CN111509784B - Uncertainty-considered virtual power plant robust output feasible region identification method and device - Google Patents

Uncertainty-considered virtual power plant robust output feasible region identification method and device Download PDF

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CN111509784B
CN111509784B CN202010333728.1A CN202010333728A CN111509784B CN 111509784 B CN111509784 B CN 111509784B CN 202010333728 A CN202010333728 A CN 202010333728A CN 111509784 B CN111509784 B CN 111509784B
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power plant
virtual power
feasible region
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CN111509784A (en
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钟海旺
谭振飞
夏清
康重庆
王宣元
汤洪海
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Tsinghua University
State Grid Corp of China SGCC
State Grid Jibei Electric Power Co Ltd
State Grid Beijing Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Jibei Electric Power Co Ltd
State Grid Beijing Electric Power Co Ltd
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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
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Abstract

The invention discloses a virtual power plant robust output feasible region identification method and device considering uncertainty, wherein the method comprises the following steps: equating an active power distribution network containing distributed power generation and flexible load to a virtual power plant with adjustable active and reactive power output; constructing a virtual power plant safe operation feasible region considering renewable energy output and power load uncertainty; projecting the safe operation feasible region of the virtual power plant into a robust output feasible region of the virtual power plant through constraint aggregation; and identifying the vertex of the feasible region of the robust output of the virtual power plant through a vertex enumeration and column constraint generation algorithm, and further obtaining a linear inequality set for describing the feasible region. The method realizes that uncertainty factors are embedded and considered in the identification of the output feasible region of the virtual power plant, can ensure the output feasible region of the virtual power plant which can safely operate under any uncertainty disturbance, is favorable for promoting the efficient utilization of distributed generation resources and is favorable for ensuring the safe and reliable operation of a power system containing distributed power supplies.

Description

Uncertainty-considered virtual power plant robust output feasible region identification method and device
Technical Field
The invention relates to the technical field of power system dispatching operation, in particular to a virtual power plant robust output feasible region identification method and device considering uncertainty.
Background
With the continuous development of economy, the power load of cities, towns and industrial parks is rapidly increased. Distributed power supplies such as distributed photovoltaic power, wind power, energy storage, small cogeneration units, biomass power generation and the like are connected to a power distribution network in a large number with the advantages of high efficiency, economy and environmental protection. The continuous access of the distributed power supply can not only supply local loads, but also deliver power through the power distribution network when the new energy power generation is increased and the local loads are in a low ebb, so that support is provided for loads in other areas in the power transmission network. Meanwhile, distributed power source cluster control can provide more adjusting means for power grid dispatching operation. Therefore, power distribution networks containing a large number of distributed power sources are gradually evolving into virtual power plants that exchange energy with the power grid in both directions.
The virtual power plant aggregates massive distributed resources in the power distribution network to participate in the optimized scheduling operation of the power transmission network, and can provide active and reactive power regulation flexibility for the operation of the power transmission network. The typical operation mode is that a transmission network dispatching mechanism optimizes and decides the active and reactive output of a virtual power plant, and the virtual power plant controls an internal distributed power supply to execute a dispatching result according to the transmission network dispatching result. The key of the virtual power plant participating in the optimized dispatching operation of the power transmission network is that the output feasible region of the virtual power plant needs to be calculated, namely the active and reactive output ranges of the virtual power plant do not violate the safe operation constraints of a power distribution system and a distributed power supply. However, output of intermittent distributed power sources such as distributed photovoltaic power, distributed wind power and the like has significant uncertainty and volatility, and active and reactive loads in a distribution network also have uncertainty. If the feasible output area of the virtual power plant is calculated only according to the point prediction result, the scheduling result cannot be executed on the virtual power plant due to the fluctuation of the output of the distributed power supply and the error of load prediction, and safety problems such as power shortage of a power distribution network, voltage limit crossing of the power distribution network, power flow limit crossing of the power distribution network and the like can be caused.
The existing literature and technology cannot consider the uncertainty of the distributed power supply output and the power load in the feasible output domain calculation of the virtual power plant, and the virtual power plant can not be ensured to run safely and reliably under any uncertainty fluctuation.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, one purpose of the invention is to provide a robust output feasible region identification method for a virtual power plant considering uncertainty, which realizes that uncertainty factors are embedded and considered in output feasible region identification of the virtual power plant, can ensure an output feasible region of the virtual power plant which can safely operate under any uncertainty disturbance, and is beneficial to promoting efficient utilization of distributed power generation resources and ensuring safe and reliable operation of a power system containing a distributed power supply.
Another objective of the present invention is to provide a virtual power plant robust output feasible region identification device considering uncertainty.
In order to achieve the above object, an embodiment of the present invention provides a method for identifying a robust output feasible region of a virtual power plant considering uncertainty, including the following steps: acquiring operation parameters of an internal power distribution system of a virtual power plant; constructing a virtual power plant safe operation feasible region model considering uncertainty according to the operation parameters to obtain a safe operation constraint coefficient matrix; constructing a virtual power plant operation uncertain set according to the operation parameters, and constructing a virtual power plant robust output feasible region model according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set; and identifying the robust output feasible region of the virtual power plant through vertex enumeration, and solving the problem of identifying the vertex of the feasible region through a column constraint generation method.
