# Upper Limit and Power Generation Loss of Water Supplement from Cascade Hydropower Stations to Downstream under Lancang-Mekong Cooperation

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s to implement emergency water supplement for the downstream [18]. This water supplement has dramatically alleviated the drought in countries along the Mekong River, especially Vietnam. As a successful cross-border water resources cooperation practice in the Lancang-Mekong basin, the China-Vietnam water supplement incident in 2016 is a significant reference event. Due to the geographical location and water resources, the interests of upstream China and downstream Southeast Asian countries are relatively independent; as such, this modular cooperation of “application-negotiation-water supplement” is also a direct, efficient mode of cooperation and worthy of further study.

## 2. Study Area and Data

## 3. Methodology

#### 3.1. Calculation of ULF

- (1)
- Set ${Z}_{1,ini}$ and ${Z}_{1,fin}$ as the initial and final water level constraints of XW, respectively. Set ${Z}_{2,ini}$ and ${Z}_{2,fin}$ as the initial and final water level constrains of NZD, respectively.
- (2)
- The operation process of XW within the year is carried out by using SOP according to the initial output process of XW. If the initial output process is feasible, enter step (3); otherwise, it indicates that the inflow condition of the year is not suitable for water supplement, which means, even there is no water supplement requirements from the downstream countries, that part of the periods still lacks water, and water supplement may cause greater burden on the upstream power generation task.
- (3)
- Based on the initial output process of XW, increase the output in the water supplement period gradually (the output of other periods remains unchanged), until continuous increase will cause the output process to be not feasible. Save the water level process derived by SOP and the output of XW in the water supplement period at the time. Record the output of XW as ${N}_{1,max}$, and the final water level derived by SOP operation now is ${Z}_{1,fin}^{\prime}$. Due to the fact that ${Z}_{1,fin}^{\prime}$ must be higher than or equal to ${Z}_{1,fin}$, replace ${Z}_{1,fin}^{\prime}$ with ${Z}_{1,fin}$, and the water level process after the replacement is the final water level process of XW under the limit state of water supplement;
- (4)
- Keep the final water level process of XW under the limit state of water supplement obtained in step (3) unchanged, and then the operation process of NZD within the year is carried out by using SOP according to the initial output process of NZD. If the initial output process is feasible, enter step (5); otherwise, it indicates that the inflow condition of the year is not suitable for water supplement. Water supplement may cause greater burden on the upstream power generation task.
- (5)
- Based on the initial output process of NZD, increase the output in the water supplement period gradually (the output of other periods remains unchanged), until continuous increase will cause the output process to be not feasible. Save the water level process derived by SOP and the output of NZD in the water supplement period at the time. Record the output of NZD as ${N}_{2,max}$, and the final water level derived by SOP operation now is ${Z}_{2,fin}^{\prime}$. Due to the fact that ${Z}_{2,fin}^{\prime}$ must be higher than or equal to ${Z}_{2,fin}$, replace ${Z}_{2,fin}^{\prime}$ with ${Z}_{2,fin}$, and the water level process after the replacement is the final water level process of NZD under the limit state of water supplement;

#### 3.2. Optimization of Maximum Power Generation under Water Supplement Constraints

- (1)
- Objective function

^{3}/kwh) is the average water consumption rate of reservoir j in time period t, and it depends on h

_{j,t}, the average hydraulic head of time period t; f

_{j}is the relationship between the water consumption rate and average hydraulic head of reservoir j; P

_{j,t}(10

^{4}kw) is the output of reservoir j in time period t (3600/10,000 is to transform the unit from kWh/s to 10

^{4}kW); QG

_{j,t}(m

^{3}/s) is the discharge flow for power generation at reservoir j in time period t; W (10

^{4}kwh) = total hydropower generation; Δt (h) is the operation time step; k is the total number of hydropower stations studied (2 in this paper); and T = total number of time intervals during the operation period (12 in this paper, for 12 months in one year).

- (2)
- Decision variables

- (3)
- Constraints

- ①
- Water balance constraints

_{j,t+}

_{1}(m

^{3}) is the final water storage of reservoir j in time period t; S

_{j,t}(m

^{3}) is the initial water storage of reservoir j in time period t; QI

_{j,t}(m

^{3}·s

^{−1}) is the total water inflow to reservoir j in time period t; QR

_{j,t}(m

^{3}·s

^{−1}) is the discharge from reservoir j in time period t; ${q}_{j,t}$(m

^{3}·s

^{−1}) is the runoff contribution from the interzone between the two reservoirs in time period t; and QS

_{j,t}(m

^{3}·s

^{−1}) is the discharge that does not go through the turbine and is not used for power generation of reservoir j in time period t. In this paper, as long as the installed capacity and the turbine overflow capacity have not been reached, reservoirs’ discharge will be used preferentially for power generation. The time delay for the flow stretch between reservoirs is neglected, as the time step (month) adopted in this study is longer than the maximum flow time-lag between the reservoirs.

- ②
- Water storage constraints

^{3}) is the dead storage of reservoir j. ${S}_{j,t}^{max}$(m

^{3}) is the maximum water storage permissible of reservoir j in time period t.

- ③
- Hydropower station output constraints

_{j}and ${P}_{j}^{min}$ are installed capacity and firm power of reservoir j, respectively.

