A peer-to-peer trading method for a producer-consumer electricity-carbon coupled market

Abstract

This invention discloses a peer-to-peer trading method for a producer-consumer electricity-carbon coupling market. The method includes: proposing a method to measure the low-carbon contribution of producers-consumers based on the marginal carbon emission factor of the power system at distribution network nodes; establishing a producer-consumer electricity-carbon coupling peer-to-peer trading market model under a free competitive environment using a multi-master, multi-slave Stackelberg game; proposing an analytical solution method for the equilibrium of the electricity-carbon coupling peer-to-peer trading market based on the supply and demand balance of electricity and carbon quotas, deriving expressions for electricity prices and carbon prices, and thus obtaining the peer-to-peer trading results of the producer-consumer electricity-carbon coupling market. This invention provides a valuable reference for peer-to-peer trading methods in the producer-consumer electricity-carbon coupling market.

Description

Technical Field

[0001] This patent relates to a peer-to-peer trading method for a producer-consumer electricity-carbon coupling market. Based on a method for measuring the low-carbon contribution of producers and consumers, it utilizes a multi-master, multi-slave Stackelberg game to establish a producer-consumer electricity-carbon coupling peer-to-peer trading market model under a free competitive environment, and analyzes and solves its market equilibrium. This patent belongs to the field of electricity-carbon coupling trading in power distribution networks. Background Technology

[0002] With the development of distributed renewable energy generation, traditional electricity users have transformed from consumers to prosumers. To accommodate the high proportion of distributed renewable energy integration and promote resource complementarity among prosumers, current research is focusing on designing local energy trading and sharing mechanisms to incentivize prosumers to participate in peer-to-peer trading markets. Furthermore, carbon emissions from fossil fuel combustion should be considered in energy management to build environmentally friendly power systems. In recent years, many countries have formulated corresponding power industry policies to achieve the global goal of carbon neutrality.

[0003] Currently, carbon taxes, carbon quotas, and carbon trading are effective mechanisms for further reducing carbon emissions from the energy system. Compared to carbon taxes and carbon quotas, carbon trading, due to its market-based nature, is more flexible and can achieve emission reduction targets more efficiently. However, existing research on coupling carbon trading with peer-to-peer trading is still incomplete. On the one hand, centralized trading models may harm the interests of some users and cannot achieve equilibrium in reality; on the other hand, decentralized trading models such as auctions require historical auction prices as a basis for bidding, and the trading results are random. In addition, peer-to-peer trading mechanisms based on game theory require the buyer and seller roles to be determined in advance and cannot be changed during the trading process, which limits the flexibility of market trading; and carbon prices are not time-varying, failing to reflect the advantage of carbon trading in adjusting supply and demand over a time scale, and unable to incentivize users to participate in carbon emission reduction in real time according to market conditions.

[0004] In terms of carbon measurement, existing research on carbon trading focuses on the difference between the carbon allowance allocated to the trading entity and the actual carbon emissions generated by its power generation behavior. It does not consider the contribution of clean energy power generation to the system's low carbon emissions or the virtual carbon emissions generated by electricity consumption behavior. Therefore, it cannot measure the marginal cost of carbon emissions generated by its power generation or electricity consumption behavior, and cannot accurately incentivize low-carbon behavior in market transactions.

[0005] To address this, this patent proposes a peer-to-peer trading method for a producer-consumer electricity-carbon coupling market based on a multi-leader, multi-follower Stackelberg game. First, based on the marginal carbon emission factor of the power system at the distribution network nodes, a method for measuring the low-carbon contribution of producer-consumers is proposed. Second, using a multi-leader, multi-follower Stackelberg game, a producer-consumer electricity-carbon coupling peer-to-peer trading market model is established under a free competitive environment. Finally, based on the supply and demand balance of electricity and carbon quotas, an analytical solution method for the equilibrium of the electricity-carbon coupling peer-to-peer trading market is proposed, deriving expressions for electricity price and carbon price, thereby obtaining the peer-to-peer trading results of the producer-consumer electricity-carbon coupling market. This invention considers the differentiated low-carbon contributions of different distributed generation devices, ensuring the maximization of the individual interests of producer-consumers, and allowing them to flexibly change their roles as producers and consumers when receiving different price signals in energy and carbon quota trading, providing a reference for peer-to-peer trading methods in the producer-consumer electricity-carbon coupling market. Summary of the Invention