According to the method for identifying the robust output feasible region of the virtual power plant considering the uncertainty, uncertainty factors are considered in the calculation of the output feasible region of the virtual power plant through the method of uncertainty set and robustness optimization, the robust output feasible region of the virtual power plant is constructed and identified, the active and reactive output ranges of the virtual power plant which can safely operate under any uncertainty disturbance are explicitly described, the safe operation constraint in the virtual power plant can be guaranteed not to be violated by any scheduling result in the feasible region under the disturbance of any uncertainty variable, and the safety and the economy of a power system comprising a distributed power supply are improved.
In addition, the method for identifying the robust output feasible region of the virtual power plant considering the uncertainty according to the embodiment of the invention may further have the following additional technical features:
further, in one embodiment of the invention, the operating parameters include one or more of distribution network parameters, distributed generation operating parameters, and predictive parameters.
Further, in an embodiment of the present invention, the virtual power plant operation uncertainty set is:
Figure GDA0003413593790000021
wherein w is an uncertain variable of virtual power plant operation, comprising active power load, reactive power load, intermittent distributed resource active output,
Figure GDA0003413593790000022
upper and lower bounds, respectively, of a confidence interval for the kth uncertain variable;
Figure GDA0003413593790000023
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure GDA0003413593790000024
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ wA peptide; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set.
Further, in an embodiment of the present invention, the identifying the robust output feasible region of the virtual power plant through vertex enumeration includes: searching vertexes of a feasible robust output domain of the virtual power plant along different directions, and constructing an approximate polygon by using the searched vertexes; updating the vertex searching direction through normal vectors of all boundaries of the approximate polygon, and searching other vertexes of a robust output feasible region of the virtual power plant; and repeating the process to calculate the feasible region of the robust output of the virtual power plant.
Further, in an embodiment of the present invention, by solving a two-stage adjustable robust optimization problem, an initial vertex set and an initial approximate polygon of a robust output feasible region of a virtual power plant are calculated:
Figure GDA0003413593790000031
wherein, F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, s is a relaxation variable, and 1 represents a column vector with all elements being 1; m0The real number is a positive real number far greater than 1, and the typical value of the real number can be 1000 times of the capacity of a gateway transformer of a power distribution network; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4。
In order to achieve the above object, an embodiment of the present invention provides a robust output feasible region identification apparatus for a virtual power plant, which includes: the acquisition module is used for acquiring the operation parameters of the internal power distribution system of the virtual power plant; the first construction module is used for constructing a virtual power plant safe operation feasible region model considering uncertainty according to the operation parameters to obtain a safe operation constraint coefficient matrix; the second construction module is used for constructing a virtual power plant operation uncertain set according to the operation parameters and constructing a virtual power plant robust output feasible region model according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set; and the identification module is used for identifying the robust output feasible region of the virtual power plant through vertex enumeration and solving the problem of identifying the vertex of the feasible region through a column constraint generation method.
According to the uncertainty-considered robust output feasible region identification device for the virtual power plant, uncertainty factors are considered in the calculation of the output feasible region of the virtual power plant through the uncertainty set and robust optimization method, the robust output feasible region of the virtual power plant is constructed and identified, the active and reactive output ranges of the virtual power plant which can safely operate under any uncertainty disturbance are explicitly described, the safe operation constraint in the virtual power plant can be guaranteed not to be violated by any scheduling result in the feasible region under the disturbance of any uncertainty variable, and the safety and the economy of a power system with a distributed power supply are improved.
In addition, the virtual power plant robust output feasible region identification device considering the uncertainty according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the invention, the operating parameters include one or more of distribution network parameters, distributed generation operating parameters, and predictive parameters.
Further, in an embodiment of the present invention, the virtual power plant operation uncertainty set is:
Figure GDA0003413593790000032
wherein w is an uncertain variable of virtual power plant operation, comprising active power load, reactive power load, intermittent distributed resource active output,
Figure GDA0003413593790000033
upper and lower bounds, respectively, of a confidence interval for the kth uncertain variable;
Figure GDA0003413593790000034
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure GDA0003413593790000041
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ w; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set.
Further, in an embodiment of the present invention, the identification module is further configured to search vertices of the robust output feasible region of the virtual power plant along different directions, and construct an approximate polygon using the searched vertices; and updating the vertex searching direction through the normal vector of each boundary of the approximate polygon, searching the other vertexes of the feasible robust output domain of the virtual power plant, repeating the process, and calculating to obtain the feasible robust output domain of the virtual power plant.
