Power-carbon transaction method based on multi-leader and multi-follower Stackelberg game

Abstract

The invention provides a power-carbon transaction method based on a multi-leader and multi-follower Stackelberg game, and the method comprises the following steps: S1, enabling carbon emission to be embedded into the income of each producer in a currency manner based on the MLMF Stackelberg game, and forming a power-carbon integrated market; s2, for an MLMF game model with the electric power and carbon transaction prices as decision variables, proving the existence and uniqueness of Stackelberg equalibrium; s3, deducing an electric power and carbon transaction price formula under the SE by adopting a centralized analysis algorithm; and S4, expanding the two-stage transaction to the electric power-carbon integrated market. According to the invention, low-carbon operation is realized, fairness of a transaction market and security of a network are ensured, carbon emission is significantly reduced, and the total income of producers and sellers is not damaged.

Description

Technical Field

[0001] The present invention relates to the field of power system optimization. Background Art

[0002] With the widespread integration of distributed generation (DG) such as solar panels, wind turbines, and micro-generators, traditional electricity users have transformed from consumers to prosumers. To promote the complementary advantages between prosumer resources, local energy trading and sharing mechanisms are designed to motivate these emerging stakeholders to participate in the trading market. Interactive energy with value as the key operating parameter is considered to be the next energy management approach to accommodate a large number of DGs. In addition, carbon emissions, which are mainly generated by the combustion of fossil fuels, should also be considered in energy management to build an environmentally friendly power system.

[0003] The effective operation of the integrated electricity-carbon market is the key foundation for ensuring the low-carbon and economic operation of the energy system. With the significant increase in the installed capacity of distributed energy resources (such as solar energy, wind energy, etc.) in the power system, the trading mechanism and stability control of the integrated electricity-carbon market have been more severely challenged. At present, academia and industry are actively studying the construction and optimization of the integrated electricity-carbon market, focusing on the design of the market framework, the establishment of the trading model, the dynamic adjustment of the trading price, and the analysis of the behavioral strategies of market participants. The key technologies used include the multi-level market (MLMF) Stackelberg game model, network reconstruction optimization, privacy protection mechanism, and distributed trading algorithm based on price signals. These technologies jointly promote the stable operation and efficient development of the integrated electricity-carbon market.

[0004] In the integrated electricity and carbon trading market, the traditional single market mechanism design cannot fully reflect the complex relationship between electricity production and carbon emissions; and the construction of complex market models, such as those based on detailed data analysis and highly parameterized models, is often accompanied by heavy computational burdens, which indirectly increases the complexity of market management and operation, and is often difficult to respond quickly to market changes in practical applications; at the same time, although adaptive market regulation strategies and fixed trading rules can optimize resource allocation to a certain extent, they are often limited to short-term profit maximization, ignoring the long-term low-carbon transformation goals, and their market stability also faces many challenges. Therefore, it is urgent to develop a new integrated trading framework that combines electricity and carbon allowances to try to solve the above problems. Summary of the invention

[0005] In order to solve the above problems existing in electricity and carbon trading, the present invention provides an electricity-carbon trading method based on multi-leader and multi-follower Stackelberg game.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a power-carbon trading method based on multi-leader multi-follower Stackelberg game, comprising the following steps:

[0007] Step S1: Based on the MLMF Stackelberg game, carbon emissions are embedded into the income of each producer and consumer in monetary terms to form an integrated electricity-carbon market;

[0008] Step S2: For the MLMF game model with electricity and carbon trading prices as decision variables, prove the existence and uniqueness of Stackelberg equilibrium;

[0009] Step S3: Using a centralized analysis algorithm, derive the price formulas for electricity and carbon trading under SE;

[0010] Step S4: Extend the two-stage transaction to the integrated electricity-carbon market.

[0011] In step S1, the MLMF Stackelberg game model is:

[0012] The objective function minNB for prosumers to buy / sell energy and carbon quotas to others or DSOs i,t for:

[0013]

[0014] where the subscript i,t represents the i-th prosumer at hour t, B represents revenue, C represents price, N is the number of prosumers, PG represents microturbine output, PL is load demand, and π t , ρ t The price of electricity and carbon emission quota in P2P transactions, PS i,t P2P and PB i,t P2P Represents the electricity traded by prosumers through the P2P market, PS i,t DSO and PB i,t DSO Trading electricity with DSO on behalf of prosumers, CS i,t P2P and CB i,t P2P For producers and consumers to trade carbon quotas based on the P2P market, CS i,t DSO and CB i,t DSO is the carbon limit traded between the prosumer and the DSO, ρ t min and ρ t maxare the lower and upper bounds of the carbon quota, respectively, t min and π t max are the lower and upper bounds of electricity transaction prices respectively;

[0015] The benefits to prosumers measured by energy consumption are as follows:

[0016] B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t ) 2

[0017] Among them, λ i,t and β i,t is a parameter related to the benefits of prosumers;

[0018] The cost of electricity generated by micro-turbines is measured, ignoring the cost of electricity generated by renewable energy sources:

[0019] C i,t (PG i,t )=a i (PG i,t ) 2 +b i PG i,t +c i

[0020] Among them, a i ,b i ,c i is a parameter related to the microturbine output;

[0021] Energy and carbon emission balance per prosumer:

