Research on the stability evolution mechanism and combinatorial optimization decision‐making of multitype heterogeneous energy cooperative operation

Considering the cooperative willingness of multiple heterogeneous energy sources to participate in the alliance, the stability of the cooperative operation of each entity (hereinafter referred to as stability) and the supporting mechanism of its optimal combination to realize the high proportion of new energy generation are studied. Through simulating load peak‐cutting and valley‐filling in the power system, the difference between the load value and the base load in the 24 h of the daily load curve is used as the calculation condition for the supply balance of the alliance. Based on the source‐load power balance model, the feasibility of power data normalization is derived and demonstrated. Simultaneously, taking into account the time‐of‐use price cost of each entity, a multiscale operation cost allocation and stability evolution analysis model for the alliance is constructed using the Shapley value and the largest consistent set method. By comparing the willingness of each entity to engage in the alliance, as well as the multiscale operation stability and economic change rule of different alliances, the results demonstrate that: (1) Alliance 1 has the advantage of economic operation. (2) The common stability period of different alliances is influenced by the participation preferences of each entity (wind power, photovoltaic, and thermal power tend to participate in Alliance 1, while hydropower tends to participate in Alliance 2). (3) Alliance internal restructuring can be carried out by utilizing spatial and temporal difference characteristics of different entities’ participation in alliance preferences, thereby achieving alliance stability and efficient operation. This study provides a theoretical basis for making decisions regarding the optimized stable operation of the alliance.


| INTRODUCTION
With the high proportion of renewable energy integrated into the power system, a new energy-based power system will be formed in the future.Therefore, after the high integration of renewable energy and conventional energy power generation, it is necessary to solve the problems of power system operation stability, operation cooperation stability, income balance distribution, cost balance allocation, and collaborative scheduling optimization.At present, there are mainly the following aspects of research at home and abroad: The first is to optimize the distribution of operating benefits based on multitype energy complementarity.According to the data on renewable energy development in Germany from 2013 to 2020, Schill et al. 1 analyzes that for every 1 MWh increase in the market share of renewable energy, the start-up cost of thermal power plants increases by 0.7 euros.Increasing the proportion of renewable energy generation increases the start-up cost of thermal power, but more flexible biomass power plants and energy storage can offset a certain start-up cost of thermal power.Zhao et al. 2 considered renewable energy and load uncertainty, an economic operation strategy of Multi-Energy Complementary Microgrids (MECMs) supported by a Transactive Energy (TE) mechanism is proposed, which can realize multienergy interconnection and local consumption based on system economy and flexibility.In research, 3 a unit combination model of an active distribution network and transmission network is proposed, to fully exploit the flexible complementary potential of multilevel and multienergy and improve energy utilization efficiency.Yang et al. 4 based on the Shapley value method, construct an internal benefit distribution model for users and gas supply systems participating in the PIES.It also allocates the internal benefits of PIES based on the contributions of various entities to the cooperative alliance to maximize the internal linkage of the park.
The second aspect is the study of time-of-use price mechanisms on the generation and demand sides, based on supply and demand balance responses.Based on the power market model, Yang et al. 5 proposed an optimal scheduling strategy for household photovoltaic-battery energy storage system (PV-BESS) joint power generation guided by a time-of-price strategy and sold the surplus power generated by the PV system to the grid or stored in the battery, thus improving the operating efficiency and user benefits of PV-BESS.
The third is the research on the willingness and stability of different players to participate in the alliance based on the cooperative game.To maximize the power generation benefits of cascade hydropower stations in the basin, Song et al. 6 has constructed a dynamic alliance game model of different cascade hydropower stations in the basin under the assumption of complete information.The model uses the largest consistent set (LCS) method to determine the dynamic stability of the alliance.The results demonstrate the deviation direction of different cascade hydropower station alliance forms and the final alliance structure.Hairong et al. 7 considered the carbon trading mechanism, a game model of ordering cost allocation is established based on the ordering decision problem of multiple retailers' alliances.The model verifies the long-term stability of large retailer alliances using the LCS method.The results show that the total cost and carbon emissions of the multiretailer alliances are less than those of the multiretailer independent decision.[9][10][11][12] The existing research shows that: (1) The development of power systems mainly based on new energy has attracted attention.Using the complementary characteristics of new energy and conventional energy power generation, there have been many studies in related fields such as integrated energy, multienergy complementarity, and multienergy alliance optimization operations.However, there are few studies on the influence of the willingness of each entity to participate in the joint operations and its differentiation on the stability of the joint operation.The willingness of generating entities to participate in joint energy supply is affected by the different dynamic costs or benefits of multiscale combinations.The stability of each entity participating in joint operation needs further study.(2) The Shapley value method has been used to study the reasonable distribution of benefits or costs among various entities.However, the research on the relationship between the dynamic cost allocation of the alliance operation and the optimal operation decision of the alliance under the load realtime power vacancy balance mode is insufficient.(3)  There have been many studies on the generation side and demand side pricing mechanism in guiding load peakcutting and valley-filling and reducing system operating costs.However, there is a lack of research on the relationship between the time and space differences in power generation costs of various entities, and participation in different alliance preferences.Moreover, the stable operation of the alliance, as well as how to effectively support the high proportion of new energy generation in the alliance.
Based on the above research deficiencies, this paper aims to promote the consumption of a high proportion of new energy, considering the cooperation willingness of various heterogeneous energy to participate in the alliance, the internal relationship between the stability of each entity participating in the alliance cooperation and the multiscale combination operation is studied.The potential academic contributions are as follows: (1) Based on the source-load power balance model, the feasibility of power data normalization is deduced and proven.This simplifies the calculation and analysis process for multiscale cost allocation within the alliance, enabling efficient comparative analysis of data indicators with different dimensions.(2) Considering the differentiation of time-of-use electricity prices of each entity, an analysis model of multitime-space cooperative operation stability of alliance based on Shapley value and LCS method is constructed, which provides data support for determining the cooperative stability and economic operation scheme of alliance.(3) Considering the largest consistency of the interests of each entity participating in different alliances and different participation preferences, exploring the cost optimization control space under the multitime-space combination of different entities can effectively verify the feasibility of the multienergy alliance optimization operation mechanism, and provide decision-making reference for the optimal allocation of resources within the alliance and the operation cost control of each entity.(4) Based on the extreme value of multitime and space cost of each entity and the change rule of participation preference, it is proposed to reveal the stable evolution process of the multienergy alliance, provide a research paradigm for efficient integration and stable operation of new energy and conventional energy, and provide theoretical research and reference data for the construction of optimal operation mechanism of power system based on new energy.

