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CN112736914B - Available transmission capacity probability calculation method considering wind power correlation - Google Patents

Available transmission capacity probability calculation method considering wind power correlation Download PDF

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Publication number
CN112736914B
CN112736914B CN202011594967.9A CN202011594967A CN112736914B CN 112736914 B CN112736914 B CN 112736914B CN 202011594967 A CN202011594967 A CN 202011594967A CN 112736914 B CN112736914 B CN 112736914B
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atc
power
wind power
output
correlation
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CN112736914A (en
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宋晓喆
姜涛
李雪
李佳奇
陈厚合
张儒峰
李国庆
李本新
孙福寿
傅吉悦
许铎
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State Grid Jilin Electric Power Corp
Northeast Electric Power University
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Northeast Dianli University
State Grid Jilin Electric Power Corp
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

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  • Power Engineering (AREA)
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Abstract

The invention discloses a wind power correlation-related available transmission capacity probability calculation method, which comprises the following steps of: obtaining a wind power output sample considering wind power correlation based on the conditional probability and a Copula function, and taking historical load data as a load sample set; calculating the ATC under each scene through an ATC double-layer optimization model by using the wind power output sample and the load sample set; judging whether the output of the unit in the power transmission area under the current scene reaches the upper limit or not, if the output of all the units reaches the upper limit and only the power transmission line does not reach the transmission capacity limit, removing the current scene, and recording the ATC under the effective scene, wherein other scenes are effective scenes; and performing probability density fitting on ATC results in all effective scenes, and analyzing the influence of correlation on ATC. The invention realizes the accurate and rapid calculation of the ATC between the areas.

Description

Available transmission capacity probability calculation method considering wind power correlation
Technical Field
The invention relates to the field of power systems, in particular to an Available Transfer Capability (ATC) probability calculation method for power system inter-area considering wind power correlation.
Background
In recent years, with the rapid development of renewable energy sources, a global power system is seriously changed, the national wind power installed capacity is estimated to reach 14.4 hundred million kilowatts in 2050, and the new energy power generation accounts for 70 percent in the power generation installed ratio [1] . Wind power has become the fastest growing clean energy in the world as one of the most mature new energy power generation types. However, with the continuous expansion of the wind power grid-connected scale, the permeability of wind power in the power grid gradually expands, and the strong uncertainty and intermittency of wind power output bring new challenges to the calculation of available transmission capacity between system regions.
The ATC between the areas of the power system, namely the transmission capacity of the system in a certain running state between fixed areas, can be accurately calculated, so that the safe running of the system can be ensured, and other reliability problems such as overload and the like of the system are avoided [2] And the cost benefit of the transmission network can be improved to a certain extent. Mathematically, the ATC is the difference between the Total Transmission Capacity (TTC) and the Existing transmission protocols (ETC), the Capacity Benefit Margin (CBM), and the Transmission Reliability Margin (TRM) [3] 。
The solving calculation methods of the existing research can be divided into two types: deterministic solution method [4-6] And solving method based on probability [7-10] . The solution to determinism is single in the probabilistic methodThe solution method of the scenario, namely, the solution of the described problem is directly obtained by adopting an optimization method or other methods. The probabilistic-based solving method can comprehensively describe the power transmission capacity of the power grid under the influence of uncertainty factors, so that an ATC statistical index and a probability distribution curve thereof are obtained, and the probabilistic-based solving method is an effective tool for long-term planning and research of a system.
In the research, the ground state tidal current solutions are all given artificially, and the wind power correlation and the uncertainty are only considered in the ATC calculation model and are not considered in the ground state. Therefore, in order to calculate the ATC between the power grid regions under the condition of large-scale wind power integration more accurately, the consideration of wind power uncertainty and relevance in an ATC calculation model and an economic dispatching model simultaneously has important significance.
Disclosure of Invention
The invention provides a method for calculating the probability of available transmission capacity by taking wind power correlation into account, which realizes accurate and rapid calculation of the ATC between areas, and is described in detail in the following description: a method of calculating a probability of available transmission capacity taking into account wind-power correlations, the method comprising:
obtaining a wind power output sample considering wind power correlation based on the conditional probability and a Copula function, and taking historical load data as a load sample set;
calculating the ATC under each scene through an ATC double-layer optimization model by using the wind power output sample and the load sample set;
judging whether the output of the unit in the power transmission area under the current scene reaches the upper limit or not, if the output of all the units reaches the upper limit and only the power transmission line does not reach the transmission capacity limit, removing the current scene, and recording the ATC under the effective scene, wherein other scenes are effective scenes;
and performing probability density fitting on ATC results in all effective scenes, and analyzing the influence of correlation on ATC.
