# Development of a High-Fidelity Model for an Electrically Driven Energy Storage Flywheel Suitable for Small Scale Residential Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Description of Flywheel Energy Storage Systems

#### 2.1. Background

#### 2.2. Structure and Components of FESS: Priciples and Components of FESS

#### 2.2.1. The Rotor

_{min}) and maximum speed (𝜔

_{max}) to limit maximum torque on the MG for a given power rating, and also avoid abundant voltage variations. The useful stored energy of the flywheel between (𝜔

_{min}) and (𝜔

_{max}) can be obtained by

#### Intermediate Speed Flywheels

#### 2.2.2. Electric Machine

#### 2.2.3. Power Electronics Interface

#### 2.2.4. Bearing System

#### 2.2.5. Containment

## 3. Characteristics of FESS

## 4. Applications of FESS

## 5. Calculation of Losses in FESS

#### 5.1. Copper Loss

#### 5.2. Mechanical Losses

_{g}/m

^{3}), ${D}_{ro}$ is the rotor outer diameter (m) and ${D}_{s}$ is the shaft diameter (m). The torque coefficient is dependent on coolant viscosity, speed and size of the rotating disc. The increase in velocity changes the flow type of a rotating disc in a medium from laminar to turbulent. This transition is determined by Reynolds number 3 × 10

^{5}, a dimensionless parameter calculated using Equation (16).

_{g}/m·s). ${C}_{M}$ is calculated using Equations (14) or (15), depending on the size of the Reynolds number.

#### 5.3. Other Losses

- The clearances between stationary and rotating components is small, such that the boundary layers on stationary and rotating surfaces merge.
- The flywheel rotor is assumed to be a drum type steel laminated cylinder.
- The windage losses are calculated under maximum pressure conditions of 100 Pa at 40 °C and maximum speed of 20,000 rpm.
- Density values are calculated from temperature and pressure using ideal gas law.
- Windage on the motor–generator is neglected, since its rotor diameter is much smaller than that of the main rotor, and the power law on diameter for windage is 5.
- Switching loss and IGBT conduction loss in power converters are neglected as these losses are small compared to other losses in a FESS. Although, this might not be the case in some other storage systems, where they may need to be considered.
- It is assumed that the combined axial load on the bearing is 10% of the total flywheel rotor weight with the rest taken by the passive magnetic bearing.

## 6. Analysis and Control of FESS

#### 6.1. System Configuration and Mathematical Model

^{2}; B = Friction of viscous in N·m/rad/s; P = Number of poles; ${\lambda}_{m}$ = Rotor flux constant in V/rad/s; ${\omega}_{e}$ = Rotor’s electrical speed in rad/s; ${T}_{L}$ = Load torque in N·m; ${T}_{e}$ = Electromagnetic torque in N·m; ${\omega}_{m}$ = Rotor’s mechanical speed in rad/s.

#### 6.2. System Operation and Control Strategy

## 7. Results Analysis

#### 7.1. System Losses

#### 7.2. Simulated Results

#### 7.2.1. Charging State

#### 7.2.2. Discharging State

#### 7.2.3. Charge–Discharge State

#### 7.2.4. Discussion

## 8. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Power loss vs speed: windage loss (top left); bearing friction loss (top right); resistive loss (bottom left); stray loss (bottom right).

**Figure 11.**FESS in charging mode: Three-phase current (top left); Flywheel stored energy (top right); Electromagnetic torque (bottom left); Flywheel SOC (bottom right).

**Figure 12.**FESS in discharging mode: Three-phase current at t = 900 s (top left); Three-phase current at t = 1200 s (top right); Torque Te at t = 900 s (bottom left); Torque Te at t = 1200 s (bottom right).

**Figure 14.**FESS in step-charging mode: Torque, power, and three-phase current (top left, top right, and bottom left); PMSM no load speed (bottom right).

**Figure 15.**FESS in step-charging mode: Inverter output voltage and DC-bus voltage at ($t=2\mathrm{s})$ (top left); Inverter output voltage and DC-bus voltage at ($t=8\mathrm{s})$ (top left); FESS state-of-charge (bottom left); DC-bus voltage at ($t=2,8,10\mathrm{s})$ (bottom right).

Attribute | Carbon Fibre V _{max} = 790 m/sa = 2/3 b ^{1} | Steel Laminate V _{max} = 427 m/sa = 0 (No Hole) |
---|---|---|

Mass | 1 | 4.53 |

Volume | 1 | 0.503 |

^{1}a is the inner radius and b is the outer radius of a hollow flywheel.

**Table 2.**Comparison of the characteristic properties of different commercial flywheel systems adopted from [59] and manufacturers’ websites.