| RESEARCH HYPOTHESIS
1.The joint operation of multitype heterogeneous energy proposed in this paper (hereinafter referred to as "multienergy alliance") mainly considers the differentiation of power generation characteristics.Different energy can be combined based on their power generation characteristics and cost dynamic changes to achieve a stable and economical combined operation mode.It is assumed that the four main power generation entities of wind power, photovoltaic, hydropower, and thermal power can be combined in a variety of combinations to form an alliance (in this paper, multiple combinations of at least three or more energy are combined to form an alliance).2. There are differences in the electricity cost of a single unit of different power generation entities.This paper takes different power generation entities as a whole to participate in the operation of the alliance, designing the time-of-use price mechanism on the generation side (The grid-connected price of power generation is divided according to the time period).And it takes the time-ofuse price of each entity as its grid connection power generation cost (the electricity cost data of each entity is not easy to obtain, ignoring the profit space of different entities, hereinafter referred to as the time-of-use price cost).The influence of the time-of-use price of different power generation entities on the operation cost or stability of the alliance is discussed and analyzed.3. It is assumed that a region has load demand side response policy conditions; in this paper, the difference between the load value at 24 h of the load curve and its base load value is taken as the power vacancy of the supply balance of the alliance to achieve the goal of stabilizing the peak and valley load demand and smooth load operation in the region.4. The electricity market is opening, and the alliance operation mode can be realized between regional or cross-regional energy.The power transmission and distribution network can independently provide power transmission services and meet the requirements of free trading in the energy market.5.The power generation capacity of the four energy sources can meet the operating needs of the alliance.Considering the sunlight conditions in different seasons in China, it is assumed that photovoltaic power generation can operate at full power from 9:00 to 16:00; from 6:00 to 9:00 and from 16:00 to 20:00, photovoltaic power generation can achieve 50% rated power operation, 13 and it is assumed that the photovoltaic power generation power is zero from 21:00 to 06:00.Wind power and hydropower are affected by seasonal climate change.For example, there are wet periods and dry periods in hydropower generation.Wind power is affected by the winter monsoon and the summer monsoon.Taking the typical daily load curve of a certain place as an example, this paper assumes that the output of wind power and hydropower is not affected by the monsoon climate and can generate electricity 24 h a day.

| OPERATION MECHANISM MODEL OF MULTIENERGY ALLIANCE
To construct the operational mechanism model of the multienergy alliance, the following three challenges need to be addressed: First, dealing with a large amount of power generation or load data, as well as potential anomalies in the sample data.To simplify the calculation and analysis process for multiscenario and multiscale cost allocation equilibrium within the new energy alliance, and to eliminate the impact of differing dimensions among indicators, ensuring comparability among data indicators with varying characteristic dimensions.It is essential to assess the feasibility of data normalization under the source and load power balance mode.Second, it is necessary to construct the overall cost calculation of the alliance and the balanced cost allocation model of each entity to realize the multiscenario and multiscale accounting of operating costs, and provide a decision-making basis for each entity to form different combinations.Thirdly, it is necessary to consider the basic conditions for the cooperation of each entity.At the same time, due to the difference in the time-of-use price cost of each entity, the cost and preference of each entity participating in the alliance change with time.It is necessary to identify the tendency of individual entities to deviate from the alliance and to take into account the consistency of the multitime scale changes of the interests of each entity after the operation of the alliance.That is, through the analysis of the multiscale evolution process of the operation cost of the alliance, the optimal stable combination mode is determined.

| Feasibility derivation of normalized calculation of generation power or load curve
The power generation power and load curve power are taken per unit value respectively, that is, the data are normalized (0,1), and according to the energy supply and demand balance condition, the feasibility is deduced and proved as follows.
First, the per unit value of power generation power or load curve power is taken, as shown in formulas (1) and (2).
where f t *( ) is the normalized value of the power generation entity i in time t, p u ..f t ( ) is the actual value of the power generation entity i in time t.f iN is the base value of the generating entity (according to the rated capacity of the power generation entity).i is the number of the generating entity, i n = 1, 2, 3, …, .
where f t ( ) 0 is the normalized value of the load curve in time t, p u . .f t ( ) is the actual value of the load curve in time t, kW.f N 0 is the base value of the load curve (take the peak value of the load curve).
When the electric energy is transmitted from the power generation side to the user side, the power balance should satisfy Formula (3), where δ t ( ) is the power transmission loss.
Formulas ( 1) and ( 3) are transformed into: , representing the ratio of the load curve reference value to the reference value of the power generation entity, then formula (5) becomes: The simultaneous formulas (2), ( 4) and ( 6) are obtained: The line loss rate is the percentage of the loss power to the total power supply.Combined with formula (3), r t ( ) is defined as follows: Transform formula (8) into: According to formula (9): The transformation formula (11) can be obtained by summing the two sides of formula (6) and combining formula (1).

