CN112132427A - Power grid multi-layer planning method considering user side multiple resource access - Google Patents

Power grid multi-layer planning method considering user side multiple resource access Download PDF

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CN112132427A
CN112132427A CN202010946881.1A CN202010946881A CN112132427A CN 112132427 A CN112132427 A CN 112132427A CN 202010946881 A CN202010946881 A CN 202010946881A CN 112132427 A CN112132427 A CN 112132427A
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photovoltaic
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CN112132427B (en
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黄家祺
贺继锋
颜炯
桑子夏
徐敬友
杨东俊
王思聪
阮博
熊炜
刘君瑶
罗纯坚
张宇威
杨军
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State Grid Corp of China SGCC
Wuhan University WHU
Economic and Technological Research Institute of State Grid Hubei Electric Power Co Ltd
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Wuhan University WHU
Economic and Technological Research Institute of State Grid Hubei Electric Power Co Ltd
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Abstract

A power grid multi-layer planning method considering multiple resource accesses at a user side comprises the following steps: aiming at the uncertainty of various resources at a user side, modeling the uncertainty of fan output, photovoltaic output and load power by adopting a robust optimized box-type uncertain set; aiming at the uncertainty of adapting to various resources at a user side, and taking the access positions, the installation number and the newly-built grid structure of the distributed power supplies as investment decision content, establishing a double-layer power distribution network planning model considering the whole life cycle investment cost and the operation cost of a planning scheme; providing a two-stage robust planning method for a power distribution network based on an extreme scene method; and splitting the two-stage robust planning problem into main and sub problems through an improved C & CG algorithm based on an extreme scene method to solve the main and sub problems in an iterative manner. The design can improve the robustness and economy of power distribution network planning and the capability of the power distribution network for dealing with uncertain risks, and the model is simple to solve and high in calculation efficiency.

Description

Power grid multi-layer planning method considering user side multiple resource access
Technical Field
The invention relates to the field of power distribution network planning, in particular to a power distribution network multilayer planning method considering multiple resource accesses of a user side.
Background
In recent years, with the large-scale access of various resources such as distributed power sources and electric vehicles to a power distribution network, uncertain factors of the power distribution network can challenge the planning and operation of the power distribution network. At present, the processing method for uncertain factors mainly comprises random optimization, opportunity constraint optimization and robust optimization. Although the random optimization can simulate daily uncertain scenes, the random optimization is difficult to deal with extreme scenes; opportunity constraint optimization requires calculation of an accurate probability distribution function of an uncertain variable, and data acquisition difficulty is high; the robust optimization adopts an interval to describe the uncertainty of parameters, so that the requirements on the accuracy probability and the fuzzy membership degree of the uncertain parameters are avoided, and the robustness of the power distribution network is improved.
Disclosure of Invention
The invention aims to overcome the defects and problems of low reliability and economy of power distribution network planning, complex model solution and low efficiency in the prior art, and provides a power grid multi-layer planning method which has high reliability and economy of power distribution network planning, simple model solution and high efficiency and considers the access of various resources at a user side.
In order to achieve the above purpose, the technical solution of the invention is as follows: a power grid multi-layer planning method considering multiple resource accesses at a user side comprises the following steps:
A. aiming at the uncertainty of various resources at a user side, modeling the uncertainty of fan output, photovoltaic output and load power by adopting a robust optimized box-type uncertain set;
B. aiming at the uncertainty of adapting to various resources at a user side, and taking the access positions, the installation number and the newly-built grid structure of the distributed power supplies as investment decision content, establishing a double-layer power distribution network planning model considering the whole life cycle investment cost and the operation cost of a planning scheme, wherein a planning layer objective function is the lowest total construction cost and operation cost, and an operation layer objective function is the lowest operation cost under the determined planning scheme;
C. an extreme scene method is adopted to process uncertainty factors of a double-layer power distribution network planning model, and a power distribution network two-stage robust planning method based on the extreme scene method is provided; the first stage is a planning construction stage, and the access positions and the installation number of the distributed power supplies and the newly-built positions of the lines are determined; the second stage is an operation stage, under the planning scheme of the first stage, the operation condition of the power distribution network under each limit scene is simulated, and the worst scene is optimized;
D. the method comprises the steps of splitting a two-stage robust planning problem into main and sub problems through an improved C & CG algorithm based on a limit scene method, iteratively solving the main problem, solving an optimal planning scheme under a single limit scene through the main problem, transmitting the optimal planning scheme to the sub problems, searching the worst scene under the current planning scheme through the limit scene method through the sub problems, influencing main problem decision through adding relevant operation constraint conditions of the worst scene to the main problem, and finally solving the optimal solution of the iterative robust planning problem through the main and sub problems.
In the step a, uncertainty of fan output, photovoltaic output and load power is represented as:
Figure BDA0002675585260000021
wherein the content of the first and second substances,
Figure BDA0002675585260000022
respectively representing fan output data, photovoltaic output data and load power requirements;
Figure BDA0002675585260000023
respectively predicting the output of a fan, the photovoltaic output and the load power; beta is a1、β2、β3The maximum ranges of the possible deviation predicted values of the fan output, the photovoltaic output and the load power are respectively.
In the step B, the double-layer power distribution network planning model is expressed by a mathematical model as follows:
Figure BDA0002675585260000024
wherein, CINVThe investment cost; cOPEFor operating costs; g (-) and H (-) are planning layer constraints; g (-) and f (-) are constraint conditions of the operation layer; x is the number ofinvDetermining the commissioning of the lines and the distributed power supply for constructing variables; x is the number ofopeOperating variables including line power and node voltage; xi is uncertainty parameter of fan, photovoltaic and load, and is mainly concentrated on the operation layer.
