CN113629779A - Multi-agent power demand response method for service carbon emission reduction - Google Patents

Multi-agent power demand response method for service carbon emission reduction Download PDF

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CN113629779A
CN113629779A CN202110903703.5A CN202110903703A CN113629779A CN 113629779 A CN113629779 A CN 113629779A CN 202110903703 A CN202110903703 A CN 202110903703A CN 113629779 A CN113629779 A CN 113629779A
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power
generator
marginal
demand response
load
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杨娜
刘亚南
朱刘柱
王宝
葛成
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Economic and Technological Research Institute of State Grid Anhui Electric Power Co Ltd
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Economic and Technological Research Institute of State Grid Anhui Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • 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
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
    • H02J3/144—Demand-response operation of the power transmission or distribution network
    • 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
    • H02J2310/00—The network for supplying or distributing electric power characterised by its spatial reach or by the load
    • H02J2310/50—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads
    • H02J2310/56—The network for supplying or distributing electric power characterised by its spatial reach or by the load for selectively controlling the operation of the loads characterised by the condition upon which the selective controlling is based
    • H02J2310/62—The condition being non-electrical, e.g. temperature
    • H02J2310/64—The condition being economic, e.g. tariff based load management
    • 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
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
    • Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
    • 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
    • Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
    • Y04S20/20—End-user application control systems
    • Y04S20/222—Demand response systems, e.g. load shedding, peak shaving

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  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The invention discloses a multi-agent power demand response method for service carbon emission reduction, which is characterized in that a local controller is embedded into each generator set and a demand response elastic load, and the marginal cost or marginal benefit of the local controller is updated according to the adjacent marginal cost or demand response marginal benefit; during scheduling, judging whether to increase or reduce global marginal cost or marginal benefit by selecting one main generator and one main load; particularly, marginal cost of a generator set and marginal benefit of demand response are used as consistency variables, and a consistency technical scheme is designed to realize the multi-agent demand response distributed economic operation scheduling of the power system considering carbon emission reduction. The method provided by the invention can realize elastic load response or plug-and-play under incomplete information, reduce network investment, and effectively solve the problems of variable network topological structures and the like.

Description

Multi-agent power demand response method for service carbon emission reduction
Technical Field
The invention relates to the technical field of output distribution of generators, in particular to a multi-agent power demand response method for carbon emission reduction service.
Background
The power system is an organic combination of a series of controllable power devices, including a generator, a flexible load demand response and the like, and the controllable power devices realize information interaction through a network. The economic operation of the power system is an optimization problem of maximizing the social welfare of the operation of the whole power system under the condition that the generator and the elastic load meet a series of operation constraints. In the traditional method, a centralized optimization method is adopted for economic operation scheduling, a scheduling center is required to issue instructions to schedule all generators and elastic loads in the whole system, and the scheduling center is required to exchange information with each scheduling object. The wide demand response of the elastic load and the plug and play of the power elements can make the topological structure of the power grid more variable, so that the centralized optimization method needs higher construction cost. Therefore, a more adaptive multi-agent distributed optimization method needs to be adopted, and the method can still effectively operate under the condition of limited or asymmetric information and even failure of a centralized scheduling center.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a multi-agent power demand response method for service carbon emission reduction.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multi-agent power demand response method for service carbon emission reduction is characterized in that a local controller is embedded into each generator set and a demand response elastic load, and the marginal cost or marginal benefit of the local controller is updated according to the adjacent marginal cost or demand response marginal benefit; during scheduling, judging whether to increase or reduce global marginal cost or marginal benefit by selecting one main generator and one main load; the scheduling is performed by the following algorithm:
1) establishing a mathematical model for scheduling an electric power system comprising a generator set and a flexible load:
Figure BDA0003200864300000021
Figure BDA0003200864300000022
Figure BDA0003200864300000023
Figure BDA0003200864300000024
Figure BDA0003200864300000025
the first four formulas are respectively an updating formula of the marginal cost of the main generator, an updating formula of the marginal benefit of the main load, a generator power constraint formula and an elastic load power constraint formula; delta P represents the difference between the actual demand of the elastic load and the actual output of the generator set; τ is a convergence coefficient, which is related to the distributed optimized convergence speed of the main generator and the main load;
2) initializing parameters such as a convergence coefficient tau, the required power of elastic load, the output power of a generator and the like;
3) and updating the required power of the elastic load and the output power of the generator until the absolute value delta P is less than tau, and judging that the convergence condition is met.