 
Combined with the formula (3) and (8), the line loss rate of the power grid is between 0 and 1.
It shows that the per unit value function f t *( ) i of the generator set is linear with the unit value function f t *( ) 0 of the load curve.Based on the matrix data, the dot product operation is carried out, and the formula ( 14) is deduced to obtain the linear relationship expression (15).
where f t *( ) is the dot product of matrix ξ and the sum of the product of the corresponding elements in the matrix can be equivalent to the (14).

| Objective function
The objective function is shown in the following formula: where C i is the i energy cost in the alliance, yuan.V C ( ) i is the total operation cost of the multienergy alliance, yuan.

| Constraint conditions
The power balance between power generation and electricity consumption is satisfied, and the cost apportionment value of each entity after participating in the operation of the alliance does not exceed its independent operation cost.The constraints are as follows: where C i ( ) is the independent operation cost of the energy entity i, yuan.t is time (unit h : ).P i t ( , ) g is the active power of the power generation entity in time t (unit : MW).P j t ( , ) load is the active load power of the load in time t.P t Δ ( ) is the active power loss of the power grid in time t.To simplify the calculation, the simulation calculation in the following text will be ignored P Δ .

| Total cost model of alliance based on time-of-use price mechanism
According to the research hypothesis 2, each entity is involved in the construction of the alliance as a whole.
For the n entities to form the alliance, the power generation output proportion meets the following constraints: where λ i is the output proportion of the generator unit i .The power generation cost matrix of each entity is i n where b i is the power generation cost of the ith generator unit, yuan/kWh.CUI ET AL.
| 877 The power generation cost of the alliance 24 h a day where P is the real-time power shortage value of the supply balance of the alliance.(Assumed condition 3).
To simulate and analyze the influence mechanism of time-of-use price in different periods on the multiscale combination of each entity, and based on the difference of multiscale operation cost of the alliance body, the specific operation strategy is formulated.Considering the power generation characteristics of each entity, the on-grid electricity price of wind power, photovoltaic, hydropower, and thermal power is divided into three periods, namely, peak period, flat period, and valley period, as shown in the following equation: is the time-of-use price of power generation entity i (unit: yuan/kWh).c c c , , p f v represent the time-ofuse price cost of each power generation entity in peak, flat, and valley periods, respectively.

| Multiscale operation cost balanced allocation model of multienergy alliance
Combined with the characteristics of the Shapley value method, 10 the total operating cost of the alliance is balanced according to the marginal contribution of each entity's power generation output.The Shapley cost equilibrium allocation value of an entity i is where Y i is the Shapley value of an entity i, s is the coalition subset containing entity i, y s ( ) is the cost of subset s, s i \ is the subset of set s after removing entity i. y s i ( \ ) is the cost of subset s i \ .w is the cost allocation weighting factor, and the solution method is shown in the following formula: where n is the number of entities forming the alliance, and   s is the number of entities in the subset s of the alliance,   s n  .
The operation of the alliance composed of three entities is simulated, and the wind power in the alliance composed of wind power, photovoltaic, and hydropower is taken as an example to illustrate the solution process of wind power cost allocation value.First, the number of alliance subsets containing wind power is analyzed, and the weighted factor of the cost value of each subset is calculated.There are four alliance subsets including wind power in the alliance of the three entities, namely {wind power} = {1}, {wind power, photovoltaic} = {1, 2}, {wind power, hydro-power} = {1, 3}, {wind power, photovoltaic, hydro-power} = {1, 2, 3}.The cost allocation weighting factor matrix of four subsets containing wind power is calculated according to Formula (23).
When n = 3, s = 1, the subset is {1}, and the cost allocation weight of subset {1} is When n = 3 and s = 2, the subsets are {1, 2} and {1, 3}, and the corresponding cost allocation weights of the two subsets are When n = 3, s = 3, the subset is {1, 2, 3}, and the corresponding cost allocation weights are Combining the Equations ( 24) to (26), the weighted factor matrix of the four alliance subsets with wind power is obtained as follows: According to Formula (22), the cost values of different numbers of entity combinations (including wind power) to form a subset of the alliance are calculated respectively.
When s = 1, there is only one entity in the alliance subset, the cost allocation weighting factor is ω (1) = 1 3 , and the cost of the coalition subset {1} is y 2 , and the cost of subset {1,3} is y y ( − ) According to the formula (22), the wind power operating cost allocation value is where Y 1 is the multiscale combination of three entities to form the wind power operation cost value in the alliance.
The cost values of photovoltaic and hydropower can be calculated separately according to the derivation in this paper.

| Stable operating conditions of multienergy alliance
Due to differences in output characteristics, profitability, electricity price level, and the marginal cost of wind power, photovoltaic, hydropower, and thermal power, individuals have different willingness and expectations to participate in the alliance game.The alliance formed by the cooperation of different power generation entities is expected to be profitable, so the stable operation of a multienergy alliance needs to meet the basic condition of a cooperative game.Condition 1, individual rationality where x i represents the benefits distributed by the game player i within the alliance, and v i ( ) represents the benefits obtained by the independent operation of the game player i, the benefit of the player's participation in the alliance is not lower than its independent operation.Condition 2, alliance rationality where x i represents the interests of the game player i distributed within the alliance L j , v L ( ) k represents the interests of the game player i in the alliance L k .The game player i participates in the alliance L j and gains no less benefit than the alliance L k .
Condition 3, group rationality where x i represents the income of the game player participating in the distribution in the i alliance N .The income of all entities should meet the distribution equilibrium, and the total income of the alliance v N ( ) and the total income of all subjects.

| Analysis model of alliance operation stability based on the LCS method
To determine the multispace-time stable operation scheme of the alliance, it is necessary to distinguish the willingness of each entity to participate in different alliances and the stability of the operation after participating in the alliance.Based on the change of multiscale cost value of each entity, this paper constructs the identification model of alliance operation stability combined with the LCS method. 14,15It mainly includes the following two parts: 1. Evolutionary analysis model of each player participating in different alliance preferences Assume that game players i, under the alliance L 1 's operating cost u i L 1 is greater than the alliance's If formula (32) is satisfied, the game player thinks that the alliance L 2 is greater than L 1 , which is recorded as If formulas (32) and ( 33) are satisfied, it shows that player i prefers alliance L 2 .The deviation from alliance L 1 to L 2 changes the alliance from L 1 to L 2 , which is recorded as The subset S i of any player participating in the alliance needs to satisfy the formula (35): L k will be included in the federation structure set: | 879 S i will be included in the game set S:


(37) According to the formula (35), the cycle of judgment is carried out.For each calculation of formula (35), the structure adjustment of formulas (36) and (37) is carried out once.Through repeated circular judgment and structural adjustment of the alliance subset, until any game party satisfies the formula (38), the alliance set is the LCS of the interests of each game party.
(2) Multitime-space stability analysis model of each player participating in alliance operation Firstly, combined with formulas ( 16)-( 28), the cost values of each game player in different periods are solved according to the linear programming method.Then use formulas (32)-(38) to compare the preferences of each entity participating in different alliance operations at different times.Based on formula (39), the multitemporal stability of each player participating in alliance operation is analyzed.
where, L i is an optional federation set.V L x t λ ( ( ( , ))) is the cost of the player x in the alliance L in the t time period, and V L x t λ ( ( ( , ))) i is the cost of the player x in the alliance L i in the t time period.The output ratio x of the bodies is λ.