[0006] To address the shortcomings and deficiencies in existing technologies, this patent proposes a peer-to-peer trading method for the producer-consumer electricity-carbon coupling market. Based on a multi-leader, multi-follower Stackelberg game, a producer-consumer electricity-carbon coupling peer-to-peer trading market model under a free competitive environment is established and analyzed for solution.

[0007] Specifically, the peer-to-peer trading method for the producer-consumer electricity-carbon coupling market proposed in this application includes:

[0008] (1) Based on the marginal carbon emission factor of the power system at the distribution network node, a method for measuring the low-carbon contribution of producers and consumers is proposed;

[0009] (2) Using the Stackelberg game with multiple masters and multiple followers, a method for constructing a producer-consumer electricity-carbon coupled peer-to-peer trading market model under free competition is proposed;

[0010] (3) Based on the supply and demand balance of electricity and carbon quotas, an analytical solution method for the equilibrium of the electricity-carbon coupled peer-to-peer trading market is proposed, and the expressions for electricity price and carbon price are derived, thereby obtaining the peer-to-peer trading results of the producer-consumer electricity-carbon coupled market.

[0011] Step (1) proposes a method for measuring the low-carbon contribution of producers and consumers, including:

[0012] Producers and consumers possess resources such as solar power, wind turbines, micro gas turbines, and flexible electrical loads. Because different resources have varying impacts on carbon emissions, the carbon allowances they generate or consume differ. Specifically, renewable energy sources such as solar power and wind turbines can generate additional carbon allowances without carbon emissions; while micro gas turbines, while providing carbon allowances, consume some carbon allowances due to carbon emissions from natural gas combustion. The low-carbon contributions of different distributed generation devices are as follows:

[0013]

[0014]

[0015] Among them, C e,t The marginal carbon emission factor of the power distribution system; C g,t Carbon emission factor of gas grid; PR i,t and PG i,t These represent the outputs of distributed renewable energy and micro gas turbines from producer-consumer i, respectively.

[0016] Step (2) utilizes a multi-master, multi-slave Stackelberg game to propose a method for constructing a producer-consumer electricity-carbon coupled peer-to-peer trading market model under a free competitive environment, including:

[0017] This patent assumes that the producer-consumer electricity-carbon coupling peer-to-peer trading market is a free competitive market. When the free competitive market is in equilibrium, the transaction prices are the same, i.e.

[0018]

[0019]

[0020] Where, π t The transaction price for electricity in a peer-to-peer trading market; ρ t The carbon price is traded in a peer-to-peer trading market.

[0021] In an electricity-carbon coupled peer-to-peer trading market, prosumers can buy or sell electricity and carbon allowances to other prosumers or distribution system operators (DSOs). The multi-master, multi-slave game theory established in this patent aims to minimize the cost for each prosumer. The objective function for prosumer i is as follows:

[0022]

[0023] B i,t (PL i,t )=λ i,t PL i,t -β i,t (PL i,t ) 2

[0024] C i,t (PG i,t ) = a i (PG i,t ) 2 +b i PG i,t +c i

[0025] Among them, PL i,t For the burden of producers and consumers; and Electricity sold and purchased in transactions with other producers and consumers; and The electricity price sold by the DSO and the on-grid electricity price; and This refers to the sales and purchase volume of electricity generated through interactions between producers and consumers (DSOs). and The amount of carbon sold and purchased in transactions with other producers and consumers; and The selling price and purchasing price of carbon for DSO; and This refers to the amount of carbon sold and purchased by producers and consumers in their interactions with DSO. (B) i,t () is the utility function of user energy consumption, where λ i,t With β i,t C is the coefficient; i,t () represents the cost function of the gas turbine, and the power generation cost of renewable energy is negligible.

