Cuboid and convex hull combining method oriented to heterogeneous adjustable resource polymerization

Abstract

The invention provides a cuboid and convex hull merging method for heterogeneous adjustable resource polymerization, which comprises the following steps of: constructing a polyhedral feasible region model of common direct regulation type and response type adjustable monomers, approximating a feasible region of each adjustable resource monomer by utilizing a cuboid and convex hull merging algorithm, and combining a Minkowski sum distribution law to obtain a polymerization feasible region in a union set form; and a result is solved by a convex hull approximation algorithm generated by a surface, so that the accuracy and the response speed of the adjustable resources participating in system optimization operation are improved, the flexibility and the response speed of the resources participating in regulation and control are remarkably improved, and the scheduling plan optimization of the adjustable resources on the demand side is realized. The method provides an efficient scheduling plan optimization scheme for the power industry.

Description

Technical Field

[0001] The invention relates to the field of power systems, and in particular to a cuboid convex hull method for aggregating heterogeneous adjustable resources. Background Art

[0002] With the continuous development of distributed energy, its inherent random and fluctuating characteristics have posed new challenges to the safe and stable operation of the power system. my country has abundant adjustable resources on the demand side, including thermal power clusters, hydropower stations, energy storage, electric vehicles, etc., covering different links of source-load-storage and providing regulation services for the power system. However, such resources are scattered, uneven in capacity, and some single units are small in size, making it difficult to achieve direct dispatch of the power grid. Therefore, the aggregation of adjustable resources on the demand side provides a new idea for realizing centralized dispatch of the power grid.

[0003] In terms of technology, the aggregation method of adjustable resources is reflected in the feasible domain of the sum of all adjustable powers of the same aggregator. Many scholars have studied the mathematical model of feasible domain aggregation, such as using convex polyhedrons for characterization, and proposed an approximate simplified method for simplifying the aggregation of the feasible domain of delayable loads, constant temperature loads and energy storage; the external model of the aggregation feasible domain is calculated based on the k-order approximate model. However, due to the large differences in the types and parameters of adjustable resources within the same aggregator, the feasible domains of adjustable resources vary greatly and the heterogeneity is more obvious. The above-mentioned methods further expand the original feasible domain, and the accuracy of the approximate aggregation feasible domain is often low. The approximate accuracy and solution speed of the aggregation feasible domain reflect the accuracy and response speed of the adjustable resources participating in the scheduling. Therefore, it is urgent to propose a calculation method to improve the aggregation of heterogeneous adjustable resources. Summary of the invention

[0004] The purpose of the present invention is to propose a cuboid convex hull method for heterogeneous adjustable resource aggregation to address the deficiencies in the prior art, improve the efficiency and accuracy of optimized scheduling, and reduce the workload of dispatchers.

[0005] To achieve the above purpose, the technical solution of the present invention is: a cuboid convex hull method for heterogeneous adjustable resource aggregation, which mainly includes the following steps:

[0006] Step 1: Modeling the polyhedral feasible domain of adjustable resource monomers, select directly adjustable resources, such as thermal power clusters, hydropower stations, energy storage (battery energy storage, pumped storage, etc.), and electric hydrogen adjustable loads; select aggregated responsive adjustable resources, such as electric vehicles, temperature control loads (such as heat pumps, air conditioning loads). Combine equation elimination and Fourier-Motzkin elimination method to construct the above two types of resources.

[0007] Step 2: Based on the cuboid, approximate the feasible domain of each resource. First, solve the maximum volume of the axially filled cuboid inside a polyhedron; then, set the optimization objective function to the maximum volume of the cuboid; finally, divide the sub-regions and calculate the maximum axially filled cuboid respectively.

[0008] Step 3: Minkowski sum calculation approximates the feasible domain of aggregation. First, based on the distributive law of the Minkowski sum, that is, the Minkowski sum of the union is equal to the union of the Minkowski sum, a new set consisting of the Cartesian product is generated; secondly, considering the large number of sets, the internal redundant cuboids are discarded; finally, based on the Minkowski sum calculation results of the cuboids with different adjustable resources at the same level and in the same direction, the convex hull of the union is output.

[0009] Step 4: Convex hull approximation algorithm based on surface generation. First, use the vertices of the farthest cuboid in all directions along the coordinate axis to generate the initial approximate convex hull; second, based on the initialized convex hull surface, find the farthest point outside the surface, use the farthest point to generate a new surface, replace the original partial surface, and gradually expand outward; finally, output the convex hull approximation result according to actual engineering needs.