In step B, the planning layer objective function is min F ═ CINV+COPEThe method specifically comprises the following steps:
CINV＝CWTG+CPVG+CLINE
Figure BDA0002675585260000031
Figure BDA0002675585260000032
Figure BDA0002675585260000033
wherein subscript j represents the node number; subscript ij denotes a line between node i and node j; cLINE、CWTG、CPVGRespectively converting the total construction cost of the line, the fan and the photovoltaic into the total construction cost of the line, the fan and the photovoltaic; z is the inflation rate for the cargo; y isLINE、YWTG、YPVGThe service lives of the line, the fan and the photovoltaic are respectively prolonged;
Figure BDA0002675585260000034
the construction cost per kilometer of the line; c. CWTG、cPVGThe construction cost of each fan and each photovoltaic unit is respectively the construction cost of each fan and each photovoltaic unit; l isijThe length of each alternative line; omegaLINE、ΩWTG、ΩPVGRespectively obtaining a candidate set of lines to be built, a candidate node set of fans to be built and a candidate node set of photovoltaic cells to be built;
Figure BDA0002675585260000036
is a variable of 0 to 1, determines whether a line, a fan and a photovoltaic are put into operation or not, and for the established line,
Figure BDA0002675585260000037
is 1;
Figure BDA0002675585260000038
wherein T is the number of time periods of operation in one day; Δ t is the time of each time interval;
Figure BDA0002675585260000039
the electricity price for purchasing electricity from the main network for the t period; c. Closs、cLS、cLW、cLPVRespectively unit network loss cost, load loss cost, wind abandoning cost and light abandoning cost;
Figure BDA00026755852600000310
respectively obtaining main network output, loss load power, fan output data, fan actual output, photovoltaic output data and photovoltaic actual output; i isij，tIs the line current; r isijIs a line electric group; omegaTRIs a collection of transformer nodes; elineCollecting all the lines which are built and are to be built for the power distribution network; omegaENSIs the set of all load nodes;
the running layer objective function is:
min f＝COPE。
in the step B, the constraint conditions of the planning layer comprise equipment investment construction constraint, network radial constraint and network connectivity constraint;
assuming that the maximum number of the connected fans and the maximum number of the photovoltaic circuits are specified in the power distribution network planning, and the number of the newly-built lines is also determined, the equipment investment construction constraint is specifically as follows:
Figure BDA0002675585260000041
wherein N isWTGSetting the maximum number of the newly built fans; n is a radical ofPVGSetting the maximum number of newly-built photovoltaic cells; n is a radical ofLINEPredicting the number of newly built lines;
in order to ensure the connectivity of each node of the planned power grid and avoid the operation of the roundabout, the connectivity inspection and radial inspection of the topological structure of the planned distribution network are required.
In the step B, the constraint conditions of the operation layer comprise node power balance constraint, line voltage balance constraint, line capacity constraint, transformer capacity constraint, safety constraint, distributed power supply output constraint and loss load constraint;
to eliminate non-linear terms in the AC power flow, for the current Iij，tSum voltage Uj，tThrough variable replacement and second-order cone relaxation, the nonlinear constraint in the alternating current power flow is converted into a second-order cone constraint:
Figure BDA0002675585260000042
wherein the content of the first and second substances,
Figure BDA0002675585260000043
is the square of the current value of line ij;
Figure BDA0002675585260000044
is the square of the voltage value of node j;
then the run level constraints are:
node power balance constraint:
Figure BDA0002675585260000051
Figure BDA0002675585260000052
Figure BDA0002675585260000053
Figure BDA0002675585260000054
wherein, (j) is a line set with the node j as a head end; k is the end node of the line jk; pi (j) is a line set taking the node j as a tail end; omegaFIs a collection of load nodes; pjk，tThe active power transmitted by the line jk at the moment t; qjk，tThe reactive power transmitted by the line jk at the moment t; pij，t、Qij，tRespectively the active power and the reactive power transmitted by the line ij at the moment t;
Figure BDA0002675585260000055
respectively the active load demand and the reactive load demand of the node j; x is the number ofijIs the reactance value of line ij;
Figure BDA0002675585260000056
the main network reactive power, the fan reactive power, the photovoltaic reactive power and the loss load reactive power are respectively;
Figure BDA0002675585260000057
is the square of the voltage value of the node i;
line voltage balance constraint:
Figure BDA0002675585260000058
Figure BDA0002675585260000059
Figure BDA00026755852600000510
wherein M is a large enough solidCounting; elineCollecting all the lines which are built and are to be built for the power distribution network;
and (3) line capacity constraint:
Figure BDA0002675585260000061
Figure BDA0002675585260000062
wherein the content of the first and second substances,
Figure BDA0002675585260000063
the maximum current-carrying capacity of the line;
and (3) transformer capacity constraint:
Figure BDA0002675585260000064
Figure BDA0002675585260000065
wherein the content of the first and second substances,
Figure BDA0002675585260000066
minimum active and reactive output thresholds of the transformer are respectively set;
Figure BDA0002675585260000067
the maximum active and reactive output thresholds of the transformer are respectively set;
safety restraint:
Figure BDA0002675585260000068
Figure BDA0002675585260000069
wherein the content of the first and second substances,
Figure BDA00026755852600000610
is the minimum value of the node voltage;
Figure BDA00026755852600000611
is the maximum value of the node voltage;
Figure BDA00026755852600000612
is the maximum line current;
and (3) output constraint of the distributed power supply:
Figure BDA00026755852600000613
Figure BDA00026755852600000614
and (4) load loss constraint:
Figure BDA00026755852600000615
wherein the content of the first and second substances,
Figure BDA00026755852600000616
is the maximum load loss percentage for node j;
Figure BDA00026755852600000617
is the load power factor.
In the step C, a specific mathematical model of the two-stage robust planning of the power distribution network is as follows:
Figure BDA0002675585260000071
Dx≤d
Ex＝e
Figure BDA0002675585260000072
Figure BDA0002675585260000073
Figure BDA0002675585260000074
wherein x is a construction variable of a line, a fan and a photovoltaic; subscript s denotes the limit scene number; n is a radical ofsRepresenting the number of limit scenes; xisRepresenting values of fan output, photovoltaic output and load power under a limit scene s; y issRepresenting the operation decision variables of the line power and the voltage under the limit scene; ax is the construction cost; bys+CξsThe running cost under the limit scene s; A. b, C, D, E, F, G, H, L, M, D, E, F, G, H are coefficient matrixes.
In step D, the mathematical model of the main problem is as follows:
Figure BDA0002675585260000075
Dx≤d
Ex＝e
Figure BDA0002675585260000076
Figure BDA0002675585260000077
Figure BDA0002675585260000078
Figure BDA0002675585260000079
wherein x is a construction variable of a line, a fan and a photovoltaic; eta is the actual operation cost of the power distribution network; n is C&The iteration times of the CG algorithm; k is a radical ofmNumbering the limit scenes selected in the mth iteration;
Figure BDA00026755852600000710
as extreme scene kmRunning decision variables;
Figure BDA00026755852600000711
as extreme scene kmAnd values of uncertain variables of lower fan output, photovoltaic output and load power.
In step D, the mathematical model of the subproblem is:
Figure BDA0002675585260000081
Figure BDA0002675585260000082
Figure BDA0002675585260000083
Figure BDA0002675585260000084
wherein the content of the first and second substances,
Figure BDA0002675585260000085
and constructing and planning an optimal solution for the main problem in the nth iteration.