In the above technical scheme:
further, the mathematical model is established by the following process:
assuming that the power generation cost function, the carbon emission function and the power utilization benefit function of demand response of the generator set are all quadratic functions, the power generation cost function of the generator set is as follows:
Figure BDA0003200864300000026
wherein alpha isi、βi、γiConstant term, primary term and secondary term coefficients of the power generation cost function;
Figure BDA0003200864300000027
ζci、ξciconstant term, primary term and quadratic term coefficient of the power generation side carbon emission quadratic function;
the electricity utility function of the demand response is as follows:
Figure BDA0003200864300000031
wherein, aj、bj、cjConstant term, primary term and secondary term coefficients of the demand side benefit function; u. ofcj、vcj、wcjConstant term, primary term and quadratic term coefficient of the secondary function of carbon emission reduction on the demand side;
the multi-agent demand response is the optimization of the social welfare of the operation of the whole power system by the generator and the elastic demand response under the condition of meeting a series of operation constraints, namely:
Figure BDA0003200864300000032
Figure BDA0003200864300000033
Figure BDA0003200864300000034
Figure BDA0003200864300000035
wherein the content of the first and second substances,
Figure BDA0003200864300000036
the required power of the elastic load j;
Figure BDA0003200864300000037
is the output power of the generator i; sGIs a generator set; sDIs an elastic demand response set;
Figure BDA0003200864300000038
and
Figure BDA0003200864300000039
minimum and maximum output of the generator respectively;
Figure BDA00032008643000000310
and
Figure BDA00032008643000000311
minimum and maximum power consumption of the elastic load respectively; let λ represent lagrangian multipliers corresponding to equality constraints, and the equality constraint optimization problem turns into:
Figure BDA00032008643000000312
to variable quantity
Figure BDA00032008643000000313
And lambda partial derivation to obtain an optimality condition, namely:
Figure BDA00032008643000000314
the above equation is the coordination equation, and can be obtained according to the coordination equation:
Figure BDA0003200864300000041
that is, the optimal solution for economic operation is to equalize the marginal cost of the generator to the marginal benefit of the compliant load, where e represents the number of generators and r represents the number of demand responses;
setting all demand responses and generator sets to operate within the power constraint range; in this consistency approach, the marginal cost of the genset and the marginal benefit of the elastic load are as follows:
Figure BDA0003200864300000042
Figure BDA0003200864300000043
taking the marginal cost and the marginal benefit as consistency variables, and the updating formula of the marginal cost of the generator set is as follows:
Figure BDA0003200864300000044
the updating formula of the marginal benefit of the load is as follows:
Figure BDA0003200864300000045
in order to satisfy the power balance constraint in the power system, the difference between the actual demand of the elastic load and the actual output of the generator set is represented by the marginal benefit:
Figure BDA0003200864300000046
the marginal cost updating formula of the main generator and the marginal benefit updating formula of the main load are respectively as follows:
Figure BDA0003200864300000047
Figure BDA0003200864300000048
further, it can be seen that:
Figure BDA0003200864300000049
Figure BDA0003200864300000051
thus, the generator power constraint is:
Figure BDA0003200864300000052
the elastic load power constraint is:
Figure BDA0003200864300000053
further, the process of determining that the convergence condition is satisfied is:
1) firstly, carrying out consistency calculation according to an updating formula of marginal cost and an updating formula of marginal benefit;
2) then, judge
Figure BDA0003200864300000054
Whether the value exceeds the limit value or not is judged, so that different values in a generator power constraint formula and an elastic load power constraint formula are selected to calculate a delta P value;
3) and finally judging whether | delta P | is less than tau or not.
