# Fuel Cell Hybrid Locomotive with Modified Fuzzy Logic Based Energy Management System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Modeling of Power System for Fuel Cell Hybrid Locomotive

#### 2.1.1. Modeling of Fuel Cell

_{s}is the stack voltage/output voltage, N is the number of series-connected cells in the stack, E

_{Nernst}is the reversible fuel cell voltage, V

_{act}is the voltage drop due to activation losses at the lower currents, V

_{con}is the voltage drop due to concentration voltage losses at higher currents, and V

_{ohmic}is the voltage drop due to the ohmic losses at the intermediate currents. Neglecting the concentration voltage drop for simplification, the E

_{Nernst}can be calculated as Equation (3). The further details can be found in [30]:

_{d}represents the cell operating temperature in Kelvin, P

_{H}

_{2}and P

_{O}

_{2}are partial pressures of hydrogen and oxygen in atm, where F is Faraday constant and R is gas constant. The activation losses can be represented as Equation (4) based on [30]:

_{o}exchange current density, i

_{fc}fuel cell current. The ohmic loss can be expressed as Equation (5):

_{ohm}is the equivalent internal resistance of the fuel cell. The output voltage can be defined as Equation (6):

#### 2.1.2. Modeling of Battery

_{0}is the electromotive force of the battery, V

_{o}and I

_{0}are the voltage and current of the battery, and r shows the internal resistance of the battery. Through adopting the Ternary lithium battery parameters and setting the battery type to a lithium battery with regulated parameters, the SOC calculation can be shown as Equation (8):

#### 2.1.3. Modeling of DC-DC Converters

#### Unidirectional Converter

#### Bidirectional Converter

#### 2.1.4. Modeling of DC-AC Converters

_{α}and V

_{β}, then the signals transferred to the sector determine the block to realize the sector. As shown in the figure, there are 6 sectors. Not only the period of PWM and V

_{dc}, but also V

_{α}and V

_{β}are the input of the Time Calculation block. This block outputs the time signal XYZ, which represents different sectors of SVPWM. X, Y, and Z are sent into the Time Determine block, and finally, time signals T1 and T2 are generated. These two signals are injected into the Sector Calculation Change block to output Tem1, Tem2, and Tem3 time signals for the PWM waveform.

#### 2.1.5. Modeling of Traction Motors

_{sa}, u

_{sb}, u

_{sc}are the terminal voltage of stator windings, u

_{ra}, u

_{rb}, u

_{rc}are the terminal voltage of rotor windings, i

_{sa}, i

_{sb}, i

_{sc}are the terminal current of stator windings, i

_{ra}, i

_{rb}, i

_{rc}are the terminal current of rotor windings, Ψ

_{sa}, Ψ

_{sb}, Ψ

_{sc}are the terminal flux of stator windings, Ψ

_{r}

_{a}, Ψ

_{rb}, Ψ

_{rc}are the terminal flux of rotor windings, and R

_{S}and R

_{r}are the resistance of stator and rotor windings. The flux-linkage of each winding is the summation of its self-inductance and the mutual induction of other windings and can be calculated as Equation (10):

_{AA}, L

_{BB}, L

_{CC}, L

_{aa}, L

_{bb}, L

_{cc}are dedicated to the self-inductance of each winding, and L

_{AB}, L

_{AC}, L

_{Aa}, L

_{Ab}, L

_{Ac}are mutual inductance between windings. The electromagnetic torque of a motor can be obtained by the law of conservation of energy. According to the principle of energy conversion, in a multi-phase winding motor, the magnetic energy equation can be calculated as Equation (11):

_{p}is the number of pole pairs. With the assumption of neglecting the friction and torsional elasticity in the transmission mechanism of the electric drive system, the torque balance equation of the asynchronous motor is as Equation (13):

_{L}is load torque, J is rotational inertia, and D is damping coefficient. These equations constitute a multi-variable nonlinear mathematical model of a three-phase asynchronous motor under a constant torque load. It is complicated to directly calculate and analyze them. Therefore, converting the mathematical model of the asynchronous motor in a two-phase rotating coordinate system, with the rotation speed of ω

