
the sample establishing module is used for generating a sample set of uncertain errors of the comprehensive energy microgrid and determining a mean value and a covariance matrix of the sample set;
the sample principal component analysis module is used for determining the characteristic value and the characteristic direction of the covariance matrix of the sample set based on a principal component analysis method;
the sample partitioning module is used for determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic value, determining the half-axis direction according to the characteristic direction, and partitioning the sample set into a plurality of high-dimensional ellipsoid regions;
and the uncertain set building module is used for integrating the sample points in the high-dimensional ellipsoid region into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertain set based on the multi-interval convex hulls.
In a third aspect, an embodiment of the present invention provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor executes the program to implement the steps of the uncertainty set construction method suitable for the integrated energy microgrid robust optimization according to the embodiment of the first aspect of the present invention.
In a fourth aspect, an embodiment of the present invention provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the uncertainty set construction method for integrated energy microgrid robust optimization according to the embodiment of the first aspect of the present invention.
The embodiment of the invention provides an uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization, which are used for generating an uncertain quantity error sample set and solving the mean value of the sample set
Figure BDA0003390229500000051
Sum covariance matrix
Figure BDA0003390229500000052
A matrix; when there is a large amount of historical error data, the mean and variance matrices can be counted directly from the historical error data based on a data-driven approach. When the historical error data samples are not enough, some symmetric distribution such as normal distribution, t distribution, Cauchy distribution, and the like can be used to generate the error distribution of the uncertain quantity. In particular, when the edge distributions corresponding to different uncertainties are different, a gaussian Copula function may be used to construct a joint distribution function of known edge distributions to generate enough samples. And finding information such as correlation, eigenvalue and eigenvector of the sample by using PCA. Such as eigenvalues and eigenvectors, will be used to determine the semi-axis length and axial direction of the inner ellipsoid; dividing a sample set area into k intervals, and establishing a high-dimensional ellipsoid area; constructing k convex hulls from the point set of k intervals based on a Quickhull convex hull algorithm, and finally establishing an uncertain set based on the multi-interval convex hull. Based on the uncertainty set of the multi-interval convex hull, the relevance between uncertainty quantities is considered and a plurality of intervals are set appropriatelyThe scene with low probability is avoided in practice, and the conservative degree of robust optimization is reduced.
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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 described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
Fig. 1 is a flow chart of an uncertain set construction method suitable for comprehensive energy microgrid robust optimization according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of three uncertainty sets according to an embodiment of the present invention;
fig. 3 is a structural diagram of an integrated energy microgrid system according to an embodiment of the present invention;
FIG. 4(a) is a comparison graph of the optimization results of three uncertain sets under a sunny day electrical-thermal load scenario according to an embodiment of the present invention;
FIG. 4(b) is a comparison graph of the optimization results of three uncertain sets under cloudy day electro-thermal load scenarios according to an embodiment of the present invention;
FIG. 4(c) is a comparison graph of the optimization results of three uncertain sets under an electric-thermal load scene in a rainy day according to the embodiment of the invention;
FIG. 5 is a comparison of the cost of the integrated energy microgrid for three uncertain sets under different robust budgets according to an embodiment of the present invention;
fig. 6 is a schematic physical structure diagram according to an embodiment of the invention.
Detailed Description
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 obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
In the embodiment of the present application, the term "and/or" is only one kind of association relationship describing an associated object, and means that three relationships may exist, for example, a and/or B may mean: a exists alone, A and B exist simultaneously, and B exists alone.
The terms "first" and "second" in the embodiments of the present application are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a system, product or apparatus that comprises a list of elements or units is not limited to only those elements or units but may alternatively include other elements or units not expressly listed or inherent to such product or apparatus. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless explicitly specifically limited otherwise.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.
