A decentralized coupon incentive demand response efficiency improvement method

Abstract

The present invention discloses a method for improving the efficiency of a decentralized coupon incentive demand response, which relates to the field of electric power technology and includes the following steps: (1) constructing a three-layer demand response framework based on coupon incentive (CIDR) and establishing the objective functions of each layer; (2) comparing the optimal demand response results under the decentralized incentive demand response mechanism and the centralized demand response mechanism; (3) proposing an additional incentive method for decentralized incentive demand response and constructing an equivalent virtual generator model under demand response. The method for improving the efficiency of the incentive demand response proposed by the present invention is based on a multi-layer demand response model. The method can effectively improve the optimal capacity of the incentive demand response and better solve the problems of low efficiency of the decentralized demand response model and low computing power of the three-layer demand response framework.

Description

Technical Field

[0001] The present invention belongs to the field of electric power technology, and specifically relates to a method for improving the efficiency of decentralized coupon incentive-based demand response. Background Art

[0002] As a core technology of smart grid, demand response technology has been increasingly valued in recent years with the increase in photovoltaic and wind power installed capacity. In addition to smoothing the fluctuations in new energy output, demand response also plays a role in maximizing the utilization rate of flexible loads on the user side. Traditional demand response is centralized demand response, that is, centralized demand response. Operators control global information, and users cannot hide their privacy information when participating in demand response. The proposal of decentralized demand response can effectively ensure user privacy security, but compared with the centralized economic dispatch of demand response, the current decentralized mechanism is inefficient. Although the conventional hierarchical demand response model has a certain role in promoting efficiency improvement, it does not achieve maximum social welfare under Nash equilibrium. Therefore, it is necessary to find a method to promote the efficiency improvement of decentralized demand response and provide guarantees for the promotion of decentralized demand response. Summary of the invention

[0003] In view of the deficiencies of the prior art, the object of the present invention is to provide a decentralized coupon incentive demand response efficiency improvement method to solve the problems raised in the above background technology.

[0004] The purpose of the present invention can be achieved through the following technical solutions: a method for improving the efficiency of decentralized coupon incentive demand response,

[0005] The following steps are involved:

[0006] Step (1) construct a three-layer demand response framework based on coupon incentives and establish the objective function of each layer;

[0007] Step (2) comparing the optimal demand response results under the decentralized incentive demand response mechanism and the centralized demand response mechanism;

[0008] Step (3) proposes an additional incentive method for decentralized incentive-based demand response and constructs an equivalent virtual generator model under demand response.

[0009] As a further solution of the present invention, in step (1), the coupon incentive objects include independent system operators (ISOs), load service entities (LSEs) and end users, and the three-layer demand includes the top layer corresponding to the independent system operator, the middle layer corresponding to the load service entity and the bottom layer corresponding to the end user, and the corresponding models of the three-layer demand are constructed respectively:

[0010] 1) Top layer (ISO)

[0011]

[0012] 2) Middle layer (LSE)

[0013]

[0014] 3) Bottom layer (user)

[0015]

[0016] Among them, λ is the market-clearing price; λ R is the retail electricity price; a D D 2 +b D D represents the demand response cost; π is the unit compensation price for demand response, and M is the maximum value of the pre-set demand response amount.

[0017] As a further solution of the present invention, the specific steps of step (2) are as follows:

[0018] (2-1) Solution of centralized demand response model

[0019] The centralized demand response mechanism is also called centralized demand response scheduling. Under this mechanism, it is assumed that the demand response cost functions of all users have been informed to the independent system operator. The goal is to maximize social welfare while effectively implementing demand response. The centralized DR scheduling can be modeled as a single-layer optimization problem as follows:

[0020]

[0021] Assuming that the generating capacity is sufficient, the actual market clearing price is equal to the marginal cost of the generator (and DR), which can be described as:

[0022] λ=2a G P G +b G =2a D D+b D (5)

[0023] Therefore, the optimal DR capacity (i.e., LSE response function) under the centralized demand response mechanism can be obtained as:

[0024]

[0025] We note that formula (6) only D ≤λ<2a D M+b D When the market price is lower than , LSE will not be able to provide demand response due to insufficient price incentives for LSE; when the market price is higher than 2aD M+b D , even though there is a profit surplus, the response capacity of LSE cannot exceed the pre-set limit M.

