^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

The main advantage of hybrid powertrains is based on the efficient transfer of power and torque from power sources to the powertrain as well as recapturing of reversible energies without effecting the vehicle performance. The benefits of hybrid hydraulic powertrains can be better utilized with an appropriate power management. In this paper, different types of power management algorithms like off-line and on-line methods are briefly reviewed and classified. Finally, the algorithms are evaluated and compared. Therefore, different related criteria are evaluated and applied.

Hybrid powertrain technology as a potential solution for reduction of vehicle fuel consumption is the central topic in the context of green powertrain technologies. By definition, hybrid powertrain includes two or more power sources combined with either a conventional transmission system or a hydraulic/electric transmission system to overcome power demand of the vehicle [

In the context of vehicle longitudinal dynamics, different definitions for the performance of the vehicle exist. Acceleration rate, maximum vehicle velocity, and gradeability are known as typical criteria defining vehicle performance in practice. In the context of hybrid vehicles, one of the typical definitions describing vehicle performance is reference velocity tracking. In other words, for the improvement of vehicle performance, it can be expected that the hybrid vehicle can also track the expected drive cycle. For this reason, one of the objective functions in optimal control of power management is related to vehicle velocity and reference velocity difference minimization.

Typical researches in the field of hybrid powertrains deal with topologies design, comparison between different topologies, and the evaluation of different topologies on the vehicle's performance [

Furthermore, methodologies to optimize components size by means of performance and efficiency improvement of hybrid powertrain are given in [

In review papers, different classifications for power management are given. In [

Whether a power management is applicable to an on-line hybrid powertrain depends on the available information regarding vehicle power demand as well as the future vehicle velocity. For off-line power management optimization, the past, present, future information about the vehicle velocity is needed as depicted in

In this contribution, typical topologies and types of hybrid vehicles are briey introduced and compared. The direct comparison of HEV and HHV is not within the focus of this paper. Different developed power management approaches are investigated and partially compared. A new classification based on the real-time applicability of the power management approaches is proposed. Typical off-line power management optimization methods and algorithms are explained. Further, on-line and real-time power management methods are reviewed, the introduced power management approaches are rule-based controller, fuzzy logic controller, equivalent consumption minimization strategy. Moreover, typical approaches for estimation of the vehicle velocity are discussed. Finally, the power management approaches are evaluated and compared analytically, based on different criteria, and published results. Because of the quantities of the discussed power management approaches and using different models, drive cycles, and topologies in different literatures, a numerical comparison of the results is not possible.

Typical topologies of hybrid powertrains are series, parallel, and power split. The parallel hybrid vehicle is also known as power assist topology. It contains a hydraulic/electric motor coupled to the conventional transmission system. The accumulator charging can be realized by recapturing during braking or deceleration (regenerative braking mode) or parallel during driving by the power of the engine (power split mode). Also possible is the use of the power of the engine only for charging the accumulator (stationary charging mode).

In series topology, the mechanical connection between engine and vehicle is replaced by a hydraulic/electric transmission system using direct coupling of the hydraulic/electric motor to the drive shaft and the hydraulic pump/electric generator to the flywheel. Because of the mechanical decoupling of vehicle and engine, optimal operation of the engine with an appropriate controller is realizable. To recapture braking energy, the hydraulic/electric motor connected to the drive shaft changes its operating mode to hydraulic pump/electric generator during deceleration. By using the valves in HHV and DC/DC-converters in HEV, different topologies for series hybrid vehicles can be realized. However, each topology has its individual characteristic and control strategy. In

According to

The comparison of HEV and HHV is discussed in [

Off-line power management is usually used to define optimal power-management control parameters in advance. Therefore, the approaches use knowledge of the vehicle drive cycle, briefly speaking: it is assumed that the knowledge is exact and known in advance. Depending on the class of power management, both static and dynamic optimization methods can be applied to off-line power management. Static optimization methods use the quasi-static model of the powertrain to be controlled, such as instantaneous power balance method. In contrast, dynamic optimization methods such as DP, use dynamic models of the subsystems during the optimization process [

Because of the necessity of prior knowledge about the vehicle drive cycle, in off-line power management strategies, both global and local optimization algorithms are applicable. However off-line globally optimized power managements are more optimal in comparison to the locally optimized power management, because global optimization methods use a wide range of input information for optimization, while local optimization methods define the optimal control based on individual working points.

