Efficient energy management strategies for hybrid electric vehicles using shuffled frog-leaping algorithm

Abstract

This paper proposes two novel approaches for the problem of energy management in hybrid electric vehicles. Shuffled frog-leaping algorithm (SFLA) is a recently proposed population-based optimization algorithm. This paper first formulates energy management as an optimization problem and optimizes the problem using SFLA. Then the paper makes use of SFLA as a training algorithm to train artificial neural network (ANN) and this SFLA-trained ANN is used for energy management. Interestingly, the proposed approaches of this paper are found to be robust and more efficient than contemporary approaches.

Keywords::

• energy management
• hybrid electric vehicles
• neural networks

1. Introduction

Energy management is an important aspect in the field of vehicular technology. The problem of energy management in an automotive vehicle deals with controlling the amount of power exchange (among sources and storage devices) and other available input variables such that the desired behaviour of the vehicle is obtained. Strategies based on heuristics can easily be implemented in a real vehicle using a rule-based strategy (Baumann et al. 2000) or using fuzzy logic (Schouten, Salman, and Kheir 2002). Although these strategies can offer a significant improvement in energy efficiency, they do not guarantee an optimal result in all situations. Consequently, strategies are developed that are based on optimization techniques (Delprat et al. 2004; Sciarretta, Back, and Guzzella 2004; Lin et al. 2003; Scordia et al. 2005). Optimization at each time instant can be beneficial, but profits will be limited (Paganelli et al. 2001). Hybrid search algorithms have recently gained a lot of attention from the optimization research community (Yildiz and Ozturk 2006; Yildiz 2008). But, the attempts made to apply these techniques to vehicles were limited to topology design (Yildiz et al. 2004; Yildiz and Solanki 2012). Once again, the results are constrained by efficiency. Hence, this paper proposes shuffled frog-leaping algorithm (SFLA) (Eusuff and Lansey 2003) for energy management.

The art of using artificial neural network (ANN) for development of energy management strategy (EMS) has been gaining momentum since the last two decades (Ates et al. 2009, 2010; Moreno, Ortúzar, and Dixon 2006, Gong, Li, and Peng 2009; Feldkamp, Abou-Nasr, and Kolmanovsky 2009). Use of ANN with wavelet (Ates et al. 2009, 2010), ultra-capacitor (Moreno, Ortúzar, and Dixon 2006) and also trip modelling NN (Gong, Li, and Peng 2009) and use of recurrent neural network (Feldkamp, Abou-Nasr, and Kolmanovsky 2009; Prokhorov 2008) are popular methods in energy management. ANN trained with back propagation (ANN-BP) once again falls short of providing an exact solution to the problem (Patra et al. 2011). Hence, this paper proposes SFLA (Eusuff and Lansey 2003) as a training algorithm for ANN to be used in energy management.

Advantages of the strategies proposed in this paper, as compared with those of the literature, can be seen as (1) proposed strategies guarantee an optimal result in all situations, which could not be delivered by heuristics (Baumann et al. 2000; Schouten, Salman, and Kheir 2002), (2) proposed strategies provide optimal results in all situations, unlike other optimization strategies optimizing at each instant and (3) paves a way for researchers to a new direction of applying population-based techniques to the field of energy management of hybrid electric vehicles (HEVs).

The organization of this paper is as follows: Section 2 discusses the problem statement. The proposed EMS, SFLA and ANN-SFLA are discussed in Sections 3 and 4, respectively. Simulation results and discussion are discussed in Section 5. Finally conclusion of the paper is outlined in Section 6.

2. The problem

This paper uses a simple power-based model. Model of the vehicle used is parallel and explained in the appendix.

The energy management problem can be formulated as an optimization problem, where a cost function is to be minimized subject to constraints. Because energy is temporarily stored and later retrieved, the optimization problem is usually defined over a time horizon instead of at a single time instant.

The idea of controlling the vehicle power is initiated by the fact that energy losses in the internal combustion engine, alternator and battery change according to their operating point. Minimizing these energy losses will result in an EMS achieving higher fuel economy.

The control objective of energy management is to lower the fuel consumption and exhaust emissions while satisfying several constraints. This control problem can be formulated as a dynamic optimization problem.

If are the state variables (corresponding HEV states), such as vehicle speed, engine speed and energy storage levels and are the control variables at instant, the control variables can be continuous, for instance the power flow, discrete, such as engine on/off or complementary, meaning that only one of a set of variables can be non-zero at a time, like the gear position.