The invention has the beneficial effects that:
the invention provides a multi-agent power demand response method for service carbon emission reduction, which takes marginal cost of a generator set and marginal benefit of demand response as consistency variables, designs a consistency technical scheme to realize multi-agent demand response distributed economic operation scheduling of a power system considering carbon emission reduction, and can realize elastic load response or plug and play under incomplete information, reduce network investment, effectively solve the problems of variable network topological structure and the like.
Drawings
Fig. 1 shows the operation process of the algorithm according to the present invention.
Fig. 2 is a schematic diagram of building a node system and performing simulation.
Fig. 3-5 are generator marginal cost, demand response marginal benefit, total generated power, and total load power, respectively, for scenario one (τ ═ 0.001).
Fig. 6-8 are generator marginal cost, demand response marginal benefit, total generated power, and total load power, respectively, for scenario two (τ ═ 0.001).
Fig. 9-11 are generator marginal cost, demand response marginal benefit, total generated power, and total load power, respectively, for scenario one (τ ═ 0.0005).
Fig. 12-14 are generator marginal cost, demand response marginal benefit, total generated power, and total load power, respectively, for scenario two (τ ═ 0.0005).
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only preferred embodiments of the present invention, and not all embodiments.
The multi-agent power demand response method for service carbon emission reduction, provided by the invention, takes the Marginal Cost (MC) of a generator set and the Marginal Benefit (MB) of demand response as consistency variables, and realizes the multi-agent demand response distributed economic operation scheduling of the power system considering carbon emission reduction by designing a consistency technical scheme.
The method relates to the consistency of graph theory and multiple intelligent agents, and specifically comprises the following steps:
1. theory of the drawings
Let MAP represent the network topology structure diagram of the system. The MAP is a set (N, S), where N is the set of all nodes in the MAP,i.e., a set of nodes, is a finite, non-empty set, and S is an unordered set of tuples formed by nodes in N, i.e., a set of edges. If a path exists between any 2 different nodes, the graph is connected. The structure of the diagram is represented by a symmetrical n × n order adjacency matrix M, the elements M of whichijIs the weight of the edge between nodes i, j. N is a radical ofiA set of contiguous nodes representing a top node i, which includes node i, and the sum of the number of edges associated with node i is diI.e. degree of node i, i.e. di＝|NiL. The edges of the topological graph satisfy two directions and are equally weighted, and an element M of the adjacency matrix M is definedijComprises the following steps:
Figure BDA0003200864300000071
2. multi-agent coherence
Let xiIndicating the state of node i. If and only if the state values of all nodes in the network are equal, the nodes of the network all reach the same value, namely: x is the number of1＝x2＝…＝xn (2)
The multi-agent system consistency method comprises the following steps:
Figure BDA0003200864300000072
the matrix form is:
Figure BDA0003200864300000073
wherein L isnIs the n × n Laplace matrix of the graph M; x ═ x1,x2,…,xn]T
Information interaction can be carried out between the multi-agent generator and the demand response. Thus, the state characteristic may be expressed as:
Figure BDA0003200864300000074
since the matrix M is a row random matrix, the above equation can be simplified as:
Figure BDA0003200864300000075
2 multi-agent distributed economic operation scheduling
The goal of economic operation of power systems is to maximize social welfare when considering demand impact and carbon emissions reduction. From the perspective of multi-agent distributed optimization, the consistency is applied, the marginal cost MC of the generator set and the MB of demand response are used as consistency variables, and economic operation is optimized in a distributed mode. The local controller is embedded in each genset and demand response elastic load, updating its MC or MB from the adjoining MC or MB. Selecting a "host group" and a "primary load" determines whether to increase or decrease the global MC and MB. When the total generated power of the generator is larger than the total required power of the load, the global MC is reduced, otherwise, the global MC is increased. When the total power demand of the load is greater than the total power generated by the generator, the global MB is increased, otherwise the global MB is decreased.