[0026] Therefore, the expression of the LSE response function is:

[0027]

[0028] (2-2) Solution of decentralized demand response model

[0029] The LSE response function in the decentralized demand response model is obtained through Stackelberg competition. The three-layer model can be decomposed into two Stackelberg models. Two backward induction methods are used to solve the problem, starting from solving formulas (1) and (2) and ending with solving formula (3).

[0030] The Lagrangian function of formula (3) is expressed as:

[0031]

[0032] Under unconstrained conditions, the Lagrange multiplier μ 3,1 =μ 3,2 =0, the user-side response function in formula (3) can be described as:

[0033]

[0034] Among them, is the incentive price signal provided by LSE, and the user's optimal demand response increases with the increase of π;

[0035] Similarly, for the intermediate layer model formula (2), the backward induction method is used again to determine the response of LSE, that is, the optimal response D of LSE to the wholesale market clearing price λ. By constructing the Lagrangian function, according to equation (9), it can be obtained:

[0036] F A2 (π,μ 2,1 )=(λ-λ R )L+(π+λ R -λ)D-μ 2,1 π (10)

[0037] Assuming μ 2,1 = 0, partial derivative We can get the optimal incentive price that LSE issues to consumers as

[0038]

[0039] Combining formula (9) and formula (11), the optimal DR capacity under the decentralized demand response mechanism under unconstrained conditions is:

[0040]

[0041] Comparing formula (6) and formula (12), it can be found that under unconstrained conditions, the optimal DR capacity of decentralized demand response can only reach 1 / 2 of the centralized demand response capacity;

[0042] (2-3) Decentralized LSE response function based on bounded rationality

[0043] In reality, it is difficult for rational users to spontaneously participate in demand response without incentives. Bounded rationality assumes that without voluntary response, the demand response amount will increase linearly from 0 to M. Based on the rational participation conditions, the decentralized LSE response function is discussed in two cases as follows:

[0044] 1) When λ R ≥ b D hour

[0045] Similar to the solution steps of the decentralized model, the LSE response function expression under user rationality conditions is obtained by reverse induction:

[0046]

[0047] Similarly, the LSE response function expression under the condition of user limited rationality is:

[0048]

[0049] 2) When λ R <b D hour

[0050] In this case, no “voluntary feedback” phenomenon is observed, so there is no case of bounded rationality. The LSE response function expression under user rationality conditions is:

[0051]

[0052] As a further solution of the present invention, in step S3:

[0053] (3-1) Constructing external excitation function;

[0054] Compared with the centralized demand response model, the optimal demand response capacity of the ordinary three-layer decentralized demand response model is only 1 / 2 of that of the centralized demand response model. Therefore, it is necessary to improve the efficiency of decentralized demand response through an external incentive function. In terms of its form, since the ISO pays the LSE an out-of-market fee, the incentive function should be related to the total amount of DR that the LSE can provide. Let the external incentive function be I(D), and bring it into the middle layer of the decentralized demand response model to obtain:

[0055]

[0056] In order to make the efficiency of decentralized demand response with external incentives equal to that of centralized demand response, combining formulas (6) and (9) yields:

[0057] π=λ-λ R (17)

[0058] After substituting formula (17) into the previous Lagrangian function, the expression is as follows:

[0059]

[0060] Where I'(D) is defined as After solving, the expression of I(D) is as follows:

[0061] I'(D)=λ-b D (19)

[0062] Therefore, the external activation function expression can be described as:

[0063] I(D)=(λ-b D )D (20)

[0064] Among them, since when λ<b D When , the value of is negative, which does not meet the actual situation. Therefore, the final expression of the non-negative external excitation function can be described as:

[0065] I(D)=max((λ-b D )D,0) (21)

[0066] From formula (21), it can be seen that the external incentive is mainly proportional to the market price and the demand response amount, and is a non-negative real number.