[0026] Its constraints include power balance constraints, carbon quota balance constraints, energy use range constraints, and gas turbine capacity limits.

[0027]

[0028]

[0029]

[0030]

[0031] in, The initial carbon allowance allocated to producers and consumers.

[0032] Since electricity prices and carbon prices always fall between the upstream market selling price and the purchase price, the objective function, electricity balance constraint, and carbon quota balance constraint in the above model can be expressed in the following form:

[0033] min NB i,t =C i,t (PG i,t )-B i,t (PL i,t )-π t PT i,t -ρ t CT i,t

[0034] PL i,t +PTi,t =PG i,t +PR i,t

[0035]

[0036] Among them, PT i,t and CT i,t This represents the electricity and carbon allowances purchased and sold by prosumers. When the value is greater than 0, it indicates that the prosumer is selling electricity and carbon allowances; conversely, it indicates that the prosumer is purchasing electricity and carbon allowances. This representation does not distinguish whether the electricity and carbon allowances purchased or sold by the prosumer come from peer-to-peer trading markets or higher-level markets.

[0037] Step (3) proposes an analytical solution method for the equilibrium of the electricity-carbon coupled peer-to-peer trading market based on the supply and demand balance of electricity and carbon quotas. It derives expressions for electricity prices and carbon prices, and obtains the peer-to-peer trading results of the producer-consumer electricity-carbon coupled market, including:

[0038] When the electricity-carbon coupled peer-to-peer trading market is in equilibrium, there exists

[0039]

[0040]

[0041] In this context, the superscript * represents the optimal solution for the variable.

[0042] Therefore, the essence of the electricity-carbon coupled market equilibrium is that the operating results of N producers and consumers satisfy the equality of supply and demand for electricity and carbon quotas in the peer-to-peer trading market. Based on this, this invention starts by analyzing market equilibrium in a specific scenario and gradually extends it to the general case.

[0043] 1) Assuming there are no constraints such as electricity price and carbon price limits, user energy consumption range constraints, and gas turbine capacity limitations, the optimal solution for the decision variables in the operating model of producer-consumer i can be obtained by setting the first-order partial derivative of the objective function with respect to the decision variables to 0:

[0044]

[0045]

[0046] Substituting this into the equilibrium conditions of the electricity-carbon coupled peer-to-peer trading market, we get:

[0047]

[0048]

[0049] The above equation is a problem with two unknowns (i.e., π). t and ρ tThe linear equations of the system can be directly solved to obtain the expressions for electricity price and carbon price:

[0050]

[0051]

[0052] By plotting carbon price on the x-axis and electricity price on the y-axis, we can draw an electricity balance curve and a carbon quota balance curve, such as... Figure 1 As shown in (a), their intersection is the equilibrium point of the coupled market.

[0053] 2) Assuming there are no constraints related to electricity prices and carbon prices, but considering the constraints on the range of energy consumption by users and the capacity limitations of gas turbines, the optimal solution of the producer-consumer i operating model can be represented piecewise:

[0054]

[0055]

[0056] Its segmentation conditions will Figure 1 (a) The plane is divided into multiple regions, and the electricity balance curve and carbon quota balance curve are different in different regions. Furthermore, because... and Since they are continuous, the electricity balance curve and the carbon quota balance curve are two broken lines in a two-dimensional plane, as shown below. Figure 1 As shown in (b), the dashed lines represent the inequality constraints of the piecewise conditions, and the solid lines represent the power balance curve and carbon quota balance curve of the coupled market. The intersection of the two broken lines is the equilibrium point of the coupled market.

[0057] 3) When simultaneously considering constraints such as electricity price and carbon price limits, user energy consumption range constraints, and gas turbine capacity limitations, as long as... Figure 1 (b) can be used to analyze the market equilibrium point by adding price constraints, such as Figure 1 As shown in (c), the rectangle enclosed by the red dashed line represents the price constraint.

