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An energy management optimization approach for proton exchange membrane fuel cell-battery hybrid energy system for railway applications

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Abstract

In this paper, an optimization approach is formulated to determine the optimal power split in a proton exchange membrane fuel cell-battery-hybrid energy system (PEMFC-battery-HES) to meet the dynamically varying locomotive power demand. The optimization approach aims to determine the power references for the PEMFC at each loading point of the locomotive power demand with the objective function of minimization of the PEMFC fuel consumption over the driving period. The constraints of optimization include the instantaneous power balance between the source and the load, the limits on the variation of battery state-of-charge and PEMFC output power, and the durability constraints in terms of the maximum rate of change in PEMFC output power, and maximum allowable degradation in the state-of-health of the battery over a specified planning period. The optimization model is solved using the CONOPT solver of General Algebraic Modeling System. The performance of the proposed energy management optimization approach is tested through comparison with some of the already available approaches for different drive cycle scenarios. Simulation results confirm that the proposed approach results in 1–5.5% reduction in the PEMFC fuel consumption with optimum utilization of the capacities of the energy sources.

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Abbreviations

\(P_{load}\) :

Power demand for the original and reduced scaled drive cycle (in W)

\(P_{aux}\) :

Power consumed by the auxiliaries of the train (in W)

\(F_{drag}\) :

Aerodynamic drag

\(F_{rr}\) :

Frictional force between the wheels and the railway track

\(F_{grad}\) :

Force required to climb a slope

\(F_{acc}\) :

Acceleration force

Ρ :

Air density (in kg/m3)

D :

Drag coefficient

σ :

Locomotive cross-sectional area (in m2)

\(\upsilon\) :

Locomotive speed (in m/s)

\(R_{r}\) :

Coefficient of rolling resistance

β :

Slope of the railway track

M :

Mass of the train (in kg)

g :

Acceleration due to gravity (in m/s2)

\(M_{loco} ,\;M_{coach}\) :

Mass of the locomotive and non-air-conditioned coach (in kg)

\(N_{coach}\) :

Number of non-air-conditioned coach

\(P_{fc} ,\;P_{bat}\) :

Output power of the PEMFC system and the battery, respectively (in W)

\(v_{fc,stack} ,i_{fc,stack} ,P_{fc,stack}\) :

Output voltage (in V), current (in A)and power of the PEMFC stack (in W), respectively

\(P_{fc,aux}\) :

Power consumed by the PEMFC auxiliaries (in W)

E :

Theoretical cell potential (in V)

\(v_{act} ,v_{ohmic} ,v_{con}\) :

Voltage drops due to activation, ohmic and concentration losses, respectively (in V)

\(R_{max}\) :

Maximum rate of change of PEMFC output power (in W/s)

\(SOC\) :

State-of-charge

\(SOC_{max} ,SOC_{min}\) :

Upper and lower limit of SOC, respectively

\(SOC_{mean}\) :

Mean value of SOC

\(SOH\) :

State-of-health

\(SOH_{bat}\) :

State-of-health of the battery

c :

Battery c-rate

\(N\left( c \right)\) :

Number of battery cycles

E :

Battery energy (in J)

\(A\left( c \right)\) :

Total amount of throughput in the battery (in Ah)

R :

Ideal gas constant (in J/mol·K)

T :

Battery temperature (in K)

\(E_{a} \left( c \right)\) :

Activation energy (in J/mol)

z:

Power law factor

\(\Delta P_{fc} ,\;\Delta SOH_{bat} ,\;\Delta t,\;\Delta E\) :

Change in \(P_{fc}\), \(SOH_{bat}\), time and energy, respectively

\(\Delta SOH_{bat,max}\) :

Upper limit on the change of battery state-of-health

\(N_{trip}\) :

No. of trips of the passenger train per day

\(m_{{H_{2} }}\) :

Mass of hydrogen consumption of the PEMFC (in kg)

LHV :

Lower heating value of hydrogen

\(\eta_{fc} ,\;\eta_{bat}\) :

Efficiencies of the PEMFC and the battery, respectively

\(\eta_{chg} /\eta_{dis}\) :

Charging/discharging efficiencies of the battery

\(P_{fc}^{min}\) :

Minimum output power of the PEMFC

\(P_{fc}^{rated}\) :

Power rating of the PEMFC (in MW)

\(Q_{bat}^{rated}\) :

Capacity rating of the battery (in MWh)

\(V_{OC}\) :

Open circuit voltage of the battery (in V)

\(t_{0} , t_{f}\) :

Start and final time of the drive cycle

\(\tau_{bat,day}\) :

Replacement time (in days) of the battery

\(P_{fc}^{ref}\) :

PEMFC power reference

\(j\) :

Index representing the MISO converter layers (j = 1 for unidirectional and j = 2 for bidirectional layer)

\(L_{j} ,\;C\) :

Inductors and capacitor of the converter, respectively

\(i_{L,j} ,\;v_{DC}\) :

Inductor currents and DC-bus voltage, respectively

\(d_{j} ,\;\hat{d}_{j}\) :

Duty ratios and its complement

\(V_{DC}^{ref} ,\;I_{L}^{ref}\) :

Voltage and current references, respectively

\(SW_{2} , SW_{3} ,SW_{1}\) :

IGBTs with (without) the antiparallel diode

\(D_{1}\) :

Diode of the converter

EMO:

Energy management optimization

EMS:

Energy management strategy

ESS:

Energy storage system

FC:

Fuel cell

GAMS:

General algebraic modeling system

HES:

Hybrid energy system

PEMFC:

Proton exchange membrane fuel cell

PV:

Photo-voltaic

SC:

Super-capacitor

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Acknowledgements

The authors are sincerely obliged for the funding support received from the Science and Engineering Research Board, Grant no. YSS/2014/000028, DST, Govt. of India.

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  1. Department of Electronics and Electrical Engineering, Indian Institute of Technology, Guwahati, 781039, India

    Upasana Sarma & Sanjib Ganguly

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  1. Upasana Sarma
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Sarma, U., Ganguly, S. An energy management optimization approach for proton exchange membrane fuel cell-battery hybrid energy system for railway applications. Electr Eng 104, 4179–4195 (2022). https://doi.org/10.1007/s00202-022-01617-1

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