# Game Approach to HDR-TS-PV Hybrid Power System Dispatching
## 3 **Hdr-Ts-PV** Game Model  
### ElementTS of the Game  
Compared with other coordinated dispatching methods, game theory can better clarify the internal mechanisms of multi-agent competition and cooperation to quantify each party's benefits. The elements of the game include Player, Strategy, and Payoff.  
1 Player  
The \(HDR\) power station, \(TS\) power station, and \(PV\) plant are the three players, denoted by H, T, and P, respectively.  
2 Strategy  
The operational goal of the \(HDR\) power station is to obtain as much profit as possible to rapidly recoup the high costs of construction by changing the mass flow of brine to dispatch the power. Therefore, the strategy set of the \(HDR\) power station is  
\[\Omega_{\rm H}=\Big{\{}P_{Hf}^{t}\Big{|}P_{H}^{\rm min}\leq P_{Hf}^{t}\leq P_{ H}^{install}\Big{\}}, \tag{5}\]  
where \(P_{H}^{install}\) represents the installed capacity of the \(HDR\) power station, and \(P_{H}^{\rm min}\) is the output power that meets the minimum power generation requirements of the \(ORC\) generator, which is generally 10% of the installed capacity.  
The \(TS\) power station primarily realizes the arbitrage of the electricity price peak-valley difference by dispatching purchased power and generating power. Therefore, the strategy set of the \(TS\) power station is  
\[\Omega_{\rm T}=\left\{\begin{array}{c}P_{purch}^{t}\Big{|}0\leq P_{purch}^{t }\leq P_{heat}^{\rm max}\\ P_{T}^{t}\Big{|}P_{T}^{\rm min}\leq P_{T}^{t}\leq P_{T}^{install}\end{array} \right\}, \tag{6}\]  
where \(P_{purch}^{t}\) is the electric power purchased from the grid during the low \(TOU\) price period and limited by the maximum power \(P_{heat}^{\rm max}\) of the electric heating device. \(P_{T}^{t}\) represents the power generation capacity of the \(TS\) power station, and its upper and lower limits are the installed capacity \(P_{T}^{install}\) and the \(ORC\) generator and the minimum power generation condition \(P_{T}^{\rm min}\), respectively.  
The operational goal of a \(PV\) plant is to formulate a credible output power plan based on the weather forecast data to increase the credible capacity connected to the grid as much as possible so as to reduce the loss of surplus power and penalty incurred by abandoning loads. its strategy set is  
\[\Omega_{\rm P}=\Big{\{}P_{PV}^{t}\Big{|}0\leq P_{PV}^{t}\leq P_{PV}^{install} \Big{\}}, \tag{7}\]where \(P_{PV}^{t}\) is the credible output power of the \(PV\) plant, and its corresponding installed capacity is the credible capacity of the \(PV\) plant, denoted by \(P_{PV}\). \(P_{PV}^{install}\) represents the installed capacity of the \(PV\) plant.
3 Payoff  
All three players profit by selling electricity to the grid so that we can define the payoff vector of the game as  
\[I=\left(I_{\text{H}},I_{\text{T}},I_{\text{P}}\right), \tag{8}\]  
where \(I_{\text{H}}\), \(I_{\text{T}}\) and \(I_{\text{P}}\) represent the payoff of the \(HDR\) power station, \(TS\) power station, and \(PV\) plant, respectively.  
Each player has an independent and equal status and can either compete in a non-cooperative game or try to increase profits through cooperation. The coordination dispatching models of the two types of games are given below.