[0058] Supply and demand can be used to analyze market equilibrium under price constraints. At any point on the plane, the supply and demand relationship for electricity and carbon allowances in the coupled market can be calculated at the current price. Points on the electricity or carbon allowance equilibrium curve represent the supply and demand balance for that traded commodity. Above the curve, at the carbon and electricity prices, the supply of that commodity is less than demand, and the price should be lowered to adjust the supply and demand relationship, and vice versa. The impact of supply and demand on prices in the coupled market is as follows: Figure 2 As shown, when the price is at a point above the two curves, the supply of electricity is less than the demand, so the electricity price should decrease; the supply of carbon quotas is less than the demand, so the carbon price should also decrease. The carbon price and the electricity price change towards the intersection of the broken lines.

[0059] Since the relative positions of the electricity balance curve and the carbon quota balance curve with the price constraint are uncertain, the market equilibrium under various possible scenarios is analyzed below, assuming that the initial price is at the maximum value of the carbon price and the electricity price.

[0060] ① The intersection of the curves is within the price constraints. The market equilibrium point is the intersection of the two curves.

[0061] ② The intersection of the curves is not within the price limit, and the curve and the price limit do not intersect, such as... Figure 3 As shown in (a) and (b), in (a), the supply of electricity and carbon allowances is less than demand at the initial price, causing the price to fall until it reaches its minimum. In (b), the supply of electricity is less than demand at the initial price, causing the price to fall, while the supply of carbon allowances is greater than demand at the initial price, causing the price to rise. Since the carbon price is already at its maximum, it remains unchanged, and the final market equilibrium point is located at the minimum electricity price and the maximum carbon price. Therefore, if the curve and the price limit do not intersect, the market equilibrium point is located at the extreme points of the electricity and carbon prices, and the maximum or minimum value depends on the relative positions of the curve and the price limit.

[0062] ③ The intersection of the curves is not within the price limit, but the curve and the price limit do intersect, such as... Figure 3 As shown in (c) and (d).

[0063] In scenario (c), the supply of electricity and carbon allowances is less than demand at the initial price, causing the price to fall. This price may fall to several different carbon-electricity price levels, as shown by points A, B, and C in the diagram. At point A, the electricity price has reached its minimum and remains unchanged. The supply of carbon allowances is less than demand, causing the carbon price to fall until the equilibrium point in the diagram is reached. At point B, the carbon allowances are balanced, the carbon price remains unchanged, the supply of electricity is less than demand, and the price falls. Due to the falling electricity price, the carbon allowances are no longer balanced but are in a region of oversupply, so the carbon price increases until the equilibrium point in the diagram is reached. At point C, the carbon price has reached its minimum and remains unchanged. The supply of electricity is less than demand, causing the electricity price to fall until the intersection of the carbon allowance balance curve and the minimum carbon price is reached. Further analysis based on the scenario at point B will ultimately lead to the equilibrium point in the diagram.

[0064] In (d), at the initial price, the supply of electricity and carbon allowances is less than the demand, causing the price to fall. This price may fall to several different carbon-electricity price levels, as shown by points A and B in the diagram. At point A, electricity is in balance, the electricity price remains unchanged, the supply of carbon allowances is less than the demand, and the carbon price falls. Simultaneously, due to the decrease in the carbon price, electricity is no longer in balance but in a region of oversupply, so the electricity price increases until it reaches the equilibrium point shown in the diagram. At point B, the carbon price has reached its minimum value, the carbon price remains unchanged, the supply of electricity is less than the demand, and the electricity price falls until it reaches the equilibrium point shown in the diagram.

[0065] Other scenarios can be analyzed using similar methods to obtain the market equilibrium point. Furthermore, the market equilibrium point obtained from the analysis is consistent regardless of the initial price.

[0066] Beneficial effects:

[0067] (1) Coupling carbon trading to energy trading can further tap the emission reduction potential on the user side, incentivize low-carbon energy use, reduce carbon emissions on the user side, and provide an effective way to achieve dual carbon goals.