As a core of robust optimization, the construction of an uncertain set largely determines the degree of conservation of the robust optimization. Traditional boxed-based uncertainty sets (BBUS) that take robust budgets into account are widely used. But the uncertain set ignores the distribution characteristics of the uncertain parameters and makes the optimization result too conservative. The ambiguity set based on the ellipsoid is less conservative than BBUS. However, the quadratic form of the high-dimensional ellipsoid is transformed into a second-order cone plan when robust peer-to-peer conversion is performed, so that the calculation difficulty is increased. Further, a convex hull based data driven uncertainty set has been proposed in recent years. Compared with BBUS and an ellipse uncertainty set, the convex hull uncertainty set can adaptively adjust the polyhedron set according to historical data so as to reduce the conservative degree. However, the above-mentioned consideration of only a single interval of the uncertain Set of Convex Hulls (SCHUS) makes the worst case the pole of the outermost convex hull, and these extreme cases only occur with a small probability in practice, so that the scheduling scheme is still conservative. Therefore, if uncertainty is considered to be possibly generated inside the polyhedral convex hull in the optimization period, an uncertainty set (MCHUS) which considers the multi-interval convex hull is constructed to be more fit to the reality and can also reduce the conservative degree of robust optimization.
Therefore, the embodiment of the invention provides an uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization. The following description and description will proceed with reference being made to various embodiments.
Fig. 1 provides an uncertain set construction method suitable for comprehensive energy microgrid robust optimization in an embodiment of the present invention, including:
step S1, generating a sample set of uncertainty errors of the comprehensive energy microgrid, and determining a mean value and a covariance matrix of the sample set;
in the embodiment, a sample set of uncertainty errors is constructed based on historical error data of the comprehensive energy microgrid; firstly, generating a sample set of uncertainty errors, and then solving a mean matrix of the sample set
Figure BDA0003390229500000071
Sum covariance matrix
Figure BDA0003390229500000072
If the data quantity of the historical error data is larger than a preset data threshold, based on a data driving method, calculating a mean value and a covariance matrix according to the historical error data;
if the data volume of the historical error data is not larger than a preset data threshold, generating error distribution of uncertain quantity based on a symmetric distribution method, and calculating a mean value and a covariance matrix; the symmetric distribution method comprises normal distribution, t distribution and Cauchy distribution.
Preferably, in step S1, if the edge distributions corresponding to different uncertainty errors are different, a joint distribution function of the known edges is constructed based on the gaussian function, and uncertainty error samples are generated based on the joint distribution function:
H(x1,x2,…,xm)＝C[F(x1),F(x1),…,F(xm)] (1)
in the above formula, F (x)1),F(x1),…,F(xm) Respectively uncertainty error x1,x2,…,xmThe function C is a gaussian function; h (x)1,x2,…,xm) Is a corresponding joint distribution function;
based on the joint distribution function H (x)1,x2,…,xm) Generating N m-dimensional uncertainty error samples u ═ { u ═1,u2,…,uNMean value of }
Figure BDA0003390229500000081
Sum covariance matrix
Figure BDA0003390229500000082
The calculation formula is as follows:
Figure BDA0003390229500000083
Figure BDA0003390229500000084
step S2, determining eigenvalues and eigen directions of a covariance matrix of the sample set based on a Principal Component Analysis (PCA);
and finding information such as correlation, eigenvalue and eigenvector of the sample by using PCA. Firstly, centralizing the data of the sample set to zero mean, and decomposing based on the eigenvalue to obtain the eigenvalue and eigenvector of the covariance matrix:
Figure BDA0003390229500000085
in the above formula, the first and second carbon atoms are,
Figure BDA0003390229500000086
is a covariance matrix; q is an orthogonal matrix composed of eigenvectors, and
Figure BDA0003390229500000087
λirespectively, the scaling factor in the corresponding dimension i.
Step S3, determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic values, determining the half-axis direction according to the characteristic direction, and dividing the sample set into a plurality of high-dimensional ellipsoid regions;
in this embodiment, the sample set region is divided into k sections. Theoretically, the more uncertain sets of interval division are more accurate, but the reliability of robust budget of each interval is reduced and the solving difficulty is increased. The number of interval divisions must therefore depend on the decision maker's balance of economy and robustness.
According to the 3 σ principle of one-dimensional normal distribution as an example, 99.73% of random samples are all within three standard deviations σ around the mean. Therefore, the embodiment of the invention divides the sample with the uncertain quantity into 3 intervals, wherein k is 3, the first partial interval is a first high-dimensional ellipsoid region which is constructed by taking 1-time eigenvalue σ as each half axis and taking the eigenvector as the direction; the second high-dimensional ellipsoid region is constructed by taking the 2-time eigenvalue sigma of the second partial interval region as each half axis; the third partial interval is a third high-dimensional ellipsoid region constructed for the remaining sample space of the sample set, wherein:
Figure BDA0003390229500000091
Figure BDA0003390229500000092
P1＝QΛ-1QT (7)
Figure BDA0003390229500000093
in the above formula, Q is an orthogonal matrix composed of eigenvectors, and
Figure BDA0003390229500000094
λirespectively representing the expansion coefficients in the corresponding dimension i; c (u)1) Is a first high-dimensional ellipsoid region, C (u)2) Is a first high-dimensional ellipsoid region.