[0067] (3-2) Decentralized demand response mechanism with external incentives;

[0068] According to the obtained external incentive function expression, since the underlying function of the decentralized demand response model remains unchanged, according to the original solution method, the Lagrangian function can be described as:

[0069]

[0070] By solving similarly, we can get R ≥ b D When , the LSE response function expression under the conditions of user rationality and bounded rationality is:

[0071]

[0072] When R ≥ b D When , the LSE response function expression under user rational conditions is:

[0073]

[0074] (3-3) Construct an equivalent virtual generator model under demand response;

[0075] By analyzing the impact of the response function of LSE in the three-tier CIDR mechanism on different external incentives, we can construct a "virtual generator" model to represent the optimal demand response behavior of LSE in the whole market. Referring to the parameters of typical generators, the power generation of the "virtual generator" is equivalent to the maximum demand response potential, and the cost parameters of the "virtual generator" are equivalent to the demand response cost parameters. Considering the "voluntary" demand response in some scenarios, the equivalent baseline of the load is greater than the nominal load.

[0076] Combined with the calculation formulas of the equivalent parameters of the virtual generator, the voluntary demand response has been obtained as (λ R -b D ) / 2a D , so the load reference value L e It can be described as:

[0077] L e =L-(λ R -b D ) / 2a D (25)

[0078] Similarly, the power generation of the virtual generator can be described as:

[0079] M e =M-(λ R -b D ) / 2a D (26)

[0080] Cost parameter a of the virtual generator D e Related to the slope of the LSE response function, combined with formula (15), the cost parameter can be described as:

[0081] a D e =2a D (27)

[0082] Another cost parameter b of the virtual generator D e It is equal to the market price when users start to participate in demand response, which can be described as:

[0083] b D e =2λ R -b D (28).

[0084] Beneficial effects of the present invention: First, a three-layer model of decentralized coupon-incentive demand response is proposed, which can be applied to the construction of a distributed demand response system and effectively protect the privacy and security of information at each layer; then, in view of the low efficiency of distributed demand response compared to centralized demand response, external incentives are imposed on load service entities to increase overall social welfare, so that the optimal response capacity of distributed demand response is infinitely close to that of centralized demand response; finally, the constructed "virtual generator" model provides convenience for demand response regulation analysis by converting the demand response amount into a virtual generator for regulation. The above achievements can promote the promotion of distributed incentive demand response. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0086] Figure 1 It is a flow chart of the present invention;

[0087] Figure 2 It is a diagram of a three-layer demand response model based on coupon incentives of the present invention;

[0088] Figure 3 is a diagram of an equivalent model of a virtual generator and demand response of the present invention;

[0089] Figure 4 is the LSE response function diagram without additional excitation in the present invention (λ R ≥ b D );

[0090] Figure 5 is the LSE response function diagram without additional excitation in the present invention (λ R <b D );

[0091] Figure 6 is the LSE response function diagram with additional excitation in the present invention (λ R ≥ b D );

[0092] Figure 7 is the LSE response function diagram with additional excitation in the present invention (λ R <b D ); DETAILED DESCRIPTION

[0093] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0094] refer to Figure 1 to Figure 7 The content of the present invention is a method for improving the efficiency of decentralized coupon-incentive demand response, and each step is described in detail below.

[0095] Step 1: Construct a three-layer demand response framework based on coupon incentive (CIDR) and establish the objective function of each layer.

