# Sizing Hydrogen Energy Storage in Consideration of Demand Response in Highly Renewable Generation Power Systems

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Renewable Generation Modelling

^{th}percentile was selected for each case.

#### 2.2. Electric Storage Space Heating System

#### Space Heating Estimation

_{m}, which is located in the depth of the building. The dynamic response was modelled through a state space equation given the following:

## 3. Sizing Energy Storage to Firm up Intermittent Renewable Generation

## 4. Case Studies and Results

#### 4.1. Input Data

**Case 1**- This represents a base case, in which hydrogen energy storage capacity is optimized to accommodate renewable generation without coordinating with demand response.
**Case 2**- This represents a case of hydrogen energy storage sizing in the presence of demand response through domestic thermal storages. Demand response enrollment was considered to be 100%.
**Case 3**- This represents a case of hydrogen energy storage sizing in the presence of 25% of base-load generation in the system.

#### 4.2. Simulation Results

**Case 1 Hydrogen Energy Storage Sizing without Demand Response**

**Case 2 Hydrogen Energy Storage Sizing with Demand Response through Domestic Thermal Storages**

**Case 3 Energy Storage Sizing in the Presence of Base-Load Generation**

#### Sensitivity Analyses

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Indices and Sets | |

n, N | Index and set of customers |

t, T | Index and set of time e.g., hours |

Parameters and Constants | |

C_{a} | Heat capacity of the indoor air (MJ/°C) |

C_{m} | Heat capacity of the building fabric (MJ/°C) |

H_{e} | Summation of the infiltration heat capacity flow and house’s window heat conductance (W/°C) |

H_{g} | Floor heat conductance (W/°C) |

H_{m} | Thermal conductance which allows C_{m} to be lumped in the mass node point (W/°C) |

H_{x} | Ventilation air heat conductance (W/°C) |

H_{y} | Heat conductance in the solid walls and convection of surface (W/°C) |

${P}_{n}^{TS,\mathrm{max}}$ | Power rating of thermal storage (kW) |

${P}_{n,t}^{crit}$ | Power of all critical appliances at time t of customer n (kW) |

${Q}_{n,t}^{dhw}$ | Domestic hot water consumption of customer n at time t |

$So{C}_{n}^{TS,\mathrm{max}}$ | Maximum allowable state of charge of thermal storage (of customer n) |

$So{C}_{n}^{TS,\mathrm{min}}$ | Minimum allowable state of charge of thermal storage (of customer n) |

${T}_{n,t}^{a}$ | Temperature of dwelling at time t (of customer n) (°C) |

${T}_{t}^{e}$ | Outside temperature at time t (°C) |

${T}_{t}^{g}$ | Ground temperature at time t (°C) |

${T}_{t}^{x}$ | Ventilation supply air temperature (°C) |

${\lambda}_{t}^{r}$ | Renewable generation at time t (kW) |

${\lambda}_{t}^{c}$ | Conventional generation at time t (kW) |

$\Delta t$ | Duration of time slot (hours) |

$({\eta}^{e}/{\eta}^{f})$ | Charging/Discharging efficiency of hydrogen energy storage |

${\upsilon}_{n}$ | Demand limit (kW) |

${\varphi}_{n}$ | Internal temperature dead-band (of customer n) (°C) |

${E}_{n,t}^{TS,\mathrm{max}}$ | Maximum thermal energy storage capacity (kWH) |

${Q}_{n,t}^{sh}$ | Space heating load at time t |

${Q}_{n,t}^{dhw}$ | Domestic heating load at time t |

${\xi}_{n,t}$ | Thermal energy storage heat loss rate |

${\theta}^{n}$ | Thermal energy storage heat loss coeff. |

Functions and Variables | |

${D}_{t}^{crit}$ | Critical demand at time t (kW) |

${D}_{t}^{flex}$ | Heating demand at time t (kW) |

${D}_{t}^{total}$ | Total demand at time t (kW) |

${P}_{n,t}^{TS}$ | Electrical power supplied to storage space heating unit at time t (of customer n) (kW) |

${Q}_{n,t}^{sh}$ | HVAC thermal output power at time t (of customer n) (kW) |

$So{C}_{t}^{ES}$ | State of charge of Energy storage at time t |

${T}_{n,t}^{a}$ | Indoor ambient temperature of dwelling at time t (of customer n) (°C) |

${T}_{t}^{m}$ | Thermal mass temperature at time t (°C) |

${\xi}_{n,t}$ | Thermal Storage losses at time t (of customer n) (kWh) |

${v}_{t}^{r}$ | Variable to regulate renewable generation |

${P}_{n,t}^{TS}$ | Charging rate of thermal energy storage |

${P}_{t}^{ES}$ | Power of energy storage at time t |

${E}_{n,t}^{TS}$ | Charge level of thermal energy storage at time t |

${P}_{}^{ES,\mathrm{max}}$ | Maximum power capacity of hydrogen energy storage |

${E}_{}^{ES,\mathrm{max}}$ | Maximum energy capacity of hydrogen energy storage |

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**Figure 10.**Hydrogen energy storage size (% of demand) and spillage (% of generation) in different cases.

Energy Storage Size | |||
---|---|---|---|

Mean | Standard Deviation | Lower 95% Confidence Interval | Upper 95% Confidence Interval |

73.9 TWh | 3.6 TWh | 73.1 TWh | 74.6 TWh |

Generation (p.u) | Hydrogen Storage Size (%) | Spillage (%) | ||||
---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | |

1 | 82% | 71% | 56% | 0% | 0% | 0% |

1.1 | 36% | 28% | 7% | 0% | 0% | 0% |

1.2 | 7% | 6% | 5% | 1% | 1% | 2% |

1.3 | 5% | 5% | 3% | 1.8% | 1.3% | 3% |

1.4 | 4.1% | 4% | 2% | 3.8% | 3.1% | 3% |

1.5 | 3.3% | 3.0% | 2% | 6.4% | 8.2% | 4% |

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**MDPI and ACS Style**

Ali, M.; Ekström, J.; Lehtonen, M.
Sizing Hydrogen Energy Storage in Consideration of Demand Response in Highly Renewable Generation Power Systems. *Energies* **2018**, *11*, 1113.
https://doi.org/10.3390/en11051113

**AMA Style**

Ali M, Ekström J, Lehtonen M.
Sizing Hydrogen Energy Storage in Consideration of Demand Response in Highly Renewable Generation Power Systems. *Energies*. 2018; 11(5):1113.
https://doi.org/10.3390/en11051113

**Chicago/Turabian Style**

Ali, Mubbashir, Jussi Ekström, and Matti Lehtonen.
2018. "Sizing Hydrogen Energy Storage in Consideration of Demand Response in Highly Renewable Generation Power Systems" *Energies* 11, no. 5: 1113.
https://doi.org/10.3390/en11051113