Step S4, integrating the sample points in the high-dimensional ellipsoid area into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertainty set based on the multi-interval convex hull.
Since the worst case in the robust optimization occurs on the boundary of the uncertainty set, it is only necessary to construct the convex hull of the region to which the robust optimization belongs and find the vertex on the convex hull, and the optimal solution of the robust optimization necessarily belongs to a certain vertex. In this embodiment, the uncertainty set based on the multi-interval convex hull is:
Figure BDA0003390229500000095
in the above formula, the first and second carbon atoms are,
Figure BDA0003390229500000096
the vertex coordinates of a kth interval are represented, wherein t represents scheduling time, s represents the number of scenes, k represents the number of convex hulls, and v represents the number of vertices of the corresponding interval;
Figure BDA0003390229500000097
respectively representing the electric load, the heat load and the cold load in the comprehensive energy micro-grid; ξ denotes the set of polyenergetic loads,
Figure BDA0003390229500000098
representing a predicted value of the multi-energy load;
Figure BDA0003390229500000099
the method comprises the steps that binary variables are used for representing whether a v-th vertex of a k-th interval is taken at t moment in an s scene, if the value is 1, the implementation of the uncertainty quantity is represented, otherwise, the implementation is not achieved when the value is 0; gamma-shapedξAn uncertainty budget for the entire scheduling period;
Figure BDA00033902295000000910
an uncertain budget for the kth interval;
Figure BDA00033902295000000911
and obtaining the probability of the corresponding interval by calculating the proportion of the error samples to the total number of the error samples in the corresponding interval.
The second row in equation (7) indicates that the uncertainty quantity is equal to the mean of the uncertainty quantities plus the error. The third row indicates that in the scene s, at most a certain vertex v of a certain interval k can be obtained at any time t. The fourth row represents any scene s for which the uncertainty error scene cannot be implemented beyond the uncertainty budget Γξ. The fifth row further represents any scenario s where the implementation of the uncertainty error scenario on interval k cannot exceed the uncertainty budget for the kth interval
Figure BDA0003390229500000101
The sixth row indicates that the uncertainty budget for the k-th and k + 1-th intervals can be calculated by taking the ratio of the probabilities of the respective intervalsAnd (6) obtaining.
In summary, the comparison effect of the box-based ambiguity set (BBUS), the convex hull ambiguity set (SCHUS) considering only a single interval, and the multi-interval convex hull (MCHUS) proposed by the present invention is shown in fig. 2. The invention uses Gaussian copula function combined edge distribution as normal distribution and t distribution respectively, and generates 5000 uncertain error samples. The BBUS represented by the outermost rectangular dashed box ignores the distribution characteristics of the uncertain parameters and always takes the boundary of the feasible region so as to maximize the area. And the area of the SCHUS described by the outermost convex hull based on the whole interval is far smaller than that of the BBUS, so that the accuracy of the model is improved. However, the extreme case represented by the poles of the outermost convex hull has a very small probability of occurring in practice, which makes the optimization result still conservative. Therefore, the present invention divides the entire error sample set into 3 intervals according to the sample probability, and constructs 3 convex hulls of the corresponding intervals to constitute the MCHUS. In the scheduling period of the comprehensive energy microgrid (such as 24 hours and 1 hour of scheduling interval), when uncertainty is realized, a certain probability is obtained to each convex hull in turn, so that the method is more practical and the conservative degree of robust optimization is reduced.
