# Hybrid Energy Network Management: Simulation and Optimisation of Large Scale PV Coupled with Hydrogen Generation

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## Abstract

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## 1. Introduction

## 2. Description of the Hybrid Energy System

#### 2.1. Modelling of the HES

- Definition of a scheduling interval and its discretisation. The number of intervals of equal length $\Delta t$ is ${N}_{int}$, for instance a one day scheduling period can be divided either into 24 intervals of 1 h or in 96 intervals of 15 min. Time profiles of the energy production such as production of the PV plant and demand of the local energy load, together with the time profiles of the energy prices, are considered to be known data. This phase is carried out by reading different files containing the time series of data, either obtained by environmental conditions (solar irradiation) or by market prices (purchasing and selling of electrical energy). As the approach proposed is more oriented toward energy flows, every power variable in the system is modelled as constant in each time interval. Transient phenomena, related for instance to power–electronics converters connecting PV output in DC and electrical grid in AC, are neglected and, furthermore, HES is considered to be in steady-state in each time interval.
- Definition of technical and operational characteristics of the different sources as well as connections among them. Mathematically, these constraint equations are divided into two categories:
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- Balance equations represent the energy balance of each energy carrier in order to ensure feasible solutions where output is covered by production.
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- Constitutive equations represent the relations between the input and output power of a source, as well as its operational limits.

The first set of equation is linear by definition; its structure is in fact made up of an algebraic sum of energy values over a given time interval. Each energy vector is characterised by its own balance equation and a constraint equation is defined for every single time interval. The second set of equations does not have an a priori structure, as the input–output relation of one module could be in general a nonlinear function. In most application cases, these relations are linear or can be approximated by piece-wise linear relations. - Computation of the target function to be optimised and evaluation of the scheduling strategy minimising/maximising it. As an example, if an economical target function is adopted, the sum over the time intervals of earnings obtained by selling the electrical energy to the grid has to be maximised. In this last case, the objective function is expressed as a linear form made by multiplying the energy sold to the grid in each interval by the unit selling price.

#### 2.2. PV Plant

#### 2.3. Electrical Grid and Load

#### 2.4. Electrolyser

#### 2.5. Fuel Cell

#### 2.6. Hydrogen Tank

#### 2.7. Natural Gas Grid

#### 2.8. Battery Energy Storage System

## 3. MILP Optimisation Procedure

#### 3.1. Electrical Balance

#### 3.2. Hydrogen Balance

#### 3.3. Objective Function

## 4. Case Studies

#### 4.1. Computational Cost

#### 4.2. Case 1: Connection with Natural Gas Grid

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- PV plant:$$P{V}_{rate}=120\phantom{\rule{3.33333pt}{0ex}}\mathrm{MW}$$
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- Electrical network:$${P}_{grid}^{max}=200\phantom{\rule{3.33333pt}{0ex}}\mathrm{MW}$$The unit price of electricity is defined on the basis of market data and one day series is reported in Figure 4.
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- Electrolyser:$${P}_{e{l}_{max}}=20\phantom{\rule{3.33333pt}{0ex}}\mathrm{MW}$$$${P}_{e{l}_{min}}=20\%\xb7{P}_{e{l}_{max}}=4\phantom{\rule{3.33333pt}{0ex}}\mathrm{MW}$$$${\eta}_{el}=0.7$$$${c}_{el}=160.00\phantom{\rule{3.33333pt}{0ex}}\u20ac/\mathrm{h}$$It is considered that hydrogen is produced at the pressure of $30\mathrm{bar}$, which is suitable for natural gas grid output and for short term storage.
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- Natural gas grid:$${q}_{grid}^{max}=1000\phantom{\rule{3.33333pt}{0ex}}\mathrm{kg}/\mathrm{h}$$The hydrogen selling price is set as fixed externally.

#### 4.3. Case 2: Hydrogen Storage and Fuel Cell Generation

#### 4.4. Case 3: Dispatching Constraint

## 5. Discussion and Further Developments

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

HEN | Hybrid Energy Network |

HES | Hybrid Energy System |

RES | Renewable Energy Source |

PV | PhotoVoltaics |

LP | Linear programming |

MILP | Mixed Integer Linear programming |

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**Figure 5.**Hourly diagram of electrical power produced by PV, sold to the grid and used to supply electrolyser at the selling hydrogen price of $4.2\phantom{\rule{3.33333pt}{0ex}}\u20ac/\mathrm{kg}$.