The power generation cost function, the carbon emission function and the power utilization benefit function of demand response of the generator set are all quadratic functions, and the power generation cost function of the generator set is as follows:
Figure BDA0003200864300000081
wherein: alpha is alphai、βi、γiConstant term, primary term and secondary term coefficients of the power generation cost function;
Figure BDA0003200864300000082
ζci、ξciconstant term, first term and second term coefficient of the power generation side carbon emission second-order function.
The electricity utility function of the demand response is as follows:
Figure BDA0003200864300000083
wherein: a isj、bj、cjConstant term, primary term and secondary term coefficients of the demand side benefit function; u. ofcj、vcj、wcjConstant term, primary term and secondary term coefficient of the secondary function of carbon emission reduction on the demand side.
The multi-agent demand response is the optimization of the social welfare of the operation of the whole power system by the generator and the elastic demand response under the condition of meeting a series of operation constraints, namely:
Figure BDA0003200864300000084
Figure BDA0003200864300000085
Figure BDA0003200864300000086
Figure BDA0003200864300000087
wherein the content of the first and second substances,
Figure BDA0003200864300000088
the required power of the elastic load j;
Figure BDA0003200864300000089
is the output power of the generator i; sGIs a generator set; sDIs an elastic demand response set;
Figure BDA00032008643000000810
and
Figure BDA00032008643000000811
are respectively generatorsMinimum and maximum forces of;
Figure BDA00032008643000000812
and
Figure BDA00032008643000000813
respectively the minimum and maximum power usage of the elastic load. Let λ represent the lagrangian multiplier corresponding to the equality constraint, and the equality constraint optimization problem can be transformed without considering the constraint equations (10) and (11):
Figure BDA00032008643000000814
to variable quantity
Figure BDA00032008643000000815
And lambda partial derivation to obtain an optimality condition, namely:
Figure BDA0003200864300000091
the above equation is the coordination equation, and can be obtained according to the coordination equation:
Figure BDA0003200864300000092
i.e., the optimal solution for economic operation, is to equalize the MC of the generator to the MB of the compliant load, where e represents the number of generators and r represents the number of demand responses.
All demand response and gensets are assumed to operate within their power constraints. In this consistency approach, the MC and the MB of the elastic load for the genset are as follows:
Figure BDA0003200864300000093
Figure BDA0003200864300000094
taking MC and MB as consistency variables, the updating formula of the MC of the generator set is as follows:
Figure BDA0003200864300000095
the load MB update formula is:
Figure BDA0003200864300000096
to satisfy the power balance constraint (9) in the power system, the difference between the actual demand of the elastic load and the actual output of the generator set is represented by Δ P:
Figure BDA0003200864300000097
the updated formula for the MC of the main generator is:
Figure BDA0003200864300000101
Figure BDA0003200864300000102
where τ is a convergence factor, which is a positive scalar quantity related to the distributed optimized convergence speed of the main generator and the main load. The primary generator or primary load may be determined by a "centrality" search, including centrality, feature vector centrality, etc.
From equations (15) and (16):
Figure BDA0003200864300000103
Figure BDA0003200864300000104
thus, the generator power constraint is:
Figure BDA0003200864300000105
the elastic load power constraint is:
Figure BDA0003200864300000106
the formula (17) - (25) is a main mathematical function formula related to the multi-agent operation scheduling based on consistency, and forms a mathematical model of the application, and the operation flow is shown in fig. 1, and the specific steps are as follows:
1) initializing parameters such as convergence coefficients, the required power of elastic load, the output power of a generator and the like;
2) updating the required power of the elastic load and the output power of the generator;
3) firstly, carrying out consistency calculation according to an updating formula of marginal cost and an updating formula of marginal benefit;
4) then, judge
Figure BDA0003200864300000111
Whether the value exceeds the limit value or not is judged, so that different values in a generator power constraint formula and an elastic load power constraint formula are selected to calculate a delta P value;
5) and finally, judging whether | delta P | is less than tau, namely judging that the convergence condition is met.
