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Nikolce Murgovski, Lars Johannesson, Jonas Sjöberg, Bo Egardt, Component sizing of a plug-in hybrid electric powertrain via convex optimization, Mechatronics, Volume 22, Issue 1, February 2012, Pages 106-120, ISSN 0957-4158,

http://dx.doi.org/10.1016/j.mechatronics.2011.12.001

Abstract

This paper presents a novel convex modeling approach which allows for a simultaneous optimization of battery size and energy management of a plug-in hybrid powertrain by solving a semidefinite convex problem. The studied powertrain belongs to a city bus which is driven along a perfectly known bus line with fixed charging infrastructure. The purpose of the paper is to present the convexifying methodology and validate the necessary approximations by comparing with results obtained by Dynamic Programming when using the original nonlinear, non-convex, mixed-integer models. The comparison clearly shows the importance of the gear and engine on/off decisions, and it also shows that the convex optimization and Dynamic Programming point toward similar battery size and operating cost when the same gear and engine on/off heuristics are used. The main conclusion in the paper is that due to the low computation time, the convex modeling approach enables optimization of problems with two or more state variables, e.g. allowing for thermal models of the components; or to include more sizing variables, e.g. sizing of the engine and the electric machine simultaneously.

Keywords: Plug-in hybrid electric vehicle; Slide-in electric vehicle; Battery sizing; Power management; Convex optimization

http://www.sciencedirect.com/science/article/pii/S0957415811002005


Murgovski, N.; Johannesson, L.M.; Sjoberg, J., "Engine On/Off Control for Dimensioning Hybrid Electric Powertrains via Convex Optimization," Vehicular Technology, IEEE Transactions on , vol.62, no.7, pp.2949,2962, Sept. 2013

doi: 10.1109/TVT.2013.2251920

Abstract

This paper presents a novel heuristic method for optimal control of mixed-integer problems that, for given feasible values of the integer variables, are convex in the rest of the variables. The method is based on Pontryagin's maximum principle and allows the problem to be solved using convex optimization techniques. The advantage of this approach is the short computation time for obtaining a solution near the global optimum, which may otherwise need very long computation time when solved by algorithms guaranteeing global optimum, such as dynamic programming (DP). In this paper, the method is applied to the problem of battery dimensioning and power split control of a plug-in hybrid electric vehicle (PHEV), where the only integer variable is the engine on/off control, but the method can be extended to problems with more integer variables. The studied vehicle is a city bus, which is driven along a perfectly known bus line with a fixed charging infrastructure. The bus can charge either at standstill or while driving along a tramline (slide in). The problem is approached in two different scenarios: First, only the optimal power split control is obtained for several fixed battery sizes; and second, both battery size and power split control are optimized simultaneously. Optimizations are performed over four different bus lines and two different battery types, giving solutions that are very close to the global optimum obtained by DP.

keywords:P computational complexity;convex programming;hybrid electric vehicles;integer programming;maximum principle;on-off control;power control;power transmission (mechanical);DP;PEHV;Pontryagin maximum principle;battery dimensioning;bus line;city bus;computation time;convex techniques;dynamic programming;engine on-off control;fixed battery sizes;fixed charging infrastructure;global optimum;heuristic method;hybrid electric powertrains dimensioning;integer variables;mixed-integer problems;optimal control;plug-in hybrid electric vehicle;power split control;tramline;Batteries;Convex functions;Engines;Mechanical power transmission;Optimal control;Optimization;Vehicles;Battery sizing;Pontryagin's maximum principle;convex optimization;plug-in/slide-in hybrid electric vehicle (HEV);power management

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6476747&isnumber=6595631


Egardt, B.; Murgovski, N.; Pourabdollah, M.; Johannesson Mardh, L., "Electromobility Studies Based on Convex Optimization: Design and Control Issues Regarding Vehicle Electrification," Control Systems, IEEE , vol.34, no.2, pp.32,49, April 2014

doi: 10.1109/MCS.2013.2295709

Abstract

The electrification of road transport is accelerating globally, propelled by a mix of environmental concerns, legislative mandates, and business opportunities. Relying to a larger extent on electricity in the transportation sector provides new opportunities to reduce carbon dioxide (CO2) emissions, fossil fuel consumption, and local air pollution by improving energy efficiency and employing renewable energy. As part of this development, leading vehicle manufacturers are currently making a substantial effort to provide hybrid electric vehicles (HEVs), plug-in hybrid EVs (PHEVs), and pure EVs to the market.

keywords: air pollution control;convex programming;energy conservation;fossil fuels;hybrid electric vehicles;power transmission (mechanical);renewable energy sources;road vehicles;CO2;PHEVs;business opportunities;carbon dioxide emission reduction;control issue;convex optimization;design issue;electromobility studies;energy efficiency;environmental concerns;fossil fuel consumption reduction;hybrid electric powertrain;hybrid electric vehicles;legislative mandates;local air pollution reduction;plug-in hybrid EVs;renewable energy;road transport electrification;transportation sector;vehicle electrification;Batteries;Convex functions;Energy management;Generators;Load flow;Mechanical power transmission;Vehicles

