# Probabilistic-Multiobjective Comparison of User-Defined Operating Rules. Case Study: Hydropower Dam in Spain

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodological Framework

## 3. Methodology Implementation

#### 3.1. Ensemble of Flood Hydrograph Generation

#### 3.2. Flood Control Operating Policies

#### 3.3. Characterization, Evaluation and Comparison

Characterization Variable | Objective Function |
---|---|

Peak released flow (Q_{max}) | Minimize risk of flooding downstream (R1) |

Maximum level in the reservoir (N_{max}) | Minimize risk of overtopping (R2) |

Mean daily number of gate maneuvers (during the flood peak) (M) | Minimize gate operations during the flood peak (EV1) |

Released volume through spillways (U) | Minimize unproductive spillages (EV2) |

Gross generated energy (E) | Maximize hydropower (EV3) |

## 4. Case Study

^{2}and the mean annual flow is 100 m

^{3}/s. Observed rainfall series of 24 to 67 years long were used to generate the synthetic rainfall series by means of the RainSim model.

#### 4.1. Reservoir Characteristics

^{3}/s. The maximum flood control level (FCL) is 330 m (storage = 654 × 10

^{6}m

^{3}). The maximum (MOL) and minimum operating levels are 327.5 m (608 × 10

^{6}m

^{3}) and 262.5 m (48 × 10

^{6}m

^{3}), respectively. The crest dam level (CDL) is 332 m (692 × 10

^{6}m

^{3}).

^{3}/s being based on the Dam Master Plan and the experience of the dam operators. In this case, the TLD was defined in a section immediately downstream of the dam as a measure of non-damaging flow for the downstream river. The TLD was defined to make this measure of the system resistance comparable with the loading (released flow).

#### 4.2. Flood Control Operations

^{3}/s, the spillway gates are also opened. If the level drops below 327 m, the gates are closed regardless of inflow. The maximum increase (or decrease) in the gate opening (or closing) in a single maneuver is 2 m. The minimum time step between consecutive maneuvers is two hours. For inflows less than 2500 m

^{3}/s the outflows are limited to 1600 m

^{3}/s.

_{max}) and the level gradient (∆WL) required to increase the release (only for S2). Six configurations were considered for the S1 policy and 18 for S2 and are summarized in Table 2.

Parameter | S1p | S2p |
---|---|---|

Maximum operating level, MOL | 327, 327.5 and 328 m | 326, 327 and 328 m |

Maximum step for gate opening, G_{max} | 1 and 2 m | 0.5, 1 and 2 m |

Water level gradient required for opening, ∆WL | – | 0.02 and 0.05 m |

_{max}are related to the downstream channel capacity and suitable flow rates.

## 5. Results and Discussion

**Figure 7.**Ensemble of flood hydrographs. (

**a**) Stochastically generated flood events (selected hydrographs are highlighted to visualize the variety of shapes and duration); and (

**b**) Calibration of the flood peak frequency curve.

^{3}/s. When high inflows occur, such limitation leads to higher maximum levels and, in some cases, overtopping. This behavior may also lead to release flows that are lower than MTC, especially during the decreasing limb of the flood hydrographs. Thus, the expected energy production is reduced.

Strategy | MOL | Initial Level | R1 ↓ | R2 ↓ | EV1 ↓ | EV2 ↓ | EV3 ↑ |
---|---|---|---|---|---|---|---|

[m] | [m] | – | – | – | [10^{6} m^{3}] | [MW h] | |

S1 | 327.5 | 327.0 | 0.001 | 0.009 | 6 | 209 | 73080 |

S2 | 326.0 | 325.5 | 0.040 | 0.000 | 1 | 239 | 85475 |

S2M | 327.5 | 327.0 | 0.038 | 0.000 | 1.5 | 202 | 86638 |

^{3}/s for inflows smaller than 2500 m

^{3}/s. However, this behavior leads to elevated water levels for S1, reaching the flood control level (entering the uncontrolled flood pool) or even exceeding the CDL. S2 reaches lower maximum water levels because the corresponding MOL and, consequently, the initial water level are lower than for S1 and S2M. These two strategies achieve similar water levels (or higher for S2M) up to the arrival of the peak flow. After this, S1 follows the inflow hydrograph and causes rapid and accentuated variations in outflows and water level. This can lead to a drop of the released flows, even below the MTC, in the final intervals of the hydrograph, causing a reduction in energy production. The water level gradient threshold included in the S2 and S2M operating rules provides a smoother evolution of discharge and water level, and delays the beginning of the operation when compared with S1. However, it also delays the date of closing that leads, in many cases, to greater unproductive spillages, especially for S2. Such behavior allows rapid reduction of the water level to safe values. Although this performance may be considered better from the point of view of dam safety, it is worse from the perspective of storing water for future energy generation. Once again, both the multiobjective and stochastic nature of the flood control problem in hydropower reservoirs is shown.