| Simulation calculation steps
Taking the load forecasting value of a certain power grid as an example, according to the research hypothesis and construction model of this paper, the implementation steps are as follows: 1. Simulation alliance matrix, this paper mainly considers at least three players participating in an alliance, four players all participate in the alliance is called the big alliance, three players participate in the alliance is called the small alliance; moreover it mainly uses three types of alliances for comparative analysis; specifically as follows: "Wind power, photovoltaic, hydropower, thermal power" four power generation entities constitute alliance 1; the three power generation entity "wind power, photovoltaic, hydropower" constitute alliance 2; "wind power, photovoltaic, thermal power" constitute alliance 3; 2. Select the load forecasting value of a power system in China, and construct the load forecasting value matrix, as shown in Equation (40); in the formula: LC 1 is the load curve 24 h load value (MW), the peakto-valley difference rate is 55.68%, each column represents 8 h load; the segmented power vacancy of 24 periods in the load curve is calculated respectively, that is, the power vacancy of 24 periods can be obtained according to the hypothesis condition (3).At the same time, according to the 3.1 scheme, the load curve or power generation is normalized; 3. Design the peak, flat, and valley time division scheme of the power generation side; drawing on the notice of the Guangdong Provincial Development and Reform Commission on further improving the relevant issues of the peak-valley time-of-use price policy in our province (Guangdong Development and Reform Price [2021], 331), the demand-side peak and valley time-of-use price period division standards (peak hours are 10:00-12:00 and 14:00-19:00; the valley period is 0:00-8:00 the rest of the period is flat); according to the on-grid price of wind power, photovoltaic, hydropower, and thermal power in Meng and colleagues, [16][17][18][19] combined with the policy of promoting new energy development and the power generation characteristics of each entity, the time-ofuse price of four kinds of energy generation side is drawn up, as shown in Table A2.According to Hypothesis 2 and Table A2, the peak, flat, and valley power generation cost matrix of the four energy sources are constructed respectively to provide basic data for the calculation of the Shapley cost value of the alliance in each period.4. According to assumed condition 3, the output ratio of each entity is adjusted according to the load period, and the step size of the output ratio is 0.1.Using relevant software programming simulation, the multiscale combined cost allocation values of each entity in (according to Formulas 16-25).The Shapley cost value of multiple entities is not unique, and there are maximum and minimum values.The data related to the proportion of power generation output corresponding to different alliances and multiscale combinations of each entity and the cost limit value (maximum or minimum) of each entity are mined and extracted, and the multiscale cost extreme values of each entity in different alliances are simulated and compared.5.According to the calculation results of step 4, based on the corresponding cost equilibrium values (maximum and minimum) under the multiscale combination of different entities, the total cost change area of the alliance or each entity can be obtained by integrating the cost limit values of 24 periods.The area enclosed by the two limit value curves represents the adjustable area of the operating cost of the alliance or each entity, and the highest point in the area represents the upper limit of cost fluctuation.

| Basic data
Select a power load curve of a certain place in China as the demand side case data.as shown in the following formula: The load curve matrix is normalized according to Formulas (1)-( 15), as shown in Figure B1.Combined with references, [16][17][18][19][20] the time-of-use price data of a certain place in China is designed as Table A2.As can be seen from Figure B2, 5:00 is the corresponding moment of the base load of the load curve.According to research hypothesis 3, the power vacancy at this moment is zero, and the cost of each entity is zero in different scenarios.The corresponding cost value during peak load hours (11:00, 12:00, and 19:00) is high.The relative change of the cost value of each entity is consistent with the fluctuation trend of the load curve.Photovoltaic costs fluctuate the most at 17:00 and 20:00, followed by the relatively large change in the cost of thermal power at 11:00 and 19:00.The cost value of each entity participating in a big alliance operation is less than the cost value of the independent operation, which meets the basic assumptions for stable operation of the alliance.2. Alliance operating cost fluctuation interval analysis.
It can be seen from Figure B3 that the output ratio of each entity in the alliance is different over any period.The total operating cost limit value of the alliance shows multiple spatial and temporal changes with consistent trends.For Alliance 1, the adjustable interval area of the total cost is the smallest (1705.82),while for alliance 3 is the biggest (1867.81).From the changing trend of the overall cost of the alliance, it can be seen that the overall cost of the alliance is relatively large during the peak load period.The maximum cost of each alliance appears at 19:00 (307.059,312.008, 318.010).The adjustable cost area is relatively large in the peak and flat hours of the load, and the adjustable cost area is small in the 0:00-8:00 valley period.It shows that after the operation of the alliance, it has more cost control optimization space value in the load peak and normal period.

Analysis of cost changes of each entity in the alliance
It can be seen from Figure B4 that the area of the hydropower cost change range is the smallest (1312.47).The area of wind power cost change range is the largest (2953.30).The wind power photovoltaic costs of the four main bodies are relatively high.They occur respectively in the peak periods (The maximum cost time of wind power, hydropower, and thermal power is 19:00, and the maximum cost time of photovoltaic is 11:00).The large change area of wind power cost indicates that the adjustable time and space range of the wind power generation output ratio is large.Meanwhile, due to the temporal and spatial differences between the maximum cost of wind power and photovoltaic, the full power generation characteristics of photovoltaic from 9:00 to 16:00 in the daytime can be used to increase its power generation proportion.At night, the proportion of wind power generation will be increased, while hydropower and thermal power will participate in the regulation of auxiliary power generation output during the whole operation process.Multitemporal and spatial operating cost change data of each entity reflects the complementary characteristics of different energy generation and the adjustable space range of a high proportion of new energy consumption

| Comparative analysis of the stability of big alliance and small alliance based on multiscale changes in cost
There is a lot of data on the multiple space-time cost limit values of each entity.First, based on the LCS mechanism, the multiple space-time cost interval intersection of different alliances is constructed to analyze the relative relationship between the cost limit values of different alliances and the intersection of cost intervals.Then clarify the differences in operational stability between different alliances, and provide a decision-making basis for each entity to choose to participate in different alliances.In this paper, the comparison between the two is carried out by using the big alliance or the small alliance (in view of the length for the article, the comparative analysis of Alliances 1,2 and Alliance 1,3).