[0022]

[0023] Among them, PR is the renewable energy power generation, CA i,t 0 is the initial carbon emission limit of the prosumer, CA i,t REG Carbon emissions cap for renewable energy generation, CA i,t MT The carbon emission limit generated by the microturbine output, C e,t is the carbon emissions per unit of energy consumption;

[0024] The ultimate load demand and DG output are:

[0025]

[0026] Among them, PL i,t min ,PL i,t max is the lower and upper bounds of the load demand, PG i,t max is the upper bound for the microturbine output;

[0027] [π t min , π t max ] and [ρ t min ,ρ t max ] represents the price range of energy trading and carbon trading. Assuming that each stakeholder is rational, π t and ρ t Specifically, if ρ t Higher than ρ t max , consumers will purchase carbon allowances from DSOs instead of other producers in the distribution network if ρt is lower than ρ t min , producers will sell carbon quotas to DSOs instead of other consumers in the distribution network. At the same time, if the supply of producers can balance the demand of consumers, then prosumers will not trade with DSOs, which can be restated as:

[0028] minNB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t

[0029] PL i,t +PT i,t =PG i,t +PR i,t

[0030]

[0031] Among them, PT is the trading electricity of the prosumer when the supply and demand are balanced, and CT is the trading carbon limit of the prosumer when the supply and demand are balanced.

[0032] In step 3, electricity and carbon trading prices are formulated through a centralized algorithm, and the balance in energy and carbon trading is expressed as:

[0033]

[0034] For simplicity, assume that PL i,t and PG i,t In the following analysis, the limit is not reached. When the first-order partial derivative decision variable is 0, its optimal value reaches

[0035]

[0036] π t and ρ t It can be expressed by a system of linear equations:

[0037]

[0038]

[0039] Among them, C g The carbon emissions for each electricity generation are then protected by introducing a decentralized algorithm to protect the internal information of the producers and consumers. Each producer and consumer may change the role of consumer or producer in energy and carbon quotas according to iterative price signals. t and ρ t The initial values ​​are:

[0040]

[0041] The transaction prices of electricity and carbon obtained through algorithm iteration are:

[0042]

[0043] where σ t and θ t is the price of electricity and carbon trading in the iteration (π h t and ρ h t ) price adjustment parameter, PT s,t * and CT s,t * Indicates the amount of electricity and carbon emission quotas provided by seller s to the market, PT b,t * and CT b,t * Indicates the amount of electricity and carbon emission that buyer b purchases from the market; if:

[0044]

[0045] Then terminate this iterative algorithm, otherwise, set h = h + 1 and repeat the above steps, where ε is a positive threshold.

[0046] In step 4, in order to ensure network security under the operation strategy of the producer and consumer, the transaction power obtained in the first stage is used to achieve network reconstruction through DSO in the second stage, and the interaction results are recalculated with constraints until the network security constraints are met. The network reconstruction model is as follows:

[0047]

[0048] Among them, r ij is the branch ij resistance, I ij is the current of branch ij;

[0049] (1) Power flow constraints

[0050] The rules of power dialogue are:

[0051]

[0052] Among them, P ij,t and Q ij,t are the active and reactive power of branch ij, r ij and x ij is the resistance and reactance of branch ij

[0053] Ohm's law on branch ij is:

[0054]

[0055] U is the voltage, corresponding to nodes i and j;

[0056] Relax the following constraint

[0057]

[0058] Can be converted to the second-order cone formula

[0059]

[0060] (2) Network security constraints

[0061] The node voltage constraints and line capacity constraints are:

[0062]

[0063] U min and U max are the lower and upper limits of the voltage respectively, S L is the line capacity constraint;

[0064] (3) Network Reconfiguration Constraints

[0065] The branch condition constraint is

[0066]

[0067] δ ij,t is the binary variable of the branch condition, W represents the switch state, when W is equal to 0, it means that the branch is disconnected;

[0068] Ensure that when the branch is disconnected, P ij,t and Q ij,t is equal to 0:

[0069]

[0070] M is a sufficiently large positive number in the Big-M method to handle the situation when the switch is disconnected, ensuring the accuracy and feasibility of the mathematical model; then, the Big-M method is usually used to expand to the disconnected branch:

[0071]

[0072] In this way, the second-stage network management model is transformed into a mixed integer second-order cone programming that can be directly solved by IBM CLPEX.

[0073] A device for applying a power-carbon trading method based on a multi-leader multi-follower Stackelberg game, comprising:

[0074] The electricity-carbon integrated market formation module is used to embed carbon emissions into the income of each producer and consumer in a monetary manner to form an electricity-carbon integrated market;

[0075] The Stackelberg equilibrium proof module is used to prove the existence and uniqueness of the Stackelberg equilibrium for the MLMF game model with electricity and carbon trading prices as decision variables in the electricity-carbon integrated market;

[0076] The electricity and carbon trading price calculation module is used to derive the electricity and carbon trading price formulas under the above-mentioned Stackelberg equilibrium;

[0077] The transaction expansion module is used to reconstruct the network in the second phase with the transaction volume obtained in the first phase, and to expand the two-phase transaction to the electricity-carbon integrated market.