Wherein the ATC double-layer optimization model comprises: the upper ATC calculation model, the lower ETC calculation model and the wind power correlation and uncertainty are simultaneously considered in the ETC optimization model and the ATC calculation model.
Further, the ATC calculation model of the upper layer is calculated by maximizing power transmitted in the power generation area and the power receiving area and using an alternating current model.
The ATC calculation model of the upper layer specifically comprises the following steps:
Figure BDA0002870083190000021
Figure BDA0002870083190000022
Figure BDA0002870083190000023
Figure BDA0002870083190000024
Figure BDA0002870083190000026
Figure BDA0002870083190000027
Figure BDA0002870083190000028
Figure BDA0002870083190000029
Figure BDA00028700831900000210
Figure BDA00028700831900000211
Figure BDA0002870083190000031
Figure BDA0002870083190000032
Figure BDA0002870083190000033
where Ψ represents the set of all nodes in the power system; omega l Represents a set of all branches in the power system; source is the power generation area;
Figure BDA00028700831900000313
and
Figure BDA00028700831900000314
respectively the output of the generator, the output of the wind turbine generator and the load;
Figure BDA00028700831900000315
reactive load for node i; m is a group of il The element of the ith row and the ith column of the node branch power flow incidence matrix is taken as the element of the ith row and the ith column of the node branch power flow incidence matrix; m loss,il The ith row and the l column of elements of the node branch network loss incidence matrix are set; c is a branch circuit incidence matrix; u. u i Represents the square of each node voltage;
Figure BDA0002870083190000034
and
Figure BDA0002870083190000035
respectively representing the upper limit and the lower limit of the voltage of each node; p loss,l And Q loss,l Line loss; limit is the transmission Limit of the line l; r l And X l Respectively the resistance and reactance of each branch circuit; p is e,l And Q e,l The power flow of each branch circuit respectively; u. of e,i To receiveThe square term of the terminal voltage; p i The output of a conventional unit under the ground state, P wi The force, P, of the wind-power unit in the ground state Di Load level in the ground state, in MW; c is the cost of power generation of the conventional unit, c wi The cost of electricity generated by a wind turbine in units of $ MW; GSF l-i Is the power generation transfer coefficient from node i to line l;
Figure BDA0002870083190000036
the upper and lower limits of the output of the conventional unit;
Figure BDA0002870083190000037
the output power of the wind turbine generator is the upper limit;
Figure BDA0002870083190000038
and
Figure BDA0002870083190000039
respectively the output of a conventional generator and the reactive output of a wind turbine generator; l e,l Intermediate variables required for linearizing the model;
Figure BDA00028700831900000310
the upper and lower limits of the output of the conventional unit;
Figure BDA00028700831900000311
and
Figure BDA00028700831900000312
the output power of the wind turbine generator is the upper limit and the lower limit of the output power of the wind turbine generator.
The technical scheme provided by the invention has the beneficial effects that:
1. the wind power uncertainty and the correlation are simultaneously considered in the ATC calculation model and the economic dispatching model, so that a more accurate calculation result is obtained;
2. the invention provides a data-driven wind power correlation modeling method based on historical data, which analyzes the wind power output probability distribution characteristics and the spatial correlation, and further discloses the complex relationships of the outputs of different wind power plants in multiple regions;
3. the invention adopts an alternating current model in an ATC calculation model, and converts a nonlinear optimal power flow model into a second-order cone programming model through convex relaxation; in the process of calculating the ATC, the double-layer model is converted into a mixed integer second-order cone programming, and the problem that a global optimal solution is difficult to solve by nonlinear programming is solved.
Drawings
FIG. 1 is a flowchart of ATC calculation;
FIG. 2 is a sample wind power scenario;
FIG. 3 is a sample wind power scene probability density curve;
FIG. 4 is a probability density curve corresponding to the output of the wind farm 1 and the wind farm 2 when the correlation of the output between the wind farms is calculated;
FIG. 5 is a wind power scenario generation that accounts for correlation;
FIG. 6 is a diagram of an example system for IEEE-30 node standard;
FIG. 7 is an ATC probability density distribution curve under different scenarios;
FIG. 8 is an ATC probability density distribution curve of wind power plant integration under different correlation coefficients in a power transmission region;
FIG. 9 is an ATC probability density distribution curve of wind farm integration under different correlation coefficients of a powered region.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
In order to calculate the inter-regional ATC of the power grid under the condition of large-scale wind power integration more accurately, the embodiment of the invention provides a wind power correlation-considering method for calculating the inter-regional ATC probability of the power system.
