## 5 Case Study
### Results Discussion
#### 5.2.2 Effectiveness Analysis  
The effectiveness of the proposed model was verified by the comparison with the conventional model. In the conventional model, the electricity price factor was not included, but only to achieve the maximum expected power generation in the scheduling horizon, maintain an adequate security of supply, and arrange the cascade plants to deliver electricity outwards in a certain proportion in case of spilled water in the flood seasons. In 2016, the natural inflow concentrated from June to August, accounted for 50% of the total inflow in the year. There was a risk of spilled water, and so the  
Figure 5: The diagram of silhouette values in each month.  
cascade hydropower plants were arranged to deliver electricity outwards, i.e., participate the external electricity market. Other constraints, such as the final water level, maximum and minimum power output, combined MCP scenarios, and so on, were the same for the two models.  
Figure 6 shows the water level of the cascade hydropower plants with regulation capacity, and the power output process were also obtained. It was found that the water level change trend of each hydropower plant was consistent for both the proposed model and conventional model. Generally, before the flood seasons, the water level of each hydropower plant fell, vacating the reservoir. During the flood seasons, the water was stored, the water level rose, and the generation water head increased. After the flood seasons, the water level reduced back to the control water level. These trends were in line with the cascade hydropower operation rules.  
In terms of power generation in different months, the power generation of the proposed model during the dry seasons was much more than the conventional model, and the water level drops of each hydropower plant before the flood seasons were greater. This was because the power market was of a high proportion of hydropower and price in dry seasons was much higher. The hydropower plants with regulation ability preferred to use a self-regulating storage capacity to achieve the redistribution of water, so as to respond to price changes and improve their benefits. For example, in the proposed model, the water level drop at the Hogjiadu plant (i.e., the first stage of the cascade plants) was serious before the flood seasons, and it was close to the lowest operation water level. When the flood seasons came, the Hongjiadu plant was concentrated to store water and almost no power was generated. The water level of the downstream plants, including Dongfeng, Wujiangdu, and Goupitan, changed lightly between the flood seasons and dry seasons, which, to some extent, benefitted from inflow compensation of the Hongjiadu plant. Therefore, these downstream hydropower plants could keep a high water head for high generation efficiency.  
Figure 7 shows the supply energy for the two different markets obtained by the two comparison models under the assumptions that the same MCP scenarios were adopted. According to the analysis, on the basis of ensuring the power supply in the province market during the scheduling horizon, the proposed model responded better to the changing of market electricity prices and arranged the electricity delivery plan rationally. The power generation in the dispatching periods was 23.98 billion  
Figure 6: The optimization process of regulating reservoirs (M1 represents the proposed model, M2 represents the conventional model).  
kWh, and the power generation revenue was 7.11 billion yuan. They were 24.07 billion kWh and 7.00 billion yuan, respectively, for the conventional model. It was found that, based on the same energy storage at the end of scheduling period, the proposed model resulted in an increase of 106.93 million yuan for the total income, although the power generation was less, compared with the conventional model. This proved that the electricity price factors would greatly influence the expected benefits in the market of the cascade hydropower plants.