[0078] The MLMF Stackelberg game model in the Stackelberg equilibrium proof module is:

[0079] The objective function minNB for prosumers to buy / sell energy and carbon quotas to others or DSOs i,t for:

[0080]

[0081] where the subscript i,t represents the i-th prosumer at hour t, B represents revenue, C represents price, N is the number of prosumers, PG represents microturbine output, PL is load demand, and π t , ρ t The price of electricity and carbon emission quota in P2P transactions, PS i,t P2P and PB i,t P2P Represents the electricity traded by prosumers through the P2P market, PS i,t DSO and PB i,t DSO Trading electricity with DSO on behalf of prosumers, CS i,t P2P and CB i,t P2P For producers and consumers to trade carbon quotas based on the P2P market, CS i,t DSO and CB i,t DSO is the carbon limit traded between the prosumer and the DSO, ρ t min and ρ t max are the lower and upper bounds of the carbon quota, respectively, t min and π t max are the lower and upper bounds of electricity transaction prices respectively;

[0082] The benefits to prosumers measured by energy consumption are as follows:

[0083] B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t ) 2

[0084] Among them, λ i,t and β i,t is a parameter related to the benefits of prosumers;

[0085] The cost of electricity generated by micro-turbines is measured, ignoring the cost of electricity generated by renewable energy sources:

[0086] C i,t (PG i,t )=a i (PG i,t ) 2 +b i PGi,t +c i

[0087] Among them, a i ,b i ,c i is a parameter related to the microturbine output;

[0088] Energy and carbon emission balance per prosumer:

[0089]

[0090] Among them, PR is the renewable energy power generation, CA i,t 0 is the initial carbon emission limit of the prosumer, CA i,t REG Carbon emissions cap for renewable energy generation, CA i,t MT The carbon emission limit generated by the microturbine output, C e,t is the carbon emissions per unit of energy consumption;

[0091] The ultimate load demand and DG output are:

[0092]

[0093] Among them, PL i,t min ,PL i,t max is the lower and upper bounds of the load demand, PG i,t max is the upper bound for the microturbine output;

[0094] [π t min , π t max ] and [ρ t min ,ρ t max ] represents the price range of energy trading and carbon trading. Assuming that each stakeholder is rational, π t and ρ t Specifically, if ρ t Higher than ρ t max , consumers will purchase carbon allowances from DSOs instead of other producers in the distribution network if ρt is lower than ρ t min , producers will sell carbon quotas to DSOs instead of other consumers in the distribution network. At the same time, if the supply of producers can balance the demand of consumers, then prosumers will not trade with DSOs, which can be restated as:

[0095] minNB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t

[0096] PL i,t +PT i,t =PG i,t +PR i,t

[0097]

[0098] Among them, PT is the trading electricity of the prosumer when the supply and demand are balanced, and CT is the trading carbon limit of the prosumer when the supply and demand are balanced.

[0099] In the electricity and carbon trading price calculation module, the balance in energy and carbon trading is expressed as:

[0100]

[0101]

[0102] For simplicity, assume that PL i,t and PG i,t In the following analysis, the limit is not reached. When the first-order partial derivative decision variable is 0, its optimal value reaches

[0103]

[0104] π t and ρ t It can be expressed by a system of linear equations:

[0105]

[0106] Among them, C g The carbon emissions for each electricity generation are then protected by introducing a decentralized algorithm to protect the internal information of the producers and consumers. Each producer and consumer may change the role of consumer or producer in energy and carbon quotas according to iterative price signals. t and ρ t The initial values ​​are:

[0107]

[0108] The transaction prices of electricity and carbon obtained through algorithm iteration are:

[0109]

[0110] where σ t and θ t is the price of electricity and carbon trading in the iteration (π h t and ρ h t ) price adjustment parameter, PT s,t * and CT s,t * Indicates the amount of electricity and carbon emission quotas provided by seller s to the market, PT b,t * and CT b,t * Indicates the amount of electricity and carbon emission that buyer b purchases from the market; if:

[0111]

[0112] Then terminate this iterative algorithm, otherwise, set h = h + 1 and repeat the above steps, where ε is a positive threshold.

[0113] In the transaction extension module, the network reconstruction model is as follows:

[0114]

[0115] Among them, r ij is the branch ij resistance, I ij is the current of branch ij;

[0116] In the transaction extension module, the network reconstruction constraints include:

[0117] (1) Power flow constraints

[0118] The rules of power dialogue are:

[0119]

[0120] Among them, P ij,t and Q ij,t are the active and reactive power of branch ij, r ij and x ij is the resistance and reactance of branch ij

[0121] Ohm's law on branch ij is:

[0122]

[0123] U is the voltage, corresponding to nodes i and j;

[0124] Relax the following constraint

[0125]

[0126] Can be converted to the second-order cone formula

[0127]

[0128] In the transaction extension module, the network reconstruction constraints include:

[0129] (2) Network security constraints

[0130] The node voltage constraints and line capacity constraints are:

[0131]

[0132] U min and U max are the lower and upper limits of the voltage respectively, S L is the line capacity constraint;

[0133] In the transaction extension module, the network reconstruction constraints include:

[0134] (3) Network Reconfiguration Constraints

[0135] The branch condition constraint is

[0136]

[0137] δ ij,t is the binary variable of the branch condition, W represents the switch state, when W is equal to 0, it means that the branch is disconnected;

[0138] Ensure that when the branch is disconnected, P ij,t and Q ij,t is equal to 0:

[0139]

[0140] M is a sufficiently large positive number in the Big-M method to handle the situation when the switch is disconnected, ensuring the accuracy and feasibility of the mathematical model; then, the Big-M method is usually used to expand to the disconnected branch:

[0141]

[0142] The second-stage network management model is transformed into a mixed integer second-order cone programming that can be directly solved by IBM CLPEX.

