Flexible power load dispatching system based on game model

Abstract

The invention provides a flexible power load scheduling method and system based on a game model, and the method comprises the steps: building an aggregation load provider non-cooperative game model considering a load scale effect and risks in order to achieve the maximum effectiveness at an aggregation provider level, and adjusting the electricity price through adjusting the risk attention; in the user layer, an evolutionary game model enabling the effectiveness of the user to be maximum is established to describe the selection behavior of the user, theoretical support and decision basis are provided for efficient operation and resource optimization configuration of the power system, the relation between the load aggregator and the power user is balanced, and the overall benefit and operation stability of the power system are improved.

Description

Technical Field

[0001] This invention relates to the field of flexible load regulation and optimization technology in power systems, and more specifically to a flexible power load dispatching method, system and electronic equipment based on a game theory model. Background Technology

[0002] In recent years, my country has successively introduced energy policies such as the "dual carbon" target and the construction of a new power system, accelerating the construction of wind and photovoltaic power generation. Modern power systems are gradually developing towards a high proportion of renewable energy and high proportion of power electronic devices. As the proportion of renewable energy in the power system continues to increase, its impact on grid operation becomes more pronounced. On the one hand, the large-scale grid connection of new energy sources has led to high uncertainty on the power supply side, changing the system balance mechanism from "source follows load" to "source interacts with load," increasing the difficulty of maintaining power supply and demand balance and reducing the overall stability of the power system. On the other hand, to meet the control needs of the randomness and uncertainty of renewable energy, people have begun to vigorously explore the regulation potential of flexible resources on the load side. In the process of building a new power system, completing the modeling and coordinated control strategy research of heterogeneous flexible loads, and optimizing the decision-making behavior of various stakeholders to protect the rights and interests of all parties, is of great significance in providing peak shaving, valley filling, voltage regulation, and frequency regulation services to the power grid. Summary of the Invention

[0003] This invention provides a flexible power load dispatching system based on a game theory model. It considers the flexible load adjustment optimization of the distribution network carrying capacity and adopts a flexible load optimization dispatching strategy based on a multi-level game theory model. At the aggregator level, in order to maximize the utility of the aggregator, a non-cooperative game model of the aggregator considering the load scale effect and risk is established, and the electricity price is adjusted by adjusting the risk attention. At the user level, an evolutionary game model that maximizes the utility of the user is established to describe the user's choice behavior.

[0004] The first aspect of this invention discloses a flexible power load dispatching system based on a game theory model, the system comprising: Load aggregator module: used to obtain the load scale of load aggregators, and obtain the clean energy consumption revenue based on the obtained load scale. Taking the maximization of aggregator utility as the objective function, the clean energy consumption revenue is combined with conditional value at risk to construct a non-cooperative game model of aggregators. The particle swarm optimization algorithm is used to solve the non-cooperative game model of aggregators. When the game in the non-cooperative game model of aggregators reaches equilibrium, the load aggregator obtains the maximum revenue. User layer module: A user evolution game model based on load aggregator decision-making is constructed at the user layer. The user evolution game model is modified based on user utility. When user behavior changes, the market share of load aggregators is updated in real time, the revenue from clean energy consumption changes, and user utility changes. Users continue to change their behavior based on their utility changes until evolutionary equilibrium is reached.

[0005] According to the game-theoretic model-based flexible power load dispatching system described in the first aspect, the load scale is specifically as follows: Load size of load aggregator j The average daily load curve is used as a representation, and the calculation formula is as follows: in, The number of typical daily load curves is represented by T; T is the number of time periods. Let u be the load demand at time t; To measure the stability of the load curve, the formula for calculating the ramp index r is defined as follows: in, This represents the average value of the u-th load curve over all time periods.

[0006] According to the game-theoretic model-based flexible power load dispatching system described in the first aspect, the benefits of clean energy consumption include: The expression for a user's responsiveness is: in, y represents the user response rate, i.e., market share, when the load aggregator's incentive strategy is y; K represents the user response coefficient; D represents the user response constant. Let t represent the clean energy consumption revenue of the load aggregator from the user at time t, and p represent the clean energy consumption revenue of the load aggregator from the user.