3. Example simulation and analysis
As shown in fig. 2, to verify the validity of the distributed scheduling algorithm, Matlab simulation analysis is performed on a 32-machine, 17-load, 24-node system in the IEEE 11 plant. Wherein nodes 1, 2, 7, 8, 13, 15, 16, 18, 21, 22, 23 represent generator nodes G1-G11, respectively, and nodes 3, 4, 5, 6, 9, 10, 11, 12, 14, 17, 19, 20, 24 represent demand responses 1-13, respectively.
Scenarios 1, 2 verify the adaptability of the multi-agent approach to different topologies.
Scene 1: optimizing the effectiveness of the scheduling. During distributed optimization scheduling, G1 is selected as a main generator set, the flexible load 11 is selected as a main flexible load, the sampling step length is 0.02s, the convergence coefficient tau is 0.001, and the simulation result is shown in the figure. 3-5, all of the consistency variables in the system converge to optimal values and the total supply and demand power of the system is balanced.
Scene 2: validity for different topologies. The topology of the system is changed, and although the information topology is different, as can be seen from fig. 6-8, the consistency variables in the system can still converge to the optimal values, and the total supply and demand power in the system still reaches the balance. The power supply and demand is synchronized with the convergence speed of the consistency variable. Compared with scenario 1, scenario 2 lacks several paths, such as node 17 and node 16. Thus, scene 2 information conditions are worse than scene 1. Although scenario 2 lacks some information paths, the system information paths still have connectivity. In both scenarios, the system consistency variable and the supply and demand power convergence speed are the same.
In addition, the parameter configuration of the algorithm may affect the convergence speed, for example, the selection of the main generator set or the main load, the sampling speed, the communication topology of the power grid, the transmission delay of information, and the like. The main genset or main load controls an increase or decrease in a compliance variable. The convergence factor epsilon may control their convergence speed. Referring to fig. 9-14, the example simulations show that for the same topology and sampling step size, the system convergence increases from the convergence time at τ of 0.001 when τ is 0.0005.
The method solves the power system demand response economic dispatch with consistency in a multi-agent system. Matlab programming simulation analysis shows that the method has good convergence. In the future, demand response and elastic load in a power grid greatly permeate, and demand side users are response loads participating in system operation and realizing interaction with a power supply. The method has application prospect in future power grid source and grid load economic operation scheduling in the aspects of realizing demand response plug and play, coping with variable information network topological structures and the like.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1. A multi-agent power demand response method for service carbon emission reduction is characterized in that a local controller is embedded into each generator set and demand response elastic load, and the marginal cost or marginal benefit of the local controller is updated according to the adjacent marginal cost or demand response marginal benefit; during scheduling, judging whether to increase or reduce global marginal cost or marginal benefit by selecting one main generator and one main load; the scheduling is performed by the following algorithm:
1) establishing a mathematical model for scheduling an electric power system comprising a generator set and a flexible load:
Figure FDA0003200864290000011
Figure FDA0003200864290000012
Figure FDA0003200864290000013
Figure FDA0003200864290000014
Figure FDA0003200864290000015
the first four formulas are respectively an updating formula of the marginal cost of the main generator, an updating formula of the marginal benefit of the main load, a generator power constraint formula and an elastic load power constraint formula; delta P represents the difference between the actual demand of the elastic load and the actual output of the generator set; τ is a convergence coefficient, which is related to the distributed optimized convergence speed of the main generator and the main load;
2) initializing parameters such as a convergence coefficient tau, the required power of elastic load, the output power of a generator and the like;
3) and updating the required power of the elastic load and the output power of the generator until the absolute value delta P is less than tau, and judging that the convergence condition is met.