[0096] (1-1) Construction of a three-layer demand response framework based on coupon incentives;

[0097] Participants in CIDR include independent system operators (ISOs), load service entities (LSEs), and end users. At the top level, the ISO is responsible for organizing the wholesale electricity market with the goal of maximizing social welfare. The main body in the middle level is the LSE, whose goal is to maximize the network's net profit, which consists of three parts: wholesale market procurement costs, retail market sales revenue, and incentive costs provided to end users. End consumers are at the bottom level, and their goal is to achieve maximum benefits while considering the convenience changes caused by participating in demand response. Its structure is shown in the figure below. Figure 2 shown.

[0098] (1-2) A three-tier demand response model based on coupon incentives;

[0099] Based on the above three-tier demand response framework, for simplicity, we assume that all end consumers are the same and sign the same retail price with the load service entity. Then the three-tier demand response model can be described as:

[0100] 1) Top layer (ISO)

[0101]

[0102] 2) Middle layer (LSE)

[0103]

[0104] 3) Bottom layer (user)

[0105]

[0106] Among them, λ is the market-clearing price; λ R is the retail electricity price; a D D 2 +b D D represents the demand response cost; π is the unit compensation price for demand response, and M is the maximum value of the pre-set demand response amount.

[0107] Step 2: Compare the optimal demand response results under the decentralized incentive demand response mechanism and the centralized demand response mechanism.

[0108] (2-1) Solution of centralized demand response model

[0109] The centralized demand response mechanism is also called centralized demand response scheduling. Under this mechanism, it is assumed that the DR cost functions of all users have been informed to the ISO. The goal is to maximize social welfare while effectively implementing demand response. The centralized DR scheduling can be modeled as a single-layer optimization problem as follows:

[0110]

[0111] Assuming that the generating capacity is sufficient, the actual market clearing price is equal to the marginal cost of the generator (and DR), which can be described as:

[0112] λ=2a G P G +b G =2a D D+b D (5)

[0113] Therefore, the optimal DR capacity (i.e., LSE response function) under the centralized demand response mechanism can be obtained as:

[0114]

[0115] We note that formula (6) only D ≤λ<2a D M+b D When the market price is lower than b D When the market price is higher than 2a, LSE will not be able to provide demand response due to insufficient price incentives for LSE. D M+b D , even though there is a profit surplus, the response capacity of LSE cannot exceed the pre-set limit M.

[0116] Therefore, the expression of the LSE response function is:

[0117]

[0118] (2-2) Solution of decentralized demand response model

[0119] The LSE response function in the decentralized demand response model is obtained through Stackelberg competition. The three-layer model can be decomposed into two Stackelberg models. The problem is solved by two backward induction methods, starting from solving formulas (1) and (2) and ending with solving formula (3).

[0120] The Lagrangian function of formula (3) is expressed as:

[0121]

[0122] Under unconstrained conditions, the Lagrange multiplier μ 3,1 =μ 3,2 =0, the user-side response function in formula (3) can be described as:

[0123]

[0124] Among them, π is the incentive price signal provided by LSE, and the user's optimal demand response increases with the increase of π.

[0125] Similarly, the backward induction method is used again for the intermediate layer model formula (2) to determine the response of the LSE, that is, the optimal response D of the LSE to the wholesale market clearing price λ. By constructing the Lagrangian function F A2 According to equation (9), we can get:

[0126] F A2 (π,μ 2,1 )=(λ-λ R )L+(π+λ R -λ)D-μ 2,1 π (10)

[0127] Assuming μ 2,1 = 0, partial derivative We can get the optimal incentive price that LSE issues to consumers as

[0128]

[0129] Combining formula (9) and formula (11), the optimal DR capacity under the decentralized demand response mechanism under unconstrained conditions is:

[0130]

[0131] Comparing formula (6) and formula (12), it can be found that under unconstrained conditions, the optimal DR capacity of decentralized demand response can only reach 1 / 2 of the centralized demand response capacity.