[0068] (2) The low-carbon contribution measurement method can transfer the benefits of producers and consumers from producers and consumers with high energy consumption to producers and consumers with high distributed renewable energy configuration capacity, providing a trading and operation basis for low-carbon planning.

[0069] (3) The analysis and solution method establishes the direct relationship between the internal parameters of producers and consumers and the transaction price, providing a basis for market supervision and regulation. Attached Figure Description

[0070] To more clearly illustrate the technical solution of the present invention, the drawings used in the claims and the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some reference descriptions and embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 Coupling market equilibrium curves for various scenarios

[0072] Figure 2 A chart analyzing the supply and demand relationship in the electricity-carbon coupling market.

[0073] Figure 3 Market equilibrium under scenarios where curves and price constraints have no intersection.

[0074] Figure 4 The diagram shows the structure of the 4-node power distribution system used in the implementation case.

[0075] Figure 5 For DSO purchase and sale electricity prices and carbon prices, and coupling market transaction electricity prices and carbon prices Detailed Implementation

[0076] To make the structure and advantages of the present invention clearer, the structure of the present invention will be further described below with reference to the accompanying drawings.

[0077] The 4-node computational structure used in this embodiment is shown in the attached figure. Figure 4As shown, the effectiveness of peer-to-peer trading in the producer-consumer electricity-carbon coupling market is verified. The marginal carbon emission factor of the power grid fluctuates between 0.3 and 1.1 kg / kWh, while that of the gas grid is 0.51 kg / kWh.

[0078] Figure 5 This illustrates the fluctuations in electricity and carbon prices between their upper and lower limits. Price signals represent the supply and demand relationship for the corresponding commodities. If supply is less than or greater than system demand, the trading price of the relevant commodity will reach its upper or lower limit. If supply and demand are in equilibrium within the system, the trading price in the coupled market will remain within the range.

[0079] Table 1 Comparison of Producer-Consumer Total Revenue and System Carbon Emissions

[0080]

[0081] Table 1 shows the total revenue of producers and consumers and the carbon emissions of the system under the scenario of whether producers and consumers engage in peer-to-peer transactions in the electricity-carbon coupling market. Through comparative analysis, it can be seen that peer-to-peer transactions in the electricity-carbon coupling market can increase the revenue of producers and consumers and reduce the carbon emissions of the system, since they avoid arbitrage behavior of buying low and selling high in the upstream market.

[0082] The serial numbers in the above embodiments are for descriptive purposes only and do not represent the order in which the components are assembled or used.

[0083] The above description is merely an embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A peer-to-peer trading method for a producer-consumer electricity-carbon coupled market, characterized in that, The method includes: Step 1: Based on the marginal carbon emission factor of the power system at the distribution network node, a method for measuring the low-carbon contribution of producers and consumers is proposed; Step 2: Utilize a multi-master, multi-slave Stackelberg game to establish a model for a peer-to-peer electricity-carbon coupling trading market under a free competitive environment; Step 3: Based on the supply and demand balance of electricity and carbon quotas, an analytical solution method for the equilibrium of the electricity-carbon coupled peer-to-peer trading market is proposed, and the expressions for electricity price and carbon price are derived, thereby obtaining the peer-to-peer trading results of the producer-consumer electricity-carbon coupled market.

2. Step 1 of the peer-to-peer trading method for a producer-consumer electricity-carbon coupled market according to claim 1, characterized in that, The low-carbon contribution of producers and consumers is measured by the marginal carbon emission factor at the distribution network node, specifically including: Producers and consumers include photovoltaic (PV), wind turbines, micro gas turbines, and flexible electrical loads. Because these resources have different impacts on carbon emissions, the carbon allowances they generate or consume vary. PV and wind turbines generate additional carbon allowances even without carbon emissions; while micro gas turbines, while providing carbon allowances, consume some carbon allowances due to carbon emissions from natural gas combustion. The low-carbon contributions of different distributed power generation devices are as follows: ， ， in, C e,t The marginal carbon emission factor of the power distribution system; C g The carbon emission factor of the gas grid; PR i , t and PG i , t Producers and consumers respectively i The output of distributed renewable energy and micro gas turbines.

