# Research on Electricity Market Trading Mechanism Considering Peak-to-Valley Ratio and Multitime Coupling

Authors: Rongmao Wang; Qingchun Li; Jian Zhang; Ye Zhang; Xilin Xu; Kai Zhang
Journal: Mathematical Problems in Engineering
 (2023)

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## Abstract

With the development of the economy and society, electricity demand is increasing. However, there are some problems on the power grid side, such as the excess capacity of power installed, abandoned power of renewable energy, low overall utilization rate, and high pressure of stable operation. The problem stems from the inconsistency between the peak of electricity production and consumption and the lack of obvious power price signals. In this article, the market development objectives are combined with the time-divided transaction, and two objectives of market development are proposed: (1) Reduce the peak-valley difference of power supply and demand; (2) Expand the peak-valley price difference in the market. Combined with the physical properties of the power market, a multiperiod coupling trading mechanism is designed. The results show that the speculative and profit-seeking behavior of power producers will be stopped under the proposed trading mode, the potential of users for peak-valley filling will be effectively developed, the peak-valley gap of the power system can be controlled within a reasonable range, and the peak-valley gap of power trading can be further amplified.


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## Body

## 1. Introduction

In order to avoid market risk, the electricity medium- and long-term transaction is put forward, which gives consideration to the economy of the market and the stability of the power system. However, due to such factors as the long span of medium- and long-term trading and uncertain demand, electricity medium- and long-term trading contracts often play the role of locking the price and giving market members operational space. As a result, the peak-valley difference in the power system cannot be narrowed and the peak-valley difference in the electricity price cannot be amplified.The research on electric power medium- and long-term trading mainly focuses on the following three aspects: (1)Market Mechanism Research [1–3]. Most scholars have studied the existing rules. Wan and Zhang have made a comparative analysis of the trading rules in many places [4]. From the perspectives of market members, trading varieties, trading cycles, trading methods, and price mechanisms, a comparative analysis of the medium- and long-term trading rules and organization process of each province has been summarized. (2) Study on Operation Strategies of Market Entities [5, 6]. The main body of the electricity market is mainly divided into power generation companies, electricity selling companies (agent retail users), and large power users. Wang combined the characteristics and established the medium- and long-term trading decision-making information system of power generation enterprises, and then quantified the market trading risk through the fuzzy comprehensive evaluation method[7]. According to the cost-volume-profit model and game theory, the electricity market bidding model of power generation enterprises is established. (3) Market Simulation [8]. In consideration of the different medium- and long-term centralized bidding rules in different provinces, Zhou adopts a multiagent technique to simulate the behavior strategies of market members under different rules, so as to provide a reference for the power market [9].Reasonable multiperiod division of the electricity market plays an important role in multiperiod electricity price optimization. At present, scholars at home and abroad mainly study the time division from the algorithm [10, 11]. Yang et al. proposed the influence of time-sharing prices in the electricity market on the path optimization of electric vehicles considering quick charging and regular charging [12]. However, all the abovementioned literature simply divides the time, and the result of period division is not commensurate with the actual load level.Different pricing objectives correspond to different pricing strategies. At present, domestic and foreign scholars mainly have three pricing and optimization strategies for multiperiod electricity prices in the power market. (1) To minimize the peak-valley difference, multiperiod electricity price design optimization is carried out. For the operation of the power grid, power transmission enterprises hope to guide users’ power consumption behavior by dividing multiperiod electricity prices, so as to make it conform to the unit output curve [13–15]. (2) From the perspective of the implementer, the multiperiod electricity price design optimization is carried out with the maximization of the revenue of the implementer as the objective function [16–18]. (3) From the perspective of users, multiperiod electricity price design optimization is carried out to maximize user satisfaction [19, 20].In terms of trading variety coupling, existing studies take into account the impact of green card trading and carbon trading on the power market and study the coupling effect between them, so as to further inspire the market to optimize the power supply structure and promote the development of new energy [21–23]. In general, the existing research on power market coupling is mostly focused on the trading mechanism, the coupling mode of trading varieties, the clearing algorithm, and lack of research on the time-segment coupling under the medium- and long-term trading of power [24–26].Based on the background of the reform of China’s electricity market and the development status of medium- and long-term electricity trading, this article conducts an in-depth study on the multiperiod coupling trading mechanism and its benefits under the time division of the electricity market. With the advance of the reform of the electric power system, all provinces are carrying out the market transaction mode suitable for their development. Some provinces are focusing on spot transactions, while some provinces are exploring the medium- and long-term electric power transaction mode connecting with the spot market. The development degree and characteristics of each province are different. One of the difficulties in this article is how to calculate the peak-valley ratio which is in line with the development of the electricity market and makes the parameter play a role in the development of the market. Although there is mature experience in foreign countries, how to develop the power market reform path with Chinese characteristics is a key issue in China’s power market reform practice. This article attempts to solve the profit-seeking problem of trading subjects in time-divided trading by introducing a multiperiod-coupled trading mechanism.The innovation points of this article include the following:(1)
Given the excessive speculation on the power generation side and the transmission of power price signals under the time-divided trading model, a multiperiod-coupled trading mechanism is proposed to restrict the original time-divided trading model and make the market trading results more efficient.(2)
In this article, the relationship between the peak-valley ratio coefficient and social welfare is studied. Through the supply-demand model in microeconomics, the size changes of social welfare under different peak-valley ratios are studied, which lays a foundation for the subsequent proposal of the market model.


## 2. Research on the Restriction Means of Electric Power Medium- and Long-Term Trading Market

### 2.1. Restrictions on the Prior Declaration

In a time-sharing transaction, the power trading center usually notifies market participants of the trading conditions prior to the commencement of the transaction. For example, the declared price shall not exceed the given price, the declared quantity shall not exceed the given quantity, and so on, this is because of the particularity of electric power commodities. Although the reform of the electric power system is to excavate the commodity attribute of electric energy continuously, it is undeniable that electric power also has the function of guaranteeing the basic people’s livelihood and ensuring the normal operation of the social economy. Therefore, the market transaction of electricity must be the competition under the safe boundary with supervision, and the competition of the electricity market must be the incomplete competition state. The declaration restriction in the pretransaction stage of electricity trading is to ensure that the trading result is within the scope of the transaction space expected by the market organizer.The setting of limit price abides by the following principle commonly:(1)
To leave sufficient bidding space for market players to ensure the market efficiency within the allowable range(2)
To guarantee the effectiveness of the market price and give market subjects sufficient and reasonable returns(3)
To reflect the scarcity of power resources in different periods, and guide the power generation side and the power consumption side to actively change behavior strategies(4)
To promote technological progress, improve the industry environment, and push the market forward to a more efficient state


#### 2.1.1. Category Price Limit and Determination Method

(1) Price Ceiling. The price ceiling is a price cap set by the government for a product or service. The price ceiling is generally lower than the equilibrium price in a freely competitive market. The reason why the ceiling price exists is that the price of the product or service under the condition of free competition may be manipulated by a certain market entity, which leads to the distortion of the price signal and deviation from the essence of the market. In an imperfectly competitive electricity market, if the price of electricity transactions is liberalized, it may lead to the power generation companies obtaining excess profits by exercising market power, thus increasing the cost of electricity for users. Therefore, a price limit is one of the effective means to avoid market risk in the electricity market trading; in the electricity market trading, there are a lot of price ceilings.The general determination of the price ceiling includes the following three methods:(1)
Cost-oriented method: set a price ceiling based on the marginal cost (or variable cost) of the unit. If every generator set in the market is quoted at its marginal cost, the market transaction price will never exceed the marginal cost of the unit.(2)
Set the maximum price according to the proportion of the online power of the covered units. The total installed capacity of the power generation side is multiplied by a coverage factor as the tradable capacity, which is the reflection of the market abundance. Then, according to the measured transaction capacity, the unit is sorted according to the price of electricity, and the price of the last unit that meets the demand for electricity is taken as the highest price of the transaction.(3)
Set the maximum price based on the value of the lost load. But when the electricity load is met, this method will lose its effect.(2) Price Floor. Price floor, also known as “protection price,” refers to the lowest price limit set by the government for a certain commodity or service, generally to support a certain product or service. Under the protection of floor price, market entities can maintain normal operation, so floor price may inhibit enterprises from seeking technological progress and hinder the development of the industry. Referring to the lowest price in economics, in the electric power market, the lower limit of quotation set by market entities when they declare is to avoid the malicious competition of bidding entities, protect the basic interests of electric power investors, and reduce their investment risks.The determination method of general price lower limit includes the following several kinds:(1)
Cost-oriented method: set the minimum price based on the marginal cost (or variable cost) of the unit(2)
Minimum price considering downtime loss(3)
Minimum price based on the benchmark electricity price(3) Static and Dynamic Price Limits. Typical power market price fixing methods are mainly divided into static price fixing and dynamic price fixing. Among them, the static price limit has the following three ways:(1)
A relatively stable price is used as a market price limit in a market with greater price risk, such as Nordic Power’s real-time market. There are increased and decreased output prices in the Nordic real-time electricity market, in which the increase and decrease output price refers to the price per unit capacity of the market trading members to increase generation output or reduce power load, and the minimum price is the spot market price of the day before. The quotation of reduced output refers to the quotation of the unit capacity of the market trading members to reduce the power generation output or increase the power load, and the maximum price is the spot market price of the day before.(2)
Determine the price ceiling by the value of the lost load.According to the value of electric energy, the ceiling price is set in segments according to the price of the lost load. This method makes the ceiling price consistent with the demand response. The price limit scheme is the premise of a load to participate in market bidding, but the value of the lost load is difficult to estimate.(3)
Determine the ceiling price according to historical data.Under the condition that the available capacity of the bidding unit is unchanged and the bidding load is increasing, the relationship between the average price and the maximum price is analyzed and fitted by the statistical method.Dynamic price limits include the following:(1)
Determine whether there is a spike risk in the price of electricity, and if any, carry out market price fixing. For example, the Australian electricity market will make a judgment according to whether the sum of the electricity prices in the specified period before the trading period exceeds the accumulative price limit. If the sum exceeds the limit, the market price limit after the trading period will be implemented.(2)
ixing of price according to market power. For example, in the New York electricity market, the automatic market power removal program initiates a price limit program if it detects that the unit price in the area exceeds a given threshold. Threshold = Average Electricity Price∗ 2% ∗ 8760/Number of Restricted Hours in the Previous 12 Months.(3)
In case of local blockage, the settlement shall be based on the price limit. In Texas’s real-time trading market, for example, sets are settled on a cost-plus basis. The application of dynamic and static price limits are shown in Table1.In addition to quotation restrictions on the price of electricity, there are also a large number of electricity limits in practice. For example, on the power generation side, the annual direct trading electric quantity limit of ClassB units is set in the medium- and long-term power trading rules of the Beijing-Tianjin-Tangshan Power Grid. In order to ensure the smooth transition of the market, its trading power is gradually opened. The calculation formula is as follows: upper limit of unit direct trading electric quantity = scale of direct trading electric quantity in the next year/installed capacity of admissible power generation enterprises × unit capacity × K. Among them, the installed capacity of preparing power generation enterprises includes Class B units and Class C units, and K is the upper limit coefficient of electric quantity. In terms of electricity consumption, the Guangdong power market stipulates that the electricity sales formula of the same investment subject should not exceed 15% of the total electricity of the monthly centralized competition transaction, in order to prevent market members from manipulating market transactions by market power.Table 1
Contrastive analysis of static and dynamic price limits.
TypeStaticDynamicComplexitySimpleComplexMarket riskLimited market size with an unreasonable limitDispersed market risk among the subjectsTrade leadsLagged price signalEffective price signalCompetitionLimited market responseTimely market responsePrice limit settingWithout definitive wayDynamic adjustment


#### 2.1.2. Impact Analysis of Prior Declaration on Social Welfare

As shown in Figure1, the feasible space of the market (the blue area in the figure) consists the upper limit of price, the lower limit of price, and the upper limit of quantity. The declaration curve of the part beyond the blue area is the invalid part. At this point, when the equilibrium price E in the market is within the feasible space, at least the social welfare of the gray part is lost, and the size of the lost area is related to the intercept and slope of the supply curve and the demand curve.Figure 1
The effect of price limits on market transactions.In general, the current price floor will not cause the loss of producer surplus. The market boundary framed by the upper limit of the number of transactions in the market is to enable the smooth transition of the market and prevent large-scale power failure losses caused by marketization transactions. When the quantity ceiling falls below the quantity at the market equilibrium point, there will be a new loss of social welfare, as shown in Figure2.Figure 2
The effect of quantity limit on market transactions.Therefore, according to the principles of economics, the price limit and limit in the market should give enough space to the market subjects, so as to ensure that the market can realize the function of price discovery and at the same time achieve the goal of economical and efficient allocation of resources.


### 2.2. Interim Transaction Result Constraint

When the market clears, it is necessary to ensure that the peak-to-valley ratio of the market players is within the specified range. This not only helps the power system to reduce the peak-valley difference but also helps the market entities to meet the economic demand for electricity consumption.


#### 2.2.1. Trade Leads Model and Peak-to-Valley Ratio Coefficient

Using the supply-demand model in microeconomics, this article studies the effect of the peak-valley ratio on social welfare. In order to simplify the model, it is assumed that the supply function and demand function in the power market is linear. Figure3 describes the influence process of the peak-valley ratio coefficient which changes the market clearing state.Figure 3
The impact of peak-to-valley ratio on market clearing: (a) peak market clearance process; (b) valley market clearance process.
(a)(b)The line segmentAB represents the power demand curve Dpeak at the peak period under the initial peak-to-valley ratio, and the line segment CD represents the power supply curve Speak at the peak period under the initial peak-to-valley ratio. The intersection point H of segment AB and segment CD represents the market clearing result in the peak period, where the trading volume is Qpeak, the market clearing price is PU, and the market welfare in the peak period is the area SAHC of the triangle AHC.Line segmentEF represents the power demand curve in the low valley period under the initial peak-to-valley ratio Dvalley. Line segment MN represents the power supply curve in the low valley period under the initial peak-to-valley ratio Svalley. The intersection point K of segment EF and segment MN represents the market clearing result in the valley period, where the trading volume is Qvalley, the market clearing price is PL, and the market welfare in the valley period is the area SEKM of the triangle EKM.It is assumed that the total electricity demand of users is fixed in the short term. The sum of peak and valley demand is fixed. Peak electric quantity can only be transferred to the valley, or valley electric quantity can only be transferred to the peak. In the case of peak-to-valley ratio change, it is assumed that the peak-to-valley ratio becomes smaller and the demand in the peak segment shifts to the valley segment, resulting in the shift ofDpeak to the left and lower side of Dpeak′ (line segment A′B′). A′B′ intersects the supply curve CD of the original peak segment at point H′AB. At this time, the trading volume is reduced from Qpeak to Qpeak′, and the reduction amount is ΔQpeak. The market welfare of the peak segment reduces the area SAHH′A′ of the quadrilateral AHH′A′.It is assumed that the total power demand does not change in the short term, so the power consumption behavior occurs either in the valley or in the peak. Add the reduced demandΔQpeak in the peak segment to the valley segment, and then the transaction quantity in the valley segment changes from Qvalley to Qvalley′:(1)Qvalley′=Qvalley+∆Qpeak.The valley period of electricity consumption represents that the supply is greater than the demand at this time. It is assumed that the supply in the valley period is the maximum supply that the generation side is willing to provide, that is, the supply curve does not move. Therefore, a vertical line atQvalley′ intersects Svalley at point K′, and a demand curve K′ with the same slope as curve E is drawn along Dvalley. In this case, Dvalley represents the demand curve after the increase of demand in the valley segment, and the market welfare in the valley segment increases the area SE′K′KE of the quadrilateral E′K′KE.To study the influence of the peak-valley ratio coefficient on the total welfare of the peak-valley segment market, that is, to study the positive and negative problems of∆W under the change of peak-valley ratio coefficient. ∆W is the difference between the increased market welfare in the trough period and the reduced market welfare in the peak period:(2)∆W=SE′K′KE−SAHH′A′.