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6766816&isnumber=6766690


Murgovski, N.; Johannesson, L.M.; Egardt, B., "Optimal Battery Dimensioning and Control of a CVT PHEV Powertrain," Vehicular Technology, IEEE Transactions on , vol.63, no.5, pp.2151,2161, Jun 2014

doi: 10.1109/TVT.2013.2290601

Abstract

This paper presents convex modeling steps for the problem of optimal battery dimensioning and control of a plug-in hybrid electric vehicle with a continuous variable transmission. The power limits of the internal combustion engine and the electric machine are approximated as convex/concave functions in kinetic energy, whereas their losses are approximated as convex in both kinetic energy and power. An example of minimizing the total cost of ownership of a city bus including a battery wear model is presented. The proposed method is also used to obtain optimal charging power from an infrastructure that is to be designed at the same time the bus is dimensioned.

keywords: battery powered vehicles;convex programming;hybrid electric vehicles;internal combustion engines;optimal control;power transmission (mechanical);CVT PHEV powertrain;battery wear model;city bus;concave functions;continuous variable transmission;convex modeling;internal combustion engine;optimal battery dimensioning;optimal control;plug-in hybrid electric vehicle;Batteries;Gears;Ice;Mechanical power transmission;Optimization;Torque;Vehicles;Battery sizing;battery sizing;convex optimization;plug-in hybrid electric vehicle;plug-in hybrid electric vehicles (HEVs);power management

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6662478&isnumber=6832681


Murgovski, N.; Johannesson, L.M.; Sjoberg, J., "Engine On/Off Control for Dimensioning Hybrid Electric Powertrains via Convex Optimization," Vehicular Technology, IEEE Transactions on , vol.62, no.7, pp.2949,2962, Sept. 2013

doi: 10.1109/TVT.2013.2251920

Abstract

This paper presents a novel heuristic method for optimal control of mixed-integer problems that, for given feasible values of the integer variables, are convex in the rest of the variables. The method is based on Pontryagin's maximum principle and allows the problem to be solved using convex optimization techniques. The advantage of this approach is the short computation time for obtaining a solution near the global optimum, which may otherwise need very long computation time when solved by algorithms guaranteeing global optimum, such as dynamic programming (DP). In this paper, the method is applied to the problem of battery dimensioning and power split control of a plug-in hybrid electric vehicle (PHEV), where the only integer variable is the engine on/off control, but the method can be extended to problems with more integer variables. The studied vehicle is a city bus, which is driven along a perfectly known bus line with a fixed charging infrastructure. The bus can charge either at standstill or while driving along a tramline (slide in). The problem is approached in two different scenarios: First, only the optimal power split control is obtained for several fixed battery sizes; and second, both battery size and power split control are optimized simultaneously. Optimizations are performed over four different bus lines and two different battery types, giving solutions that are very close to the global optimum obtained by DP.

keywords: computational complexity;convex programming;hybrid electric vehicles;integer programming;maximum principle;on-off control;power control;power transmission (mechanical);DP;PEHV;Pontryagin maximum principle;battery dimensioning;bus line;city bus;computation time;convex techniques;dynamic programming;engine on-off control;fixed battery sizes;fixed charging infrastructure;global optimum;heuristic method;hybrid electric powertrains dimensioning;integer variables;mixed-integer problems;optimal control;plug-in hybrid electric vehicle;power split control;tramline;Batteries;Convex functions;Engines;Mechanical power transmission;Optimal control;Optimization;Vehicles;Battery sizing;Pontryagin's maximum principle;convex optimization;plug-in/slide-in hybrid electric vehicle (HEV);power management

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6476747&isnumber=6595631


Pourabdollah, M.; Murgovski, N.; Grauers, A.; Egardt, B., "Optimal Sizing of a Parallel PHEV Powertrain," Vehicular Technology, IEEE Transactions on , vol.62, no.6, pp.2469,2480, July 2013

doi: 10.1109/TVT.2013.2240326

Abstract

This paper introduces a novel method for the simultaneous optimization of energy management and powertrain component sizing of a parallel plug-in hybrid electric vehicle (PHEV). The problem is formulated as a convex optimization problem to minimize an objective function, which is a weighted sum of operational and component costs. The operational cost includes the consumed fossil fuel and electrical energy, whereas the component cost includes the cost of the battery, electric motor (EM), and internal combustion engine (ICE). The powertrain model includes quadratic losses for the powertrain components. Moreover, the combustion engine and the electric motor losses are assumed to linearly scale with respect to the size and the losses of baseline components. The result of the optimization is the variables of the global optimal energy management for every time instant and optimal component sizes. Due to the dependency of the result on the driving cycle, a long real-life cycle with its charging times is chosen to represent a general driving pattern. The method allows the study of the effect of some performance requirements, i.e., acceleration, top speed, and all-electric range, on the component sizes and total cost.

keywords: battery powered vehicles;convex programming;electric motors;hybrid electric vehicles;internal combustion engines;power transmission (mechanical);secondary cells;EM;ICE;component costs;convex optimization problem;electric motor;electrical energy;fossil fuel;global optimal energy management;internal combustion engine;objective function;optimal component sizes;optimal sizing;parallel PHEV powertrain components;parallel plug-in hybrid electric vehicle;Acceleration;Batteries;Energy management;Gears;Ice;Optimization;Vehicles;Convex optimization;energy management;hybrid electric vehicles;optimal control;sizing

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6423969&isnumber=6557008

 

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