3. Step 2 of the peer-to-peer trading method for a producer-consumer electricity-carbon coupled market according to claim 1, characterized in that, Using a multi-master, multi-slave Stackelberg game, a model for a producer-consumer coupled peer-to-peer trading market for electricity and carbon under a free competitive environment is established, specifically including: Assuming the producer-consumer electricity-carbon coupling peer-to-peer trading market is a free competitive market, when the free competitive market is in equilibrium, the transaction prices are the same, i.e. ， Where, π t The electricity price is for transactions in a peer-to-peer market; The carbon price is traded in a peer-to-peer trading market. In an electricity-carbon coupled peer-to-peer trading market, prosumers buy or sell electricity and carbon allowances to other prosumers or distribution system operators (DSOs). The resulting multi-owner, multi-slave game aims to minimize the cost for each prosumer. i The objective function is as follows: ， in, PL i , t For the burden of producers and consumers; and Electricity sold and purchased in transactions with other producers and consumers; and The electricity price sold by the DSO and the on-grid electricity price; and This refers to the sales and purchase volume of electricity generated through interactions between producers and consumers (DSOs). and The amount of carbon sold and purchased in transactions with other producers and consumers; and The selling price and purchasing price of carbon for DSO; and This refers to the amount of carbon sold and purchased by producers and consumers in their interactions with DSOs. B i,t ( ) is the utility function of user energy consumption, where λ i,t With β i,t For coefficients; C i,t ( ) represents the cost function of the gas turbine, with the power generation cost of renewable energy being negligible. Its constraints include electricity balance constraints, carbon quota balance constraints, energy use scope constraints, and gas turbine capacity limitations. ， in, The initial carbon allowances allocated to producers and consumers. Since electricity prices and carbon prices always fall between the upstream market selling price and the purchase price, the objective function, electricity balance constraint, and carbon quota balance constraint in the above model can be expressed in the following form: ， in, PT i , t and CT i , t This represents the electricity and carbon allowances purchased and sold by prosumers. When it is greater than 0, it means that prosumers sell electricity and carbon allowances to external parties. Conversely, it means that prosumers purchase electricity and carbon allowances. This representation does not distinguish whether the electricity and carbon allowances purchased or sold by prosumers come from peer-to-peer trading markets or higher-level markets.