#### 2.2.2. Impact Analysis of Peak-Valley Ratio Coefficient on Social Welfare

Assuming that the up-and-down movement of the demand curve does not affect the supply curve in the short term, the supply curves at the peak and valley segments remain unchanged before and after the peak-to-valley ratio changes. The supply curve function of the peak segment is as follows:(3)Speak∶P=α0+β0Q.The supply curve function of the valley segment is as follows:(4)Svalley∶P=α1+β1Q.Before the peak-to-valley ratio coefficient changes, the peak segment market demand function is as follows:(5)Dpeak:P=a0+b0Q.The market demand function of the valley segment is as follows:(6)Dvalley:P=a1+b1Q.Then, the peak segment market clears before the peak-to-valley ratio changes:(7)Speak=Dpeak.The market clearing result of the peak segment is calculated as follows:(8)Qpeak=a0−α0β0−b0,Ppeak=a0β0−α0b0β0−b0,Wpeak=∫0QpeakDpeak−SpeakdQ=a0−α0Q+b0−β02Q20Qpeak=12⋅α0−a02β0−b0.Similarly, the market clearing result of the trough segment is calculated as follows:(9)Qvalley=a1−α1β1−b1,Pvalley=a1β1−α1b1β1−b1,Wvalley=12⋅α1−a12β1−b1.In the short term, the total market sizeQtotal is as follows:(10)Qtotal=Qpeak+Qvalley=a0−α0β0−b0+a1−α1β1−b1.The peak-to-valley ratio coefficient is as follows:(11)η=QpeakQvalley=a0−α0a1−α1⋅β1−b1β0−b0.After the peak-to-valley ratio coefficient changes, the peak segment market demand function becomes(12)Dpeak′:P=a0′+b0Q.The valley segment market demand function becomes(13)Dvalley′:P=a1′+b1Q.When the peak segment market clears,Speak=Dpeak′, the clearing result becomes(14)Qpeak′=a0′−α0β0−b0,Ppeak′=a0′β0−a0′b0β0−b0,Wpeak′=12⋅α0−a0′2β0−b0.When the valley segment market clears,Svalley=Dvalley′, the clearing result becomes(15)Qvalley′=a1′−α1β1−b1,Pvalley′=a1′β1−α1′b1β1−b1,Wvalley′=12⋅α1−a1′2β1−b1.Since the total market size does not change in the short term,Qvalley′ also equals to the following formula:(16)Qvalley′=Qtotal−Qpeak′=a0−α0β0−b0+a1−α1β1−b1−a0′−α0β0−b0=a0−a0′β0−b0+a1−α1β1−b1.It follows that(17)a0−a0′β0−b0=a1′−a1β1−b1.The change of total social welfare before and after the peak-valley ratio coefficient is as follows:(18)∆W=Wpeak′+Wvalley′−Wpeak+Wvalley=12⋅a0′−a0−2⋅α0a0′−a0β0−b0+a1′−a1−2⋅α1a1′−a1β1−b1.At this point, the peak-to-valley ratio coefficient is as follows:(19)η′=Qpeak′Qvalley′=a0′−α0a1′−α1⋅β1−b1β0−b0.It is found that, whenη′−η<0 and ∆W>0, that is, when the peak-valley ratio of the market becomes smaller, the total welfare of the market transaction becomes larger. This also means that improving the market peak-to-trough ratio helps increase market welfare. When the price elasticity of the peak market is the same as that of the trough market, the total social welfare is maximized.(20)ηopt=a0′−α0a1′−α1,Wmax=a0−α02β0−b0.


## 2.1. Restrictions on the Prior Declaration

In a time-sharing transaction, the power trading center usually notifies market participants of the trading conditions prior to the commencement of the transaction. For example, the declared price shall not exceed the given price, the declared quantity shall not exceed the given quantity, and so on, this is because of the particularity of electric power commodities. Although the reform of the electric power system is to excavate the commodity attribute of electric energy continuously, it is undeniable that electric power also has the function of guaranteeing the basic people’s livelihood and ensuring the normal operation of the social economy. Therefore, the market transaction of electricity must be the competition under the safe boundary with supervision, and the competition of the electricity market must be the incomplete competition state. The declaration restriction in the pretransaction stage of electricity trading is to ensure that the trading result is within the scope of the transaction space expected by the market organizer.The setting of limit price abides by the following principle commonly:(1)
To leave sufficient bidding space for market players to ensure the market efficiency within the allowable range(2)
To guarantee the effectiveness of the market price and give market subjects sufficient and reasonable returns(3)
To reflect the scarcity of power resources in different periods, and guide the power generation side and the power consumption side to actively change behavior strategies(4)
To promote technological progress, improve the industry environment, and push the market forward to a more efficient state


### 2.1.1. Category Price Limit and Determination Method

(1) Price Ceiling. The price ceiling is a price cap set by the government for a product or service. The price ceiling is generally lower than the equilibrium price in a freely competitive market. The reason why the ceiling price exists is that the price of the product or service under the condition of free competition may be manipulated by a certain market entity, which leads to the distortion of the price signal and deviation from the essence of the market. In an imperfectly competitive electricity market, if the price of electricity transactions is liberalized, it may lead to the power generation companies obtaining excess profits by exercising market power, thus increasing the cost of electricity for users. Therefore, a price limit is one of the effective means to avoid market risk in the electricity market trading; in the electricity market trading, there are a lot of price ceilings.The general determination of the price ceiling includes the following three methods:(1)
Cost-oriented method: set a price ceiling based on the marginal cost (or variable cost) of the unit. If every generator set in the market is quoted at its marginal cost, the market transaction price will never exceed the marginal cost of the unit.(2)
Set the maximum price according to the proportion of the online power of the covered units. The total installed capacity of the power generation side is multiplied by a coverage factor as the tradable capacity, which is the reflection of the market abundance. Then, according to the measured transaction capacity, the unit is sorted according to the price of electricity, and the price of the last unit that meets the demand for electricity is taken as the highest price of the transaction.(3)
Set the maximum price based on the value of the lost load. But when the electricity load is met, this method will lose its effect.(2) Price Floor. Price floor, also known as “protection price,” refers to the lowest price limit set by the government for a certain commodity or service, generally to support a certain product or service. Under the protection of floor price, market entities can maintain normal operation, so floor price may inhibit enterprises from seeking technological progress and hinder the development of the industry. Referring to the lowest price in economics, in the electric power market, the lower limit of quotation set by market entities when they declare is to avoid the malicious competition of bidding entities, protect the basic interests of electric power investors, and reduce their investment risks.The determination method of general price lower limit includes the following several kinds:(1)
Cost-oriented method: set the minimum price based on the marginal cost (or variable cost) of the unit(2)
Minimum price considering downtime loss(3)
Minimum price based on the benchmark electricity price(3) Static and Dynamic Price Limits. Typical power market price fixing methods are mainly divided into static price fixing and dynamic price fixing. Among them, the static price limit has the following three ways:(1)
A relatively stable price is used as a market price limit in a market with greater price risk, such as Nordic Power’s real-time market. There are increased and decreased output prices in the Nordic real-time electricity market, in which the increase and decrease output price refers to the price per unit capacity of the market trading members to increase generation output or reduce power load, and the minimum price is the spot market price of the day before. The quotation of reduced output refers to the quotation of the unit capacity of the market trading members to reduce the power generation output or increase the power load, and the maximum price is the spot market price of the day before.(2)
Determine the price ceiling by the value of the lost load.According to the value of electric energy, the ceiling price is set in segments according to the price of the lost load. This method makes the ceiling price consistent with the demand response. The price limit scheme is the premise of a load to participate in market bidding, but the value of the lost load is difficult to estimate.(3)
Determine the ceiling price according to historical data.Under the condition that the available capacity of the bidding unit is unchanged and the bidding load is increasing, the relationship between the average price and the maximum price is analyzed and fitted by the statistical method.Dynamic price limits include the following:(1)
Determine whether there is a spike risk in the price of electricity, and if any, carry out market price fixing. For example, the Australian electricity market will make a judgment according to whether the sum of the electricity prices in the specified period before the trading period exceeds the accumulative price limit. If the sum exceeds the limit, the market price limit after the trading period will be implemented.(2)
ixing of price according to market power. For example, in the New York electricity market, the automatic market power removal program initiates a price limit program if it detects that the unit price in the area exceeds a given threshold. Threshold = Average Electricity Price∗ 2% ∗ 8760/Number of Restricted Hours in the Previous 12 Months.(3)
In case of local blockage, the settlement shall be based on the price limit. In Texas’s real-time trading market, for example, sets are settled on a cost-plus basis. The application of dynamic and static price limits are shown in Table1.In addition to quotation restrictions on the price of electricity, there are also a large number of electricity limits in practice. For example, on the power generation side, the annual direct trading electric quantity limit of ClassB units is set in the medium- and long-term power trading rules of the Beijing-Tianjin-Tangshan Power Grid. In order to ensure the smooth transition of the market, its trading power is gradually opened. The calculation formula is as follows: upper limit of unit direct trading electric quantity = scale of direct trading electric quantity in the next year/installed capacity of admissible power generation enterprises × unit capacity × K. Among them, the installed capacity of preparing power generation enterprises includes Class B units and Class C units, and K is the upper limit coefficient of electric quantity. In terms of electricity consumption, the Guangdong power market stipulates that the electricity sales formula of the same investment subject should not exceed 15% of the total electricity of the monthly centralized competition transaction, in order to prevent market members from manipulating market transactions by market power.Table 1
Contrastive analysis of static and dynamic price limits.
TypeStaticDynamicComplexitySimpleComplexMarket riskLimited market size with an unreasonable limitDispersed market risk among the subjectsTrade leadsLagged price signalEffective price signalCompetitionLimited market responseTimely market responsePrice limit settingWithout definitive wayDynamic adjustment


### 2.1.2. Impact Analysis of Prior Declaration on Social Welfare

As shown in Figure1, the feasible space of the market (the blue area in the figure) consists the upper limit of price, the lower limit of price, and the upper limit of quantity. The declaration curve of the part beyond the blue area is the invalid part. At this point, when the equilibrium price E in the market is within the feasible space, at least the social welfare of the gray part is lost, and the size of the lost area is related to the intercept and slope of the supply curve and the demand curve.Figure 1
The effect of price limits on market transactions.In general, the current price floor will not cause the loss of producer surplus. The market boundary framed by the upper limit of the number of transactions in the market is to enable the smooth transition of the market and prevent large-scale power failure losses caused by marketization transactions. When the quantity ceiling falls below the quantity at the market equilibrium point, there will be a new loss of social welfare, as shown in Figure2.Figure 2
The effect of quantity limit on market transactions.Therefore, according to the principles of economics, the price limit and limit in the market should give enough space to the market subjects, so as to ensure that the market can realize the function of price discovery and at the same time achieve the goal of economical and efficient allocation of resources.


## 2.1.1. Category Price Limit and Determination Method

(1) Price Ceiling. The price ceiling is a price cap set by the government for a product or service. The price ceiling is generally lower than the equilibrium price in a freely competitive market. The reason why the ceiling price exists is that the price of the product or service under the condition of free competition may be manipulated by a certain market entity, which leads to the distortion of the price signal and deviation from the essence of the market. In an imperfectly competitive electricity market, if the price of electricity transactions is liberalized, it may lead to the power generation companies obtaining excess profits by exercising market power, thus increasing the cost of electricity for users. Therefore, a price limit is one of the effective means to avoid market risk in the electricity market trading; in the electricity market trading, there are a lot of price ceilings.The general determination of the price ceiling includes the following three methods:(1)
Cost-oriented method: set a price ceiling based on the marginal cost (or variable cost) of the unit. If every generator set in the market is quoted at its marginal cost, the market transaction price will never exceed the marginal cost of the unit.(2)
Set the maximum price according to the proportion of the online power of the covered units. The total installed capacity of the power generation side is multiplied by a coverage factor as the tradable capacity, which is the reflection of the market abundance. Then, according to the measured transaction capacity, the unit is sorted according to the price of electricity, and the price of the last unit that meets the demand for electricity is taken as the highest price of the transaction.(3)
Set the maximum price based on the value of the lost load. But when the electricity load is met, this method will lose its effect.(2) Price Floor. Price floor, also known as “protection price,” refers to the lowest price limit set by the government for a certain commodity or service, generally to support a certain product or service. Under the protection of floor price, market entities can maintain normal operation, so floor price may inhibit enterprises from seeking technological progress and hinder the development of the industry. Referring to the lowest price in economics, in the electric power market, the lower limit of quotation set by market entities when they declare is to avoid the malicious competition of bidding entities, protect the basic interests of electric power investors, and reduce their investment risks.The determination method of general price lower limit includes the following several kinds:(1)
Cost-oriented method: set the minimum price based on the marginal cost (or variable cost) of the unit(2)
Minimum price considering downtime loss(3)
Minimum price based on the benchmark electricity price(3) Static and Dynamic Price Limits. Typical power market price fixing methods are mainly divided into static price fixing and dynamic price fixing. Among them, the static price limit has the following three ways:(1)
A relatively stable price is used as a market price limit in a market with greater price risk, such as Nordic Power’s real-time market. There are increased and decreased output prices in the Nordic real-time electricity market, in which the increase and decrease output price refers to the price per unit capacity of the market trading members to increase generation output or reduce power load, and the minimum price is the spot market price of the day before. The quotation of reduced output refers to the quotation of the unit capacity of the market trading members to reduce the power generation output or increase the power load, and the maximum price is the spot market price of the day before.(2)
Determine the price ceiling by the value of the lost load.According to the value of electric energy, the ceiling price is set in segments according to the price of the lost load. This method makes the ceiling price consistent with the demand response. The price limit scheme is the premise of a load to participate in market bidding, but the value of the lost load is difficult to estimate.(3)
Determine the ceiling price according to historical data.Under the condition that the available capacity of the bidding unit is unchanged and the bidding load is increasing, the relationship between the average price and the maximum price is analyzed and fitted by the statistical method.Dynamic price limits include the following:(1)
Determine whether there is a spike risk in the price of electricity, and if any, carry out market price fixing. For example, the Australian electricity market will make a judgment according to whether the sum of the electricity prices in the specified period before the trading period exceeds the accumulative price limit. If the sum exceeds the limit, the market price limit after the trading period will be implemented.(2)
ixing of price according to market power. For example, in the New York electricity market, the automatic market power removal program initiates a price limit program if it detects that the unit price in the area exceeds a given threshold. Threshold = Average Electricity Price∗ 2% ∗ 8760/Number of Restricted Hours in the Previous 12 Months.(3)
In case of local blockage, the settlement shall be based on the price limit. In Texas’s real-time trading market, for example, sets are settled on a cost-plus basis. The application of dynamic and static price limits are shown in Table1.In addition to quotation restrictions on the price of electricity, there are also a large number of electricity limits in practice. For example, on the power generation side, the annual direct trading electric quantity limit of ClassB units is set in the medium- and long-term power trading rules of the Beijing-Tianjin-Tangshan Power Grid. In order to ensure the smooth transition of the market, its trading power is gradually opened. The calculation formula is as follows: upper limit of unit direct trading electric quantity = scale of direct trading electric quantity in the next year/installed capacity of admissible power generation enterprises × unit capacity × K. Among them, the installed capacity of preparing power generation enterprises includes Class B units and Class C units, and K is the upper limit coefficient of electric quantity. In terms of electricity consumption, the Guangdong power market stipulates that the electricity sales formula of the same investment subject should not exceed 15% of the total electricity of the monthly centralized competition transaction, in order to prevent market members from manipulating market transactions by market power.Table 1
Contrastive analysis of static and dynamic price limits.
TypeStaticDynamicComplexitySimpleComplexMarket riskLimited market size with an unreasonable limitDispersed market risk among the subjectsTrade leadsLagged price signalEffective price signalCompetitionLimited market responseTimely market responsePrice limit settingWithout definitive wayDynamic adjustment


## 2.1.2. Impact Analysis of Prior Declaration on Social Welfare

As shown in Figure1, the feasible space of the market (the blue area in the figure) consists the upper limit of price, the lower limit of price, and the upper limit of quantity. The declaration curve of the part beyond the blue area is the invalid part. At this point, when the equilibrium price E in the market is within the feasible space, at least the social welfare of the gray part is lost, and the size of the lost area is related to the intercept and slope of the supply curve and the demand curve.Figure 1
The effect of price limits on market transactions.In general, the current price floor will not cause the loss of producer surplus. The market boundary framed by the upper limit of the number of transactions in the market is to enable the smooth transition of the market and prevent large-scale power failure losses caused by marketization transactions. When the quantity ceiling falls below the quantity at the market equilibrium point, there will be a new loss of social welfare, as shown in Figure2.Figure 2
The effect of quantity limit on market transactions.Therefore, according to the principles of economics, the price limit and limit in the market should give enough space to the market subjects, so as to ensure that the market can realize the function of price discovery and at the same time achieve the goal of economical and efficient allocation of resources.