[0143] The invention discloses a power-carbon trading method based on a multi-leader multi-follower Stackelberg game, which allows producers and sellers to flexibly switch buying and selling roles in the energy and carbon trading markets, and embeds carbon emissions into the revenue of each producer and seller in a monetary manner. In addition, by verifying the existence and uniqueness of market equilibrium, centralized and decentralized algorithms are developed to solve the game model, the two-stage P2P trading framework is extended to support the trading results of power and carbon quotas, and the limitation of node injection power is avoided to the maximum extent through network reconstruction. Not only low-carbon operation is achieved, but also the fairness of the trading market and the security of the network are ensured, and carbon emissions are significantly reduced without damaging the total income of producers and sellers. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] Figure 1 It is a 4-node network structure diagram of the present invention;

[0145] Figure 2 It is a price graph of energy and carbon trading in the P2P market under the 4-node system of the present invention;

[0146] Figure 3 is a graph of power generation or consumption by a prosumer of the present invention;

[0147] Figure 4 It is the prosumer or carbon emission graph of the present invention;

[0148] Figure 5 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0149] The invention discloses a power-carbon trading method based on the multi-leader multi-follower (MLMF) Stackelberg game, which fully considers the changes in the roles of stakeholders between producers and consumers in energy and carbon quota trading, supports the interaction results to the greatest extent, avoids the limitation of node injection power, can effectively reduce carbon emissions, and can meet the needs of practical applications. Figure 5 As shown, the method is as follows:

[0150] Step 1: Based on the MLMF Stackelberg game, carbon emissions are embedded in the benefits of each prosumer in a monetary manner, and an integrated electricity-carbon market is proposed. This market can reflect the relationship between energy / carbon prices and prosumer business strategies, and induce low-carbon behavior of prosumers. At the same time, the role of each prosumer in energy or carbon trading (buyer or seller) does not need to be defined in advance. The two-stage P2P trading framework aims to promote local energy trading and sharing under the safe operation of the distribution network. The electricity-carbon integrated trading market realizes the low-carbon economic operation of the integrated energy system through the carbon trading mechanism.

[0151] Step 2: For the MLMF game model with electricity and carbon trading prices as decision variables, prove the existence and uniqueness of Stackelberg equilibrium (SE), where there is a non-cooperative relationship between producers and consumers, whose goal is to maximize their own interests. First, it is necessary to prove the existence of Nash equilibrium in non-cooperative countermeasures. Then, verify the uniqueness of SE.

[0152] Step 3: Introduce a centralized analysis algorithm to derive the price formula for electricity and carbon trading under SE. At the same time, in order to protect the internal information of stakeholders, a decentralized iterative algorithm is combined to use the supply and demand relationship to improve the calculation efficiency.

[0153] Step 4: To support the trading results of electricity and carbon emission rights, the two-stage trading framework is extended to the electricity-carbon integrated market. In the first stage, each prosumer participates in local energy and carbon quota trading by contributing to the mechanism in (1). In the second stage, the distributed system operator (DSO) uses network reconstruction to ensure safe operation and minimize the reduction of DG.

[0154] After the electricity-carbon integration market is established in step one, the role of each consumer (consumer or producer) is allowed to change according to the benefits rather than being pre-defined. This means that each participant in the market has the right to act as a price-making entity. Specifically, for a prosumer who decides to become a consumer, if the external price is high enough, this stakeholder is likely to change the decision and increase the output of the micro-turbine to become a producer. The goal of the established MLMF Stackelberg game is to maximize the profit of each prosumer at each hour t or minimize the operating cost of each prosumer. The specific model is as follows:

[0155] First, the objective function minNB for prosumers to buy / sell energy and carbon quotas to others or DSOs is i,t for:

[0156]

[0157] Where the superscript i,t represents the i-th prosumer at hour t, B represents revenue, C represents price, and N represents the number of prosumers. PG represents the microturbine output, PL represents the load demand, and π t , ρ t The price of electricity and carbon emission quota in P2P transactions, PS i,t P2P and PB i,t P2P Represents the electricity traded by prosumers through the P2P market, PS i,t DSO and PB i,t DSOTrading electricity with DSO on behalf of prosumers, CS i,t P2P and CB i,t P2P For producers and consumers to trade carbon quotas based on the P2P market, CS i,t DSO and CB i,t DSO is the carbon limit traded between the prosumer and the DSO, ρ t min and ρ t max are the lower and upper bounds of the carbon quota, respectively, t min and π t max are the lower and upper bounds of electricity transaction prices respectively.

[0158] The benefits to prosumers measured by energy consumption are as follows:

[0159] B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t ) 2

[0160] Among them, λ i,t and β i,t is a parameter related to the benefits of producers and consumers.