Further, in an embodiment of the present invention, by solving a two-stage adjustable robust optimization problem, an initial vertex set and an initial approximate polygon of a robust output feasible region of a virtual power plant are calculated:
Figure GDA0003413593790000042
wherein, F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, s is a relaxation variable, and 1 represents a column vector with all elements being 1; m0Is a positive real number far greater than 1, and its typical valueThe capacity of the transformer can be 1000 times of that of the gateway transformer of the power distribution network; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4。
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a virtual power plant robust output feasible region identification method accounting for uncertainty according to an embodiment of the invention;
FIG. 2 is a flow diagram of a virtual power plant robust output feasible region identification method accounting for uncertainty in accordance with one embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a virtual power plant robust output feasible region identification device with uncertainty taken into account according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention aims to fill the technical blank that uncertainty of output and power load of a distributed power supply cannot be considered in calculation of the output feasible region of a virtual power plant, and provides a method and a device for identifying the robust output feasible region of the virtual power plant, wherein the uncertainty is considered, the robust output feasible region of the virtual power plant is constructed by an uncertain set and robust optimization method, the robust output feasible region of the virtual power plant is identified by a vertex enumeration algorithm and a column constraint generation algorithm, explicit inequality constraints on active output and reactive output of the virtual power plant are output, any scheduling result in the feasible region can be guaranteed not to violate the safe operation constraints in the virtual power plant under the disturbance of any uncertain variable, and the safe and reliable operation of a power system is guaranteed while the advantages of distributed power generation economy and environmental protection are fully exerted.
The method and the device for identifying the robust output feasible region of the virtual power plant considering the uncertainty provided by the embodiment of the invention are described below with reference to the accompanying drawings, and firstly, the method for identifying the robust output feasible region of the virtual power plant considering the uncertainty provided by the embodiment of the invention is described with reference to the accompanying drawings.
FIG. 1 is a flowchart of a virtual power plant robust output feasible region identification method that accounts for uncertainty according to an embodiment of the invention.
As shown in fig. 1, the method for identifying the robust output feasible region of the virtual power plant considering the uncertainty includes the following steps:
in step S101, operating parameters of the power distribution system inside the virtual power plant are obtained.
In one embodiment of the invention, an active power distribution network containing distributed power generation and flexible load is equivalent to a virtual power plant with adjustable active and reactive power output; the operating parameters include one or more of distribution network parameters, distributed generation operating parameters, and predictive parameters.
In step S102, a virtual power plant safe operation feasible region model considering uncertainty is constructed according to the operation parameters, and a safe operation constraint coefficient matrix is obtained.
It can be understood that the embodiment of the invention constructs a virtual power plant safe operation feasible domain considering renewable energy output and power load uncertainty according to the power distribution network parameters and the distributed power generation operation parameters.
In step S103, a virtual power plant operation uncertain set is constructed according to the operation parameters, and a virtual power plant robust output feasible region model is constructed according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set.
It can be understood that the virtual power plant operation uncertain set is constructed according to the prediction parameters, and the virtual power plant safe operation feasible region is projected into the virtual power plant robust output feasible region through constraint aggregation.
In step S104, the robust output feasible region of the virtual power plant is identified through vertex enumeration, and the feasible region vertex identification problem is solved through a column constraint generation method.
It can be understood that the vertex of the robust output feasible region of the virtual power plant is identified through vertex enumeration and a column constraint generation algorithm, and then a linear inequality set describing the feasible region is obtained.
In conclusion, the method provided by the embodiment of the invention realizes that uncertainty factors are embedded and considered in the identification of the output feasible region of the virtual power plant, can ensure the output feasible region of the virtual power plant which can safely operate under any uncertainty disturbance, is favorable for promoting the efficient utilization of distributed power generation resources, and is favorable for ensuring the safe and reliable operation of a power system containing distributed power supplies.
The method for identifying the robust output feasible region of the virtual power plant considering the uncertainty is described in detail with reference to fig. 2, which specifically includes:
1) obtain the inside distribution system operating parameter of virtual power plant, specifically include:
1-1) the virtual power plant means that an active power distribution network containing a distributed power supply and provided with a power distribution energy management system is equivalent to a power plant, can participate in the optimized operation of a power transmission network, and can adjust the active power and the reactive power of a power distribution system and a gateway port according to a scheduling instruction of a power grid scheduling mechanism;
1-2) obtaining operation basic parameters of an internal power distribution system of a virtual power plant, which specifically comprises the following steps:
1-2-1) network parameters of the power distribution network: the method comprises the following steps of connecting topology of a power distribution network, conductance of a power distribution line and a transformer, susceptance parameters, transmission capacity limits of the power distribution line, and upper and lower limits of node voltage allowed by safe operation;
1-2-2) distributed generation operating parameters: the installed capacity, the minimum active output and the maximum power factor angle of each distributed power supply in the power distribution network;