Piller Power Bridge | Active Power | Temporal Power | Beacon Power Gen 4 | Rosseta T2 | Vycon | Kinetic Traction Systems | Stornetic | PowerThru | Gyrotricity | Amber Kintetics | |
---|---|---|---|---|---|---|---|---|---|---|---|

Origin | Germany | USA | Canada | USA | Germany | USA | USA | Germany | USA | UK | USA |

Rated Power | 1600 | 250 kW | 100-500 kW | 100 kW | 500 kW | 500 kW | 200 kW | 22 kW | 190 kW | 100 kW | 8 kW |

Rated Energy Capacity | 4 kWh | 0.9 kWh | 50 kWh | 25 kWh | 4 kWh | 0.83 kWh | 1.5 kWh | 4 kWh | 0.63 kWh | 5 kWh | 32 kWh |

Application area | UPS | UPS | Voltage Stability/ Maintenance | Frequency Stability/ Maintenance | Recuperation | UPS, Recuperation | UPS, Power Quality, Micro-grid & Railway | Grid services, Railway | UPS | Frequency Stability, Railway | Micro-grid, Telecoms, Utilities |

Maximum rpm | 3300 | 7700 | 11,500 | 16,000 | 25,000 | 36,000 | 37,800 | 45,000 | 52,000 | 20,000 | 10,000 |

Bearing concept | Rolling bearings, relieved magnetically | Rolling bearings, relieved magnetically | Unclear | Rolling bearings, relieved magnetically | Rolling bearings | Active magnetic bearings | Magnetic & hydrodynamic bearings | Active magnetic bearings | Active magnetic bearings | Mechanical & magnetic bearings | Not stated |

Electrical machine type | Not provided | Not provided | Permanent magnet | Permanent magnet | Not provided | Permanent magnet | Permanent magnet | Permanent magnet | Synchronous Reluctance | Permanent magnet | Permanent magnet |

Flywheel material | Steel | Steel | Steel | Fibre composite | Fibre composite | Steel | Fibre composite | Fibre composite | Fibre composite | Laminated Steel | Steel |

Topology | |||||||||||

Configuration |

**Table 3.**Values of permissible static load factor fs [63].

Operating Conditions | Lower Limit of ${\mathit{f}}_{\mathit{s}}$ = ${\mathit{C}}_{\mathit{s}}$/${\mathit{F}}_{\mathit{s}}$ | |
---|---|---|

Ball Bearings | Roller Bearings | |

Low-noise applications | 2.0 | 3.0 |

Bearings subjected to vibration and shock loads | 1.5 | 2.0 |

Standard operating conditions | 1.0 | 1.5 |

Equivalent Load Factors | Load Torque Factors | Lubrication Factor, ${\mathit{f}}_{0}$ | |||||
---|---|---|---|---|---|---|---|

Bearing type | Xs | Ys | z | y | Oil Mist/Injection | Oil Bath/Grease | Oil Bath/Jet |

Single row radial | 0.6 | 0.5 | 0.0007 | 0.55 | 1.0 | 3.0 | 6.0 |

Angular contact, (α = 15–40°) | 0.5 | 0.26–0.47 | 0.001 | 0.33 | 0.33 | 0.47 | 0.47 |

Angular contact double row | - | - | - | - | 2.0 | 6.0 | 9.0 |

**Table 5.**Parameters and coefficients of a combined surface-mounted permanent magnet synchronous motor (PMSM)

^{1}and flywheel energy storage systems (FESS).

Stator winding resistance (R_{s}) | 0.20 Ω |

Armature inductance (L_{d} = L_{q}) | 0.834 mH |

Combined inertia (PMSM and flywheel) (J) | 12 kg m^{2} |

Friction coefficient (B_{m}) | 0.8 × 10^{−4} N·m·s |

Permanent magnet flux (λ) | 0.175 Wb |

Number of poles | 2 |

Power rating | 10 kW |

Energy storage rating | 5 kWh |

Maximum torque | 12 N·m |

Maximum output power | 15 kW |

Rated torque | 8 N·m |

Maximum angular speed | 20,000 rpm |

Minimum angular speed | 10,000 rpm |

Machine rated over speed | 25,000 rpm |

Switching frequency | 10 kHz |

Filter damping resistance | 0.75 Ω |

Filter capacitance | 4 × 10^{−5} F |

Filter inductance | 640 × 10^{−6} H |

DC-bus voltage | 600 V |

Voltage constant (${K}_{e}$) | $2\times {10}^{-3}\mathrm{V}\xb7\mathrm{s}/\mathrm{rad}$ |

Air density ($\rho $) | 0.0011 kg/m^{3} |

Air dynamic viscosity ($\mu $) | 1.91 × 10^{−5} kg/m·s |

Flywheel rotor outer diameter (${D}_{ro})$ | 0.4 m |

Shaft diameter (${D}_{s})$ | 0.025 m |

Torque coefficient (${C}_{M}$) | 0.0554 |

Bearing design factor (${f}_{L}$) | 0.0007 |

Kinematics oil viscosity (${V}_{o}$) | 130 mm^{2}/s (40 °C) |

^{1}PMSM parameters obtained from real data of the motor manufacturer.

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**MDPI and ACS Style**

Amiryar, M.E.; Pullen, K.R.; Nankoo, D. Development of a High-Fidelity Model for an Electrically Driven Energy Storage Flywheel Suitable for Small Scale Residential Applications. *Appl. Sci.* **2018**, *8*, 453.
https://doi.org/10.3390/app8030453

**AMA Style**

Amiryar ME, Pullen KR, Nankoo D. Development of a High-Fidelity Model for an Electrically Driven Energy Storage Flywheel Suitable for Small Scale Residential Applications. *Applied Sciences*. 2018; 8(3):453.
https://doi.org/10.3390/app8030453

**Chicago/Turabian Style**

Amiryar, Mustafa E., Keith R. Pullen, and Daniel Nankoo. 2018. "Development of a High-Fidelity Model for an Electrically Driven Energy Storage Flywheel Suitable for Small Scale Residential Applications" *Applied Sciences* 8, no. 3: 453.
https://doi.org/10.3390/app8030453