Using discrete time, the vehicle is represented by a dynamic system (Lin et al. 2001):

(1)

where is the present state and is previous state of HEV, as defined earlier.

Which has to be controlled, such that the cost criterion:

(2)

is minimized, satisfying the constraints:

(3)

In this application, the only relevant state is the energy level in the battery .

The energy level of the battery is given by a discrete time version of (1):

(4)

Assuming the signals engine speed (), mechanical drive train power () and electrical load power () to be known, and combining the characteristics of all components given by:

(5)

where is battery power, is stored battery power, is electrical motor power, is mechanical motor power, is mechanical engine power and is fuel rate, the fuel rate can be expressed as a function of the battery storage power:

(6)

The cost function expresses the fuel use over the driving cycle in the time interval , so (2) becomes:

(7)

where

(8)

By choosing as decision variable , the characteristics of all components are included in the cost function. The actual controlled input in the vehicle is . Because the relation between and is known, can be computed from the optimal .

The operating range of the components is limited, so bounds have to be set on the engine power, electrical power and battery power throughput. This can be done using the following constraints:

(9)

These constraints can be translated to time-varying bounds on . Combining them leads to one lower and upper bound for at each time instant:

(10)

The bounds on the battery energy level can also be translated to constraints on :

(11)

A charge-sustaining vehicle requires some kind of endpoint penalty to guarantee that the state of charge of the battery remains in a neighbourhood around a desired value. An endpoint constraint will be used here, requiring the state of energy (SOE) at the end of the cycle to be the same as at the beginning:

(12)

3. SFLA and energy management

The SFLA (Eusuff and Lansey 2003) is a recently proposed meta-heuristic optimization method that mimics the memetic evolution of a group of frogs when searching for the maximum food location. Memeplexes pass on information in a shuffling process among them after a number (pre-defined) of memetic evolution steps. This ensures right path towards a particular interest and is free from bias. Memetic evolution and the shuffling go on till the convergence criterion is satisfied. Here are some terms:

• Memetic vector: frogs (hosts for memes), responsible for improving the memes by passing information among each other. Number of frogs denoted by .

• Memeplex: frog community, a type of meme, permitted to evolve independently to search the space in different directions. Number of memeplexes given by , and being total number of frogs and number of frogs in each memeflexes, respectively.

• Submemeplex: intended to avoid local optima, constructed by selected (the better the fitness, the higher probability a frog will be selected) frogs in a multiplex.

• Population: solution space, collection of memeplexes.

• Initial population: formed by randomly generated frogs , .

• Fitness: feasible solution to the problem corresponds to a frog with its adaptability (performance). Fitness adaptability of frog is defined as . Fitness, , defines the memeplex for a frog, frog as per its belongs to first memeplex, frog belongs to second memeplex and so on (where ). Fitness, , also defines the best (X_b) and the worst frog (X_W) in each memeplex as well as best (X_g) in the entire population.

• Memetic evolution: frogs in each memeplex conduct local exploration of population according to predefined strategies and allow the transfer of meme among local individuals.

Update equations:

(13)

(14)

where and respectively, represent the updated step size for frog leaping and maximum allowed distance of one jump, is a random number between (0, 1).

3.1 Steps in SFLA

• During memeplex evolution, leaps towards , as per updating rule in Equations (13) and (14).

• If the leaping goes towards a better solution, then it replaces . Otherwise, replaces .

• If this still cannot produce a better solution, then the new position of is randomly generated.

The process continues till a pre-defined number of iterations reached within each memeplex, and then the whole population is shuffled.

In developing the SFLA-based EMS in this paper, a set of memes within bound (9) are selected, each representing the weight vector of Equation (8). Then, SFLA starts from the initial random memeplexes to proceed repeatedly from generation to generation through the above-mentioned steps. This produces highly fitted individuals that provide best possible EMS.

For comparison with the proposed equalizers, we have also reproduced genetic algorithm (GA), particle swarm optimization (PSO)-based EMS. In developing the GA-based EMS, a set of chromosomes within the same bound are selected, each representing the weight vector of Equation (8). Then, GA starts from the initial random strings to proceed repeatedly from generation to generation through three genetic operators. In developing the PSO-based EMS in this paper, the coefficients are initially chosen from a population of M ( = 2 × N) particles. Each particle constitutes p number of parameters and each parameter represents one coefficient of (8).