In order to verify the effectiveness of the model and the algorithm provided by the invention, as shown in fig. 3, a comprehensive energy microgrid of a certain actual park level of Changsha in Hunan is selected as a typical scene for verification. The comprehensive energy microgrid takes electricity and natural gas as input. The intermediate energy conversion device mainly includes units such as a Gas Boiler (GB), a Heat Pump (HP), a Gas Turbine (GT), a transformer (transformer), a heat recovery unit (HR), an electric refrigerating centrifuge (EC), a lithium bromide unit (LB), and a heat storage tank (HS). And the terminal load comprises an electric load, a heat load and a cold load required in the energy supply range of the comprehensive energy microgrid. The method selects 3 typical days (sunny days, cloudy days and rainy days) of the comprehensive energy microgrid as s typical scenes to analyze the influence of the uncertain sets on the multi-energy load. Since heat supply is not needed in winter, only electric load and heat load are needed. The present invention therefore constructs an MCHUS uncertainty set that accounts for the electrical-thermal load uncertainty. The robust optimization model employed is a two-stage robust optimization and solved for (C & CG) using a column and constraint generation algorithm.
As shown in fig. 4(a) to 4(c), the present invention compares the optimization results of BBUS, SCHUS and MCHUS proposed by the present invention on the uncertainty of the electric-thermal load. The combined error distribution of the electricity-heat load follows normal distribution with the predicted value as the mean value and 5% of the predicted value as the standard deviation sigma. The dotted lines in the figure divide the whole area into 8 areas in turn: [ - ∞, -3 σ ], [ -3 σ, -2 σ ], [ -2 σ, -1 σ ], [ -1 σ,0], [0,1 σ ], [1 σ,2 σ ], [2 σ,3 σ ], [3 σ, + ∞ ]. The results of the three uncertain sets are higher than the predicted load value, and the increase of the electric load and the heat load can increase the operation cost, so that the worst scene is found by the robust optimization to ensure the robustness. In the three uncertain sets, because the BBUS is based on the maximum deviation of the uncertain quantity, the whole curve of the BBUS is positioned above the SCHUS and the MCHUS, and the conservation degree of the optimization result is the maximum. Whereas the SCHUS conservation based on single inter-convex hull is reduced. For example, at t11, in fig. 4(a) representing a sunny day, the electrical load is in the [3 σ, + ∞ ] interval at this time, and the thermal load is only in the [1 σ,2 σ ] interval at the corresponding time because the electricity price is high; however, the electrical and thermal loads in the BBUS are always in the [3 σ, + ∞ ] range.
Further, comparing the scuus and the MCHUS, it can be found that the scuus always takes the outermost convex hull, and the MCHUS takes the convex hulls of each section in the scheduling period due to the consideration of the probability and budget of the sections. For example, MCHUS is located at the outermost convex hull only at the time t9-t12 when the price of electricity is high, and the electric-thermal loads are all located in the [0,1 sigma ] interval, namely, the convex hull in the elliptical region with 1 sigma as the axis, at the time t1-t 7. Therefore, corresponding convex hulls and probabilities are constructed by dividing a plurality of intervals, the optimized result of the MCHUS does not always obtain the outermost convex hull (SCHUS) or the outermost boundary (BBUS) with low probability, but the convex hulls in different intervals are uniformly obtained according to probability characteristics, so that the method is more practical and the conservative degree of robust optimization is reduced.
Fig. 5 compares the cost of the integrated energy microgrid for three uncertain sets under different robust budgets. With the increase of the uncertain budget, the worst situation is meant, so that the cost of the comprehensive energy microgrid corresponding to three uncertain sets is increased. The decision maker therefore needs to select a suitable uncertainty budget to balance economy and robustness in the optimization. In addition, when the uncertainty budget is 24, compared with the costs 6575.23 and 6843.44 of the SCHUS and the BBUS respectively, the cost corresponding to the MCHUS is the lowest 6225.06, which effectively reduces the scheduling cost. In conclusion, the MCHUS considers the correlation between the uncertainty quantity and avoids the small probability of occurrence in practice by setting a plurality of suitable intervals.
The embodiment of the invention provides an uncertain set construction method suitable for comprehensive energy microgrid robust optimization. The embodiment of the invention combines PCA and Quickhull convex hull algorithm, and provides an uncertain set based on a multi-interval convex hull by dividing a plurality of intervals and constructing the convex hull of an internal ellipsoid region. The multi-interval convex packet uncertain set can capture the distribution characteristics and the correlation of uncertain quantity in a self-adaptive mode, and through setting a plurality of suitable intervals, scenes with low probability in practice are avoided, the accuracy of the uncertain set is improved, and the conservative degree of robust optimization is reduced.