1-2-3) prediction parameters: confidence interval of active load prediction, confidence interval of reactive load prediction and confidence interval of active output prediction of intermittent distributed power supply
2) Constructing a virtual power plant safe operation feasible domain model considering uncertainty, and specifically comprising the following steps:
2-1) writing a safety operation constraint condition of the virtual power plant according to the power distribution system operation basic parameter columns in 1-2-1) and 1-2-2), wherein the detailed expression is as follows:
Figure GDA0003413593790000061
Figure GDA0003413593790000062
Figure GDA0003413593790000063
Figure GDA0003413593790000064
Figure GDA0003413593790000065
Figure GDA0003413593790000071
Figure GDA0003413593790000072
Figure GDA0003413593790000073
Figure GDA0003413593790000074
Figure GDA0003413593790000075
wherein formula 1 and formula 2 are the active and reactive power flows of the distribution line ij based on the reduced order power flow equation,
Figure GDA0003413593790000076
Figure GDA0003413593790000077
respectively the active and reactive power flow of the distribution line, bij、gijRespectively series susceptance, series conductance, u, of the distribution linei、ujThe square of the voltage amplitude of node i and node j, θi、θjThe phase angles of the voltages at node i and node j respectively,
Figure GDA0003413593790000078
is a collection of numbers of nodes of the power distribution network,
Figure GDA0003413593790000079
representing a set of node numbers directly connected with the node i through the distribution line;
formula 3 and formula 4 are the active and reactive balance equations of each node of the distribution network respectively; in the formula
Figure GDA00034135937900000710
Respectively the active output and the reactive output of the distributed power supply at the node i;
Figure GDA00034135937900000711
respectively the active load and the reactive load of the node i; p0、Q0Respectively representing active output and reactive output of the virtual power plant;
equation 5 represents the transmission capacity constraint of the distribution line ij, where
Figure GDA00034135937900000712
Is the transmission capacity limit, N, of the distribution linesIs the number of segments that represent the transmission capacity constraint in a linearized segment;
equation 6 represents the distribution transformer capacity constraint at the distribution grid gateway, where
Figure GDA00034135937900000713
Is the upper limit of the capacity of the distribution transformer;
equation 7 represents the upper and lower voltage limits of each node of the distribution network, where
Figure GDA00034135937900000714
v iRespectively an upper limit and a lower limit of the voltage amplitude allowed by the node i;
the active output upper and lower limit constraints, the power factor constraints and the capacity constraints of the distributed power supply i are respectively described in a formula 8, a formula 9 and a formula 10; in the formula
Figure GDA00034135937900000715
The active output upper and lower limits of the distributed power supply of the node i;
Figure GDA00034135937900000716
is the maximum power factor angle of the distributed power source i;
Figure GDA00034135937900000717
is the upper limit of the capacity of the distributed power source i;
2-2) defining the coordinating variable x as P0、Q0Is a column vector of elements, i.e. x ═ P0,Q0) (ii) a Defining an uncertain variable w as
Figure GDA0003413593790000081
Is a column vector of elements, i.e.:
Figure GDA0003413593790000082
defining the operation decision variable y as ui、θi、
Figure GDA0003413593790000083
Is a column vector of elements, i.e.:
Figure GDA0003413593790000084
further, the constraints (1) to (10) can be arranged in the following form:
Ax+By+Cw≤d (11)
wherein A, B, C is a coefficient matrix and d is a constant vector;
2-3) constructing a virtual power plant safe operation feasible domain, recording as phi, which is a value set of variables (x, w, y) under the virtual power plant safe operation constraint and can be expressed as follows:
Φ＝{(x,w,y)|Ax+By+Cw≤d} (12)
3) constructing a virtual power plant operation uncertain set, which is marked as W, according to the prediction parameters of 1-2-3); w is described by a set of linear inequalities for W, as follows:
Figure GDA0003413593790000085
wherein,
Figure GDA0003413593790000086
upper and lower bounds, respectively, of a confidence interval for the kth uncertain variable;
Figure GDA0003413593790000087
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure GDA0003413593790000088
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ w; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set;
4) constructing a robust output feasible region model of the virtual power plant, which specifically comprises the following steps:
4-1), the so-called robust output feasible region of the virtual power plant is a feasible value set of a coordinated variable x, and the feasible region phi of the virtual power plant in safe operation is not empty when any variable in an uncertain set W is satisfied;
4-2) the robust output feasible region mathematical representation of the virtual power plant is as follows:
Figure GDA0003413593790000089
the virtual plant robust output feasible region Ω defined according to equation 15 is a bounded region in two dimensions, where points within the feasible region correspond to the virtual plant output (P)0,Q0) The method can be executed in a power distribution system in a virtual power plant under the disturbance of any uncertain variable without violating the safe operation constraint of the power distribution system;
5) identifying a virtual power plant robust output feasible region through vertex enumeration: searching the peak of the robust output feasible region omega of the virtual power plant along different directions, constructing an approximate polygon by using the searched peak, updating the searching direction by the normal vector of each boundary of the approximate polygon, and repeating the steps to calculate and obtain the robust output feasible region of the virtual power plant; the specific flow of the algorithm is described as follows:
5-1) calculating an initial vertex set and an initial approximate polygon of a robust output feasible region of the virtual power plant by solving the following two-stage adjustable robust optimization problem:
Figure GDA0003413593790000091
wherein F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, and s is relaxation changeQuantity, 1 represents a column vector with elements all being 1; m0The real number is a positive real number far greater than 1, the typical value of the real number can be 1000 times of the capacity of a gateway transformer of a power distribution network, and the specific value of the real number does not influence the calculation result of the model; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); solving the problem (16) by the algorithm in 6); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4；
5-2) initializing a newly added boundary set HNIs empty, i.e.
