CN111724034B - Power distribution network planning scheme evaluation method based on safety domain body surface ratio and roundness - Google Patents
Power distribution network planning scheme evaluation method based on safety domain body surface ratio and roundness Download PDFInfo
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Abstract
The invention discloses a power distribution network planning scheme evaluation method based on a security domain body surface ratio and roundness degree, which mainly comprises the following steps: calculating the projection coefficient of a safety boundary for a given known power distribution network; reducing the dimension of the safety boundary and calculating the area of the safety boundary; defining and calculating the surface area, the volume, the surface ratio and the roundness of the whole security domain, wherein the surface area of the security domain is the sum of all the security boundary areas, and the surface ratio of the security domain is the reciprocal of the required surface area when the security domain is surrounded into a unit volume; security domain roundness is the degree describing a euclidean geometry or a degree of approximation to a circle on a security domain geometry; and evaluating the advantages and disadvantages of the security domain from the aspect of domain shape efficiency, and further evaluating the advantages and disadvantages of the power distribution network and a power distribution network planning scheme, namely, under the same-scale power distribution network, the larger the body surface ratio is, the smaller the surface area required by the domain shape is, and the larger the degree of being close to a circle is. The body surface ratio and the roundness of the DSSR have application value in planning and running. In the planning of the power distribution network, the power distribution network with a large body surface ratio and a large degree of roundness is selected.
Description
Technical Field
The invention belongs to power distribution network planning, and particularly relates to a method for evaluating a security domain and a power distribution network planning scheme.
Background
A Distribution network Security Region (DSSR) is a set of all operating points of a Distribution network that meet certain Security criteria, and has a closed boundary, all of which are secure within the boundary and all of which are non-secure outside the boundary. The DSSR provides a new basic theory for planning and operating the power distribution network. DSSR is a high-dimensional geometry in the operating state space of a distribution network. Existing research observations have found some geometric features of DSSR: DSSR is a super-geometric body formed by a series of super-planes which are approximately linear, compact and can not be knotted and coordinate axis planes[1](ii) a The common DSSR two-dimensional view presents images of triangle, trapezoid, pentagon and the like[2](ii) a By volume[3]Equivalent radius of[4]Area of domain-shaped spiral graph[5]The overall size of the domain may be described. Document [3]The volume definition of the DSSR is provided, and two matches with equal maximum power supply capacity are foundThe power grid has obvious difference in the volume of a security domain, and a power distribution network with large domain volume has better security performance.
[ reference documents ]
[1] The intelligent distribution network N-1 safety boundary topology property and boundary algorithm [ J ]. the chinese electro-mechanical engineering newspaper, 2014, 34 (04): 545-554.
[2] The power system automation, 2019, 24 (43): 96-103.
[3] The volume of a safety domain of a power distribution system [ J ]. Chinese Motor engineering bulletin, 2017, 37 (08): 2222-2231.
[4] The power distribution network safety domain is observed in a full-dimensional manner [ J ] in the power system automation, 2018, 42 (16): 73-79.
[5] Zhang Bao Qiang, observation method and property mechanism research of distribution network security domain [ D ]. Tianjin university, 2019.
[6] Liu, calculation of high-dimensional space surface score of the first category and median theorem [ J ]. sheng yang university of science, 2012, 31 (03): 43-46.
[7] The severe, shoujuan, zhangliyuan, et al, strict and non-strict safety boundary of power distribution networks [ J ] electrotechnical technical report, 2019 (12): 2637-2648.
[8] The evaluation method of the safe operation range of the distribution network N-1 based on the volume of the safety domain comprises the following steps: china, 201510992296.4[ P ].2016-05-04.
[9]Zhufang Yuan, He bin Wu, Fu lp (C)n) Volume of unit sphere in space and its asymptotic properties [ J]Apply math and computational math report, 2016, 28 (01): 47-52.
