An optimisation approach for the operating rule curves of the A Vuong reservoir, Vietnam Open Access

Water reservoirs are one of the most important components of the water resource system. Their main purpose is to control natural flow by storing excess water during the rainy season and releasing it during the dry season for different purposes (Jain 2019). Reservoirs serve as important sources of many water supply systems around the world and have become increasingly vital as water pollution problems worsen (Panagopoulos 2022a, 2022b; Panagopoulos & Giannika 2022). In addition, reservoirs are also used to generate electricity and prevent floods. Conflicts between flood control and other water uses are common when operating a multi-purpose reservoir. These operating goals of one reservoir will be achieved if it has a reasonable operating strategy. At the end of its regulation cycle, one reservoir's water level needs to reach the normal level for power generation, water supply, and irrigation. If flows are plentiful, there should be no problem in achieving reservoir operational goals. On the other hand, if river flow is limited, the reservoir's volume will be difficult to fill, leading to an insufficient water supply.

Flood limited water level (FLWL), or the empty space for flood control, is an important factor that greatly affects water allocation for flood prevention and other purposes. In order to maintain flood control during the flood season, reservoir water levels are generally not permitted to exceed the FLWL. In the past, many authors have studied this matter (Wu & Ping 2018; Xie et al. 2018; Li et al. 2022). The effects of reservoir operation on flood inundation in the Vu Gia Thu Bon basin were investigated by To et al. (2022). Vu et al. (2021) also studied and proposed a reasonable FLWL to replace the current one in the inter-reservoir procedure promulgated by the Prime Minister for the Tra Khuc basin. Moreover, if the flood control storage capacity is fixed during the flood season, a water shortage can happen due to the reservoir not being full at the end of the regulation cycle (Li et al. 2010). Liu et al. (2011) also confirmed the benefits of having these flood control storage capacity changes during the flood season while not affecting flood control objectives. The studies above show that determining the reservoir's flood control capacity is critical. However, these studies are mainly conducted on single-purpose reservoirs, very few of them include multi-purpose reservoirs. In this study, we will provide an option to determine the appropriate change in flood control storage capacity during flood season for a multi-purpose reservoir based on the assessment of the power output and the ability of the reservoir to be filled with water after each regulation cycle.

Today, the operation of most reservoirs is contingent on the operating rule curves due to their simplicity. These rules, presented in graphs or tables, guide the discharge based on the reservoir's water level status, hydrological conditions, and time of year. Generally, they are established at the reservoir construction planning stage (Wang et al. 2014). Though being simple, these operating rules must be constantly renewed to adapt with changes, especially when there is a shift in hydrological conditions or the reservoir's objectives (Oliveira & Daniel 1997). To reduce conflicts among operational goals, reservoir managers are trying to come up with reasonable operating rule curves. There are two main types of methods to develop the operating rule curves, i.e., conventional and optimization methods (Jiang et al. 2018). Between these two, optimization methods are widely used in water resource engineering. Labadie (2004) provided a summary of the optimization techniques used in water resource allocation in single-purpose and multi-purpose reservoir systems. When supporting data is available, optimization approaches provide direct optimal reservoir operation solutions (Thang et al. 2020).