2. The multi-agent power demand response method of claim 1, wherein the mathematical model is established by:
assuming that the power generation cost function, the carbon emission function and the power utilization benefit function of demand response of the generator set are all quadratic functions, the power generation cost function of the generator set is as follows:
Figure FDA0003200864290000021
wherein alpha isi、βi、γiConstant term, primary term and secondary term coefficients of the power generation cost function;
Figure FDA0003200864290000022
ζci、ξciconstant term, primary term and quadratic term coefficient of the power generation side carbon emission quadratic function;
the electricity utility function of the demand response is as follows:
Figure FDA0003200864290000023
wherein, aj、bj、cjConstant term, primary term and secondary term coefficients of the demand side benefit function; u. ofcj、vcj、wcjConstant term, primary term and quadratic term coefficient of the secondary function of carbon emission reduction on the demand side;
the multi-agent demand response is the optimization of the social welfare of the operation of the whole power system by the generator and the elastic demand response under the condition of meeting a series of operation constraints, namely:
Figure FDA0003200864290000024
Figure FDA0003200864290000025
Figure FDA0003200864290000026
Figure FDA0003200864290000027
wherein the content of the first and second substances,
Figure FDA0003200864290000028
the required power of the elastic load j;
Figure FDA0003200864290000029
is the output power of the generator i; sGIs a generator set; sDIs an elastic demand response set;
Figure FDA00032008642900000210
and
Figure FDA00032008642900000211
minimum and maximum output of the generator respectively;
Figure FDA00032008642900000212
and
Figure FDA00032008642900000213
minimum and maximum power consumption of the elastic load respectively; let λ represent lagrangian multipliers corresponding to equality constraints, and the equality constraint optimization problem turns into:
Figure FDA00032008642900000214
to variable quantity
Figure FDA0003200864290000031
And lambda partial derivation to obtain an optimality condition, namely:
Figure FDA0003200864290000032
the above equation is the coordination equation, and can be obtained according to the coordination equation:
Figure FDA0003200864290000033
that is, the optimal solution for economic operation is to equalize the marginal cost of the generator to the marginal benefit of the compliant load, where e represents the number of generators and r represents the number of demand responses;
setting all demand responses and generator sets to operate within the power constraint range; in this consistency approach, the marginal cost of the genset and the marginal benefit of the elastic load are as follows:
Figure FDA0003200864290000034
Figure FDA0003200864290000035
taking the marginal cost and the marginal benefit as consistency variables, and the updating formula of the marginal cost of the generator set is as follows:
Figure FDA0003200864290000036
the updating formula of the marginal benefit of the load is as follows:
Figure FDA0003200864290000037
in order to satisfy the power balance constraint in the power system, the difference between the actual demand of the elastic load and the actual output of the generator set is represented by the marginal benefit:
Figure FDA0003200864290000038
the marginal cost updating formula of the main generator and the marginal benefit updating formula of the main load are respectively as follows:
Figure FDA0003200864290000041
Figure FDA0003200864290000042
further, it can be seen that:
Figure FDA0003200864290000043
Figure FDA0003200864290000044
thus, the generator power constraint is:
Figure FDA0003200864290000045
the elastic load power constraint is:
Figure FDA0003200864290000046
3. the multi-agent power demand response method of claim 2, wherein the process of determining that the convergence condition is satisfied is:
1) firstly, carrying out consistency calculation according to an updating formula of marginal cost and an updating formula of marginal benefit;
2) then, judge
Figure FDA0003200864290000047
Whether the value exceeds the limit value or not is judged, so that different values in a generator power constraint formula and an elastic load power constraint formula are selected to calculate a delta P value;
3) and finally judging whether | delta P | is less than tau or not.
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