4. SFLA trained ANN (ANN-SFLA) for energy management

This section first discusses ANN in energy management and then discusses the proposed method of training ANN using SFLA.

4.1 ANN in energy management

As mentioned earlier, works on ANN-based EMS is an established field of research, the main aim of this section is to outline the concept for the ease of the reader.

We in this paper chose a three-layer ANN for the purpose. Minimum mean square error is taken as the criterion for the second layer of ANN to train the weights. In the third layer we use SFLA for training and to provide an estimate of the input symbols. Then this estimated symbol is fed back to the second layer that performs energy management. This enhances the performance of the EMS. The second layer computes the weights of ANN, while the third layer calculates the one-step prediction of the EMS and estimates input using the SFLA. The feedback of the estimation results is sent to the second layer for energy management.

4.2 ANN-SFLA

The proposed ANN training using SFLA is outlined in Figure 1. Also, the introduction of SFLA into ANN in ANN-SFLA is another improvement, because introduction of population-based approaches to ANN increases stability of the solutions (Wang and Chiang 2011).

Figure 1 ANN training using SFLA.

The training process takes the form of teaching in an organization, i.e. administrator, teacher and student. Here, ANN takes two possible roles; that of an administrator and a student, while SFLA discharges the function of a teacher.

5. Simulations

The vehicle model that is used for simulations is based on a Ford Mondeo with the 42 V power net built in 2001, with a 2.0 l spark ignition engine and a five-gear manual transmission. The 42 V power net consists of a 5 kW alternator and a 36 V absorbed glass material lead–acid battery with a capacity of 27.5 A h, which corresponds to an energy capacity of 4 MJ. The power net is equipped with a programmable electric load in addition to the electric loads already present in the vehicle. (Details of power flow, drive train, parameter values for the simulation of this vehicle are provided in the appendix.)

Simulations are done for the new European driving cycle (NEDC). For the electric power request, simulations were carried out for the loads of 500, 1000 and 2000 W.

The battery has an energy capacity of and is operated around 70% SOE, because the efficiencies for both charging and discharging in this range are acceptable. The battery losses are approximated as quadratic with the stored power, such that

Parameter b is chosen at a value of , which gives an energy efficiency of 95% at 1000 W and 90% at 2000 W (Samanta et al. 2013). When the drive train power is negative and the clutch is closed, the drive train power is partly delivered by the internal combustion engine (which has a negative drag power), by the alternator and by the brakes. Because regenerative braking delivers electrical power without extra fuel use, it is expected that it will be used as much as possible. The brakes are only used when the desired deceleration power is larger than the maximum negative power that can be taken up by the engine and the alternator.

The fuel consumption and emissions are evaluated with the control model, using the nonlinear fuel and alternator map and the quadratic battery losses. When the cost function represents only the fuel consumption, it turns out that for this case CO₂, CO and NO_x emissions are also reduced significantly. However, the emission of hydrocarbons (HCs) increases. Therefore, a weighted sum of fuel and HC emission is used as cost function. The weighting factors in (7) are and . Simulation parameters used for GA, PSO and SFLA are outlined in Table 1.

Table 1 Simulation parameters.

GA		PSO		SFLA
Parameter	Value	Parameter	Value	Parameter	Value
Number of iterations	1000	Number of iterations	1000	Number of iterations	1000
Number of individuals	50	Number of particles	50	Population size	100
Mutation ratio	0.03	Coefficient C1	0.7	Memeplexes	10
Crossover ratio	0.9	Coefficient C2	0.7	Memes in memeplexes	10
Mutation type	Uniform			Memes in sub-memeplexes	08
Crossover type	Single point			Memetic evolutions in each sub-memeplex	10

This time, all emissions are reduced, at the cost of a slight decrease in fuel reduction. Fuel consumption by different strategies is provided in Table 2. It is seen that as per fuel consumption is concerned, the EMS proposed in this paper is more effective than contemporary GA-, PSO- and ANN-based approaches. Simulation runtime (s) using MATLAB is outlined in Table 3. As evident, though SFLA and ANN-SFLA takes an affordable longer time because of increased stability, still stability is increased.

Table 2 Fuel consumption.

Pl	500 W	1000 W	2000 W
Strategy	Fuel use (g)	Fuel use (g)	Fuel use (g)
GA	557.261	590.442	662.141
PSO	556.157	589.862	661.464
SFLA	551.112	585.242	659.101
ANN-BP	547.126	583.151	657.112
ANN-SFLA	541.224	577.726	652.181

Table 3 Simulation runtime(s) using MATLAB.