[0010] Optimally, the feasible domain of thermal power cluster c In the formula, the superscript G represents thermal power, and the subscript c represents thermal power cluster c. represents the power generation of thermal power cluster c, A represents the coefficient matrix, and b represents the constant term vector; and According to whether it is a timing coupling constraint, it is divided into two parts, namely in,

[0011]

[0012]

[0013]

[0014]

[0015] In the formula, represents the installed capacity of thermal power cluster c; It represents the down-ramp capability limit between two time sections of thermal power cluster c; It represents the climbing capacity limit between two time sections of thermal power cluster c; Indicates the minimum technical output percentage requirement of thermal power cluster c; 0 D represents a D-dimensional column vector whose elements are all 0; 1 D represents a D-dimensional column vector whose elements are all 1; I D represents the D-dimensional identity matrix;

[0016] Polyhedral feasible region of hydropower station h is the output of the hydropower station, matrix and vector The specific form is as follows:

[0017]

[0018]

[0019] In the formula, the superscript H represents hydropower, and the subscript h represents the hydropower station. is the minimum output of the hydropower station. is the rated capacity of the hydropower station, It indicates the forced output of the hydropower station affected by downstream demand. represents the average output of the hydropower station, and E represents the number of sections corresponding to the total analysis time;

[0020] Polyhedral feasible region of energy storage ESS in is the net discharge power of energy storage, matrix and vector The specific form is as follows:

[0021]

[0022]

[0023] In the formula, the superscript S is used to identify the energy storage device, and the subscript ess represents energy storage. It is a parameter equivalent to the charge / discharge efficiency. is the discharge efficiency of energy storage, is the charging efficiency of energy storage, Indicates the maximum discharge power of the energy storage, Indicates the maximum charging power of the energy storage, Indicates the initial storage capacity of the energy storage, Indicates the minimum storage capacity requirement for energy storage, Indicates the maximum storage capacity requirement of energy storage, L v represents a v-dimensional lower triangular matrix with all non-zero elements set to 1, n v =[1,2,…,v] T , I v represents the v-dimensional identity matrix;

[0024] Polyhedral feasible region of adjustable load l for hydrogen production from electricity In the formula is the power of hydrogen production by electrolysis, matrix and vector The specific expression is as follows:

[0025]

[0026]

[0027] In the formula, the superscript H2 is used to identify the load of hydrogen production by electricity, and the subscript l represents the adjustable load l of hydrogen production by electricity. Indicates the conversion coefficient between the hydrogen production quality and the electrical power used by the electrolyzer, represents the minimum electrolytic hydrogen production power, Indicates the maximum electrolytic hydrogen production power, To meet the quality requirements of hydrogen production, is the allowable fluctuation coefficient of hydrogen production quality.

[0028] Preferably, the polyhedron feasible domain of the electric vehicle load e is The matrix and vector The specific form is as follows:

[0029]

[0030]

[0031] In the formula, the superscript EV is used to identify the electric vehicle load, and the subscript e represents the electric vehicle load e. represents the minimum electric vehicle charging power, represents the maximum electric vehicle charging power, For charging capacity requirements, is the allowable fluctuation coefficient of the charging capacity;

[0032] Polyhedral feasible region of temperature control load tc The matrix and vector As shown below:

[0033]

[0034]

[0035] In the formula, All are intermediate quantities:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] In the formula, a tc and r tc It is a parameter defined in order to simplify the formula expression during the derivation process. Indicates the maximum power consumption of temperature control load. and They represent the lower and upper limits of the indoor temperature fluctuation respectively. Indicates the outdoor ambient temperature. is the building thermal resistance, represents the heat capacity of the building, Indicates the electrothermal conversion efficiency.

[0043] Preferably, the calculation of step S2 is specifically as follows:

[0044] In a polyhedron Internal solution for the maximum volume of the axially filled cuboid It is equivalent to the optimization problem shown below:

[0045]

[0046]

[0047] In the formula, d represents the geometric center vector of the cuboid, x represents the power vector, β represents the half-side length, and I D represents the D-dimensional identity matrix, represents the half-edge length vector, the subscripts i and j represent the load, and D represents the D dimension. (A) ij They represent the maximum value of the coefficient matrix element, the minimum value of the coefficient matrix element, and the element value of the i-th row and j-th column of the coefficient matrix respectively;

[0048] Define the first largest axial inward filling cuboid obtained for the original feasible domain as the first layer of cuboids. This cuboid divides the N-dimensional original feasible domain into 2D sub-regions. The largest axial inward filling cuboid obtained for each sub-region is called the second layer of cuboids. The nth layer has a total of (2D) n-1 axial cuboids, each cuboid is divided into at most 2D sub-regions, and the maximum axial inner filling cuboids are calculated for these sub-regions to form the n+1th layer of cuboids. The oth cuboid in the nth layer is recorded as

[0049] Preferably, in step S3, the Minkowski sum calculation for the cuboids with different adjustable resources in the same layer and in the same direction is specifically as follows:

[0050]

[0051] It is assumed that the rectangular blocks in the same layer y along the same axis have the same number z, and the represents the Minkowski sum of W adjustable resources in the same layer and in the same direction. According to the Minkowski sum property, It is also a cuboid in space. Represents the zth cuboid in the yth layer.