The embodiment of the invention also provides an uncertain set construction system suitable for the comprehensive energy microgrid robust optimization, and based on the uncertain set construction method suitable for the comprehensive energy microgrid robust optimization in the embodiments, the uncertain set construction method comprises the following steps:
the sample establishing module is used for generating a sample set of uncertain errors of the comprehensive energy microgrid and determining a mean value and a covariance matrix of the sample set;
the sample principal component analysis module is used for determining the characteristic value and the characteristic direction of the covariance matrix of the sample set based on a principal component analysis method;
the sample partitioning module is used for determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic value, determining the half-axis direction according to the characteristic direction, and partitioning the sample set into a plurality of high-dimensional ellipsoid regions;
and the uncertain set building module is used for integrating the sample points in the high-dimensional ellipsoid region into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertain set based on the multi-interval convex hulls.
Based on the same concept, an embodiment of the present invention further provides an entity structure schematic diagram, as shown in fig. 6, the server may include: a processor (processor)810, a communication Interface 820, a memory 830 and a communication bus 840, wherein the processor 810, the communication Interface 820 and the memory 830 communicate with each other via the communication bus 840. The processor 810 may invoke logic instructions in the memory 830 to perform the steps of the uncertainty set construction method applicable to the integrated energy microgrid robust optimization as described in the various embodiments above. Examples include:
step S1, generating a sample set of uncertainty errors of the comprehensive energy microgrid, and determining a mean value and a covariance matrix of the sample set;
step S2, determining the eigenvalue and the eigen direction of the covariance matrix of the sample set based on a principal component analysis method;
step S3, determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic values, determining the half-axis direction according to the characteristic direction, and dividing the sample set into a plurality of high-dimensional ellipsoid regions;
step S4, integrating the sample points in the high-dimensional ellipsoid area into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertainty set based on the multi-interval convex hull.
Furthermore, the logic instructions in the memory 830 may be implemented in software functional units and stored in a computer readable storage medium when the logic instructions are sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Based on the same concept, embodiments of the present invention further provide a non-transitory computer-readable storage medium, where a computer program is stored, where the computer program includes at least one code, and the at least one code is executable by a master control device to control the master control device to implement the steps of the uncertainty set constructing method applicable to the robust optimization of the integrated energy microgrid according to the embodiments described above. Examples include:
step S1, generating a sample set of uncertainty errors of the comprehensive energy microgrid, and determining a mean value and a covariance matrix of the sample set;
step S2, determining the eigenvalue and the eigen direction of the covariance matrix of the sample set based on a principal component analysis method;
step S3, determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic values, determining the half-axis direction according to the characteristic direction, and dividing the sample set into a plurality of high-dimensional ellipsoid regions;
step S4, integrating the sample points in the high-dimensional ellipsoid area into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertainty set based on the multi-interval convex hull.
Based on the same technical concept, the embodiment of the present application further provides a computer program, which is used to implement the above method embodiment when the computer program is executed by the main control device.
The program may be stored in whole or in part on a storage medium packaged with the processor, or in part or in whole on a memory not packaged with the processor.
Based on the same technical concept, the embodiment of the present application further provides a processor, and the processor is configured to implement the above method embodiment. The processor may be a chip.
In summary, the uncertain set construction method and system suitable for comprehensive energy microgrid robust optimization provided by the embodiments of the present invention generate an uncertain quantity error sample set, and solve the mean value of the sample set
Figure BDA0003390229500000131
Sum covariance matrix
Figure BDA0003390229500000132
A matrix; when a large amount of historical error data exists, the mean value and the variance matrix can be directly counted according to the historical error data based on a data driving method. When the historical error data samples are not enough, some symmetric distributions, such as normal distribution, t distribution, Cauchy distribution, and the like, can be used to generate the error distribution of the uncertain quantity. In particular, when the edge distributions corresponding to different uncertainties are different, a gaussian Copula function can be used to construct a joint distribution function of known edge distributions to generate enough samples. And finding information such as correlation, eigenvalue and eigenvector of the sample by using PCA. Such as eigenvalues and eigenvectors, will be used to determine the semi-axis length and axial direction of the inner ellipsoid; dividing a sample set area into k intervals, and establishing a high-dimensional ellipsoid area; constructing k convex hulls from the point set of k intervals based on a Quickhull convex hull algorithm, and finally establishing an uncertain set based on the convex hulls of multiple intervals. Based on the uncertain set of the multi-interval convex hull, the relevance among the uncertain quantities is considered, and through setting a plurality of proper intervals, the scene with low probability in practice is avoided, and the conservative degree of robust optimization is reduced.
