# Game Approach to HDR-TS-PV Hybrid Power System Dispatching
## 4 Case Study
### Sensitivity Analysis  
The extra profits of the grand coalition generated by the cooperative game are closely related to the allowed fluctuation rate that the power grid can tolerate and the penalty coefficient for abandoning loads. Therefore, based on the preceding section, the allowed fluctuation rate and penalty coefficient are varied to further analyze the role of the \(HDR\), PV, and \(TS\) plants in the grand coalition.  
Under the parameters in Table 1, the allowed fluctuation rates are set at 0%, 1%, 2%, and 3%. Simultaneously, when the penalty coefficients are 2, 3, 4, and 5, respectively, the payoff of the grand coalition and the extra profits obtained by each player are calculated. Figure 10 shows the relationship between the overall payoffs, the allowed fluctuation rate, and the penalty coefficient.  
In Figure 10, 1, 2, 3, and 4 correspond to the scenarios where the penalty coefficients \(p\) are equal to 2, 3, 4, and 5, respectively. The overall payoff of the coalition increases with the increasing allowed fluctuation rate, mainly due to an increase in the grid-connected power of the \(PV\) plant and the penalty reduction. The overall payoff of the coalition decreases with an increase in the penalty coefficient, and the payoff of the \(PV\) plant is affected directly by the penalty coefficient. However, the payoff of the \(HDR\) power station is almost constant, reflecting the characteristics of stability and continuity of  
Figure 10: The payoff allocation in the grand coalition.  
Figure 9: Stability of the Shapley value.  
_HDR_ resources. The _TS_ power station is mainly responsible for creating profits and saving penalties by supporting the grid connection of the _PV_ plant.  
Figure 11 shows the changes in the allocation of the extra profits to the _HDR_, _PV_, and _TS_ power stations with the change in the allowed fluctuation rate. The overall extra profits decrease with an increase in the allowed fluctuation rate, which indicates that the extra profits of the coalition decrease with an increase in the ability of the power grid to withstand power fluctuation. These extra profits are mainly caused by the curtailment of energy and penalty cost generated by the _PV_ plant. Simultaneously, the extra profits of the _HDR_ power station do not change with the penalty coefficient changes and are not sensitive to the allowed fluctuation rates, indicating that the extra profit of the _HDR_ power station is obtained by the peak regulation of geothermal energy, which is not affected by the _PV_ plant.  
The variation trends of the extra profits obtained by the _PV_ and _TS_ power stations are similar. The higher the penalty coefficient, the more the extra profits that are allocated. The relationship between the penalty coefficient and extra profits indicates that the _TS_ power station is the main contributor that supports the grid connection of the _PV_ station, realizes the value of the surplus _PV_ power, and reduces the penalty.  
Analysis of Figures 10 and 11 shows that the extra profits in the grand coalition, generated by the cooperative game, result from three factors. First, owing to the peak-regulating effect of the _TS_ power station, the _HDR_ generation period shifts from the low _TOU_ price period to the high _TOU_ price period. Second, through the flexible operation of the _HDR_ and the _TS_ power stations, a greater capacity of the _PV_ station can track the dispatching curve, thus reducing the penalty. Third, the curtailed power and geothermal energy are stored and utilized by the _TS_ power station.