[0052] Preferably, the calculation of step S4 is specifically as follows:

[0053] The convex hull updated after each cycle of all surfaces of the original convex hull is called a surface generation. The convex hull after k surface generation cycles is recorded as

[0054] Assumptions The equation of a surface of is α T Q = υ, finding the point farthest from the outside of the surface is equivalent to the following optimization problem:

[0055]

[0056] stQ∈V

[0057] α T Q>υ

[0058] Among them, V represents all The vertex set of , dd represents the distance, α coefficient matrix, Q represents the vertex, υ represents the outer side of the convex hull;

[0059] Find the farthest point Q outside a surface of the convex hull * Then, use the existing convex hull and this point Q * Construct a new convex hull;

[0060] First, we need to determine the surface whose convex hull needs to be replaced. Assume The sth surface equation of is α s T Q=υ s , then the inner side of the convex hull is α s T Q<υ s The criteria for deleting the surface are:

[0061] α s T Q * -υ s >0

[0062] By looping over the existing convex hull Surfaces, you can find all the surfaces that need to be deleted;

[0063] Then use all the vertices of the surface that need to be replaced and the farthest point Q * Generate a new incremental convex hull

[0064] Finally, merge and constitute

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention includes polyhedral feasible domain modeling of adjustable resource monomers, feasible domain approximation of each resource based on cuboids, Minkowski and calculation approximation of aggregation feasible domain, and convex hull approximation algorithm based on surface generation. Through the cuboid convex hull algorithm for heterogeneous resource aggregation, the feasible domain accuracy of adjustable resource aggregation is improved, the accuracy and response speed of resource participation in regulation are improved, the dispatch plan optimization and utilization of demand-side adjustable resources are realized, and an efficient dispatch plan optimization solution is provided for the power industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic diagram of the overall structure of the system of the present invention;

[0068] Figure 2 Schematic diagram of the cuboid convex hull algorithm;

[0069] Figure 3 Schematic diagram of feasible domain aggregation;

[0070] Figure 4 It is a schematic diagram of Minkowski and calculation of two feasible domains in two dimensions;

[0071] Figure 5 Schematic diagram of the algorithm for 2D surface generation. DETAILED DESCRIPTION

[0072] The following is combined with Figure 1-5 , the technical solution of the present invention is specifically described.

[0073] The present invention proposes a cuboid convex hull method for heterogeneous adjustable resource aggregation, which is used to improve the accuracy and calculation speed of adjustable resource optimization scheduling, and improve the accuracy and response speed of resource participation regulation. Figure 1-Figure 2 , mainly includes the following steps:

[0074] Step 1: Modeling the polyhedral feasible domain of adjustable resource monomers.

[0075] There are many types of adjustable resources in extremely high-proportion systems, and they have significant time-series coupling characteristics, and their adjustment capabilities change dynamically over time. This paper uses polyhedral feasible domains to uniformly model the adjustment capabilities of different types of adjustable resources, and achieves a complete characterization of time-series coupling constraints. The aggregation of feasible domains is as follows: Figure 3 As shown. Combining equation elimination and Fourier-Motzkin elimination method, a polyhedral feasible domain model of common direct control type and aggregate response type adjustable resource monomers is constructed, involving different links such as source, load, and storage. Other adjustable resource types not introduced can also be derived according to this method to obtain a polyhedral feasible domain.

[0076] 1. Directly controllable adjustable resources

[0077] (1) Thermal Power Cluster Modeling

[0078] The operation constraints that thermal power clusters need to meet include variable logic constraints, power upper and lower limit constraints, start and stop time constraints, ramp constraints, variable non-negative constraints, etc. Variable logic constraints are defined as:

[0079]

[0080] Among them, the superscript G represents thermal power, represents the available capacity of thermal power cluster c in time period t, and It represents the capacity of thermal power cluster c that switches from shutdown to startup and from startup to shutdown in time period t.

[0081] The upper and lower power constraints are defined as:

[0082]

[0083] in, represents the minimum technical output percentage requirement of thermal power cluster c, represents the power generation of thermal power cluster c in time period t, represents the maximum power generation of thermal power cluster c in time period t, Represents the installed capacity of thermal power cluster c.

[0084] The start and stop time constraints are defined as:

[0085]

[0086]

[0087] Among them, UT c Indicates the minimum time interval required for thermal power cluster c to switch from shutdown to startup; DT c Indicates the minimum time interval requirement for thermal power cluster c to switch from startup to shutdown.

[0088] The hill climbing constraint is defined as:

[0089]

[0090]

[0091] in, It represents the climbing capacity limit between two time sections of thermal power cluster c; Represents the downward climbing capacity limit between two time sections of thermal power cluster c.

[0092] The variable non-negativity constraint is defined as:

[0093]

[0094] Based on the above constraints, the feasible region of thermal power cluster c is obtained Need to be eliminated Variables other than represents the power generation of thermal power cluster c in time period t, t∈[1,...,D], A represents the coefficient matrix, and b represents the constant term vector. The above formula can be expressed as a variable and function, eliminate it, and the variable The above formula can be eliminated by Fourier-Motzkin elimination to obtain Therefore, the focus of elimination is to deal with variables and The inequality constraints that need to be satisfied are as follows:

[0095]

[0096] Combining the two upper bounds with the lower bounds can eliminate The constraint set is obtained as shown below.