_{e}, after adopting Clark transformation and then using Park transformation, the electromagnetic matrix equation of the asynchronous motor can be expressed as Equation (14):

#### Space Vector Control Based on Rotor Field Orientation Control (FOC)

_{e}in the steady-state can be calculated as Equation (17):

_{r}= L

_{r}/R

_{r}is the time constant of the rotor. By observing the equations of (17), the electromagnetic torque is determined by stator current i

_{sq}and rotor flux Ψ

_{r}. The rotor flux Ψ

_{r}is controlled by i

_{sd}, so the electromagnetic torque can be regulated and controlled indirectly by the current i

_{sq}. With this relationship and the above mathematical equations, the three-phase asynchronous motor can be modeled as shown in Figure 7 converting three-phase currents to dq coordinate systems by abc/dq block.

_{sd}and i

_{sq}influences the stator voltage. To decouple the stator voltage with the current, a transfer function with stator resistance and inductance can be utilized. Therefore, the reference stator current equation could be written as Equation (19):

## 3. Fuzzy Logic-Based Modified Control Energy Management Strategy

#### 3.1. Quantization Factor

_{i}, and belongs to M

_{i}= [−m

_{i}, m

_{i}], then M is the physical theory domain of x

_{i}. The input of continuous real number components to the fuzzy controller needs to be fuzzified and mapped to the corresponding fuzzy subset. Suppose the domain of the fuzzy subset A

_{ik}(k = 1,2,3…n) corresponding to the component x of X after being fuzzified is Ni = [−n

_{i}, n

_{i}], then N

_{i}is the fuzzy domain of x

_{i}. In most cases, the physical theory domain of the input of the fuzzy controller is different from the fuzzy theory domain, so the coefficient transformation needs to be performed through the quantization factor module.

_{i}is M

_{i}= [−m

_{i}, m

_{i}], and its fuzzy theory domain is N

_{i}= [−n

_{i}, n

_{i}], so the definition of the transform coefficient k from M to N as the quantization factor is as Equation (21):

^{5}] W, SOC belongs to [0–100]%, P

_{ref}belongs to [0–3 × 10

^{5}] W, so the corresponding values of the quantization factor are as ${k}_{1}=\frac{1}{3\times {10}^{5}}$, ${k}_{2}=\frac{1}{100}$. Therefore, the fuzzy domain of the input and output of the fuzzy logic controller is [0, 1].

#### 3.2. Scale Factor

#### 3.3. Approximate Reasoning and Clarification

#### 3.4. Fuzzification

_{i}fuzzy, it is necessary to determine the number of fuzzy subsets covering the fuzzy domain N

_{i}. Secondly, to determine the fuzzy subset distribution covering the entire fuzzy domain, three characteristics of completeness, consistency, and interaction must be considered. Finally, the membership function of each fuzzy subset is determined. The discreteness or continuity of the fuzzy domain determines the selection of the membership function. Commonly used types of membership functions are Z-shaped, triangle-shaped, bell-shaped, Gauss-shaped, trapezoidal, and S-shaped. There is no standard for the selection and design of the membership function, which mainly depends on the situation of the controlled object and the personal habits of the designer. Generally speaking, close to the system equilibrium point, choosing a steep membership function to improve control sensitivity and move away from the system equilibrium point, and choosing a gentle membership function to speed up the adjustment time, is appropriate. The fuzzy subset of the fuel cell power of the locomotive is divided into zero, positive small, positive median, and positive big, using symbols to indicate {Zero, Posmin, Posmed, Posmax}. The fuzzy subset of the battery state of charge SOC is divided into low, medium, and high, using symbols denoted as {Low, Med, High}. Furthermore, the fuzzy subset of the reference electrical power signal of the fuel cell side DC-DC converter is divided into off, off–average hold, average, average–medium hold, medium, medium–maximum hold, and maximum. It is represented by symbols as {Off, HoldofAve, Ave, HoldofMed, Med, HoldofMax, Max}. A non-uniformly distributed membership function is used to improve the sensitivity of fuzzy control. The proposed fuzzy distribution and membership functions of input and output variables are shown in Figure 9.