[0007] According to the game-theoretic model-based flexible power load dispatching system described in the first aspect, the conditional risk value includes the load aggregator risk value VaR. In the risk assessment of the load aggregator, it is defined that the loss in all scenarios is no greater than the loss boundary value. The total expected loss is as follows: in, Confidence level The load aggregator's value at risk; x represents a random variable, namely the fluctuation factor of clean energy consumption. Indicates the boundary value of the loss; This represents the loss function exhibited by the load aggregator due to fluctuations in user load or clean energy consumption. Let x represent the probability density function; Indicates confidence level; The discrete expression for the conditional value at risk is: The constraints are: in, It is the conditional value of risk for load aggregators; Indicates that the loss is less than The probability of; Indicates in the scene The losses exceeded Part of, when As load increases, the profits of load aggregators decrease, and their risk aversion increases; Indicates the time point t and the scene The weighting factors are used to adjust the risk weights under different times and scenarios; The load aggregator j represents the load aggregator j in time t and scenario. Decision variables under; The electricity purchase price represents time t; The parameter representing the load aggregator j in market k; It is a weighting factor used to balance market risk; Indicates in the scene The losses exceeded The part.

[0008] According to the game-theoretic model-based flexible power load dispatching system described in the first aspect, the objective function is specifically: The objective function of the load aggregator j is expressed as: in, Let be a risk metric, representing the degree of risk focus of the j-th load aggregator, when The larger the load aggregator, the more risk-averse it becomes; R is the conditional value at risk for the load aggregator, R is the total revenue of the load aggregator, and F is the total cost of the load aggregator.

[0009] According to the flexible power load dispatching system based on the game model described in the first aspect, the following constraints need to be satisfied in the non-cooperative game model of the load aggregator: Constraints include: supply and demand balance in the electricity market; revenue maximization constraint for load aggregators; user satisfaction with electricity consumption; electricity purchase constraint for aggregators; average clean energy consumption revenue constraint; load regulation capacity constraint; and user choice behavior constraint.

[0010] According to the flexible power load dispatching system based on a game theory model as described in the first aspect, the user utility in the user layer module is: Where i represents the i-th type of user, and there exists , j represents the j-th load aggregator, and there exists ; , , , , represent the normalized values ​​of the electricity price, contract structure, power supply reliability, and value-added services offered by the j-th load aggregator to electricity users, respectively. , , , Let represent the weight coefficients of the corresponding indicators, and satisfy the following: .

[0011] According to the flexible power load dispatching system based on a game theory model described in the first aspect, the user layer constructs a user evolution game model based on load aggregator decision-making, which includes: at each moment, the user adjusts their selection behavior strategy based on the information they possess, wherein some users change their electricity consumption strategy and choose other load aggregators, the proportion of which is... To indicate, Let be the proportion of users of type i who shift from choosing the m-th load aggregator to choosing the j-th load aggregator. Then, when all users adjust their selection strategies based on their own information, the evolution process is as follows: in, This represents the proportion of users of type i who choose the m-th load aggregator. This represents the proportion of users of type i who have switched from selecting the m-th load aggregator to selecting the j-th load aggregator.

[0012] According to the flexible power load dispatching system based on the game theory model described in the first aspect, the solution process of the user evolution game model is as follows: Step S1: Initialize the state of each type of user group; Step S2: Calculate the effect of selecting load aggregator j for user group i; Step S3: Update the correction protocol according to the logit model; Step S4: Update the state of each type of user group according to the user dynamic evolution equation. If evolutionary equilibrium is reached, the process ends; otherwise, update the market share of each load aggregator and return to step S3.