## 2.2. Interim Transaction Result Constraint

When the market clears, it is necessary to ensure that the peak-to-valley ratio of the market players is within the specified range. This not only helps the power system to reduce the peak-valley difference but also helps the market entities to meet the economic demand for electricity consumption.


### 2.2.1. Trade Leads Model and Peak-to-Valley Ratio Coefficient

Using the supply-demand model in microeconomics, this article studies the effect of the peak-valley ratio on social welfare. In order to simplify the model, it is assumed that the supply function and demand function in the power market is linear. Figure3 describes the influence process of the peak-valley ratio coefficient which changes the market clearing state.Figure 3
The impact of peak-to-valley ratio on market clearing: (a) peak market clearance process; (b) valley market clearance process.
(a)(b)The line segmentAB represents the power demand curve Dpeak at the peak period under the initial peak-to-valley ratio, and the line segment CD represents the power supply curve Speak at the peak period under the initial peak-to-valley ratio. The intersection point H of segment AB and segment CD represents the market clearing result in the peak period, where the trading volume is Qpeak, the market clearing price is PU, and the market welfare in the peak period is the area SAHC of the triangle AHC.Line segmentEF represents the power demand curve in the low valley period under the initial peak-to-valley ratio Dvalley. Line segment MN represents the power supply curve in the low valley period under the initial peak-to-valley ratio Svalley. The intersection point K of segment EF and segment MN represents the market clearing result in the valley period, where the trading volume is Qvalley, the market clearing price is PL, and the market welfare in the valley period is the area SEKM of the triangle EKM.It is assumed that the total electricity demand of users is fixed in the short term. The sum of peak and valley demand is fixed. Peak electric quantity can only be transferred to the valley, or valley electric quantity can only be transferred to the peak. In the case of peak-to-valley ratio change, it is assumed that the peak-to-valley ratio becomes smaller and the demand in the peak segment shifts to the valley segment, resulting in the shift ofDpeak to the left and lower side of Dpeak′ (line segment A′B′). A′B′ intersects the supply curve CD of the original peak segment at point H′AB. At this time, the trading volume is reduced from Qpeak to Qpeak′, and the reduction amount is ΔQpeak. The market welfare of the peak segment reduces the area SAHH′A′ of the quadrilateral AHH′A′.It is assumed that the total power demand does not change in the short term, so the power consumption behavior occurs either in the valley or in the peak. Add the reduced demandΔQpeak in the peak segment to the valley segment, and then the transaction quantity in the valley segment changes from Qvalley to Qvalley′:(1)Qvalley′=Qvalley+∆Qpeak.The valley period of electricity consumption represents that the supply is greater than the demand at this time. It is assumed that the supply in the valley period is the maximum supply that the generation side is willing to provide, that is, the supply curve does not move. Therefore, a vertical line atQvalley′ intersects Svalley at point K′, and a demand curve K′ with the same slope as curve E is drawn along Dvalley. In this case, Dvalley represents the demand curve after the increase of demand in the valley segment, and the market welfare in the valley segment increases the area SE′K′KE of the quadrilateral E′K′KE.To study the influence of the peak-valley ratio coefficient on the total welfare of the peak-valley segment market, that is, to study the positive and negative problems of∆W under the change of peak-valley ratio coefficient. ∆W is the difference between the increased market welfare in the trough period and the reduced market welfare in the peak period:(2)∆W=SE′K′KE−SAHH′A′.


### 2.2.2. Impact Analysis of Peak-Valley Ratio Coefficient on Social Welfare

Assuming that the up-and-down movement of the demand curve does not affect the supply curve in the short term, the supply curves at the peak and valley segments remain unchanged before and after the peak-to-valley ratio changes. The supply curve function of the peak segment is as follows:(3)Speak∶P=α0+β0Q.The supply curve function of the valley segment is as follows:(4)Svalley∶P=α1+β1Q.Before the peak-to-valley ratio coefficient changes, the peak segment market demand function is as follows:(5)Dpeak:P=a0+b0Q.The market demand function of the valley segment is as follows:(6)Dvalley:P=a1+b1Q.Then, the peak segment market clears before the peak-to-valley ratio changes:(7)Speak=Dpeak.The market clearing result of the peak segment is calculated as follows:(8)Qpeak=a0−α0β0−b0,Ppeak=a0β0−α0b0β0−b0,Wpeak=∫0QpeakDpeak−SpeakdQ=a0−α0Q+b0−β02Q20Qpeak=12⋅α0−a02β0−b0.Similarly, the market clearing result of the trough segment is calculated as follows:(9)Qvalley=a1−α1β1−b1,Pvalley=a1β1−α1b1β1−b1,Wvalley=12⋅α1−a12β1−b1.In the short term, the total market sizeQtotal is as follows:(10)Qtotal=Qpeak+Qvalley=a0−α0β0−b0+a1−α1β1−b1.The peak-to-valley ratio coefficient is as follows:(11)η=QpeakQvalley=a0−α0a1−α1⋅β1−b1β0−b0.After the peak-to-valley ratio coefficient changes, the peak segment market demand function becomes(12)Dpeak′:P=a0′+b0Q.The valley segment market demand function becomes(13)Dvalley′:P=a1′+b1Q.When the peak segment market clears,Speak=Dpeak′, the clearing result becomes(14)Qpeak′=a0′−α0β0−b0,Ppeak′=a0′β0−a0′b0β0−b0,Wpeak′=12⋅α0−a0′2β0−b0.When the valley segment market clears,Svalley=Dvalley′, the clearing result becomes(15)Qvalley′=a1′−α1β1−b1,Pvalley′=a1′β1−α1′b1β1−b1,Wvalley′=12⋅α1−a1′2β1−b1.Since the total market size does not change in the short term,Qvalley′ also equals to the following formula:(16)Qvalley′=Qtotal−Qpeak′=a0−α0β0−b0+a1−α1β1−b1−a0′−α0β0−b0=a0−a0′β0−b0+a1−α1β1−b1.It follows that(17)a0−a0′β0−b0=a1′−a1β1−b1.The change of total social welfare before and after the peak-valley ratio coefficient is as follows:(18)∆W=Wpeak′+Wvalley′−Wpeak+Wvalley=12⋅a0′−a0−2⋅α0a0′−a0β0−b0+a1′−a1−2⋅α1a1′−a1β1−b1.At this point, the peak-to-valley ratio coefficient is as follows:(19)η′=Qpeak′Qvalley′=a0′−α0a1′−α1⋅β1−b1β0−b0.It is found that, whenη′−η<0 and ∆W>0, that is, when the peak-valley ratio of the market becomes smaller, the total welfare of the market transaction becomes larger. This also means that improving the market peak-to-trough ratio helps increase market welfare. When the price elasticity of the peak market is the same as that of the trough market, the total social welfare is maximized.(20)ηopt=a0′−α0a1′−α1,Wmax=a0−α02β0−b0.


## 2.2.1. Trade Leads Model and Peak-to-Valley Ratio Coefficient

Using the supply-demand model in microeconomics, this article studies the effect of the peak-valley ratio on social welfare. In order to simplify the model, it is assumed that the supply function and demand function in the power market is linear. Figure3 describes the influence process of the peak-valley ratio coefficient which changes the market clearing state.Figure 3
The impact of peak-to-valley ratio on market clearing: (a) peak market clearance process; (b) valley market clearance process.
(a)(b)The line segmentAB represents the power demand curve Dpeak at the peak period under the initial peak-to-valley ratio, and the line segment CD represents the power supply curve Speak at the peak period under the initial peak-to-valley ratio. The intersection point H of segment AB and segment CD represents the market clearing result in the peak period, where the trading volume is Qpeak, the market clearing price is PU, and the market welfare in the peak period is the area SAHC of the triangle AHC.Line segmentEF represents the power demand curve in the low valley period under the initial peak-to-valley ratio Dvalley. Line segment MN represents the power supply curve in the low valley period under the initial peak-to-valley ratio Svalley. The intersection point K of segment EF and segment MN represents the market clearing result in the valley period, where the trading volume is Qvalley, the market clearing price is PL, and the market welfare in the valley period is the area SEKM of the triangle EKM.It is assumed that the total electricity demand of users is fixed in the short term. The sum of peak and valley demand is fixed. Peak electric quantity can only be transferred to the valley, or valley electric quantity can only be transferred to the peak. In the case of peak-to-valley ratio change, it is assumed that the peak-to-valley ratio becomes smaller and the demand in the peak segment shifts to the valley segment, resulting in the shift ofDpeak to the left and lower side of Dpeak′ (line segment A′B′). A′B′ intersects the supply curve CD of the original peak segment at point H′AB. At this time, the trading volume is reduced from Qpeak to Qpeak′, and the reduction amount is ΔQpeak. The market welfare of the peak segment reduces the area SAHH′A′ of the quadrilateral AHH′A′.It is assumed that the total power demand does not change in the short term, so the power consumption behavior occurs either in the valley or in the peak. Add the reduced demandΔQpeak in the peak segment to the valley segment, and then the transaction quantity in the valley segment changes from Qvalley to Qvalley′:(1)Qvalley′=Qvalley+∆Qpeak.The valley period of electricity consumption represents that the supply is greater than the demand at this time. It is assumed that the supply in the valley period is the maximum supply that the generation side is willing to provide, that is, the supply curve does not move. Therefore, a vertical line atQvalley′ intersects Svalley at point K′, and a demand curve K′ with the same slope as curve E is drawn along Dvalley. In this case, Dvalley represents the demand curve after the increase of demand in the valley segment, and the market welfare in the valley segment increases the area SE′K′KE of the quadrilateral E′K′KE.To study the influence of the peak-valley ratio coefficient on the total welfare of the peak-valley segment market, that is, to study the positive and negative problems of∆W under the change of peak-valley ratio coefficient. ∆W is the difference between the increased market welfare in the trough period and the reduced market welfare in the peak period:(2)∆W=SE′K′KE−SAHH′A′.


## 2.2.2. Impact Analysis of Peak-Valley Ratio Coefficient on Social Welfare

Assuming that the up-and-down movement of the demand curve does not affect the supply curve in the short term, the supply curves at the peak and valley segments remain unchanged before and after the peak-to-valley ratio changes. The supply curve function of the peak segment is as follows:(3)Speak∶P=α0+β0Q.The supply curve function of the valley segment is as follows:(4)Svalley∶P=α1+β1Q.Before the peak-to-valley ratio coefficient changes, the peak segment market demand function is as follows:(5)Dpeak:P=a0+b0Q.The market demand function of the valley segment is as follows:(6)Dvalley:P=a1+b1Q.Then, the peak segment market clears before the peak-to-valley ratio changes:(7)Speak=Dpeak.The market clearing result of the peak segment is calculated as follows:(8)Qpeak=a0−α0β0−b0,Ppeak=a0β0−α0b0β0−b0,Wpeak=∫0QpeakDpeak−SpeakdQ=a0−α0Q+b0−β02Q20Qpeak=12⋅α0−a02β0−b0.Similarly, the market clearing result of the trough segment is calculated as follows:(9)Qvalley=a1−α1β1−b1,Pvalley=a1β1−α1b1β1−b1,Wvalley=12⋅α1−a12β1−b1.In the short term, the total market sizeQtotal is as follows:(10)Qtotal=Qpeak+Qvalley=a0−α0β0−b0+a1−α1β1−b1.The peak-to-valley ratio coefficient is as follows:(11)η=QpeakQvalley=a0−α0a1−α1⋅β1−b1β0−b0.After the peak-to-valley ratio coefficient changes, the peak segment market demand function becomes(12)Dpeak′:P=a0′+b0Q.The valley segment market demand function becomes(13)Dvalley′:P=a1′+b1Q.When the peak segment market clears,Speak=Dpeak′, the clearing result becomes(14)Qpeak′=a0′−α0β0−b0,Ppeak′=a0′β0−a0′b0β0−b0,Wpeak′=12⋅α0−a0′2β0−b0.When the valley segment market clears,Svalley=Dvalley′, the clearing result becomes(15)Qvalley′=a1′−α1β1−b1,Pvalley′=a1′β1−α1′b1β1−b1,Wvalley′=12⋅α1−a1′2β1−b1.Since the total market size does not change in the short term,Qvalley′ also equals to the following formula:(16)Qvalley′=Qtotal−Qpeak′=a0−α0β0−b0+a1−α1β1−b1−a0′−α0β0−b0=a0−a0′β0−b0+a1−α1β1−b1.It follows that(17)a0−a0′β0−b0=a1′−a1β1−b1.The change of total social welfare before and after the peak-valley ratio coefficient is as follows:(18)∆W=Wpeak′+Wvalley′−Wpeak+Wvalley=12⋅a0′−a0−2⋅α0a0′−a0β0−b0+a1′−a1−2⋅α1a1′−a1β1−b1.At this point, the peak-to-valley ratio coefficient is as follows:(19)η′=Qpeak′Qvalley′=a0′−α0a1′−α1⋅β1−b1β0−b0.It is found that, whenη′−η<0 and ∆W>0, that is, when the peak-valley ratio of the market becomes smaller, the total welfare of the market transaction becomes larger. This also means that improving the market peak-to-trough ratio helps increase market welfare. When the price elasticity of the peak market is the same as that of the trough market, the total social welfare is maximized.(20)ηopt=a0′−α0a1′−α1,Wmax=a0−α02β0−b0.


## 3. Multiperiod Coupling Mechanism Based on the Reasonable Peak-to-Valley Ratio

### 3.1. Independent Clearing Mode of Each Period under Time-Divided Trading

Time-sharing bidding means that the bidding cycle is divided into several bidding periods, and the electric energy is traded on time. The limit case of time-share bidding is that the division of time period tends to be infinitesimal, and the electric energy traded belongs to real-time trading. In this case, the market clearing price can represent the change of real-time load. Since there are peak and trough periods of electricity consumption, the shortage degree and supply cost of electricity are different in different periods, so it is necessary to reflect the price of electric energy in different periods. This can not only guide users to use electricity reasonably, but also reduce the peak-valley imbalance of the power system and alleviate the supply and demand situation. However, the current power market does not support refined time division, so the transition stage can be divided into four segments: spike, peak, trough, and flat segment. As shown in Figure4, it describes the concept of electric energy commodities in the electric power spot market: a period of 24 h is divided into several parts at the same time interval, which serves as the nodes for collecting data of electric power metering devices. When the market is clearing, the clearing price and the clearing quantity are calculated according to the time-segment electric quantity balance model. In the transition stage, the time interval is mostly more than 1 h, but its clearing principle is the same as the spot market.Figure 4
Conceptual diagram of electricity time-sharing trading.In medium- and long-termtime-sharing trading, the trading varieties include annual base contract trading, annual base contract transfer trading, annual bilateral trading, monthly centralized trading, intramonth continuous trading, and monthly prelisting trading. Each trading variety contains four time slots. The trading institution will match the high and low prices according to the information of the reported volume and quotation declared by the power sellers and power buyers in the four periods, and determine the market trading price by means of summary clearing or marginal clearing.Although in time, each time period is cleared independently and does not interfere with each other, there are implicit coupling restrictions for market players in each time period. For the generation side, the generation unit’s output characteristics limitations need to be considered during the contract execution, such as minimum output conditions, maximum climbing rate, continuity output limitations, and available capacity limitations. Therefore, for the generation side, the physical characteristics of the units restrict their performance in the time-sharing transactions. For the electricity consumption side, the sum of the cleared power in each time period is limited by the total demand for electricity, and the power purchasers aim to minimize their own power purchase cost and buy the most power at the same cost, while the short-term power consumption remains stable. For the consumer side, the peak-to-valley price difference is not enough to attract customers to participate in peak-shaving and valley-filling.It is assumed that the segmentation is based on the value of electricity: (1) flat segment market means that the price of electricity in this market is equal to its value, the seller can make normal profit in the flat segment, and the buyer pays the normal cost of electricity in the flat segment. (2) Peak hour represents that the price of electricity in this market is slightly higher than its value, and the power seller can make high profit in the peak hour, and the power buyer has to pay higher cost than its normal cost in the peak hour. (3) The peak hours represent a tighter power supply and demand situation; therefore, the power generation side can make higher excess profit in the peak hours, and the power purchaser has to pay higher electricity cost in the peak hours. (4) The price during the low hours indicates that the power seller can only meet its minimum operating needs without excess profit, and the power buyer has the lowest energy cost at this time. The relationship between the price and value of the electricity commodity is shown in Figure5.Figure 5
The relationship between the value of electricity and the price of electricity.From Figure5, it can be seen that due to the different identities, the goal for the generation side is to seek to maximize its own interests in the unconstrained situation. The generation side is more willing to participate in power trading during peak hours to obtain the maximum profit. The power purchasing side is more willing to participate in the power trading in the low and flat periods to reduce the cost of electricity consumption. However, the storage and consumption of electric energy commodities occur at the same time, so the market organizer needs to design the market mechanism to induce the power generation side to reduce the proportion of electricity traded during peak hours and increase the proportion of electricity traded during low hours, to guide the power consumption side to increase the proportion of electricity traded during low hours and raise the revenue of the power generation side during low hours. Finally, through the behavior correction of both power generation and consumption sides, the price change curve of electric energy is symmetrically distributed above and below the value of electric energy, so that the market goal of widening the peak-valley price difference and narrowing the peak-valley difference of electricity consumption can be achieved while ensuring the efficient allocation of market resources.