[0132] (2-3) Decentralized LSE response function based on bounded rationality

[0133] In reality, it is difficult for rational users to spontaneously participate in demand response without incentives. Bounded rationality assumes that without voluntary response, the demand response amount will increase linearly from 0 to M. Based on the rational participation conditions, the decentralized LSE response function is discussed in two cases as follows:

[0134] 1) When λ R ≥ b D hour

[0135] Similar to the solution steps of the decentralized model, the LSE response function expression under user rationality conditions is obtained by reverse induction:

[0136]

[0137] Similarly, the LSE response function expression under the condition of user limited rationality is:

[0138]

[0139] 2) When λ R <b D hour

[0140] In this case, no “voluntary feedback” phenomenon is observed, so there is no λ R ≥ b D In the case of bounded rationality, the LSE response function under user rationality is expressed as:

[0141]

[0142] Figure 4 and Figure 5 It is the original LSE response function diagram, that is, the demand response function image of the load service entity before external incentives are added to improve efficiency.

[0143] Step 3: Propose an additional incentive method for decentralized incentive-based demand response and construct an equivalent virtual generator model under demand response.

[0144] (3-1) Constructing external excitation function;

[0145] Compared with the centralized demand response model, the optimal demand response capacity of the ordinary three-layer decentralized demand response model is only 1 / 2 of that, so the efficiency of decentralized demand response needs to be improved through an external incentive function. In terms of its form, since the ISO pays the LSE an out-of-market fee, the incentive function should be related to the total amount of DR that the LSE can provide. Let the external incentive function be I(D), and bring it into the middle layer of the decentralized demand response model to obtain:

[0146]

[0147] In order to make the efficiency of decentralized demand response with external incentives equal to that of centralized demand response, combining formulas (6) and (9) yields:

[0148] π=λ-λ R (17)

[0149] After substituting formula (17) into the previous Lagrangian function, the expression is as follows:

[0150]

[0151] Where I'(D) is defined as After solving, the expression of I(D) is as follows:

[0152] I'(D)=λ-b D (19)

[0153] Therefore, the external activation function expression can be described as:

[0154] I(D)=(λ-b D )D (20)

[0155] Among them, since when λ<b D When , the value of I(D) is negative, which does not meet the actual situation. Therefore, the final expression of the non-negative external excitation function can be described as:

[0156] I(D)=max((λ-b D )D,0) (21)

[0157] It can be seen from formula (21) that the external incentive is mainly proportional to the market price and the demand response amount, and is a non-negative real number.

[0158] (3-2) Decentralized demand response mechanism with external incentives;

[0159] By applying external incentives to load service entities to increase overall social welfare, the optimal response capacity of distributed demand response is infinitely close to that of centralized demand response. According to the obtained external incentive function expression, since the underlying function of the decentralized demand response model remains unchanged, according to the original solution method, the Lagrangian function can be described as:

[0160]

[0161] By solving similarly, we can get R ≥ b D When , the LSE response function expression under the conditions of user rationality and bounded rationality is:

[0162]

[0163] When R ≥ b D When , the LSE response function expression under user rational conditions is:

[0164]

[0165] Figure 6 and Figure 7 This is the LSE response function diagram after adding external incentives. It can be found that after adding external incentives, at the same demand response capacity level, the market price on the horizontal axis is greatly reduced, which promotes the improvement of social welfare.

[0166] (3-3) Construct an equivalent virtual generator model under demand response;

[0167] By analyzing the impact of the LSE response function in the three-tier CI demand response mechanism on different external incentives (especially wholesale market prices), we can construct a "virtual generator" model to represent the optimal demand response behavior of LSE in the whole market. e Equivalent to the maximum demand response potential, the cost parameter a of the “virtual generator” D e and b D e Equivalent to the demand response cost parameter, considering the “voluntary” demand response in some scenarios, the equivalent baseline L of the load e To be greater than the nominal load L, the virtual generator and demand response equivalent model are as follows Figure 3 shown.