- Ensure the power demand of the hybrid locomotive;
- Reduce the dynamic load of the fuel cell and optimize its working performance;
- Maintain the state of charge of the battery near the expected value, and, at the same time, make full use of the energy stored and absorbed by the battery, reduce fuel costs, and improve the economy of the hybrid locomotive.

_{ref}is the reference power of the fuel cell side converter, P

_{fcmin}is the minimum output power of the fuel cell, and P

_{fcmax}is the maximum output power of the fuel cell.

## 4. Results and Discussion

_{fcmin}= 25 kW, the maximum fuel cell output power P

_{fcmax}= 300 kW, the maximum dynamic changing rate of the fuel cell power as 50 kW/s, the upper limit of the battery state of charge SOC

_{h}= 80%, the lower limit of the battery state of charge SOC

_{l}= 40%, and the initial state of charge of the battery SOC = 70%. Figure 12 illustrates that the output power of the fuel cell is determined and distributed suitably by both powers following the energy management strategies, according to the required power profile of Figure 11. More specifically, it varies according to the requirements of the traction demand power of the vehicle, corresponding to the dedicated driving cycle for 560 s. As can be seen from the results of this figure, the proposed MFL-EMS reduces the dynamic load of the fuel cell and the sharp changes. Under hypothetical driving conditions and conventional PF-EMS, the FCHL adopts power following an energy management strategy with a hydrogen consumption of 0.05471 kg. However, the hydrogen consumption of the FCHL adopting the proposed MLF-EMS is 0.05370 kg. Compared with the conventional EMS, hydrogen consumption is reduced by 1.846%.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronyms | |

BESS | battery energy storage system |

BNSF | Burlington North America the Santa Fe |

FCHL | fuel cell hybrid locomotive |

MFL-EMS | fuzzy logic-based energy management system |

PF-EMS | power flow energy management system |

FCS | fuel cell stack |

EMS | energy management strategy |

FRC | fluffy rationale control |

ECMS_DFC | EMS technique dependent on dynamic following coefficient |

FCHPS | fuel cell hybrid power system |

PEMFC | proton exchange membrane fuel cell |

SOC | State of charge |

SVPWM | space vector pulse width modulation |

FOC | field orientation control |

Indexes | |

V [V]_{s} | stack voltage/output voltage |

N | number of series-connected cells in the stack |

E [V]_{Nernst} | reversible fuel cell voltage |

V [V]_{act} | voltage drop at the lower currents |

V [V]_{con} | voltage drop at higher currents |

V [V]_{ohmic} | voltage drop at the intermediate currents |

T [K]_{d} | cell operating temperature in Kelvin |

P [Pa]_{H2} | partial pressures of hydrogen |

P [Pa]_{O2} | partial pressures of oxygen |

F | Faraday constant |

R | gas constant |

A [mV/decade] | Tafel slope |

i [A]_{o} | exchange current density |

i [A]_{fc} | fuel cell current |

r [Ω]_{ohm} | equivalent internal resistance of the fuel cell |

I [A] | output current of the battery |

Q [Ah] | maximum capacity of the battery |

V [V]_{dc} | DC bus voltage of converter |

u, _{sa}u, _{sb}u [V]_{sc} | terminal voltage of stator windings |

u [V]_{ra}, u_{rb}, u_{rc} | terminal voltage of rotor windings |

i [A]_{sa}, i_{sb}, i_{sc} | terminal current of stator windings |

i, _{ra}i, _{rb}i [A]_{rc} | terminal current of rotor windings |

Ψ [A]_{sa}, Ψ_{sb}, Ψ_{sc} | terminal flux of stator windings |

Ψ, _{ra}Ψ, _{rb}Ψ [Wb]_{rc} | terminal flux of rotor windings |

W [J]_{m} | magnetic energy |

T [N·m]_{e} | electromagnetic torque |

n_{p} | number of pole pairs |

T [N·m]_{L} | load torque |

J [kg·m^{2}] | rotational inertia |

D [N s/m] | damping coefficient |

ω [rad/s]_{e} | rotation speed |

i [A]_{sq} | stator current in q axis |

i [A]_{sd} | stator current in d axis |

X | input signal vector of the fuzzy controller |

M | physical theory domain of input signal |

A_{ik} | domain of the fuzzy subset |

Ni | domain of the fuzzified fuzzy subset |

k_{i} | quantization factor |

P [W]_{ref} | reference power of the fuel cell |

w | scale factor |

A*o R | approximate reasoning module |

F/D | clarification module |

D/F | fuzzy module |

μ | membership function information module |

P [W]_{fcmin} | minimum output power of the fuel cell |

P [W]_{fcmax} | maximum output power of the fuel cell |

SOC [%]_{h} | upper limit of the battery state of charge |

SOC [%]_{l} | lower limit of the battery state of charge |

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**Figure 9.**Fuzzy membership functions. (

**a**) membership function of fuel cell power as input. (

**b**) membership function of SOC as input. (

**c**) membership function of reference power as output.

**Figure 11.**Driving cycle features of the locomotive in the proposed system. (

**a**) Speed. (

**b**) Required power.

**Figure 17.**Fuel cell voltage and current profile in FCHPS for proposed MFL-EMS and traditional method. (

**a**) Voltage. (

**b**) Current.

SOC | P_{req} | |||
---|---|---|---|---|

Zero | Posmin | Posmed | Posmax | |

Low | Hold of Ave | Ave | Med | Max |

Med | Off | Hold of Ave | Hold of Med | Hold of Max |

High | Off | Off | Ave | Med |

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

Fuel cell | Type | HD6 |

Nominal power (kW) | 300 kW | |

Rated working efficiency | 55% | |

Fuel/oxidant | Hydrogen/Air | |

Motor | Nominal/maximum power (kW) | 150/300 |

Nominal/maximum speed (rpm) | 1500/3200 | |

Maximum traction torque (n.m) | 430 | |

Maximum braking torque (n.m) | 550 | |

No-load current | 67 A | |

Battery | Type | Lithium-ion |

Rated Capacity (Ah) | 120 | |

Maximum discharging rate (C) | 5 | |

Internal impedance (mΩ) | 35 | |

Rated voltage (V) | 380 |

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

Vehicle Mass | 45 t | Axle | B-B |

Maximum Speed | 70 km/h | Maximum Gradient | 6.50% |

Maximum Acceleration | 1 m/s^{2} | Maximum Grade Speed | 30 km/h |

Inertia | 0.1 | Gravitational Acceleration | 9.8 N/kg |

Critical Speed | 30 km/h | Transmission System Efficiency | 0.95 |

Davis Coefficient A | 2.591 | Traction Inverter Efficiency | 0.95 |

Davis Coefficient B | 0.00078 | Davis Coefficient C | 0.0911 |

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## Share and Cite

**MDPI and ACS Style**

Jafari Kaleybar, H.; Brenna, M.; Li, H.; Zaninelli, D.
Fuel Cell Hybrid Locomotive with Modified Fuzzy Logic Based Energy Management System. *Sustainability* **2022**, *14*, 8336.
https://doi.org/10.3390/su14148336

**AMA Style**

Jafari Kaleybar H, Brenna M, Li H, Zaninelli D.
Fuel Cell Hybrid Locomotive with Modified Fuzzy Logic Based Energy Management System. *Sustainability*. 2022; 14(14):8336.
https://doi.org/10.3390/su14148336

**Chicago/Turabian Style**

Jafari Kaleybar, Hamed, Morris Brenna, Huan Li, and Dario Zaninelli.
2022. "Fuel Cell Hybrid Locomotive with Modified Fuzzy Logic Based Energy Management System" *Sustainability* 14, no. 14: 8336.
https://doi.org/10.3390/su14148336