CN113538169A - AC/DC series-parallel urban power grid development adaptability evaluation method - Google Patents

AC/DC series-parallel urban power grid development adaptability evaluation method Download PDF

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CN113538169A
CN113538169A CN202110837631.9A CN202110837631A CN113538169A CN 113538169 A CN113538169 A CN 113538169A CN 202110837631 A CN202110837631 A CN 202110837631A CN 113538169 A CN113538169 A CN 113538169A
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power grid
power
under
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adaptability
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张天宇
王魁
闫大威
宋佳
雷铮
李媛媛
丁承第
李慧
刘忠义
宣文博
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
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State Grid Tianjin Electric Power Co Ltd
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    • G06Q50/00Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/15Correlation function computation including computation of convolution operations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/0639Performance analysis of employees; Performance analysis of enterprise or organisation operations
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70Smart grids as climate change mitigation technology in the energy generation sector
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04SSYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention provides an AC/DC hybrid urban power grid development adaptability evaluation method, which comprises the following steps: constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment, and solving the power grid operation optimization robust model to obtain the power grid operation state; constructing an alternating current-direct current hybrid urban power grid development adaptability evaluation system so as to obtain an adaptability evaluation index; and evaluating the development adaptability of the AC/DC series-parallel urban power grid through the obtained adaptability evaluation index. Under the future development uncertainty condition, the invention provides a quantitative evaluation method and related evaluation indexes for the development adaptability aspect of the urban power grid, and the evaluation indexes can guide the planning construction of the urban power grid in the future under the condition of facing a plurality of uncertainty factors, so that the urban power grid is more suitable for the future urban development.

Description

AC/DC series-parallel urban power grid development adaptability evaluation method
Technical Field
The invention relates to the technical field of urban power grid planning evaluation, in particular to an alternating current-direct current hybrid urban power grid development adaptability evaluation method.
Background
The evaluation of the power grid development adaptability is to comprehensively consider the aspects of national economy and social development, national energy safety, scientific and technical progress and the like, provide a set of objective and reasonable power grid adaptability evaluation index system and evaluation method, and evaluate the adaptability degree of a power grid to the aspects in the planning and operation processes. Currently, with the gradual maturity of power electronic technology and the gradual reduction of costs of related products and equipment, a power supply connected to the power electronic converter and flexible direct-current transmission equipment are connected to a power grid in a large scale, an urban power grid is gradually developed from a pure alternating-current system to an alternating-current/direct-current hybrid system, and a development adaptability evaluation system of the power grid also needs to be converted from a traditional alternating-current power grid to the alternating-current/direct-current hybrid power grid.
Therefore, it is necessary to research an ac/dc hybrid urban power grid development adaptability evaluation method for providing a quantitative evaluation tool and an index support for the development adaptability of a power grid in various uncertain environments.
Disclosure of Invention
The invention aims to design an AC/DC hybrid urban power grid development adaptability evaluation method for providing a quantitative evaluation tool and index support for the development adaptability of a power grid in various uncertain environments.
The invention provides an AC/DC hybrid urban power grid development adaptability evaluation method, which comprises the following steps:
constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment, and solving the power grid operation optimization robust model to obtain the power grid operation state;
constructing an alternating current-direct current hybrid urban power grid development adaptability evaluation system so as to obtain an adaptability evaluation index;
and evaluating the development adaptability of the AC/DC series-parallel urban power grid through the obtained adaptability evaluation index.