The embodiments of the present invention can be arbitrarily combined to achieve different technical effects.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the procedures or functions described in accordance with the present application are generated, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, from one website site, computer, server, or data center to another website site, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid state disk), among others.
One of ordinary skill in the art will appreciate that all or part of the processes of the methods of the above embodiments may be implemented by a computer program that can be stored in a computer-readable storage medium and that, when executed, can include the processes of the above method embodiments. And the aforementioned storage medium includes: various media capable of storing program codes, such as ROM or RAM, magnetic or optical disks, etc.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. An uncertain set construction method suitable for comprehensive energy microgrid robust optimization is characterized by comprising the following steps:
step S1, generating a sample set of uncertainty errors of the comprehensive energy microgrid, and determining a mean value and a covariance matrix of the sample set;
step S2, determining the eigenvalue and the eigen direction of the covariance matrix of the sample set based on a principal component analysis method;
step S3, determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic value, determining the half-axis direction according to the characteristic direction, and dividing the sample set into a plurality of high-dimensional ellipsoid regions;
step S4, based on the Quickhull convex hull algorithm, the sample points in the high-dimensional ellipsoid region are collected into convex hulls, the vertex coordinates on each convex hull are determined, and uncertainty budgets of each convex hull are distributed, so that an uncertainty set based on the multi-interval convex hull is formed.
2. The uncertainty set construction method applicable to the robust optimization of the integrated energy microgrid according to claim 1, wherein the step S1 specifically includes:
constructing a sample set of uncertainty errors based on historical error data of the comprehensive energy microgrid;
if the data quantity of the historical error data is larger than a preset data threshold, based on a data driving method, calculating a mean value and a covariance matrix according to the historical error data;
if the data volume of the historical error data is not larger than a preset data threshold, generating error distribution of uncertain quantity based on a symmetric distribution method, and calculating a mean value and a covariance matrix; the symmetric distribution method comprises normal distribution, t distribution and Cauchy distribution.
3. The method for constructing an uncertainty set suitable for the robust optimization of the integrated energy microgrid according to claim 2, wherein in the step S1, if the edge distributions corresponding to different uncertainty errors are different, a joint distribution function of known edges is constructed based on a gaussian function, and uncertainty error samples are generated based on the joint distribution function:
H(x1,x2,…,xm)＝C[F(x1),F(x1),…,F(xm)]
in the above formula, F (x)1),F(x1),…,F(xm) Respectively uncertainty error x1,x2,…,xmThe function C is a gaussian function; h (x)1,x2,…,xm) Is a corresponding joint distribution function;
based on the joint distribution function H (x)1,x2,…,xm) Generating N m-dimensional uncertainty error samples u ═ { u ═1,u2,…,uNMean value of }
Figure FDA0003390229490000011
Sum covariance matrix
Figure FDA0003390229490000012
The calculation formula is as follows:
Figure FDA0003390229490000013
Figure FDA0003390229490000021
4. the uncertainty set construction method applicable to the robust optimization of the integrated energy microgrid according to claim 1, wherein the step S2 specifically includes:
centralizing the data of the sample set to zero mean, and decomposing based on the eigenvalue to obtain the eigenvalue and eigenvector of the covariance matrix:
Figure FDA0003390229490000022
in the above formula, the first and second carbon atoms are,
Figure FDA0003390229490000023
is a covariance matrix; q is an orthogonal matrix composed of eigenvectors, and
Figure FDA0003390229490000024
λirespectively, the scaling factor in the corresponding dimension i.
5. The method for constructing an uncertain set suitable for robust optimization of integrated energy microgrid according to claim 3, wherein in the step S3, the sample set region is divided into k partial intervals.
