# Computer Model for a Wind–Diesel Hybrid System with Compressed Air Energy Storage

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## Abstract

**:**

## 1. Introduction

## 2. Model-Based System Design

#### 2.1. Basic Parameters

#### 2.1.1. Simulation Time and Time Step

#### 2.1.2. Energy Balance

#### 2.2. Subsystems Modeling

#### 2.2.1. Load

#### 2.2.2. Wind Turbine

#### 2.2.3. Diesel Generator

#### 2.2.4. Compressed Air Storage

#### 2.2.5. Storage Tank

#### 2.3. Definition of the System Operating Modes

#### 2.4. Case Study

^{−1}. As wind speed probability distribution values are unknown, a Weibull function with a shape parameter of two (Rayleigh distribution) is considered.

## 3. Results And Discussion

#### 3.1. WDCAS and HOMER Software Comparison Results

#### 3.2. WDCAS Software Validation under Ideal Conditions

- Assuming ideal conditions, there is not limit on the required storage capacity of the tank;
- The overall power dissipated by the ESS is null, it means that the excess of power is used by the storage unit;
- For an ideal compressor, the power losses are diminished since motor/compressor efficiency is 100%, as well as the mechanical losses as polytropic efficiency is 100%;
- Compression performance improvement is achieved when increasing the number of compressor stages;
- The compression is done under the following conditions: the outdoor air pressure is equal to 1 bar, the storage temperature is set at 20 ${}^{\circ}$C and the polytropic index of air at room temperature is ${n}_{c}=1.3$.

#### 3.3. WDCAS Software Validation

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Abbreviations | |

CAES | Compressed air energy storage |

ESS | Energy storage system |

GHG | Greenhouse gas |

HOMER | Hybrid optimization of multiple energy resources |

WDCAS | Wind–diesel hybrid system with CAES |

WEPR | Wind energy penetration rate |

WPPR | Wind power penetration rate |

WT | Wind turbine |

Greek Letters | |

$\alpha $ | Wind shear coefficient |

${\eta}_{{e}_{WT}}$ | Electric efficiency of the WT |

${\eta}_{DG}$ | Efficiency of the diesel engine |

${\eta}_{{p}_{C}}$ | Polytropic efficiency of the compressor |

${\eta}_{tr}$ | Transmission efficiency between the engine and the compressor |

$\lambda $ | Stoichiometric air/fuel ratio |

${\pi}_{C}$ | Total compression ratio |

${\pi}_{{i}_{C}}$ | Compression ratio for each stage |

${\rho}_{a}$ | Air density |

Symbols | |

A | Fuel consumption parameter |

B | Fuel consumption parameter |

c | Scale parameter describing the height of a Weibull distribution |

${C}_{{P}_{WT}}$ | Power coefficient |

${E}_{Load}$ | Annual load demand of the system |

${E}_{{\overline{v}}_{w}}$ | Total amount of wind energy produced annually |

$f\left({v}_{w}\right)$ | Weibull density probability function |

${h}_{0}$ | Reference height |

${h}_{WT}$ | WT hub height |

k | Shape parameter describing the variation of a Weibull distribution about the mean |

${\dot{m}}_{c}$ | Compressed air mass flow rate through the compressor |

${\dot{m}}_{{f}_{DG}}$ | Fuel mass flow injected in the cylinders of the internal combustion engine |