Many optimization algorithms have been used in reservoir operation, such as genetic algorithms (Feng et al. 2018; Olukanni et al. 2018; Tegegne & Kim 2020), particle swarm optimization (Oussama et al. 2019; Jahandideh et al. 2020), and progressive optimality algorithms. However, according to Jiang et al. (2018), these algorithms do have three disadvantages. Firstly, they often require a set of initial solutions and can only perform simulation optimization on those initial solutions. As a result, the quality of these initial solutions can greatly impact the final result. Secondly, it is very hard to attain a global optimal solution. Although many evolutionary algorithms have been shown to have global convergence, they are influenced by stochastic features, and hence they cannot guarantee a global optimal solution within a finite number of iteration calculations. Thirdly, some optimization methods, such as the progressive optimality algorithm, require constraints on the unsmooth and non-convex nature of the problems. Meanwhile, dynamic programming (DP) is a highly efficient optimization technique (Marano et al. 2012; Jiang et al. 2017). The most notable feature is that it can guarantee the global optimum without requiring an initial solution. Furthermore, there are no requirements for non-convex and unsmooth optimization problems in DP. DP is widely used in traditional optimization algorithms (Yakowitz 1982; Zhao & Jianshi 2014). Dynamic programming was used by Jiang et al. (2018) to create a new reservoir operation chart, which enhanced the power output by 2.68%. Pourahmadi & Boomsma (2022) proposed an approximate dynamic programming technique to assist reservoir operations that forecasts the future value of water using a linear approximation architecture. The results demonstrate that profit estimation improves by around 20% when the linear approximation includes inflow variables. Pant & Rani (2021) suggested an integrated approach that combines traditional dynamic programming and metaheuristic technique differential evolution. Kim et al. (2021) used stochastic dynamic programming to improve the robustness of reservoir operations. They introduced a new framework called robust stochastic dynamic programming, which combines robust optimization with objective function or constraint formulations used in stochastic dynamic programming.

An important consideration when creating an operating rule curve is the ease of use in assisting reservoir operators to make their decisions. Indeed, although optimal operating rule curves can significantly increase the efficiency of reservoir operation, researchers have also recognized that a gap still exists between theoretical models and practical activities (Yeh 1985; Pinthong et al. 2009). The problem with current operating rules for many reservoirs, including the A Vuong reservoir, is that there is a relatively large range between the limit lines. In practice, the presence of such a wide range can make it difficult for operators to make a quick decision on a course of action.

The purpose of this study is to use dynamic programming techniques to develop operating rules that are both convenient and optimized for operation. The A Vuong reservoir was selected as the case study. First, we suggest a reasonable time-varying flood control storage capacity. Then, we identify a number of operating rule curves for various initial water levels, along with the average line among limit lines. These simple, convenient, and optimal operating rules are essential for reservoir operators, who can easily accept and use them in practical operation. Finally, we compare power output performance with that of the current operating rules.

The construction of the A Vuong reservoir began in 2003 and was completed in 2008. The primary purpose of the reservoir is power generation, but it was later on assigned additional tasks of flood control and water supply. As a result, many contradictions have arisen during the operational process. The operator wishes to maintain a high water level in order to increase power output, but in order to prevent flooding, they must have an empty capacity. Moreover, as reservoirs lower their water level, the risk of not being fully filled before the next cycle becomes higher, especially if the natural flow is low. These conflicts between flood control and downstream water supply are quite common for multi-purpose reservoirs (Nga et al. 2019; Nguyen 2019; Le et al. 2021; To et al. 2022). It is critical to find ways of improving operational efficiency to meet A Vuong reservoir's water consumption targets.

The capacity, efficiency, power output, and operational documents of the hydroelectric power plant are taken from the reservoir design documents that have been approved by the appropriate authorities. Additional documents are collected, including those related to evaporation loss, water level relationships, and the reservoir characteristic curve. Table 1 shows the main characteristics of the A Vuong reservoir.

Since the A Vuong is a multi-purpose reservoir, we first need to establish a multi-objective optimal operation. The optimization model's objective functions and constraints are as follows:

Constraints:

• - Water volume balance:

  

  (4)

  

  (5)

  where V_i and V_i+1 represent the reservoir storages at the beginning of time periods i and i+1, respectively, in volume units; I_i, EL_i are inflow and evaporation, respectively; V_power and V_spillway are water discharges through the turbine and spillway, respectively.
• - Reservoir storage volumes limits:

  

  (6)

  where V_dead and V_normal represent the reservoir storage corresponding to the dead water level and the normal water level, repectively, unit: m³.
• - Power generation limits:

  

  (7)

  where N_min and N_max represent the minimum and maximum power capabilities, unit: KW
• - Flood control storage capacity limits:

  

  (8)

The specific steps involved in calculating reservoir operation based on DP are summarized below.

Step 1: Divide the entire operation period into n stages, and then get the discrete water level combinations in the range of Z_dead to Z_normal for each stage. There will be m discrete water level points in each stage.