Intervals intersection of alliance operating costs:
The area between the upper and lower limits of the alliance's multitemporal and spatial operating costs is a variable cost interval.Different alliances have different ranges of cost intervals.Under the unified space-time dimension, the cost intervals that belong to two different alliances are called the intersection of alliance cost intervals (recorded as intersection A). 2. Alliance stability judgment: According to the analysis in 4.3, the cost fluctuation values of different alliances are consistent with the changes in the load curve.The corresponding cost fluctuation ranges are different.So the area of intersection A between different alliances is different.Then the multitemporal and spatial scale changes of the cost values of the two alliances are within the scope of intersection A. It is considered that the two alliances have the same multitemporal and spatial operation cost interval.When the lower cost boundary value of two different alliances is close to the lower limit boundary of intersection A in a certain period.Based on the LCS principle, it can be considered that the two alliances have the same operational stability.When the lower limit value of a certain alliance's cost is below the lower limit value of intersection A's cost, it indicates that the alliance's operating cost is relatively low and has more stable operating advantages.
3. Comparison of cost limits of different alliances.Based on the LCS model, the upper or lower cost limits of different entities participating in different alliances are compared respectively.Based on the principle that each entity participates in the alliance and prefers small operating costs, considering the difference of cost limits of each entity in different periods, the length of the time interval with lower alliance cost (upper or lower limit) is used as a reference for each entity to participate in alliance preference selection.
To facilitate the comprehensive balance of the relative changes of the upper or lower limits of the cost, determine the final choice of each entity, and ignore the impact of the relatively small changes in the cost limits of each entity in different alliances on the willingness to participate in the alliance.

Comparative analysis of the stability of Alliance 1 and Alliance 2
In Figure B5A, compared with the cost-lower limit of Alliance 1 and Alliance 2, the cost-lower limit values of the two alliances in different periods are close, and their cost values have little difference.Between 04:00 and 06:00, the upper-cost limits of Alliance 1 and Alliance 2 are relatively close.However, from 01:00 to 03:00 and 07:00 to 24:00 (a total of 19 periods), the upper-cost limit of Alliance 2 is greater than the upper-cost limit of cost intersection A (the upper-cost limit of Alliance 2 at 24:00 is above cost intersection A).The upper-cost limit of Alliance 2 is higher than the upper-cost limit of Alliance 1.It can be seen that Alliance 1 has more advantages in economic operation.
In Figure B5B, the upper-cost limit of wind power in each period of Alliance 1 is lower than that in Alliance 2. In addition, between 18:00 and 24:00, the lower cost limit of Alliance 1 is lower than that of Alliance 2. In other periods, the lower cost limit of wind power of two different alliances is relatively close, which has no significant impact on the choice of wind power strategy.Therefore, wind power tends to participate in Alliance 1.
In Figure B5C, from 01:00 to 04:00 and from 21:00 to 24:00, photovoltaic does not generate electricity.The cost under both alliances is 0. From 05:00 to 20:00, the upper-cost limit of PV in Alliance 1 is lower than that in Alliance 2. At the same time, from 05:00 to 20:00, the lower limit of the cost in Alliance 1 and Alliance 2 is basically close.The willingness of PV to participate in Alliance 1 and Alliance 2 has no significant impact, so PV prefers to participate in Alliance 1.
In Figure B5D, from 01:00 to 02:00 and from 16:00 to 24:00, the upper-cost limit of hydropower in Alliance 1 is slightly lower than that in Alliance 2, and the upper-cost limits in the other two cases are relatively close (the upper-cost limit changes relatively small), which has no significant impact on the preference of hydropower to participate in different alliances.However, the lower limit value of hydropower cost in Alliance 2 is lower than that in Alliance 1 (24 periods), so hydropower tends to participate in Alliance 2.

Comparative analysis on stability of Alliance 1 and
Alliance 3 In Figure B6A, compared with the lower-cost limits of Alliance 1 and Alliance 3, the lower-cost limits of the two alliances in different periods are relatively close, with little difference in their cost values.From 01:00 to 03:00 and from 7:00 to 24:00 (a total of 19 periods), the uppercost limit of Alliance 3 is above the upper limit of the intersection interval.The upper-cost limit of Alliance 3 is higher than the upper-cost limit of Alliance 1, indicating that Alliance 1 has more advantages in economic operation stability at this time.
In Figure B6B, the upper-cost limit of wind power in each period of Alliance 1 is lower than that in Alliance 2. Between 01:00 and 21:00, the lower-cost limit of wind power in Alliances 1 and 3 has relatively little change, which has no significant impact on the willingness of wind power to choose to participate in different alliances.But between 22:00 and 24:00, the lower-cost limit of Alliance 1 is lower than that of Alliance 3, so wind power tends to participate in Alliance 1.
In Figure B6C, from 01:00 to 04:00 and from 21:00 to 24:00, photovoltaic does not generate electricity.And the cost of both alliances is 0. The upper limit value of PV cost in the period from 05:00 to 20:00 in Alliance 1 is lower than that in Alliance 2, while the lower limit value of PV cost in the period from 05:00 to 20:00 in Alliance 1 and 2 is relatively close.Small changes in the lower limit values of different alliances have no significant impact on PV's choice to participate in Alliance 1 and 2, so PV prefers to participate in Alliance 1.
In Figure B6D, the upper-cost limit of thermal power in each period of Alliance 1 is lower than that of Alliance 3. The lower cost limit of thermal power in Alliance 1 is lower than that of Alliance 3 from 01:00 to 02:00, 07:00 to 08:00, and 18:00 to 24:00.While the lower-cost limit of the two alliances is relatively small or close in other periods.This has no significant impact on the selection of thermal power to participate in the two alliances.Therefore, thermal power prefers to participate in Alliance 1.The multitemporal scale alliance preferences of each entity are shown in Appendix Table A2.

