# Capacity Value from Wind and Solar Sources in Systems with Variable Dispatchable Capacity—An Application in the Brazilian Hydrothermal System

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Reliability Concepts

#### 2.2. ELCC Standard Calculation

#### 2.3. ELCC with Variable Dispatchable Capacity

#### The Performed Simulation

## 3. Results

#### 3.1. Variability of Hydropower Availability throughout the Year

#### 3.2. ELCC Results

#### 3.2.1. Brazil-SIN

#### 3.2.2. Northeast Subsystem

#### 3.3. Capacity Credit

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANA | National Water Regulatory Agency or Agência Nacional de Águas in Portuguese |

SIN | Interconnected National System or Sistema Interligado Nacional in Portuguese |

ONS | National System Operator or Operador Nacional do Sistema in Portuguese |

VG | Variable Generation |

PV | Photovoltaic |

FOR | Forced Outage Rate |

ELCC | Effective Load Carrying Capability |

SEB | Brazilian Electric System or Sistema Elétrico Brasileiro in Portuguese |

ECP | Equivalent Conventional Power |

EFC | Equivalent Firm Capacity |

LOLE | Loss of Load Expectation |

LOLP | Loss of Load Probability |

CSP | Concentrating Solar Power |

## Appendix A. Brazil Daily Availability Hydropower Calculation

**Figure A1.**Hydraulic capacity and maximum power output of turbine-generator set as function of net head. Adapted from [32].

**Figure A2.**Performance curves of a Francis type hydraulic turbine. Adapted from [36].

- By inspection of Equation (A1), it is noticeable that headwater and tailwater values are needed to calculate the head. Headwater values come directly from the National Water Regulatory Agency (ANA) database [29]. The tailwater values are calculated using downstream polynomials and streamflow data, both extracted from the National Water Regulatory Agency (ANA) database [29].
- Net head value makes it possible to calculate the turbine maximum water intake of one machine (the hydraulic capacity of a single machine) using Equation (A3). In sequence, the maximum water intake of a set of equal hydraulic turbines is determined by multiplying the number of units of that particular set and the maximum water intake of an individual machine, as shown in Equation (A5):$${q}_{max,setj}={n}_{machine,j}.{q}_{max,machinej}$$
- The upper limit of the total water intake of the plant is the sum of the maximum water intake of all set of different machines in the plant as shown in Equation (A6):$${q}_{max,plant}=\sum _{j=1}^{{n}_{set}}{q}_{max,setj}$$
- Assuming that there is no evaporation or infiltration, the net head corresponds only to convertible electrical power. This conversion requires inflows and outflows of water through the reservoir-turbine system. In this context, the mass balance of the reservoir-turbine system requires that:$$Inflow-Outflow-Evaporation=\Delta Storage$$$$Outflow=Spill+TurbineDischarge$$
- If ${q}_{max,plant}>Outflow$, then $Outflow={q}_{max,plant}$ and ${q}_{discharged}={q}_{max,plant}$Where ${q}_{discharged}$ is the actual water flow discharged by the turbines.
- If ${q}_{max,plant}<Outflow$, then ${q}_{discharged}={q}_{max,plant}$. In this case, $Spill>0$.

After analyzing the decision rule, the value for $Outflow$ can be determined. With this value, a new net head is calculated using the downstream polynomial. - In step 5, the hydraulic capacity and the net head are recalculated. Step 6 assesses if the difference between net head value in iterations $i+1$ and i is greater than an established convergence criterion. In each iteration, the net head is recalculated and compared to the former value. If $\Delta NetHead=NetHea{d}_{i+1}-NetHea{d}_{i}$ is lower than a specified limit, the process stops; otherwise, the process restarts in Step 5 until $\Delta NetHead$ meets the desired criterion. In this study $\Delta NetHead<{10}^{-5}m$ is adopted as limit criterion.

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**Figure 1.**A general flowchart of the employed method to determine ELCC in systems with variable dispatchable capacity.

**Figure 3.**Graph representation of accumulated probabilities of COPT for 2019 for the first day of the selected months.

**Figure 18.**Load, PV generation, ELCC in an hourly basis for the first two weeks of 2019 for the Northeast subsystem.

**Figure 19.**Load, wind generation, ELCC in an hourly basis for the first two weeks of 2019 for the Northeast subsystem.

**Figure 20.**Monthly ELCC in percentages for the SIN calculated based on the monthly installed capacity data.

**Figure 21.**Monthly ELCC in percentages for the Northeast subsystem calculated based on the monthly installed capacity data.

Capacity Level | Probability | Acum. Prob |
---|---|---|

${C}_{1}$ | ${P}_{1}$ | ${\sum}_{1}^{1}{P}_{n}$ |

${C}_{2}$ | ${P}_{2}$ | ${\sum}_{1}^{2}{P}_{n}$ |

${C}_{3}$ | ${P}_{3}$ | ${\sum}_{1}^{3}{P}_{n}$ |

⋮ | ⋮ | ⋮ |

${C}_{n}$ | ${P}_{n}$ | ${\sum}_{1}^{n}{P}_{n}$ |

⋮ | ⋮ | ⋮ |

${C}_{N}$ | ${P}_{N}$ | ${\sum}_{1}^{N}{P}_{n}$ |

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**MDPI and ACS Style**

Amado, N.B.; Pelegia, E.D.B.; Sauer, I.L.
Capacity Value from Wind and Solar Sources in Systems with Variable Dispatchable Capacity—An Application in the Brazilian Hydrothermal System. *Energies* **2021**, *14*, 3196.
https://doi.org/10.3390/en14113196

**AMA Style**

Amado NB, Pelegia EDB, Sauer IL.
Capacity Value from Wind and Solar Sources in Systems with Variable Dispatchable Capacity—An Application in the Brazilian Hydrothermal System. *Energies*. 2021; 14(11):3196.
https://doi.org/10.3390/en14113196

**Chicago/Turabian Style**

Amado, Nilton Bispo, Erick Del Bianco Pelegia, and Ildo Luís Sauer.
2021. "Capacity Value from Wind and Solar Sources in Systems with Variable Dispatchable Capacity—An Application in the Brazilian Hydrothermal System" *Energies* 14, no. 11: 3196.
https://doi.org/10.3390/en14113196