In the step D, the specific flow of the improved C & CG algorithm based on the extreme scene method is as follows:
(1) setting a lower bound LB ═ infinity, an upper bound UB +∞, and an algorithm iteration number n ═ 1;
(2) solving the main problem to obtain the optimal solution of the construction plan
Figure BDA0002675585260000086
And operating costs under the scenario
Figure BDA0002675585260000087
And updating the lower bound value
Figure BDA0002675585260000088
(3) Fixed construction plan optimal solution
Figure BDA0002675585260000089
Solving the sub-problems to obtain the sub-problems under all limit scenes
Figure BDA00026755852600000810
If all the sub-problems in the extreme scenes have solutions, finding the maximum value of feasible solutions in all the scenes
Figure BDA00026755852600000811
Obtaining the number s of the limit scene and updating the upper bound value
Figure BDA00026755852600000812
If the subproblem is not feasible under the limit scene s, the current worst limit scene is s;
(4) if UB-LB <, the convergence precision is given, then the iteration is finished, and the optimal solution of the current construction plan is obtained
Figure BDA00026755852600000813
Otherwise, updating the worst limit scene s under the current planning condition, and adding the constraint condition corresponding to the scene to the main problem;
(5) and (4) returning to the step (2) when n is n + 1.
Compared with the prior art, the invention has the beneficial effects that:
the power grid multilayer planning method considering the access of various resources at the user side can effectively improve the capability of a power distribution network for coping with the uncertainty of various resources at the user side, simultaneously reduces the operating cost of the power distribution network, and considers the economy of power distribution network planning; in addition, compared with a two-stage robust programming model adopting a conventional method, the design is simpler in solution and higher in calculation efficiency. According to the design, a power distribution network planning model considering various resources at the user side is established, scientific planning basis is provided for power distribution network planning personnel, and the reliability and economy of power distribution network planning are improved.
Drawings
Fig. 1 is a flowchart of a power grid multi-layer planning method considering multiple resource accesses at a user side according to the present invention.
FIG. 2 is a schematic diagram of a limit scenario approach.
Fig. 3 is a flow chart of a C & CG algorithm based on the extreme scene method.
Fig. 4 is a power distribution network planning scheme obtained according to simulation calculation in the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following description and embodiments in conjunction with the accompanying drawings.
Referring to fig. 1 to 4, a method for multi-layer planning of a power grid considering multiple resource accesses at a user side includes the following steps:
A. aiming at the uncertainty of various resources at a user side, modeling the uncertainty of fan output, photovoltaic output and load power by adopting a robust optimized box-type uncertain set;
B. aiming at the uncertainty of adapting to various resources at a user side, and taking the access positions, the installation number and the newly-built grid structure of the distributed power supplies as investment decision content, establishing a double-layer power distribution network planning model considering the whole life cycle investment cost and the operation cost of a planning scheme, wherein a planning layer objective function is the lowest total construction cost and operation cost, and an operation layer objective function is the lowest operation cost under the determined planning scheme;
C. an extreme scene method is adopted to process uncertainty factors of a double-layer power distribution network planning model, and a power distribution network two-stage robust planning method based on the extreme scene method is provided; the first stage is a planning construction stage, and the access positions and the installation number of the distributed power supplies and the newly-built positions of the lines are determined; the second stage is an operation stage, under the planning scheme of the first stage, the operation condition of the power distribution network under each limit scene is simulated, and the worst scene is optimized;
D. the method comprises the steps of splitting a two-stage robust planning problem into main and sub problems through an improved C & CG algorithm based on a limit scene method, iteratively solving the main problem, solving an optimal planning scheme under a single limit scene through the main problem, transmitting the optimal planning scheme to the sub problems, searching the worst scene under the current planning scheme through the limit scene method through the sub problems, influencing main problem decision through adding relevant operation constraint conditions of the worst scene to the main problem, and finally solving the optimal solution of the iterative robust planning problem through the main and sub problems.
In the step a, uncertainty of fan output, photovoltaic output and load power is represented as:
Figure BDA0002675585260000091
wherein the content of the first and second substances,
Figure BDA0002675585260000092
respectively representing fan output data, photovoltaic output data and load power requirements;
Figure BDA0002675585260000101
respectively predicting the output of a fan, the photovoltaic output and the load power; beta is a1、β2、β3The maximum ranges of the possible deviation predicted values of the fan output, the photovoltaic output and the load power are respectively.
In the step B, the double-layer power distribution network planning model is expressed by a mathematical model as follows:
Figure BDA0002675585260000102
wherein, CINVThe investment cost; cOPEFor operating costs;g (-) and H (-) are planning layer constraints; g (-) and f (-) are constraint conditions of the operation layer; x is the number ofinvDetermining the commissioning of the lines and the distributed power supply for constructing variables; x is the number ofopeOperating variables including line power and node voltage; xi is uncertainty parameter of fan, photovoltaic and load, and is mainly concentrated on the operation layer.
In step B, the planning layer objective function is min F ═ CINV+COPEThe method specifically comprises the following steps:
CINV＝CWTG+CPVG+CLINE
Figure BDA0002675585260000103
Figure BDA0002675585260000104
Figure BDA0002675585260000105
wherein subscript j represents the node number; subscript ij denotes a line between node i and node j; cLINE、CWTG、CPVGRespectively converting the total construction cost of the line, the fan and the photovoltaic into the total construction cost of the line, the fan and the photovoltaic; z is the inflation rate for the cargo; y isLINE、YWTG、YPVGThe service lives of the line, the fan and the photovoltaic are respectively prolonged;
Figure BDA0002675585260000106
the construction cost per kilometer of the line; c. CWTG、cPVGThe construction cost of each fan and each photovoltaic unit is respectively the construction cost of each fan and each photovoltaic unit; l isijThe length of each alternative line; omegaLNE、ΩWTG、ΩPVGRespectively obtaining a candidate set of lines to be built, a candidate node set of fans to be built and a candidate node set of photovoltaic cells to be built;
Figure BDA0002675585260000111
is a variable of 0 to 1, determines whether a line, a fan and a photovoltaic are put into operation or not, and for the established line,
Figure BDA0002675585260000112
is 1;
Figure BDA0002675585260000113
wherein T is the number of time periods of operation in one day; Δ t is the time of each time interval;
Figure BDA0002675585260000114
the electricity price for purchasing electricity from the main network for the t period; c. Closs、cLS、cLW、cLPVRespectively unit network loss cost, load loss cost, wind abandoning cost and light abandoning cost;
Figure BDA0002675585260000115
respectively obtaining main network output, loss load power, fan output data, fan actual output, photovoltaic output data and photovoltaic actual output; i isij，tIs the line current; r isijIs a line electric group; omegaTRIs a collection of transformer nodes; elineCollecting all the lines which are built and are to be built for the power distribution network; omegaENSIs the set of all load nodes;
the running layer objective function is:
min f＝COPE。
in the step B, the constraint conditions of the planning layer comprise equipment investment construction constraint, network radial constraint and network connectivity constraint;
assuming that the maximum number of the connected fans and the maximum number of the photovoltaic circuits are specified in the power distribution network planning, and the number of the newly-built lines is also determined, the equipment investment construction constraint is specifically as follows:
Figure BDA0002675585260000116
wherein N isWTGSetting the maximum number of the newly built fans; n is a radical ofPVGSetting the maximum number of newly-built photovoltaic cells; n is a radical ofLINEPredicting the number of newly built lines;
in order to ensure the connectivity of each node of the planned power grid and avoid the operation of the roundabout, the connectivity inspection and radial inspection of the topological structure of the planned distribution network are required.