[0097]

[0098] Among them, the definition In the above formula, only the first and third rows are constrained. The constraint combination can be rearranged as shown below.

[0099]

[0100] The upper and lower bounds of the inequality constraints in the above formula are eliminated And remove the ineffective constraints, add The variable non-negative constraint is as follows:

[0101]

[0102] Arrange the above formula into matrix form and and According to whether it is a timing coupling constraint, it is divided into two parts, namely Then we can get the following formula:

[0103]

[0104]

[0105]

[0106]

[0107] Among them, 0 D represents a D-dimensional column vector whose elements are all 0; 1 D represents a D-dimensional column vector whose elements are all 1; I D Represents the D-dimensional identity matrix.

[0108] It should be noted that a more sophisticated operation model of the thermal power cluster can be constructed by considering factors such as the difference in ramp rates at different operating points. As long as the constraint functions are linear, the same derivation method can be used to obtain the polyhedral feasible domain.

[0109] (2) Hydropower Station Modeling

[0110] The polyhedral feasible region of the hydropower station is constructed according to the three-stage output model. The model constraints of the hydropower station h include upper and lower output constraints, forced output constraints, expected output constraints, and power constraints.

[0111] The output upper and lower constraints are defined as:

[0112]

[0113] The superscript H stands for hydropower. is the minimum output of the hydropower station h, is the rated capacity of the hydropower station, is the output of the hydropower station in time period t.

[0114] The forced output and expected output constraints are defined as:

[0115]

[0116] in, It indicates the forced output of the hydropower station affected by downstream demand. Indicates the maximum expected output.

[0117] The power constraint is defined as:

[0118]

[0119] in, represents the average output of the hydropower station, and E represents the number of sections corresponding to the total analysis time.

[0120] Rearranging the above formula, we can get the polyhedral feasible domain of the hydropower station h Medium Matrix and vector The specific form of is the output of the hydropower station, and the expression is as follows:

[0121]

[0122]

[0123] (3) Energy storage modeling

[0124] The energy storage here refers to generalized energy storage, which can include battery energy storage, pumped storage, etc. According to the linear model, the operating constraints that the energy storage needs to meet include upper and lower limit constraints on charging and discharging power, storage power constraints, variable logic constraints, etc.

[0125] The upper and lower limits of charge and discharge power are defined as:

[0126]

[0127]

[0128] Among them, the superscript dis is used to indicate discharge, and ch is used to indicate charge. The energy storage equipment here can correspond to different types such as battery energy storage and pumped storage. represents the discharge power of the energy storage, Indicates the maximum discharge power of the energy storage, represents the charging power of the energy storage, Indicates the maximum charging power of the energy storage.

[0129] The storage power constraint is defined as:

[0130]

[0131] The superscript S is used to identify energy storage equipment. Indicates the initial storage capacity of the energy storage, is the discharge efficiency of energy storage, is the charging efficiency of energy storage, Indicates the minimum storage capacity requirement for energy storage, Indicates the maximum storage capacity requirement of energy storage.

[0132] The variable logical constraints are defined as:

[0133]

[0134]

[0135] in, It represents the net discharge power of energy storage at time t as seen from the system side.

[0136] To derive the polyhedron feasible domain of energy storage ess, we need to obtain in is the net discharge power of the energy storage, Medium Matrix and vector The specific form of , which requires eliminating variables and Using the above equation, we can first replace Replace with As shown in the following formula, we only need to eliminate That's it.

[0137]

[0138] For the convenience of elimination, it is further sorted as follows:

[0139]

[0140] in, It is a parameter derived based on the charge / discharge efficiency.

[0141] Considering the non-negative constraint of the variables, we can eliminate Then remove the ineffective constraints and obtain the constraint set as shown below.

[0142]

[0143] Arranging the above formula into matrix form, we can get the following formula:

[0144]

[0145]

[0146] Among them, L v represents a v-dimensional lower triangular matrix with all non-zero elements set to 1, n v =[1,2,…,v] T , I v Represents the v-dimensional identity matrix.

[0147] (4) Modeling of adjustable load for hydrogen production

[0148] The linear operation constraints that the adjustable load l of hydrogen production needs to meet include the upper and lower limits of power consumption and the demand constraints of hydrogen production. The upper and lower limits of power consumption can be defined as:

[0149]

[0150]

[0151] The superscript H2 is used to identify the electric hydrogen production load. represents the power of hydrogen production by electrolysis, represents the minimum electrolytic hydrogen production power, Indicates the maximum electrolytic hydrogen production power.

[0152] The hydrogen production demand constraint can be defined as:

[0153]

[0154]

[0155] in, Indicates the conversion coefficient between the hydrogen production quality and the electrical power used by the electrolyzer, To meet the quality requirements of hydrogen production, is the allowable fluctuation coefficient of hydrogen production quality.