[0013] Based on the flexible power load dispatching system based on the game model described in the first aspect, a modified equation for the evolutionary game model is established using the logit model, and the expression is as follows: ; in, This represents the proportion of users of type i who switch from choosing the m-th load aggregator to choosing the j-th load aggregator, reflecting the users' tendency to switch between different aggregators; Let represent the utility function of the j-th load aggregator for the i-th type of user; By exponentializing the utility function, the impact of utility differences on user choice behavior is amplified, making it easier for aggregators with higher utility to attract users to switch. The exponential utility of all load aggregators is summed as a normalization factor to ensure that the sum of the transfer ratios is 1, meaning that the user's choice is distributed among all possible aggregators. The expression for the user evolutionary game model is: ; in, This represents the proportion of users of type i who choose the j-th load aggregator, reflecting the current distribution of users among different aggregators; This represents the original proportion of users of type i who selected the j-th load aggregator before the transfer occurred.

[0014] In summary, this invention proposes a flexible power load dispatching system based on a game theory model. The aim of this invention is to construct an effective two-layer game theory optimization model between load aggregators and power users to address the flexible load optimization problem. At the load aggregator level, a non-cooperative game theory model is established with the objective function of maximizing the aggregator's utility, comprehensively considering load scale effects and risk factors. At the user level, an evolutionary game theory model based on the load aggregator's decision-making is constructed to simulate the user's choice behavior and maximize their utility. Simulation examples are used to analyze the optimal dispatching process between load aggregators and users to verify the effectiveness and rationality of the constructed two-layer game theory optimization model in solving the flexible load optimization problem. This provides theoretical support and decision-making basis for the efficient operation and optimal resource allocation of the power system, balances the interests between load aggregators and power users, and improves the overall efficiency and operational stability of the power system. Attached Figure Description

[0015] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 This is a flowchart of the particle swarm algorithm in this invention; Figure 2 This is a flowchart of the user evolution game model solution based on the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] The scale effect of load aggregators is mainly reflected in the scale of their load holdings. When the number of electricity loads is small, their consumption behavior curves are highly random. However, when a large number of electricity loads are aggregated, the consumption behavior curves become more regular. Load aggregators utilize this characteristic to participate in the electricity market by aggregating electricity loads to form a consumption behavior curve that is as stable and smooth as possible. They also act as a link between the dispatch center and users, selling the electricity they obtain from the dispatch center to users at relatively fixed prices. This reduces dispatch pressure on the one hand, and shares the risks of individual users directly participating in the electricity market on the other. At the same time, load aggregators with a large load scale have a wide variety of loads under their management. They can adjust the usage time of different loads through price incentives and other means, thereby making the consumption curves of different loads complementary, reducing the volatility of the consumption curves, and lowering the purchase price of electricity when aggregators negotiate with the dispatch center in the electricity market.

[0019] This invention provides a flexible load regulation and optimization system based on the carrying capacity of a power distribution network, comprising: A non-cooperative game theory model for load aggregators based on particle swarm optimization is set up to solve the problem. According to market supply and demand, when the clean energy consumption strategy and other conditions of the load aggregators remain unchanged, their market share will change with changes in user behavior. The expression for user responsiveness is: in, The user response rate, i.e., market share, is represented by y when the load aggregator's incentive strategy is y; K represents the user response coefficient; and D represents the user response constant. K and D are not the same for different users.

[0020] The benefits of clean energy consumption are shown in the following formula: in, This represents the revenue that the load aggregator provides to users for clean energy consumption at time t. This represents the load size owned by load aggregator j at time t. This represents the total clean energy load in the electricity market at time t. The revenue of the load aggregator can be expressed as: Because the uncertainty of user load fluctuations during real-time operation affects the absorption of clean energy, load aggregators need to fully consider the dual uncertainties of load fluctuations and clean energy absorption during their decision-making process. In economics, Value at Risk (VaR) is commonly used to characterize the maximum possible loss of an asset over a specific future period at a given confidence level. When this concept is applied to load aggregators, their VaR can be expressed as: in, Confidence level Value at Risk (VaR) of the load aggregator; x represents a random variable, namely the fluctuation factor of clean energy consumption. Indicates the boundary value of the loss; This represents the loss function exhibited by the load aggregator due to fluctuations in user load or clean energy consumption. Let x represent the probability density function; Indicates the confidence level.