In the step B, the constraint conditions of the operation layer comprise node power balance constraint, line voltage balance constraint, line capacity constraint, transformer capacity constraint, safety constraint, distributed power supply output constraint and loss load constraint;
to eliminate non-linear terms in the AC power flow, for the current Iij，tSum voltage Uj，tThrough variable replacement and second-order cone relaxation, the nonlinear constraint in the alternating current power flow is converted into a second-order cone constraint:
Figure BDA0002675585260000121
wherein the content of the first and second substances,
Figure BDA0002675585260000122
is the square of the current value of line ij;
Figure BDA0002675585260000123
is the square of the voltage value of node j;
then the run level constraints are:
node power balance constraint:
Figure BDA0002675585260000124
Figure BDA0002675585260000125
Figure BDA0002675585260000126
Figure BDA0002675585260000127
wherein, (j) is a line set with the node j as a head end; k is the end node of the line jk; pi (j) is a line set taking the node j as a tail end; omegaFIs a collection of load nodes; pjk，tThe active power transmitted by the line jk at the moment t; qjk，tThe reactive power transmitted by the line jk at the moment t; pij，t、Qij，tRespectively the active power and the reactive power transmitted by the line ij at the moment t;
Figure BDA0002675585260000128
respectively the active load demand and the reactive load demand of the node j; x is the number ofijIs the reactance value of line ij;
Figure BDA0002675585260000131
the main network reactive power, the fan reactive power, the photovoltaic reactive power and the loss load reactive power are respectively;
Figure BDA0002675585260000132
is the square of the voltage value of the node i;
line voltage balance constraint:
Figure BDA0002675585260000133
Figure BDA0002675585260000134
Figure BDA0002675585260000135
wherein M is a sufficiently large positive real number; elineFor all the built and to-be-built power distribution networksThe line set of (2);
and (3) line capacity constraint:
Figure BDA0002675585260000136
Figure BDA0002675585260000137
wherein the content of the first and second substances,
Figure BDA0002675585260000138
the maximum current-carrying capacity of the line;
and (3) transformer capacity constraint:
Figure BDA0002675585260000139
Figure BDA00026755852600001310
wherein the content of the first and second substances,
Figure BDA00026755852600001311
minimum active and reactive output thresholds of the transformer are respectively set;
Figure BDA00026755852600001312
the maximum active and reactive output thresholds of the transformer are respectively set;
safety restraint:
Figure BDA00026755852600001313
Figure BDA00026755852600001314
wherein the content of the first and second substances,
Figure BDA00026755852600001315
is the minimum value of the node voltage;
Figure BDA00026755852600001316
is the maximum value of the node voltage;
Figure BDA00026755852600001317
is the maximum line current;
and (3) output constraint of the distributed power supply:
Figure BDA0002675585260000141
Figure BDA0002675585260000142
and (4) load loss constraint:
Figure BDA0002675585260000143
wherein the content of the first and second substances,
Figure BDA0002675585260000144
is the maximum load loss percentage for node j;
Figure BDA0002675585260000145
is the load power factor.
In the step C, a specific mathematical model of the two-stage robust planning of the power distribution network is as follows:
Figure BDA0002675585260000146
Dx≤d
Ex＝e
Figure BDA0002675585260000147
Figure BDA0002675585260000148
Figure BDA0002675585260000149
wherein x is a construction variable of a line, a fan and a photovoltaic; subscript s denotes the limit scene number; n is a radical ofsRepresenting the number of limit scenes; xisRepresenting values of fan output, photovoltaic output and load power under a limit scene s; y issRepresenting the operation decision variables of the line power and the voltage under the limit scene; ax is the construction cost; bys+CξsThe running cost under the limit scene s; A. b, C, D, E, F, G, H, L, M, D, E, F, G, H are coefficient matrixes.
In step D, the mathematical model of the main problem is as follows:
Figure BDA0002675585260000151
Dx≤d
Ex＝e
Figure BDA0002675585260000152
Figure BDA0002675585260000153
Figure BDA0002675585260000154
Figure BDA0002675585260000155
wherein x is a line,Construction variables of fans and photovoltaics; eta is the actual operation cost of the power distribution network; n is C&The iteration times of the CG algorithm; k is a radical ofmNumbering the limit scenes selected in the mth iteration;
Figure BDA00026755852600001517
as extreme scene kmRunning decision variables;
Figure BDA00026755852600001518
as extreme scene kmAnd values of uncertain variables of lower fan output, photovoltaic output and load power.
In step D, the mathematical model of the subproblem is:
Figure BDA0002675585260000156
Figure BDA0002675585260000157
Figure BDA0002675585260000158
Figure BDA0002675585260000159
wherein the content of the first and second substances,
Figure BDA00026755852600001510
and constructing and planning an optimal solution for the main problem in the nth iteration.
In the step D, the specific flow of the improved C & CG algorithm based on the extreme scene method is as follows:
(1) setting a lower bound LB ═ infinity, an upper bound UB +∞, and an algorithm iteration number n ═ 1;
(2) solving the main problem to obtain the optimal solution of the construction plan
Figure BDA00026755852600001511
And operating costs under the scenario
Figure BDA00026755852600001512
And updating the lower bound value
Figure BDA00026755852600001513
(3) Fixed construction plan optimal solution
Figure BDA00026755852600001514
Solving the sub-problems to obtain the sub-problems under all limit scenes
Figure BDA00026755852600001515
If all the sub-problems in the extreme scenes have solutions, finding the maximum value of feasible solutions in all the scenes
Figure BDA00026755852600001516
Obtaining the number s of the limit scene and updating the upper bound value
Figure BDA0002675585260000161
If the subproblem is not feasible under the limit scene s, the current worst limit scene is s;
(4) if UB-LB <, the convergence precision is given, then the iteration is finished, and the optimal solution of the current construction plan is obtained
Figure BDA0002675585260000162
Otherwise, updating the worst limit scene s under the current planning condition, and adding the constraint condition corresponding to the scene to the main problem;
(5) and (4) returning to the step (2) when n is n + 1.