Disclosure of Invention
In view of the prior art, the invention provides a power distribution network planning scheme evaluation method based on a security domain surface area ratio and circularity, wherein the surface area definition of a power distribution network security domain DSSR is provided, and a first-class curved surface integral in a high-dimensional space is used for reference[6]Calculating and providing a DSSR surface area calculation method for dimensionality reduction sampling; combined DSSR volume researchThe body surface ratio definition is further provided. The body surface ratio may characterize the overall shape of the DSSR. And the roundness degree of the security domain is defined by directly comparing the body surface ratio parameters of the European geometric figure under the same dimension. The degree of roundness can quantify the degree that the security domain of the power distribution network is close to a circle in the same dimension and different dimensions. The circle has the highest graphic efficiency, and the larger the roundness value of the security domain is, the higher the security domain shape is close to the circle is, and the higher the shape efficiency of the domain is. In conclusion, by utilizing the body surface ratio and the roundness, the advantages and disadvantages of the security domain can be evaluated from the aspect of domain shape efficiency, and further the advantages and disadvantages of the power distribution network and the power distribution network planning scheme can be evaluated.
In order to solve the technical problems, the invention provides a power distribution network planning scheme evaluation method based on a safety domain body surface ratio and roundness degree, which comprises the following steps:
1) calculating the projection coefficient of a safety boundary for a given known power distribution network;
2) reducing the dimension of the safety boundary and calculating the area of the safety boundary;
3) defining and calculating the surface area, the volume, the body surface ratio and the roundness of the whole security domain;
defining the surface area of the safety domain as the sum of all safety boundary areas;
defining the surface area ratio of the security domain as the reciprocal of the required surface area when the security domain of unit volume is enclosed;
defining the security domain roundness degree to describe the degree of the European geometric figure or the security domain geometric shape approaching to a circle;
4) and evaluating the advantages and disadvantages of the power distribution network and the power distribution network planning scheme by comparing the body surface ratio and the roundness of the power distribution network with different contact modes and network parameters.
Furthermore, in the method for evaluating the power distribution network planning scheme,
step 1) the process of calculating the projection coefficient of the safety boundary is as follows: given a given distribution network, the analytic expression of a certain safety boundary i is as follows:
in the formula (1), ciFor element capacity, y is the operating point vector (F)1,F2……Fn)，FiThe feeder load is the size, m is the number of boundaries, and n is the number of feeder/feeder segments;
the projection coefficient k of the safety margin iseiCalculated from the following formula:
in the formula (2), J is a Jacobian matrix and satisfies the following conditions:
step 2) the process of reducing the dimension of the safety boundary and calculating the area of the safety boundary is as follows: take the medium constraint f (y) c in equation (1)i1 variable FjWill FjBy dividing F by variables contained in equality constraintsjOther variables FkShows that k ≠ j, and substitutes formula (1) again, eliminating all FjObtaining boundary B 'after 1D reduction'seiAnd calculating the size of the boundary i after dimensionality reduction according to a Monte Carlo algorithm shown in an equation (4):
in the formula (4), Total ' is the Total sampling point number, v ' is the number of boundary points in all sampling points, v '/Total ' represents the ratio of the security domain volume after dimensionality reduction in the Total capacity space, C is the maximum value of the feeder capacity, C is the Total value of the Total capacity, V is the number of the boundary points in all sampling points, V ', V is the ratio of the security domain volumen-1Then representing the size of the space capacity after dimension reduction;
the area of boundary i is calculated by:
step 3) calculating the surface area, the volume, the body surface ratio and the roundness of the whole security domain comprises the following steps: the surface area of the security domain is SDSSR：
The volume of the safety domain is VDSSR：
In the formula (7), Total is the Total sampling point number, v is the number of safety points in all sampling points, v/Total represents the ratio of the safety domain volume in the Total capacity space, C is the maximum value of the feeder capacitynThen the size of the total capacity space is indicated;
the body surface ratio of the security domain is CDSSR：
In the formula (8), n is the spatial dimension of the power distribution network security domain and is equal to the number of feeder lines/feeder line sections;
let the surface ratio of the security domain in the n-dimensional Euclidean space be CDSSRThe surface ratio of the n-dimensional sphere is CoThe circularity R of the security domainDSSRCalculated from the following formula:
in the formula (9), CoSatisfies the following conditions:
in step 4), the conclusion of the evaluation is: the safety domain shape efficiency and the body surface ratio of the whole safety domain are in direct proportion to the degree of roundness, wherein the degree of roundness and the body surface ratio are in a positive correlation relationship, and the larger the body surface ratio is, the larger the degree of roundness is.