Figure GDA0003413593790000092
5-3) vertex search: by following the distance v0Is translated in the direction HTSearching the vertex of omega by the boundary in (1); for HTThe m-th boundary of (1), the equation of the boundary is
Figure GDA0003413593790000093
The vertexes at both ends of the boundary are vm1、vm2(ii) a Solving the problem (16) by the algorithm in 6), and recording the optimal solution as vmThe optimum value is recorded as
Figure GDA0003413593790000094
5-4) updating the vertex set: adding the vertex into a feasible region vertex set V;
5-5) judging whether a boundary to be translated needs to be added or not, specifically comprising the following steps:
5-5-1) calculating the improvement amount of the vertex search in step 5-3) according to the following formula:
Figure GDA0003413593790000101
5-5-2) if Δ gm>0, respectively calculate vmAnd vm1、vm2Equation h for a defined straight linem1、hm2Adding it to the newly added boundary set HNReturning to step 5-3), using HTPerforming vertex search on the m +1 th boundary;
5-5-3) if Δ gmGo back to step 5-3) with H ═ 0)TPerforming vertex search on the m +1 th boundary;
5-6) judging whether the algorithm is terminated: to HTAfter searching the vertexes of all the boundary equations in (1), judging HNWhether the algorithm is terminated is judged for the empty set, namely:
5-6-1) if
Figure GDA0003413593790000102
Set of boundaries to be searched HTIs updated to HNI.e. HT←HNAnd returning to the step 5-3) for the updated HTPerforming vertex search on the boundary in (1);
5-6-2) if
Figure GDA0003413593790000103
The algorithm terminates; a polygon determined by the vertexes in the vertex set V is a calculation result of the robust output feasible region of the virtual power plant, and each boundary inequality of the polygon is a linear inequality constraint representing the robust output feasible region of the virtual power plant;
6) solving a feasible domain vertex identification problem (16) by a column constraint generation method, specifically comprising:
6-1) initializing extreme scenes
Figure GDA0003413593790000104
Initializing extreme scene set
Figure GDA0003413593790000105
Initializing an iteration count variable k to 0
6-2) solving the robust optimization main problem:
Figure GDA0003413593790000106
the problem is a linear programming problem and can be solved by a commercial solver (such as CPLEX and GUROBI); through the optimization solution, the optimal solution of the problem (18) is
Figure GDA0003413593790000107
6-3) given
Figure GDA0003413593790000108
Solving a robust optimization sub-problem:
Figure GDA0003413593790000109
for the convenience of solving, the robust optimization sub-problem can be further converted into a mixed integer linear programming problem by a dual principle as follows:
Figure GDA0003413593790000111
wherein μ is the dual variable of (11); z is a radical of+、z-Is a 0-1 variable, z, representing the value of an uncertain variable+i＝1,z-iUncertainty variable w when equal to 0iReaching an upper bound of the prediction interval, z+i＝0,z-iUncertainty variable w when 1iReaching the lower bound of the prediction interval; tau is+、τ-Is an aid decision variable; m is a large enough positive real number, and the value of M is not less than 1-norm of C, i.e. M is not less than | | | C | | counting1(ii) a Solving the mixed integer linear programming problem using a commercial solver (e.g., CPLEX, GUROBI) with an optimal solution of
Figure GDA0003413593790000112
The optimum value is
Figure GDA0003413593790000113
6-4) if
Figure GDA0003413593790000114
: updating a counting variable, k being k + 1; will be provided with
Figure GDA0003413593790000115
Joining extreme scene collections
Figure GDA0003413593790000116
I.e. by
Figure GDA0003413593790000117
Returning to 6-2), continuing to execute the algorithm;
6-5) if
Figure GDA0003413593790000118
The algorithm terminates, at this point
Figure GDA0003413593790000119
This is the solution to the problem (16).
According to the method for identifying the robust output feasible region of the virtual power plant considering the uncertainty, which is provided by the embodiment of the invention, uncertainty factors are considered in the calculation of the output feasible region of the virtual power plant through the methods of uncertainty set and robustness optimization, the active and reactive output ranges of the virtual power plant which can safely operate under any uncertainty disturbance are explicitly described through constructing and identifying the robust output feasible region of the virtual power plant, the safe operation constraint in the virtual power plant can not be violated by any scheduling result in the feasible region under the disturbance of any uncertainty variable, and the safety and the economy of a power system containing a distributed power supply are favorably improved.
The proposed virtual power plant robust output feasible region identification device considering uncertainty according to the embodiment of the invention is described next with reference to the attached drawings.
FIG. 3 is a schematic structural diagram of a virtual power plant robust output feasible region identification device with uncertainty taken into account according to an embodiment of the invention.
As shown in fig. 3, the uncertainty-considered virtual plant robust output feasible region identification device 10 includes: an acquisition module 100, a first construction module 200, a second construction module 300 and a recognition module 400.
The obtaining module 100 is configured to obtain an operation parameter of a power distribution system in a virtual power plant; the first construction module 200 is used for constructing a virtual power plant safe operation feasible region model considering uncertainty according to the operation parameters to obtain a safe operation constraint coefficient matrix; the second construction module 300 is used for constructing a virtual power plant operation uncertain set according to the operation parameters, and constructing a virtual power plant robust output feasible region model according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set; the identification module 400 is configured to identify the robust output feasible region of the virtual power plant through vertex enumeration, and solve the feasible region vertex identification problem through a column constraint generation method. The device 10 provided by the embodiment of the invention realizes that uncertainty factors are embedded and considered in the output feasible region identification of the virtual power plant, can ensure the output feasible region of the virtual power plant which can safely operate under any uncertainty disturbance, is favorable for promoting the efficient utilization of distributed power generation resources, and is favorable for ensuring the safe and reliable operation of a power system containing distributed power supplies.
