# Evolutionary Game Analysis of Power Generation Groups Considering Energy Price Fluctuation
## 3 Analysis of Power Generation Cost under Primary Energy Price Fluctuation
### Gas-Fired Power Generation Cost Analysis
Based on this, according to the total market demand for power generation \(Q_{DM}\) and the power generation capacity participating in market competition \(Q_{SP}\), it can be divided into the following two typical situations under the influence of different supply and demand relationships and the fluctuation of primary energy prices:  
Scenario 1: \(\sum\limits_{i=1}^{m}Q_{coal,i}<Q_{DM}\), \(\sum\limits_{i=1}^{n}Q_{gas,i}<Q_{DM}\), \(\sum\limits_{i=1}^{m}Q_{coal,i}+\sum\limits_{i=1}^{n}Q_{gas,i}\geq Q_{DM}\), the bidding power on the generation side exceeds bidding power on the consumption side, and the power generation of coal-fired and gas-fired power generators participating in the market is each smaller than the market demand, and the total power generation of coal-fired and gas-fired power generators participating in the market is greater than the market demand;  
Scenario 2: \(\sum\limits_{i=1}^{m}Q_{coal,i}\geq Q_{DM}\), \(\sum\limits_{i=1}^{n}Q_{gas,i}\leq Q_{DM}\), the market supply exceeds the demand, and the coal-fired power generation group participating in the market generates more power than the market demand, and the gas-fired power generation group participating in the market generates less power than the market demand. In order to represent the change in the cost of electricity generation caused by fluctuations in energy prices, the cost ratio of coal and gas is introduced as \(\varepsilon\), let \(\varepsilon=C_{coal}/C_{gas}\), for the various situations mentioned above, this section will discuss the equilibrium points' stable situation of the two groups of power generators when \(0<\varepsilon<1\) (i.e., the cost of coal-fired power generation is lower than that of gas) and \(\varepsilon>1\) (i.e., the cost of coal-fired power generation is higher than that of gas). The four cases of \(0<\varepsilon<1\) and \(\varepsilon>1\) in the two scenarios are discussed below. Scenario 1: \(\sum\limits_{i=1}^{m}Q_{coal,i}<Q_{DM}\), \(\sum\limits_{i=1}^{n}Q_{gas,i}<Q_{DM}\), \(\sum\limits_{i=1}^{m}Q_{coal,i}+\sum\limits_{i=1}^{n}Q_{gas,i}\geq Q_{DM}\), the bidding power on the generation side exceeds bidding power on the consumption side, the power generation of coal-fired and gas-fired power generators participating in the market is smaller than the market demand, and the total power generation of coal-fired and gas-fired power generators participating in the market is greater than the market demand;  
Scenario 1.1: \(C_{coal}=\varepsilon C_{gas}\), \(0<\varepsilon<1\) that is, the cost of coal-fired power generation is lower than that of gas-fired. The payment parameters for this situation are derived as follows:  
When both coal-fired and gas-fired power generation groups choose cost bidding, the calculation formulas \(u_{1}\)\(v_{1}\) are shown in Equation (19). \[\left\{ \begin{array}{l}u_{1}=P_{coal}^{L}-C_{coal}=(\mu_{coal}-1)C_{coal} \\ v_{1}=\frac{Q_{DM}-\sum\limits_{i=1}^{m}Q_{coal,i}}{\sum\limits_{i=1}^{n}Q_{ gas,i}}(P_{gas}^{L}-C_{gas})=\frac{Q_{DM}-\sum\limits_{i=1}^{m}Q_{coal,i}}{ \sum\limits_{i=1}^{n}Q_{gas,i}}(\mu_{gas}-1)C_{gas}\end{array} \right. \tag{19}\]  
When the coal-fired power generation group chooses cost bidding and the gas-fired power generation group chooses strategic bidding, the calculation formulas \(u_{2}\)\(v_{2}\) are shown in Equation (20):  
\[\left\{ \begin{array}{l}u_{2}=P_{coal}^{L}-C_{coal}=(\mu_{coal}-1)C_{coal}\\ v_{2}=\frac{Q_{DM}-\sum\limits_{i=1}^{m}Q_{coal,i}}{\sum\limits_{i=1}^{n}Q_{ gas,i}}(P_{gas}^{H}-C_{gas})=\frac{Q_{DM}-\sum\limits_{i=1}^{m}Q_{coal,i}}{ \sum\limits_{i=1}^{n}Q_{gas,i}}(v_{gas}-1)C_{gas}\end{array} \right. \tag{20}\]  
When the gas-fired power generation group chooses cost bidding and the coal-fired power generation group chooses strategic bidding, \(P_{coal}^{H}=v_{coal}C_{coal}=v_{coal}\varepsilon C_{gas}\); \(P_{gas}^{L}=\mu_{gas}C_{gas}\).