Real-Time Dynamic Optimal Power Flow in Electric Vehicles Considering the Lifetime of the Components in the E-Powertrain

Different types of energy sources (e.g., batteries, supercapacitors, fuel cells) can be utilized in electric vehicles to store and provide energy in the e-powertrain through power electronic devices [1-6]. The lifetime of the components in the e-powertrain depends on their load profile [7,8]. For instance, the lifetime of a battery highly depends on the depth of discharge and the number of charge/discharge cycles [9-13]. The lifetime of an inverter mostly depends on the variations in the active-reactive power passing through it. This means that the expended life cost of the components can be decreased by allocating an optimal share of the total power to each energy source and power electronic device at an optimal time instance. In addition, the driving range of a vehicle can be prolonged by decreasing the energy loss i.e., operating the components in their high-efficiency region. Therefore, it is necessary to perform Optimal Power Flow (OPF) in the operation of the e-powertrain. The OPF aims to minimize the expended life cost of the components and maximize the driving range of the vehicle by optimizing the following decision variables while satisfying technical constraints:

• The charge/discharge power of battery storage and supercapacitor systems ‘at each time instance’

• The charge power of fuel cell systems at each time instance

• The load share of each DC/DC converter

• The bidirectional active and reactive power profiles of each DC/AC inverter

• The length of charge and discharge periods of batteries and supercapacitors

• The number of charge-discharge cycles of each storage unit in each prediction horizon

• The status of charge/discharge of batteries and supercapacitors

• The depth of discharge for storage systems at each time instance

This leads to a large-scale (with hundreds of variables), non-convex, stochastic (due to uncertain parameters), dynamic (due to storage components), multi-timescale, and mixed-integer nonlinear programming (MINLP) problem. Thus, the computation time to solve the problem can be much higher than required for ‘real-time’ application [14,15]. In addition, the feasibility of the real-time solutions should be also ensured for the safe operation of the vehicle [16]. For this reason, MicroFuzzy GmbH, in collaboration with the Technische Universität Ilmenau, develops a multi-time-horizon framework to solve this challenging optimization problem in real-time (Figure 1). The computation time is decreased using parallel computing to achieve the online OPF. The solutions also safeguard both feasibility and optimality of the operations in real-time, while minimizing the total operation costs.

Figure 1: Offline optimal power flow (gray) and online optimal power flow (black).

1. García P, Torreglosa JP, Fernández LM, Jurado F (2013) Control strategies for high-power electric vehicles powered by hydrogen fuel cell, battery and supercapacitor. Expert Systems with Applications 40: 4791-4804. Link: https://bit.ly/2EFdhMC
2. Fu Z, Li Z, Si P, Tao F (2019) A hierarchical energy management strategy for fuel cell/battery/supercapacitor hybrid electric vehicles. International Journal of Hydrogen Energy  44: 22146-22159. Link: https://bit.ly/3gCQ76T
3. Wu Y, Gao H (2006) Optimization of fuel cell and supercapacitor for fuel-cell electric vehicles. IEEE transactions on Vehicular Technology 55: 1748-1755. Link: https://bit.ly/2QwyL0T
4. Khaligh A, Li Z (2010) Battery, ultracapacitor, fuel cell, and hybrid energy storage systems for electric, hybrid electric, fuel cell, and plug-in hybrid electric vehicles: State of the art. IEEE transactions on Vehicular Technology 59: 2806-2814. Link: https://bit.ly/2DcxyZy
5. Fathabadi H (2018) Novel fuel cell/battery/supercapacitor hybrid power source for fuel cell hybrid electric vehicles. Energy 143: 467-477. Link: https://bit.ly/2ECRx42
6. Li H, Zhou Y, Gualous H, Chaoui H, Boulon L (2020) Optimal Cost Minimization Strategy for Fuel Cell Hybrid Electric Vehicles Based on Decision Making Framework. IEEE Transactions on Industrial Informatics. Link: https://bit.ly/2Qz84IQ
7. Vernica I, Wang H, Blåbjerg F (2018) Uncertainties in the Lifetime Prediction of IGBTs for a Motor Drive Application. 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC) IEEE 1-6. Link: https://bit.ly/2EKdiPf
8. Ma K, Liserre M, Blaabjerg F, Kerekes T (2014) Thermal loading and lifetime estimation for power device considering mission profiles in wind power converter. IEEE Transactions on Power Electronics 30: 590-602. Link: https://bit.ly/3lGPMDZ
9. Mohagheghi E, Alramlawi M, Gabash A, Blaabjerg F, Li P (2020) Real-time active-reactive optimal power flow with flexible operation of battery storage systems. Energies 13: 1697. Link: https://bit.ly/3lrak2S
10. Mohagheghi E (2019) Real-Time Optimization of Energy Networks with Battery Storage Systems under Uncertain Wind Power Penetration. Technische Universität Ilmenau. Link: https://bit.ly/2QyFJm4
11. Abdeltawab HH, Mohamed YARI (2015) Market-oriented energy management of a hybrid wind-battery energy storage system via model predictive control with constraint optimizer. IEEE Transactions on Industrial Electronics 62: 6658-6670. Link: https://bit.ly/2ExnT0n
12. Alramlawi M, Gabash A, Mohagheghi E, Li P (2018) Optimal operation of hybrid PV-battery system considering grid scheduled blackouts and battery lifetime. Solar Energy 161: 125-137. Link: https://bit.ly/2YQK2h0
13. Alramlawi M, Mohagheghi E, Li P (2019) Predictive active-reactive optimal power dispatch in PV-battery-diesel microgrid considering reactive power and battery lifetime costs. Solar Energy 193: 529-544. Link: https://bit.ly/3b5CGLm
14. Mohagheghi E, Gabash A, Li P (2017) A Framework for Real-Time Optimal Power Flow under Wind Energy Penetration. Energies 10: 535. Link: https://bit.ly/2YHETHM
15. Mohagheghi E, Alramlawi M, Gabash A, Li P (2018) A survey of real-time optimal power flow. Energies 11: 3142. Link: https://bit.ly/3hFSZB5
16. Mohagheghi E, Gabash A, Alramlawi M, Li P (2018) Real-time optimal power flow with reactive power dispatch of wind stations using a reconciliation algorithm. Renewable Energy 126: 509-523. Link: https://bit.ly/34DjxPT