Research on Multi-Distributed Node Power System Modeling and Stackelberg Game Energy Management Effect for Dual-Carbon Goal
https://doi-001.org/1025/17609702951159
Jiajia Huan1,a*, Jiawen Liu1,b
1Guangdong Power Grid Co，Ltd.
aJiajia Huan: huangjj@126.com
bJiawen Liu: 102361651@qq.com
Funding：China Southern Power Grid Special Project on Power Grid Planning Project No.: 031000QQ00240007
Abstract: In the development of modern society, in order to build a sustainable ecological environment, the state puts forward the goals of “carbon neutral” and “carbon peak”. As the main driving force to realize the goal of “double carbon”, the energy Internet can provide an open network framework for the integration of energy production, transmission, storage and other equipment, and improve the level of China’s energy management and control in an all-round way, after understanding the status quo of energy management and the development of related technologies in the new period, we constructed the Stackelberg game model based on the problem of energy management. Stackelberg game model, and utilize the electric energy prediction method to effectively guide energy management. The actual simulation results prove the effectiveness of constructing renewable energy management model with big data technology as the core.
Keywords: Double carbon” target; energy management; Stackelberg game; big data technology.
1.Introduction
In the development of urban construction, all areas of life and work need to obtain sufficient energy for development [1]. As a participant and promoter in realizing the goal of “dual-carbon”, it can provide an open framework for energy production, energy transmission, energy distribution, energy conversion, and exchange and consumption equipment technology, which can control the operation of the energy system in a comprehensive way, and also solve the technical problems of the traditional system such as centralized power generation and unidirectional flow [2]. At this stage, there are more and more research on the design of energy management in power grids, such as scholars combined with the requirements of energy management of microgrids proposed a two-tier control model, which is divided into two levels: on the one hand, the scheduling layer will provide the output power of each unit according to the real-time data, and on the other hand, the scheduling layer will provide the results of operation optimization in combination with the forecast data; there are scholars who have used the stochastic unit combination model to put forward a dynamic planning algorithm that can effectively coordinate the energy demand and distributed renewable energy supply problems [3]. In the face of the diversified energy requirements put forward by the development of modern social construction, in order to comprehensively improve the application efficiency of distributed energy, effectively improve the overall energy scheduling level, in-depth study of the competitive game relationship within the system, the use of effective programs to optimize the objective function of the participants, and ultimately, based on the accurate prediction, the results of the appropriate processing countermeasures, so as to facilitate the realization of the energy management and control objectives [4].
2.Building Stackelberg game model based on energy management
2.1 System architecture
In this paper, according to the basic requirements put forward by the “dual-carbon” goal, more distributed energy will be connected to the grid on a wide scale, and considering the uncontrollability and volatility of distributed energy, it is clear that the stability of the power system will be affected to a certain extent [5]. And the grid installed capacity is limited, if only rely on their own energy supply, then it is difficult to meet the user’s power demand, so the construction of microgrid-based energy management system,During the operation of the system, it contains three participants: the power supply enterprise, the energy Internet and the users [6]. Among them, in addition to power generation, cooling and heating and other related equipment, the energy Internet will also purchase electricity from the power supply enterprises, and it is assumed that the user’s basic energy needs are met by the energy Internet; the power supply enterprises, as the supplier of energy, will work with the energy Internet to adjust the price of energy sales, and the practice of the development of their own interests want to achieve the maximization of the consumer will be reasonably adjusted to the actual load of energy use, the science and the experience of balancing expenditure and energy use. Balance expenditure and energy experience, the three-party game model framework is shown in Figure 1 below:
Figure 1The framework of the tripartite Stackelberg game model
First of all, in the operation of the power supply enterprise, the objective function is composed of power sales revenue, power generation cost and unit emission cost, and the specific formula is as follows:
In the following formula, p(psc, t) Ppsc, trepresents the gain from electricity sales obtained in the time period t, ppsc, trepresents the price of electricity sales of the power supply enterprise in the time period t, Ppsc, trepresents the amount of electricity purchased by the energy internet from the power supply enterprise in the time period t, CGen, trepresents the generation cost of the generating unit, and Upsc, trepresents the the emission cost of the generating unit. The research model in this paper divides a day into 24 time periods, each of which is a basic unit for rational planning [7].
Assuming that CGen, tis a quadratic function of the amount of electricity purchased by the energy internet in question, the corresponding equation is as follows:
In the above equation, a, b, and c refer to the generation coefficients of the unit, while the emission cost of the generating unit is calculated as follows:
In the above equation, pemirepresents the emission price per unit volume of gas, and weleC, weleNare the quantities of carbon dioxide and carbon monoxide emissions corresponding to the production unit kW-h.