The principle of the invention is illustrated as follows:
in the step A, a robust optimized box-type uncertain set model is adopted to model uncertainty of user side resources, and user side uncertainty factors such as fan output, photovoltaic output and load power are mainly considered; the robust optimization considers that the wind turbine output, the photovoltaic output and the load power possibly deviate from the predicted value under the actual condition, and the uncertainty is described by adopting an interval.
In the step B, the planning layer determines construction variables and transmits the construction variables to the operation layer, and the operation layer influences planning layer decision by adding operation constraints to the planning layer.
In the step C, error scenes are defined as scenes of fan output, photovoltaic output and load power deviation predicted values, robust optimization must meet operation constraints of all the error scenes, but the number of the error scenes is infinite, and solution cannot be carried out, so that a limit scene method is introduced. The limit scene is defined as a scene in which all uncertain parameters take extreme values, the output time sequence characteristics of all fans, photovoltaic and loads in a power distribution network area are considered to have similarity, and in order to simplify the number of the uncertain parameters, three uncertain factors, namely the fans, the photovoltaic and the loads, are assumed to have the same time sequence characteristics in the area, and eight limit scenes are formed. In convex optimization, an extreme value necessarily exists at a certain endpoint of a polyhedral solution space, and an extreme scene has complete robustness for all error scenes and a construction variable xinvAs long as the operating variable x is adjustedopeThe method can adapt to all limit scenes, and can adapt to all error scenes, so that the robustness of power distribution network planning is ensured.
In the step D, the main problem determines the value of a construction decision variable x of a fan, a photovoltaic, a line and the like, and transmits the value to the sub-problem, and the sub-problem searches the worst scene under the construction condition of the main problem by a limit scene method; solving the running cost of each sub-problem under each limit scene by adopting an enumeration method, wherein if the sub-problems under all the limit scenes are solved, the scene with the largest running cost is the worst scene under the current planning condition; if a certain scene exists, so that no feasible solution exists in the planning, the scene is the worst scene; the sub-problem affects the main problem decision by adding the relevant operational constraints of the severe scenario to the main problem. Compared with the conventional dual method, the sub-problems of each limit scene in the method are linear programming problems without integer variables, and the solution is relatively simple.
Example (b):
referring to fig. 1 to 4, a method for multi-layer planning of a power grid considering multiple resource accesses at a user side includes the following steps:
A. aiming at the uncertainty of various resources at a user side, modeling the uncertainty of fan output, photovoltaic output and load power by adopting a robust optimized box-type uncertain set;
the uncertainty of the fan output, the photovoltaic output and the load power is represented as follows:
Figure BDA0002675585260000171
wherein the content of the first and second substances,
Figure BDA0002675585260000172
respectively representing fan output data, photovoltaic output data and load power requirements;
Figure BDA0002675585260000173
respectively predicting the output of a fan, the photovoltaic output and the load power; beta is a1、β2、β3The maximum ranges of the predicted values of the possible deviation of the fan output, the photovoltaic output and the load power are respectively analyzed by combining with actual scenes so as to obtain specific output deviation values, and the design beta is1、β2、β3Taking the weight percentage to be 30 percent;
B. aiming at the uncertainty of adapting to various resources at a user side, and taking the access positions, the installation number and the newly-built grid structure of the distributed power supplies as investment decision content, establishing a double-layer power distribution network planning model considering the whole life cycle investment cost and the operation cost of a planning scheme, wherein a planning layer objective function is the lowest total construction cost and operation cost, and an operation layer objective function is the lowest operation cost under the determined planning scheme;
the double-layer power distribution network planning model is expressed by a mathematical model as follows:
Figure BDA0002675585260000174
wherein, CINVThe investment cost; cOPEFor operating costs; g (-) and H (-) are planning layer constraints; g (-) and f (-) are constraint conditions of the operation layer; x is the number ofinvDetermining the commissioning of the lines and the distributed power supply for constructing variables; x is the number ofopeOperating variables including line power and node voltage; xi is uncertainty parameter of fan, photovoltaic and load, mainly concentrated on the operation layer;
planning a layer objective function to min F ═ CINV+COPEThe method specifically comprises the following steps:
CINV＝CWTG+CPVG+CLINE
Figure BDA0002675585260000181
Figure BDA0002675585260000182
Figure BDA0002675585260000183
wherein subscript j represents the node number; subscript ij denotes a line between node i and node j; cLINE、CWTG、CPVGRespectively converting the total construction cost of the line, the fan and the photovoltaic into the total construction cost of the line, the fan and the photovoltaic; z is the inflation rate for the cargo; y isLINE、YWTG、YPVGThe service lives of the line, the fan and the photovoltaic are respectively prolonged;
Figure BDA0002675585260000184
the construction cost per kilometer of the line; c. CWTG、cPVGThe construction cost of each fan and each photovoltaic unit is respectively the construction cost of each fan and each photovoltaic unit; l isijThe length of each alternative line; omegaLINE、ΩWTG、ΩPVGAre respectively candidates of the line to be establishedThe method comprises the steps of collecting, a candidate node set of a fan to be built and a candidate node set of a photovoltaic to be built;
Figure BDA0002675585260000185
is a variable of 0 to 1, determines whether a line, a fan and a photovoltaic are put into operation or not, and for the established line,
Figure BDA0002675585260000186
is 1;
Figure BDA0002675585260000187
wherein T is the number of time periods of operation in one day; Δ t is the time of each time interval;
Figure BDA0002675585260000188
the electricity price for purchasing electricity from the main network for the t period; c. Closs、cLS、cLW、cLPVRespectively unit network loss cost, load loss cost, wind abandoning cost and light abandoning cost;
Figure BDA0002675585260000189
respectively obtaining main network output, loss load power, fan output data, fan actual output, photovoltaic output data and photovoltaic actual output; i isij，tIs the line current; r isijIs a line electric group; omegaTRIs a collection of transformer nodes; elineCollecting all the lines which are built and are to be built for the power distribution network; omegaENSIs the set of all load nodes;
the running layer objective function is:
min f＝COPE；
the planning layer constraint conditions comprise equipment investment construction constraint, network radial constraint and network connectivity constraint;
assuming that the maximum number of the connected fans and the maximum number of the photovoltaic circuits are specified in the power distribution network planning, and the number of the newly-built lines is also determined, the equipment investment construction constraint is specifically as follows:
Figure BDA0002675585260000191
wherein N isWTGSetting the maximum number of the newly built fans; n is a radical ofPVGSetting the maximum number of newly-built photovoltaic cells; n is a radical ofLINEPredicting the number of newly built lines;