[0161] The cost of electricity generated by micro-turbines is measured, ignoring the cost of electricity generated by renewable energy sources:

[0162] C i,t (PG i,t )=a i (PG i,t ) 2 +b i PG i,t +c i

[0163] Among them, a i ,b i ,c i is a parameter related to the output of the microturbine.

[0164] Energy and carbon emission balance per prosumer:

[0165]

[0166] Among them, PR is the renewable energy power generation, CA i,t 0 is the initial carbon emission limit of the prosumer, CAi,t REG Carbon emissions cap for renewable energy generation, CA i,t MT The carbon emission limit generated by the microturbine output, C e,t The carbon emissions per unit of energy consumed.

[0167] The ultimate load demand and DG output are:

[0168]

[0169] Among them, PL i,t min ,PL i,t max is the lower and upper bounds of the load demand, PG i,t max Upper bound for microturbine output.

[0170] [π t min , π t max ] and [ρ t min ,ρ t max ] represents the price range of energy trading and carbon trading. Assuming that each stakeholder is rational, π t and ρ t Specifically, if ρ t Higher than ρ t max , consumers will buy carbon allowances from DSOs instead of other producers in the distribution network. t min , producers will sell carbon quotas to DSOs instead of other consumers in the distribution network. At the same time, if the supply of producers can balance the demand of consumers, prosumers will not trade with DSOs, which can be restated as:

[0171] minNB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t

[0172] PL i,t +PT i,t =PG i,t +PR i,t

[0173]

[0174] Among them, PT is the trading electricity of the prosumer when the supply and demand are balanced, and CT is the trading carbon limit of the prosumer when the supply and demand are balanced.

[0175] In this case, the setting of electricity and carbon trading prices can be carried out directly. The electricity and carbon trading prices are set by a centralized algorithm, which is suitable for situations where the producer supply can balance the consumer demand. The balance in energy and carbon trading is expressed as:

[0176]

[0177] For simplicity, assume that PL i,t and PG i,t In the following analysis, the limit was not reached. When the first-order partial derivative decision variable is 0, its optimal value reaches

[0178]

[0179] π t and ρ t It can be expressed by a system of linear equations:

[0180]

[0181] Among them, C g is the carbon emission per electricity generation. Then, the internal information of the producers and consumers is protected by introducing a decentralized algorithm. Each producer and consumer may change the role of consumer or producer in energy and carbon quota according to the iterative price signal. t and ρ t The initial values ​​are:

[0182]

[0183] The transaction prices of electricity and carbon obtained through algorithm iteration are:

[0184]

[0185] where σ t and θ t is the price of electricity and carbon trading in the iteration (π h t and ρ h t ) price adjustment parameters. s,t * and CT s,t * Indicates the amount of electricity and carbon emission quotas provided by seller s to the market, PT b,t *and CT b,t * Indicates the amount of electricity and carbon emission that buyer b purchased from the market. If:

[0186]

[0187] Then terminate this iterative algorithm, otherwise, set h = h + 1 and repeat the above steps. ε is a positive threshold.

[0188] In order to ensure network security under the operation strategy of the producer and consumer, as well as the transaction power obtained in the first stage, network reconstruction is implemented through DSO in the second stage. Specifically, it means that DSO can change the topology of the distribution network by changing the state of the candidate switches. Network reconstruction can improve the power flow and node voltage of the distribution network, thereby ensuring the efficient operation of the distribution network and the feasibility of the transaction results. Note that if the network reconstruction cannot solve the network congestion or voltage violation problems, the DSO will set corresponding restrictions on the node injection power according to the operating status. Then, the interaction results are recalculated with the constraints until the network security constraints are met. The detailed network reconstruction model is shown below:

[0189]

[0190] Among them, r ij is the branch ij resistance, I ij is the current of branch ij.

[0191] (1) Power flow constraints

[0192] The rules of power dialogue are:

[0193]

[0194] Among them, P ij,t and Q ij,t are the active and reactive power of branch ij, r ij and x ij The Ohm's law on branch ij is:

[0195]

[0196] U is the voltage, corresponding to nodes i and j.

[0197] Relax the following constraint

[0198]

[0199] Can be converted to the second-order cone formula

[0200]

[0201] (2) Network security constraints

[0202] The node voltage constraints and line capacity constraints are:

[0203]

[0204] U min and U max are the lower and upper limits of the voltage respectively, S L is the line capacity constraint.

[0205] (3) Network Reconfiguration Constraints

[0206] The branch condition constraint is

[0207]

[0208] δ ij,t is a binary variable of the branch condition, W represents the switch state, and when W is equal to 0, it means that the branch is disconnected. ij,t and Q ij,t is equal to 0:

[0209]

[0210] M is a sufficiently large positive number in the Big-M method to handle the situation when the switch is disconnected, ensuring the accuracy and feasibility of the mathematical model. Then, the Big-M method is usually extended to the disconnected branch:

[0211]

[0212] In this way, the second-stage network management model is transformed into a mixed-integer second-order cone programming that can be directly solved.