Compared with the prior art, the invention has the beneficial effects that:
according to the power distribution network planning scheme evaluation method, the body surface ratio and the roundness degree are defined, and the degree that the security domain of the power distribution network is close to the roundness under the same dimensionality and different dimensionalities is quantified. For a power distribution network with a given network structure and network parameters, the method can calculate the surface area, the surface ratio and the roundness of the security domain meeting the N-1 security criterion, and can evaluate the advantages and disadvantages of the security domain from the aspect of domain shape efficiency so as to evaluate the advantages and disadvantages of the power distribution network and a power distribution network planning scheme.
The invention provides the geometric indexes of the DSSR, namely the body surface ratio and the roundness degree, based on the calculation of the DSSR surface area of the dimensionality reduction sampling and the combination of the DSSR volume. The volume can be compared with the safe operation range of the power distribution network under the same scale; the surface area can be compared with the critical operation range of the power distribution network under the same scale; the body surface ratio can be compared with the surface size required by the unit volume of the power distribution network under the same scale; the degree of roundness can be compared with the degree that the shape of the distribution network security domain is close to that of a circle under different scales. Under the same-scale electric network, the larger the body surface ratio is, the smaller the surface area required for enclosing the domain shape is, and the larger the degree of approaching to a circle is. The body surface ratio and the roundness of the DSSR have application value in planning and running. In the planning of the power distribution network, the power distribution network with a large body surface ratio and a large degree of roundness should be selected.
Drawings
FIG. 1 is a block flow diagram of a power distribution network planning scheme evaluation method of the present invention;
FIG. 2 is a wiring diagram of distribution network A in an embodiment of the present invention;
fig. 3 is a wiring diagram of a distribution network B in the embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, which are not intended to limit the invention in any way.
As shown in fig. 1, the method for evaluating a power distribution network planning scheme based on the safety domain surface ratio and the roundness degree provided by the invention comprises the following 4 steps:
step one, calculating a projection coefficient of a safety boundary
Knowing the analytical expression of a certain safety margin i for a given distribution network[7]The following were used:
in the formula ciFor element capacity, y is the operating point vector (F)1,F2……Fn)，FiThe feeder load is, m is the number of boundaries, and n is the number of feeder/feeder segments.
The projection coefficient k of the boundary iseiIt can be calculated from the following formula:
j is a Jacobian matrix and satisfies the following conditions:
step two, reducing the dimension of the safety boundary and calculating the area of the safety boundary
Take the medium constraint f (y) c in equation (1)i1 variable FjWill FjBy dividing F by variables contained in equality constraintsjOther variables Fk(k ≠ j) is shown), then formula (1) is substituted, all F are eliminatedjObtaining boundary B 'after reducing to 1 dimension'sei. The size of the boundary i after dimensionality reduction is according to the document [8]]The Monte Carlo algorithm, the calculation formula is as follows:
wherein, Total 'is the Total sampling point number, v' is the number of boundary points in all sampling points, v '/Total' represents the volume of the security domain after dimensionality reduction in the Total capacityC is the maximum value of the capacity of the feeder line, Cn-1It represents the size of the space capacity after dimensionality reduction.
The area of boundary i can be finally calculated by:
step three, calculating the surface area, the volume, the body surface ratio and the roundness of the whole safety domain
1) The surface area defining a safety domain is the sum of all safety boundary areas, denoted SDSSR。
2) According to document [8], the volume calculation formula of the safety domain is as follows:
wherein, Total is the Total sampling point number, v is the number of safety points in all sampling points, v/Total represents the ratio of the safety domain volume in the Total volume space, C is the maximum value of the feeder volumenIt represents the size of the total capacity space.