Secondly, in the energy internet, according to the type of its transmission medium, it contains three types: electricity, heat and cold. Separate models for different energy storage and conversion devices can be obtained:
The calculation formula for the electric bus balance is as follows:
The calculation formula for the hot bus balance is as follows:
The formula for the cold bus balance is as follows:
Simulation analysis for model operation, both to analyze the internal energy bus balance and to consider the specific equations for equipment operation to handle the constraints are as follows:
In the above equations, Pce, maxand Pce, minrepresent the maximum and minimum electric power of the internal combustion unit; Pi, trepresents the electric power of the equipment of class i at time period t, Hm, trepresents the thermal power of the corresponding equipment of class m, and Cn, trepresents the cold power of the corresponding equipment of class n; Pi, maxrepresents the maximum electric power, Hm, maxrepresents the maximum thermal power, and Cn, trepresents the maximum thermal power. maximum thermal power, and Cn, maxrepresents the maximum cold power.
The power constraints of the energy storage device and the constraints of the energy storage conditions are as follows:
In the above equations, Pc, t, Pd, trepresent this time period, storage power and energy power, Pc, max, P(c,min)represent the maximum storage power and minimum storage power, SOC, trepresent the energy storage state values, represent the function of the storage device and the efficiency of the exergy, Sc, t, Sd, trepresent the function of the storage device and the exergy of the storage device in this time period, Sc, t, Sd, trepresent the function and the exergy of the storage device in this time period, Sc, tand Sd, trepresent the function and exergy of the storage device in this time period. Sessrepresents the storage capacity of the energy storage device, and represents the duration of the time period, 1h.
The objective function of the energy Internet is as follows:
In the above equation, is the revenue obtained from selling energy in time period t, pmeg, tis the price of energy sold by the energy internet in time period t, ltis the actual load of the users in time period t, and Cmeg, tis the cost of capacity of the energy internet.
Finally, the user model. In this study, the deviation value between the user’s demand and the actual electricity composite is considered as a variable, from which the dissatisfaction function is constructed [8]. The following expression is obtained based on the user’s demand for each energy source:
In the above equation, α, β, λ represent the parameters related to the function and conform to α> 1, β> 1, λ> 1, β belongs to the preset value, λ will be studied according to the adjustment ratio elasticity of the electricity load, α is closely related to the amplitude of Rt, and dtrefers to the user’s energy demand.
2.2 Stackelberg game model
In this paper, a two-layer Stackelberg game model is used to analyze the energy trading model [9]. In this case, the energy internet acts as a follower of the power supply company in the upper layer of the game, while it acts as a leader of the users in the lower layer of the game, and the game model between the three is as follows:
In the above equation, L represents participants, Ω represents strategies, and I represents utility. Constructing the two-layer Stackelberg game model with hierarchical decision-making structure, the expected results are expressed by applying the form of Stackelberg equilibrium, and if the following conditions are satisfied, then is the proposed two-layer Stackelberg game equilibrium. The specific formula is as follows:
In the above equation, l* represents the equilibrium strategy of all users, lirepresents the energy strategy of the ith user, l*-1represents the equilibrium strategy of other users except the user, Q represents the total number of users, ppsc, trepresents the price of electricity sales, Ppsc, trepresents the quantity of electricity, pmeg, trepresents the price of energy sales, and ltrepresents the actual user energy load . In the case that the strategies of all the participants of the game model are SE, then no participant can gain more by adjusting their strategies independently [10].
Taking the lower game as an example, the energy Internet as a leader can be regarded as a fixed value of 1 when calculating and analyzing the user’s optimal strategy, which can be directly ignored in the reasoning process, then the user’s objective function is as follows:
In the above formula, , take the left side of the formula is zero, then the user’s optimal strategy can be obtained, the specific formula is as follows:
And then, according to the derivation of the above, it can be obtained:
Combined with the analysis of the above formula, it can be seen that the Hessian matrix of the user’s objective function Iuserrepresents a negative definite matrix, which indicates that the user’s objective function belongs to the concave function, and refers to the optimal strategy of the user’s ability to price a given thing.
Based on the above two-layer Stackelberg game equilibrium model a distributed algorithm is proposed, which can help participants to make independent decisions without revealing their own objective functions [11]. It is assumed that the centralized control center is regarded as the middle party, which coordinates the solution of SE after collecting the dynamic information of the game participants, where the task of the control center is to obtain the latest decision information of the participants, pass it to other participants, receive the feedback decision information, and finally obtain the SE after iteration [12]. The actual process is as follows:
Fig. 3 Flowchart of Stackelberg solution
3.Experimental Analysis
3.1 Experimental Design
According to the model obtained from the above study, in order to verify the effectiveness of its algorithmic application, the simulation parameters of power plants, energy storage enterprises, microgrids, and users shown in Table 1 are collected and organized, focusing on the analysis of predicting longitude wind forecasting model.
