CN113346479B - Opportunity constraint-based economic dispatching method for power system - Google Patents

Opportunity constraint-based economic dispatching method for power system Download PDF

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CN113346479B
CN113346479B CN202110538549.6A CN202110538549A CN113346479B CN 113346479 B CN113346479 B CN 113346479B CN 202110538549 A CN202110538549 A CN 202110538549A CN 113346479 B CN113346479 B CN 113346479B
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power
renewable energy
model
constraint
power system
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CN113346479A (en
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孙勇
李宝聚
傅吉悦
吴文传
王彬
杨越
郭雷
王建勋
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Tsinghua University
State Grid Corp of China SGCC
State Grid Jilin Electric Power Corp
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State Grid Corp of China SGCC
State Grid Jilin Electric Power Corp
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION 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
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/067—Enterprise or organisation modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION 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
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION 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
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02W—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO WASTEWATER TREATMENT OR WASTE MANAGEMENT
    • Y02W30/00—Technologies for solid waste management
    • Y02W30/50—Reuse, recycling or recovery technologies
    • Y02W30/82—Recycling of waste of electrical or electronic equipment [WEEE]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS 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
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems 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 relates to an opportunity constraint-based economic dispatching method for an electric power system, and belongs to the technical field of operation control of electric power systems. Firstly, establishing an opportunity constraint-based power system economic dispatching model composed of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into quantile forms, introducing relaxation variables, establishing the relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; and obtaining a constraint condition with feasible solution of the power system economic dispatching model based on opportunity constraint by using the values of the relaxation variables, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving to obtain a final dispatching result of the power system. The invention considers the fluctuation of renewable energy sources in the power system, ensures the safety of the power system, and is suitable for being applied to the economic dispatching scene of the power system with high renewable energy source permeability.

Description

Opportunity constraint-based economic dispatching method for power system
Technical Field
The invention relates to an opportunity constraint-based economic dispatching method for an electric power system, and belongs to the technical field of operation control of electric power systems.
Background
The economic dispatching of the power system plays an important guiding role in the operation of the power system, is responsible for making an output plan of the generator set and realizes economic operation on the premise of meeting power load and ensuring the safety of the power system.
Opportunistic constrained economic dispatch is widely used to deal with uncertainty issues with renewable energy sources. In the opportunity-constrained economic dispatch, the safety of the power system is guaranteed by limiting the risks to allowable levels. With the rapid increase of the permeability of renewable energy sources, the situation that the power system has insufficient reserve or transmission is blocked in certain scenes exists, and at the moment, the traditional opportunity constraint economic dispatching model may have an unsolvable situation. Therefore, in some scenarios, for power systems with high renewable energy penetration, the renewable energy output must be reduced in order to ensure system safety.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an economic dispatching method of an electric power system based on opportunity constraint. The invention provides an effective solving method for sequentially determining the electricity abandonment amount of the renewable energy source and the output of the traditional generator, considers the fluctuation of the renewable energy source in the power system, ensures the safety of the power system, is suitable for being applied to the economic dispatching scene of the power system with high permeability of the renewable energy source, and has high application value.