3) Defining the surface ratio of the security domain as the reciprocal of the surface area required by the security domain enclosing a unit volume, and recording the reciprocal as CDSSRAnd satisfies the following conditions:
where n is the DSSR spatial dimension, equal to the number of feeders/feeder segments.
4) And (3) proposing a definition of the roundness by combining the body surface ratio: describes the degree to which a euclidean geometry or security domain geometry is close to a circle in shape. Let the surface ratio of the security domain in the n-dimensional Euclidean space be C, n-dimensional sphere[9]Body surface ratio of CoSecurity region of degree of circularity ofRDSSRSatisfies the following conditions:
in the formula CoSatisfies the following conditions:
and step four, comparing the body surface ratio and the roundness of the distribution network with different contact modes and network parameters, wherein the body surface ratio and the roundness form a positive correlation relationship. The larger the body surface ratio is, the larger the roundness is, the smaller the surface area required by the security domain enclosed in unit volume is, the closer the shape is to a circle, and the security domain shape efficiency is higher.
Example (b):
two equal-scale, comparable distribution networks a and B were constructed, as shown in fig. 2 and 3. The main transformer capacity, the number of the distribution networks A and B, the feeder capacity and the number of the feeders are the same, and only the contact modes are different. The network parameters are as follows: 4 35kV/10kV transformer substations and 8 main transformers, wherein the main transformer capacity is 20 MVA; and 24 feedback lines are provided, and the capacity of each feedback line is 9 MVA.
Distribution network B is formed by changing part of the contact positions on the basis of distribution network a, as shown by the dashed lines in fig. 3. The two links are connected between stations, but the connection positions are different, so that the matching relation is different. The matching of the main transformer capacity and the feeder capacity of the distribution network A and the distribution network B is shown in the table 1.
TABLE 1. proportion of matching of main transformer capacity in distribution network
The first step is as follows: according to the method of the document [7], a safety boundary expression is written, as shown in a formula (1). The projection coefficients for each boundary are obtained from equations (2) and (3). Taking boundary 1 as an example, the safety boundary expression is as follows:
the projection coefficient calculation process is as follows:
other security boundary calculation methods are similar, and tables 2 and 3 show all security boundary projection coefficients of the distribution network A, B.
TABLE 2 distribution network A safety boundary projection coefficients
TABLE 3 projection coefficients of each safety boundary of distribution network B
The second step is that: and reducing the dimension of the safety boundary, sampling and calculating the area of the safety boundary.
Taking boundary 1 as an example, the dimension reduction is performed on boundary 1, namely the following equivalent substitution is performed: f1＝RF1-F13All of F1By F13Alternatively, boundary B 'after dimensionality reduction for boundary 1 can be obtained'se1The expression is as follows:
assuming that the total number of sampling points is 1000000, the boundary is sampled 10 times to reduce the calculation error, and the result is shown in table 4.
Table 410 subsampled data
The number of sampling points of 10 times is averaged, the average number of sampling points is 256.5, and therefore, the size of the boundary 1 after dimensionality reduction is as follows:
thus, the area of boundary 1 is:
Ssei＝ksei×V′se1＝1.414×2.565×1018＝3.215×1018MVA23
in other boundary calculation methods, tables 5 and 6 show the safety boundary areas of the distribution network a and the distribution network B.
TABLE 5 distribution network A boundary area
Table 6 distribution network B boundary area
The third step: calculating the surface area, volume, surface ratio and roundness of the whole security domain
The safety margin surface areas were obtained by summing all safety margin areas of tables 5 and 6, respectively.
According to the document [8], the average sampling point number of the distribution network a security domain is 119.1, the average sampling point number of the distribution network B security domain is 180.8, and the volume calculation result of the security domain is as follows:
from equation (8), the body surface ratio is calculated:
according to the formula (10), when n is 24, the circular body surface ratio CoWhen the result is 0.0541, the degree of roundness is calculated by equation (9).