in order to ensure the connectivity of each node of the planned power grid and avoid the operation of a rotary island, the connectivity inspection and radial inspection of the topological structure of the planned distribution network are required;
the operation layer constraint conditions comprise node power balance constraint, line voltage balance constraint, line capacity constraint, transformer capacity constraint, safety constraint, distributed power supply output constraint and loss load constraint;
to eliminate non-linear terms in the AC power flow, for the current Iij，tSum voltage Uj，tThrough variable replacement and second-order cone relaxation, the nonlinear constraint in the alternating current power flow is converted into a second-order cone constraint:
Figure BDA0002675585260000192
wherein the content of the first and second substances,
Figure BDA0002675585260000193
is the square of the current value of line ij;
Figure BDA0002675585260000194
is the square of the voltage value of node j;
then the run level constraints are:
node power balance constraint:
Figure BDA0002675585260000201
Figure BDA0002675585260000202
Figure BDA0002675585260000203
Figure BDA0002675585260000204
wherein, (j) is a line set with the node j as a head end; k is the end node of the line jk; pi (j) is a line set taking the node j as a tail end; omegaFIs a collection of load nodes; pjk，tThe active power transmitted by the line jk at the moment t; qjk，tThe reactive power transmitted by the line jk at the moment t; pij，t、Qij，tRespectively the active power and the reactive power transmitted by the line ij at the moment t;
Figure BDA0002675585260000205
respectively the active load demand and the reactive load demand of the node j; x is the number ofijIs the reactance value of line ij;
Figure BDA0002675585260000206
the main network reactive power, the fan reactive power, the photovoltaic reactive power and the loss load reactive power are respectively;
Figure BDA0002675585260000207
is the square of the voltage value of the node i;
line voltage balance constraint:
Figure BDA0002675585260000208
Figure BDA0002675585260000209
Figure BDA00026755852600002010
the quantity level of M is higher than other variables in the formula, the M is a positive real number which is large enough to reduce the operation error, but the calculation efficiency is reduced when the M is too large, and the design M is 100000; elineCollecting all the lines which are built and are to be built for the power distribution network;
and (3) line capacity constraint:
Figure BDA0002675585260000211
Figure BDA0002675585260000212
wherein the content of the first and second substances,
Figure BDA0002675585260000213
the maximum current-carrying capacity of the line;
and (3) transformer capacity constraint:
Figure BDA0002675585260000214
Figure BDA0002675585260000215
wherein the content of the first and second substances,
Figure BDA0002675585260000216
minimum active and reactive output thresholds of the transformer are respectively set;
Figure BDA0002675585260000217
the maximum active and reactive output thresholds of the transformer are respectively set;
safety restraint:
Figure BDA0002675585260000218
Figure BDA0002675585260000219
wherein the content of the first and second substances,
Figure BDA00026755852600002110
is the minimum value of the node voltage;
Figure BDA00026755852600002111
is the maximum value of the node voltage;
Figure BDA00026755852600002112
is the maximum line current;
and (3) output constraint of the distributed power supply:
Figure BDA00026755852600002113
Figure BDA00026755852600002114
and (4) load loss constraint:
Figure BDA00026755852600002115
wherein the content of the first and second substances,
Figure BDA00026755852600002116
is the maximum load loss percentage for node j;
Figure BDA00026755852600002117
is the load power factor;
C. an extreme scene method is adopted to process uncertainty factors of a double-layer power distribution network planning model, and a power distribution network two-stage robust planning method based on the extreme scene method is provided; the first stage is a planning construction stage, and the access positions and the installation number of the distributed power supplies and the newly-built positions of the lines are determined; the second stage is an operation stage, under the planning scheme of the first stage, the operation condition of the power distribution network under each limit scene is simulated, and the worst scene is optimized;
the specific mathematical model of the two-stage robust planning of the power distribution network is as follows:
Figure BDA0002675585260000221
Dx≤d
Ex＝e
Figure BDA0002675585260000222
Figure BDA0002675585260000223
Figure BDA0002675585260000224
wherein x is a construction variable of a line, a fan and a photovoltaic; subscript s denotes the limit scene number; n is a radical ofsRepresenting the number of limit scenes; xisRepresenting values of fan output, photovoltaic output and load power under a limit scene s; y issRepresenting the operation decision variables of the line power and the voltage under the limit scene; ax is the construction cost; bys+CξsThe running cost under the limit scene s; A. b, C, D, E, F, G, H, L, M, D, E, F, G and H are coefficient matrixes;
D. splitting a two-stage robust planning problem into main and sub problems through an improved C & CG algorithm based on a limit scene method, iteratively solving the main problem, solving the optimal planning scheme under a single limit scene by the main problem, transmitting the optimal planning scheme to the sub problems, searching the worst scene under the current planning scheme by the limit scene method by the sub problems, adding relevant operation constraint conditions of the worst scene to the main problem to influence the decision of the main problem, and finally solving the optimal solution of the iterative robust planning problem through the main and sub problems;
the mathematical model of the main problem is:
Figure BDA0002675585260000226
Dx≤d
Ex＝e
Figure BDA0002675585260000227
Figure BDA0002675585260000228
Figure BDA0002675585260000229
Figure BDA00026755852600002210
wherein x is a construction variable of a line, a fan and a photovoltaic; eta is the actual operation cost of the power distribution network; n is C&The iteration times of the CG algorithm; k is a radical ofmNumbering the limit scenes selected in the mth iteration;
Figure BDA00026755852600002314
as extreme scene kmRunning decision variables;
Figure BDA00026755852600002315
as extreme scene kmValues of uncertain variables of lower fan output, photovoltaic output and load power;
the mathematical model of the subproblem is:
Figure BDA0002675585260000231
Figure BDA0002675585260000232
Figure BDA0002675585260000233
Figure BDA0002675585260000234
wherein the content of the first and second substances,
Figure BDA0002675585260000235
constructing and planning an optimal solution for the main problem in the nth iteration;
the specific flow of the improved C & CG algorithm based on the extreme scene method is as follows:
(1) setting a lower bound LB ═ infinity, an upper bound UB +∞, and an algorithm iteration number n ═ 1;
(2) solving the main problem to obtain the optimal solution of the construction plan
Figure BDA0002675585260000236
And operating costs under the scenario
Figure BDA0002675585260000237
And updating the lower bound value
Figure BDA0002675585260000238
(3) Fixed construction plan optimal solution
Figure BDA0002675585260000239
Solving the sub-problems to obtain the sub-problems under all limit scenes
Figure BDA00026755852600002310
If all the sub-problems in the extreme scene have solutions, thenFinding the maximum of feasible solutions under all scenes
Figure BDA00026755852600002311
Obtaining the number s of the limit scene and updating the upper bound value
Figure BDA00026755852600002312
If the subproblem is not feasible under the limit scene s, the current worst limit scene is s;
(4) if UB-LB is less than the given convergence precision, the value is 0.1, the iteration is finished, and the optimal solution of the current construction plan is obtained
Figure BDA00026755852600002313
Otherwise, updating the worst limit scene s under the current planning condition, and adding the constraint condition corresponding to the scene to the main problem;
(5) and (4) returning to the step (2) when n is n + 1.
