# Evaluating the Impact of Streamflow Rating Curve Precision on Firm Energy of Hydropower Plants

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## Abstract

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## 1. Introduction

#### 1.1. The Study Aim: Firm Energy

**Firm Energy of the System:**According to the National Power System Operator (ONS), the firm energy of the system can be defined as being the highest possible value of energy capable of being supplied continuously by the system. This supply must occur without any deficit and considering the system configuration and market characteristics constant. It should also be considered a repetition of the flow of the historical record;**Firm Energy of a hydropower Plant:**Defined as the contribution of this plant to the system’s firm energy that corresponds to its average production over the critical period;**Critical Period:**Longer time interval in which the reservoirs of the system’s set of plants are depleted to the maximum. Reservoirs must start full (storage greater than 98% of Maximum Storable Energy) and without intermediate total refills. In addition, the system must be submitted to its firm energy, considering the configuration of its generators, its interconnections and its set of storage reservoirs constant;**Maximum Storable Energy:**Defined as the total storage capacity of all reservoirs that compose the system. It can be evaluated as being all the energy produced when the reservoirs of the system are completely depleted (from maximum to minimum storage);**Assured Energy:**Defined as the maximum energy production that can be maintained almost continuously by hydropower plants over the years. Therefore, the occurrence of each one of the thousands of possibilities of flow sequences statistically created is simulated, and a certain risk of not meeting the load is admitted, i.e., in a certain percentage of the simulated years, rationing is allowed within a limit considered acceptable by the system. In the current regulation, this risk is 5%. The Assured Energy of a hydropower plant is the fraction allocated to it of the system’s assured energy.**Energy Reallocation Mechanism (MRE):**Financial mechanism that aims to share the hydrological risks that affect generators, in the quest to guarantee the optimization of the system’s hydroelectric resources. The purpose is to ensure that all participating generators sell the assured energy that has been allocated to them. Regardless of their actual energy production, as long as the MRE plants, as a whole, have generated enough energy to do so.

#### 1.2. The Study Place: Itapebi Hydropower Plant

#### 1.3. The Study Contributions

- To evaluate the impact on the calculation of firm energy of a hydropower plant caused by a possible measurement error in the plant’s affluent incremental flow;
- To evaluate the impact in the calculation of firm energy of a hydropower plant caused by a possible change in parameters of the plant’s downstream level flow polynomial.

- Application of Dual Deterministic Dynamic Programming for the calculation of firm energy;
- Application of the linear approach by parts of the hydroelectric generation in the calculation of firm energy;
- Real case study in a large Brazilian hydropower plant.

## 2. Materials and Methods

#### 2.1. Dual Deterministic Dynamic Programming

#### 2.2. Objective Function

#### 2.3. Future Impact

#### 2.4. Energy Balance

#### 2.5. Water Balance

#### 2.6. Hydraulic Production Function

#### 2.7. Operating Limits of Variables

#### 2.8. Applied Dual Deterministic Dynamic Programming

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANA | National Water Agency |

ANEEL | National Electric Energy Agency |

CAPES | Coordination for the Improvement of Higher Education Personnel |

CNPq | National Council for Scientific and Technological Development |

SNIRH | National Water Resources Information System |

ADCP | Acoustic Doppler Current Profiler |

ONS | National Power System Operator |

ISO | Brazilian Independent System Operator |

MRE | Energy Reallocation Mechanism |

MG | Minas Gerais |

HPF | Hydraulic Production Function |

LP | Linear Problem |

DDDP | Dual Deterministic Dynamic Programming |

AHPF | Approximate Hydraulic Production Function |

PMO | Monthly Energy Operation Program |

UFJF | University of Juiz de Fora |

INESC | Institute of Engineering Systems and Computers, Research and Development of Brazil |

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**Figure 1.**Examples of equipment used to measure streamflow in fluviometric gage stations in Brazil: (

**A**): ADCPs (S5, M9 and Rio Grande, models), that shows great detail of the velocity variation in the cross-section and (

**B**): Current Meter (horizontal and vertical axis), with a few points of discharge measurement and poor detail of the velocity variation in the cross-section, consequently.

**Figure 7.**Itapebi’s Firm Energy Values – Evaluation of Impacts by Variation of Itapebi’s Affluent Incremental Flow Values.

**Figure 8.**Itapebi’s Firm Energy Values - Evaluation of Impacts by Variation of Parameters of Itapebi’s Downstream Flow Level Polynomial.

Simulation | Considerations |
---|---|

1 | No variations in the parameters |

2 | Itapebi’s affluent incremental flow 0.2% higher |

3 | Itapebi’s affluent incremental flow 0.2% lower |

4 | Positive variation of 5% in Itapebi’s downstream level flow polynomial |

5 | Negative variation of 5% in Itapebi’s downstream level flow polynomial |

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## Share and Cite

**MDPI and ACS Style**

Westin, L.G.F.; Conceição, L.R.; Bortoni, E.C.; Marcato, A.L.M.; Ribeiro, C.B.d.M.; Honório, L.d.M. Evaluating the Impact of Streamflow Rating Curve Precision on Firm Energy of Hydropower Plants. *Water* **2021**, *13*, 1016.
https://doi.org/10.3390/w13081016

**AMA Style**

Westin LGF, Conceição LR, Bortoni EC, Marcato ALM, Ribeiro CBdM, Honório LdM. Evaluating the Impact of Streamflow Rating Curve Precision on Firm Energy of Hydropower Plants. *Water*. 2021; 13(8):1016.
https://doi.org/10.3390/w13081016

**Chicago/Turabian Style**

Westin, Luiz Gustavo F., Lucas R. Conceição, Edson C. Bortoni, André Luís Marques Marcato, Celso Bandeira de Melo Ribeiro, and Leonardo de Mello Honório. 2021. "Evaluating the Impact of Streamflow Rating Curve Precision on Firm Energy of Hydropower Plants" *Water* 13, no. 8: 1016.
https://doi.org/10.3390/w13081016