[0156] The polyhedral feasible domain of the adjustable load l for electric hydrogen production can be obtained by arranging the upper and lower limits of power consumption and the hydrogen production demand constraints. in is the power of hydrogen production by electrolysis, Medium Matrix and vector The specific form of is as follows:

[0157]

[0158]

[0159] 2. Aggregate responsive adjustable resources

[0160] Since the individual capacity of adjustable resources such as residential or commercial adjustable loads and distributed energy storage equipment is less than the access capacity requirement for demand response, it is necessary to achieve demand response through aggregation and participate in the system power balance. The types of actual aggregated responsive adjustable resources are complex and it is difficult to list all types in the paper. Here we take electric vehicles and temperature control loads (such as heat pumps and air conditioning loads), which are currently hot topics in research, as examples for explanation.

[0161] It should be noted that the cuboid convex hull algorithm to be introduced later is not limited to aggregate responsive adjustable resources, as long as its feasible domain is in the form of a polyhedron.

[0162] (1) Electric vehicle modeling

[0163] The electric vehicles considered here are of the type that achieve load regulation response through orderly charging, which is usually called V1G. They do not return power to the grid. Their constraints include upper and lower limits on power consumption and charging demand constraints.

[0164] The upper and lower limits of power consumption are defined as:

[0165]

[0166]

[0167] Among them, the superscript EV is used to identify the electric vehicle load, and the subscript e represents the electric vehicle load e. Indicates the charging power of electric vehicles, represents the minimum electric vehicle charging power, Indicates the maximum electric vehicle charging power.

[0168] The charge demand constraint is defined as:

[0169]

[0170]

[0171] in, For charging capacity requirements, is the allowable fluctuation coefficient of the charging capacity.

[0172] By sorting out the upper and lower limits of power consumption and the definition of charging demand constraints, we can get the polyhedral feasible domain of electric vehicle load e Medium Matrix and vector The specific form is shown below:

[0173]

[0174]

[0175] (2) Temperature control load modeling

[0176] Temperature control loads need to meet upper and lower limits of power consumption, electric-thermal power conversion constraints, first-order dynamic equations of indoor temperature, indoor temperature constraints, etc.

[0177] The upper and lower limits of power consumption are defined as:

[0178]

[0179]

[0180] Among them, the superscript TCL is used to identify temperature control loads. Indicates the power consumption of temperature control loads. Indicates the minimum power consumption of temperature control load. Indicates the maximum power consumption of temperature control load.

[0181] The electric-thermal power conversion constraint combined with the electric-thermal power conversion relationship of the temperature control load can be defined as:

[0182]

[0183] in, represents the thermal power, Represents the electric-to-heat conversion efficiency. Since the conversion efficiency of some types of temperature-controlled loads (such as heat pumps) is related to the indoor and outdoor temperature difference, the conversion efficiency is given with a time subscript t to reflect its time-varying characteristics. Considering that the indoor temperature fluctuation is small, the conversion efficiency can be modeled as a function of the outdoor temperature, and the outdoor temperature is considered to be a known parameter, so the conversion efficiency is also a given parameter.

[0184] The first-order dynamic equation of indoor temperature (taking heating mode as an example) can be defined as:

[0185]

[0186] in, represents the heat capacity of the building, is the building thermal resistance, Indicates the indoor temperature. Indicates the outdoor ambient temperature.

[0187] The indoor temperature constraint can be defined as:

[0188]

[0189]

[0190] in, and They respectively represent the lower and upper limits of the allowable fluctuation of indoor temperature.

[0191] The above constraints involve thermal power and indoor temperature variables, and Gaussian elimination is needed to transform the above constraints into constraints only related to electrical power. The first-order dynamic equation of indoor temperature is differentiated and substituted into the result after differentiation, and the following equation can be obtained:

[0192]

[0193]

[0194] Rewriting the above formula into matrix form, we can get the following result:

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201] in, Both are intermediate quantities, a tc and r tc It is a parameter defined to simplify the formula expression during the derivation process.

[0202] Therefore, the indoor temperature can be expressed as a linear function of the electrical power consumption, as shown in the following formula:

[0203]

[0204] Considering the requirement of limiting indoor temperature fluctuation, the following formula can be obtained:

[0205]

[0206]

[0207] Therefore, the polyhedral feasible domain of temperature control load tc is Medium Matrix and vector As shown below:

[0208]

[0209]

[0210] Step 2: Approximate the feasible domain of each adjustable resource based on the cuboid.

[0211] Using special polyhedrons to approximate the real feasible domain of each adjustable resource can make full use of the excellent properties of the Minkowski sum of special polyhedrons. Through the application of the Minkowski sum distributive law, the poor approximation of a single special polyhedron can be improved. Since the solution model of the maximum axial inner filling cuboid of a polyhedron is relatively simple, this paper chooses the axial cuboid as the basis for the union approximation.

[0212] In a polyhedron Internal solution for the maximum volume of the axially filled cuboid It is equivalent to the optimization problem shown below:

[0213]

[0214]

[0215] In the formula, d represents the geometric center vector of the cuboid, x represents the power vector, β represents the half-side length, and I D represents the D-dimensional identity matrix, represents the half-edge length vector, the subscripts i and j represent the load, and D represents the D dimension. (A) ij They represent the maximum value of the coefficient matrix element, the minimum value of the coefficient matrix element, and the element value of the i-th row and j-th column of the coefficient matrix respectively;

[0216] The formula for calculating the volume of a cuboid is: but The requirement for maximum volume can be reflected by the objective function maxlogV(B).