Table 1 Parameter design of experimental simulation
| parameter | describe | threshold value |
| Power plant power generation cost parameters | 0.03 | |
| Utility pollutant emission cost parameters | 0.08 | |
| Unit cost of operation and maintenance | 1.5 | |
| Charging efficiency of storage devices | 0.5 | |
| Emission efficiency of storage equipment | 0.5 | |
| Microgrid power generation cost parameters | 0.05 | |
| Pollutant emission cost parameters of microgrid | 0.05 | |
| Power plant satisfaction parameters | 5 | |
| Energy storage company satisfaction parameters | 10 | |
| Microgrid satisfaction parameters | 50 | |
| Maximum capacity of microgrid company | 200 kW | |
| Maximum capacity of energy storage company | 100 kW | |
| The highest price a user can pay | 500/kW·h | |
| Real wind power | 20 kW | |
| penalty factor | −50 |
In order to accurately obtain the various data information obtained during the experiment, the study constructed a prediction model with genetic algorithm as the core, using genetic algorithm to optimize the parameters of the self-encoder and the whole network, so as to improve the application performance of the model, specific algorithm training as Table 2:
Table 2 Algorithm training steps
| Description | |
| Algorithm 1: Proposed SAE Algorithm | |
| 1 | Initialize the population P(d,t), t=0 |
| 2 | While t<T and d<D do |
| Training Process | |
| Evaluate the fitness of P(d,t); calculate and store the best, worst, and average fitness values of the current individuals. | |
| Select the best P(d,t); choose the best individuals for the next generation. | |
| Fine-tuning Process | |
| Perform crossover operation on P(d,t); conduct crossover operations on selected individuals to obtain better individuals. | |
| Perform mutation operation on P(d,t); mutate P(d,t) with a certain mutation probability. | |
| End | |
| Update t=t+1 | |
| 3 | End |
Collect data according to the above algorithm, complete the training and preprocessing, remove unnecessary information, obtain the parameters of the energy storage equipment as shown in Table 3 below, and evaluate the budget on this basis.
Table 3 Parameter design of energy storage equipment
3.2 Experimental results
First of all, after obtaining the optimal tariffs of power plants, energy storage companies and microgrids with the basic electricity demand of users, the calculation results show that power plants, energy storage companies and microgrids will increase monotonically with the increase in the number of users, which is in line with the reality. The reason for this is that the cost of electricity generation increases with the number of users [13]. In this case, the optimal price of electricity for the energy storage firm is lower than that of the power plant because the microgrid is more willing to use the clean renewable energy stored by the storage firm and the optimal price of the microgrid is higher than the other two due to the fact that in the second stage, only one microgrid is considered, which can make a profit by posting a higher price to the users than the other two.
Secondly, after obtaining the optimal quantity of power purchased by power plants, enterprises and microgrids for the users’ basic electricity demand, the numerical simulation results show that the values of power plants and energy storage enterprises will follow the increase in the number of users, and microgrids need to obtain more power from power plants and energy storage enterprises in order to satisfy the increasing users’ electricity demand. At the same time, it can be found that energy storage firms are significantly higher than power plants, which is due to the fact that microgrids prefer to use clean renewable energy stored by energy storage firms [14].
Again, the basic electricity demand data of power plants, energy storage firms, and microgrid revenues and users are obtained, and the relationship between them is explored and it is found that: all three rise monotonically following the increase in the number of users, and have a very high correlation with each other. In particular, power plants are higher than microgrids, while microgrids are higher than energy storage firms due to the low transmission losses and monopoly position of microgrids, as well as frequent access to stored renewable energy [15].
Finally, based on the optimal return and wind power prediction results in different scenarios, the prediction errors between the two are compared and analyzed: represents that the actual output is less than the predicted quantity, which requires the microgrid to acquire more electric energy from utilities and storage companies; represents that the actual wind power output exceeds the predicted quantity, and the microgrid does not need to procure the specified quantity of electricity consumption from power plants and storage companies at the same time. In the case of , the drop in optimal returns is more severe compared to . The reason is that at , the electricity price of the utility and the energy storage enterprise is significantly higher than the case of . On this basis, the genetic algorithm is used to obtain the MAPE value for the prediction step, and SVM and Adam algorithms are selected for control analysis. The results of practical simulation found that the MAPE value will follow the increase of the prediction step, while the accuracy of the actual results will decrease. Being able to obtain the minimum prediction error, the absolute prediction error can be decreased by 7.3% to 32.4%, and with the increasing number of iterations, no matter whether it is the Stackelberg game proposed in the study or the classical Adam non-cooperative game algorithm, after a smaller number of iterations, it can achieve a very obvious convergence effect. In this study, compared with other algorithms, the Stackelberg game can bring more benefits to the microgrid system.
Conclusion
In summary, in the development of modern society, in order to fully utilize renewable energy, this paper studies the energy management problem as a three-stage Stackelberg game model, on the basis of guaranteeing the safe and stable operation of the system, to truly satisfy the user’s energy needs, to achieve the maximization of the benefits of the participating individuals, and at the same time constructs the power generation prediction technology with big data technology as the core, from which it obtains the short-term wind power prediction results, which can help microgrids fully implement effective energy management strategies.
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