Further, a method for constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment, solving the power grid operation optimization robust model and obtaining the power grid operation state comprises the following steps:
constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment: with the power transmission system economy as a target, the objective function is as follows:
Figure RE-GDA0003215563410000021
Figure RE-GDA0003215563410000022
Figure RE-GDA0003215563410000023
g is a set of a traditional unit, T is a time set, N is a set of all nodes, and omega, phi and psi are respectively an integer decision variable set, a continuity decision variable set and an uncertainty decision variable set in an optimization model; s is a line scene to be built;
Figure RE-GDA0003215563410000024
the economic cost of the power system under the commissioning scene s and the load type w is calculated;
Figure RE-GDA0003215563410000025
the construction cost of the scene s;
Figure RE-GDA0003215563410000026
the operation cost of the generator set under the condition of a commissioning scene s and a load type w is calculated;
Figure RE-GDA0003215563410000027
the penalty cost of abandoning renewable energy and cutting load of the system under the investment scene s and the load type w;
Figure RE-GDA0003215563410000028
and
Figure RE-GDA0003215563410000029
respectively is a starting cost coefficient of the generator, a stopping cost coefficient of the generator and an output cost coefficient of the generator;
Figure RE-GDA00032155634100000210
and
Figure RE-GDA00032155634100000211
punishment cost coefficients of abandoning renewable energy sources and cutting load respectively; alpha is alphas,w,j,tAnd betas,w,j,tThe starting-up and stopping marker bits of the generator are respectively under a commissioning scene s and a load type w;
Figure RE-GDA00032155634100000212
the active power output of the generator is under the commissioning scene s and the load type w;
Figure RE-GDA00032155634100000213
and
Figure RE-GDA00032155634100000214
respectively abandoning the active power of renewable energy and the active power of load shedding under the commissioning scene s and the load type w;
establishing constraint conditions, wherein the constraint conditions comprise line power flow constraint, power balance constraint and generator constraint;
and solving the power grid operation optimization robust model under the constraint condition to obtain the power grid operation state.
Further, the line flow constraint is:
Figure RE-GDA00032155634100000215
Figure RE-GDA00032155634100000216
wherein, Ps,w,ij,tIs the active power flow of line ij; ps,w,j,tIs the active power flow injected into node j;
Figure RE-GDA0003215563410000031
the maximum active capacity of the line ij under the commissioning scene s is obtained; r is a renewable energy set, ptdfsA power transfer distribution factor corresponding to a motor node under a commissioning scene s is obtained;
the power balance constraint is:
Figure RE-GDA0003215563410000032
Figure RE-GDA0003215563410000033
wherein the content of the first and second substances,
Figure RE-GDA0003215563410000034
is an uncertainty variable representing the project scenario s, loadUnder the type w, the active power output of the distributed power supply can be regenerated;
Figure RE-GDA0003215563410000035
the output reduction amount of the node j can be regenerated distributed power supply;
Figure RE-GDA0003215563410000036
is the load demand of node j;
Figure RE-GDA0003215563410000037
reducing the load;
Figure RE-GDA0003215563410000038
the method comprises the steps of generating a predicted value of active power output of a renewable distributed power supply under a commissioning scene s and a load type w;
Figure RE-GDA0003215563410000039
under a commissioning scene s and a load type w, the prediction error of the active power output of the renewable distributed power supply is determined; l is a load node set;
the generator constraints are:
Figure RE-GDA00032155634100000310
Figure RE-GDA00032155634100000311
Figure RE-GDA00032155634100000312
and
Figure RE-GDA00032155634100000313
minimum and maximum output of the generator respectively;
Figure RE-GDA00032155634100000314
and
Figure RE-GDA00032155634100000315
representing maximum rates of power drop and power rise, respectively, of the renewable distributed power source; when the generator is in operation, cs,w,j,t1 is ═ 1; when the generator is in a standstill state, cs,w,j,t=0。
Further, the suitability evaluation index includes:
economic adaptability index:
Figure RE-GDA00032155634100000316
w is a future power grid development environment set; m iswProbability under a w environment faced by future power grid development;
adaptability index of renewable energy utilization:
Figure RE-GDA0003215563410000041
and power supply reliability adaptability index:
Figure RE-GDA0003215563410000042
system branch load rate expected value:
Figure RE-GDA0003215563410000043
wherein R represents the line operating time period.
The invention has the advantages and positive effects that:
under the future development uncertainty condition, the invention provides a quantitative evaluation method and related evaluation indexes for the development adaptability aspect of the urban power grid, and the evaluation indexes can guide the planning construction of the urban power grid in the future under the condition of facing a plurality of uncertainty factors, so that the urban power grid is more suitable for the future urban development.