- ④
- Flow constraints

^{min}

_{j}and QR

^{max}

_{j}are the minimum discharge constraints and maximum discharge capacity of reservoir j, respectively; $Q{G}_{j}^{max}$ is the turbine overflow capacity of reservoir j, and $Q{G}_{j,t}^{IC}$ is the power generation flow which brings the installed capacity power of reservoir j in time period t when $Q{G}_{j,t}^{IC}$< $Q{G}_{j}^{max}$.

- (4)
- Optimization method details

## 4. Application Results and Analysis

#### 4.1. Limit State of Water Supplement

#### 4.2. Effect Evaluation of “Collaborative Independent” Joint Optimization Method

^{3}/s (black vertical dotted line), the maximum power generation obtained by collaborative optimization is ${S}_{1}$. The corresponding generation loss is ${D}_{1}$. The maximum power generation obtained by independent optimization is ${S}_{2}$. The corresponding generation loss is ${D}_{2}$. Thus, the power generation difference of the two methods is $\Delta $, and the improvement ratio of the PGL caused by the application of the two methods is $p$:

^{3}/s), due to the fact that the water supplement flow is near the lower limit (flow that just meets the firm power constraint of NZD). Both ${D}_{1}$ and ${D}_{2}$ are very small, so the denominator in Equation (3) is also very small. In this case, the improvement percentage $p$ could be abnormally high. However, considering that the water supplement flow in this interval is nearly the same as the discharge flow that just meets the firm power, the water supplement would be of little significance. Therefore, only the intervals with large water supplement flow (>1500 m

^{3}/s) are analyzed. It can be seen that the “collaborative-independent” joint optimization method applied in this paper can significantly reduce the PGL, and the maximum improvement of PGL is about 18% in Figure 12a, about 16% in Figure 12b, and about 33% in Figure 12c when the water supplement flow is greater than 1500 m

^{3}/s. The improvement is significant enough to affect to water supplement cooperation so the method is meaningful and necessary.

#### 4.3. Power Generation Loss (PGL) of Water Supplement

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**The calculation of process of “flow-energy” relationship and PGL using the “collaborative-independent” joint optimization method.

**Figure 7.**The water level processes of XW (

**a**) and NZD (

**b**) under the limit state of water supplement in 2001 (wet year, P = 25%).

**Figure 8.**The water level processes of XW (

**a**) and NZD (

**b**) under the limit state of water supplement in 1997 (dry year, P = 75%).

**Figure 9.**The water level processes of XW (

**a**) and NZD (

**b**) under the limit state of water supplement in 1983 (dry year, P = 81%).

**Figure 10.**Optimization results of “flow-energy” relationship under “collaborative-independent” joint optimization. (

**a**) April 1997, (

**b**) March 1999, and (

**c**) March 2001.

**Figure 12.**Effect evaluation of “collaborative independent” joint optimization. (

**a**) April 1997, (

**b**) March 1999, (

**c**) March 2001.

**Figure 13.**Results of PGL of the three typical years, (

**a**) Dry year, P = 75%; (

**b**) normal year, P = 50%; and (

**c**) wet year, P = 25%.

**Figure 14.**Optimized strategy combinations of hydropower stations during water supplement period (water supplement in March 1999).

Term | Explanation |
---|---|

Firm power | Firm power refers to the value that the output of hydropower station, under normal operation, shall not be lower than. If the output in a certain period is lower than the firm power, it indicates that the power generation task is damaged. |

Initial output process | Initial output process is the output process in which the ouput in each time period equals to the firm power of the corresponding hydropower station. |

Standard operating policy (SOP) | SOP means releasing water just to the meet the output of the hydropower stations in every time period. |

Initial water level and final water level constraints | Initial water level means the water level at the beginning of the operation period in each reservoir; and final water level means the water level at the end of the operation period in each reservoir. |

Feasible output process | If the SOP operations of the hydropower stations can be completed under the premise of meeting all constraints, and the water level at the end of the operation period is higher than or equal to the final water level constraint, then the output process is feasible, otherwise it is not feasible. |

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**MDPI and ACS Style**

Deng, J.; Li, Y.; Ding, W.; Zhang, B.; Xu, B.; Zhou, H.
Upper Limit and Power Generation Loss of Water Supplement from Cascade Hydropower Stations to Downstream under Lancang-Mekong Cooperation. *Water* **2021**, *13*, 2826.
https://doi.org/10.3390/w13202826

**AMA Style**

Deng J, Li Y, Ding W, Zhang B, Xu B, Zhou H.
Upper Limit and Power Generation Loss of Water Supplement from Cascade Hydropower Stations to Downstream under Lancang-Mekong Cooperation. *Water*. 2021; 13(20):2826.
https://doi.org/10.3390/w13202826

**Chicago/Turabian Style**

Deng, Jiahui, Yu Li, Wei Ding, Bingyao Zhang, Bo Xu, and Huicheng Zhou.
2021. "Upper Limit and Power Generation Loss of Water Supplement from Cascade Hydropower Stations to Downstream under Lancang-Mekong Cooperation" *Water* 13, no. 20: 2826.
https://doi.org/10.3390/w13202826