### 3.2. Generation-Side Clearing Model under Multitime Coupling

#### 3.2.1. Study of Coupling Methods

(1) Electricity Coupling. In practice, the trading rules for medium- and long-term power trading in time slots are as follows: the power trading time slots are divided into peak, sharp, valley, and flat slots, and when the market is mature, the power generation and consumption sides can declare the power and price at the same time. According to the quotation information provided by the market players, the trading institution will sort the prices on the power generation side in the order low to high and the prices on the electricity consumption side in the order high to low, match the high with the low, and aggregate the clearing or marginal clearing until the price on the electricity consumption side is lower than the price on the power generation side or one of the two is fully traded.We assume that according to the abovementioned rules, the pretransaction quantity of the four sections of peak, flat, valley, and tip can be obtained asQpeak, Qflat, Qvalley, and Qc−peak.(1)
WhenQvalley≠0, according to the historical performance of market entities and combined with the peak-to-valley ratio tradable coefficient given by the market ηpeak and ηc−peak, calculate the ideal value of peak segments Q˜peak and Q˜c−peak:(21)Q˜peak=ηpeak⋅Qpeak,Q˜c−peak=ηc−peak⋅Qc−peak.At this point, the tradable coefficient of peak-valley ratio and the optimal peak-valley ratio mentioned above can be given a reasonable value by the trading institution in combination with the actual market situation (such as historical peak-valley ratio data and future development planning), which will change with the different stages of the market.Note: the difference between the ideal value and the pretransaction structure is the quantity of excess trade.If the ideal value is greater than or equal to the pretransaction result, the contract will be executed according to the pretransaction result, and the excess transaction quantity is 0. If the ideal value is less than the pretransaction result, then the overtrading quantity is calculated as∆Qpeak and ∆Qc−peak:(22)∆Qpeak=Qpeak−Q˜peak,∆Qc−peak=Qc−peak−Q˜c−peak.(2)
WhenQvalley=0, means that the power plant plays a nonpositive role in subduing the peak-valley difference of power, so set Q˜peak=0 and Q˜c−peak=0. At this point, all the peak and peak preclinched electric quantities are regarded as overtraded electric quantity, that is:(23)∆Qpeak=Qpeak,∆Qc−peak=Qc−peak.(2) Electricity Price Coupling. According to the above rules, the result of pretransaction electricity quantity can also be obtained as follows: Ppeak, Pflat, Pvalley, and Pc−peak. If the amount of overtraded electricity is 0, the contract will be executed according to the result of the preconcluded electricity price. If the amount of excess transaction electricity is not 0, then the transaction income of the excess part is adjusted, which is the correction of the pretransaction electricity price:(24)∆Ppeak=αpeak⋅Ppeak,∆Pc−peak=αc−peak⋅Pc−peak,where αpeak and αc−peak are the adjustment coefficients of the electricity price of peak and peak segments, generally between 0 and 1. The electricity sale income of the overtraded electricity on the power generation side is adjusted as follows:(25)Rex−peak=∆Qpeak×∆Ppeak,Rex−c−peak=∆Qc−peak×∆Pc−peak.That is, when there is no excess traded electricity on the generation side, the revenue from electricity sales on the generation side is as follows:(26)Rtotal=Rpeak+Rflat+Rvalley+Rc−peak=Qpeak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+Qc−peak×Pc−peak.When there is excess traded electricity on the generation side, the revenue from electricity sales on the generation side is adjusted as follows:(27)Rtotal−adjust=Rpeak+Rflat+Rvalley+Rc−peak=∆Qpeak×∆Ppeak+Q˜peak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+∆Qc−peak×∆Pc−peak+Q˜c−peak×Pc−peak.Up to this point, the power trading agency uses the pretraded power results of the valley section on the power generation side as a reference for the pretraded power of the peak and peak sections, and calculates the ideal value of the traded power during the peak and peak periods by combining the market peak-to-valley ratio it wants to achieve. The pretransacted electricity price is adjusted for the part exceeding the ideal value, thus realizing the market regulation means based on physical electricity and limited by economic income. The fees charged can be used as a source of incentive funds for peak reduction and valley filling in the market as a whole, which will be rewarded to the market players who play a positive role in leveling out the peak-to-valley difference in electricity.


#### 3.2.2. Market-Clearing Model Considering Multitime Coupling

Suppose there aren sellers in the market and each seller is quoted as(28)P1S,a,P2S,a,⋯,PiS,a,⋯,PnS,aP1S,b,P2S,b,⋯,PiS,b,⋯,PnS,bP1S,c,P2S,c,⋯,PiS,c,⋯,PnS,cP1S,d,P2S,d,⋯,PiS,d,⋯,PnS,d,and the amount as(29)Q1S,a,Q2S,a,⋯,QiS,a,⋯,QnS,aQ1S,b,Q2S,b,⋯,QiS,b,⋯,QnS,bQ1S,c,Q2S,c,⋯,QiS,c,⋯,QnS,cQ1S,d,Q2S,d,⋯,QiS,d,⋯,QnS,d.There arem power purchasers (such as power selling companies and large users), and the quotation of each power purchaser is(30)P1D,a,P2D,a,⋯,PjD,a,⋯,PmD,aP1D,b,P2D,b,⋯,PjD,b,⋯,PmD,bP1D,c,P2D,c,⋯,PjD,c,⋯,PmD,cP1D,d,P2D,d,⋯,PjD,d,⋯,PmD,d,and the amount as(31)Q1D,a,Q2D,a,⋯,QjD,a,⋯,QmD,aQ1D,b,Q2D,b,⋯,QjD,b,⋯,QmD,bQ1D,c,Q2D,c,⋯,QjD,c,⋯,QmD,cQ1D,d,Q2D,d,⋯,QjD,d,⋯,QmD,d.Among them,S and D distinguish the supply side and the demand side, that is, the electricity sale side (generation side) and the electricity purchase side (electricity side). a,b,c,andd represent the peak, flat, valley, and critic-peak period in time-segment trading, respectively. The declared electricity price of the power seller and the power buyer is positive. The declared electric quantity of the purchaser is positive, while the declared electric quantity of the seller is negative.When the market is cleared by the marginal clearing method, the objective function is the maximization of market welfareW, namely:(32)maxW=∑i=1n∑j=1mPjD,a−PiS,aQi,ja+∑i=1n∑j=1mPjD,b−PiS,bQi,jb+∑i=1n∑j=1mPjD,c−PiS,cQi,jc+∑i=1n∑j=1mPjD,d−PiS,dQi,jd−lossF,where F is a penalty parameter.The constraint conditions are as follows:(1)
Supply and demand balance constraint:(33)s.t.∑i=1nQi,j≤Qjd,j=1,⋯,m,∑j=1mQi,j≤Qis,i=1,⋯,n,Qi,j≥0,i=1,⋯,n,j=1,⋯,m.In the formula,Qi,j is the transaction quantity between the power seller i and the power purchaser j. Qis refers to the quantity of electricity declared by seller i; Pis shall declare the electricity price for the electricity seller i; Qjd refers to the quantity of electricity declared by the purchaser j; Pjd shall declare the price of electricity for the purchaser j.(2)
Electricity price constraint:(34)Pi,LS,a≤PiS,a≤Pi,US,a,Pj,LD,a≤PjD,a≤Pj,UD,a,Pi,LS,b≤PiS,b≤Pi,US,b,Pj,LD,b≤PjD,b≤Pj,UD,b,Pi,LS,c≤PiS,c≤Pi,US,c,Pj,LD,c≤PjD,c≤Pj,UD,c,Pi,LS,d≤PiS,d≤Pi,US,d,Pj,LD,d≤PjD,d≤Pj,UD,d.In the formula,Pi,LS,a, Pi,LS,b, Pi,LS,c, and Pi,LS,d, respectively, represent the lower limit of electricity selling price in four periods of peak, flat, valley, and peak; Pi,US,a, Pi,US,b, Pi,US,c, and Pi,US,d, respectively, represent the upper limit of electricity selling price in four periods of peak, flat, valley, and peak; Pj,LD,a and Pj,LD,b and Pj,LD,c and Pj,LD,d, respectively, represent the lower limit of electricity purchase price in four periods of peak, flat, valley, and peak; Pj,UD,a, Pj,UD,b, Pj,UD,c, and Pj,UD,d, respectively, represent the upper limit of electricity purchase price in the four periods of peak, flat, valley, and peak.(3)
Constraint on declared quantity:On the electricity purchasing side, there are two types of market users: large power users and electricity selling companies. For electricity selling companies, they limit their trading shares to not exceed the maximum amount of declaration, otherwise the maximum amount of declaration shall be declared.(35)Qi,ECD,a=minQi,ECD,a,rsharea×QD,a,Qi,ECD,b=minQi,ECD,b,rshareb×QD,b,Qi,ECD,c=minQi,ECD,c,rsharec×QD,c,Qi,ECD,d=minQi,ECD,d,rshared×QD,d.The amount declared by each entity shall not exceed the given direct trading volume.(36)∑i=1nQiS,a≤Qa,∑j=1mQiD,a≤Qa,∑i=1nQiS,b≤Qb,∑j=1mQiD,b≤Qb,∑i=1nQiS,c≤Qc,∑j=1mQiD,c≤Qc,∑i=1nQiS,d≤Qd,∑j=1mQiD,d≤Qd,whereEC represents that the main type of the electricity purchasing side is the electricity selling company; rsharea, rshareb, rsharec, and rshared, respectively, represent the maximum market share that the electricity selling company can occupy in the four periods of peak, flat, valley, and peak; Qa, Qb, Qc, and Qd, respectively, represent the direct trading upper limits of the market at four periods of the peak, flat, valley, and peak.(4)
Constraint of peak-to-valley ratio on the electricity selling side:When declaring, the declared electric quantity of a single e-commerce seller during peak hours shall not exceed the maximum peak-to-valley ratio constraint of the market:(37)QiS,a=minQiS,a,ηh−peak×Qc,QiS,d=minQiS,d,ηh−c−peak×Qc,whereηh−peak=Qh−peak/Qh−valley, ηh−c−peak=Qh−c−peak/Qh−valley, ηh−peak, and ηh−c−peak, respectively, represent the maximum value of the peak/valley segment electric quantity and the peak/valley segment electric quantity.(5)
Price constraint under optimal peak-to-valley ratio:In the objective function, it is the welfare value of the peak market and peak market loss when the e-commerce seller does not meet the optimal peak-to-valley ratio.(38)lossF=lossA+lossD,lossA=0,QiS,a≤ηopt−peak×QiS,c,∑i=1n1−αpeakPiS,aQiS,a−ηopt−peak×QiS,c,others,lossD=0,QiS,d≤ηopt−c−peak×QiS,c,∑i=1n1−αc−peakPiS,dQiS,d−ηopt−c−peak×QiS,c,others,wherelossA represents the welfare value of the market loss in the peak segment, lossD represents the welfare value of the market loss in the peak segment, and ηopt−peak and ηopt−c−peak are the ideal peak-valley coefficient of the peak segment and the critic-peak segment. It can be calculated by the above mentioned method.After solving the model, it is obtained that the volume of transactions of each subject is the sum of transactions in each period:(39)Qi,∆S=Qi,∆S,a+Qi,∆S,b+Qi,∆S,c+Qi,∆S,d=∑j=1mQi,jS,a+∑j=1mQi,jS,b+∑j=1mQi,jS,c+∑j=1mQi,jS,d,Qj,∆D=Qj,∆D,a+Qj,∆D,b+Qj,∆D,c+Qj,∆D,d=∑i=1nQi,jD,a+∑i=1nQi,jD,b+∑i=1nQi,jD,c+∑i=1nQi,jD,d,In the formula,Qi,∆S is the transaction quantity of the first power seller i; Qj,∆D is the transaction quantity of the purchaser j.The final volume of transactions in each segment of the market is as follows:(40)Q∆a=∑i=1nQi,∆S,a=∑j=1mQj,∆D,a,Q∆b=∑i=1nQi,∆S,b=∑j=1mQj,∆D,b,Q∆c=∑i=1nQi,∆S,c=∑j=1mQj,∆D,c,Q∆d=∑i=1nQi,∆S,d=∑j=1mQj,∆D,d.


### 3.3. Incentive Mechanism of the Electricity Consumption Side under Multihour Coupling

For the electricity consumers, the incentive to change their own electricity consumption behavior comes from the market—if the cost of purchasing electricity in the peak and peak hours increases and the cost of purchasing electricity in the valley hours decreases, the consumers will choose to shift their electricity demand as much as possible, shifting the peak and peak electricity consumption to the flat and valley electricity consumption. Therefore, the market can promote the use of electricity to achieve peak and valley reduction by means of economic incentives, thereby reducing the peak-valley difference in electricity and widening the peak-valley difference in electricity prices. The process of capital flow in the electricity market at this point is shown in Figure6.Figure 6
Schematic diagram of user-side incentives under multitime coupling.The incentive mechanism for the user side mainly contains the following elements.


#### 3.3.1. Incentive Principle

In order to encourage customers to use more electricity during the low hours, the design mechanism gives incentives for more electricity use in the low hours or less electricity use in the peak hours.


#### 3.3.2. Incentive Method

Because the power and price each time will fluctuate with market changes under time-sharing trading, and it is impossible to guarantee the same price of electricity in consecutive moments, so the means of power incentive is not applicable to time-sharing trading. Therefore, under the time-sharing trading mode, the incentive on the user side mainly takes the form of an economic incentive, which is aimed at the users who actively participate in the trading during the low valley hours to further reduce the cost of electricity use during the low valley hours.


#### 3.3.3. Incentive Process

(1)
Determining the total incentive amount:Figure6 shows that incentive funds on the user side come from excess transaction fees on the power generation side. Therefore, the total amount of funds that can be rewarded on the user side is ΔRreturn:(41)∆Rreturn=∆Rreturn−peak+∆Rreturn−valley=1−αpeak×Ppeak×∆Qpeak+1−αvalley×Pvalley×∆Qvalley.(2)
Determining the compensation amountrreturn−valley per unit of electric quantity during the valley period:(42)rreturn−valley=∆RreturnQvalley,where∆Rreturn is the total incentive amount; Qvalley is the volume of transactions during the trough period of the market.(3)
Determining the compensation benefits of each subject:(43)Ri=rreturn−valley×Qiu,whereRi is the trough electric excitation obtained by the user i; Qiu is the transaction quantity of the first user in the trough period.It follows that(44)∑Qiu=Q谷,∑Ri=∆Rreturn.The electricity market funds realize the flow from the generation side to the customer side, and this flow process will push the customer side to change their own electricity consumption behavior and push the power system to reduce the peak-to-valley difference.