Step 2: Start the backward recursion from stage n. In this step, the calculation of the reservoir's storage capacity in the current stage must be repeated for each discretized water level combination in order to obtain the optimal cumulative benefit (power generation) of the current stage. Set i=i−1 and proceed to the next stage of the calculation.

Step 3: Once the first stage's calculation is completed, the reverse recursion procedure is finished. Then, using the saved optimal candidate paths, retrace the optimal path from the first to the n_th stage to obtain the best combination of power output and reservoir operation water level.

In this section, we use the above optimization model to calculate reservoir regulation and find a reasonable flood control storage capacity. Suggested scenarios are listed in Table 2, along with water levels, flood control storage capacities, and their duration. There is no flood control storage in the base scenario (Scenario 1a). The proposed V_pl varies from 10% to 50% of the active storage capacity (V_hi), with a duration of 30, 60, or 90 days starting from September 1st (Scenarios 2a–16a). We determine the ability to refill the reservoir to its normal water level, the reduction in power output for each scenario, and compared them to one another. From there, we can select the best option for flood control storage capacity. In the next part, the selected storage capacity will be used to develop the optimal operating rule curves.

The authors develop a new operating rule curve based on the previously mentioned flood control capacities. Using the DP technique, we perform optimal calculations for different water levels on January 1st, changing from 368 m to 380 m. The scenarios of different water levels at the beginning of the cycle are depicted in Table 3. During operation, the reservoir water level will be controlled to: (1) reach the water level corresponding to the flood control capacities of 50%V_hi, 30%V_hi, and 10%V_hi in September, October, and November, respectively; and (2) reach 380 m at the end of the cycle. Our results show that for each scenario of the water level on January 1st, there are 20 optimal operating curves that correspond to the 20 years of hydrological data (2002–2021). The upper limit lines are derived from the maximum water level values of the 20 optimal operating lines. Similarly, the lower limit lines are derived using the lowest water level values. In addition, the average line between the two limit lines is also derived from the average values of the water levels.

In cases where the duration is extended to 90 days (scenarios 12a–16a), the effect of different flood control capacities on power output becomes clear (Figure 6(c)). However, there is a small difference in the power output when the flood control capacity changes for a few years, including 2012, 2018, and 2019. This can be explained by the fact that the inflow is small in these years, the reservoir water level is low, and there is almost no discharge of water over the spillway. The amount of water in the reservoir for power generation is nearly the same among these flood control capacity options, so the power output varies slightly. In contrast, the power outputs in 2007, 2009, 2013, 2020, and 2021 have a more visible change. In these years, there may have been major floods and large inflows. The amount of water discharged through the spillway is high, and the size of the flood control capacity will have a significant impact on the power output. For example, with the option of V_pl = 50%V_hi, the large flood control capacity leads to more water being discharged through the spillway, resulting in a decrease in power output.

Table 5 shows the possibilities of the reservoir being refilled at the end of each regulation cycle for different scenarios. The number of times when the reservoir was refilled fully (hereinafter referred to as T_f) for the simulation 21-year time series is also displayed. If the duration is 30 days, T_f can reach a maximum of 17 regardless of the flood control capability (scenarios 2a–6a). The smallest T_f is 2 when the V_pl is 40%–50% of the V_hi and lasts for three months (scenarios 15a, 16a). It should also be noted that in some years, such as 2012 and 2019, the reservoir cannot be fully refilled for all scenarios, even when the flood control capacity and duration are short. According to historical data, these have been years of very low inflows. In contrast, in years with large inflows, such as 2016 and 2020, the reservoir can be fully refilled for all scenarios.

The average, upper and lower limit lines for scenario 1b are shown in Figure 9(b). Based on these curves’ operating ranges, particularly the position of the average line, operators can select the right action plan. From January 1st to September 1st, the water level gradually decreases but is guaranteed not to be lower than 340 m (the dead water level). The water level begins to rise after September 1st. From September to October, flood control capacity ranges from 50% to 30% of the V_hi. During this time, the probability of a flood occurring is relatively high. With this change in flood control capacity, the reservoir ensures flood control, optimal power output, and the ability to be completely refilled at the end of the cycle to serve other water needs. Flooding becomes less likely after October 30th, and flood control capacity has fallen to 10%V_hi. The water level gradually rises until it reaches its normal level of 380 m by December 31st.