[0213] The device applied to the above-mentioned power-carbon trading method based on multi-leader multi-follower Stackelberg game comprises:

[0214] The electricity-carbon integrated market formation module is used to embed carbon emissions into the income of each producer and consumer in a monetary manner to form an electricity-carbon integrated market;

[0215] The Stackelberg equilibrium proof module is used to prove the existence and uniqueness of the Stackelberg equilibrium for the MLMF game model with electricity and carbon trading prices as decision variables in the electricity-carbon integrated market;

[0216] The electricity and carbon trading price calculation module is used to derive the electricity and carbon trading price formulas under the above-mentioned Stackelberg equilibrium;

[0217] The transaction expansion module is used to reconstruct the network in the second phase with the transaction volume obtained in the first phase, and to expand the two-phase transaction to the electricity-carbon integrated market.

[0218] The MLMF Stackelberg game model in the Stackelberg equilibrium proof module is:

[0219] The objective function minNB for prosumers to buy / sell energy and carbon quotas to others or DSOs i,t for:

[0220]

[0221] where the subscript i,t represents the i-th prosumer at hour t, B represents revenue, C represents price, N is the number of prosumers, PG represents microturbine output, PL is load demand, and π t , ρ t The price of electricity and carbon emission quota in P2P transactions, PS i,t P2P and PB i,t P2P Represents the electricity traded by prosumers through the P2P market, PS i,t DSO and PB i,t DSO Trading electricity with DSO on behalf of prosumers, CS i,t P2P and CB i,t P2P For producers and consumers to trade carbon quotas based on the P2P market, CS i,t DSO and CB i,t DSO is the carbon limit traded between the prosumer and the DSO, ρ t min and ρ t max are the lower and upper bounds of the carbon quota, respectively, t min and π t max are the lower and upper bounds of electricity transaction prices respectively;

[0222] The benefits to prosumers measured by energy consumption are as follows:

[0223] B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t )2

[0224] Among them, λ i,t and β i,t is a parameter related to the benefits of prosumers;

[0225] The cost of electricity generated by micro-turbines is measured, ignoring the cost of electricity generated by renewable energy sources:

[0226] C i,t (PG i,t )=a i (PG i,t ) 2 +b i PG i,t +c i

[0227] Among them, a i ,b i ,c i is a parameter related to the microturbine output;

[0228] Energy and carbon emission balance per prosumer:

[0229]

[0230] Among them, PR is the renewable energy power generation, CA i,t 0 is the initial carbon emission limit of the prosumer, CA i,t REG Carbon emissions cap for renewable energy generation, CA i,t MT The carbon emission limit generated by the microturbine output, C e,t is the carbon emissions per unit of energy consumption;

[0231] The ultimate load demand and DG output are:

[0232]

[0233] Among them, PL i,t min ,PL i,t max is the lower and upper bounds of the load demand, PG i,t max is the upper bound for the microturbine output;

[0234] [π t min , π t max ] and [ρ t min ,ρ t max] represents the price range of energy trading and carbon trading. Assuming that each stakeholder is rational, π t and ρ t Specifically, if ρ t Higher than ρ t max , consumers will purchase carbon allowances from DSOs instead of other producers in the distribution network if ρt is lower than ρ t min , producers will sell carbon quotas to DSOs instead of other consumers in the distribution network. At the same time, if the supply of producers can balance the demand of consumers, then prosumers will not trade with DSOs, which can be restated as:

[0235] minNB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t

[0236] PL i,t +PT i,t =PG i,t +PR i,t

[0237]

[0238] Among them, PT is the trading electricity of the prosumer when the supply and demand are balanced, and CT is the trading carbon limit of the prosumer when the supply and demand are balanced.

[0239] In the electricity and carbon trading price calculation module, the balance in energy and carbon trading is expressed as:

[0240]

[0241] For simplicity, assume that PL i,t and PG i,t In the following analysis, the limit is not reached. When the first-order partial derivative decision variable is 0, its optimal value reaches

[0242]

[0243]

[0244] π t and ρ t It can be expressed by a system of linear equations:

[0245]

[0246] Among them, C g The carbon emissions for each electricity generation are then protected by introducing a decentralized algorithm to protect the internal information of the producers and consumers. Each producer and consumer may change the role of consumer or producer in energy and carbon quotas according to iterative price signals. t and ρ t The initial values ​​are:

[0247]

[0248] The transaction prices of electricity and carbon obtained through algorithm iteration are:

[0249]

[0250] where σ t and θ t is the price of electricity and carbon trading in the iteration (π h t and ρ h t ) price adjustment parameter, PT s,t * and CT s,t * Indicates the amount of electricity and carbon emission quotas provided by seller s to the market, PT b,t * and CT b,t * Indicates the amount of electricity and carbon emission that buyer b purchases from the market; if:

[0251]

[0252] Then terminate this iterative algorithm, otherwise, set h = h + 1 and repeat the above steps, where ε is a positive threshold.