Firstly, processing historical data by using a conditional probability principle, and modeling wind power correlation by using a Copula function; secondly, the calculation process of the ATC between the areas relates to the calculation of the maximum power transmission capacity and the existing power transmission protocol, so the embodiment of the invention provides an ATC double-layer optimization model, wherein the upper layer model is an ATC calculation model, the lower layer model is an ETC calculation model, the wind power correlation and the uncertainty are simultaneously considered in the ETC optimization model and the ATC calculation model, and on the basis, the lower layer model is converted by using the Karush-Kuhn-Tucker (KKT) optimal condition, namely the double-layer model is converted into a balanced Constraint Mathematical Programming (MPEC) model; converting the MPEC model into a mixed integer second-order cone programming problem, and solving by using a commercial solver; and finally, carrying out probability calculation on the inter-region ATC taking the wind power correlation into account by adopting Monte Carlo simulation.
Example 1
The embodiment of the invention provides a method for calculating an ATC probability between power system areas by taking wind power correlation into account, the specific flow is shown in figure 1, and the method comprises the following steps:
101: obtaining a wind power output sample considering wind power correlation based on a conditional probability principle and a Copula function, and taking historical load data as a load sample set;
102: calculating the ATC in each scene through an ATC double-layer optimization model by using the wind power output sample and the load sample set which are obtained in the step 101 and are used for calculating the wind power correlation;
103: and judging whether the unit output of the power transmission area under the current scene reaches the upper limit, if the unit output reaches the upper limit and only the power transmission line does not reach the transmission capacity limit, removing the current scene (namely an invalid scene), and recording the ATC under the valid scene, wherein other scenes are valid scenes.
104: and after the screening is finished, performing probability density fitting on ATC results in all effective scenes, and analyzing the influence of the correlation on the ATC.
In summary, in the embodiment of the present invention, the double-layer optimization model taking the wind power correlation into account is used to perform probability calculation on the ATC between the power grid regions through the steps 101 to 104, and the wind power uncertainty and the correlation are considered in the ATC calculation model and the economic dispatch model at the same time, so as to obtain a more accurate calculation result.
Example 2
The scheme of example 1 is further described below with reference to specific calculation formulas and examples, which are described in detail below:
201: analyzing wind power output probability distribution characteristics and spatial correlation based on wind power historical measured data, revealing complex relationships of output of different wind power plants in multiple regions, and constructing a wind power output probability model considering the spatial correlation on the basis;
wherein, this step 201 includes:
1) And (3) fitting historical wind speed data based on a conditional probability principle:
firstly, a reference wind field is selected, and probability distribution of each wind power plant based on the reference wind field is obtained, wherein the probability distribution is shown in formula (1).
Figure BDA0002870083190000051
In the formula: b represents a reference wind farm; m is a wind field to be solved; n is the total number of the wind power plants;
Figure BDA0002870083190000052
representing wind speed.
By taking one wind power plant as a reference and using the conditional probability formula (1), the probability distribution of other wind power plants in the fixed output range of the reference wind power plant can be calculated according to historical data.
From the known historical wind speed data, a kernel density estimation method can be used to further solve the samples considering the correlation between the powers. Setting the output of a certain wind power plant as a random variable X, wherein a sample point is in a vector form (X) 1 ，x 2 ，…，x N ) The sample length is N, the probability density function is f (x), and the kernel density estimation formula is shown in formula (2):
Figure BDA0002870083190000053
in the formula: h is the length of the sliding window and h is greater than 0; and K (-) is a kernel function, and the cumulative probability distribution function of the corresponding variable can be obtained by integrating f (x).
2) Modeling the wind speed correlation based on a Copula function:
the multivariate joint probability distribution is established through the Copula function, and the spatial correlation among the wind power plants can be modeled. There are various Copula functions, and different Copula functions are suitable for describing different types of correlation coefficients, and usually, the Copula function needs to be optimized, and the best Copula function is selected for fitting. The index for measuring the fitting effect is generally Euclidean distance d, and the smaller d is, the closer the Copula function is to the actual empirical probability distribution function is; in addition, the fitting effect can be measured by other correlation indexes, such as Spearman and Kendall correlation coefficients and the like.
The embodiment of the invention selects a t-Copula function for fitting, and is characterized by symmetrical distribution and capability of reflecting tail correlation, the parameters in the t-Copula are taken as a certain deterministic function of time for modeling, the deviation caused by model assumed errors is reduced, and the two-dimensional t-Copula function is shown as a formula (3):
Figure BDA0002870083190000061
in the formula: f is an edge distribution function of the random variable x; g is an edge distribution function of a random variable y; rho is a correlation coefficient;
Figure BDA0002870083190000062
is the inverse function of the unitary t distribution function with the degree of freedom k; s is a corresponding variable; in the two-dimensional t-Copula function, F and G follow a t distribution. After the marginal probability distribution of the dependent variables is obtained through calculation, the parameters of the t-Copula model can be obtained through calculation of the formula (3).