[0168] Next, the calculation formulas for the equivalent parameters of the virtual generator are given. The voluntary demand response has been calculated as (λ R -b D ) / 2a D , so the load reference value Le Can be described as:

[0169] L e =L-(λ R -b D ) / 2a D (25)

[0170] Similarly, the power generation of the virtual generator M e Can be described as:

[0171] M e =M-(λ R -b D ) / 2a D (26)

[0172] Cost parameter a of the virtual generator D e Related to the slope of the LSE response function, combined with formula (15), the cost parameter a D e Can be described as:

[0173] a D e =2a D (27)

[0174] Another cost parameter b of the virtual generator D e It is equal to the market price when users start to participate in demand response, which can be described as:

[0175] b D e =2λ R -b D (28)

[0176] For those skilled in the art, it is understood that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. Therefore, from any point of view, the embodiments should be regarded as instructive and non-restrictive. The scope of the present invention is limited by the attached claims rather than the above description. It is only a preferred embodiment of the present invention and is not intended to limit the present invention. All modifications, equivalent substitutions, improvements, etc. within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A decentralized coupon incentive demand response efficiency improvement method, characterized in that: The following steps are involved: Step (1) construct a three-layer demand response framework based on coupon incentives and establish the objective function of each layer; Step (2) comparing the optimal demand response results under the decentralized incentive demand response mechanism and the centralized demand response mechanism; Step (3) proposes a decentralized incentive demand response additional incentive method and constructs an equivalent virtual generator model under demand response; In the step (3): (3-1) Constructing external excitation function; Compared with the centralized demand response model, the optimal demand response capacity of the ordinary three-layer decentralized demand response model is only 1 / 2 of that of the centralized demand response model. Therefore, it is necessary to improve the efficiency of decentralized demand response through an external incentive function. In terms of its form, since the ISO pays the LSE an out-of-market fee, the incentive function should be related to the total amount of DR that the LSE can provide. Let the external incentive function be I(D), and bring it into the middle layer of the decentralized demand response model to obtain: In order to make the efficiency of decentralized demand response with external incentives equal to that of centralized demand response, combining formulas (6) and (9) yields: p=l-l R (17) After substituting formula (17) into the previous Lagrangian function, the expression is as follows: Where I'(D) is defined as After solving, the expression of I(D) is as follows: I'(D)=λ-b D (19) Therefore, the external activation function expression can be described as: I(D)=(λ-b D )D (20) Among them, since when λ<b D When , the value of is negative, which does not meet the actual situation. Therefore, the final expression of the non-negative external excitation function can be described as: I(D)=max((λ-b D )D,0)(21) From formula (21), it can be seen that the external incentive is mainly proportional to the market price and the demand response amount, and is a non-negative real number; (3-2) Decentralized demand response mechanism with external incentives; By applying external incentives to load service entities to increase overall social welfare, the optimal response capacity of distributed demand response is infinitely close to that of centralized demand response. According to the obtained external incentive function expression, since the underlying function of the decentralized demand response model remains unchanged, according to the original solution method, the Lagrangian function can be described as: By solving similarly, we can get R ≥ b D When , the LSE response function expression under the conditions of user rationality and bounded rationality is: When R ≥ b D When , the LSE response function expression under user rational conditions is: (3-3) Construct an equivalent virtual generator model under demand response; By analyzing the impact of the response function of LSE in the three-tier CIDR mechanism on different external incentives, we can construct a "virtual generator" model to represent the optimal demand response behavior of LSE in the whole market. Referring to the parameters of typical generators, the power generation of the "virtual generator" is equivalent to the maximum demand response potential, and the cost parameters of the "virtual generator" are equivalent to the demand response cost parameters. Considering the "voluntary" demand response in some scenarios, the equivalent baseline of the load is greater than the nominal load. Combined with the calculation formulas of the equivalent parameters of the virtual generator, the voluntary demand response has been obtained as (λ R -b D ) / 2a D , so the load reference value L e Can be described as: L e =L-(λ R -b D ) / 2a D (25) Similarly, the power generation of the virtual generator can be described as: M e =M-(λ R -b D ) / 2a D (26) Cost parameter a of the virtual generator D e Related to the slope of the LSE response function, combined with formula (15), the cost parameter can be described as: a D e =2a D (27) Another cost parameter b of the virtual generator D e It is equal to the market price when users start to participate in demand response, which can be described as: b D e =2λ R -b D (28)。 2. A method for improving the efficiency of decentralized coupon-incentive demand response according to claim 1, characterized in that: In the step (1), the coupon incentive objects include independent system operators (ISOs), load service entities (LSEs) and end users. The three-layer demand includes the top layer corresponding to the independent system operators, the middle layer corresponding to the load service entities and the bottom layer corresponding to the end users, and the corresponding models of the three-layer demand are constructed respectively.

