# Evolutionary Game Analysis of Power Generation Groups Considering Energy Price Fluctuation
## 5 Case Analysis
### Primary Energy Price Fluctuation and Power Generation Cost Analysis
The conditional relations in scenario 2.2-b are shown in inequalities (38) and (39):  
Table 5.8  
Table 5.9  
In February 2021, the cost of coal-fired power generation was much lower than the cost of gas-fired power generation, which belongs to the situation of phase 1 in Figure 2b, and the evolution simulation results are shown in Figure 11a. In this case, there is no stable equilibrium point, and the coal-fired power generation group chooses the strategic bidding, the gas-fired power generation group has a huge disadvantage in power generation cost, and the power generation side market has been completely occupied by the coal-fired power generation group, so the revenue is 0. The bidding strategy of the game subject cannot reach a stable equilibrium state, but the electricity price can reach a stable state, which keeps \(v_{coal}\) times the cost of coal-fired power generation. In January and May 2021, the cost of coal-fired power generation is much higher than that of gas-fired power generation, which belongs to the situation of phase 4 in Figure 2b, and the evolution simulation results are shown in Figure 11b. Coal-fired and gas-fired power generators all choose strategic bidding. The market has reached equilibrium, but the electricity price is high. The coal-fired electricity price is \(v_{coal}\) times the cost of its power generation, and the gas-fired electricity price is \(v_{gas}\) times the cost of its power generation. Figure 5.0 Evolution trend of bidding entities in phase 3 under scenario 2. (**a**) Simulation results of the evolution of the cost of coal-fired electricity from August to December 2020 and April and June 2021 with a slightly higher cost of electricity than gas-fired electricity, (**b**) Simulation results for the evolution of a gas-fired power producer with a higher feed-in tariff for lower electricity prices. In addition, according to the discussion in Section III and the parameter settings in Section V, the cost relationship between primary and secondary energy can be quantified as follows. First, the relationship between the cost of coal-fired electricity and the price of thermal coal can be expressed as Equation (40):  
Figure 5.1  
Formula (26), \(\lambda_{coal}\) is the price of thermal coal. Secondly, the relationship between the cost of gas-fired electricity and the price of natural gas can be expressed as Equation (41):  
Figure 5.2  
Formula (27), \(\lambda_{gas}\) is the price of natural gas. When a certain supply-demand relationship is met, same-stage bidding will not increase the overall electricity price. There is little difference in electricity cost. That is, the price based on cost quotation chosen by high-cost generators is lower than the price quoted by low-cost generators using strategy. Specifically, two types of generators can be represented in Equation (42):  
Figure 5.3  
When \(\mu_{coal}=\mu_{gas}=1.1\), \(\
u_{coal}=\
u_{gas}=1.3\), the cost ratio of coal and gas power generation can be obtained between 0.846 and 1.182. In the context of using primary energy prices, it can be quantified as Equation (43):  
Figure 5.4  
If let \(\lambda_{coal}\)= 600, then when \(1542<\lambda_{gas}<2492\), that is, when the cost ratio of coal and gas power generation is between 2.57 and 4.15. The bidding of gas and coal-fired power generation groups on the same stage will not lead to an increase in electricity prices, and the market can maintain a balanced state. Figure 5.5 Evolution trend of bidding entities in phases 1 and 4 under scenario 2. (**a**) Simulation results of the evolution of the cost of coal-fired electricity at a much lower cost than gas-fired electricity in February 2021, (**b**) Evolutionary simulation results when the cost of coal-fired electricity is much higher than the cost of gas-fired electricity in January and May 2021.