3) Wind power scene generation method considering correlation
Fitting the t-Copula function parameters to obtain a corresponding t-Copula function, and sampling the t-Copula function to obtain an initial wind power scene gamma 1 The matrix form is shown in formula (4):
Figure BDA0002870083190000063
in the formula: x is a wind power output value; n represents the total number of wind farms; n represents the total number of wind farm output sequences. The row vectors represent output sequences of different wind power plants, the column vectors represent wind power output calculated based on a certain reference wind power place, and different column vectors contain spatial correlation information among the wind power plants. And calculating the correlation coefficient of the obtained sample, comparing the obtained result with the difference value of the correlation coefficient of the original data, and verifying by adopting a Spearman or Kendall correlation coefficient.
202: calculating the ATC between areas by adopting an ATC double-layer optimization model, and respectively considering the influence of wind power correlation on the ATC in an upper-layer ATC calculation model and a lower-layer ETC calculation model;
wherein the step 202 comprises:
1) ATC computing framework overview
The upper layer model is an ATC calculation model, and the power transmitted between the power generation area and the power receiving area is maximized. Thus, the ATC computational model can be expressed as the following nonlinear programming problem:
max f 1 (x,u) (5)
s.t.g 1 (x,u)＝0 (6)
h 1 (x,u)≤0 (7)
in the formula: objective function f 1 (x, u) represents maximizing the transmitted power from the power generation area to the power reception area; equality constraint and inequality constraint comprise a power balance equation, node voltage constraint, branch thermal stability limit and the like, and x and u are respectively a state variable and a control variable in the model; g is a radical of formula 1 (x, u) is the set of all equality constraints in the upper model, h 1 (x, u) is the set of all inequality constraints in the upper model.
In the lower model, the embodiment of the invention calculates the ETC based on the economic dispatching model, the economic dispatching model determines the ETC and the ground state power flow, and the economic dispatching model based on the direct current optimal power flow can be expressed as the following Linear Programming (LP) problem:
min f 2 (x,u) (8)
s.t.g 2 (x,u)＝0 (9)
h 2 (x,u)≤0 (10)
in the formula: objective function f 2 (x, u) represents minimizing the total cost of power generation; equations (9) and (10) are direct current flow equality and inequality constraint, and x and u are respectively a state variable and a control variable in the model; g is a radical of formula 2 (x, u) is the set of all equality constraints in the underlying model, h 2 (x, u) is the set of all inequality constraints in the underlying model.
2) Double-layer ATC calculation model
The ATC double-layer optimization model is specifically set forth. Wherein, the ATC in the upper layer model maximizes the power transmitted in the power generation area and the power receiving area and adopts the AC model to calculate, because the traditional AC power flow model comprises: nonlinear and non-convex constraints are adopted, and solving is difficult, so that second-order cone transformation is carried out on a nonlinear term, and loop phase angle constraints in a grid model of the power transmission network are considered.
The ATC two-layer optimization model is specifically shown as follows, equations (11) - (23) are upper-layer ATC calculation models, and equations (24) - (28) are lower-layer ETC calculation models:
Figure BDA0002870083190000081
Figure BDA0002870083190000082
Figure BDA0002870083190000083
Figure BDA0002870083190000084
Figure BDA0002870083190000085
Figure BDA0002870083190000086
Figure BDA0002870083190000087
Figure BDA0002870083190000088
Figure BDA0002870083190000089
Figure BDA00028700831900000810
Figure BDA00028700831900000811
Figure BDA00028700831900000812
Figure BDA00028700831900000813
Figure BDA00028700831900000814
Figure BDA00028700831900000815
Figure BDA00028700831900000816
Figure BDA00028700831900000817
Figure BDA00028700831900000818
in the ATC double-layer optimization model, psi represents the set of all nodes in the power system; omega l Represents a set of all branches in the power system; source is the power generation area;
Figure BDA00028700831900000819
and
Figure BDA00028700831900000820
respectively calculating the output power of a conventional generator, the output power of a wind turbine generator and the load in the ATC calculation model;
Figure BDA00028700831900000916
reactive load at node i for the power system; m il The element of the ith row and the ith column of the node branch power flow incidence matrix is taken as the element of the ith row and the ith column of the node branch power flow incidence matrix; m is a group of loss,il The ith row and the l column of elements of the node branch network loss incidence matrix are set; c is a branch circuit incidence matrix; u. of i Represents the square of each node voltage;
Figure BDA0002870083190000091
and
Figure BDA0002870083190000092
respectively representing the upper limit and the lower limit of the voltage of each node; p is loss,l And Q loss,l Line loss; limit is the transmission Limit of the line l; r l And X l Respectively the resistance and reactance of each branch circuit; p e,l And Q e,l The power flow of each branch circuit respectively; u. u e,i A square term of the receive terminal voltage; p is i The output of a conventional unit in the ground state, P wi The force, P, of the wind-power unit in the ground state Di Is the load level in the ground state, and has the unit of MW; c is the cost of generating electricity of the conventional unit, c wi The cost of electricity generated by a wind turbine in units of $ MW; GSF l-i The power generation transfer coefficient from the node i to the line l;