Drawings
Fig. 1 is a flowchart of an ac/dc series-parallel urban power grid development adaptability evaluation method provided in an embodiment of the present invention;
fig. 2 is a circuit diagram of a city power grid provided in an embodiment of the present invention;
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. 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. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The retail package pricing method considering price type demand response constructs a demand response model, analyzes the cost-income function of the electricity selling company containing electricity selling income, electricity purchasing expenditure, response income and the like, constructs the retail package pricing model, and provides decision support for the retailer from the perspective of optimized pricing.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for evaluating the development adaptability of the alternating current-direct current hybrid urban power grid includes the following steps:
s1, constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment, and solving the power grid operation optimization robust model to obtain the power grid operation state;
s2, constructing an alternating current-direct current parallel serial urban power grid development adaptability evaluation system, and thus obtaining an adaptability evaluation index;
and S3, evaluating the development adaptability of the AC/DC series-parallel city power grid through the obtained adaptability evaluation indexes.
It should be noted that, the method for constructing the alternating current-direct current hybrid power grid operation optimization robust model under the uncertainty operation environment, solving the power grid operation optimization robust model and obtaining the power grid operation state includes:
constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment: with the power transmission system economy as a target (including line construction cost, generator operation cost, penalty cost of abandoning renewable energy and load shedding), the objective function is as follows:
Figure RE-GDA0003215563410000051
Figure RE-GDA0003215563410000052
Figure RE-GDA0003215563410000053
g is a set of a traditional unit, T is a time set, N is a set of all nodes, and omega, phi and psi are respectively an integer decision variable set, a continuity decision variable set and an uncertainty decision variable set in an optimization model; s is a line scene to be built;
Figure RE-GDA0003215563410000054
the economic cost of the power system under the commissioning scene s and the load type w is calculated;
Figure RE-GDA0003215563410000055
the construction cost of the scene s;
Figure RE-GDA0003215563410000056
the operation cost of the generator set under the condition of a commissioning scene s and a load type w is calculated;
Figure RE-GDA0003215563410000057
the penalty cost of abandoning renewable energy and cutting load of the system under the investment scene s and the load type w;
Figure RE-GDA0003215563410000058
and
Figure RE-GDA0003215563410000059
respectively is a starting cost coefficient of the generator, a stopping cost coefficient of the generator and an output cost coefficient of the generator;
Figure RE-GDA0003215563410000061
and
Figure RE-GDA0003215563410000062
punishment cost coefficients of abandoning renewable energy sources and cutting load respectively; alpha is alphas,w,j,tAnd betas,w,j,tThe starting-up and stopping marker bits of the generator are respectively under a commissioning scene s and a load type w;
Figure RE-GDA0003215563410000063
the active power output of the generator is under the commissioning scene s and the load type w;
Figure RE-GDA0003215563410000064
and
Figure RE-GDA0003215563410000065
respectively abandoning the active power of renewable energy and the active power of load shedding under the commissioning scene s and the load type w;
establishing constraint conditions, wherein the constraint conditions comprise line power flow constraint, power balance constraint and generator constraint;
and solving the power grid operation optimization robust model under the constraint condition to obtain the power grid operation state.
Specifically, the line power flow constraint is as follows:
Figure RE-GDA0003215563410000066
Figure RE-GDA0003215563410000067
wherein, Ps,w,ij,tIs the active power flow of line ij; ps,w,j,tIs the active power flow injected into node j;
Figure RE-GDA0003215563410000068
the maximum active capacity of the line ij under the commissioning scene s is obtained; r is a renewable energy set, ptdfsA power transfer distribution factor corresponding to a motor node under a commissioning scene s is obtained;
the power balance constraint is:
Figure RE-GDA0003215563410000069
Figure RE-GDA00032155634100000610
wherein the content of the first and second substances,
Figure RE-GDA00032155634100000611
the uncertainty variable represents the active output of the renewable distributed power supply under the commissioning scene s and the load type w;
Figure RE-GDA00032155634100000612
the method comprises the steps of generating a predicted value of active power output of a renewable distributed power supply under a commissioning scene s and a load type w;
Figure RE-GDA00032155634100000613
the output reduction amount of the node j can be regenerated distributed power supply;
Figure RE-GDA00032155634100000614
is the load demand of node j;
Figure RE-GDA00032155634100000615
reducing the load;
Figure RE-GDA00032155634100000616
under a commissioning scene s and a load type w, the prediction error of the active power output of the renewable distributed power supply is determined; l is a load node set;
the generator constraints are:
Figure RE-GDA0003215563410000071
Figure RE-GDA0003215563410000072
Figure RE-GDA0003215563410000073
and
Figure RE-GDA0003215563410000074
minimum and maximum output of the generator respectively;
Figure RE-GDA0003215563410000075
and
Figure RE-GDA0003215563410000076
representing maximum rates of power drop and power rise, respectively, of the renewable distributed power source; when the generator is in operation, cs,w,j,t1, the output force should be between the maximum and minimum output force; when the generator is in a standstill state, cs,w,j,tWhen the output force is 0, the output force is 0.