[0021] However, in actual optimization, the VaR value is difficult to solve, and such methods suffer from tail risk. Therefore, this paper uses the Conditional Value at Risk (VaR) method to measure risk, and its discrete expression is as follows: The constraints are: in, It is the Value at Risk (CVaR) of the load aggregator. Indicates that the loss is less than The probability of; Indicates in the scene The losses exceeded The part. When As load increases, the profits of load aggregators decrease, and their risk aversion increases.

[0022] To protect its own interests, while taking into account both risk and load scale effects, the objective function of the load aggregator j can be expressed as: in, Let be a risk metric, representing the degree of risk focus of the j-th load aggregator, when The larger the load aggregator, the more risk-averse it becomes.

[0023] In the non-cooperative game of load aggregators, the following constraints must be satisfied: 1) Electricity Market Supply and Demand Balance Constraints: Load aggregators must ensure supply and demand balance in the electricity market during the purchase and sale of electricity. That is, the difference between the purchased and sold electricity volume must meet the real-time balance requirements of the power system. Its mathematical expression is: in, This represents the total electricity demand during time period t.

[0024] 2) Load aggregator revenue maximization constraint: The goal of load aggregators is to maximize their own revenue. Their revenue calculation needs to consider clean energy consumption revenue, electricity purchase costs, and risk costs. The specific expression is: 3) User electricity satisfaction constraint: To ensure a good user electricity experience, the benefits of clean energy consumption must be controlled within a certain range. The constraint expression is as follows: 4) Aggregated commercial electricity purchase constraints: in, This represents the total electricity purchased by load aggregator j from power generator k; , These represent the maximum and minimum output values ​​of generator k, respectively.

[0025] 5) Average Clean Energy Consumption Revenue Constraint: To maintain the stability of the electricity market, the average clean energy consumption revenue of load aggregators must be controlled within a certain range. The constraint is as follows: 6) Load Regulation Capacity Constraints: Load aggregators must possess a certain load regulation capacity to cope with fluctuations in the electricity market. This capacity can be measured by the adjustable range of the aggregated flexible loads and must meet the following requirements: 7) User Selection Constraints: When selecting a load aggregator, electricity users comprehensively consider factors such as clean energy consumption benefits, contract structure, power supply reliability, and additional value-added services. These factors collectively influence the user's utility function, thus determining the user's selection behavior. The user's utility function can be expressed as: , , , These represent the normalized index values ​​of clean energy consumption revenue, contract structure, power supply reliability, and value-added services of load aggregator j, respectively. , , , Let be the weighting coefficients of user i for each indicator, and satisfy: The load aggregators engage in a non-cooperative game. When the game reaches equilibrium, all load aggregators will obtain the maximum payoff under this state. This can be solved using the particle swarm optimization (PSO) algorithm. The following is a solution for the non-cooperative game model of load aggregators based on the PSO algorithm.

[0026] like Figure 1 The diagram shows the flowchart of the particle swarm optimization algorithm. If each particle is considered as a decision made after a game between load aggregators, then... This indicates that a Nash equilibrium representing non-game cooperation has been established when these components are in their optimal positions. In a Nash equilibrium, every decision made by load aggregator j is the best response to the decisions of other load aggregators, and thus the particle fitness representing the Nash equilibrium is optimal. The particle fitness function is defined as: The above formula indicates that the particle fitness function is equal to 0 only when the game is in Nash equilibrium.