### 3.4. Effect Analysis

#### 3.4.1. Analysis of Generation-Side Revenue

Under the multihour coupling, the total revenue of power generation entities participating in the time-sharing transactions is as follows:(45)RiS=RiS,a+RiS,b+RiS,c+RiS,d,where(46)RiS,a=Qi,∆S,a×PMCa,Qi,∆S,a≤ηopt−peak×Qc,ηopt−peak×Qc×PMCa+Qi,∆S,a−ηopt−peak×Qc×PMCa×αpeak,Qi,∆S,a>ηopt−peak×Qc,RiS,b=Qi,∆S,b×PMCb,RiS,c=Qi,∆S,c×PMCc,RiS,d=Qi,∆S,d×PMCd,Qi,∆S,d≤ηopt−c−peak×Qc,ηopt−c−peak×Qc×PMCd+Qi,∆S,d−ηopt−c−peak×Qc×PMCd×αc−peak,Qi,∆S,d>ηopt−c−peak×Qc.In the formulaRiS,a, RiS,b, RiS,c, and RiS,d, respectively, represent the electricity sales revenue of the power generation subject in the peak, flat, valley, and tip segments of the market; PMCa, PMCb, PMCc, and PMCd, respectively, represent the clearing price of peak, flat, valley, and top four periods.According to the income expression of power generation companies, it can be seen that when the demand of the valley segmentQc is known, the income of power generation companies at peak and critic-peak segments depends on the relationship between Qi,∆S,d and the ideal value. When PMCa×αc−peak<PMCc and PMCd×α尖<PMCc, the power generation will transfer the part of the peak and peak electric quantity beyond the ideal value to the valley, so as to maximize the electricity sales income. On the contrary, power producers will continue to release electricity to the peak and peak segments for sale until the market demand is met.


#### 3.4.2. Analysis of Power Consumption Side Benefits

The cost of electricity consumption on the electricity consumption side under multihour coupling can be expressed by the following equation:(47)CjD=CjD,a+CjD,b+CjD,c+CjD,d−RCjc=Qj,∆D,a×PMCa+Qj,∆D,b×PMCb+Qj,∆D,c×PMCc−∆RCQ∆D,c+Qj,∆D,d×PMCd,RCjc=∆RCQ∆D,c×Qj,∆D,c.In the formula, RCjc represents the incentive obtained by the power consumption subject at the low ebb; Qj,∆D,c is the transaction amount of the valley segment of the main body of electricity consumption; Q∆D,c is the total volume of transactions by all users in the valley.It can be seen that customers are incentivized by low valley electricity consumption to boost low valley electricity consumption and reduce the overall cost of electricity consumption. Until the cost of changing electricity consumption behavior is equal to the benefit obtained, users will stop peak and valley cutting behavior.


#### 3.4.3. Analysis of Market Cycle Effects

From the perspective of the market organizer, whenPMCa×αpeak<PMCc, PMCd×αc−peak<PMCc, Qi,∆S,a>ηopt−peak×Qc, and Qi,∆S,d>ηopt−c−peak×Qc, the power producer will transfer the part of the peak and tip section power exceeding the ideal value to the valley section, and the transferred power will be as follows:(48)∆trans=∑i=1mQi,∆S,a−ηopt−peak×Qc+∑i=1mQi,∆S,d−ηopt−c−peak×Qc.Then, the overall market peak-to-valley ratio at this point becomes(49)ηmarket=ηopt−peak+ηopt−c−peak×QcQ∆D,c+∆trans.The peak-valley spread becomes(50)∆P=maxPMCa,PMCd−PMCc−∆RCQ∆D,c.Under the two-sided choice, the peak-to-valley difference of electricity in the market narrows and the peak-to-valley difference in electricity price increases.At this point, the value of the market fluctuates as shown in Figure7. The revenue in the peak and spike hours shifts to the low valley segment, and at the same time, the demand for electricity in the peak and spike hours shifts to the low valley segment.Figure 7
Electricity price distribution after multitime coupling.


## 3.1. Independent Clearing Mode of Each Period under Time-Divided Trading

Time-sharing bidding means that the bidding cycle is divided into several bidding periods, and the electric energy is traded on time. The limit case of time-share bidding is that the division of time period tends to be infinitesimal, and the electric energy traded belongs to real-time trading. In this case, the market clearing price can represent the change of real-time load. Since there are peak and trough periods of electricity consumption, the shortage degree and supply cost of electricity are different in different periods, so it is necessary to reflect the price of electric energy in different periods. This can not only guide users to use electricity reasonably, but also reduce the peak-valley imbalance of the power system and alleviate the supply and demand situation. However, the current power market does not support refined time division, so the transition stage can be divided into four segments: spike, peak, trough, and flat segment. As shown in Figure4, it describes the concept of electric energy commodities in the electric power spot market: a period of 24 h is divided into several parts at the same time interval, which serves as the nodes for collecting data of electric power metering devices. When the market is clearing, the clearing price and the clearing quantity are calculated according to the time-segment electric quantity balance model. In the transition stage, the time interval is mostly more than 1 h, but its clearing principle is the same as the spot market.Figure 4
Conceptual diagram of electricity time-sharing trading.In medium- and long-termtime-sharing trading, the trading varieties include annual base contract trading, annual base contract transfer trading, annual bilateral trading, monthly centralized trading, intramonth continuous trading, and monthly prelisting trading. Each trading variety contains four time slots. The trading institution will match the high and low prices according to the information of the reported volume and quotation declared by the power sellers and power buyers in the four periods, and determine the market trading price by means of summary clearing or marginal clearing.Although in time, each time period is cleared independently and does not interfere with each other, there are implicit coupling restrictions for market players in each time period. For the generation side, the generation unit’s output characteristics limitations need to be considered during the contract execution, such as minimum output conditions, maximum climbing rate, continuity output limitations, and available capacity limitations. Therefore, for the generation side, the physical characteristics of the units restrict their performance in the time-sharing transactions. For the electricity consumption side, the sum of the cleared power in each time period is limited by the total demand for electricity, and the power purchasers aim to minimize their own power purchase cost and buy the most power at the same cost, while the short-term power consumption remains stable. For the consumer side, the peak-to-valley price difference is not enough to attract customers to participate in peak-shaving and valley-filling.It is assumed that the segmentation is based on the value of electricity: (1) flat segment market means that the price of electricity in this market is equal to its value, the seller can make normal profit in the flat segment, and the buyer pays the normal cost of electricity in the flat segment. (2) Peak hour represents that the price of electricity in this market is slightly higher than its value, and the power seller can make high profit in the peak hour, and the power buyer has to pay higher cost than its normal cost in the peak hour. (3) The peak hours represent a tighter power supply and demand situation; therefore, the power generation side can make higher excess profit in the peak hours, and the power purchaser has to pay higher electricity cost in the peak hours. (4) The price during the low hours indicates that the power seller can only meet its minimum operating needs without excess profit, and the power buyer has the lowest energy cost at this time. The relationship between the price and value of the electricity commodity is shown in Figure5.Figure 5
The relationship between the value of electricity and the price of electricity.From Figure5, it can be seen that due to the different identities, the goal for the generation side is to seek to maximize its own interests in the unconstrained situation. The generation side is more willing to participate in power trading during peak hours to obtain the maximum profit. The power purchasing side is more willing to participate in the power trading in the low and flat periods to reduce the cost of electricity consumption. However, the storage and consumption of electric energy commodities occur at the same time, so the market organizer needs to design the market mechanism to induce the power generation side to reduce the proportion of electricity traded during peak hours and increase the proportion of electricity traded during low hours, to guide the power consumption side to increase the proportion of electricity traded during low hours and raise the revenue of the power generation side during low hours. Finally, through the behavior correction of both power generation and consumption sides, the price change curve of electric energy is symmetrically distributed above and below the value of electric energy, so that the market goal of widening the peak-valley price difference and narrowing the peak-valley difference of electricity consumption can be achieved while ensuring the efficient allocation of market resources.


## 3.2. Generation-Side Clearing Model under Multitime Coupling

### 3.2.1. Study of Coupling Methods

(1) Electricity Coupling. In practice, the trading rules for medium- and long-term power trading in time slots are as follows: the power trading time slots are divided into peak, sharp, valley, and flat slots, and when the market is mature, the power generation and consumption sides can declare the power and price at the same time. According to the quotation information provided by the market players, the trading institution will sort the prices on the power generation side in the order low to high and the prices on the electricity consumption side in the order high to low, match the high with the low, and aggregate the clearing or marginal clearing until the price on the electricity consumption side is lower than the price on the power generation side or one of the two is fully traded.We assume that according to the abovementioned rules, the pretransaction quantity of the four sections of peak, flat, valley, and tip can be obtained asQpeak, Qflat, Qvalley, and Qc−peak.(1)
WhenQvalley≠0, according to the historical performance of market entities and combined with the peak-to-valley ratio tradable coefficient given by the market ηpeak and ηc−peak, calculate the ideal value of peak segments Q˜peak and Q˜c−peak:(21)Q˜peak=ηpeak⋅Qpeak,Q˜c−peak=ηc−peak⋅Qc−peak.At this point, the tradable coefficient of peak-valley ratio and the optimal peak-valley ratio mentioned above can be given a reasonable value by the trading institution in combination with the actual market situation (such as historical peak-valley ratio data and future development planning), which will change with the different stages of the market.Note: the difference between the ideal value and the pretransaction structure is the quantity of excess trade.If the ideal value is greater than or equal to the pretransaction result, the contract will be executed according to the pretransaction result, and the excess transaction quantity is 0. If the ideal value is less than the pretransaction result, then the overtrading quantity is calculated as∆Qpeak and ∆Qc−peak:(22)∆Qpeak=Qpeak−Q˜peak,∆Qc−peak=Qc−peak−Q˜c−peak.(2)
WhenQvalley=0, means that the power plant plays a nonpositive role in subduing the peak-valley difference of power, so set Q˜peak=0 and Q˜c−peak=0. At this point, all the peak and peak preclinched electric quantities are regarded as overtraded electric quantity, that is:(23)∆Qpeak=Qpeak,∆Qc−peak=Qc−peak.(2) Electricity Price Coupling. According to the above rules, the result of pretransaction electricity quantity can also be obtained as follows: Ppeak, Pflat, Pvalley, and Pc−peak. If the amount of overtraded electricity is 0, the contract will be executed according to the result of the preconcluded electricity price. If the amount of excess transaction electricity is not 0, then the transaction income of the excess part is adjusted, which is the correction of the pretransaction electricity price:(24)∆Ppeak=αpeak⋅Ppeak,∆Pc−peak=αc−peak⋅Pc−peak,where αpeak and αc−peak are the adjustment coefficients of the electricity price of peak and peak segments, generally between 0 and 1. The electricity sale income of the overtraded electricity on the power generation side is adjusted as follows:(25)Rex−peak=∆Qpeak×∆Ppeak,Rex−c−peak=∆Qc−peak×∆Pc−peak.That is, when there is no excess traded electricity on the generation side, the revenue from electricity sales on the generation side is as follows:(26)Rtotal=Rpeak+Rflat+Rvalley+Rc−peak=Qpeak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+Qc−peak×Pc−peak.When there is excess traded electricity on the generation side, the revenue from electricity sales on the generation side is adjusted as follows:(27)Rtotal−adjust=Rpeak+Rflat+Rvalley+Rc−peak=∆Qpeak×∆Ppeak+Q˜peak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+∆Qc−peak×∆Pc−peak+Q˜c−peak×Pc−peak.Up to this point, the power trading agency uses the pretraded power results of the valley section on the power generation side as a reference for the pretraded power of the peak and peak sections, and calculates the ideal value of the traded power during the peak and peak periods by combining the market peak-to-valley ratio it wants to achieve. The pretransacted electricity price is adjusted for the part exceeding the ideal value, thus realizing the market regulation means based on physical electricity and limited by economic income. The fees charged can be used as a source of incentive funds for peak reduction and valley filling in the market as a whole, which will be rewarded to the market players who play a positive role in leveling out the peak-to-valley difference in electricity.