Figure BDA0002870083190000093
the upper and lower limits of the output of the conventional unit;
Figure BDA00028700831900000917
the output power of the wind turbine generator is the upper limit;
Figure BDA0002870083190000094
and
Figure BDA0002870083190000095
respectively the output of a conventional generator and the reactive output of a wind turbine generator; l. the e,l Intermediate variables required for linearizing the model;
Figure BDA0002870083190000096
the upper and lower limits of the output of the conventional unit;
Figure BDA0002870083190000097
and
Figure BDA0002870083190000098
the output power of the wind turbine generator is the upper limit and the lower limit of the output power of the wind turbine generator; after the above formula, ": "represents the dual variable corresponding to the constraint, wherein eta is the dual variable of the power balance equation;
Figure BDA0002870083190000099
and
Figure BDA00028700831900000910
dual variables related to the upper and lower limits of transmission power of the transmission line;
Figure BDA00028700831900000911
and
Figure BDA00028700831900000912
dual variables related to upper and lower limits of the generating capacity of the conventional unit;
Figure BDA00028700831900000913
and
Figure BDA00028700831900000914
and the dual variables are related to the upper and lower limits of the generated energy of the wind turbine generator.
The upper layer of the ATC double-layer optimization model adopts a second-order cone optimal power flow optimization model to solve the problem that the traditional alternating current optimal power flow model is not convex and difficult to solve. Equation (11) is to maximize the power transmitted in a designated area to obtain the ATC of the upper layer; equations (12) and (13) are power balance equations; equation (14) is a voltage drop equation; equations (15) and (16) are variables required for the conversion process; the formula (17) is a loop phase angle constraint, and because the power transmission network is an annular network, the power flow distribution in the network needs to be controlled through the constraint; the formula (18) is the constraint of the upper and lower limits of the node voltage; equation (19) is the upper and lower limit constraints for the reactive power considered; equation (20) is the upper and lower limit constraints of the line transmission power; equation (21) is a second order cone relaxation constraint; equations (22) and (23) are control variables for maximizing the accumulated value of the output of the power transmission region generator by increasing the load in the power reception region with the power transmission region generator and the power reception region load as control variables; equation (24) is to minimize the total power generation cost; equation (25) is the power balance equation; equation (26) is the upper and lower limits of the transmission power of the line; the formulas (27) and (28) are respectively the upper and lower limits of the output of the traditional unit and the upper and lower limits of the output of the wind generation unit.
3) MPEC conversion
The double-layer model is difficult to directly solve, is considered to be converted into a single-layer model for solving, and is converted into a single-layer mathematical problem with equilibrium constraint based on KKT optimal conditions, and the corresponding MPEC model can be expressed as follows:
Figure BDA00028700831900000915
Figure BDA00028700831900001022
Figure BDA0002870083190000101
Figure BDA0002870083190000102
Figure BDA0002870083190000103
Figure BDA0002870083190000104
Figure BDA0002870083190000105
Figure BDA0002870083190000106
Figure BDA0002870083190000107
Figure BDA0002870083190000108
the vertical sign ±) in the above constraints (32) to (37) indicates that the product of two vectors is equal to 0, and the left and right sides of ±) satisfy the condition of being equal to or greater than 0 at the same time.
4) Mixed integer second order cone programming
The MPEC model has complementary constraints and is a nonlinear model, so the nonlinear model can be converted into a mixed integer second order cone problem by introducing an auxiliary binary variable using a large M method (well known to those skilled in the art):
Figure BDA0002870083190000109
Figure BDA00028700831900001010
Figure BDA00028700831900001011
Figure BDA00028700831900001012
Figure BDA00028700831900001013
Figure BDA00028700831900001014
Figure BDA00028700831900001015
Figure BDA00028700831900001016
Figure BDA00028700831900001017
Figure BDA00028700831900001018
Figure BDA00028700831900001019
Figure BDA00028700831900001020
Figure BDA00028700831900001021
in the formula:
Figure BDA0002870083190000111
is a sufficiently large constant;
Figure BDA0002870083190000112
Figure BDA0002870083190000113
is an auxiliary binary variable.
203: probabilistic ATC calculation framework
After the ATC double-layer optimization model is converted into a single-layer model, the ATC calculation model under a certain wind power output scene can be simplified and expressed as formulas (51) to (53):
max ATC (51)
s.t.Aτ＝b (52)
Cτ≤d (53)
in the formula: τ are all variables in equations (38) - (50), equations (52), (53) represent equality and inequality constraints in models (38) - (50), and a, b, C, d are known parameters in equality and inequality constraints, respectively.