The average, upper and lower limit lines for scenarios 2b–7b with water levels ranging from 378 m to 368 m at the beginning of the regulation cycle are depicted in Figure 10. Depending on the water level at the beginning of the regulation cycle, there will be corresponding operating curves. These operating curves all comply with the values of flood storage capacities defined above, ensuring the safety of flood control and water supply. In addition, they also help to improve power output in cases where the water levels at the beginning of the cycle are different. Unlike the current operating chart, providing each specific case of the beginning water level simplifies operations for managers. Operators can select the appropriate operating chart based on the water level at the beginning of the cycle. Furthermore, the presence of an average line specifically assists operators in making decisions. Details will be discussed further in the following section.

The decision to operate a reservoir at one point in time will have an impact on not only power output and water supply at that time, but also on all subsequent stages in the reservoir's regulatory cycle. The hydrological regime in Vietnam is complex, and long-term forecasting is still challenging. Furthermore, power generation planning is typically developed for 10-day periods at the request of the power authority. Under the current operating rules, the range between the limit lines is quite large, causing operational difficulties. Operational decisions are easily influenced by the subjectivity of the users in the absence of proper instructions.

Most of the previous studies mainly focused on optimization algorithms and were performed on a general graph (Jiang et al. 2018; Thang et al. 2020; Pant & Rani 2021; Pourahmadi & Boomsma 2022). Few studies have been conducted on a large number of cases corresponding to different early-cycle water levels. Meanwhile, this water level does not always reach the normal water level. Offering a variety of operating charts depending on the beginning water level will allow operators to act more accurately, reducing the operator's subjective factors. In addition, the introduction of the average line makes the operation process run more conveniently. Indeed, the average line will serve as a guide for operators to follow. Operation managers can increase or decrease the number of turbine sets and adjust the water level to follow the average line.

In addition to the amount of the inflow, the power output of the A Vuong reservoir in each period is determined by the power system's requirements. The output power is generally registered 10 days in advance. Based on the prior period's inflow, the number of turbine units used to generate electricity will be estimated. If the inflow is small, register one turbine unit; otherwise, register two turbine units. It should be noted that the goal of the reservoir operation is to maximize total power output while also satisfying the reservoir's other functions. As a result, it is critical to follow these guidelines to ensure that the goals are met. Due to the small amount of inflow, the operators must accept little power generation for a few months during the operation, not generating electricity in any way that causes the water level to exceed the established limits.

The current operation of the A Vuong reservoir has several conflicts among its flood prevention, power generation, and water supply goals. In addition, the current operation curves with a wide range also cause difficulties for the operator. This study contributes to resolving the above conflicts and improving the operational efficiency of the reservoir. The study's main findings are as follows:

• - The V_pl options were proposed to ensure the objectives of flood control, power output, and water supply. The best solution is that V_pl has values of 50, 30, and 10% of V_hi in September, October, and November, respectively.

• - The study developed a new optimal operation curve, including the limit and average curves. These new curves help to meet operational goals and are also more convenient for operators. In addition, to meet actual operational needs, various scenarios for the beginning water levels from 360 m to 380 m were considered. The optimal operation curves can boost power output by 3.5% and 3.1% for the dry season and the whole year, respectively, in check for 2018.

• - We also recommend some adjustments for reservoir operation practice: the operator should always stay close to the average curve. The number of turbine units can be adjusted based on the value and frequency of incoming flow, as well as the current water level position relative to the average line.

• - Although this paper proposes a new method for constructing operation rule curves, there are some limitations and simplifications, such as a calculation time step of 10 days and implementation for single reservoirs. All of the above are aspects worth researching further in the future.

The authors wish to express their appreciation to the Ministry of Education and Training for supporting this research project # B2021-DNA-13.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.