Dynamic programming is a numerical sequential global optimization approach based on Bellman's principle of optimality [

The optimality resulting from DP depends on the number of grid points on the trajectory plan of the state of the system. Decrement of the size of stages as well as steps increase the number of grid points and the optimality of the DP is increased consequently. However, the increase in the number of grid points leads to an increment of the computation load. To decrease the computation load, infeasible states can be omitted as depicted in

In [

In [

A comparison between rule-based power management and two variables SDP power management applied to a parallel hybrid hydraulic powertrain in [

In [

Genetic algorithm (GA) is a numerical optimization approach for constrained, multi-objective multi-parametric, and complex nonlinear problems. In the process of GA optimization, instead of using analytical methods, techniques such as selection, encoding, mutation, and crossover are used. Through an iterative loop, a batch of variable is generated and for each batch, the objective function is evaluated with respect to a given objective function. Finally, during a multi-loop iteration process, the algorithm defines those samples which converge to the optimal solution with respect to the given objective function. Although, GA can be used for the optimization of complex nonlinear multi-input multi-output (MIMO) hybrid powertrains, its computational load is high. Because of convergence toward an optimal answer, all possible combinations of samples must be iteratively evaluated. For this reason, GA is only appropriate for application in off-line power management [

A GA-QP-based power management for a power split HEV is developed in [

The threshold-based energy control strategy is a rule-based on-line power management discussed in the on-line power management section. This strategy involves two parameters, torque difference and pressure limit of active-charging-pressure, related to the output torque of the engine and demanded torque, as well as pressure of the hydraulic accumulator. In [

A non-dominated sorting genetic algorithm (NSGA) based on GA is applied for optimization of power management of parallel HEV and HHV as depicted in

The application of power management strategies to on-line or real-time systems involves solving basic problems, namely those of unknown upcoming power demand trajectory and computational load. Lack of the knowledge of future power demand trajectories, makes global optimization of the power management impossible in real-time. Therefore, only optimization methods based on instantaneous vehicle speed data can be implemented. However, efficiency and performance of the on-line power management strategies are consequently lower than those resulting from off-line power management strategies. Development of on-line power managements start with realization of rule-based controllers [

Rule-based power managements are simple to design and implement. Based on an on-line controller for implementation of supervisory power management strategies, the rules can be typical heuristic experiences or results combining if-then conditions. The concept of rule-based power management is an instantaneous determination of power split ratio based on logical rules and local constrains. Therefore, rule-based power management cannot be optimal. As the logical rules depend on the system characteristics, topology, and design goals, an unique method for synthesizing the rules does not exist. The first step to design a rule-based power management is often based on the determination of vehicle operational modes. Using driver command the operational mode of the vehicle is divided to four modes, namely acceleration, deceleration, stop, and constant velocity. Depending on the SoC and demanded torque, different sub-modes may be selected e.g., braking energy regeneration and conventional braking combination during deceleration, accumulator charging during acceleration, using only the engine in acceleration mode

The threshold-based energy control strategy is one of the conventional rule-based power management controller. In [

In [

Optimization of the applied logic of rule-based power management using the results of globally optimized power management such as DP is usual. The difference between demanded torque and efficient torque of the engine as well as the SoC threshold are the main control variables of rule-based power management [

The bang-bang controller (also known as two points switching control, is in [

In [

In [

Although rule-based power management controller is applicable to on-line and even real-time power management, it is not an optimal power management. Despite ability to improve the efficiency of the rule-based power management, the efficiency of the explained method is always less than both global and local optimization algorithms. Therefore, the rule-based power management controller is a sub-optimal, on-line and real-time-applicable power management.

In contrast to rule-based power management, fuzzy-based power management controller is based on partially true logics. In other words, the rules are not necessarily true or false rules. Fuzzy controller contains a series of linguistic rules and each rule contains one antecedent and two consequents. The fuzzy logic controller consists of fuzzification, inference engine, rule base, and defuzzification. Application of partially true logics in fuzzy-based power management, causes a smooth transition of the dynamic behavior of the powertrain in contrast to true or false logics in the rule-based power management. Therefore, fuzzy controller may guarantee the robustness of the power management.

In [

The fuzzy controller uses driver command as well as SoC as the control inputs. By definition, the relation of captured braking energy to the available braking energy is regeneration ratio. The effect of this factor on the efficiency of the power management is studied and on-line control of this factor by means of vehicle performance improvement is confirmed. The control strategy is applied to Toyota Pirus model, the used drive cycle is the combination of three different drive cycles by means of long trip realization. Simulation results show efficient operation of the engine. The undesirable engine on/off switching is detected in the one segment of the drive cycle which contains more stop and go maneuvers. Comparison of the SoC shows better sustainability of SoC in the fuzzy-based power management in comparison with Prius HEV. The similar controller is used in [

A generalized fuzzy logic-based power management controller for three typical topologies of the HEV, namely parallel, series, power split is developed in [