[0027] In the user-level module, the expression for the benefits of clean energy consumption is: in, This represents the revenue that the load aggregator provides to users for clean energy consumption at time t; y represents the user response rate, i.e., market share, when the load aggregator's incentive strategy is y; K represents the user response coefficient; and D represents the user response constant. Electricity sales prices are related to the load aggregator's market share, which can be calculated from the selection results of various types of users within the region. For other indicators, professional institutions (such as power trading centers) evaluate scores based on their historical operating conditions and the power market environment, resulting in the user's utility: Where i represents the i-th type of user, and there exists , j represents the j-th load aggregator, and there exists ; , , , , represent the normalized values ​​of the electricity price, contract structure, power supply reliability, and value-added services offered by the j-th load aggregator to electricity users, respectively. , , , These represent the weighting coefficients of the corresponding indicators. And they satisfy: Assume that the proportion of users of type i choosing the j-th load aggregator is , The following conditions must be met: The expression for different types of electricity users in the same area is: In the evolutionary game among electricity users, at each moment they adjust their selection strategies based on the information they have. Some users may change their electricity consumption strategies due to economic factors and choose other load aggregators, and the proportion of these users is... To express. The proportion of users of type i who switch from choosing the m-th load aggregator to choosing the j-th load aggregator is related to factors such as user utility and the current market environment. When all users adjust their selection strategies based on their own information, the evolution process is as follows: in, This represents the proportion of users of type i who choose the m-th load aggregator. This represents the proportion of users of type i who switch from choosing the m-th load aggregator to choosing the j-th load aggregator. A modified equation for the evolutionary game model is established using the logit model, expressed as: The expression for the user evolutionary game model is: As the user evolution game progresses, when user behavior changes, the market share of load aggregators is updated in real time, leading to changes in their clean energy consumption revenue. This ultimately causes changes in user utility, and users continue to change their choices based on these changes in utility, in a cyclical process until an evolutionary equilibrium is reached. The user evolution game equation can be written as a discrete-state expression as follows: In the formula, g represents the number of iterations; This indicates the iteration step size.

[0028] like Figure 2 As shown, the solution process for the user evolution game model in the user layer module is as follows: Step S1: Initialize the state of each type of user group; Step S2: Calculate the effect of selecting load aggregator j for user group i; Step S3: Update the correction protocol according to the logit model; Step S4: Update the state of each type of user group according to the user dynamic evolution equation. If evolutionary equilibrium is reached, the process ends; otherwise, update the market share of each load aggregator and return to step S3.

[0029] In summary, the multi-level game-based flexible load optimization scheduling strategy system proposed in this invention establishes a non-cooperative game model for aggregators at the aggregator level, considering load scale effects and risks, to maximize their utility and adjust electricity prices by adjusting risk awareness. At the user level, an evolutionary game model that maximizes user utility is established to describe user choice behavior.