[0253] In the transaction extension module, the network reconstruction model is as follows:

[0254]

[0255] Among them, r ij is the branch ij resistance, I ij is the current of branch ij;

[0256] In the transaction extension module, the network reconstruction constraints include:

[0257] (1) Power flow constraints

[0258] The rules of power dialogue are:

[0259]

[0260] Among them, P ij,t and Q ij,t are the active and reactive power of branch ij, r ij and x ij The Ohm's law on branch ij is:

[0261]

[0262] U is the voltage, corresponding to nodes i and j;

[0263] Relax the following constraint

[0264]

[0265] Can be converted to the second-order cone formula

[0266]

[0267] In the transaction extension module, the network reconstruction constraints include:

[0268] (2) Network security constraints

[0269] The node voltage constraints and line capacity constraints are:

[0270]

[0271] U min and U max are the lower and upper limits of the voltage respectively, S L is the line capacity constraint;

[0272] In the transaction extension module, the network reconstruction constraints include:

[0273] (3) Network Reconfiguration Constraints

[0274] The branch condition constraint is

[0275]

[0276] δ ij,t is the binary variable of the branch condition, W represents the switch state, when W is equal to 0, it means that the branch is disconnected;

[0277] Ensure that when the branch is disconnected, P ij,t and Q ij,t is equal to 0:

[0278]

[0279] M is a sufficiently large positive number in the Big-M method to handle the situation when the switch is disconnected, ensuring the accuracy and feasibility of the mathematical model; then, the Big-M method is usually used to expand to the disconnected branch:

[0280]

[0281] The network management model of the second stage is transformed into a mixed integer second-order cone programming that can be directly solved by IBM CLPEX. In order to better verify the effectiveness of the established electricity-carbon integrated market, we use a 4-node community system to verify the establishment of case I and case II to verify that the established P2P market can stimulate the initiative of producers and consumers and increase their income, such as Figure 1 In addition, the optimization results of the centralized algorithm and the distributed algorithm are compared.

[0282] Case 1: Each prosumer can only trade electricity and carbon emission quotas with the DSO.

[0283] Case 2: Allow each producer and consumer to trade electricity and carbon emission quotas through the established P2P market.

[0284] like Figure 2 As shown in (a) and (b), Figure 3 In (a)-(d), the operating strategies of each producer and consumer are different, and the P2P transaction electricity price and carbon quota price fluctuate between the upper and lower bounds. Figure 4 The carbon contribution or carbon emission of each producer and consumer is given. In the established P2P market, the price signal represents the supply and demand relationship of the corresponding commodity. Take the carbon trading price from 1 am to 6 am as an example. During this period, the additional carbon quota provided by the wind power output of producer and consumer 4 exceeds the total demand of this 4-node community system. Therefore, producer and consumer 4 needs to sell the excess carbon quota generated by renewable energy to DSO, and the carbon trading price reaches the lower limit due to oversupply. In summary, if the supply is less than or greater than the system demand, the trading price of the relevant commodity will reach the upper or lower limit. Conversely, if the supply and demand are balanced in the system, the P2P trading price will be within the range.

[0285] Table 1 shows the total income of each stakeholder under different scenarios. Compared with case one (i.e., trading only with DSO), prosumers usually obtain higher returns through established P2P trading markets. This advantage will enhance the initiative of prosumers to use their resources and participate in interactive markets. At the same time, the MLMF Stackelberg game model proposed in the present invention is solved in case two using a centralized analysis algorithm and a decentralized iterative algorithm. The results show that the total income of prosumers calculated by the two algorithms is the same. This phenomenon shows that although the centralized algorithm and the decentralized algorithm are based on different solution processes, they can obtain equivalent results.

[0286] Table 1 Total income of each producer and consumer under different circumstances

[0287]

Claims

1. A power-carbon trading method based on multi-leader multi-follower Stackelberg game, characterized by: The following steps are involved: Based on the MLMF Stackelberg game, carbon emissions are embedded into the income of each producer and consumer in monetary form, forming an integrated electricity-carbon market; In the electricity-carbon integrated market, for the MLMF game model with electricity and carbon trading prices as decision variables, the existence and uniqueness of the Stackelberg equilibrium are proved; According to the MLMF game model, the centralized analysis algorithm is used to derive the price formulas for electricity and carbon trading under the above Stackelberg equilibrium; The trading electricity obtained in the first phase will be used to reconstruct the network in the second phase, and the two-phase transactions will be expanded to the electricity-carbon integrated market.