### 3.2.2. Market-Clearing Model Considering Multitime Coupling

Suppose there aren sellers in the market and each seller is quoted as(28)P1S,a,P2S,a,⋯,PiS,a,⋯,PnS,aP1S,b,P2S,b,⋯,PiS,b,⋯,PnS,bP1S,c,P2S,c,⋯,PiS,c,⋯,PnS,cP1S,d,P2S,d,⋯,PiS,d,⋯,PnS,d,and the amount as(29)Q1S,a,Q2S,a,⋯,QiS,a,⋯,QnS,aQ1S,b,Q2S,b,⋯,QiS,b,⋯,QnS,bQ1S,c,Q2S,c,⋯,QiS,c,⋯,QnS,cQ1S,d,Q2S,d,⋯,QiS,d,⋯,QnS,d.There arem power purchasers (such as power selling companies and large users), and the quotation of each power purchaser is(30)P1D,a,P2D,a,⋯,PjD,a,⋯,PmD,aP1D,b,P2D,b,⋯,PjD,b,⋯,PmD,bP1D,c,P2D,c,⋯,PjD,c,⋯,PmD,cP1D,d,P2D,d,⋯,PjD,d,⋯,PmD,d,and the amount as(31)Q1D,a,Q2D,a,⋯,QjD,a,⋯,QmD,aQ1D,b,Q2D,b,⋯,QjD,b,⋯,QmD,bQ1D,c,Q2D,c,⋯,QjD,c,⋯,QmD,cQ1D,d,Q2D,d,⋯,QjD,d,⋯,QmD,d.Among them,S and D distinguish the supply side and the demand side, that is, the electricity sale side (generation side) and the electricity purchase side (electricity side). a,b,c,andd represent the peak, flat, valley, and critic-peak period in time-segment trading, respectively. The declared electricity price of the power seller and the power buyer is positive. The declared electric quantity of the purchaser is positive, while the declared electric quantity of the seller is negative.When the market is cleared by the marginal clearing method, the objective function is the maximization of market welfareW, namely:(32)maxW=∑i=1n∑j=1mPjD,a−PiS,aQi,ja+∑i=1n∑j=1mPjD,b−PiS,bQi,jb+∑i=1n∑j=1mPjD,c−PiS,cQi,jc+∑i=1n∑j=1mPjD,d−PiS,dQi,jd−lossF,where F is a penalty parameter.The constraint conditions are as follows:(1)
Supply and demand balance constraint:(33)s.t.∑i=1nQi,j≤Qjd,j=1,⋯,m,∑j=1mQi,j≤Qis,i=1,⋯,n,Qi,j≥0,i=1,⋯,n,j=1,⋯,m.In the formula,Qi,j is the transaction quantity between the power seller i and the power purchaser j. Qis refers to the quantity of electricity declared by seller i; Pis shall declare the electricity price for the electricity seller i; Qjd refers to the quantity of electricity declared by the purchaser j; Pjd shall declare the price of electricity for the purchaser j.(2)
Electricity price constraint:(34)Pi,LS,a≤PiS,a≤Pi,US,a,Pj,LD,a≤PjD,a≤Pj,UD,a,Pi,LS,b≤PiS,b≤Pi,US,b,Pj,LD,b≤PjD,b≤Pj,UD,b,Pi,LS,c≤PiS,c≤Pi,US,c,Pj,LD,c≤PjD,c≤Pj,UD,c,Pi,LS,d≤PiS,d≤Pi,US,d,Pj,LD,d≤PjD,d≤Pj,UD,d.In the formula,Pi,LS,a, Pi,LS,b, Pi,LS,c, and Pi,LS,d, respectively, represent the lower limit of electricity selling price in four periods of peak, flat, valley, and peak; Pi,US,a, Pi,US,b, Pi,US,c, and Pi,US,d, respectively, represent the upper limit of electricity selling price in four periods of peak, flat, valley, and peak; Pj,LD,a and Pj,LD,b and Pj,LD,c and Pj,LD,d, respectively, represent the lower limit of electricity purchase price in four periods of peak, flat, valley, and peak; Pj,UD,a, Pj,UD,b, Pj,UD,c, and Pj,UD,d, respectively, represent the upper limit of electricity purchase price in the four periods of peak, flat, valley, and peak.(3)
Constraint on declared quantity:On the electricity purchasing side, there are two types of market users: large power users and electricity selling companies. For electricity selling companies, they limit their trading shares to not exceed the maximum amount of declaration, otherwise the maximum amount of declaration shall be declared.(35)Qi,ECD,a=minQi,ECD,a,rsharea×QD,a,Qi,ECD,b=minQi,ECD,b,rshareb×QD,b,Qi,ECD,c=minQi,ECD,c,rsharec×QD,c,Qi,ECD,d=minQi,ECD,d,rshared×QD,d.The amount declared by each entity shall not exceed the given direct trading volume.(36)∑i=1nQiS,a≤Qa,∑j=1mQiD,a≤Qa,∑i=1nQiS,b≤Qb,∑j=1mQiD,b≤Qb,∑i=1nQiS,c≤Qc,∑j=1mQiD,c≤Qc,∑i=1nQiS,d≤Qd,∑j=1mQiD,d≤Qd,whereEC represents that the main type of the electricity purchasing side is the electricity selling company; rsharea, rshareb, rsharec, and rshared, respectively, represent the maximum market share that the electricity selling company can occupy in the four periods of peak, flat, valley, and peak; Qa, Qb, Qc, and Qd, respectively, represent the direct trading upper limits of the market at four periods of the peak, flat, valley, and peak.(4)
Constraint of peak-to-valley ratio on the electricity selling side:When declaring, the declared electric quantity of a single e-commerce seller during peak hours shall not exceed the maximum peak-to-valley ratio constraint of the market:(37)QiS,a=minQiS,a,ηh−peak×Qc,QiS,d=minQiS,d,ηh−c−peak×Qc,whereηh−peak=Qh−peak/Qh−valley, ηh−c−peak=Qh−c−peak/Qh−valley, ηh−peak, and ηh−c−peak, respectively, represent the maximum value of the peak/valley segment electric quantity and the peak/valley segment electric quantity.(5)
Price constraint under optimal peak-to-valley ratio:In the objective function, it is the welfare value of the peak market and peak market loss when the e-commerce seller does not meet the optimal peak-to-valley ratio.(38)lossF=lossA+lossD,lossA=0,QiS,a≤ηopt−peak×QiS,c,∑i=1n1−αpeakPiS,aQiS,a−ηopt−peak×QiS,c,others,lossD=0,QiS,d≤ηopt−c−peak×QiS,c,∑i=1n1−αc−peakPiS,dQiS,d−ηopt−c−peak×QiS,c,others,wherelossA represents the welfare value of the market loss in the peak segment, lossD represents the welfare value of the market loss in the peak segment, and ηopt−peak and ηopt−c−peak are the ideal peak-valley coefficient of the peak segment and the critic-peak segment. It can be calculated by the above mentioned method.After solving the model, it is obtained that the volume of transactions of each subject is the sum of transactions in each period:(39)Qi,∆S=Qi,∆S,a+Qi,∆S,b+Qi,∆S,c+Qi,∆S,d=∑j=1mQi,jS,a+∑j=1mQi,jS,b+∑j=1mQi,jS,c+∑j=1mQi,jS,d,Qj,∆D=Qj,∆D,a+Qj,∆D,b+Qj,∆D,c+Qj,∆D,d=∑i=1nQi,jD,a+∑i=1nQi,jD,b+∑i=1nQi,jD,c+∑i=1nQi,jD,d,In the formula,Qi,∆S is the transaction quantity of the first power seller i; Qj,∆D is the transaction quantity of the purchaser j.The final volume of transactions in each segment of the market is as follows:(40)Q∆a=∑i=1nQi,∆S,a=∑j=1mQj,∆D,a,Q∆b=∑i=1nQi,∆S,b=∑j=1mQj,∆D,b,Q∆c=∑i=1nQi,∆S,c=∑j=1mQj,∆D,c,Q∆d=∑i=1nQi,∆S,d=∑j=1mQj,∆D,d.


## 3.2.1. Study of Coupling Methods

(1) Electricity Coupling. In practice, the trading rules for medium- and long-term power trading in time slots are as follows: the power trading time slots are divided into peak, sharp, valley, and flat slots, and when the market is mature, the power generation and consumption sides can declare the power and price at the same time. According to the quotation information provided by the market players, the trading institution will sort the prices on the power generation side in the order low to high and the prices on the electricity consumption side in the order high to low, match the high with the low, and aggregate the clearing or marginal clearing until the price on the electricity consumption side is lower than the price on the power generation side or one of the two is fully traded.We assume that according to the abovementioned rules, the pretransaction quantity of the four sections of peak, flat, valley, and tip can be obtained asQpeak, Qflat, Qvalley, and Qc−peak.(1)
WhenQvalley≠0, according to the historical performance of market entities and combined with the peak-to-valley ratio tradable coefficient given by the market ηpeak and ηc−peak, calculate the ideal value of peak segments Q˜peak and Q˜c−peak:(21)Q˜peak=ηpeak⋅Qpeak,Q˜c−peak=ηc−peak⋅Qc−peak.At this point, the tradable coefficient of peak-valley ratio and the optimal peak-valley ratio mentioned above can be given a reasonable value by the trading institution in combination with the actual market situation (such as historical peak-valley ratio data and future development planning), which will change with the different stages of the market.Note: the difference between the ideal value and the pretransaction structure is the quantity of excess trade.If the ideal value is greater than or equal to the pretransaction result, the contract will be executed according to the pretransaction result, and the excess transaction quantity is 0. If the ideal value is less than the pretransaction result, then the overtrading quantity is calculated as∆Qpeak and ∆Qc−peak:(22)∆Qpeak=Qpeak−Q˜peak,∆Qc−peak=Qc−peak−Q˜c−peak.(2)
WhenQvalley=0, means that the power plant plays a nonpositive role in subduing the peak-valley difference of power, so set Q˜peak=0 and Q˜c−peak=0. At this point, all the peak and peak preclinched electric quantities are regarded as overtraded electric quantity, that is:(23)∆Qpeak=Qpeak,∆Qc−peak=Qc−peak.(2) Electricity Price Coupling. According to the above rules, the result of pretransaction electricity quantity can also be obtained as follows: Ppeak, Pflat, Pvalley, and Pc−peak. If the amount of overtraded electricity is 0, the contract will be executed according to the result of the preconcluded electricity price. If the amount of excess transaction electricity is not 0, then the transaction income of the excess part is adjusted, which is the correction of the pretransaction electricity price:(24)∆Ppeak=αpeak⋅Ppeak,∆Pc−peak=αc−peak⋅Pc−peak,where αpeak and αc−peak are the adjustment coefficients of the electricity price of peak and peak segments, generally between 0 and 1. The electricity sale income of the overtraded electricity on the power generation side is adjusted as follows:(25)Rex−peak=∆Qpeak×∆Ppeak,Rex−c−peak=∆Qc−peak×∆Pc−peak.That is, when there is no excess traded electricity on the generation side, the revenue from electricity sales on the generation side is as follows:(26)Rtotal=Rpeak+Rflat+Rvalley+Rc−peak=Qpeak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+Qc−peak×Pc−peak.When there is excess traded electricity on the generation side, the revenue from electricity sales on the generation side is adjusted as follows:(27)Rtotal−adjust=Rpeak+Rflat+Rvalley+Rc−peak=∆Qpeak×∆Ppeak+Q˜peak×Ppeak+Qflat×Pflat+Qvalley×Pvalley+∆Qc−peak×∆Pc−peak+Q˜c−peak×Pc−peak.Up to this point, the power trading agency uses the pretraded power results of the valley section on the power generation side as a reference for the pretraded power of the peak and peak sections, and calculates the ideal value of the traded power during the peak and peak periods by combining the market peak-to-valley ratio it wants to achieve. The pretransacted electricity price is adjusted for the part exceeding the ideal value, thus realizing the market regulation means based on physical electricity and limited by economic income. The fees charged can be used as a source of incentive funds for peak reduction and valley filling in the market as a whole, which will be rewarded to the market players who play a positive role in leveling out the peak-to-valley difference in electricity.


## 3.2.2. Market-Clearing Model Considering Multitime Coupling

Suppose there aren sellers in the market and each seller is quoted as(28)P1S,a,P2S,a,⋯,PiS,a,⋯,PnS,aP1S,b,P2S,b,⋯,PiS,b,⋯,PnS,bP1S,c,P2S,c,⋯,PiS,c,⋯,PnS,cP1S,d,P2S,d,⋯,PiS,d,⋯,PnS,d,and the amount as(29)Q1S,a,Q2S,a,⋯,QiS,a,⋯,QnS,aQ1S,b,Q2S,b,⋯,QiS,b,⋯,QnS,bQ1S,c,Q2S,c,⋯,QiS,c,⋯,QnS,cQ1S,d,Q2S,d,⋯,QiS,d,⋯,QnS,d.There arem power purchasers (such as power selling companies and large users), and the quotation of each power purchaser is(30)P1D,a,P2D,a,⋯,PjD,a,⋯,PmD,aP1D,b,P2D,b,⋯,PjD,b,⋯,PmD,bP1D,c,P2D,c,⋯,PjD,c,⋯,PmD,cP1D,d,P2D,d,⋯,PjD,d,⋯,PmD,d,and the amount as(31)Q1D,a,Q2D,a,⋯,QjD,a,⋯,QmD,aQ1D,b,Q2D,b,⋯,QjD,b,⋯,QmD,bQ1D,c,Q2D,c,⋯,QjD,c,⋯,QmD,cQ1D,d,Q2D,d,⋯,QjD,d,⋯,QmD,d.Among them,S and D distinguish the supply side and the demand side, that is, the electricity sale side (generation side) and the electricity purchase side (electricity side). a,b,c,andd represent the peak, flat, valley, and critic-peak period in time-segment trading, respectively. The declared electricity price of the power seller and the power buyer is positive. The declared electric quantity of the purchaser is positive, while the declared electric quantity of the seller is negative.When the market is cleared by the marginal clearing method, the objective function is the maximization of market welfareW, namely:(32)maxW=∑i=1n∑j=1mPjD,a−PiS,aQi,ja+∑i=1n∑j=1mPjD,b−PiS,bQi,jb+∑i=1n∑j=1mPjD,c−PiS,cQi,jc+∑i=1n∑j=1mPjD,d−PiS,dQi,jd−lossF,where F is a penalty parameter.The constraint conditions are as follows:(1)
Supply and demand balance constraint:(33)s.t.∑i=1nQi,j≤Qjd,j=1,⋯,m,∑j=1mQi,j≤Qis,i=1,⋯,n,Qi,j≥0,i=1,⋯,n,j=1,⋯,m.In the formula,Qi,j is the transaction quantity between the power seller i and the power purchaser j. Qis refers to the quantity of electricity declared by seller i; Pis shall declare the electricity price for the electricity seller i; Qjd refers to the quantity of electricity declared by the purchaser j; Pjd shall declare the price of electricity for the purchaser j.(2)
Electricity price constraint:(34)Pi,LS,a≤PiS,a≤Pi,US,a,Pj,LD,a≤PjD,a≤Pj,UD,a,Pi,LS,b≤PiS,b≤Pi,US,b,Pj,LD,b≤PjD,b≤Pj,UD,b,Pi,LS,c≤PiS,c≤Pi,US,c,Pj,LD,c≤PjD,c≤Pj,UD,c,Pi,LS,d≤PiS,d≤Pi,US,d,Pj,LD,d≤PjD,d≤Pj,UD,d.In the formula,Pi,LS,a, Pi,LS,b, Pi,LS,c, and Pi,LS,d, respectively, represent the lower limit of electricity selling price in four periods of peak, flat, valley, and peak; Pi,US,a, Pi,US,b, Pi,US,c, and Pi,US,d, respectively, represent the upper limit of electricity selling price in four periods of peak, flat, valley, and peak; Pj,LD,a and Pj,LD,b and Pj,LD,c and Pj,LD,d, respectively, represent the lower limit of electricity purchase price in four periods of peak, flat, valley, and peak; Pj,UD,a, Pj,UD,b, Pj,UD,c, and Pj,UD,d, respectively, represent the upper limit of electricity purchase price in the four periods of peak, flat, valley, and peak.(3)
Constraint on declared quantity:On the electricity purchasing side, there are two types of market users: large power users and electricity selling companies. For electricity selling companies, they limit their trading shares to not exceed the maximum amount of declaration, otherwise the maximum amount of declaration shall be declared.(35)Qi,ECD,a=minQi,ECD,a,rsharea×QD,a,Qi,ECD,b=minQi,ECD,b,rshareb×QD,b,Qi,ECD,c=minQi,ECD,c,rsharec×QD,c,Qi,ECD,d=minQi,ECD,d,rshared×QD,d.The amount declared by each entity shall not exceed the given direct trading volume.(36)∑i=1nQiS,a≤Qa,∑j=1mQiD,a≤Qa,∑i=1nQiS,b≤Qb,∑j=1mQiD,b≤Qb,∑i=1nQiS,c≤Qc,∑j=1mQiD,c≤Qc,∑i=1nQiS,d≤Qd,∑j=1mQiD,d≤Qd,whereEC represents that the main type of the electricity purchasing side is the electricity selling company; rsharea, rshareb, rsharec, and rshared, respectively, represent the maximum market share that the electricity selling company can occupy in the four periods of peak, flat, valley, and peak; Qa, Qb, Qc, and Qd, respectively, represent the direct trading upper limits of the market at four periods of the peak, flat, valley, and peak.(4)
Constraint of peak-to-valley ratio on the electricity selling side:When declaring, the declared electric quantity of a single e-commerce seller during peak hours shall not exceed the maximum peak-to-valley ratio constraint of the market:(37)QiS,a=minQiS,a,ηh−peak×Qc,QiS,d=minQiS,d,ηh−c−peak×Qc,whereηh−peak=Qh−peak/Qh−valley, ηh−c−peak=Qh−c−peak/Qh−valley, ηh−peak, and ηh−c−peak, respectively, represent the maximum value of the peak/valley segment electric quantity and the peak/valley segment electric quantity.(5)
Price constraint under optimal peak-to-valley ratio:In the objective function, it is the welfare value of the peak market and peak market loss when the e-commerce seller does not meet the optimal peak-to-valley ratio.(38)lossF=lossA+lossD,lossA=0,QiS,a≤ηopt−peak×QiS,c,∑i=1n1−αpeakPiS,aQiS,a−ηopt−peak×QiS,c,others,lossD=0,QiS,d≤ηopt−c−peak×QiS,c,∑i=1n1−αc−peakPiS,dQiS,d−ηopt−c−peak×QiS,c,others,wherelossA represents the welfare value of the market loss in the peak segment, lossD represents the welfare value of the market loss in the peak segment, and ηopt−peak and ηopt−c−peak are the ideal peak-valley coefficient of the peak segment and the critic-peak segment. It can be calculated by the above mentioned method.After solving the model, it is obtained that the volume of transactions of each subject is the sum of transactions in each period:(39)Qi,∆S=Qi,∆S,a+Qi,∆S,b+Qi,∆S,c+Qi,∆S,d=∑j=1mQi,jS,a+∑j=1mQi,jS,b+∑j=1mQi,jS,c+∑j=1mQi,jS,d,Qj,∆D=Qj,∆D,a+Qj,∆D,b+Qj,∆D,c+Qj,∆D,d=∑i=1nQi,jD,a+∑i=1nQi,jD,b+∑i=1nQi,jD,c+∑i=1nQi,jD,d,In the formula,Qi,∆S is the transaction quantity of the first power seller i; Qj,∆D is the transaction quantity of the purchaser j.The final volume of transactions in each segment of the market is as follows:(40)Q∆a=∑i=1nQi,∆S,a=∑j=1mQj,∆D,a,Q∆b=∑i=1nQi,∆S,b=∑j=1mQj,∆D,b,Q∆c=∑i=1nQi,∆S,c=∑j=1mQj,∆D,c,Q∆d=∑i=1nQi,∆S,d=∑j=1mQj,∆D,d.