Further, in one embodiment of the invention, the operating parameters include one or more of distribution network parameters, distributed generation operating parameters, and predictive parameters.
Further, in one embodiment of the present invention, the virtual plant operation uncertainty set is:
Figure GDA0003413593790000121
wherein w is an uncertain variable of virtual power plant operation, comprising active power load, reactive power load, intermittent distributed resource active output,
Figure GDA0003413593790000122
respectively, the setting of the kth uncertain variableUpper and lower bounds of the signal interval;
Figure GDA0003413593790000123
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure GDA0003413593790000124
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ w; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set.
Further, in an embodiment of the present invention, the identification module 400 is further configured to search vertices of the robust output feasible region of the virtual power plant along different directions, and construct an approximate polygon using the searched vertices; and updating the vertex searching direction through the normal vectors of all the boundaries of the approximate polygon, searching the other vertexes of the robust output feasible region of the virtual power plant, repeating the process, and calculating to obtain the robust output feasible region of the virtual power plant.
Further, in an embodiment of the present invention, by solving a two-stage adjustable robust optimization problem, an initial vertex set and an initial approximate polygon of a robust output feasible region of a virtual power plant are calculated:
Figure GDA0003413593790000125
wherein, F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, s is a relaxation variable, and 1 represents a column vector with all elements being 1; m0The real number is a positive real number far greater than 1, and the typical value of the real number can be 1000 times of the capacity of a gateway transformer of a power distribution network; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4。
It should be noted that the explanation of the embodiment of the robust output feasible region identification method for a virtual power plant considering uncertainty is also applicable to the robust output feasible region identification device for a virtual power plant considering uncertainty of the embodiment, and details are not repeated here.
According to the device for identifying the robust output feasible region of the virtual power plant considering the uncertainty, which is provided by the embodiment of the invention, uncertainty factors are considered in the calculation of the output feasible region of the virtual power plant through the method of uncertainty set and robustness optimization, the active and reactive output ranges of the virtual power plant which can safely operate under any uncertainty disturbance are explicitly described through constructing and identifying the robust output feasible region of the virtual power plant, the safe operation constraint in the virtual power plant can not be violated by any scheduling result in the feasible region under the disturbance of any uncertainty variable, and the safety and the economy of a power system containing a distributed power supply are favorably improved.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (6)

1. A virtual power plant robust output feasible region identification method considering uncertainty is characterized by comprising the following steps:
acquiring operation parameters of an internal power distribution system of a virtual power plant;
according to the operation parameters, a virtual power plant safe operation feasible region model considering uncertainty is constructed, and a safe operation constraint coefficient matrix is obtained, wherein the construction of the virtual power plant safe operation feasible region model considering uncertainty specifically comprises the following steps: writing a safety operation constraint condition of a virtual power plant according to an operation basic parameter list of a power distribution system, wherein the expression is as follows:
Figure FDA0003413593780000011
Figure FDA0003413593780000012
Figure FDA0003413593780000013
Figure FDA0003413593780000014
Figure FDA0003413593780000015
Figure FDA0003413593780000016
Figure FDA0003413593780000017
Figure FDA0003413593780000018
Figure FDA0003413593780000019
Figure FDA00034135937800000110
wherein formula 1 and formula 2 are the active and reactive power flows of the distribution line ij based on the reduced order power flow equation,
Figure FDA00034135937800000111
Figure FDA00034135937800000112
respectively the active and reactive power flow of the distribution line, bij、gijRespectively series susceptance, series conductance, u, of the distribution linei、ujThe square of the voltage amplitude of node i and node j, θi、θjThe phase angles of the voltages at node i and node j respectively,
Figure FDA00034135937800000113
is a collection of numbers of nodes of the power distribution network,
Figure FDA0003413593780000021
representing a set of node numbers directly connected with the node i through the distribution line;
formula 3 and formula 4 are the active and reactive balance equations of each node of the distribution network respectively; in the formula Pi g、Qi gRespectively the active output and the reactive output of the distributed power supply at the node i;
Figure FDA0003413593780000022
respectively the active load and the reactive load of the node i; p0、Q0Respectively representing active output and reactive output of the virtual power plant;
equation 5 represents the transmission capacity constraint of the distribution line ij, where
Figure FDA0003413593780000023
Is the transmission capacity limit, N, of the distribution linesIs the number of segments that represent the transmission capacity constraint in a linearized segment;
equation 6 represents the distribution transformer capacity constraint at the distribution grid gateway, where
Figure FDA0003413593780000024
Is the upper limit of the capacity of the distribution transformer;
equation 7 represents the upper and lower voltage limits of each node of the distribution network, where
Figure FDA0003413593780000025
v iRespectively an upper limit and a lower limit of the voltage amplitude allowed by the node i;
the active output upper and lower limit constraints, the power factor constraints and the capacity constraints of the distributed power supply i are respectively described in a formula 8, a formula 9 and a formula 10; in the formula
Figure FDA0003413593780000026