Table 7 surface area of distribution grid A, B and related results
The fourth step: comparing the body surface ratio and the roundness of the distribution network with different contact modes and network parameters
From table 7, these two distribution networks of the same size and different contact locations have the same TSC, but the security domains are significantly different:
(1) and compared with the distribution network A, the distribution network B increases the domain volume by 1.52 times and increases the surface area by 1.36 times.
(2) The distribution network B has larger body surface ratio, higher roundness, higher domain shape efficiency and smaller surface area required by unit volume. In conclusion, the distribution network B of the planning scheme is superior to the distribution network A.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.
Claims (1)
1. A power distribution network planning scheme evaluation method based on a safety domain body surface ratio and roundness degree is characterized by comprising the following steps:
1) calculating the projection coefficient of a safety boundary for a given known power distribution network;
2) reducing the dimension of the safety boundary and calculating the area of the safety boundary;
3) defining and calculating the surface area, the volume, the body surface ratio and the roundness of the whole security domain;
defining the surface area of the safety domain as the sum of all safety boundary areas;
defining the surface area ratio of the security domain as the reciprocal of the required surface area when the security domain of unit volume is enclosed;
defining the security domain roundness degree to describe the degree of the European geometric figure or the security domain geometric shape approaching to a circle;
4) evaluating the advantages and disadvantages of the power distribution network and a power distribution network planning scheme by comparing the body surface ratio and the roundness of the power distribution network with different contact modes and network parameters;
in step 1), the process of calculating the projection coefficient of the safety boundary is as follows:
given a given distribution network, the analytic expression of a certain safety boundary i is as follows:
in the formula (1), ciFor element capacity, y is the operating point vector F1,F2……Fn，FiThe feeder load is the size, m is the number of boundaries, and n is the number of feeder/feeder segments;
the projection coefficient k of the safety margin iseiCalculated from the following formula:
in the formula (2), J is a Jacobian matrix and satisfies the following conditions:
in step 2), the process of reducing the dimension of the safety boundary and calculating the area of the safety boundary is as follows:
take the medium constraint f (y) c in equation (1)i1 variable FjWill FjBy dividing F by variables contained in equality constraintsjOther variables FkShows that k is not equal to j, and then substituted with formula (1) to eliminate all FjObtaining boundary B 'after reducing to 1 dimension'seiAnd calculating the size of the boundary i after dimensionality reduction according to a Monte Carlo algorithm shown in an equation (4):
in the formula (4), Total' is the Total sampleThe number of points, v ' is the number of boundary points in all sampling points, v '/Total ' represents the ratio of the volume of the security domain after dimensionality reduction in the Total capacity space, C is the maximum value of the capacity of the feeder line, C is the maximum value of the capacity of the security domain, Cn-1Then representing the size of the space capacity after dimension reduction;
the area of boundary i is calculated by:
in the step 3), the process of calculating the surface area, the volume, the body surface ratio and the roundness of the whole security domain is as follows:
the surface area of the security domain is SDSSR：
The volume of the safety domain is VDSSR：
In the formula (7), Total is the Total sampling point number, v is the number of safety points in all sampling points, v/Total represents the ratio of the safety domain volume in the Total capacity space, C is the maximum value of the feeder capacitynThen the size of the total capacity space is indicated;
the body surface ratio of the security domain is CDSSR：
In the formula (8), n is the spatial dimension of the power distribution network security domain and is equal to the number of feeder lines/feeder line sections;
let the surface ratio of the security domain in the n-dimensional Euclidean space be CDSSRThe surface ratio of the n-dimensional sphere is CoThe circularity R of the security domainDSSRCalculated from the following formula:
in the formula (9), CoSatisfies the following conditions:
in the step 4), the evaluation of the power distribution network and the power distribution network planning scheme is as follows: the safety domain shape efficiency and the body surface ratio of the whole safety domain are in direct proportion to the degree of roundness, wherein the degree of roundness and the body surface ratio are in a positive correlation relationship, and the larger the body surface ratio is, the larger the degree of roundness is.
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