[0030] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A flexible power load dispatching system based on a game model, characterized in that, The system comprises: The load aggregator module is used for obtaining a load scale of a load aggregator, obtaining a clean energy consumption benefit based on the obtained load scale, taking a maximum aggregator utility as an objective function, constructing an aggregator non-cooperative game model based on the clean energy consumption benefit and a conditional value at risk, and solving the aggregator non-cooperative game model by using a particle swarm algorithm, so that the load aggregator obtains a maximum benefit when a game in the aggregator non-cooperative game model reaches equilibrium; The user layer module is used for constructing a user evolutionary game model based on a load aggregator decision at a user layer, correcting the user evolutionary game model based on a user utility, updating a market share of the load aggregator in real time, changing a clean energy consumption benefit, and causing a user utility to change when a user selection behavior changes, so that the user continues to change the selection behavior according to the self utility change until an evolutionary equilibrium is reached. 2.The game model based flexible power load dispatching system according to claim 1, wherein, The load scale is specifically: Load size of load aggregator j The average of the daily load curve is used to represent, the calculation formula is: wherein, is the number of typical daily load curves to be statistically analyzed; T is the number of time periods, is the load demand of the curve u at time t. To measure the stability of the load curve, a climbing index r of the curve is defined, and a calculation formula of the climbing index r is: wherein represents the average value of the u-th load curve over all time periods. 3.The game model based flexible power load dispatching system according to claim 2, wherein, The clean energy consumption benefit includes: A response degree expression of the user is: wherein, represents the user response rate, i.e. market share, when the incentive strategy of the load aggregator is y; K represents the user response coefficient; D represents the user response constant; represents the clean energy consumption income of the load aggregator to the user at time t, and p is the clean energy consumption income of the load aggregator to the user. 4.The game model based flexible power load dispatching system according to claim 1, wherein, The conditional value at risk includes a load aggregator value at risk, VaR, defined as the total expected loss of all scenarios in a load aggregator's risk assessment where the loss is not greater than a loss boundary value is given by: in, Confidence level Value at risk for load aggregators; x represents a random variable, i.e., the fluctuation factor of clean energy consumption; Indicates the boundary value of the loss; This represents the loss function exhibited by the load aggregator due to fluctuations in user load or clean energy consumption. express The probability density function; Indicates confidence level; A discrete expression of the conditional value at risk is: A constraint condition is: wherein, is the value at risk of the load aggregator conditional on the market price; denotes the probability that the loss is less than ; denotes the fraction of scenarios in which the loss exceeds . As increases, the load aggregator profit decreases and the degree of risk aversion increases; denotes the weight factor at time point t and scenario for adjusting the risk weight at different times and scenarios; denotes the decision variable of the load aggregator j at time t and scenario ; denotes the electricity purchase price at time t; denotes the parameter of the load aggregator j in the market k; is the weight factor for balancing the market risk; denotes the fraction of scenarios in which the loss exceeds . 5.The game model based flexible power load dispatching system according to claim 1, wherein, The objective function is specifically: An objective function of the load aggregator j is represented as: wherein, is a risk measure factor, representing the degree of concern of the jth load aggregator to risk, when is a risk measure factor, representing the degree of concern of the jth load aggregator to risk, when is a risk measure factor, representing the degree of concern of the jth load aggregator to risk, when 6.The game model based flexible power load dispatching system according to claim 1, wherein, In the non-cooperative game model of the load aggregator, the following constraint conditions need to be met: A power market supply-demand balance constraint, a load aggregator benefit maximization constraint, a user power consumption satisfaction constraint, a load aggregator electricity purchase quantity constraint, an average clean energy consumption benefit constraint, a load regulation capability constraint, and a user selection behavior constraint. 7.The game model based flexible power load dispatching system according to claim 5, wherein, A user utility in the user layer module is: where i denotes the ith type of user, and there are , j denotes the jth load aggregator, and there are ; , , , , respectively denote the normalized values of the electricity selling price, contract structure, power supply reliability rate, and additional value-added services of the jth load aggregator to the power user, , , , respectively denote the weight coefficients of the corresponding indicators, and satisfy: 。 8.The game model based flexible power load dispatching system according to claim 5, wherein, The user layer constructs a user evolutionary game model based on load aggregator decision, including that each time the user corrects the selection behavior strategy according to the information mastered, wherein part of the users change the power consumption strategy and select other load aggregators, and the proportion is represented by , is the proportion of the i-th type of user transferred from selecting the m-th load aggregator to selecting the j-th load aggregator, and when all users correct the selection behavior strategy according to the information mastered, the evolution process is as follows: wherein, represents the proportion of the i-th type of users selecting the m-th load aggregator, represents the proportion of the i-th type of users shifting from selecting the m-th load aggregator to selecting the j-th load aggregator. 9.The game model based flexible power load dispatching system according to claim 9, wherein: A solving process of the user evolutionary game model is: Step S1: initializing states of each type of user group; Step S2: calculating an effect of selecting the load aggregator j by the i-type user group by using uij; Step S3: updating and correcting an agreement according to a logit model; Step S4: updating the states of each type of user group according to a user dynamic evolutionary equation, and if an evolutionary equilibrium is reached, the process is ended; otherwise, a market share of each load aggregator is updated, and the process returns to step S3. 10.The game model based flexible power load dispatching system according to claim 9, wherein, A correction equation of the evolutionary game model established by using the logit model is expressed as: ； wherein, represents the proportion of the i-th type of users transferring from the m-th load aggregator to the j-th load aggregator, reflecting the transfer tendency of users between different aggregators; represents the utility function of the j-th load aggregator to the i-th type of users; The utility function is exponentially processed to amplify the influence of utility difference on user selection behavior, so that the aggregator with higher utility is more likely to attract user transfer; The exponential utility of all load aggregators is summed up as a normalization factor to ensure that the sum of the transfer proportions is 1, i.e. the selection distribution of users is among all possible aggregators; An expression of the user evolutionary game model is: ； wherein, represents the proportion of the i-th type of users selecting the j-th load aggregator, reflecting the distribution of the current users among different aggregators; represents the original proportion of the i-th type of users selecting the j-th load aggregator before the transfer behavior occurs.

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