${\dot{m}}_{i{n}_{DG}}$ | Air mass flow entering the engine |

${\dot{m}}_{u}$ | Capacity of a storage unit |

$N{B}_{DG}$ | Number of diesel generators |

$N{B}_{WT}$ | Number of wind turbines |

${n}_{c}$ | Polytropic index |

${N}_{C}$ | Number of compressor stages |

$N{D}_{auto}$ | Number of days of autonomy |

${N}_{uni{t}_{max}}$ | Maximum number of storage units |

${p}_{a}$ | Inlet atmospheric pressure of the compressor |

${P}_{{C}_{1}}$ | Single-stage compressor power |

${P}_{C}$ | Multi-stage compressor power |

${P}_{CAES}$ | Compressed air energy storage power |

${P}_{CAE{S}_{min}}$ | Minimum compressed air energy storage power |

$PCI$ | Lower calorific value of the fuel |

${P}_{Load}$ | Load power |

${P}_{Loa{d}_{ave}}$ | Average load power |

${P}_{Loa{d}_{max}}$ | Maximum load power |

${P}_{Loa{d}_{min}}$ | Minimum load power |

${P}_{DG}$ | Diesel generator power |

${P}_{D{G}_{nom}}$ | Nominal power of the diesel generator |

${p}_{o{u}_{C}}$ | Outlet pressure of the compressor |

${p}_{st}$ | Storage pressure |

${P}_{WT}$ | Wind power |

${P}_{W{T}_{a}}$ | Wind power generated for a specific WT |

${P}_{W{T}_{ex}}$ | Wind power surplus |

${P}_{W{T}_{max}}$ | Maximum wind power |

R | Perfect gas constant |

${S}_{WT}$ | Swept area |

${T}_{st}$ | Storage temperature |

${t}_{step}$ | Time step |

${V}_{st}$ | Total volume of the storage system |

${v}_{w}$ | Wind speed |

${v}_{{0}_{w}}$ | Wind speed at a reference height |

${\overline{v}}_{w}$ | Average wind speed |

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**Figure 2.**Load and wind data in Esker Camp: (

**a**) annual average load profile; (

**b**) average wind speed per month.

**Figure 5.**Parameter influence on fuel consumption: (

**a**) number of compressor stages; (

**b**) polytropic efficiency; (

**c**) compressor motor efficiency; (

**d**) storage pressure.

**Figure 6.**Dependency on the minimum required power storage: (

**a**) fuel consumption; (

**b**) dissipated energy.

**Figure 7.**WDCAS software results at 120% WPPR: (

**a**) average wind speed of $5.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$; (

**b**) average wind speed of $6.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$.

**Figure 8.**Diesel generators comparison as a function of the number of operating hours: (

**a**) at 120% WPPR; (

**b**) average wind speed of $6.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$.

**Figure 9.**Correlation between the number of operating hours and the operation mode per diesel generator: (

**a**) at 120% WPPR; (

**b**) average wind speed of $6.5\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$.

Software | Country | Goals | Energy Source | ESS |
---|---|---|---|---|

HOMER | USA | Analyzes technical and economic feasibility of hybrid renewable energy systems. | Photovoltaic (PV), wind turbine (WT), hydroelectric, diesel generator, biomass. | Electrochemical cells, flywheel, hydrogen storage. |

RETScreen | CAN | Analyzes technical, economic and environmental feasibility of hybrid systems. | PV, WT, hydroelectric, diesel generator, gas turbine, geothermal, biomass. | Thermal storage, hydrogen storage. |

JPElec | FRA | Optimizes steady state stability of power grids. | PV, WT, hydroelectric, diesel generator. | Electrochemical cells. |

Hybrid 2 | USA | Sizes and analyzes the techno economic impact of hybrid networks with renewable energy. | PV, WT, diesel generator. | Electrochemical cells. |

HySim | USA | Analyzes technical and economic feasibility of hybrid systems. | PV, diesel generator. | Electrochemical cells. |

HySys | ESP | Sizes and analyzes off grid hybrid systems. | PV, WT, diesel generator. | - |

Hybrid Designer | ZAF | Analyzes technical and economic feasibility of hybrid renewable energy systems. | PV, WT, diesel generator. | Electrochemical cells. |

SOLSIM | DEU | Analyzes technical and economic feasibility of hybrid systems. | PV, WT, diesel generator, biomass. | Electrochemical cells. |

TRNSYS | USA | Simulates transient system behavior. | PV, WT, diesel generator. | Electrochemical cells. |

CAES | ${\mathit{P}}_{\mathit{WT}}=0$ | ${\mathit{P}}_{\mathit{WT}}<{\mathit{P}}_{\mathit{Load}}$ | ${\mathit{P}}_{\mathit{WT}}>{\mathit{P}}_{\mathit{Load}}$ | ||
---|---|---|---|---|---|

${\mathit{P}}_{\mathit{Load}}<\mathbf{0.3}\mathit{P}{}_{\mathit{DG}}$ | ${\mathbf{P}}_{\mathit{Load}}>\mathbf{0.3}{\mathit{P}}_{\mathit{DG}}$ | ${\mathbf{P}}_{\mathit{Load}}<\mathbf{0.3}{\mathit{P}}_{\mathit{DG}}$ | ${\mathit{P}}_{\mathit{Load}}>\mathbf{0.3}{\mathit{P}}_{\mathit{DG}}$ | ||

Full | |||||

Medium | |||||

Empty | |||||

No wind power | Empty air tank | Generator stopped | |||

Partial wind power | Partially filled air tank | Generator started | |||

Strong wind power | Full air tank | Consumption |

Parameter | Data | Details |
---|---|---|

Annual load power | ${P}_{Loa{d}_{ave}}$: 19.9 kW | |

${P}_{Loa{d}_{max}}$: 50 kW | ||

${P}_{Loa{d}_{min}}$: 7 kW | ||

Annual wind resource | ${\overline{v}}_{w}$: $5.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$ | |

