# Evolutionary Game Analysis of Power Generation Groups Considering Energy Price Fluctuation
### Main Work and Innovations
Power producers, large industrial consumers, and electricity sellers participate in bidding in the electricity market and then conduct electricity exchange. The specific clearing electricity quantity and electricity price are determined by the market mechanism. When the price of the primary energy market fluctuates, the clearing price of the electricity market will fluctuate due to the change in the power generation cost of the power suppliers. According to evolutionary game theory, the power market management department can simulate the bidding trend of coal-fired power generation units and gas-fired power generation units, respectively, and analyze their optimal bidding strategies. Then adjust the bidding electricity of the two types of generating units to change the electricity structure on the generation side and avoid sharp fluctuations in the transaction price. The bidding strategies of the power generation group in the electricity market are divided into two types, one type is cost-based bidding based on the price of primary energy, and the other type is strategic bidding that pursues high-profit margins. Cost-based bidding means that the bidding price is lower, and more electricity will be cleared; Strategic bidding means a higher bidding price and more profits. Suppose the two bidding strategies of coal-fired power generation groups are cost bidding \(P_{coal}^{L}\) and strategic bidding \(P_{coal}^{H}\), and the proportion of power generation groups who choose these two strategies are \(p\)\(1-p\) (\(0\leq p\leq 1\)); The two bidding strategies of the gas-fired power generation group are cost bidding \(P_{gas}^{L}\) and strategic bidding \(P_{gas}^{H}\), and the proportions of power generators who choose these two strategies are \(q\), \(1-q\) (\(0\leq q\leq 1\)). The payoff matrix of the evolutionary game of market competition among power generation groups is shown in Table 1. Table 1 \(u_{i}\) and \(v_{i}\) (\(i=1,2,3,4\)) denote the revenue from coal-fired power generators and gas-fired power generators, respectively. Based on the above game model assumptions, the gas-fired generation group's expected revenue when bidding based on cost is, as described in Equation (1). \[E_{gas}^{L}=pv_{1}+(1-p)v_{3} \tag{1}\]  
Based on the strategic tender, the expected revenue of the gas-fired generation group is shown in Equation (2)  
\[E_{gas}^{H}=pv_{2}+(1-p)v_{4} \tag{2}\]  
The average expected revenue of the gas-fired generation group is shown in Equation (3)  
\[\overline{E}_{gas}=qE_{gas}^{L}+(1-q)E_{gas}^{H} \tag{3}\]  
Based on the cost bidding, the expected revenue of the coal-fired generation group is as described in Equation (4)  
\[E_{coal}^{L}=qu_{1}+(1-q)u_{2} \tag{4}\]  
The expected revenue of the coal-fired generation group based on the strategic tender is shown in Equation (5)  
\[E_{coal}^{H}=qu_{3}+(1-q)u_{4} \tag{5}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group Bidding Strategy of** & **Group Bidding Strategy of Gas-Fired Power Generators** \\ \cline{2-3}
**Coal-Fired Power Generators** & \(P_{gas}^{L}(q)\) & \(P_{gas}^{H}(1-q)\) \\ \hline \(P_{coal}^{L}(p)\) & \((u_{1},v_{1})\) & \((u_{2},v_{2})\) \\ \(P_{coal}^{H}(1-p)\) & \((u_{3},v_{3})\) & \((u_{4},v_{4})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Power market operation situation system dynamics model module division. The average expected revenue of the coal-fired generation group is shown in Equation (6)  
\[\overline{E}_{coal}=pE_{coal}^{L}+(1-p)E_{coal}^{H} \tag{6}\]  
Based on the set of equations in Equations (1)-(6), the replicated dynamic differential equations for coal-fired and gas-fired generating units are shown in Equations (7) and (8) as follows. \[\dot{p}=\frac{dp}{dt}=p(1-p)[(u_{2}-u_{4})+q(u_{1}-u_{3}-u_{2}+u_{4})] \tag{7}\]  
\[\dot{q}=\frac{dq}{dt}=q(1-q)[(v_{3}-v_{4})+p(v_{1}-v_{3}-v_{2}+v_{4})] \tag{8}\]  
Therefore, the evolutionary bidding state on the power generation side can be described by Equations (7) and (8). Let Equations (7) and (8) be equal to 0.