3. A method for improving the efficiency of decentralized coupon-incentive demand response according to claim 1, characterized in that: The specific steps of step (2) are as follows: (2-1) Solution of the centralized demand response model The centralized demand response mechanism is also called centralized demand response scheduling. Under this mechanism, it is assumed that the demand response cost functions of all users have been informed to the independent system operator. The goal is to maximize social welfare while effectively implementing demand response. The centralized DR scheduling can be modeled as a single-layer optimization problem as follows: Assuming that the generating capacity is sufficient, the actual market clearing price is equal to the marginal cost of the generator (and DR), which can be described as: λ=2a G P G +b G =2a D D+b D (5) Therefore, the optimal DR capacity (i.e., LSE response function) under the centralized demand response mechanism can be obtained as: We note that formula (6) only D ≤λ<2a D M+b D When the market price is lower than , LSE will not be able to provide demand response due to insufficient price incentives for LSE; when the market price is higher than 2a D M+b D When , despite the existence of profit surplus, the response capacity of LSE cannot exceed the preset limit M, so the expression of LSE response function is: (2-2) Solution of decentralized demand response model The LSE response function in the decentralized demand response model is obtained through Stackelberg competition. The three-layer model can be decomposed into two Stackelberg models. Two backward induction methods are used to solve the problem, starting from solving formulas (1) and (2) and ending with solving formula (3). The Lagrangian function of formula (3) is expressed as: Under unconstrained conditions, the Lagrange multiplier μ 3,1 =μ 3,2 =0, the user-side response function in formula (3) can be described as: Among them, is the incentive price signal provided by LSE, and the user's optimal demand response increases with the increase of π; Similarly, for the intermediate layer model formula (2), the backward induction method is used again to determine the response of LSE, that is, the optimal response D of LSE to the wholesale market clearing price λ. By constructing the Lagrangian function, according to equation (9), it can be obtained: F A2 (a.m 2,1 )=(λ-λ R )L+(π+λ R -λ)D-μ 2,1 p(10) Assuming μ 2,1 = 0, partial derivative We can get the optimal incentive price that LSE issues to consumers as Combining formula (9) and formula (11), the optimal DR capacity under the decentralized demand response mechanism under unconstrained conditions is: Comparing formula (6) and formula (12), it can be found that under unconstrained conditions, the optimal DR capacity of decentralized demand response can only reach 1 / 2 of the centralized demand response capacity; (2-3) Decentralized LSE response function based on bounded rationality In reality, without incentives, it is difficult for rational users to spontaneously participate in demand response. Under the limited rationality assumption, without voluntary response, the demand response amount will increase linearly from 0 to M. According to the rational participation conditions, the decentralized LSE response function is discussed in two cases as follows: 1) When λ R ≥ b D hour Similar to the solution steps of the decentralized model, the LSE response function expression under user rationality conditions is obtained by reverse induction: Similarly, the LSE response function expression under the condition of user limited rationality is: 2) When λ R <b D hour In this case, no "voluntary feedback" phenomenon is observed, so there is no case of bounded rationality. The LSE response function expression under user rationality conditions is: 。

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