**Figure 10.**Comparison of the S1, S2 and S2M operating rules applied to selected flood hydrographs (10 < Tr < 200 years).

## 6. Summary and Conclusions

- A stochastic rainfall generator model (e.g., RainSim V3), further coupled with a simple parametric hydrologic model, is useful for determining the ensemble of annual maximum flood hydrograph for a wide range of return periods. This procedure provides a large variety of hydrograph shapes and durations, and characterizes the recorded floods for the case studied reasonably well. In addition, the procedure avoids assumptions regarding the shape and, specially, the duration of storm events. However, it requires rainfall series to be available at some rainfall gauges in the basin.
- Regarding the particular case of study considered here, recorded rainfall series with a length of 25–65 years appear to be long enough to appropriately represent the flood frequency curve (for return periods of 2 to more than 200 years).
- The obtained ensemble of flood hydrographs avoided the determination of design floods which may lead to a performance evaluation limited to the occurrence of similar hydrological situations.
- The multiobjective and risk-based approach provides a valuable tool for evaluation and comparison of operating rules across a wide range of hydrological events. This tool can assist dam managers in defining operating policies. It offers a rational basis for the decision-making process and further improvements in the hydropower flood control operations.
- This methodology may also be extended to assess the behavior of multipurpose reservoirs, involving purposes other than hydropower—for example, ecological aspects, water supply or irrigation ([10,20,41], among others). These aspects may be incorporated through indices such as minimizing the expected deficit of water availability (for a certain purpose) or maximizing the reliability of satisfying downstream requirements. For example, these indices may be useful for evaluating the reservoir drought management. Additionally, this methodological framework may help in determining the operational water levels within a probabilistic context. In other words, the operational water level is determined considering a range of inflow hydrographs instead of just a few hydrological scenarios.
- Studies involving multiobjective analysis and determination of compromise solutions usually consider two to five objective functions [7,20,41]. Two or three objective functions may be represented in a single graph (Pareto front and contour curves) to obtain compromise solutions. However, if more than three objective functions are considered, they may be contrasted using the scatter plot matrix. Although there is no mathematical limit on the number of OFs, a very large set of these indices complicates the selection of suitable compromise solutions (from a practical point of view). In the other hand, the smaller the number of OFs considered, the more robust the result. In contrast, fewer aspects are taken into account in the multiobjective problem. Consequently, a solution considered as appropriate could become biased. Further research should be conducted to establish the optimal number (or range) of OFs.
- For the case studied, the alternative strategy developed, based on the parameterization of an available operating rule, affords a good tradeoff between safety, functionality of the operation, and hydropower generation.
- The procedure used to enhance the operating rules may be improved through coupling the parameterization with an efficient optimum search algorithm, such as the shufflex complex evolution algorithm [42].

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Bianucci, P.; Sordo-Ward, Á.; Moralo, J.; Garrote, L. Probabilistic-Multiobjective Comparison of User-Defined Operating Rules. Case Study: Hydropower Dam in Spain. *Water* **2015**, *7*, 956-974.
https://doi.org/10.3390/w7030956

**AMA Style**

Bianucci P, Sordo-Ward Á, Moralo J, Garrote L. Probabilistic-Multiobjective Comparison of User-Defined Operating Rules. Case Study: Hydropower Dam in Spain. *Water*. 2015; 7(3):956-974.
https://doi.org/10.3390/w7030956

**Chicago/Turabian Style**

Bianucci, Paola, Álvaro Sordo-Ward, Javier Moralo, and Luis Garrote. 2015. "Probabilistic-Multiobjective Comparison of User-Defined Operating Rules. Case Study: Hydropower Dam in Spain" *Water* 7, no. 3: 956-974.
https://doi.org/10.3390/w7030956