2. The method for electricity-carbon trading based on multi-leader and multi-follower Stackelberg game according to claim 1 is characterized by: The MLMF Stackelberg game model is: The objective function minNB for prosumers to buy / sell energy and carbon quotas to others or DSOs i,t for: where the subscript i,t represents the i-th prosumer at hour t, B represents revenue, C represents price, N is the number of prosumers, PG represents microturbine output, PL is load demand, and π t , ρ t The price of electricity and carbon emission quota in P2P transactions, PS i,t P2P and PB i,t P2P Represents the electricity traded by prosumers through the P2P market, PS i,t DSO and PB i,t DSO Trading electricity with DSO on behalf of prosumers, CS i,t P2P and CB i,t P2P For producers and consumers to trade carbon quotas based on the P2P market, CS i,t DSO and CB i,t DSO is the carbon limit traded between the prosumer and the DSO, ρ t min and ρ t max are the lower and upper bounds of the carbon quota, respectively, t min and π t max are the lower and upper bounds of electricity transaction prices respectively; The benefits to prosumers measured by energy consumption are as follows: B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t ) 2 Among them, λ i,t and β i,t is a parameter related to the benefits of prosumers; The cost of electricity generated by micro-turbines is measured, ignoring the cost of electricity generated by renewable energy sources: C i,t (PG i,t )=a i (PG i,t ) 2 +b i PG i,t +c i Among them, a i ,b i ,c i is a parameter related to the microturbine output; Energy and carbon emission balance per prosumer: Among them, PR is the renewable energy power generation, CA i,t 0 is the initial carbon emission limit of the prosumer, CA i,t REG Carbon emissions cap for renewable energy generation, CA i,t MT The carbon emission limit generated by the microturbine output, C e,t is the carbon emissions per unit of energy consumption; The ultimate load demand and DG output are: Among them, PL i,t min ,PL i,t max is the lower and upper bounds of the load demand, PG i,t max is the upper bound for the microturbine output; [π t min , π t max ] and [ρ t min ,ρ t max ] represents the price range of energy trading and carbon trading. Assuming that each stakeholder is rational, π t and ρ t Specifically, if ρ t Higher than ρ t max , consumers will purchase carbon allowances from DSOs instead of other producers in the distribution network if ρt is lower than ρ t min , producers will sell carbon quotas to DSOs instead of other consumers in the distribution network. At the same time, if the supply of producers can balance the demand of consumers, then prosumers will not trade with DSOs, which can be restated as: minNB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t P.L. i,t +PT i,t =PG i,t +PR i,t Among them, PT is the trading electricity of the prosumer when the supply and demand are balanced, and CT is the trading carbon limit of the prosumer when the supply and demand are balanced.

3. The method for electricity-carbon trading based on multi-leader multi-follower Stackelberg game according to claim 2 is characterized by: The electricity and carbon trading prices are set by a centralized algorithm, and the balances in energy and carbon trading are expressed as: For simplicity, assume that PL i,t and PG i,t In the following analysis, the limit is not reached. When the first-order partial derivative decision variable is 0, its optimal value reaches π t and ρ t It can be expressed by a system of linear equations: Among them, C g The carbon emissions for each electricity generation are then protected by introducing a decentralized algorithm to protect the internal information of the producers and consumers. Each producer and consumer may change the role of consumer or producer in energy and carbon quotas according to iterative price signals. t and ρ t The initial values ​​are: The transaction prices of electricity and carbon obtained through algorithm iteration are: where σ t and θ t is the price of electricity and carbon trading in the iteration (π h t and ρ h t ) price adjustment parameter, PT s,t * and CT s,t * Indicates the amount of electricity and carbon emission quotas provided by seller s to the market, PT b,t * and CT b,t * Indicates the amount of electricity and carbon emission that buyer b purchases from the market; if: Then terminate this iterative algorithm, otherwise, set h = h + 1 and repeat the above steps, where ε is a positive threshold.

4. The method for electricity-carbon trading based on multi-leader and multi-follower Stackelberg game according to claim 1 is characterized by: In order to ensure network security under the operation strategy of the producer and consumer, the transaction power obtained in the first stage is used to achieve network reconstruction through DSO in the second stage, and the interaction results are recalculated with constraints until the network security constraints are met. The network reconstruction model is as follows: Among them, r ij is the branch ij resistance, I ij is the current of branch ij.

5. The method for electricity-carbon trading based on multi-leader and multi-follower Stackelberg game according to claim 4 is characterized by: The constraints include: (1) Power flow constraints The rules of power dialogue are: Among them, P ij,t and Q ij,t are the active and reactive power of branch ij, r ij and x ij The Ohm's law on branch ij is: U is the voltage, corresponding to nodes i and j; Relax the following constraint Can be converted to the second-order cone formula 6. The method for electricity-carbon trading based on multi-leader and multi-follower Stackelberg game according to claim 4 is characterized by: The constraints include: (2) Network security constraints The node voltage constraints and line capacity constraints are: U min and U max are the lower and upper limits of the voltage, S L is the line capacity constraint.

7. The method for electricity-carbon trading based on multi-leader and multi-follower Stackelberg game according to claim 4 is characterized by: The constraints include: (3) Network Reconfiguration Constraints The branch condition constraint is δ ij,t is the binary variable of the branch condition, W represents the switch state, when W is equal to 0, it means that the branch is disconnected; Ensure that when the branch is disconnected, P ij,t and Q ij,t is equal to 0: M is a sufficiently large positive number in the Big-M method to handle the situation when the switch is disconnected, ensuring the accuracy and feasibility of the mathematical model; then, the Big-M method is usually used to expand to the disconnected branch: The second-stage network management model is transformed into a mixed integer second-order cone programming that can be directly solved by IBM CLPEX.

8. A device for a power-carbon trading method based on a multi-leader multi-follower Stackelberg game, characterized in that: include: The electricity-carbon integrated market formation module is used to embed carbon emissions into the income of each producer and consumer in a monetary manner to form an electricity-carbon integrated market; The Stackelberg equilibrium proof module is used to prove the existence and uniqueness of the Stackelberg equilibrium for the MLMF game model with electricity and carbon trading prices as decision variables in the electricity-carbon integrated market; The electricity and carbon trading price calculation module is used to derive the electricity and carbon trading price formulas under the above-mentioned Stackelberg equilibrium; The transaction expansion module is used to reconstruct the network in the second phase with the transaction volume obtained in the first phase, and to expand the two-phase transaction to the electricity-carbon integrated market.

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