In detail, the suitability evaluation index includes:
economic adaptability index:
Figure RE-GDA0003215563410000077
w is a future power grid development environment set; m iswProbability under a w environment faced by future power grid development;
adaptability index of renewable energy utilization:
Figure RE-GDA0003215563410000078
and power supply reliability adaptability index:
Figure RE-GDA0003215563410000079
system branch load rate expected value:
Figure RE-GDA00032155634100000710
wherein R represents the line operating time period.
And evaluating the development adaptability of the AC/DC series-parallel urban power grid through the adaptability evaluation index.
By way of example, in this embodiment, an urban power grid in fig. 2 is taken as an example to describe a vulnerability evaluation flow; the city grid in fig. 2 includes 24 nodes and 33 lines, and the city has 4 development environments in the future, as shown in the following table:
load demand (megawatt) New energy access requirement (megawatt)
Development ofEnvironment 1 7000 3000
Development Environment 2 7000 5000
Development Environment 3 5000 3000
Development Environment 4 5000 5000
Line capacity is shown in the table below
Line Capacity (MW) Line Capacity (MW)
L1-2 157.5 L12-13 450
L1-3 157.5 L12-23 450
L1-5 157.5 L13-23 450
L2-4 157.5 L14-16 450
L2-6 157.5 L15-16 450
L3-9 157.5 L15-21 450
L3-24 360 L15-21 450
L4-9 157.5 L15-24 450
L5-10 157.5 L16-17 360
L6-10 157.5 L16-19 450
L7-8 157.5 L17-18 450
L8-9 157.5 L17-22 450
L8-10 157.5 L18-21 450
L9-11 360 L18-21 450
L9-12 360 L19-20 450
L10-11 360 L19-20 450
L10-12 360 L20-23 450
L11-13 450 L20-23 450
L11-14 450 L21-22 450
Based on the AC/DC hybrid power grid operation optimization robust model under the uncertain operation environment, the optimal operation states of the urban power grid in the example under 4 development environments are solved, and the economic adaptability, the renewable energy utilization adaptability, the power supply reliability adaptability and the expected value index of the branch load rate of the system of the urban power grid are further given as shown in the table.
Figure RE-GDA0003215563410000091
As can be seen from the above table, in the case that there is uncertainty in the development of the load and the new energy, the economic adaptability, the renewable energy utilization adaptability, the reliable power supply adaptability, and the expected value index of the branch load rate of the system of the urban power grid in the example are respectively 2.85 × 106Ten thousand yuan, 88.5%, 98.88% and 42.58%.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (4)

1. The AC/DC hybrid urban power grid development adaptability evaluation method is characterized by comprising the following steps of:
constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment, and solving the power grid operation optimization robust model to obtain the power grid operation state;
constructing an alternating current-direct current hybrid urban power grid development adaptability evaluation system so as to obtain an adaptability evaluation index;
and evaluating the development adaptability of the AC/DC series-parallel urban power grid through the obtained adaptability evaluation index.