P i gThe active output upper and lower limits of the distributed power supply of the node i;
Figure FDA0003413593780000027
is the maximum power factor angle of the distributed power source i;
Figure FDA0003413593780000028
is the upper limit of the capacity of the distributed power source i;
defining a coordination variable x as P0、Q0Is a column vector of elements, i.e. x ═ P0,Q0) (ii) a Defining an uncertain variable w as
Figure FDA0003413593780000029
Is a column vector of elements, i.e.:
Figure FDA00034135937800000210
defining the operation decision variable y as ui、θi、Pi g、
Figure FDA00034135937800000211
Is a column vector of elements, i.e.:
Figure FDA00034135937800000212
the constraints (1) to (10) are arranged in the following form:
Ax+By+Cw≤d (11)
wherein A, B, C is a coefficient matrix and d is a constant vector;
constructing a virtual power plant safe operation feasible region, marking as phi, which is a value set of variables (x, w, y) under the virtual power plant safe operation constraint and is expressed as:
Φ＝{(x,w,y)|Ax+By+Cw≤d} (12)；
establishing a virtual power plant operation uncertain set according to the operation parameters, and establishing a virtual power plant robust output feasible region model according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set, wherein the virtual power plant operation uncertain set is as follows:
Figure FDA0003413593780000031
wherein w is an uncertain variable of virtual power plant operation, comprising active power load, reactive power load, intermittent distributed resource active output,
Figure FDA0003413593780000032
upper and lower bounds, respectively, of a confidence interval for the kth uncertain variable;
Figure FDA0003413593780000033
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure FDA0003413593780000034
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ w; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set; the method for constructing the robust output feasible region model of the virtual power plant specifically comprises the following steps: the robust output feasible region of the virtual power plant is a feasible value set of a coordinated variable x, and the condition that any variable in an uncertain set W is not null is met, so that the feasible region phi of the safe operation of the virtual power plant is not null; the robust output feasible region mathematical representation of the virtual power plant is as follows:
Figure FDA0003413593780000035
the robust output feasible region omega of the virtual power plant defined according to the formula is a bounded region in a two-dimensional spacePoint-corresponding virtual plant output (P) within the feasible region0,Q0) The method can be executed in a power distribution system in a virtual power plant under the disturbance of any uncertain variable without violating the safe operation constraint of the power distribution system; and
identifying the feasible region of virtual power plant robust output through vertex enumeration, and solving the problem of identifying the feasible region of vertex through a column constraint generation method, wherein identifying the feasible region of virtual power plant robust output through vertex enumeration comprises: searching vertexes of a feasible robust output domain of the virtual power plant along different directions, and constructing an approximate polygon by using the searched vertexes; updating the vertex searching direction through normal vectors of all boundaries of the approximate polygon, and searching other vertexes of a robust output feasible region of the virtual power plant; and repeating the process to calculate the feasible region of the robust output of the virtual power plant.
2. The method of claim 1, wherein the operating parameters comprise distribution network parameters, distributed generation operating parameters, and predictive parameters.
3. The method of claim 1, wherein the initial vertex set and the initial approximation polygon of the robust output feasible region of the virtual power plant are calculated by solving a two-stage adjustable robust optimization problem:
Figure FDA0003413593780000036
wherein, F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, s is a relaxation variable, and 1 represents a column vector with all elements being 1; m0The real number is a positive real number larger than 1, and the typical value of the real number is 1000 times of the capacity of a gateway transformer of a power distribution network; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4。
4. A virtual power plant robust output feasible region identification device considering uncertainty is characterized by comprising the following components:
the acquisition module is used for acquiring the operation parameters of the internal power distribution system of the virtual power plant;
the first construction module is used for constructing a virtual power plant safe operation feasible region model considering uncertainty according to the operation parameters to obtain a safe operation constraint coefficient matrix, wherein the construction of the virtual power plant safe operation feasible region model considering uncertainty specifically comprises the following steps: writing a safety operation constraint condition of a virtual power plant according to an operation basic parameter list of a power distribution system, wherein the expression is as follows:
Figure FDA0003413593780000041
Figure FDA0003413593780000042
Figure FDA0003413593780000043
Figure FDA0003413593780000044
Figure FDA0003413593780000045
Figure FDA0003413593780000046
Figure FDA0003413593780000047
Figure FDA0003413593780000048
Figure FDA0003413593780000049
Figure FDA00034135937800000410
wherein formula 1 and formula 2 are the active and reactive power flows of the distribution line ij based on the reduced order power flow equation,
Figure FDA00034135937800000411
Figure FDA0003413593780000051
respectively the active and reactive power flow of the distribution line, bij、gijRespectively series susceptance, series conductance, u, of the distribution linei、ujThe square of the voltage amplitude of node i and node j, θi、θjThe phase angles of the voltages at node i and node j respectively,
Figure FDA0003413593780000052
is a collection of numbers of nodes of the power distribution network,
Figure FDA0003413593780000053
the representation is directly connected with the node i through a distribution lineA set of node numbers of;
formula 3 and formula 4 are the active and reactive balance equations of each node of the distribution network respectively; in the formula Pi g、
Figure FDA0003413593780000054
Respectively the active output and the reactive output of the distributed power supply at the node i;