A new fuzzy logic controller based on travel distance information is developed in [

The equivalent consumption minimization strategy (ECMS) is an instantaneously optimized power management strategy. In ECMS, the accumulator is considered as a subsidiary reversible fuel tank. Based on the ECMS strategy, the fluctuation of the energy level in secondary power source will be compensated by replacement of the equivalent fuel power in the future [

By using the equivalency factor as the only control variable, proper charge and discharge of the accumulator considering variable boundary conditions cannot be guaranteed. In other words, accumulator may be overcharged or undercharged. To avoid this problem, with the help of an iterative loop, the value of SoC is compared to the boundary values and if needed the equivalency factor is corrected. Due to difference between efficiency of the power transmission in charge and discharge operational modes, a method is developed to distinguish equivalency factor in charge and discharge modes of the secondary power source in [

Performance of ECMS is preferred in comparison with the global optimization algorithms such as simulated annealing in [

A new strategy to improve the efficiency of the ECMS is presented in [

In [

Inaccessibility of the drive cycle in future is a crucial problem for the realization of real-time power management approaches. The assumption of prior-knowledge about the “drive cycle” is unrealistic and it is used just for off-line optimization of power management. To overcome this drawback, methods such as drive cycle recognition [

Telematics technology is one of the new developments within the field of intelligent vehicle technologies. In general, this technology realizes the communication of the vehicles with other vehicles and environment. With the help of information getting through this system, different intelligent systems such as vehicle tracking can be realized. Telematics technology can be used for adjustment of instantaneous vehicle velocity in urban environment [

Model predictive control is a mathematical method for calculation of the system input trajectory to optimize the output of the system in the future. Based on the current dynamics of the system, the future of the system for a specific prediction horizon is predicted and the control inputs are calculated. The performance of the MPC drastically depends on the prediction window. The application of this method to hybrid powertrain can decrease the fuel consumption by prediction of the system inputs such as power split factor. If the computation load of this method is decreased, this method can be used as a real-time power management.

A two level nonlinear model predictive power management controller is developed for a power split HEV [

The performance of nonlinear MPC-based power management in association with an adaptive prediction time horizon is presented in [

In contrast to the MPC, which uses prior knowledge about drive cycle, stochastic model predictive control (SMPC) uses random information about vehicle velocity for optimization of power management. Using a Markov chain, the distribution of the power demand in the future can be assumed based on previous experiences. The integration of the stochastic power demand prediction with DP is already explained. Because of the high computation load of DP, it is not implementable as real-time power management. However, SMPC uses supervisory optimization methods such as linear or QP with low computational load. Therefore, it is a real-time power management strategy.

In [

Similar power management is applied to a HHV. The control variables are pump/motor displacement ratio as well as engine power variation. The objective functions are operation of the engine, vehicle performance, and the brake energy regeneration. Based on two operational modes of the engine, namely engine on and off, two predictive models are developed. The states of the prediction model are vehicle velocity, SoC, and output power of the engine. For simplicity, the complex model of the powertrain is linearized and discretized. Comparison of the results with frozen-time MPC, and prescient MPC verifies the results presented in [

Comparison of different power management approaches show that except optimization of the power management, computation load, ability to easily implement, and information about upcoming vehicle velocity are the other important criteria for realization of a real-time power management. The first problem associated with the implementation of power management to real-time systems, regardless of control strategy, is the lack of information about upcoming vehicle power demand. Additionally, backward model of the powertrain is needed to calculate power demand regarding the vehicle velocity. The complexity and non-linearity of the powertrain model must be simplified by linearization, and simplification of the model. Although the recommended methods are able to solve these problems theoretically, reduction of computation load is unavoidable for real-time implementation of power management. Use of powerful processors or simplification of e.g., predictive model to decrease the computation load, sequentially increase the cost and inaccuracy. Therefore, between simplicity and accuracy of the powertrain backward model a weighted balance has to be considered. Nevertheless, optimality of power management is usually sacrificed. Moreover, unavailability of experimental results or even possibility of comparison respect to practical oriented benchmarks results makes it impossible to judge about power management strategies. Different power management optimization strategies have their individual drawbacks. In

Rule-based power managements are based on predefined constant logical rules and real-time applicable. Performance and efficiency of rule-based controller depend on a wide variety of rules, logics, and conditions. Rule-based controller improves the optimal operation of the individual components without consideration of the overall efficiency of the powertrain. Near optimal point and near optimal line operation of the engine, on and off switching of the engine, reducing transient operation of the engine, engine constant speed with variable torque, SoC bound control, and maximum recapturing of braking energy are usual control strategies. Applicability of a specific strategy depends on the type of hybrid powertrain, degree of hybridization, size of the components, and drive cycle. To improve the efficiency and performance of the rule-based power management, controller adjustment is unavoidable. However optimization of power management depends on drive cycle. Therefore, generalization of a unique rule-based power management to all drive cycles and driver behavior is impossible. These types of power management are simple to implement. It can be applied as on-line and real-time power management. Nevertheless, it is not an optimal power management. Moreover, the time-delay between the feedback signal of vehicle velocity and output signal of power management is unavoidable. This drawback proves the superiority of predictive power management to the instantaneous power management optimization. All in all, rule-based as an instantaneous and sub-optimal control approach, is the usual real-time power management in context of hybrid powertrains.