Strategy	GA	PSO	SFLA	ANN-BP	ANN-SFLA
Runtime (s)	22	23	25	26	26

Figure 2 shows the SOE for all strategies. The battery is operated around 70% of SOE, from where it is made to deliver power and discharge till a lowest level of 35%. All trajectories of SOE show a similar behaviour. The variation in SOE is small, because of the large capacity of the battery. This justifies that for this simulation, the battery efficiency is chosen independently of .

Figure 2 Battery SOE.

The simulations show that the strategies, SFLA and ANN-SFLA, are effective, as they succeed in lowering the fuel consumption and the exhaust emissions. SFLA and ANN-SFLA methods are better than existing methods as the results are for the entire diving cycle, NEDC. The results might be still improved by fine-tuning the weighting factors of the cost function. Most of the profit comes from regenerative braking, which delivers a certain amount of energy for free.

Both PSO and GA do not find the global optimum of the original nonlinear optimization problem. The ANN-SFLA network uses the original nonlinear cost criterion and finds the global optimum of a quadratic approximation of the original problem. The small difference between SFLA and ANN-SFLA for fuel use and CO₂ indicates that these terms in the nonlinear cost function are approximated adequately.

6. Summary and future work

This paper presented two novel and efficient strategies for energy management of the electrical power net, SFLA and ANN-SFLA, to reduce the fuel consumption and exhaust emissions over a driving cycle.

A comparison between methods discussed in this paper with respect to their suitability for solving energy management problems reveals the following:

• Both the proposed approaches, SFLA and ANN-SFLA, are robust since the curves are smooth enough and do not flicker (swing) like that of GA and PSO.

• In the standard PSO, each particle converges to the global best position independently. Diversity of the search space in SFLA is more than in PSO because introduction of exponential distribution of positions makes SFLA search in a wide space.

• Also, the introduction of SFLA into ANN in ANN-SFLA is another improvement. That increases stability of the solutions.

• Flexibility of the methods and feasibility of the solutions are evident from the number of hits to the global minima.

Contributions of the paper can be outlined as:

• Development of learning method for ANN.

• Use of SFLA in energy management.

• Use of SFLA-trained ANN in energy management.

• Benefits and convenience of the proposed approaches are proved through simulation results.

This paper also paves a way for researchers to work on models with bit complicated power-train physics and operating constraints that will be reflected in our future works.

Appendix

Power flow

The drive train of a parallel HEV, used in this paper, is based on a conventional vehicle, where the alternator is replaced by an integrated starter generator (ISG) that can also be used for propulsion. The clutch can be located before or after the power split for the ISG. This is shown in Figure A1.

Figure A1 Model of the vehicle used in the paper.

The power flow in the vehicle starts with fuel that is injected in the combustion engine. The resulting mechanical power splits into two directions: one part goes to the drive train for vehicle propulsion, whereas the other part goes to the ISG. The ISG provides electric power for the electric loads , but also takes care of charging the battery . Contrary to the other components, the power flow of the battery can be positive as well as negative. In the end, all power, except for losses, is used for vehicle propulsion and for electric devices connected to the power net. The drive train block contains all drive train components including clutch, gears, wheels and vehicle inertia. The alternator is connected to the engine by a belt with a fixed gear ratio.

Drive train

The drive train consists of clutch, transmission, final drive, wheels and inertia. They are not modelled in detail, as only the relationship between vehicle speed, engine speed and drive train torque is of interest. For a given vehicle speed profile , road slope and selected gear ratio , the corresponding engine speed and torque needed for propulsion can be calculated.

When the engine speed drops below idle speed, the clutch is opened, the drive train torque becomes zero and the engine keeps running at idle speed. The engine power becomes equal to the alternator power and the drive train power becomes equal to the brake power. In Table A1, the parameters are explained and their values as used in simulations are given.

Table A1 Vehicle parameters used in simulations.

Quantity	Symbol	Value	Unit
Mass	M	1400	kg
Frontal area	Ad	2	m^2
Air drag coefficient	Cd	0.3	–
Rolling resistance	Cr	0.015	–
Wheel radius	wr	0.3	m
Final drive ratio	fr	4.0	–
Gear ratio	gr	3.4–2.1–1.4–1.0–0.77	–
Idle speed		73.3	rad/s
Air density		1.2	kg/m^3
Gravity	g	9.8	m/s^2