[0217] Define the first largest axial inward filling cuboid obtained for the original feasible domain as the first layer of cuboids. This cuboid divides the N-dimensional original feasible domain into 2D sub-regions. The largest axial inward filling cuboid obtained for each sub-region is called the second layer of cuboids. The nth layer has a total of (2D) n-1 axial cuboids, each cuboid is divided into at most 2D sub-regions, and the largest axial inner filling cuboids are calculated for these sub-regions to form the n+1th layer of cuboids. The oth cuboid in the nth layer is denoted as B o n.

[0218] Step 3: Minkowski sum is calculated to approximate the aggregate feasible domain.

[0219] According to the distributive law of Minkowski sums, the Minkowski sum of a union is equal to the union of Minkowski sums, as shown in the following formula:

[0220]

[0221] in, represents the w-th spatial geometric body, which is numbered k (w) ∈S (w) The union of a series of sub-geometries of (1) ×…×S (W) Represents the Cartesian product of numbered sets.

[0222] Due to the strict use of the distributive law of the Minkowski sum, operations are required to be performed on all elements in the Cartesian product. When the number of layers increases, the number of cuboids increases exponentially, and the number of elements in the new set composed of the Cartesian product will explode.

[0223] Considering that the convex hull of the union will be generated in the subsequent steps, discarding the redundant cuboids inside will have little effect on the final result. Therefore, this step only performs Minkowski sum calculations on cuboids of the same layer and direction with different adjustable resources, as shown in the following formula, which can greatly reduce the amount of calculation.

[0224]

[0225] It is assumed that the rectangular blocks in the same layer y along the same axis have the same number z, and the represents the Minkowski sum of W adjustable resources in the same layer and in the same direction. According to the Minkowski sum property, It is also a cuboid in space. represents the zth cuboid in the yth layer. The Minkowski sum calculation diagram of two feasible domains in two dimensions is as follows Figure 4 As shown. According to the above formula, only the Minkowski sum of 5 pairs of rectangles with the same color need to be calculated for two adjustable resources, while if the strict Minkowski sum distribution law is used, the Minkowski sum of all combinations of 25 pairs of rectangles needs to be calculated. The calculation results of the Minkowski sum in the figure are used to illustrate the position relationship, and the size and shape of each rectangle are not strictly calculated results.

[0226] Step 4: Convex hull approximation algorithm based on surface generation.

[0227] Since the process of seeking the “union” is not a convexity-preserving operation, the aggregated feasible domain result cannot be applied to the system operation optimization calculation. Therefore, it is necessary to further solve the convex hull approximation of the output result of step 2.

[0228] Since the complexity of conventional high-dimensional convex hull algorithms increases dramatically with the number of point set elements, a convex hull approximation algorithm based on face generation (Facet Generation Algorithm, FGA) is proposed. The basic idea is to use the vertices of the farthest cuboids along the coordinate axis to generate the initial approximate convex hull, and then expand and grow outward step by step based on the initialized convex hull surface. In this way, the calculation can be cut off according to the actual engineering calculation time consumption, and the convex hull approximate output result can be obtained even if the algorithm is stopped early before convergence.

[0229] The idea of ​​the surface generation algorithm is to find the farthest point outside the surface based on the existing convex hull surface, and use the farthest point to generate a new surface to replace the original surface. The convex hull after each cycle of all surfaces of the original convex hull is called a surface generation. The convex hull after k cycles of surface generation is recorded as

[0230] Assumptions The equation of a surface of is α T Q = υ, finding the point farthest from the outside of the surface is equivalent to the following optimization problem:

[0231]

[0232] stQ∈V

[0233] α T Q>υ

[0234] Among them, V represents all the The vertex set of , dd represents the distance, α represents the coefficient matrix, Q represents the vertex, and υ represents the outside of the convex hull.

[0235] Find the farthest point Q outside a surface of the convex hull * After that, the next problem is to use the existing convex hull and this point to form a new convex hull. To do this, we first need to determine the surface where the existing convex hull needs to be replaced.

[0236] Assumptions The sth surface equation of is α s T Q=υ s (The inside of the convex hull is α s T Q<υ s ), the criteria for it to be deleted are:

[0237] α s T Q * -υ s >0

[0238] By looping over the existing convex hull Then use the vertices of all the surfaces that need to be replaced and the farthest point Q * Generate a new incremental convex hull Finally, merge and constitute A two-dimensional example is Figure 5 The blue area in the figure represents the convex hull after k cycles of face generation. The purple area indicates the point Q farthest from the surface. *Generated incremental convex hull The red wireframe area is the new convex hull

[0239] Initializing the convex hull and generating the incremental convex hull in each step are all implemented by directly calling the Qhull toolkit. Since Qhull is based on the fast convex hull algorithm, the worst algorithm complexity for solving the convex hull of all vertices obtained in step 2 is O(|V| D ), where |V| represents the number of elements in the vertex set. When some vertices are used to generate the convex hull, the algorithm complexity becomes O(|V small | D ), where V small Indicates a subset of some vertices, and the computational complexity is greatly reduced. In particular, for the FGA algorithm in the cuboid convex hull algorithm, the face generation process can satisfy |V small The condition of |<<|V|.