4. Step 3 of the peer-to-peer trading method for a producer-consumer electricity-carbon coupled market according to claim 1, characterized in that, Based on the supply and demand balance of electricity and carbon quotas, this paper proposes an analytical solution method for the equilibrium of the electricity-carbon coupled peer-to-peer trading market, derives expressions for electricity prices and carbon prices, and thus obtains the peer-to-peer trading results of the producer-consumer electricity-carbon coupled market, specifically including: When the electricity-carbon coupled peer-to-peer trading market is in equilibrium, there exists ， In this context, the superscript * represents the optimal solution for the variable. Therefore, the essence of the electricity-carbon coupling market equilibrium is N The operational outcomes of individual producers and consumers satisfy the principle of equal supply and demand for electricity and carbon quotas in a peer-to-peer trading market. Based on this, we begin by analyzing market equilibrium in a specific scenario and gradually expand to the general case. 1) Assuming there are no constraints on electricity and carbon prices, user energy consumption range, or gas turbine capacity, the producer-consumer... i The optimal solution for the decision variables can be obtained by setting the first-order partial derivative of the objective function with respect to the decision variables to 0. ， ， Substituting this into the equilibrium conditions of the electricity-carbon coupled peer-to-peer trading market, we get: ， The above formula is a problem with two unknowns, π. t and The linear equations can be directly solved to obtain the expressions for electricity price and carbon price: ， ， Plot the electricity price on the x-axis and the electricity price on the y-axis, and draw the electricity balance curve and the carbon quota balance curve. The intersection of these curves represents the equilibrium point of the coupled market. 2) Assuming there are no constraints from electricity and carbon prices, but considering the constraints on the scope of user energy consumption and the capacity limitations of gas turbines, the producer-consumer... i The optimal solution of the running model can be represented in segments: ， ， Its segmentation conditions divide the plane into multiple regions. Within these regions, the energy balance curve and carbon quota balance curve differ. Furthermore, due to… and Since they are continuous, the electricity balance curve and the carbon quota balance curve are two broken lines in a two-dimensional plane. The dashed line represents the inequality constraints of the piecewise conditions, and the solid line represents the electricity balance curve and the carbon quota balance curve of the coupled market. The intersection of the two broken lines is the equilibrium point of the coupled market. 3) When considering constraints such as electricity and carbon price limits, user energy consumption range constraints, and gas turbine capacity constraints simultaneously, the market equilibrium point can be analyzed simply by adding price constraints. The rectangle enclosed by the red dashed line represents the price constraint. By analyzing supply and demand, we can determine how the market reaches equilibrium under price constraints. At any point on the graph, we can calculate the supply and demand relationship between electricity and carbon allowances in the coupled market at the current price. Points on the electricity or carbon allowance equilibrium curves represent the supply and demand balance for that commodity. Above the curves, when the carbon and electricity prices are below demand, the supply of that commodity is less than demand, and its price should be lowered to adjust the supply and demand relationship. Conversely, below the curves, when the price is above either curve, the supply of electricity is less than demand, and the electricity price should be lowered; similarly, the supply of carbon allowances is less than demand, and the carbon price should also be lowered. The carbon and electricity prices move towards the intersection of the broken lines. Since the relative positions of the electricity balance curve and the carbon quota balance curve with the price constraint are uncertain, the following analysis examines market equilibrium under various scenarios, assuming the initial price is at the maximum of the carbon price and the electricity price. ① If the intersection of the curves is within the price constraints, the market equilibrium point is the intersection of the two curves. ② If the curves do not intersect within the price constraint, and the curves and price constraints do not intersect, then at the initial price, the supply of electricity and carbon allowances is less than demand, causing prices to fall until they reach their minimum values. At the initial price, the supply of electricity is less than demand, causing prices to fall; at the initial price, the supply of carbon allowances is greater than demand, causing prices to rise. Since the carbon price is already at its maximum value, it remains unchanged. The final market equilibrium point is located at the minimum electricity price and the maximum carbon price. Therefore, if the curves and price constraints do not intersect, the market equilibrium point is located at the extreme points of electricity and carbon prices. The maximum or minimum value depends on the relative positions of the curves and price constraints. ③ The intersection of the curves is not within the price limit, but the curves and the price limit do intersect. When the supply of electricity and carbon allowances is less than demand at the initial price, the price decreases, potentially falling to several different carbon-electricity price levels. At point A, the electricity price has reached its minimum and remains unchanged. The supply of carbon allowances is less than demand, causing the carbon price to decrease until an equilibrium point is reached. At point B, the carbon allowances are in balance, the carbon price remains unchanged, the supply of electricity is less than demand, and the price decreases. Due to the decrease in the electricity price, the carbon allowances are no longer in balance but are in a region of oversupply, so the carbon price increases until an equilibrium point is reached. At point C, the carbon price has reached its minimum and remains unchanged. The supply of electricity is less than demand, causing the electricity price to decrease until it reaches the intersection of the carbon allowance balance curve and the minimum carbon price. Further analysis based on the scenario at point B will ultimately lead to the final equilibrium point. When the supply of electricity and carbon allowances is less than the demand at the initial price, the price will decrease, potentially falling to several different carbon-electricity price levels. At point A, electricity is in balance, the electricity price remains unchanged, the supply of carbon allowances is less than the demand, and the carbon price decreases. Simultaneously, due to the decrease in the carbon price, electricity is no longer in balance but in a region of oversupply, so the electricity price increases until the equilibrium point is reached. At point B, the carbon price has reached its minimum value, the carbon price remains unchanged, the supply of electricity is less than the demand, and the electricity price decreases until the equilibrium point is reached.

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