The invention provides an opportunity constraint-based power system economic dispatching method which is characterized by firstly establishing an opportunity constraint-based power system economic dispatching model composed of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into a quantile form, introducing relaxation variables, establishing a relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; and obtaining a constraint condition that an economic dispatching model of the power system based on opportunity constraint has a feasible solution by using the values of the relaxation variables, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving the models to obtain the power curtailment of each renewable energy source and the active power of each generator in each time period, thereby obtaining a final dispatching result. The method comprises the following steps:
1) Establishing an opportunity constraint-based economic dispatching model of the power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) determining an objective function of an economic dispatching model of the power system, wherein the expression is as follows:
Figure BDA0003070709540000021
wherein T is the number of time segments of the optimization cycle, N G In order to access the set of nodes of the generator,
Figure BDA0003070709540000022
for the active power of the ith generator during time period t,
Figure BDA0003070709540000023
for the generating cost of the ith generator in the time period t, N R In order to access the set of nodes of the renewable energy source,
Figure BDA0003070709540000024
the active power output upper limit for the jth renewable energy source,
Figure BDA0003070709540000025
a power abandon penalty cost for the jth renewable energy source in the time period t;
wherein the content of the first and second substances,
Figure BDA0003070709540000026
wherein A is gi ,B gi ,C gi Generating cost coefficient of the ith generator;
Figure BDA0003070709540000027
wherein, K j Penalty cost coefficient for jth renewable energy source, C j Is the maximum capacity of the jth renewable energy source,
Figure BDA0003070709540000028
a probability density function of available capacity for the jth renewable energy source over time period t;
1-2) determining the constraint conditions of the economic dispatching model of the power system, comprising the following steps:
1-2-1) generator power constraint:
Figure BDA0003070709540000029
Figure BDA00030707095400000210
Figure BDA00030707095400000211
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00030707095400000212
upper and lower power limits, rup, of the ith generator, respectively i ,Rdown i The power limit of the ith generator is limited by upward climbing power and downward climbing power;
1-2-2) renewable energy power constraints:
Figure BDA00030707095400000213
Figure BDA00030707095400000214
wherein the content of the first and second substances,
Figure BDA00030707095400000215
the power is scheduled for the jth renewable energy source for time period t,
Figure BDA00030707095400000216
the predicted power for the jth renewable energy source over time period t,
Figure BDA00030707095400000217
the actual power for the jth renewable energy source during time period t,
Figure BDA00030707095400000218
available power for the jth renewable energy source for time period t;
1-2-3) power balance constraints:
Figure BDA00030707095400000219
wherein the content of the first and second substances,
Figure BDA00030707095400000220
for node k load demand over time period t, N D A node set for accessing a load;
1-2-4) affine control and backup constraints:
Figure BDA0003070709540000031
Figure BDA0003070709540000032
Figure BDA0003070709540000033
wherein the content of the first and second substances,
Figure BDA0003070709540000034
actual power, beta, for the ith generator under consideration of affine control i Affine control participation factor, alpha, for the i-th generator UR ,α DR Respectively the maximum allowable probability of the shortage of the up-regulation equipment and the maximum allowable probability of the shortage of the down-regulation equipment;
1-2-5) line transmission capacity constraints:
Figure BDA0003070709540000035
Figure BDA0003070709540000036
wherein N is W Is a collection of lines, and is,
Figure BDA0003070709540000037
power transfer factors, P, of the line L with respect to the nodes i, j, k, respectively L For the maximum transmission capacity of the line L,
Figure BDA0003070709540000038
respectively the maximum allowable probability of forward out-of-limit and the maximum allowable probability of reverse out-of-limit of the transmission capacity of the line L;
2) Converting the model established in the step 1), establishing a relaxed opportunity constraint-based power system economic dispatching model and solving the model; the method comprises the following specific steps:
2-1) by substitution in formula (10)
Figure BDA0003070709540000039
Opportunities of model in step 1)The constraints (11) - (14) are written in the form of quantiles as follows:
Figure BDA00030707095400000310
Figure BDA00030707095400000311
Figure BDA00030707095400000312
Figure BDA00030707095400000313
Figure BDA00030707095400000314
Figure BDA00030707095400000315