## 3.3. Incentive Mechanism of the Electricity Consumption Side under Multihour Coupling

For the electricity consumers, the incentive to change their own electricity consumption behavior comes from the market—if the cost of purchasing electricity in the peak and peak hours increases and the cost of purchasing electricity in the valley hours decreases, the consumers will choose to shift their electricity demand as much as possible, shifting the peak and peak electricity consumption to the flat and valley electricity consumption. Therefore, the market can promote the use of electricity to achieve peak and valley reduction by means of economic incentives, thereby reducing the peak-valley difference in electricity and widening the peak-valley difference in electricity prices. The process of capital flow in the electricity market at this point is shown in Figure6.Figure 6
Schematic diagram of user-side incentives under multitime coupling.The incentive mechanism for the user side mainly contains the following elements.


### 3.3.1. Incentive Principle

In order to encourage customers to use more electricity during the low hours, the design mechanism gives incentives for more electricity use in the low hours or less electricity use in the peak hours.


### 3.3.2. Incentive Method

Because the power and price each time will fluctuate with market changes under time-sharing trading, and it is impossible to guarantee the same price of electricity in consecutive moments, so the means of power incentive is not applicable to time-sharing trading. Therefore, under the time-sharing trading mode, the incentive on the user side mainly takes the form of an economic incentive, which is aimed at the users who actively participate in the trading during the low valley hours to further reduce the cost of electricity use during the low valley hours.


### 3.3.3. Incentive Process

(1)
Determining the total incentive amount:Figure6 shows that incentive funds on the user side come from excess transaction fees on the power generation side. Therefore, the total amount of funds that can be rewarded on the user side is ΔRreturn:(41)∆Rreturn=∆Rreturn−peak+∆Rreturn−valley=1−αpeak×Ppeak×∆Qpeak+1−αvalley×Pvalley×∆Qvalley.(2)
Determining the compensation amountrreturn−valley per unit of electric quantity during the valley period:(42)rreturn−valley=∆RreturnQvalley,where∆Rreturn is the total incentive amount; Qvalley is the volume of transactions during the trough period of the market.(3)
Determining the compensation benefits of each subject:(43)Ri=rreturn−valley×Qiu,whereRi is the trough electric excitation obtained by the user i; Qiu is the transaction quantity of the first user in the trough period.It follows that(44)∑Qiu=Q谷,∑Ri=∆Rreturn.The electricity market funds realize the flow from the generation side to the customer side, and this flow process will push the customer side to change their own electricity consumption behavior and push the power system to reduce the peak-to-valley difference.


## 3.3.1. Incentive Principle

In order to encourage customers to use more electricity during the low hours, the design mechanism gives incentives for more electricity use in the low hours or less electricity use in the peak hours.


## 3.3.2. Incentive Method

Because the power and price each time will fluctuate with market changes under time-sharing trading, and it is impossible to guarantee the same price of electricity in consecutive moments, so the means of power incentive is not applicable to time-sharing trading. Therefore, under the time-sharing trading mode, the incentive on the user side mainly takes the form of an economic incentive, which is aimed at the users who actively participate in the trading during the low valley hours to further reduce the cost of electricity use during the low valley hours.


## 3.3.3. Incentive Process

(1)
Determining the total incentive amount:Figure6 shows that incentive funds on the user side come from excess transaction fees on the power generation side. Therefore, the total amount of funds that can be rewarded on the user side is ΔRreturn:(41)∆Rreturn=∆Rreturn−peak+∆Rreturn−valley=1−αpeak×Ppeak×∆Qpeak+1−αvalley×Pvalley×∆Qvalley.(2)
Determining the compensation amountrreturn−valley per unit of electric quantity during the valley period:(42)rreturn−valley=∆RreturnQvalley,where∆Rreturn is the total incentive amount; Qvalley is the volume of transactions during the trough period of the market.(3)
Determining the compensation benefits of each subject:(43)Ri=rreturn−valley×Qiu,whereRi is the trough electric excitation obtained by the user i; Qiu is the transaction quantity of the first user in the trough period.It follows that(44)∑Qiu=Q谷,∑Ri=∆Rreturn.The electricity market funds realize the flow from the generation side to the customer side, and this flow process will push the customer side to change their own electricity consumption behavior and push the power system to reduce the peak-to-valley difference.


## 3.4. Effect Analysis

### 3.4.1. Analysis of Generation-Side Revenue

Under the multihour coupling, the total revenue of power generation entities participating in the time-sharing transactions is as follows:(45)RiS=RiS,a+RiS,b+RiS,c+RiS,d,where(46)RiS,a=Qi,∆S,a×PMCa,Qi,∆S,a≤ηopt−peak×Qc,ηopt−peak×Qc×PMCa+Qi,∆S,a−ηopt−peak×Qc×PMCa×αpeak,Qi,∆S,a>ηopt−peak×Qc,RiS,b=Qi,∆S,b×PMCb,RiS,c=Qi,∆S,c×PMCc,RiS,d=Qi,∆S,d×PMCd,Qi,∆S,d≤ηopt−c−peak×Qc,ηopt−c−peak×Qc×PMCd+Qi,∆S,d−ηopt−c−peak×Qc×PMCd×αc−peak,Qi,∆S,d>ηopt−c−peak×Qc.In the formulaRiS,a, RiS,b, RiS,c, and RiS,d, respectively, represent the electricity sales revenue of the power generation subject in the peak, flat, valley, and tip segments of the market; PMCa, PMCb, PMCc, and PMCd, respectively, represent the clearing price of peak, flat, valley, and top four periods.According to the income expression of power generation companies, it can be seen that when the demand of the valley segmentQc is known, the income of power generation companies at peak and critic-peak segments depends on the relationship between Qi,∆S,d and the ideal value. When PMCa×αc−peak<PMCc and PMCd×α尖<PMCc, the power generation will transfer the part of the peak and peak electric quantity beyond the ideal value to the valley, so as to maximize the electricity sales income. On the contrary, power producers will continue to release electricity to the peak and peak segments for sale until the market demand is met.


### 3.4.2. Analysis of Power Consumption Side Benefits

The cost of electricity consumption on the electricity consumption side under multihour coupling can be expressed by the following equation:(47)CjD=CjD,a+CjD,b+CjD,c+CjD,d−RCjc=Qj,∆D,a×PMCa+Qj,∆D,b×PMCb+Qj,∆D,c×PMCc−∆RCQ∆D,c+Qj,∆D,d×PMCd,RCjc=∆RCQ∆D,c×Qj,∆D,c.In the formula, RCjc represents the incentive obtained by the power consumption subject at the low ebb; Qj,∆D,c is the transaction amount of the valley segment of the main body of electricity consumption; Q∆D,c is the total volume of transactions by all users in the valley.It can be seen that customers are incentivized by low valley electricity consumption to boost low valley electricity consumption and reduce the overall cost of electricity consumption. Until the cost of changing electricity consumption behavior is equal to the benefit obtained, users will stop peak and valley cutting behavior.


### 3.4.3. Analysis of Market Cycle Effects

From the perspective of the market organizer, whenPMCa×αpeak<PMCc, PMCd×αc−peak<PMCc, Qi,∆S,a>ηopt−peak×Qc, and Qi,∆S,d>ηopt−c−peak×Qc, the power producer will transfer the part of the peak and tip section power exceeding the ideal value to the valley section, and the transferred power will be as follows:(48)∆trans=∑i=1mQi,∆S,a−ηopt−peak×Qc+∑i=1mQi,∆S,d−ηopt−c−peak×Qc.Then, the overall market peak-to-valley ratio at this point becomes(49)ηmarket=ηopt−peak+ηopt−c−peak×QcQ∆D,c+∆trans.The peak-valley spread becomes(50)∆P=maxPMCa,PMCd−PMCc−∆RCQ∆D,c.Under the two-sided choice, the peak-to-valley difference of electricity in the market narrows and the peak-to-valley difference in electricity price increases.At this point, the value of the market fluctuates as shown in Figure7. The revenue in the peak and spike hours shifts to the low valley segment, and at the same time, the demand for electricity in the peak and spike hours shifts to the low valley segment.Figure 7
Electricity price distribution after multitime coupling.


## 3.4.1. Analysis of Generation-Side Revenue

Under the multihour coupling, the total revenue of power generation entities participating in the time-sharing transactions is as follows:(45)RiS=RiS,a+RiS,b+RiS,c+RiS,d,where(46)RiS,a=Qi,∆S,a×PMCa,Qi,∆S,a≤ηopt−peak×Qc,ηopt−peak×Qc×PMCa+Qi,∆S,a−ηopt−peak×Qc×PMCa×αpeak,Qi,∆S,a>ηopt−peak×Qc,RiS,b=Qi,∆S,b×PMCb,RiS,c=Qi,∆S,c×PMCc,RiS,d=Qi,∆S,d×PMCd,Qi,∆S,d≤ηopt−c−peak×Qc,ηopt−c−peak×Qc×PMCd+Qi,∆S,d−ηopt−c−peak×Qc×PMCd×αc−peak,Qi,∆S,d>ηopt−c−peak×Qc.In the formulaRiS,a, RiS,b, RiS,c, and RiS,d, respectively, represent the electricity sales revenue of the power generation subject in the peak, flat, valley, and tip segments of the market; PMCa, PMCb, PMCc, and PMCd, respectively, represent the clearing price of peak, flat, valley, and top four periods.According to the income expression of power generation companies, it can be seen that when the demand of the valley segmentQc is known, the income of power generation companies at peak and critic-peak segments depends on the relationship between Qi,∆S,d and the ideal value. When PMCa×αc−peak<PMCc and PMCd×α尖<PMCc, the power generation will transfer the part of the peak and peak electric quantity beyond the ideal value to the valley, so as to maximize the electricity sales income. On the contrary, power producers will continue to release electricity to the peak and peak segments for sale until the market demand is met.


## 3.4.2. Analysis of Power Consumption Side Benefits

The cost of electricity consumption on the electricity consumption side under multihour coupling can be expressed by the following equation:(47)CjD=CjD,a+CjD,b+CjD,c+CjD,d−RCjc=Qj,∆D,a×PMCa+Qj,∆D,b×PMCb+Qj,∆D,c×PMCc−∆RCQ∆D,c+Qj,∆D,d×PMCd,RCjc=∆RCQ∆D,c×Qj,∆D,c.In the formula, RCjc represents the incentive obtained by the power consumption subject at the low ebb; Qj,∆D,c is the transaction amount of the valley segment of the main body of electricity consumption; Q∆D,c is the total volume of transactions by all users in the valley.It can be seen that customers are incentivized by low valley electricity consumption to boost low valley electricity consumption and reduce the overall cost of electricity consumption. Until the cost of changing electricity consumption behavior is equal to the benefit obtained, users will stop peak and valley cutting behavior.


## 3.4.3. Analysis of Market Cycle Effects

From the perspective of the market organizer, whenPMCa×αpeak<PMCc, PMCd×αc−peak<PMCc, Qi,∆S,a>ηopt−peak×Qc, and Qi,∆S,d>ηopt−c−peak×Qc, the power producer will transfer the part of the peak and tip section power exceeding the ideal value to the valley section, and the transferred power will be as follows:(48)∆trans=∑i=1mQi,∆S,a−ηopt−peak×Qc+∑i=1mQi,∆S,d−ηopt−c−peak×Qc.Then, the overall market peak-to-valley ratio at this point becomes(49)ηmarket=ηopt−peak+ηopt−c−peak×QcQ∆D,c+∆trans.The peak-valley spread becomes(50)∆P=maxPMCa,PMCd−PMCc−∆RCQ∆D,c.Under the two-sided choice, the peak-to-valley difference of electricity in the market narrows and the peak-to-valley difference in electricity price increases.At this point, the value of the market fluctuates as shown in Figure7. The revenue in the peak and spike hours shifts to the low valley segment, and at the same time, the demand for electricity in the peak and spike hours shifts to the low valley segment.Figure 7
Electricity price distribution after multitime coupling.


## 4. Example Analysis

### 4.1. Example Overview

This article selects a province in China that carries out medium- and long-termtime-slot trading as the research object. Its time period power division and trading price limit are shown in Table2.Table 2
Power division and price limit.
PeakFlatValleyCritical-peakPower ratio13.2%47.6%29.8%9.4%Price ceiling0.61 yuan/kWh0.4143 yuan/kWh0.245 yuan/kWh0.91 yuan/kWhIn this article, we focus on the coupling of peak, sharp, and valley segments and do not impose constraints on flat segment trading to encourage market players to carry out flat segment trading normally and ensure market vitality. Therefore, the following research takes the trading data of the peak section, peak section and valley section, and does not conduct any research on the flat section data. The declared data of a certain monthly centralized competitive transaction that meets the market restrictions are shown in Tables3 and 4, where the unit of electricity is billion kWh and the unit of electricity price is yuan/kWh.Table 3
Power purchase side declaration information.
PeakCritical-peakValleyElectricityPriceElectricityPriceElectricityPriceUser 17918.5560.615638.9726017876.740.22User 22322.160.464557.1499114447.130.24User 36399.4010.323600.3578411413.90.26User 42869.350.422043.325536477.7750.25User 55055.820.541653.659575242.4520.28Table 4
Information of electricity sales side declaration.
PeakCritical-peakValleyElectricityPriceElectricityElectricityPriceElectricityPower plant 12322.0610.382963.8740.4517876.740.24Power plant 23532.4790.332515.5530.7214447.130.26Power plant 32544.960.312096.2080.5811413.90.21Power plant 44162.0360.451812.320.326477.7750.20Power plant 52943.6120.411653.5890.545242.4520.29


### 4.2. Trading Results under Different Trading Mechanisms

#### 4.2.1. Independent Clearing Mode for Each Time Period

Under the independent clearing mode, the trading results of peak and valley segments are independent and do not affect each other. All three segments are cleared by matching high and low, and the transaction results are shown in Tables5 and 6.Table 5
Trading results of power purchase side in independent clearing mode.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityUser 17918.5645.50368.4859.000.0024.50User 22322.1645.504557.1559.000.0024.50User 30.0045.503600.3659.0011413.9024.50User 40.0045.500.0059.005130.6324.50User 55055.8245.500.0059.005242.4524.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—Table 6
Results of power sales side transactions under the independent clearing model.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityPower plant 12322.0645.502963.8759.009396.1124.50Power plant 23532.4845.500.0059.000.0024.50Power plant 32544.9645.502096.2159.006645.4324.50Power plant 43953.4345.501812.3259.005745.4424.50Power plant 52943.6145.501653.5959.000.0024.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—


#### 4.2.2. Multiperiod Coupling Clearance Mode

In the multiperiod coupling clearance mode, the trading results of the power plant in the peak and peak segments are related to the trading results of the valley segments. Compared with the independent clearance mode, there are more constraint conditions such as electricity coupling and price coupling. Among them, electric quantity coupling is reflected in parametersηd−peak and ηd−c−peak, which represents the peak-to-valley ratio state expected by market operation. The coupling condition of electricity price is reflected in the parameter αpeak and αc−peak, which represents the overtrading price of the overtrading part of the peak and tip section of the power plant. Different parameter values represent different market schemes, and their trading results are shown in Table 7. Changes in the income of market entities under different schemes are shown in Table 8, where a negative value represents expenditure and a positive value represents income.Table 7
Values of different parameters and their trading results in the multiperiod coupling clearing mode.
Numberηd−peakηd−c−peakαpeakαc−peakThe volume of electricity tradedDifference in priceSocial welfare①0.700.390045609.5134.50713970.13②0.700.391145609.5152.50323396.85③0.700.390.50.545609.5143.50517858.21④0.350.200045609.5134.50713970.13⑤0.350.201145609.5163.83135472.60⑥0.350.200.50.545609.5149.16424721.36⑦0.40.250.20.445609.5142.62574501.47Table 8
Comparison of earnings of each market player under different scenarios.
①②③④⑤⑥⑦User 1−326605.03−263794.84−199868.02−326605.03−326605.03−326605.03−326605.03User 2−358274.95−325753.22−325753.22−358274.95−358274.95−358274.95−358274.95User 3−375234.00−310330.02−401195.79−492061.55−188994.66−340528.11−421236.70User 4−125700.39−44010.77−84855.58−125700.3910530.33−57585.03−92945.08User 5−194649.09−207097.35−248832.39−323089.16−183889.24−253489.20−289944.18Power plant 1494472.64484121.35462684.84494472.64430478.19462475.41478623.69Power plant 2136000.430.0068000.21136000.430.0068000.21107729.48Power plant 3384470.19364533.02338303.57384470.19330776.09357623.14372869.11Power plant 4399897.04302331.84286070.97399897.04285979.28342938.16381654.26Power plant 5210890.780.00105445.39210890.780.00105445.39148129.41