**Figure 6.**Hourly diagram of hydrogen produced, in $\mathrm{kg}/\mathrm{h}$, by the electrolyser at the selling hydrogen price of $4.2\phantom{\rule{3.33333pt}{0ex}}\u20ac/\mathrm{kg}$.

**Figure 7.**Daily energy sold under the form of hydrogen, in $\mathrm{MWh}$, versus its unit price in $\u20ac/\mathrm{kg}$.

**Figure 10.**Hourly diagram of electrical power produced by PV, sold to the grid and used to supply electrolyser and local load.

Name | Unit | Description | Carrier |
---|---|---|---|

${P}_{el}$ | $\mathrm{MW}$ | electrolyser input power | electrical |

${P}_{fc}$ | $\mathrm{MW}$ | Fuel Cell output power | electrical |

${P}_{bc}$ | $\mathrm{MW}$ | BESS charging power | electrical |

${P}_{bd}$ | $\mathrm{MW}$ | BESS discharging power | electrical |

${P}_{s}$ | $\mathrm{MW}$ | power sold to the grid | electrical |

${P}_{p}$ | $\mathrm{MW}$ | power purchased from the grid | electrical |

${q}_{grid}$ | $\mathrm{kg}/\mathrm{h}$ | mass flow sold to the gas grid | hydrogen |

${q}_{tank}^{in}$ | $\mathrm{kg}/\mathrm{h}$ | mass flow in the tank | hydrogen |

${q}_{tank}^{out}$ | $\mathrm{kg}/\mathrm{h}$ | mass flow out of the tank | hydrogen |

Name | Description |
---|---|

${\delta}_{el}$ | electrolyser status |

${\delta}_{fc}$ | Fuel Cell status |

${\delta}_{s}$ | electrical sell |

${\delta}_{p}$ | electrical purchase |

${\delta}_{bc}$ | BESS charge |

${\delta}_{bd}$ | BESS discharge |

${\delta}_{grid}$ | hydrogen sell to gas grid |

${\delta}_{in}$ | hydrogen tank in flow |

${\delta}_{out}$ | hydrogen tank out flow |

Scheduling | Number of Variables Real | Number of Variables Integer | Number of Constraints | CPU Time ($\mathbf{s}$) |
---|---|---|---|---|

one day | 216 | 216 | 170 | 10 |

one week | 1512 | 1512 | 1190 | 20 |

one month | 6696 | 6696 | 5270 | 120 |

three months | 20,088 | 20,088 | 15,810 | 600 |

six months | 39,312 | 39,312 | 31,620 | 3000 |

${\mathit{H}}_{2}$ Price | Electrical Energy | ${\mathit{H}}_{2}$ Energy |
---|---|---|

$\u20ac/\mathrm{kg}$ | $\mathrm{MWh}$ | $\mathrm{MWh}$ |

2.5 | 645.3 | 0.0 |

3.0 | 645.3 | 0.0 |

3.3 | 625.2 | 17.7 |

4.0 | 505.6 | 130.3 |

4.5 | 445.9 | 214.3 |

5.0 | 405.9 | 284.2 |

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**MDPI and ACS Style**

Cerchio, M.; Gullí, F.; Repetto, M.; Sanfilippo, A.
Hybrid Energy Network Management: Simulation and Optimisation of Large Scale PV Coupled with Hydrogen Generation. *Electronics* **2020**, *9*, 1734.
https://doi.org/10.3390/electronics9101734

**AMA Style**

Cerchio M, Gullí F, Repetto M, Sanfilippo A.
Hybrid Energy Network Management: Simulation and Optimisation of Large Scale PV Coupled with Hydrogen Generation. *Electronics*. 2020; 9(10):1734.
https://doi.org/10.3390/electronics9101734

**Chicago/Turabian Style**

Cerchio, Marco, Francesco Gullí, Maurizio Repetto, and Antonino Sanfilippo.
2020. "Hybrid Energy Network Management: Simulation and Optimisation of Large Scale PV Coupled with Hydrogen Generation" *Electronics* 9, no. 10: 1734.
https://doi.org/10.3390/electronics9101734