| Analysis of comprehensive operation strategy of alliance based on multiscale stability evolution of each entity
The formulation of the alliance's operating strategy primarily takes into account two crucial aspects.One is the cooperative stability based on considering the preference of different power generation entities to participate in the alliance.When the operating cost of an entity in the alliance fluctuates greatly, it affects its willingness to participate in the alliance and causes the instability of the alliance operation.Second, it is imperative to factor in the operational efficiency of the alliance and enhance the willingness of each entity to become an alliance participant.

| Multiscale evolution process and operational stability analysis of alliance
Combined with Formulas (29)-(39) and 4.3.2analysis, considering the operation period of wind power, photovoltaic, and thermal power participating in Alliance 1, the intersection of preferences of each entity participating in Alliance 1 is analyzed.The preference of each entity participating in the alliance is shown in Table A3; wind power at 18:00 to 24:00, photovoltaic at 5:00 to 20:00, and thermal power at 1:00 to 2:00, 7:00 to 8:00, 18:00 to 24:00, it can be seen that there are five time periods for the three entities to participate in the intersection of Alliance 1 preferences, that is, at 7:00 to 8:00, 18:00 to 20:00, Alliance 1 has cooperative operation stability.Combined with the analysis of Figure B5D, although hydropower is biased to participate in Alliance 2 from 1:00 to 24:00, it can be seen from the figure that the relative change of its cost upper limit or lower limit is small, which has little effect on the choice of hydropower to participate in Alliance 1 or Alliance 2.

| Economic analysis of the multiscale operation of the alliance
If the maximum operating cost of the alliance at a certain period of time is the maximum value of the operating cost of the alliance at different periods of time, in the comparison of the multiscale cost maximum value of the alliance, the maximum value of the cost is relatively small, and at the same time, compared with the maximum operating cost of other periods, the value is also relatively small.This reflects that the alliance has low-cost operational advantages, that is, the alliance has operational economy; and it can be explained that the maximum value of the operating cost of the alliance can reflect the overall economy of the alliance operation.
Compare the maximum operating costs of different alliances in different scenarios to clarify the changes in operating costs of the alliance in different periods; at the same time, the proportion of new energy power generation in the alliance is considered to determine the economic alliance.
1.In the load valley section, the maximum operating costs of Alliance 1 to Alliance 3 all appear at 8:00, as shown in Figures B5A and B6A, which are 86.039,90.056 and 95.050, respectively.The maximum operating cost of Alliance 1 is relatively the smallest (86.039), which has economic operating advantages.
According to the simulation step (4), when the cost maximum occurs in Alliance 1, the power generation proportion corresponding to the iteration of wind power, photovoltaic, hydropower, and thermal power are 0.1,0.8,0.1 and 0.1, respectively.The maximum proportion of photovoltaic power generation output is 0.8; 2. In the peak load section, the maximum operating costs of alliance 1 to alliance 3 all appear at 19:00, as shown in Figures B5A and B6A, which are 302.121,307.011and 312.007, respectively.The maximum operating cost of Alliance 1 is relatively the smallest (302.121), which has economic operating advantages.According to the simulation step (4), at the time corresponding to the maximum cost of Alliance 1, the power generation ratios of wind power, photovoltaic, hydropower, and thermal power iteration are 0.8, 0.1, 0.1, and 0.1, respectively.The maximum proportion of wind power output is 0.8.
Based on the analysis of 4.4.1 and 4.4.2, in the period of 7:00 to 8:00 and 18:00 to 20:00, Alliance 1 has more cooperative stability and economic operation advantages.At the same time, during the peak and valley load periods, the output proportion of wind power and photovoltaic power generation corresponding to Alliance 1 is the maximum value of 0.8, which meets the conditions of high proportion of new energy power generation.

| COMPREHENSIVE DISCUSSION
By comparing the relationship between the cost limit (upper limit or lower limit) and the cost intersection interval of different alliances, as well as the relative relationship between the cost extreme values of different entities in different alliances.The comprehensive discussion is as follows: 1.It is more advantageous for each entity to participate in the operation of the big alliance (Alliance 1) than to operate independently, and the operation is relatively stable.Due to the participation of wind power, photovoltaic, and thermal power in Alliance 2 and Alliance 3, the upper limit of cost in different periods is higher than that of Alliance 1.The relative change of the lower limit value of the cost of each entity in different alliances is different due to different periods.
Ignoring the influence of the small relative change of the cost limit value, wind power, photovoltaic, and thermal power tend to participate in Alliance 1, which has stable operation advantages.Hydropower tends to participate in Alliance 2, where hydropower can support the small alliance formed by wind, photovoltaic, and hydropower at lower operating costs to drive wind and photovoltaic consumption.2. According to the cost intersection interval of different alliances and the trend of multitemporal and spatial scales of the cost limit value of each entity, it can provide a supporting basis for the judgment of alliance stability.From the model built in this paper, it can be seen that the cost extreme value of each entity depends linearly on the cost of time-of-use price and the proportion of the generation output.The internal structure of the alliance can be dynamically adjusted in combination with the different preferences of each entity in different periods to achieve the goal of stable operation of the alliance.3.Under different alliances with multiple time and space operations, there are differences in the preferences of each entity.There are time and space differences in the stable operation of the alliance or each entity.Meanwhile, the cost changes of each entity participating in different alliances are different.There are two main influencing factors: First, the time-of-use price is assumed to be the power generation cost of each entity.Due to the different profit spaces of each entity, the actual electricity cost is different from the time of use price cost in this paper, which affects the accuracy of the limit value of each entity.Secondly, it is related to the calculation method of the power shortage of the system peak-cutting and valleyfilling.The variation of load and base load power difference at different times determines the power generation output level of the alliance, which directly affects the changing trend of the alliance cost and the cost limit value of each entity.4. Each entity operates within the cost intersection range and has the same willingness to participate in different alliances, but the time-of-use price cost, power generation characteristics, and power generation output ratio of each entity are different.Different entities have different preferences for participating in the alliance in time and space.Individual entities can transition from the original alliance to another alliance to form a new alliance structure, which can realize the sustainable and stable operation of the multienergy alliance through the transformation of the multitemporal and spatial structure of the alliance.Based on the multitemporal evolution mechanism between the alliance cost intersection interval and the preference of each entity participating in the alliance.An optimal combination of consultation and coordination mechanisms for each power generation entity based on the stable operation of the alliance can be constructed.With the goal of a high proportion of new energy generation, the multitemporal combination alliance mode of each entity is formed to participate in the electricity market transaction, which effectively promotes the consumption of new energy.