When there is a set of discrete wind power scenarios, the ATC computational model may be represented as:
max ATC s (54)
s.t.Aτ s ＝b (55)
Cτ s ≤d (56)
in the formula: tau is s All variables in (38) - (50) in the s-th wind power scene are shown.
Calculating ATCs (advanced control circuits) under all scenes by using a Monte Carlo method based on the proposed wind power probability output model considering wind power correlation, judging whether the output of the unit in the power transmission area of each scene reaches the upper limit, and removing the invalid scene if all the units reach the upper limit and the transmission line does not reach the transmission capacity limit; after screening is completed, probability density fitting is carried out on ATC results in all scenes, the influence of different correlations between the two wind power plants on ATC is analyzed, and the correlations represent the strength of the correlations between the two wind power plants by using correlation coefficients.
In summary, in the embodiment of the present invention, a double-layer optimization model taking wind power correlation into consideration is provided through the above steps 201 to 203 to perform probability calculation on the ATC between the grid regions, and the wind power uncertainty and the correlation are considered in the ATC calculation model and the economic dispatch model at the same time, so as to obtain a more accurate calculation result; based on historical data, a data-driven wind power correlation modeling method is provided; adopting an alternating current model in an ATC calculation model, and converting a nonlinear optimal power flow model into a second-order cone programming model through convex relaxation; in the process of calculating the ATC, converting the double-layer model into a mixed integer second-order cone plan; and finally, carrying out probability calculation on the inter-area ATC taking the wind power correlation into account by adopting Monte Carlo simulation.
Example 3
The feasibility verification of the solutions of examples 1 and 2 is carried out below with reference to the specific examples, fig. 2, fig. 3, fig. 4, fig. 5, fig. 6, fig. 7, fig. 8, fig. 9 and tables 1, 2, 3, as described in detail below:
this example was subjected to an arithmetic analysis based on the historical wind speed data of document [11 ]. Considering two wind power plants, namely a wind power plant W1 and a wind power plant W2, respectively, wherein the rated power of a single fan is 3MW, and assuming that each wind power plant is provided with 10 wind power generation units with the rated power of 3MW, processing data and analyzing the correlation of the data; and performing probability calculation on the inter-region ATC considering the wind power correlation by using an IEEE-30 node system, and verifying the effectiveness of the method.
1) Wind power correlation analysis
The output scenario for a single wind turbine of two wind farms is shown in fig. 2 (only the first 200 time points are shown). As can be seen from FIG. 2, the trends of the two sequence curves are basically the same, and it can be seen from the time sequence of the wind power output that the output variation trends of the two wind power plants have stronger correlation, so that the spatial correlation of the two wind power plants is stronger. FIG. 3 is a graph of the raw probability density curves of two wind farms calculated using a kernel density estimation method. The correlation coefficient between the two wind power plants is calculated to obtain the correlation coefficient of the two wind power plants as 0.94, and the spatial correlation between the two wind power plants is stronger as can be seen from the correlation coefficients of the wind power plants in fig. 2 and 3. If the wind power plant W1 is taken as a reference, the probability density of the wind power plant 2 when the output of a single fan of the W1 is in different ranges is calculated based on the conditional probability principle, and the obtained result is shown in FIG. 4. From the results of fig. 4, it can be seen that when the output of the W1 fan is in different ranges, the probability density curve of the W2 fan changes with the output of the W1 fan. On the premise of ensuring the correlation, a multivariate joint probability distribution is established through a Copula function to carry out a spatial correlation model between the wind power plants, and a wind speed sample is sampled, wherein the result is shown in fig. 5. As can be seen from the sampling result shown in fig. 5, the wind speed is concentrated on the diagonal line of 45 °, which indicates that the two regions have strong correlation, and the correlation coefficient is used for verification, which is almost the same as the correlation coefficient of the original sample, thereby verifying the validity of sampling.
2) Inter-region ATC probability calculation considering wind power correlation
In order to verify the accuracy and effectiveness of the ATC calculation model and the optimization algorithm considering the wind power correlation between the regions, the embodiment of the invention adopts a cvx modeling tool and a mosek solver to solve the optimization model, and calculates the ATC considering the wind power correlation between the regions based on an IEEE30 node system. The system of the example has 6 generators and 41 lines, the system is divided into 3 areas, namely a power generation area, a power receiving area and other areas, the capacity of 2 wind power plants is 30MW, and a topological diagram of the system is shown in FIG. 6.
The two wind power plants are respectively integrated at the nodes 2 and 5, and according to different generated wind power output scenes, after ATC of all scenes is obtained, the influence of the output correlation between the wind power plants on the ATC is emphatically analyzed through calculation of different indexes.