Diesel generator power | ${P}_{DG}$: $5\times 12\phantom{\rule{3.33333pt}{0ex}}\mathrm{kW}$ | D13-2 Caterpillar |

2 WT at 40% WPPR | ${P}_{WT}$: $2\times 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{kW}$ | BWC Excel-S Bergey |

4 WT at 80% WPPR | ${P}_{WT}$: $4\times 10\phantom{\rule{3.33333pt}{0ex}}\mathrm{kW}$ |

Parameter | At 40% WPPR | At 80% WPPR | ||||
---|---|---|---|---|---|---|

WDCAS | HOMER | Difference (%) | WDCAS | HOMER | Difference (%) | |

Fuel consumption (L) | 56.32 | 57.66 | 2.32 | 47.77 | 51.21 | 6.71 |

Diesel generator power (kWh) | 152.20 | 154.26 | 1.33 | 128.88 | 136.55 | 5.62 |

Wind power (kWh) | 22.26 | 20.42 | 8.26 | 51.32 | 40.85 | 20.40 |

WEPR (%) | 12.80 | 12.00 | 0.80 | 28.47 | 21.70 | 6.77 |

Operating Frequency in % | At 40% WPPR | At 80% WPPR | ||||
---|---|---|---|---|---|---|

Generator Number | WDCAS | HOMER | Difference (%) | WDCAS | HOMER | Difference (%) |

1 | 44.90 | 46.75 | 1.85 | 41.70 | 49.80 | 8.10 |

2 | 32.82 | 36.07 | 3.25 | 40.66 | 34.79 | 5.87 |

3 | 18.50 | 13.70 | 4.80 | 14.59 | 12.38 | 2.21 |

4 | 3.43 | 2.97 | 0.46 | 2.82 | 2.62 | 0.20 |

5 | 0.36 | 0.52 | 0.16 | 0.22 | 0.42 | 0.20 |

Parameter | Symbol | Value |
---|---|---|

Number of compressor stages | ${N}_{C}$ | 7 |

Polytropic index | ${n}_{c}$ | 1.3 |

Atmospheric pressure | ${p}_{a}$ | 1 bar |

Storage temperature | ${T}_{st}$ | 20 ${}^{\circ}$C |

Polytropic efficiency | ${\eta}_{{p}_{C}}$ | 100% |

Compressor motor efficiency | ${\eta}_{tr}$ | 100% |

Minimum required power for storage | ${P}_{CAE{S}_{min}}$ | 0 kW |

Storage pressure | ${p}_{st}$ | 2 bars |

Number of days of autonomy | $N{D}_{auto}$ | 1000 |

Parameter | Symbol | Value |
---|---|---|

Number of compressor stages | ${N}_{C}$ | 5 |

Polytropic index | ${n}_{c}$ | 1.3 |

Atmospheric pressure | ${p}_{a}$ | 1 bar |

Storage temperature | ${T}_{st}$ | 20 ${}^{\circ}$C |

Polytropic efficiency | ${\eta}_{{p}_{C}}$ | 85% |

Compressor motor efficiency | ${\eta}_{tr}$ | 95% |

Minimum required power for storage | ${P}_{CAE{S}_{min}}$ | 1 kW |

Storage pressure | ${p}_{st}$ | 10 bars |

Number of days of autonomy | $N{D}_{auto}$ | 7 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Martinez, N.; Benchaabane, Y.; Silva, R.E.; Ilinca, A.; Ibrahim, H.; Chandra, A.; Rousse, D.R.
Computer Model for a Wind–Diesel Hybrid System with Compressed Air Energy Storage. *Energies* **2019**, *12*, 3542.
https://doi.org/10.3390/en12183542

**AMA Style**

Martinez N, Benchaabane Y, Silva RE, Ilinca A, Ibrahim H, Chandra A, Rousse DR.
Computer Model for a Wind–Diesel Hybrid System with Compressed Air Energy Storage. *Energies*. 2019; 12(18):3542.
https://doi.org/10.3390/en12183542

**Chicago/Turabian Style**

Martinez, Nicolas, Youssef Benchaabane, Rosa Elvira Silva, Adrian Ilinca, Hussein Ibrahim, Ambrish Chandra, and Daniel R. Rousse.
2019. "Computer Model for a Wind–Diesel Hybrid System with Compressed Air Energy Storage" *Energies* 12, no. 18: 3542.
https://doi.org/10.3390/en12183542