wherein Q (xi | p) is the p quantile of the random variable xi,
Figure BDA00030707095400000316
to account for the equivalent power transfer factor of line L with respect to node j under affine control, M L Correction coefficients for affine control to the branch L power transfer factors;
let the joint distribution of renewable energy power over time period t be as follows:
Figure BDA0003070709540000041
Figure BDA0003070709540000042
wherein the content of the first and second substances,
Figure BDA0003070709540000043
a random variation of the available power composition for each renewable energy source over time t,
Figure BDA0003070709540000044
random variables composed of power output of each renewable energy source in a time period t;
2-2) use with
Figure BDA0003070709540000045
In alternative quantiles (15) - (18)
Figure BDA0003070709540000046
And introducing relaxation variables with constraints (16) and transmission power constraints (17) - (18) in the down-regulation to obtain equations (23) - (26);
Figure BDA0003070709540000047
Figure BDA0003070709540000048
Figure BDA0003070709540000049
Figure BDA00030707095400000410
wherein, drs t Slack variables in the constraints are backed up for a period of t,
Figure BDA00030707095400000411
the slack variable in the forward constraint and the slack variable in the reverse constraint of the line transmission capacity in the t period are respectively;
2-3) establishing a relaxed opportunity constraint economic dispatching model and solving;
wherein the model objective function is formula (27), the constraint conditions include formulas (4) to (7), formula (9), formulas (23) to (26), and formula (28), and the expression is as follows:
Figure BDA00030707095400000412
s.t. formulae (4) - (7), (9), (23) - (26) and (28)
Wherein the content of the first and second substances,
Figure BDA00030707095400000413
wherein, in the process,
Figure BDA00030707095400000414
respectively adjusting the standby weight coefficient and the cross section risk weight coefficient in the t time period;
solving the model to obtain
Figure BDA00030707095400000415
The optimal solution of (2);
3) Determining the electric quantity discarded by each renewable energy source and the active power of each generator to obtain a scheduling result of the power system; the method comprises the following specific steps:
3-1) utilizing the solving result of the model in the step 2-3) and relaxing the variable
Figure BDA00030707095400000416
Obtaining the constraint condition that the power system economic dispatching model based on the opportunity constraint, which is established in the step 1), has a feasible solution:
if the slack variable drs t After the renewable energy is abandoned, if the model in the step 1) has a feasible solution, the inequality constraint shown in the following formula is satisfied:
Figure BDA0003070709540000051
if the relaxation variable is changed
Figure BDA0003070709540000052
If not zero, the quantile in equation (17) satisfies the inequality constraint shown in equation (30) below:
Figure BDA0003070709540000053
if the relaxation variable is changed
Figure BDA0003070709540000054
If not, the quantile in equation (18) satisfies the inequality constraint shown in equation (31) below:
Figure BDA0003070709540000055
the constraints (29) to (31) are written as shown in the following formula:
Figure BDA0003070709540000056
wherein Ω is a subscript set of renewable energy sources participating in electricity abandonment, c j ,c k Is a constant coefficient;
3-2) establishing a renewable energy power abandoning amount scheduling model and solving;
the objective function of the renewable energy power curtailment scheduling model is shown as the following formula:
Figure BDA0003070709540000057
the first and second derivatives of equation (33) are respectively as follows:
Figure BDA0003070709540000058
Figure BDA0003070709540000059
the curtailment penalty in equation (33) is approximated by a linear inequality as shown in equation (36):
Figure BDA00030707095400000510
obtaining the electric quantity abandoned by each renewable energy source in each time period t through solving the formula (36)
Figure BDA00030707095400000511
Then, based on the probability distribution of the available power of the renewable energy source obtained by the probability prediction and quantiles in the electric quantity abandoning calculation formulas (15) to (18) obtained by solving the formula (36), the constraint formulas (15) to (18) become deterministic linear constraints;
3-3) establishing a generator output optimization model and solving by using the result of the step 3-2) to obtain the active power of each generator in each period
Figure BDA0003070709540000061
Wherein, the objective function of the optimization model is formula (37), and the constraint conditions include: formulae (4) to (7), formula (9), formulae (15) to (18), and formula (38), the expressions are as follows:
Figure BDA0003070709540000062
s.t. formulae (4) - (7), (9), (15) - (18) and (38)
Figure BDA0003070709540000063
3-4) the electric energy abandon amount of each renewable energy source obtained in the step 3-2) in each time interval and the active power of each generator obtained in the step 3-3) in each time interval are the dispatching results of the power system.