Calculating an ATC (advanced telecom computing) by utilizing historical wind speed data considering the correlation and a Copula function to generate a wind power output scene considering the correlation; table 1 shows statistical indexes of ATCs, and fig. 7 shows an ATC probability density curve fitted by a kernel density estimation method after all scene ATCs are obtained.
TABLE 1 ATC statistical index comparison calculation results
Figure BDA0002870083190000131
According to the data in the table 1, the influence of the wind power plant grid connection on the ATC between the areas can be judged through the expected value, and the fluctuation condition of the wind power plant grid connection is judged through the variance. Through comparison, the mean value of the wind power scene generated by historical data is 83.63MW and the variance is 5.31, while the mean value of the wind power scene generated by the Copula function is 82.77MW and the variance is 6.28; the extrema of the two schemes are the same. As can be seen from the two probability density curves in fig. 7 and the indexes in table 1, the probability density distribution curve of the inter-region ATC calculated directly by using the historical wind power output data considering the correlation and the wind power output samples obtained by sampling using the Copula function is substantially the same as the calculation index, which proves the correctness of the calculation of the inter-region ATC by the proposed method when the wind power correlation is considered.
3) Effect of different correlation coefficients on inter-region ATC
According to different positions of grid connection of the wind power plants, the influence of the large wind power plants on the ATC presents different characteristics. The embodiment of the invention emphasizes the calculation of the influence of different correlations of the wind power plant output on the ATC, and compares the following two conditions.
Case 1: two wind power plants are integrated at nodes 2 and 5 of a power generation area;
case 2: two wind farms are integrated at 8 nodes of the powered area and 11 nodes of the powered area.
The comparative analysis of case 1 and case 2 shows the influence of the relation number change on the ATC when the wind power plant is integrated in different areas, and the probability density distribution curves of the cases are shown in FIGS. 8 and 9.
TABLE 2 ATC statistical index comparison calculation results (case one)
Figure BDA0002870083190000132
TABLE 3 ATC statistical index comparison calculation results (case one)
Figure BDA0002870083190000133
The comparative analysis of the probability density distribution curves of fig. 8 and 9 and the indexes of table 2 and table 3 can be concluded as follows:
(1) As can be seen from the table 2, when the wind power plant is connected to the power transmission area, the correlation coefficient is increased from 0.5 to 1, and the mean value of the ATC is decreased from 83.82MW to 83.11MW along with the increase of the correlation coefficient; as can be seen from Table 3, when the wind farm is switched into the powered region, as the correlation coefficient is increased from 0.5 to 1, the mean value of ATC is decreased from 108.66MW to 95.98MW and then increased to 98.78MW as the correlation coefficient is increased; the influence of the correlation factors on the ATC mean value is different when the wind power plant is integrated in different areas.
(2) The wind power field integration position and the correlation factor have certain influence on the variance of the ATC, the variance can represent the fluctuation of the system, and when the wind power field is integrated in different areas, the wind power correlation also has certain influence on the fluctuation amplitude of the ATC.
It can be seen that when wind farms are integrated in different areas, the influence of the correlation factors on the probability calculation indexes of the ATC is also different, so that the wind power grid-connected position and the wind power correlation factors need to be considered in the calculation process of the ATC.
In conclusion, compared with the existing inter-region ATC calculation method, the method considers the wind power uncertainty and the correlation in the ATC calculation model and the economic dispatching model simultaneously, and further obtains more accurate calculation effect; based on historical data, a data-driven wind power correlation modeling method is provided; adopting an alternating current model in an ATC (automatic traffic control) calculation model, and converting the nonlinear optimal power flow model into a second-order cone programming model through convex relaxation; in the process of calculating the ATC, the double-layer model is converted into a mixed integer second-order cone plan, and the mixed integer second-order cone plan can be solved through an existing commercial solver.
Reference to the literature
[1] Ginger ocean, durch, cinnabar, etc. summary and revelation of seasonal energy storage for high-proportion renewable energy power systems [ J ] power system automation, 2020,44 (19): 194-208.
[2]FALAGHI H,RAMEZANI M,SINGH C,et al.Probabilistic Assessment of TTC in Power Systems Including Wind Power Generation[J].IEEE Systems Journal,2012,6(1):181-190.
[3] The wind power grid-connected system considering demand response can calculate the transmission capacity [ J ]. The university of northeast electric power, 2019,39 (05): 1-8.
[4]ILIC M.D,YOON Y T,ZOBIAN A.Available transmission capacity(ATC)and its value under open access[J].IEEE Transactions on Power Systems,2002,12(2):636-645.
[5] Liu huan, li yang, chengzao, available transmission capacity of the transmission grid based on continuous tidal current is calculated [ J ]. Power automation equipment, 2003, (12): 5-9.