In order to test the reliability and effectiveness of the design, under the condition of the same planning condition, the power distribution network is planned by using the design and compared with a power distribution network deterministic planning model, and the conclusion is as follows: the method provided by the design can effectively improve the capability of the power distribution network to cope with uncertainty of various resources at the user side, simultaneously reduces the operating cost of the power distribution network, and considers the economy of power distribution network planning.

Claims (10)

1. A power grid multi-layer planning method considering multiple resource accesses at a user side is characterized by comprising the following steps:
A. aiming at the uncertainty of various resources at a user side, modeling the uncertainty of fan output, photovoltaic output and load power by adopting a robust optimized box-type uncertain set;
B. aiming at the uncertainty of adapting to various resources at a user side, and taking the access positions, the installation number and the newly-built grid structure of the distributed power supplies as investment decision content, establishing a double-layer power distribution network planning model considering the whole life cycle investment cost and the operation cost of a planning scheme, wherein a planning layer objective function is the lowest total construction cost and operation cost, and an operation layer objective function is the lowest operation cost under the determined planning scheme;
C. an extreme scene method is adopted to process uncertainty factors of a double-layer power distribution network planning model, and a power distribution network two-stage robust planning method based on the extreme scene method is provided; the first stage is a planning construction stage, and the access positions and the installation number of the distributed power supplies and the newly-built positions of the lines are determined; the second stage is an operation stage, under the planning scheme of the first stage, the operation condition of the power distribution network under each limit scene is simulated, and the worst scene is optimized;
D. the method comprises the steps of splitting a two-stage robust planning problem into main and sub problems through an improved C & CG algorithm based on a limit scene method, iteratively solving the main problem, solving an optimal planning scheme under a single limit scene through the main problem, transmitting the optimal planning scheme to the sub problems, searching the worst scene under the current planning scheme through the limit scene method through the sub problems, influencing main problem decision through adding relevant operation constraint conditions of the worst scene to the main problem, and finally solving the optimal solution of the iterative robust planning problem through the main and sub problems.
2. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 1, characterized in that:
in the step a, uncertainty of fan output, photovoltaic output and load power is represented as:
Figure FDA0002675585250000011
wherein the content of the first and second substances,
Figure FDA0002675585250000012
respectively representing fan output data, photovoltaic output data and load power requirements;
Figure FDA0002675585250000013
are respectively asThe predicted output of fan output, photovoltaic output and load power; beta is a1、β2、β3The maximum ranges of the possible deviation predicted values of the fan output, the photovoltaic output and the load power are respectively.
3. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 2, characterized in that:
in the step B, the double-layer power distribution network planning model is expressed by a mathematical model as follows:
Figure FDA0002675585250000021
wherein, CINVThe investment cost; cOPEFor operating costs; g (-) and H (-) are planning layer constraints; g (-) and f (-) are constraint conditions of the operation layer; x is the number ofinvDetermining the commissioning of the lines and the distributed power supply for constructing variables; x is the number ofopeOperating variables including line power and node voltage; xi is uncertainty parameter of fan, photovoltaic and load, and is mainly concentrated on the operation layer.
4. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 3, characterized in that:
in step B, the planning layer objective function is min F ═ CINV+COPEThe method specifically comprises the following steps:
CINV＝CWTG+CPVG+CLINE
Figure FDA0002675585250000022
Figure FDA0002675585250000023
Figure FDA0002675585250000024
wherein subscript j represents the node number; subscript ij denotes a line between node i and node j; cLINE、CWTG、CPVGRespectively converting the total construction cost of the line, the fan and the photovoltaic into the total construction cost of the line, the fan and the photovoltaic; z is the inflation rate of the currency; y isLINE、YWTG、YPVGThe service lives of the line, the fan and the photovoltaic are respectively prolonged;
Figure FDA0002675585250000031
the construction cost per kilometer of the line; c. CWTG、cPVGThe construction cost of each fan and each photovoltaic unit is respectively the construction cost of each fan and each photovoltaic unit; l isijThe length of each alternative line; omegaLINE、ΩWTG、ΩPVGRespectively obtaining a candidate set of lines to be built, a candidate node set of fans to be built and a candidate node set of photovoltaic cells to be built;
Figure FDA0002675585250000032
is a variable of 0 to 1, determines whether a line, a fan and a photovoltaic are put into operation or not, and for the established line,
Figure FDA0002675585250000033
is 1;
Figure FDA0002675585250000034
wherein T is the number of time periods of operation in one day; Δ t is the time of each time interval;
Figure FDA0002675585250000035
the electricity price for purchasing electricity from the main network for the t period; c. Closs、cLS、cLW、cLPVRespectively unit network loss cost, load loss cost, wind abandoning cost and light abandoning cost;
Figure FDA0002675585250000036
respectively obtaining main network output, loss load power, fan output data, fan actual output, photovoltaic output data and photovoltaic actual output; i isij，tIs the line current; r isijIs a line electric group; omegaTRIs a collection of transformer nodes; elineCollecting all the lines which are built and are to be built for the power distribution network; omegaENSIs the set of all load nodes;
the running layer objective function is:
min f＝COPE。
5. the multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 4, characterized in that:
in the step B, the constraint conditions of the planning layer comprise equipment investment construction constraint, network radial constraint and network connectivity constraint;
assuming that the maximum number of the connected fans and the maximum number of the photovoltaic circuits are specified in the power distribution network planning, and the number of the newly-built lines is also determined, the equipment investment construction constraint is specifically as follows:
Figure FDA0002675585250000041
wherein N isWTGSetting the maximum number of the newly built fans; n is a radical ofPVGSetting the maximum number of newly-built photovoltaic cells; n is a radical ofLINEPredicting the number of newly built lines;
in order to ensure the connectivity of each node of the planned power grid and avoid the operation of the roundabout, the connectivity inspection and radial inspection of the topological structure of the planned distribution network are required.
6. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 4, characterized in that:
in the step B, the constraint conditions of the operation layer comprise node power balance constraint, line voltage balance constraint, line capacity constraint, transformer capacity constraint, safety constraint, distributed power supply output constraint and loss load constraint;
to eliminate non-linear terms in the AC power flow, for the current Iij，tSum voltage Uj，tThrough variable replacement and second-order cone relaxation, the nonlinear constraint in the alternating current power flow is converted into a second-order cone constraint:
Figure FDA0002675585250000042
wherein the content of the first and second substances,
Figure FDA0002675585250000043
is the square of the current value of line ij;
Figure FDA0002675585250000044
is the square of the voltage value of node j;
then the run level constraints are:
node power balance constraint:
Figure FDA0002675585250000045
Figure FDA0002675585250000046
Figure FDA0002675585250000051
Figure FDA0002675585250000052
wherein, (j) is a line set with the node j as a head end; k is the end node of the line jk; pi (j) is a line set taking the node j as a tail end; omegaFIs a collection of load nodes; pjk，tThe active power transmitted by the line jk at the moment t; qjk，tThe reactive power transmitted by the line jk at the moment t; pij，t、Qij，tRespectively the active power and the reactive power transmitted by the line ij at the moment t;
Figure FDA0002675585250000053
respectively the active load demand and the reactive load demand of the node j; x is the number ofijIs the reactance value of line ij;
Figure FDA0002675585250000054
the main network reactive power, the fan reactive power, the photovoltaic reactive power and the loss load reactive power are respectively;
Figure FDA0002675585250000055
is the square of the voltage value of the node i;
line voltage balance constraint:
Figure FDA0002675585250000056
Figure FDA0002675585250000057
Figure FDA0002675585250000058
wherein M is a sufficiently large positive real number; elineCollecting all the lines which are built and are to be built for the power distribution network;
and (3) line capacity constraint:
Figure FDA0002675585250000059
Figure FDA00026755852500000510
wherein the content of the first and second substances,
Figure FDA00026755852500000511
the maximum current-carrying capacity of the line;
and (3) transformer capacity constraint:
Figure FDA00026755852500000512
Figure FDA00026755852500000513
wherein the content of the first and second substances,
Figure FDA0002675585250000061
minimum active and reactive output thresholds of the transformer are respectively set;
Figure FDA0002675585250000062
the maximum active and reactive output thresholds of the transformer are respectively set;
safety restraint:
Figure FDA0002675585250000063
Figure FDA0002675585250000064
wherein the content of the first and second substances,
Figure FDA0002675585250000065
is the minimum value of the node voltage;
Figure FDA0002675585250000066
is the maximum value of the node voltage;
Figure FDA0002675585250000067
is the maximum line current;
and (3) output constraint of the distributed power supply:
Figure FDA0002675585250000068
Figure FDA0002675585250000069
and (4) load loss constraint:
Figure FDA00026755852500000610
wherein the content of the first and second substances,
Figure FDA00026755852500000611
is the maximum load loss percentage for node j;
Figure FDA00026755852500000612
is the load power factor.
7. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 4, characterized in that:
in the step C, a specific mathematical model of the two-stage robust planning of the power distribution network is as follows:
Figure FDA00026755852500000613
Dx≤d
Ex＝e
Figure FDA00026755852500000614
Figure FDA00026755852500000615
Figure FDA00026755852500000616
wherein x is a construction variable of a line, a fan and a photovoltaic; subscript S denotes a limit scene number; n is a radical ofsRepresenting the number of limit scenes; xisRepresenting values of fan output, photovoltaic output and load power under a limit scene S; y issRepresenting the operation decision variables of the line power and the voltage under the limit scene; ax is the construction cost; bys+CξsThe operating cost in the extreme scenario S; A. b, C, D, E, F, G, H, L, M, D, E, F, G, H are coefficient matrixes.
8. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 7, characterized in that:
in step D, the mathematical model of the main problem is as follows:
Figure FDA0002675585250000071
Dx≤d
Ex＝e
Figure FDA0002675585250000072
Figure FDA0002675585250000073
Figure FDA0002675585250000074
Figure FDA0002675585250000075
wherein x is a construction variable of a line, a fan and a photovoltaic; eta is the actual operation cost of the power distribution network; n is C&The iteration times of the CG algorithm; k is a radical ofmNumbering the limit scenes selected in the mth iteration;
Figure FDA0002675585250000076
as extreme scene kmRunning decision variables;
Figure FDA0002675585250000077
as extreme scene kmAnd values of uncertain variables of lower fan output, photovoltaic output and load power.
9. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 8, characterized in that:
in step D, the mathematical model of the subproblem is:
Figure FDA0002675585250000081
Figure FDA0002675585250000082
Figure FDA0002675585250000083
Figure FDA0002675585250000084
wherein the content of the first and second substances,
Figure FDA0002675585250000085
and constructing and planning an optimal solution for the main problem in the nth iteration.
10. The multi-layer planning method for power grid considering multiple resource accesses at user side according to claim 9, wherein:
in the step D, the specific flow of the improved C & CG algorithm based on the extreme scene method is as follows:
(1) setting a lower bound LB ═ infinity, an upper bound UB +∞, and an algorithm iteration number n ═ 1;
(2) solving the main problem to obtain the optimal solution of the construction plan
Figure FDA0002675585250000086
And operating costs under the scenario
Figure FDA0002675585250000087
And updating the lower bound value
Figure FDA0002675585250000088
(3) Fixed construction plan optimal solution
Figure FDA0002675585250000089
Solving the sub-problems to obtain the sub-problems under all limit scenes
Figure FDA00026755852500000810
If all the sub-problems in the extreme scenes have solutions, finding the maximum value of feasible solutions in all the scenes
Figure FDA00026755852500000811
To obtainThe extreme scene number S is updated, and the upper bound value is updated
Figure FDA00026755852500000812
If the subproblem is not feasible under the limit scene S, the current worst limit scene is S;
(4) if UB-LB <, the convergence precision is given, then the iteration is finished, and the optimal solution of the current construction plan is obtained
Figure FDA00026755852500000813
Otherwise, updating the worst limit scene S under the current planning condition, and adding the constraint condition corresponding to the scene to the main problem;
(5) and (4) returning to the step (2) when n is n + 1.
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