The invention provides an opportunity constraint-based economic dispatching method for an electric power system, which has the advantages that:
(1) The power system economic dispatching method based on opportunity constraint provided by the invention optimizes the output of the conventional generator and the renewable energy power-abandoning strategy at the same time so as to reduce the total operation cost to the maximum extent and limit the operation risk.
(2) The invention provides an effective solving method for sequentially determining the electricity abandonment amount of renewable energy sources and the output of a traditional generator, establishes an easily-solved optimization model for each step, and is suitable for being applied to an economic dispatching scene of a power system with high renewable energy permeability.
Detailed Description
The invention provides an opportunity constraint-based power system economic dispatching method which comprises the steps of firstly establishing an opportunity constraint-based power system economic dispatching model consisting of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into quantiles and introducing relaxation variables, establishing a relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; and obtaining a constraint condition that an economic dispatching model of the power system based on opportunity constraint has a feasible solution by using the values of the relaxation variables, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving the models to obtain the power curtailment of each renewable energy source and the active power of each generator in each time period, thereby obtaining a final dispatching result. The method comprises the following steps:
1) Establishing an opportunity constraint-based economic dispatching model of the power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) determining a target function of an economic dispatching model of the power system;
the objective of economic dispatch of the power system is to minimize the total cost, which includes the cost of generating power and the penalty cost of renewable energy power abandonment, and the objective function is shown as the following formula:
Figure BDA0003070709540000064
wherein T is the number of time segments of the optimization cycle, N G In order to access the set of nodes of the generator,
Figure BDA0003070709540000071
for the active power of the ith generator during time period t,
Figure BDA0003070709540000072
for the generating cost of the ith generator in the time period t, N R In order to access the set of nodes of the renewable energy source,
Figure BDA0003070709540000073
the active power output upper limit of the jth renewable energy source,
Figure BDA0003070709540000074
and charging the j-th renewable energy source by the electricity abandoning penalty cost in the time period t.
Wherein the power generation cost can be represented by a quadratic function of the following formula:
Figure BDA0003070709540000075
wherein, A gi ,B gi ,C gi The power generation cost coefficient of the ith generator.
The penalty charge for electricity abandonment of renewable energy sources is shown as follows:
Figure BDA0003070709540000076
wherein, K j Penalty cost coefficient for jth renewable energy source, C j Is the maximum capacity of the jth renewable energy source,
Figure BDA0003070709540000077
for the jth renewable energy source during time period tAvailable capacity probability density function.
1-2) determining constraint conditions of an economic dispatching model of the power system, wherein the constraint conditions comprise:
1-2-1) generator power constraint:
Figure BDA0003070709540000078
Figure BDA0003070709540000079
Figure BDA00030707095400000710
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00030707095400000711
upper and lower power limits, rup, of the ith generator, respectively i ,Rdown i The power limit for ascending and the power limit for descending grade of the ith generator are respectively.
1-2-2) renewable energy power constraints:
Figure BDA00030707095400000712
Figure BDA00030707095400000713
wherein the content of the first and second substances,
Figure BDA00030707095400000714
the power is scheduled for the jth renewable energy source for time period t,
Figure BDA00030707095400000715
the predicted power for the jth renewable energy source over time period t,
Figure BDA00030707095400000716
the actual power for the jth renewable energy source during time period t,
Figure BDA00030707095400000717
available power for the jth renewable energy source for time period t.
1-2-3) power balance constraints:
Figure BDA00030707095400000718
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00030707095400000719
for node k load demand over time period t, N D Is the set of nodes accessing the load.
1-2-4) affine control and backup constraints:
Figure BDA0003070709540000081
Figure BDA0003070709540000082
Figure BDA0003070709540000083
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003070709540000084
actual power, beta, for the ith generator under consideration of affine control i Affine control participation factor, alpha, for the i-th generator UR ,α DR The maximum allowable probability of under-provisioning and the maximum allowable probability of under-provisioning are respectively up-provisioning and down-provisioning.
