Evaluating joint operation rules for connecting tunnels between two multipurpose dams

This study aims to provide a practically ef ﬁ cient approach for determining the most ef ﬁ cient joint operation rule for two reservoirs connected by a waterway tunnel. For this purpose, the connecting tunnel ’ s effect was assessed and three heuristic joint operation rules accounting for the connecting tunnel were evaluated. A standard operation policy with the connecting tunnel led to positive effects on the water resource system of the target basin with regard to a reliable water supply. The connecting tunnel provides an additional water supply of 12.4 million m 3 /year to the basin, and the reliability of the two reservoirs increased. Among the three rules, the equivalent reservoir (ER) rule led to the most positive effect on water supply. We found that the ER rule could maximize the positive effects of the connecting tunnel by maintaining the effective water storage rates of the two reservoirs. Moreover, the effects of hydrologic uncertainty on the joint operation rules were discussed using the synthetically generated multiple stream ﬂ ow traces.


INTRODUCTION
Therefore, developing an efficient operation plan for the new system was required. The processes in this study were divided primarily into two stages. First, using previous hydrological data, we simulated the operation of the reservoirs before and after the two dams were connected; this was done to quantify the water supply increment as the effect of tunnel connection. Second, we tested several heuristic joint operating rules to propose the most efficient operating plan for the connecting tunnel. The existing joint operation rules were modified to incorporate the connecting tunnel module. If there is not yet a proper joint operation rule for the two reservoirs connected by a waterway tunnel, the preference would be to focus on incorporating the connecting tunnel module into the existing joint operation rules developed by advanced countries rather than developing a completely new rule. Although some studies have proposed heuristic optimization algorithms, such as genetic algorithm (Afshar et al. ; Ahmadianfar et al. ) and particle swarm algorithm (Afshar ), for obtaining multiple reservoir operation rules, traditional but widely applied and efficient methods were modified in this study so that people can apply them practically with ease.
Based on the results of these previous studies, we decided to test the existing joint operating rules, such as the space rule, the Revelle's allocation (RA) rule, and the ER rule, for the case study. These rules were also compared with the standard operating policy (SOP), which is the simplest policy aiming to release a quantity of water demand if possible.
We used SOP as a benchmark scheme as it is a fundamental operating rule that is currently being used. Besides releasing the target demand, SOP does not consider any joint operating concept; thus, it provides information only on the bottom-line performance of reservoir systems. The software package HEC-5, in which the ER rule was embedded, was used because this well-known simulation package has been officially used in the operation of other multipurpose dams in Korea. Each of the candidate operating rules is described in the Methods section, and the results of their application to the case study are presented in the Applications & Results section, followed by the Conclusions of the study.

Standard operating policy
SOP is the most basic method used for reservoir operation, whose primary objective is to meet the target water demand (Ministry of Land Transport and Maritime Affairs ).
According to SOP, if the available water (current storage þ incoming inflow) is less than the target water demand, all available water is discharged. If the available water exceeds the target water demand, the required amount for the target water demand is delivered and the remaining water is stored in the reservoir (Korea Water Resources Corporation a).
Furthermore, if the stored water, remaining after discharging the amount required for the target water demand, exceeds the maximum capacity of the reservoir, it is discharged through the spillway. We implemented two different versions of SOP to assess the effect of a joint operation with the connecting tunnel: (i) SOP-O, which does not consider the connecting tunnel, and (ii) SOP-W, which considers the connecting tunnel. SOP-O and SOP-W can be expressed using the following equations: where S i,t-1 is the storage of reservoir i at the end of time t À 1, I i,t is the inflow to reservoir i at time t, D i,t is the water demand from reservoir i at time t, R i,t is the discharge from reservoir i at time t, K i is the maximum capacity of reservoir i, and T divt is the amount of water passed through the connecting tunnel from Imha to Andong Dam at time t. As the connecting tunnel is designed to send water in one direction from Imha Dam to Andong Dam (i.e., send the surplus water of Imha Dam to Andong Dam), T divt is always more than or equal to zero for Andong Dam but less than or equal to zero for Imha Dam. . This is expressed as

Space rule
where E[CI i ] is the expected cumulative inflow to reservoir i from the end of the current period to that of the flood season, D t is the total water demand in the parallel reservoir group at time t, and V t is the total storage of the reservoir group at time t.
The space rule can be alternately expressed, as seen in Equation (8). The ratio of the residual space of reservoir i to the sum of the residual spaces of the reservoirs in the parallel reservoir group is the same as that of the future inflow in reservoir i to the sum of the future inflows in the parallel reservoir group.

RA rule
ReVelle () presented a water supply allocation rule that simply calculates the water supply based on storage capacities and inflow to reservoirs in parallel. Following are the three empirical allocation rules proposed by ReVelle (): (1) RA-A allocates the target water supply depending on the ratio of storage at the end of the previous unit period of reservoir i in a reservoir group parallel to the total storage of the reservoir group. The discharge from reser- (2) RA-B is the allocation method depending on the ratio of the available water storage of reservoir i at the end of the previous period (i.e., sum of storage of reservoir i at the end of the previous time period and current inflow to reservoir i) to the total available water in the parallel reservoir group. R i,t is estimated as (3) RA-C distributes the water supply according to the ratio of the water reserve rate, which is obtained by dividing the available water in reservoir i at time t by the maximum capacity of the reservoir. Thus, RA-A and RA-B are based on the storage, while RA-C is based on the water reserve rate. R i,t is estimated as follows: where q t ¼ streamflow in day t; f ave ¼ mean generated streamflow, which is set as the historical average annual streamflow; ρ flow ¼ temporal correlation of the streamflow; C v ¼ coefficient of variability; and τ ¼ random number with the standard Gaussian distribution.