6. The method for constructing an uncertainty set suitable for the robust optimization of the integrated energy microgrid according to claim 5, wherein in the step S3, k is 3, and the first high-dimensional ellipsoid region is constructed in a first partial interval with 1-time eigenvalue σ as each half axis and eigenvector as directions; the second high-dimensional ellipsoid region is constructed by taking the 2-time eigenvalue sigma of the second partial interval region as each half axis; the third partial interval is a third high-dimensional ellipsoid region constructed for the remaining sample space of the sample set, wherein:
Figure FDA0003390229490000025
Figure FDA0003390229490000026
P1＝QΛ-1QT
Figure FDA0003390229490000027
in the above formula, Q is an orthogonal matrix composed of eigenvectors, and
Figure FDA0003390229490000028
λirespectively as expansion coefficients in corresponding dimensions i; c (u)1) Is a first high-dimensional ellipsoid region, C (u)2) Is a first high-dimensional ellipsoid region.
7. The method for constructing an uncertainty set suitable for the robust optimization of the integrated energy microgrid according to claim 5, wherein in the step S4, the uncertainty set based on the multi-interval convex hull is:
Figure FDA0003390229490000031
in the above formula, the first and second carbon atoms are,
Figure FDA0003390229490000032
the vertex coordinates of a kth interval are represented, wherein t represents scheduling time, s represents the number of scenes, k represents the number of convex hulls, and v represents the number of vertices of a corresponding interval;
Figure FDA0003390229490000033
respectively representing the electric load, the heat load and the cold load in the comprehensive energy micro-grid; ξ represent the set of multipotent loads,
Figure FDA0003390229490000034
a predicted value representing a multi-energy load;
Figure FDA0003390229490000035
the method comprises the steps that binary variables are used for representing whether a v-th vertex of a k-th interval is taken at t moment in an s scene, if the value is 1, the implementation of the uncertainty quantity is represented, otherwise, the implementation is not achieved when the value is 0; gamma-shapedξBudgeting uncertainty for the entire scheduling period;
Figure FDA0003390229490000036
an uncertain budget for the kth interval;
Figure FDA0003390229490000037
and obtaining the probability of the corresponding interval by calculating the proportion of the error samples to the total number of the error samples in the corresponding interval.
8. An uncertain set construction system suitable for comprehensive energy microgrid robust optimization is characterized by comprising the following components:
the sample establishing module is used for generating a sample set of uncertain errors of the comprehensive energy microgrid and determining a mean value and a covariance matrix of the sample set;
the sample principal component analysis module is used for determining the eigenvalue and the eigen direction of the covariance matrix of the sample set based on a principal component analysis method;
the sample partitioning module is used for determining the half-axis length of each high-dimensional ellipsoid region based on the characteristic value, determining the half-axis direction according to the characteristic direction, and partitioning the sample set into a plurality of high-dimensional ellipsoid regions;
and the uncertain set construction module is used for integrating the sample points in the high-dimensional ellipsoid region into convex hulls based on a Quickhull convex hull algorithm, determining vertex coordinates on each convex hull, and allocating uncertainty budgets of each convex hull to form an uncertain set based on the multi-interval convex hull.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of the method for constructing an uncertainty set suitable for robust optimization of an integrated energy microgrid according to any one of claims 1 to 7.
10. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the steps of the method for constructing an uncertainty set suitable for robust optimization of an integrated energy microgrid according to any one of claims 1 to 7.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2019165701A1 (en) * 2018-02-28 2019-09-06 东南大学 Random robust coupling optimization scheduling method for alternating-current and direct-current hybrid micro-grids
CN111159840A (en) * 2019-11-20 2020-05-15 国网甘肃省电力公司 Data-driven new energy uncertain set modeling method
CN111401664A (en) * 2020-04-21 2020-07-10 广东电网有限责任公司电力调度控制中心 Robust optimization scheduling method and device for comprehensive energy system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2019165701A1 (en) * 2018-02-28 2019-09-06 东南大学 Random robust coupling optimization scheduling method for alternating-current and direct-current hybrid micro-grids
CN111159840A (en) * 2019-11-20 2020-05-15 国网甘肃省电力公司 Data-driven new energy uncertain set modeling method
CN111401664A (en) * 2020-04-21 2020-07-10 广东电网有限责任公司电力调度控制中心 Robust optimization scheduling method and device for comprehensive energy system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
李日福;李晋芳;: "改进的三维离散点集凸包求解算法", 现代计算机(专业版), no. 20, 15 July 2017 (2017-07-15) *

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