1-2-5) line transmission capacity constraints:
Figure BDA0003070709540000085
Figure BDA0003070709540000086
wherein N is W Is a collection of lines, and is,
Figure BDA0003070709540000087
the power transfer factors of the line L with respect to the nodes i, j, k,
Figure BDA0003070709540000088
for the maximum transmission capacity of the line L,
Figure BDA0003070709540000089
respectively, a maximum allowed probability of the transmission capacity of the line L being out of limit in the forward direction and a maximum allowed probability of the transmission capacity being out of limit in the reverse direction.
2) Detecting infeasible constraints and renewable energy power consumption, converting the model established in the step 1), establishing a relaxed power system economic dispatching model based on opportunity constraints, and solving; the method comprises the following specific steps:
2-1) by substitution in formula (10)
Figure BDA00030707095400000817
The opportunity constraints (11) - (14) are written in the form of quantiles as follows:
Figure BDA00030707095400000810
Figure BDA00030707095400000811
Figure BDA00030707095400000812
Figure BDA00030707095400000813
Figure BDA00030707095400000814
Figure BDA00030707095400000815
wherein Q (xi | p) is the p quantile of the random variable xi,
Figure BDA00030707095400000816
to account for the equivalent power transfer factor of line L relative to node j in affine control, M L And controlling a correction coefficient of the power transfer factor of the branch L for affine control.
Assuming that the joint distribution of renewable energy power over time period t is known, as follows:
Figure BDA0003070709540000091
Figure BDA0003070709540000092
wherein the content of the first and second substances,
Figure BDA0003070709540000093
a random variation of the available power composition for each renewable energy source over time t,
Figure BDA0003070709540000094
random variables composed of power output of each renewable energy source in a time period t;
actual renewable energy power in traditional opportunistic constrained economic dispatch without considering renewable energy power curtailment
Figure BDA0003070709540000095
Equal to available renewable energy power
Figure BDA0003070709540000096
However, the calculation of the number of bits in equations (16) - (18) is based on the assumption that there is no electricity curtailment for renewable energy sources, which may result in conventional generator power
Figure BDA0003070709540000097
There is no feasible solution.
2-2) renewable energy power can be curtailed by reducing the quantiles to the right of the intermediate equations (16) - (18), thereby reducing the risk of down-regulation of backup shortages and transmission blockages. By using
Figure BDA0003070709540000098
In alternative quantiles (15) - (18)
Figure BDA0003070709540000099
And introducing relaxation variables in the down-regulation by the constraint (16) and the transmission power constraints (17) to (18), the following formulas (23) to (26) can be obtained:
Figure BDA00030707095400000910
Figure BDA00030707095400000911
Figure BDA00030707095400000912
Figure BDA00030707095400000913
wherein, drs t Slack variables in the standby constraints are adjusted for a period of time t,
Figure BDA00030707095400000914
the slack variable in the forward constraint and the slack variable in the reverse constraint of the line transmission capacity in the t period are respectively;
2-3) establishing a relaxed power system economic dispatching model based on opportunity constraint and solving;
wherein the model objective function is equation (27), and the objective of equation (27) is to minimize the weighted sum of the relaxation variables to solve the generator active power
Figure BDA00030707095400000915
There is no feasible solution case. In the process of calculating the linear combination
Figure BDA00030707095400000916
After quantiles of (a), the following relaxed opportunity constraint-based power system economic dispatch model can be solved directly with linear programming.
Figure BDA00030707095400000917
s.t. formulae (4) - (7), (9), (23) - (26) and (28)
Wherein the content of the first and second substances,
Figure BDA00030707095400000918
wherein the content of the first and second substances,
Figure BDA00030707095400000919
respectively as the weight coefficient of standby and the weight coefficient of section risk under t time interval.