Based on the comparative analysis of data in
Figures B5A and B6A, Alliance 1 has the longest period of lower operating costs (from 1:00 to 3:00 and from 7:00 to 24:00, with 19 periods of lower costs than Alliance 2 and 3).Alliance 1 has economic operating advantages.However, the common stability interval of different alliances is affected by the participation preference of each entity (wind power, photovoltaic, and thermal power tend to participate in Alliance 1, and hydropower tends to participate in Alliance 2).It shows that the combination structure of each entity in different alliances has the possibility of transformation.To promote the stability of the dynamic operation of the alliance, the alliance body can be reorganized by different entities participating in the multitemporal preference differences of different alliances.

| CONCLUSIONS
The article provides an overall analysis of the stability and optimized combinations of cooperative operations among various energy entities.By analyzing the changing rules of cost allocation among different entities and the dynamic evolution process of stability in participating in different alliance operations, the following conclusions are drawn: 1. Wind power, photovoltaic, and thermal power tend to participate in Alliance 1, while hydropower tends to participate in Alliance 2. There is a possibility of transformation between different alliances in different time periods.The cost optimization space for load leveling through different alliance operations is different.By comparing Alliance 1-3 comprehensively from the aspects of the extreme values of the cost limits, the cost area, and the intersection of different alliance cost intervals, Alliance 1 is determined to have the most stable operating advantage.2. The article considers the impact of time-of-use pricing and builds a multiscale operation economy and stability analysis model of alliance using the Shapley or LCS method combined with the power shortage and demand balance mode.This model can effectively calculate and analyze the cost allocation values of each entity in different alliances and their preferences in participating in different alliances.The case study in this article demonstrates the practicality of this method.3.According to the different characteristics of the operational stability of each entity in different alliances, the stable combination operation period of the alliance can be determined by judging the operational stability of each entity participating in different alliances.At the same time, this study reveals the relationship between the stability or economy of the internal combination and the change of time and the cost allocation of each entity when the heterogeneous energy alliance is operated, which can provide a reference for the optimal combination decision of the alliance.
Based on a single scenario case, this paper analyzes the influence of the change of multitime and space cost limits of each entity on the participation preference and alliance stability of each entity.However, a comparative analysis of the change in cost constraints and alliance stability for each entity under different load curve operating modes is lacking.When the cost fluctuation of each entity in different operation modes changes greatly, the willingness of each entity to participate in different alliances will change.Consider the possibility of each entity forming the LCS of multiple space-time benefits in multiple scenarios.The significance of the cost changes of each entity in different alliance structures.We verify the impact of the fluctuation of the cost value of each entity in different operating modes and different alliances at the conclusion of this paper.Comprehensively judge the stability of the multitemporal operation of the alliance.
The next step of the research is as follows: Simulate the supply and demand balance of the consortium under different load curve operation modes.According to the method of this paper, the multispace-time cost value of each entity is obtained, and the fluctuation of the cost value of each entity in different scenarios is compared.Due to a large amount of data on the multitemporal scale cost value of each entity, the parameters that can reflect the difference of the extreme value distribution state of each entity are inconvenient to determine.It is proposed to combine the characteristics of the non-parametric test (Kolmogorov-Smirnov test) method to verify whether there are significant differences in the distribution of cost limit data in two different scenarios.Based on the significant data in different scenarios, the differences in operational stability of different alliances are compared and analyzed to further expand the applicability of this method in multispace-time stable operation analysis of multienergy alliances.It provides a method reference for the research on the stable operation mechanism of new energy power systems.3. The cost allocation scheme of the improved Owen value method in the multicommunity energy storage sharing scenario is studied.

ORCID
[9] 2021 1. Simulate the operation mechanism of the multienergy alliance and build a dynamic Shapley value analysis model for the correlation between the multiscale combination of ancillary service revenue and the output proportion of each entity.
And study the coupling relationship between peak load curve clipping and valley filling and the distribution of ancillary service revenue of the alliance.
2. This paper analyzes the variation law of the generation proportion and income of each main body under different operation modes of load peak and valley values, and studies and determines the optimal combination decision-making scheme for the alliance to participate in the auxiliary service market competition.1.It verifies the supporting role of the operation mode of the multienergy alliance in reducing the market operation risk of each entity and promoting the consumption of renewable energy, while reducing the payment cost of the auxiliary service market when renewable energy operates independently, realizing the income balance of each entity and reducing the market transaction cost.
2. It verifies the effectiveness of the optimal income distribution strategy of the multienergy alliance.
Inadequate analysis on the effect of cost-balanced allocation of each entity and the impact of the willingness of each entity to participate in the alliance on the operation stability of the multienergy alliance was not considered.
[10] 2021 Based on the operation mechanism of energy alliance, the Shapley value dynamic analysis model of the multiscale combination of auxiliary service revenue and output ratio of each subject is constructed to study the variation law between the optimal power generation ratio and revenue of each subject under different operation modes of load peak and valley.1.The operation mode of the alliance can balance the volatility of renewable energy as a whole and promote the stable operation of the renewable energy power market.
2. By studying the optimal distribution strategy within the alliance, the benefits of each subject can be balanced, and operating costs can be reduced.
However, the influence of the multiscale dynamic equilibrium optimization of the power generation cost of each subject on its participation in market decision-making is not fully considered.
[11] 2021 1.To deal with wind power uncertainty, a two-stage robust unit commitment (UC) model considering operational risk and demand response is constructed.
2. Based on a large number of wind power prediction measured data, the risk assessment model based on 0-1 programming is studied.The operational risk is combined with the uncertain 1.Based on historical wind power forecasts and measured data, the risk of power grid operation is systematically measured.In the process of solving the model, the uncertainty set boundary is adjusted through successive iterations to suppress the operation risk of the power grid.