[6] And calculating the available transmission capacity based on the Benders decomposition algorithm under the static security constraint [ J ]. The Chinese Motor engineering Commission, 2003,23 (8): 7-11.
[7] Huixinz, wind power grid-connected system taking wind speed space-time correlation into account can calculate [ D ] Jilin, northeast university of electric power, 2018 by using transmission capacity.
[8] Rough, shidong Source, chuidefu, etc. the probability of a wind farm-containing power system taking into account correlation can be quickly calculated by the transmission capability [ J ]. The Chinese Motor engineering Proc., 2014,34 (7): 1024-1032.
[9]CHEN H,FANG X,ZHANG R,et al.Available Transfer Capability Evaluation in a Deregulated Electricity Market Considering Correlated Wind Power[J].IET Generation Transmission & Distribution,2018,12(1):53-61.
[10] The research on available transmission capacity considering the comprehensive operation benefit of a wind power grid-connected system [ D ]. Jilin, northeast electric power university, 2016.
[11]DU P,LI W,KE X,et al.Probabilistic-Based Available Transfer Capability Assessment Considering Existing and Future Wind Generation Resources[J].IEEE Transactions on Sustainable Energy,2015,6(4):1-9.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-mentioned serial numbers of the embodiments of the present invention are only for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. A method for calculating available transmission capacity probability in consideration of wind power correlation is characterized by comprising the following steps:
obtaining a wind power output sample considering wind power correlation based on the conditional probability and a Copula function, and taking historical load data as a load sample set;
calculating the ATC under each scene through an ATC double-layer optimization model by using the wind power output sample and the load sample set;
judging whether the unit output of a power transmission area under the current scene reaches an upper limit, if the unit output reaches the upper limit and only the power transmission line does not reach the transmission capacity limit, removing the current scene, and recording the ATC under the effective scene, wherein other scenes are effective scenes;
performing probability density fitting on ATC results in all effective scenes, and analyzing the influence of correlation on ATC;
the ATC calculation model of the upper layer is specifically as follows:
Figure FDA0003822819460000011
Figure FDA0003822819460000012
Figure FDA0003822819460000013
Figure FDA0003822819460000014
Figure FDA0003822819460000015
Figure FDA0003822819460000016
Figure FDA0003822819460000017
Figure FDA0003822819460000018
Figure FDA0003822819460000019
Figure FDA00038228194600000110
||2P e,l 2Q e,l l e,l -u e,i ||≤l e,l +u e,i
Figure FDA00038228194600000111
Figure FDA00038228194600000112
where Ψ represents the set of all nodes in the power system; omega l Represents a set of all branches in the power system; source is the power generation area; p i 1 、
Figure FDA0003822819460000021
And
Figure FDA0003822819460000022
respectively representing the output of a generator, the output of a wind turbine generator and the load;
Figure FDA0003822819460000023
reactive load for node i; m is a group of il Elements of the ith row and the ith column of the node branch power flow incidence matrix; m is a group of loss,il The ith row and the l column of elements of the node branch network loss incidence matrix are set; c is a branch circuit incidence matrix; u. of i Represents the square of each node voltage;
Figure FDA0003822819460000024
and
Figure FDA0003822819460000025
respectively representing the upper limit and the lower limit of the voltage of each node; p loss,l And Q loss,l Line loss; limit is the transmission Limit of the line l; r l And X l Respectively the resistance and reactance of each branch circuit; p e,l And Q e,l The power flow of each branch circuit respectively; u. of e,i Is the square term of the receive terminal voltage; p i The output of a conventional unit under the ground state, P wi Is a ground stateOutput of lower wind turbine, P Di Load level in the ground state, in MW; p is i max The upper limit of the active output of the conventional unit;
Figure FDA0003822819460000026
the upper limit of the active power output of the wind turbine generator is set;
Figure FDA0003822819460000027
and
Figure FDA0003822819460000028
respectively the output of a conventional generator and the reactive output of a wind turbine generator; l e,l Intermediate variables required for linearizing the model;
Figure FDA0003822819460000029
the upper limit and the lower limit of the idle output of the conventional unit are set;
Figure FDA00038228194600000210
and
Figure FDA00038228194600000211
the upper limit and the lower limit of the reactive power output of the wind turbine generator are set.
2. The method for calculating the probability of the available transmission capacity based on the wind power correlation according to claim 1, wherein the ATC double-layer optimization model comprises: the upper ATC calculation model, the lower ETC calculation model, the wind power correlation and the uncertainty are simultaneously considered in the ETC optimization model and the ATC calculation model, and the ETC is an existing power transmission protocol.
3. The method as claimed in claim 1, wherein the ATC calculation model of the upper layer is calculated by maximizing power transmitted in a power generation area and a power receiving area and using an ac model.
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