Target basin
The target basin of this study is upstream of the Nakdong River Basin. Two reservoirs, Andong and Imha, are connected in parallel; the outflows from both reservoirs flow into the mainstream of the Nakdong River, as shown in There are two intake towers at both ends of the tunnel.
The connecting tunnel is located 141 m above sea level.

Operational and hydrologic input data
Monthly water supply plan

Hydrologic uncertainty representation
Fifty traces of 20 years' daily inflow series for the Andong Dam and Imha Dam were generated from the aforementioned synthetic streamflow generation method. Figure 4 shows ranges of the observed and generated streamflow hydrographs for both dams. It shows that the generated streamflow sequences can provide a similar range of observed streamflow. The statistical characteristics of the generated streamflow were also similar to the observed streamflow. The percent bias of mean flow of all generated streamflow traces ranged from À0.09 (À9%) to 0.07 (7%).

Simulation overview
We used Excel to assess and compare the performances of various operating rules for AICT because the system comprises only two dams. As mentioned before, the inflow time series were entered to test each operating rule. The SOP rule consists of two versions, the SOP-O rule and the SOP-W rule, to examine the bottom-line effect of the joint operation with a connecting tunnel. All other joint operating rules were then applied to the system with a connecting tunnel and expected to perform better than the SOP-W rule.
The system performance was assessed using three wellknown measures: reliability, resiliency, and vulnerability (Hashimoto et al. ). Conceptually, reliability, resiliency, and vulnerability represent the number of times a system does not fail, how quickly the system recovers from a failure, and how large each failure is on an average, respectively.
Here, reliability is described by the probability that a vulnerability where M is the total number of failures, N is the total number of time intervals, and wd(i) is the amount of water deficit in time i.

Connecting tunnel effects
The effects of the connecting tunnel are first assessed by comparing SOP-O and SOP-W. Note that the SOP-O and SOP-W rules follow Equations (1) and (2), respectively.
In terms of water supply performance, Figures 5(a) and (b) present the number of days with water shortage  Overall, the connecting tunnel's effects on the water resource system of the Andong and Imha dams are noticeably positive for water shortage prevention.

Comparison of joint operating rules
The three joint operating rulesthe space, RA, and ER rules between the two dams, and RA-C employs the ratio of the relative effective storage (effective storage/storage capacity) between the two dams. The ER rule determines the discharges of the two dams to ensure that the current relative effective storages of the two dams are equal.  It is noted that the ER rule is determined as the most effective joint operation rule with regard to both aspects, reliability and vulnerability, while the space rule is the best model if the ability of the system's restoration is solely considered.
In the practical operation of reservoirs for water supply, the ability of a reliable water supply, i.e., reliability, is usually considered as the first priority. Therefore, based on the performance criteria of the joint operation rules, the ER rule can be considered the best operation rule for the AICT project in that its performance in terms of water supply is greater than that of the other rules, although the difference is not large. In this regard, it can be inferred that maintaining effective water storage rates of multiple reservoirs in parallel at the same level is an important regulation for reservoir operation in the AICT project.  The ER rule is determined as the best method for joint operation in terms of reliability index. Besides, across the effect of hydrologic uncertainty, its superiority over SOP-W is confirmed. Nonetheless, it turns out that the ER rule is quite sustainable to hydrologic uncertainty. As there is a trade-off between reliability and vulnerability, it seems very difficult for a single method to outperform other methods across all performance indexes. Thus, the best possible option always differs depending on which criterion is required to be analyzed and evaluated.

CONCLUSIONS
This study provides a simple yet practically efficient approach to determine the optimal joint operation rule for parallel reservoirs that are linked by a connecting tunnel.
First, the effect of the connecting tunnel was evaluated by comparing the results of the two operations driven by the SOP with and without a connecting tunnel (SOP-W and SOP-O, respectively). Subsequently, the existing joint operation rules were evaluated by comparing the joint operation results with SOP-W. From our experience in practical reservoir operation, selecting the optimum predeveloped models can often be better than developing a new one as per the circumstances.
Furthermore, the effects of hydrologic uncertainty on the joint operation performance were discussed using the synthetically generated multiple streamflow traces. This is significant because a broad range of potential streamflow sequences should be comprehensively considered when testing an alternative policy.
As the connecting tunnel was built for drought mitigation, an optimal operation rule is required to maximize the advantage of using the tunnel. It was found that the reliability of the water supply system increased by passing To address the effect of hydrologic uncertainty, a wide range of possible streamflow series, which were synthetically generated, were tested for the operation rules.
This did not result in a drastic impact on the performance metrics. However, when the ER rule was applied, the vulnerability of the water supply system was found to be susceptible to the natural variability of hydrologic inputs, while the reliability and resiliency were relatively robust.
This indicates that preserving the effective water storage rates of all reservoirs at the same level can reduce the possibility of water shortage but lead to larger water shortage once the water supply fails.
On the other hand, the performance results of the joint operating rules can change if the inflow patterns change due to anthropogenic or climate change effects on the streamflow. Furthermore, the order of priorities can vary across different watersheds due to changes in geographical features and climate regimes. Thus, we cannot conclude that the ER rule will outperform the other rules in other case studies.
To extend this study to other watersheds considering a joint operation of the reservoirs, the proposed comparative study needs to be implemented to evaluate the performance of each joint operation rule, which would be affected by some external conditions such as topography and climate regime.