The type of optimization method which is used for development of power management of hybrid vehicles, depends on the availability of vehicle power demand. Using prior-knowledge about drive cycle, both local and global optimization algorithms such as GA, DP, and ECMS without consideration of computation load, are applicable. A usual instantaneous power management strategy is ECMS and it is applicable as both off-line and on-line power management strategy. In contrast to rule-based controller, ECMS provides optimal power management. However, the method is very sensitive to the control parameters mainly equivalency factor. It is a robust power management in context of sustaining SoC. For this reason, SoC must be penalized with an additional objective function. The optimality of ECMS in off-line application is close to globally optimized power managements. Although different approaches such as A-ECMS are developed to increase the optimality of ECMS, their computation load is huge. Therefore, other such optimization methods, suffer lack of optimality due to simplicity. Model predictive control is proposed as on-line and real-time power management. Unlike rule-based, which is sub-optimal power management and such as ECMS, MPC-based power management is optimal power management. Same as other optimization methods, MPC leads to large calculation load. However, simplicity of the model decreases the complexity and computation load while decreasing the optimality.

As global optimization methods such as DP need more time for computation effort involved, mostly they are not applicable as real-time power management. Among all developed optimal power managements, DP-based approaches show the most optimal power distribution. Therefore it can be used as benchmark for evaluation of other power managements. However, it is based on backward calculation of power distribution using deterministic drive cycle with mostly time consuming computational load.

Unlike numerical optimization methods, analytical optimization methods based on minimum principals such as Pontryagins minimum principle reduce the computational load substantially [

In this contribution, different power management strategies including both off-line to on-line are briefly introduced, explained, and compared. Global optimization methods can be used only for off-line power management optimization. They are used to survey the potential of the powertrain to reduce fuel consumption. Therefore, the results can be used for topology design, parameter adjustment, component size adjustment, and evaluation of other power management as benchmark. Among off-line power managements, deterministic DP is the most appropriate method. With a sequential decision, the trajectory of the system state as well as control input among all possible trajectories is selected which results in the least objective function value. Nevertheless, it is not directly appropriate for a real-time powertrain.

A rule-based and fuzzy-logic based controller, and ECMS are discussed in detail as on-line power management solutions which are implementable to the real-time powertrain. Although the fuzzy logic controller does not have the disadvantages possessed by a rule-based controller, computational effort is more than rule-based controller. Implementation of ECMS to a real-time powertrain is subject to parameter sensitivity as well as adjustment of the equivalency factor. Predictive power managements are introduced in detail and their superiority to the other power management is discussed. Moreover, different methods for prediction of vehicle velocity are reviewed. Finally, we discuss the evaluatuation of real-time implementable power managements. For the future work, based on the review of power managements, an appropriate power management for different topologies of a HHV will be designed.

The authors declare no conflict of interest.

Optimization time domain for off-line, on-line, and real-time power managements.

Series topology of (

Dynamic programming expression.

NSGA II-based hybrid powertrain optimization [

Engine threshold-based control strategy. Blue curves: the brake specific fuel consumption (BSFC) which represents the fuel consumption of the engine at each operating point; Dashed-line: output power of the engine.

Two-points switching management controller.

Power flow in the equivalent consumption minimization strategy (ECMS) algorithm in (

Classification of power management algorithms.

Dynamic programming | Rule-based controller | Telematics predictive strategy |

Genetic algorithm | Fuzzy logic controller | Model predictive strategy |

Equivalent consumption minimization strategy | Stochastic model predictive strategy |

Comparison of different power management algorithms.

DP | [ |
yes | no | no | no |

GA | [ |
yes | no | yes | no |

Rule-based | [ |
no | yes | yes | yes |

Fuzzy logic | [ |
no | yes | yes | yes |

ECMS | [ |
no | yes | yes | conditional |

Telematic-based | [ |
yes | no | yes | conditional |

MPC | [ |
yes | no | yes | conditional |

Stochastic-based | [ |
no | yes | yes | conditional |