### 4.3. Analysis of Transaction Results

The seven different trading schemes in Table7, respectively, represent different coupling degrees of electricity quantity and electricity price. In Scheme ①, the values of ηd−peak and ηd−c−peak are the market result values when each period is independently cleared. In this case, the values of αpeak and αc−peak is 0, which means that the excess trading volume of the power plant in the peak and peak segments is not processed. Therefore, the price difference at this time is still 34.50 minutes/kWh in the independent clearing mode, and the social welfare value is 713970.13. In Schemes ② and ③, the coupling parameters of electricity price are adjusted on the basis of Scheme ①. When αpeak and αc−peak is 1, it represents that the excess returns of the excess trading volume in the peak and peak segments of the power plant are all accounted for by the valley segment market. Therefore, the social welfare value at this time is reduced compared with that in Scheme ①.Scheme ④ represents thatηd−peak and ηd−c−peak are reduced on the basis of Scheme ①. Since there is no electricity price coupling at this time, all transaction results are consistent with Scheme ①. Schemes ⑤ and ⑥, respectively, represent that strict and relatively loose coupling constraints of electricity price are added on the basis of Scheme ④. In this case, the social welfare value gets the minimum value in Scheme ⑤, which means that the excessively strict coupling of electricity quantity and electricity price will lose their incentive effect, resulting in the lack of development space of the market as a whole. Scheme ⑦ represents the general level of market practice, which can reduce the peak-valley ratio and enlarge the peak-valley spread on the basis of ensuring the welfare level.Based on this example, this article studies the general relationship between peak-to-trough ratio coefficientη, price adjustment coefficient α, and changes in the social welfare value. The results are shown in Table 9, and the graphical display of the corresponding relationship is shown in Figure 8.Table 9
Correspondence of peak-to-valley ratio coefficient, price adjustment coefficient, and social welfare value.
0.10.20.30.40.50.60.70.80.910.16700856285215869585453955038314622684207043791413375782960140.26784736452976121225990575457715125964794204462454130703798940.36848946593946338946083955828955573955318965063964808974553970.46881096652516423936195345966765738185509595281015052434823840.56892036668636445236221845998445775045551645328255104854881450.66917036803706690376577056463726350396237066123736010405897070.76938926825596717426606726496036385336274646163946053245942550.86951536838206724876611546498226384896271566158236044905931570.96961346848026621366621366508036394706281376168046054715941381696919685587674254662921651588640255628922617589606256594923Figure 8
Relationship between peak-valley ratio coefficient, price adjustment coefficient, and social welfare.The example shows that the two tools proposed in this article, the peak-to-valley ratio factor and the price regulation factor, complement each other. When the market wishes to narrow the peak-to-valley ratio coefficient, a more stringent price regulation instrument can be used to adjust the price regulation coefficient value toward 1, or even higher; when the market allows a larger peak-to-valley ratio, the peak segment market can be stimulated by relaxing the tariff coupling effect. Overall, the multihour coupling trading mechanism allows market organizers to balance physical security and economic efficiency by combining both electricity coupling and tariff coupling. Market organizers can reasonably use physical and economic means to guide the market trading results within the scope of social welfare in line with market development requirements, so as to achieve the goal of narrowing the peak-to-valley power difference and widening the peak-to-valley price difference.


## 4.1. Example Overview

This article selects a province in China that carries out medium- and long-termtime-slot trading as the research object. Its time period power division and trading price limit are shown in Table2.Table 2
Power division and price limit.
PeakFlatValleyCritical-peakPower ratio13.2%47.6%29.8%9.4%Price ceiling0.61 yuan/kWh0.4143 yuan/kWh0.245 yuan/kWh0.91 yuan/kWhIn this article, we focus on the coupling of peak, sharp, and valley segments and do not impose constraints on flat segment trading to encourage market players to carry out flat segment trading normally and ensure market vitality. Therefore, the following research takes the trading data of the peak section, peak section and valley section, and does not conduct any research on the flat section data. The declared data of a certain monthly centralized competitive transaction that meets the market restrictions are shown in Tables3 and 4, where the unit of electricity is billion kWh and the unit of electricity price is yuan/kWh.Table 3
Power purchase side declaration information.
PeakCritical-peakValleyElectricityPriceElectricityPriceElectricityPriceUser 17918.5560.615638.9726017876.740.22User 22322.160.464557.1499114447.130.24User 36399.4010.323600.3578411413.90.26User 42869.350.422043.325536477.7750.25User 55055.820.541653.659575242.4520.28Table 4
Information of electricity sales side declaration.
PeakCritical-peakValleyElectricityPriceElectricityElectricityPriceElectricityPower plant 12322.0610.382963.8740.4517876.740.24Power plant 23532.4790.332515.5530.7214447.130.26Power plant 32544.960.312096.2080.5811413.90.21Power plant 44162.0360.451812.320.326477.7750.20Power plant 52943.6120.411653.5890.545242.4520.29


## 4.2. Trading Results under Different Trading Mechanisms

### 4.2.1. Independent Clearing Mode for Each Time Period

Under the independent clearing mode, the trading results of peak and valley segments are independent and do not affect each other. All three segments are cleared by matching high and low, and the transaction results are shown in Tables5 and 6.Table 5
Trading results of power purchase side in independent clearing mode.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityUser 17918.5645.50368.4859.000.0024.50User 22322.1645.504557.1559.000.0024.50User 30.0045.503600.3659.0011413.9024.50User 40.0045.500.0059.005130.6324.50User 55055.8245.500.0059.005242.4524.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—Table 6
Results of power sales side transactions under the independent clearing model.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityPower plant 12322.0645.502963.8759.009396.1124.50Power plant 23532.4845.500.0059.000.0024.50Power plant 32544.9645.502096.2159.006645.4324.50Power plant 43953.4345.501812.3259.005745.4424.50Power plant 52943.6145.501653.5959.000.0024.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—


### 4.2.2. Multiperiod Coupling Clearance Mode

In the multiperiod coupling clearance mode, the trading results of the power plant in the peak and peak segments are related to the trading results of the valley segments. Compared with the independent clearance mode, there are more constraint conditions such as electricity coupling and price coupling. Among them, electric quantity coupling is reflected in parametersηd−peak and ηd−c−peak, which represents the peak-to-valley ratio state expected by market operation. The coupling condition of electricity price is reflected in the parameter αpeak and αc−peak, which represents the overtrading price of the overtrading part of the peak and tip section of the power plant. Different parameter values represent different market schemes, and their trading results are shown in Table 7. Changes in the income of market entities under different schemes are shown in Table 8, where a negative value represents expenditure and a positive value represents income.Table 7
Values of different parameters and their trading results in the multiperiod coupling clearing mode.
Numberηd−peakηd−c−peakαpeakαc−peakThe volume of electricity tradedDifference in priceSocial welfare①0.700.390045609.5134.50713970.13②0.700.391145609.5152.50323396.85③0.700.390.50.545609.5143.50517858.21④0.350.200045609.5134.50713970.13⑤0.350.201145609.5163.83135472.60⑥0.350.200.50.545609.5149.16424721.36⑦0.40.250.20.445609.5142.62574501.47Table 8
Comparison of earnings of each market player under different scenarios.
①②③④⑤⑥⑦User 1−326605.03−263794.84−199868.02−326605.03−326605.03−326605.03−326605.03User 2−358274.95−325753.22−325753.22−358274.95−358274.95−358274.95−358274.95User 3−375234.00−310330.02−401195.79−492061.55−188994.66−340528.11−421236.70User 4−125700.39−44010.77−84855.58−125700.3910530.33−57585.03−92945.08User 5−194649.09−207097.35−248832.39−323089.16−183889.24−253489.20−289944.18Power plant 1494472.64484121.35462684.84494472.64430478.19462475.41478623.69Power plant 2136000.430.0068000.21136000.430.0068000.21107729.48Power plant 3384470.19364533.02338303.57384470.19330776.09357623.14372869.11Power plant 4399897.04302331.84286070.97399897.04285979.28342938.16381654.26Power plant 5210890.780.00105445.39210890.780.00105445.39148129.41


## 4.2.1. Independent Clearing Mode for Each Time Period

Under the independent clearing mode, the trading results of peak and valley segments are independent and do not affect each other. All three segments are cleared by matching high and low, and the transaction results are shown in Tables5 and 6.Table 5
Trading results of power purchase side in independent clearing mode.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityUser 17918.5645.50368.4859.000.0024.50User 22322.1645.504557.1559.000.0024.50User 30.0045.503600.3659.0011413.9024.50User 40.0045.500.0059.005130.6324.50User 55055.8245.500.0059.005242.4524.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—Table 6
Results of power sales side transactions under the independent clearing model.
PeakCritical-peakValleyElectricityPriceElectricityPricePriceElectricityPower plant 12322.0645.502963.8759.009396.1124.50Power plant 23532.4845.500.0059.000.0024.50Power plant 32544.9645.502096.2159.006645.4324.50Power plant 43953.4345.501812.3259.005745.4424.50Power plant 52943.6145.501653.5959.000.0024.50Summation15296.54—8525.99—21786.98—Peak-to-valley ratio0.70—0.39—1—


## 4.2.2. Multiperiod Coupling Clearance Mode

In the multiperiod coupling clearance mode, the trading results of the power plant in the peak and peak segments are related to the trading results of the valley segments. Compared with the independent clearance mode, there are more constraint conditions such as electricity coupling and price coupling. Among them, electric quantity coupling is reflected in parametersηd−peak and ηd−c−peak, which represents the peak-to-valley ratio state expected by market operation. The coupling condition of electricity price is reflected in the parameter αpeak and αc−peak, which represents the overtrading price of the overtrading part of the peak and tip section of the power plant. Different parameter values represent different market schemes, and their trading results are shown in Table 7. Changes in the income of market entities under different schemes are shown in Table 8, where a negative value represents expenditure and a positive value represents income.Table 7
Values of different parameters and their trading results in the multiperiod coupling clearing mode.
Numberηd−peakηd−c−peakαpeakαc−peakThe volume of electricity tradedDifference in priceSocial welfare①0.700.390045609.5134.50713970.13②0.700.391145609.5152.50323396.85③0.700.390.50.545609.5143.50517858.21④0.350.200045609.5134.50713970.13⑤0.350.201145609.5163.83135472.60⑥0.350.200.50.545609.5149.16424721.36⑦0.40.250.20.445609.5142.62574501.47Table 8
Comparison of earnings of each market player under different scenarios.
①②③④⑤⑥⑦User 1−326605.03−263794.84−199868.02−326605.03−326605.03−326605.03−326605.03User 2−358274.95−325753.22−325753.22−358274.95−358274.95−358274.95−358274.95User 3−375234.00−310330.02−401195.79−492061.55−188994.66−340528.11−421236.70User 4−125700.39−44010.77−84855.58−125700.3910530.33−57585.03−92945.08User 5−194649.09−207097.35−248832.39−323089.16−183889.24−253489.20−289944.18Power plant 1494472.64484121.35462684.84494472.64430478.19462475.41478623.69Power plant 2136000.430.0068000.21136000.430.0068000.21107729.48Power plant 3384470.19364533.02338303.57384470.19330776.09357623.14372869.11Power plant 4399897.04302331.84286070.97399897.04285979.28342938.16381654.26Power plant 5210890.780.00105445.39210890.780.00105445.39148129.41


## 4.3. Analysis of Transaction Results

The seven different trading schemes in Table7, respectively, represent different coupling degrees of electricity quantity and electricity price. In Scheme ①, the values of ηd−peak and ηd−c−peak are the market result values when each period is independently cleared. In this case, the values of αpeak and αc−peak is 0, which means that the excess trading volume of the power plant in the peak and peak segments is not processed. Therefore, the price difference at this time is still 34.50 minutes/kWh in the independent clearing mode, and the social welfare value is 713970.13. In Schemes ② and ③, the coupling parameters of electricity price are adjusted on the basis of Scheme ①. When αpeak and αc−peak is 1, it represents that the excess returns of the excess trading volume in the peak and peak segments of the power plant are all accounted for by the valley segment market. Therefore, the social welfare value at this time is reduced compared with that in Scheme ①.Scheme ④ represents thatηd−peak and ηd−c−peak are reduced on the basis of Scheme ①. Since there is no electricity price coupling at this time, all transaction results are consistent with Scheme ①. Schemes ⑤ and ⑥, respectively, represent that strict and relatively loose coupling constraints of electricity price are added on the basis of Scheme ④. In this case, the social welfare value gets the minimum value in Scheme ⑤, which means that the excessively strict coupling of electricity quantity and electricity price will lose their incentive effect, resulting in the lack of development space of the market as a whole. Scheme ⑦ represents the general level of market practice, which can reduce the peak-valley ratio and enlarge the peak-valley spread on the basis of ensuring the welfare level.Based on this example, this article studies the general relationship between peak-to-trough ratio coefficientη, price adjustment coefficient α, and changes in the social welfare value. The results are shown in Table 9, and the graphical display of the corresponding relationship is shown in Figure 8.Table 9
Correspondence of peak-to-valley ratio coefficient, price adjustment coefficient, and social welfare value.
0.10.20.30.40.50.60.70.80.910.16700856285215869585453955038314622684207043791413375782960140.26784736452976121225990575457715125964794204462454130703798940.36848946593946338946083955828955573955318965063964808974553970.46881096652516423936195345966765738185509595281015052434823840.56892036668636445236221845998445775045551645328255104854881450.66917036803706690376577056463726350396237066123736010405897070.76938926825596717426606726496036385336274646163946053245942550.86951536838206724876611546498226384896271566158236044905931570.96961346848026621366621366508036394706281376168046054715941381696919685587674254662921651588640255628922617589606256594923Figure 8
Relationship between peak-valley ratio coefficient, price adjustment coefficient, and social welfare.The example shows that the two tools proposed in this article, the peak-to-valley ratio factor and the price regulation factor, complement each other. When the market wishes to narrow the peak-to-valley ratio coefficient, a more stringent price regulation instrument can be used to adjust the price regulation coefficient value toward 1, or even higher; when the market allows a larger peak-to-valley ratio, the peak segment market can be stimulated by relaxing the tariff coupling effect. Overall, the multihour coupling trading mechanism allows market organizers to balance physical security and economic efficiency by combining both electricity coupling and tariff coupling. Market organizers can reasonably use physical and economic means to guide the market trading results within the scope of social welfare in line with market development requirements, so as to achieve the goal of narrowing the peak-to-valley power difference and widening the peak-to-valley price difference.


## 5. Conclusion

In order to achieve the market goal, this article studies the independent clearing mode of each period under the current time-divided trading, which serves as the basis of multiperiod coupling, analyze the demands of market subjects under the time-divided trading, and give solutions. The coupling between electricity quantity and price is realized by combining the physical level with the economic level through multiperiod coupling mode analysis of the power generation side. Under this mechanism, the market organizer will extract part of the revenue of the generation side as the incentive fund for the user side to participate in the off-peak power consumption. The power-side excitation mechanism under multiperiod coupling is studied. To reflect the fairness of the market mechanism, the trading quantity of the users in the trough period is taken as the reference to get the incentive, and all the incentive funds are returned to all the users in the trough period, to realize the efficient flow and incentive effect of funds. Finally, the effect of the multiperiod coupling mechanism is analyzed, and the effect of the market mechanism on the power generation side, the electricity consumption side, and the market as a whole are analyzed by proposing the relationship between the price of electricity and the value of electricity, which proves that the market mechanism can achieve the two objectives of the market.



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*Source: 3029278-2023-02-20.xml*