{'fraction_non_alphanumeric': 0.021455938697318006, 'fraction_numerical': 0.003393541324575807, 'mean_word_length': 4.88659793814433, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Research on bidding strategy of microgrid based on nash game theory

Based on the analysis of the characteristics of microgrid power generation, low network loss and low pollution, the microgrid power market is established based on multi-agent theory to solve the power interaction between microgrid (MG) and active power distribution network. Considering an imperfectly competitive power market, the Nash game theory is used to analyze the microgrid bidding strategy. The study found that the MG participating in the bidding can maximize the profit through the bidding strategy with high scale factor and low-cost quotation. Once the bidding strategy of a microgrid is changed, other microgrids will adjust the bidding strategy accordingly. But the electricity trading market will eventually achieve Nash equilibrium. Finally, the bidding strategy and optimal selection scheme of MG’s own profit maximization are obtained by using game theory and model.


Introduction
The next-generation power grid is considered to be a smart grid architecture. The main driving force for this structure comes from energy efficiency improvement, reduction of greenhouse gas emissions, improvement of power quality and reliability, and distributed power generation and energy storage. The inevitable result of the innovation and sustainable development of advanced power electronics and modern communication technology [1]. In order to operate such an important and complex architecture, MG, as the most important component of smart grid, can realize the integration and coordination of distributed power supply by distributed energy resource management platform.
MG is a small power generation system that distributes electrical energy more flexibly and reliably in smaller geographic areas. They typically utilize distributed energy sources, such as distributed generation units and energy storage facilities, to meet local power needs. As a result, they can reduce their reliance on traditional centralized grids (also known as power grids or backbone networks). In addition to environmental benefits, using existing local renewable energy sources, such as solar cells, fuel cells or wind turbines, MG can reduce transmission and distribution losses because supply and demand sides are adjacent in the ground. It can solve the power demand and supply complementarity in a certain area well. With the continuous maturity of distributed generation and energy storage technologies, MG will be widely used in the future. The establishment of micro grid power trading market is an important way to realize the balance of power supply and demand. mechanism based on the QoS of the power supply inside the microgrid. In particular, a noncooperative game is formulated to capture the competitive market and to study the energy supply strategies of multiple energy suppliers.
Based on the existing research and the current situation of MG, this paper constructs a MG power trading market based on multi-agent system(MAS), and uses Nash game theory to explore the optimization strategy of microgrid bidding strategy. At the same time, according to the market clearing bidding principle, the bidding mechanism and income situation are given.

Problem description and model hypothesis
This paper considers a multi-agent MG system that is connected by a large number of power electronic devices such as wind power, small hydropower, solar photovoltaic power generation, gas turbines and other distributed power sources. Combined with the traditional electricity market trading rules and the particularity of the MG, the power market trading model is constructed as shown in Figure 1.
The MG power market trading center determines the market price and realizes market transactions according to the demand situation of the distribution network. Considering the uniqueness of the MG, the power market trading center classifies the MG according to the bidding situation, and divides the MG into the power supplier and the demand side according to the time period, and then feeds back the power demand and supply data in the grid to each MG agent. Finally, the MG market trading center should calculate the balance between the supply and demand of the MG. If the supply of power is less than the demand, it needs to purchase electricity from the distribution network. Otherwise, it can sell the electricity to the active distribution network, and then settle the market. For the MG agent, it mainly predicts its own power generation and load to determine its role in the market (seller or buyer), and returns its relevant data to the MG power market trading center. The trading center gives feedback information to the microgrid agent, and the microgrid agent analyzes it with historical data, formulates its own purchase or sale plan, and uploads the determined purchase, then sale plan to the transaction center.
This article makes the following assumptions: (1) Assume that there is a MG participating in the bidding in the MG power trading market, their power generation cost is a quadratic function of output.
(2) The market power demand is uncertain, and the MG agent will bid for the cost plus.
(3) The cost information between the MGs is asymmetric, that is, the MG agent cannot obtain the cost information of its competitors.
(4) The market clearing principle is determined according to the highest quotation of the MG agent.
Other symbols used herein are described in Table 1.

MG bidding model and solution analysis
Assume that there are n MGs in the electricity market to sell electricity, and one of the specific MGs (hereinafter referred to as MG 0) is used as the entry point, and the power generation cost is C  is the production cost of MG0. Due to the uncertainty of the market, these powersellers of MG agents will usecost-plus pricing system according to the changes in the market. In other words, they are in a free market competition environment. According to the principle of economics, when these power sellers participate in bidding, they will make a proportional addition on the basis of the original cost: when the market demand is greater than supply, a scale factor 1   is added to its cost. When the market demand is less than supply, a scale factor 1   is added to its cost, then the cost function of MG 0 is specified by the following equation: It can be seen that the profit of MG 0 is According to the ideas discussed above, there is also a cost dynamic adjustment factor for the expected cost of the MG i , which is set to i  .Therefore, the expected cost addition function of the MG The profit function of MG i can be obtained in (8) At this point, the bidding game between the MGs is obviously perfect information, so it can be solved by Nash equilibrium. Using the first derivative, the corresponding results are obtained as in Eq.(10) and Eq. (11), and it is easy to judge that the second derivative is less than zero.
According to the demand forecast, the MG trading center can get the power load at this time, and then determine the total output of all bidding MG as follows: Where b  is the amount of electricity purchased by the grid trading center to the external active distribution network.
Through simultaneous formulas (10), (11) and (12), the optimal bidding capacity of MG0 can be obtained with consideration of competitors' conditions.  (11), it can be estimated that the expected price of the MG 0 competitor is Obviously, the expected price between MG 0 and its competitors is generally different, but the price in the electricity market is unique.According to the principle of unified clearing price, the bidding price of all MG participants is ranked from low to high, and the highest bidding price is the final clearing price of the power market. Therefore, the clearing price of the market is  (4) and (9), we can get the expected profits of each MG after bidding.

Conclusion
In view of the situation that multiple MGs participate in bidding power generation in the electricity market trading center, this paper proposes a multi-agent theory based bidding game model for MG, and gives the strategy of MG bidding in power generation market. It can be seen that the generation cost of MG has a direct impact on participating in bidding, and the MG with higher generation cost is forced to adopt higher quotation. According to the rules of power market trading center, those with low bidding will be given priority to power generation, so as to obtain more profits. At the same time, the research also found that the MG participating in the bidding can maximize its own revenue through the combination of bidding strategies with high scale factor and low-cost quotation, and the change of bidding strategy of one MG will lead to the adjustment of bidding strategies of other MGs. However, the MG power trading market will eventually achieve Nash equilibrium. Finally, the optimal bidding strategy and the optimal scheme for the profit maximization of MG are obtained by numerical analysis, which provides a theoretical basis for MG to obtain higher profits on the basis of considering other competitors.