Solving the model to obtain
Figure BDA0003070709540000101
The optimal solution of (2);
3) Determining the electric quantity discarded by each renewable energy source and the active power of each generator to obtain a scheduling result of the power system; the method comprises the following specific steps:
3-1) after solving the power system economic dispatching model based on the opportunity constraint after the relaxation in the step 2-3), obtaining the economic dispatching model through relaxation variables
Figure BDA0003070709540000102
Obtaining the constraint conditions of feasible solutions of the power system economic dispatching model based on the opportunity constraint established in the step 1):
if the slack variable drs in the backup constraint is adjusted downward t After the renewable energy is abandoned, in order to make the model of step 1) feasible, the inequality constraint shown in the following formula must be satisfied:
Figure BDA0003070709540000103
if the relaxation variable
Figure BDA0003070709540000104
If the value is not zero, the quantile in the transmission capacity constraint equation (17) satisfies an inequality constraint represented by the following equation (30):
Figure BDA0003070709540000105
if the relaxation variable is changed
Figure BDA0003070709540000106
If the value is not zero, the quantile in the transmission capacity constraint equation (18) satisfies an inequality constraint shown in the following equation (31):
Figure BDA0003070709540000107
the constraints (29) - (31) can be written as shown in the following formula:
Figure BDA0003070709540000108
wherein, omega is a subscript set of renewable energy sources participating in electricity abandonment, c j ,c k Is a constant coefficient.
3-2) establishing a renewable energy power abandoning amount scheduling model and solving;
the objective function of renewable energy power curtailment scheduling is to minimize the overall power curtailment penalty cost as shown in the following formula:
Figure BDA0003070709540000109
the quantile in equation (32) and the objective function in equation (33) are with respect to the upper limit of renewable energy power
Figure BDA00030707095400001010
The linear approximation of equations (32) and (33) can be used to obtain a solvable renewable energy power curtailment scheduling model, whose first and second derivatives of objective function equation (33) are respectively as follows:
Figure BDA00030707095400001011
Figure BDA00030707095400001012
since the second derivative of the objective function (33) is greater than or equal to zero, the power dump penalty is related to the upper power limit of the renewable energy source
Figure BDA0003070709540000111
A convex function of (a). The curtailment penalty in equation (33) is approximated by a linear inequality shown in equation (36) below, according to the nature of the convex function:
Figure BDA0003070709540000112
by passingThe solution formula (36) can obtain the electricity abandon quantity of each renewable energy source in each time period
Figure BDA0003070709540000113
Then, based on the probability distribution of the renewable energy available power obtained by the probability prediction and the quantiles in the electricity curtailment calculation equations (15) to (18) obtained by solving the equation (36), the constraints (15) to (18) become deterministic linear constraints.
3-3) obtaining the active power of each generator in each time period by solving a generator output optimization model shown as the following step by using the result of the step 3-2)
Figure BDA0003070709540000114
Thereby obtaining the dispatching output of the generator.
The objective function of the optimization model is equation (37), and equation (38) is used to limit the scheduled output of the renewable energy source to be lower than the upper power limit in the constraint condition.
Figure BDA0003070709540000115
s.t. formulae (4) - (7), (9), (15) - (18) and (38)
Figure BDA0003070709540000116
3-4) the electric energy abandon quantity of each renewable energy source obtained in the step 3-2) in each time interval and the active power of each generator obtained in the step 3-3) in each time interval are the power system dispatching results.