Figure FDA0003413593780000055
respectively the active load and the reactive load of the node i; p0、Q0Respectively representing active output and reactive output of the virtual power plant;
equation 5 represents the transmission capacity constraint of the distribution line ij, where
Figure FDA0003413593780000056
Is the transmission capacity limit, N, of the distribution linesIs the number of segments that represent the transmission capacity constraint in a linearized segment;
equation 6 represents the distribution transformer capacity constraint at the distribution grid gateway, where
Figure FDA0003413593780000057
Is the upper limit of the capacity of the distribution transformer;
equation 7 represents the upper and lower voltage limits of each node of the distribution network, where
Figure FDA0003413593780000058
viRespectively an upper limit and a lower limit of the voltage amplitude allowed by the node i;
the active output upper and lower limit constraints, the power factor constraints and the capacity constraints of the distributed power supply i are respectively described in a formula 8, a formula 9 and a formula 10; in the formula
Figure FDA0003413593780000059
Pi gThe active output upper and lower limits of the distributed power supply of the node i;
Figure FDA00034135937800000510
is the maximum power factor angle of the distributed power source i;
Figure FDA00034135937800000511
is the upper limit of the capacity of the distributed power source i;
defining a coordination variable x as P0、Q0Is a column vector of elements, i.e. x ═ P0,Q0) (ii) a Defining an uncertain variable w as
Figure FDA00034135937800000512
Is a column vector of elements, i.e.:
Figure FDA00034135937800000513
defining the operation decision variable y as ui、θi、Pi g、
Figure FDA00034135937800000514
Is a column vector of elements, i.e.:
Figure FDA00034135937800000515
the constraints (1) to (10) are arranged in the following form:
Ax+By+Cw≤d (11)
wherein A, B, C is a coefficient matrix and d is a constant vector;
constructing a virtual power plant safe operation feasible region, marking as phi, which is a value set of variables (x, w, y) under the virtual power plant safe operation constraint and is expressed as:
Φ＝{(x,w,y)|Ax+By+Cw≤d} (12)；
the second construction module is used for constructing a virtual power plant operation uncertain set according to the operation parameters, and constructing a virtual power plant robust output feasible region model according to the safe operation constraint coefficient matrix and the virtual power plant operation uncertain set, wherein the virtual power plant operation uncertain set is as follows:
Figure FDA0003413593780000061
wherein w is an uncertain variable of virtual power plant operation, comprising active power load, reactive power load, intermittent distributed resource active output,
Figure FDA0003413593780000062
upper and lower bounds, respectively, of a confidence interval for the kth uncertain variable;
Figure FDA0003413593780000063
is the midpoint of the confidence interval of the uncertain variable, i.e.
Figure FDA0003413593780000064
Δ w is the offset of the uncertain variable from the midpoint of the confidence interval, Δ wkIs the kth element of Δ w; n is a radical ofwIs the number of uncertain variables; gamma is the uncertain budget and takes the value of 0-NwA positive integer of (d); the gamma limits the number of uncertain variables which can deviate from the center of the prediction interval at most in the uncertain set, and further controls the size of the uncertain set; the method for constructing the robust output feasible region model of the virtual power plant specifically comprises the following steps: the robust output feasible region of the virtual power plant is a feasible value set of a coordinated variable x, and the condition that any variable in an uncertain set W is not null is met, so that the feasible region phi of the safe operation of the virtual power plant is not null; the robust output feasible region mathematical representation of the virtual power plant is as follows:
Figure FDA0003413593780000065
the robust output feasible region omega of the virtual power plant defined according to the above formula is a bounded region in two dimensions, and the corresponding virtual power plant output (P) within the feasible region0,Q0) The method can be executed in a power distribution system in a virtual power plant under the disturbance of any uncertain variable without violating the safe operation constraint of the power distribution system; and
the identification module is used for identifying the robust output feasible region of the virtual power plant through vertex enumeration and solving the identification problem of the vertexes of the feasible region through a column constraint generation method, wherein the identification module is further used for searching the vertexes of the robust output feasible region of the virtual power plant along different directions and constructing an approximate polygon by using the searched vertexes; and updating the vertex searching direction through the normal vector of each boundary of the approximate polygon, searching the other vertexes of the feasible robust output domain of the virtual power plant, repeating the process, and calculating to obtain the feasible robust output domain of the virtual power plant.
5. The apparatus of claim 4, wherein the operating parameters comprise distribution network parameters, distributed generation operating parameters, and predictive parameters.
6. The apparatus of claim 4, wherein the initial vertex set and the initial approximate polygon of the robust output feasible region of the virtual power plant are calculated by solving a two-stage adjustable robust optimization problem:
Figure FDA0003413593780000066
wherein, F (x, w) { (y, s) | By-s ≦ d-Ax-Cw, s ≧ 0}, s is a relaxation variable, and 1 represents a column vector with all elements being 1; m0The real number is a positive real number larger than 1, and the typical value of the real number is 1000 times of the capacity of a gateway transformer of a power distribution network; etamIs an optimization problem objective function coefficient, representing the search direction; to etamSequentially taking values of (1,1), (1, -1), (-1, -1); the corresponding optimal solution of the optimization problem is recorded as vmNamely the mth initial vertex; initializing a set of feasible domain vertices to V0＝{v1,v2,v3,v4}; let the set of equations for each boundary of the polygon formed by the initial vertices be denoted as HT(ii) a Calculating V0The center of the polygon formed by the points in (1), i.e. v0＝(v1+v2+v3+v4)/4。
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