The time of use price response is incorporated into the robust unit commitment model
Combining the correlation characteristics of wind power generation output in different times and spaces, the correlation of wind power output is included in the model, and improving the accuracy and calculation efficiency of wind power prediction is the next key research content.
T considering operation risk, which achieves the goal of reducing operation cost and operational risk.
[12] 2021 1. Considering the thermal load regulation effect, time of use electricity price, heating comfort, CO2 storage, and transportation cost, the IES low carbon economic dispatching model of carbon capture power plants is established to optimize the total system operation cost, and the second order cone optimization method is used to solve the operation parameters of heat network and gas network respectively.
2. Clarified the key points of low carbon transformation of thermal power units during peak load period and the carbon capture level that the carbon capture power plant needs to reach.
1.It provides a solution for the IES system with a carbon capture power plant to formulate a lowcarbon economic dispatching strategy, and achieves the economic and low-carbon operation goals of the IES system.
2. The flexibly adjustable resources on both sides of the power supply and load have been excavated, the output combination of thermal power and CHP units has been optimized, and the carbon capture level of carbon capture power plants has been effectively improved.
Further research is needed on the optimal configuration of waste heat power generation capacity, as well as the influence of heat network delay characteristics, gas flow characteristics of the gas network, and pipe storage efficiency on IES low-carbon operation characteristics.
[7] 2022 1.Based on the second-order supply chain composed of a single supplier and multiple retailers, the ordering decision problem of multiple retailer alliances under the carbon trading mechanism is studied, and the ordering decision model of multiple retailer alliances is established.
2. For the order cost allocation problem of retailer alliances under the assumption of complete information symmetry, an order cost allocation model based on cooperative game theory is established.The maximum consistent set (LCS) method is used to analyze the operation stability of multiretailer alliances.1.The feasibility of the win-win strategy of horizontal alliance among supply chain enterprises is verified.It is proved that the alliance mechanism can effectively reduce the ordering cost and carbon emissions of retailers' independent decision-making.
2. The optimal allocation scheme of the cooperative ordering cost of the alliance is formulated, and the feasibility of the long-term stable operation of the alliance is verified.
When each retailer merges their demand orders, there will be some coordination costs.The next research focus is to consider the impact of coordination costs on the retailer's cooperative decision-making and cost allocation.
this paper -1.Build a stable operation analysis model of the new energy alliance including wind power, photovoltaic, hydropower, and thermal power.
2. To reduce the complexity of calculation and analysis and realize the unity and comparability of data, the original data normalization calculation 1.To verify the feasibility of the stable operation mode of the multienergy alliance to reduce the operation costs of the alliance and each entity.multienergy alliance, and it is expected to provide a theoretical reference for the optimal operation mode of the new energy power system.
3. It is intended to reveal the correlation between the change of the cost limit value of each entity and the multitime and space operation stability of the alliance, hoping to provide reference data for the cost optimization control of each entity and the stable operation decision of the alliance.
T A B L E A2 Peak and valley time-of-use electricity price yuan/kWh.The line loss rate is the percentage of the loss power to the total power supply.

C i
The cost allocation value of the entity i in the alliance V(C i ) Total cost of alliance operation C(i) Independent operation cost of power generation entity i P g (i,t) The active power of generator i at time t P load (j,t) Active load power of load j in time t

ΔP(t)
The active loss power of the power grid at time t The time-of-use price cost of each power generation main body peak section, flat section, and valley section respectively.

Y i
The cost allocation Shapley value of power generation entity i participating in the alliance x i (i = 1,2,3,4) Represents that the game play i distributes the benefits within the alliance The operating cost of game play i in alliance L 1 The operating cost of game play i in alliance L 2

4. 3 |
Analysis of the stable operation mechanism of the alliance based on multiscale changes in cost 4.3.1 | Stability analysis of independent or alliance operation based on multiscales of cost 1.Multiscale cost value change analysis when the big alliance and each entity operate independently.

3 .
A B L E A 1 (Continued) Literature Time Research contents and methods The solution Inadequate research set boundary, and then the robust UC model considering established.Considering the influence of DR based on time-ofuse price on load, the influence of DR uncertainty on operation results is studied.

2 .
It is intended to verify the feasibility of the Shapley value and LCS method in determining the optimal combination strategy of the supply and demand balance assumptions on the generation side and load side is derived.3.Considering the time of use electricity price cost of each entity in the alliance, the Shapley cost equilibrium value method is applied to calculate the limit value (maximum or minimum value) of multitime and space operation cost of each entity, analyze the change of the limit value of each entity's cost.Then use the maximum consistent set (LCS) method to judge the operation stability of different alliances.
The output proportion of power generation entity i c iThe entity i unit cost of power generation P Real-time power vacancy value of supply and demand balance of coalition

s
Alliance The corresponding cost after the subset s removes the entity i ω Alliance subset cost allocation weighting factor n The number of entities that constitute an alliance   s Number of entities in the alliance subset

F
I G U R E B1 Normalized data of load power or power vacancy.APPENDIX B F I G U R E B2 Time-phased cost of independent or big alliance operation of each entity.(A) Wind power, (B) photovoltaic, (C) hydropower, and (D) thermalpower.F I G U R E B3 The operating cost range of each alliance in different time periods.(A) Max = 307.059,(B) max = 312.008,and (C) max = 318.010.F I G U R E B4 The time-sharing cost of each entity participating in the operation of Alliance1.(A) Wind power, (B) photovoltaic, (C) hydropower, and (D) thermalpower.F I G U R E B5 (A) Cost comparison chart of Alliance 1 and Alliance 2. (B) Cost comparison chart of wind power participating in Alliance 1 and alliance 3. (C) Cost comparison chart of photovoltaic participating in Alliance 1 and Alliance 2. (D) Cost comparison chart of hydropower participating in Alliance 1 and Alliance 2.
Difference comparison table between this paper and related representative literature research.
Time interval, 10:00-12:00 and 14:00-19:00; others, 0:00-8:00 Each main body participates in alliance preference strategy table.Per unit value, the actual value and the base value of the power generation entity at time t.Per unit value, the actual value and the base value of the load curve at time t