Claims (1)

1. The method is characterized by firstly establishing an opportunity constraint-based power system economic dispatching model composed of an objective function and constraint conditions, then converting the model, writing opportunity constraints in the model into quantile forms, introducing relaxation variables, establishing a relaxed opportunity constraint-based power system economic dispatching model, and solving to obtain values of the relaxation variables; obtaining a constraint condition that an economic dispatching model of the power system based on opportunity constraint has feasible solution by using the value of each relaxation variable, then sequentially establishing a renewable energy power curtailment dispatching model and a generator output optimization model and respectively solving the models to obtain the power curtailment of each renewable energy and the active power of each generator in each time period, thereby obtaining a final dispatching result; the method comprises the following steps:
1) Establishing an opportunity constraint-based economic dispatching model of the power system, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) determining an objective function of an economic dispatching model of the power system, wherein the expression is as follows:
Figure FDA0003926133570000011
wherein T is the number of time segments of the optimization period, N G In order to access the set of nodes of the generator,
Figure FDA0003926133570000012
for the active power of the ith generator during time period t,
Figure FDA0003926133570000013
for the generating cost of the ith generator in the time period t, N R In order to access the collection of nodes of the renewable energy source,
Figure FDA0003926133570000014
the active power output upper limit of the jth renewable energy source,
Figure FDA0003926133570000015
a power abandon penalty cost for the jth renewable energy source in the time period t;
wherein the content of the first and second substances,
Figure FDA0003926133570000016
wherein, A gi ,B gi ,C gi Generating cost coefficient of the ith generator;
Figure FDA0003926133570000017
wherein, K j Penalty cost coefficient for the jth renewable energy source, C j Is the maximum capacity of the jth renewable energy source,
Figure FDA0003926133570000018
a probability density function of available capacity for the jth renewable energy source over time period t;
1-2) determining the constraint conditions of the economic dispatching model of the power system, comprising the following steps:
1-2-1) generator power constraint:
Figure FDA0003926133570000019
Figure FDA00039261335700000110
Figure FDA00039261335700000111
wherein the content of the first and second substances,
Figure FDA00039261335700000112
P i upper and lower power limits, rup, of the ith generator, respectively i ,Rdown i The power limit of the ith generator is limited by upward climbing power and downward climbing power;
1-2-2) renewable energy power constraints:
Figure FDA0003926133570000021
Figure FDA0003926133570000022
wherein the content of the first and second substances,
Figure FDA0003926133570000023
the power is scheduled for the jth renewable energy source for time period t,
Figure FDA0003926133570000024
the predicted power for the jth renewable energy source over time period t,
Figure FDA0003926133570000025
the actual power for the jth renewable energy source during time period t,
Figure FDA0003926133570000026
available power for the jth renewable energy source for time period t;
1-2-3) power balance constraints:
Figure FDA0003926133570000027
wherein the content of the first and second substances,
Figure FDA0003926133570000028
for node k load demand over time period t, N D A node set for accessing the load;
1-2-4) affine control and backup constraints:
Figure FDA0003926133570000029
Figure FDA00039261335700000210
Figure FDA00039261335700000211
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00039261335700000212
actual power, beta, for the ith generator under consideration of affine control i Affine control participation factor, alpha, for the i-th generator UR ,α DR Respectively the maximum allowable probability of the shortage of the up-regulation equipment and the maximum allowable probability of the shortage of the down-regulation equipment;
1-2-5) line transmission capacity constraints:
Figure FDA00039261335700000213
Figure FDA00039261335700000214
wherein N is W Is a collection of lines, and is,
Figure FDA00039261335700000215
the power transfer factors of the line L with respect to the nodes i, j, k,
Figure FDA00039261335700000216
for the maximum transmission capacity of the line L,
Figure FDA00039261335700000217
respectively the maximum allowable probability of forward out-of-limit and the maximum allowable probability of reverse out-of-limit of the transmission capacity of the line L;
2) Converting the model established in the step 1), establishing a relaxed opportunity constraint-based power system economic dispatching model and solving the model; the method comprises the following specific steps:
2-1) by substitution in formula (10)
Figure FDA00039261335700000218
Writing the opportunistic constraints (11) - (14) of the model in step 1) into the form of quantiles as follows:
Figure FDA0003926133570000031
Figure FDA0003926133570000032
Figure FDA0003926133570000033
Figure FDA0003926133570000034