2. The AC-DC hybrid urban power grid development adaptability evaluation method according to claim 1, wherein a method for constructing an AC-DC hybrid power grid operation optimization robust model under an uncertain operation environment, solving the power grid operation optimization robust model and obtaining a power grid operation state comprises the following steps:
constructing an alternating current-direct current hybrid power grid operation optimization robust model under the uncertain operation environment: with the power transmission system economy as a target, the objective function is as follows:
Figure FDA0003177804880000011
Figure FDA0003177804880000012
Figure FDA0003177804880000013
wherein G is of a conventional unitThe method comprises the steps of collecting, wherein T is a time collection, N is all node collections, and omega, phi and psi are an integer decision variable collection, a continuity decision variable collection and an uncertainty decision variable collection in an optimization model respectively; s is a line scene to be built;
Figure FDA0003177804880000014
the economic cost of the power system under the commissioning scene s and the load type w is calculated;
Figure FDA0003177804880000015
the construction cost of the scene s;
Figure FDA0003177804880000016
the operation cost of the generator set under the condition of a commissioning scene s and a load type w is calculated;
Figure FDA0003177804880000017
the penalty cost of abandoning renewable energy and cutting load of the system under the investment scene s and the load type w;
Figure FDA0003177804880000018
and
Figure FDA0003177804880000019
respectively is a starting cost coefficient of the generator, a stopping cost coefficient of the generator and an output cost coefficient of the generator;
Figure FDA00031778048800000110
and
Figure FDA00031778048800000111
punishment cost coefficients of abandoning renewable energy sources and cutting load respectively; alpha is alphas,w,j,tAnd betas,w,j,tThe starting-up and stopping marker bits of the generator are respectively under a commissioning scene s and a load type w;
Figure FDA00031778048800000112
the active power output of the generator is under the commissioning scene s and the load type w;
Figure FDA0003177804880000021
and
Figure FDA0003177804880000022
respectively abandoning the active power of renewable energy and the active power of load shedding under the commissioning scene s and the load type w;
establishing constraint conditions, wherein the constraint conditions comprise line power flow constraint, power balance constraint and generator constraint;
and solving the power grid operation optimization robust model under the constraint condition to obtain the power grid operation state.
3. The AC/DC hybrid urban power grid development adaptability evaluation method according to claim 2,
the line flow constraint is as follows:
Figure FDA0003177804880000023
Figure FDA0003177804880000024
wherein, Ps,w,ij,tIs the active power flow of line ij; ps,w,j,tIs the active power flow injected into node j;
Figure FDA0003177804880000025
the maximum active capacity of the line ij under the commissioning scene s is obtained; r is a renewable energy set, ptdfsA power transfer distribution factor corresponding to a motor node under a commissioning scene s is obtained;
the power balance constraint is:
Figure FDA0003177804880000026
Figure FDA0003177804880000027
wherein the content of the first and second substances,
Figure FDA0003177804880000028
the uncertainty variable represents the active output of the renewable distributed power supply under the commissioning scene s and the load type w;
Figure FDA0003177804880000029
the output reduction amount of the node j can be regenerated distributed power supply;
Figure FDA00031778048800000210
is the load demand of node j;
Figure FDA00031778048800000211
reducing the load;
Figure FDA00031778048800000212
the method comprises the steps of generating a predicted value of active power output of a renewable distributed power supply under a commissioning scene s and a load type w;
Figure FDA00031778048800000213
under a commissioning scene s and a load type w, the prediction error of the active power output of the renewable distributed power supply is determined; l is a load node set;
the generator constraints are:
Figure FDA0003177804880000031
Figure FDA0003177804880000032
Figure FDA0003177804880000033
and
Figure FDA0003177804880000034
minimum and maximum output of the generator respectively;
Figure FDA0003177804880000035
and
Figure FDA0003177804880000036
representing maximum rates of power drop and power rise, respectively, of the renewable distributed power source; when the generator is in operation, cs,w,j,t1 is ═ 1; when the generator is in a standstill state, cs,w,j,t=0。
4. The AC-DC hybrid urban power grid development adaptability assessment method according to claim 3, wherein the adaptability evaluation index comprises:
economic adaptability index:
Figure FDA0003177804880000037
w is a future power grid development environment set; m iswProbability under a w environment faced by future power grid development;
adaptability index of renewable energy utilization:
Figure FDA0003177804880000038
and power supply reliability adaptability index:
Figure FDA0003177804880000039
system branch load rate expected value:
Figure FDA00031778048800000310
wherein R represents the line operating time period.
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