[0240] In summary, the present invention includes polyhedral feasible domain modeling of adjustable resource monomers, cuboid-based and approximate feasible domains of each resource, Minkowski and calculation approximate aggregate feasible domain, and convex hull approximation algorithm based on surface generation:

[0241] First, a polyhedral feasible domain model of common direct control and responsive adjustable monomers is constructed, involving different links such as source, load, and storage. The model includes thermal power clusters, hydropower stations, energy storage, electric hydrogen production adjustable loads, electric vehicles, and temperature control loads. The adjustment capabilities of the above different types of adjustable resources are uniformly modeled to achieve a complete description of the timing coupling constraints;

[0242] Secondly, considering that the types and parameters of adjustable resources of the same aggregator are quite different, that is, the feasible domains of adjustable resource monomers are significantly different, the rectangular parallelepiped convex hull algorithm is used to approximate the feasible domains of each adjustable resource monomer to ensure the high-precision performance of heterogeneous feasible domain aggregation and improve the accuracy and calculation speed of the Minkowski sum solution of the corresponding set of aggregation feasible domain calculation problems;

[0243] Finally, the Minkowski sum of Chino polyhedra and isomorphic polyhedra is easily calculated, and the aggregate feasible domain in the form of a union is obtained using the distributive law of the Minkowski sum. The convex hull approximation of the output result is solved based on the convex hull approximation algorithm generated by the surface, so that the aggregate feasible domain result can be applied to the system operation optimization calculation to achieve scheduling plan optimization.

[0244] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A cuboid convex hull method for heterogeneous adjustable resource aggregation, characterized in that: The following steps are involved: Polyhedral feasible domain modeling of adjustable resource monomers, constructing polyhedral feasible domain models of common direct control and response adjustable monomers, which are used to simulate adjustable resources in different links such as source, load, and storage; The cuboid-based and approximate feasible domains of each resource are used to improve the accuracy of the approximate aggregation feasible domain when the heterogeneity of the adjustable resources to be aggregated is obvious; The Minkowski sum calculation approximates the aggregate feasible domain, and with its easy-to-compute property, is used to obtain the feasible domain in the form of a union; The convex hull approximation algorithm based on surface generation is used to solve the convex hull approximation of the output result so that the output result is a convex set.

2. According to claim 1, a cuboid convex hull method for heterogeneous adjustable resource aggregation is characterized in that: The polyhedral feasible domain modeling of the adjustable resource monomer is constructed by combining equation elimination and Fourier-Motzkin elimination method, and is mainly divided into common direct control type models and common direct control type models. The common direct control type models specifically include: thermal power clusters, hydropower stations, energy storage, and electric hydrogen production adjustable loads; the common direct control type models specifically include: electric vehicles and temperature control loads.

3. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 1, characterized in that: The method based on cuboids and approximating feasible domains of various resources comprises the following specific steps: solving the maximum volume of the axially filled cuboid inside a polyhedron; setting the optimization objective function to the maximum volume of the cuboid; dividing the sub-regions and solving the maximum axially filled cuboids respectively.

4. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 1, characterized in that: The Minkowski sum calculation approximate aggregation feasible domain performs Minkowski sum calculation on rectangular blocks with the same level and the same direction of different adjustable resources according to the strict use conditions of the distribution law of the Minkowski sum.

5. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 1, characterized in that: The convex hull approximation algorithm based on surface generation specifically comprises the following steps: using the vertices of the cuboid farthest in each direction along the coordinate axis to generate an initial approximate convex hull; based on the initialized convex hull surface, finding the farthest point outside the surface, using the farthest point to generate a new surface, replacing the original partial surface, and gradually expanding outward in this way; outputting the convex hull approximation result according to actual engineering requirements.

6. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 2, characterized in that: Feasible region of thermal power cluster c In the formula, the superscript G represents thermal power, and the subscript c represents thermal power cluster c. represents the power generation of thermal power cluster c, A represents the coefficient matrix, and b represents the constant term vector; and According to whether it is a timing coupling constraint, it is divided into two parts, namely in, In the formula, represents the installed capacity of thermal power cluster c; It represents the down-ramp capability limit between two time sections of thermal power cluster c; It represents the climbing capacity limit between two time sections of thermal power cluster c; Indicates the minimum technical output percentage requirement of thermal power cluster c; 0 D represents a D-dimensional column vector whose elements are all 0; 1 D represents a D-dimensional column vector whose elements are all 1; I D represents the D-dimensional identity matrix; Polyhedral feasible region of hydropower station h is the output of the hydropower station, matrix and vector The specific form is as follows: In the formula, the superscript H represents hydropower, and the subscript h represents the hydropower station. is the minimum output of the hydropower station. is the rated capacity of the hydropower station, It indicates the forced output of the hydropower station affected by downstream demand. represents the average output of the hydropower station, and E represents the number of sections corresponding to the total analysis time; Polyhedral feasible region of energy storage ESS in is the net discharge power of energy storage, matrix and vector The specific form is as follows: In the formula, the superscript S is used to identify the energy storage device, and the subscript ess represents energy storage. It is a parameter equivalent to the charge / discharge efficiency. is the discharge efficiency of energy storage, is the charging efficiency of energy storage, Indicates the maximum discharge power of the energy storage, Indicates the maximum charging power of the energy storage, Indicates the initial storage capacity of the energy storage, Indicates the minimum storage capacity requirement for energy storage, Indicates the maximum storage capacity requirement of energy storage, L v represents a v-dimensional lower triangular matrix with all non-zero elements set to 1, n v =[1,2,…,v] T , I v represents the v-dimensional identity matrix; Polyhedral feasible region of adjustable load l for hydrogen production from electricity In the formula is the power of hydrogen production by electrolysis, matrix and vector The specific expression is as follows: In the formula, the superscript H2 is used to identify the load of hydrogen production by electricity, and the subscript l represents the adjustable load l of hydrogen production by electricity. Indicates the conversion coefficient between the hydrogen production quality and the electrical power used by the electrolyzer, represents the minimum electrolytic hydrogen production power, Indicates the maximum electrolytic hydrogen production power, To meet the quality requirements of hydrogen production, is the allowable fluctuation coefficient of hydrogen production quality.

7. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 2, characterized in that: Polyhedral feasible region of electric vehicle load e The matrix and vector The specific form is as follows: In the formula, the superscript EV is used to identify the electric vehicle load, and the subscript e represents the electric vehicle load e. represents the minimum electric vehicle charging power, represents the maximum electric vehicle charging power, For charging capacity requirements, is the allowable fluctuation coefficient of the charging capacity; Polyhedral feasible region of temperature control load tc The matrix and vector As shown below: In the formula, All are intermediate quantities: In the formula, a tc and r tc It is a parameter defined in order to simplify the formula expression during the derivation process. Indicates the maximum power consumption of temperature control load. and They represent the lower and upper limits of the indoor temperature fluctuation respectively. Indicates the outdoor ambient temperature. is the building thermal resistance, represents the heat capacity of the building, Indicates the electrothermal conversion efficiency.

8. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 3, characterized in that: The calculation of step S2 is specifically as follows: In a polyhedron Internal solution for the maximum volume of the axially filled cuboid It is equivalent to the optimization problem shown below: In the formula, d represents the geometric center vector of the cuboid, x represents the power vector, β represents the half-side length, and I D represents the D-dimensional identity matrix, represents the half-edge length vector, the subscripts i and j represent the load, and D represents the D dimension. (A) ij They represent the maximum value of the coefficient matrix element, the minimum value of the coefficient matrix element, and the element value of the i-th row and j-th column of the coefficient matrix respectively; Define the first largest axial inward filling cuboid obtained for the original feasible domain as the first layer of cuboids. This cuboid divides the N-dimensional original feasible domain into 2D sub-regions. The largest axial inward filling cuboid obtained for each sub-region is called the second layer of cuboids. The nth layer has a total of (2D) n-1 axial cuboids, each cuboid is divided into at most 2D sub-regions, and the maximum axial inner filling cuboids are calculated for these sub-regions to form the n+1th layer of cuboids. The oth cuboid in the nth layer is recorded as 9. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 4, characterized in that: In step S3, the Minkowski sum calculation for the cuboids with different adjustable resources at the same level and in the same direction is specifically as follows: It is assumed that the rectangular blocks in the same layer y along the same axis have the same number z, and the represents the Minkowski sum of W adjustable resources in the same layer and in the same direction. According to the Minkowski sum property, It is also a cuboid in space. Represents the zth cuboid in the yth layer.

10. The cuboid convex hull method for heterogeneous adjustable resource aggregation according to claim 5, characterized in that: The calculation of step S4 is specifically as follows: The convex hull updated after each cycle of all surfaces of the original convex hull is called a surface generation. The convex hull after k surface generation cycles is recorded as Assumptions The equation of a surface of is α T Q = υ, finding the point farthest from the outside of the surface is equivalent to the following optimization problem: stQ∈V a T Q>y Among them, V represents all The vertex set of , dd represents the distance, α coefficient matrix, Q represents the vertex, υ represents the outer side of the convex hull; Find the farthest point Q outside a surface of the convex hull * Then, use the existing convex hull and this point Q * Construct a new convex hull; First, we need to determine the surface whose convex hull needs to be replaced. Assume The sth surface equation of is α s T Q=υ s , then the inner side of the convex hull is α s T Q<υ s The criteria for deleting the surface are: a s T Q * -u s >0 By looping over the existing convex hull Surfaces, you can find all the surfaces that need to be deleted; Then use all the vertices of the surface that need to be replaced and the farthest point Q * Generate a new incremental convex hull Finally, merge and constitute

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