Figure FDA0003926133570000035
Figure FDA0003926133570000036
wherein Q (xi | p) is the p-quantile of the random variable xi,
Figure FDA0003926133570000037
to account for the equivalent power transfer factor of line L relative to node j in affine control, M L A correction coefficient for affine control to the branch L power transfer factor;
let the joint distribution of renewable energy power over time period t be as follows:
Figure FDA0003926133570000038
Figure FDA0003926133570000039
wherein the content of the first and second substances,
Figure FDA00039261335700000310
a random variation of the available power composition for each renewable energy source over time t,
Figure FDA00039261335700000311
random variables composed of power output of each renewable energy source in a time period t;
2-2) use with
Figure FDA00039261335700000312
In alternative quantiles (15) - (18)
Figure FDA00039261335700000313
And introducing relaxation variables with the constraints (16) and the transmission power constraints (17) - (18) in the down-regulation to obtain the equations (23) - (26);
Figure FDA00039261335700000314
Figure FDA00039261335700000315
Figure FDA00039261335700000316
Figure FDA00039261335700000317
wherein, drs t Slack variables in the standby constraints are adjusted for a period of time t,
Figure FDA00039261335700000318
the relaxation variables in the forward constraint and the reverse constraint of the line transmission capacity in the t period are respectively;
2-3) establishing a relaxed opportunity constraint economic dispatching model and solving;
wherein the model objective function is formula (27), the constraint conditions include formulas (4) to (7), formula (9), formulas (23) to (26), and formula (28), and the expression is as follows:
Figure FDA0003926133570000041
s.t. formulae (4) - (7), (9), (23) - (26) and (28)
Wherein the content of the first and second substances,
Figure FDA0003926133570000042
wherein the content of the first and second substances,
Figure FDA0003926133570000043
respectively adjusting the standby weight coefficient and the cross section risk weight coefficient in the t time period;
solving the model to obtain
Figure FDA0003926133570000044
The optimal solution of (a);
3) Determining the electric quantity discarded by each renewable energy source and the active power of each generator to obtain a scheduling result of the power system; the method comprises the following specific steps:
3-1) utilizing the solving result of the model in the step 2-3) and relaxing the variable
Figure FDA0003926133570000045
Obtaining the constraint condition that the power system economic dispatching model based on the opportunity constraint established in the step 1) has a feasible solution:
if the slack variable drs t After the renewable energy is abandoned, if the model in the step 1) has a feasible solution, the inequality constraint shown in the following formula is satisfied:
Figure FDA0003926133570000046
if the relaxation variable is changed
Figure FDA0003926133570000047
If not zero, the quantile in equation (17) satisfies the inequality constraint shown in equation (30) below:
Figure FDA0003926133570000048
if the relaxation variable
Figure FDA0003926133570000049
If not, the quantile in equation (18) satisfies the inequality constraint shown in equation (31) below:
Figure FDA00039261335700000410
the constraints (29) to (31) are written as shown in the following formula:
Figure FDA00039261335700000411
wherein Ω isSubscript set of renewable energy sources participating in electricity curtailment, c j ,c k Is a constant coefficient;
3-2) establishing a renewable energy power abandoning scheduling model and solving;
the objective function of the renewable energy power curtailment scheduling model is shown as the following formula:
Figure FDA00039261335700000412
the first and second derivatives of equation (33) are respectively as follows:
Figure FDA0003926133570000051
Figure FDA0003926133570000052
the curtailment penalty in equation (33) is approximated by a linear inequality as shown in equation (36):
Figure FDA0003926133570000053
obtaining the electric quantity abandoned by each renewable energy source in each time period t through solving the formula (36)
Figure FDA0003926133570000054
Then, based on probability distribution of available power of renewable energy sources obtained through probability prediction and quantiles in electric quantity abandoning calculation expressions (15) - (18) obtained through solving expression (36), constraint expressions (15) - (18) become deterministic linear constraint;
3-3) establishing a generator output optimization model and solving by using the result of the step 3-2) to obtain the active power of each generator in each period
Figure FDA0003926133570000055
Wherein, the objective function of the optimization model is formula (37), and the constraint conditions include: formulae (4) to (7), formula (9), formulae (15) to (18), and formula (38), the expressions are as follows:
Figure FDA0003926133570000056
s.t. formulae (4) - (7), (9), (15) - (18) and (38)
Figure FDA0003926133570000057
3-4) the electric energy abandon quantity of each renewable energy source obtained in the step 3-2) in each time interval and the active power of each generator obtained in the step 3-3) in each time interval are the power system dispatching results.
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