# Novel Energy Management Control Strategy for Improving Efficiency in Hybrid Powertrains

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Testing

- Sixty-three points from the low load (3 BMEP) to high load (around 22 BMEP) covering a wide range of the engine map at different engine speeds.
- The measurements were repeated at different coolant temperatures: 35 °C, 50 °C, 63 °C, 76 °C, and 88 °C.

#### 2.2. Numerical Model

#### 2.2.1. Internal Combustion Engine

#### 2.2.2. Electric Machine and Power Electronics

#### 2.2.3. Battery

#### 2.2.4. Transmission

#### 2.2.5. Vehicle Dynamics

- A source term representing the net torque coming from the powertrain, including the power split, efficiency, and gear transmission ratio. Additionally, the braking torque may be applied if the driver acts on the brake pedal to reduce the vehicle speed and the motor is not able to absorb the braking power.
- An inertial term, including the vehicle mass and powertrain inertia.
- A set of sink terms considering non-conservative forces, mainly friction losses due to aerodynamic drag and rolling resistance.
- An additional term may be included to consider the potential energy, allowing the assessment of the road slope effects (despite tests carried out in the present project have been conducted, considering a horizontal road).

#### 2.2.6. Driver

#### 2.3. Control Strategy

- The optimal solution to the problem described in Equation (19) should minimize the Hamiltonian (Equation 20) in every time step according to Equation (21):$${u}^{*}\left(t\right)=arg\underset{u}{min}H(x,\phantom{\rule{4pt}{0ex}}u,\phantom{\rule{4pt}{0ex}}\lambda ,\phantom{\rule{4pt}{0ex}}w,\phantom{\rule{4pt}{0ex}}t)$$
- The evolution of the co-state for the optimal solution should fulfill Equation (23):$$\dot{\lambda}\left(t\right)=-\phantom{\rule{4pt}{0ex}}\frac{\partial H}{\partial x}=\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}\frac{\partial L}{\partial x}-\lambda \frac{\partial f}{\partial x}\phantom{\rule{4pt}{0ex}}$$
- The terminal co-state should be Equation (24):$$\lambda \left({t}_{f}\right)=\frac{\partial \psi \left({t}_{f}\right)}{\partial x}\phantom{\rule{4pt}{0ex}}$$

- Assign the initial values of the states to the optimal state trajectory (${x}^{*}\phantom{\rule{4pt}{0ex}}\left({t}_{0}\right)={x}_{0}$).
- Estimate an initial value for the co-state vector (${\lambda}^{*}\phantom{\rule{4pt}{0ex}}\left({t}_{0}\right)={\lambda}_{0}$).
- Compute the optimal control action (${u}^{*}$) at the current time-step by applying Equation (21) by trying a set of candidates.
- Compute the state derivative $f(x,\phantom{\rule{4pt}{0ex}}{u}^{*},\phantom{\rule{4pt}{0ex}}\lambda ,\phantom{\rule{4pt}{0ex}}w,\phantom{\rule{4pt}{0ex}}t)$ and integrate to obtain state x in the next time-step.
- Compute the co-state derivative by Equation (23) and integrate to obtain the co-state vector $\lambda $ in the next time-step.
- Repeat steps 3–5 until the end of the problem.
- If the target state at the end of the problem is achieved ($x\left({t}_{f}\right)={x}_{{t}_{f}}$), ${\lambda}_{0}$ is a good guess, otherwise modify ${\lambda}_{0}$ and repeat steps 3–6.

#### 2.3.1. Modifications to Deal with Oscillating Behavior

- ${P}_{f}\left({u}_{k}\right)+s{P}_{b}\left({u}_{k}\right)$ is the direct application of the ECMS, with the particularity that fuel power (${P}_{f}=\phantom{\rule{4pt}{0ex}}{\dot{m}}_{f}{H}_{c}$, where ${H}_{c}$ is the fuel heating power) instead of the fuel mass flow is used to allow the s parameter to be non-dimensional.
- ${C}_{ON}$ represents the marginal cost of switching on the engine.
- ${C}_{du}$ is the marginal cost associated with the engine throttle variation.
- ${C}_{\infty}$ is an arbitrarily large cost to avoid throttle variations above a certain threshold ($\overline{du}$) or, in the case of the series mode where the engine is decoupled from the wheels, with the engine speed variations above a given limit ($\overline{d{n}^{eng}}$).

#### 2.3.2. ECMS Modifications to Deal with the Engine’s Thermal State

#### 2.3.3. ECMS Modifications to Account for Different Powertrain Modes

- (a)
- The ECMS is applied independently for the N modes available in the powertrain. In this sense, for every powertrain mode i, the optimal speed and torque for any of the j engines and motors (${n}_{i}^{j},\phantom{\rule{4pt}{0ex}}{M}_{i}^{j}$) with its corresponding minimum cost ($Cos{t}_{i}$) is calculated.
- (b)
- The previous information arrives at the mode selector, where the option with minimum cost is chosen. Directly comparing the cost of the different modes might result in a highly oscillating control policy, especially since the model barely addresses the system dynamics, which will not produce desirable results when applying the control to the actual powertrain. Every time a switch between modes is carried out, the powertrain experiences a transient that the model is not able to consider. To cope with this issue, the following optimization is proposed (Equation (32)):$${u}_{mode,k}^{*}=arg\underset{i\u03f5[1,N]}{min}\sum _{k-\Delta k}^{k}\left\{Cos{t}_{i,k}+{C}_{dmode}(i-{u}_{mode,k-1}^{*})+{C}_{mode,i}\right\}$$

## 3. Results

#### 3.1. WLTC Cycle

#### 3.2. RDE Cycle

## 4. Conclusions

- An integrated virtual model for the energy management of xEVs was developed and the study of a hybrid electric vehicle was carried out with this tool. The programmed control strategy is based on the ECMS, while additional terms to compensate for dynamic issues, to consider other potential powertrain architectures and states, such as the engine’s thermal state, have been added. The energy management strategy is able to consider the engine’s thermal state in the control algorithm, which is a novelty with respect to the state-of-the-art ECMS. In order to implement this, an extensive experimental campaign was performed at different engine coolant temperatures in order to implement a temperature-dependent 3D map.
- Simulation results show that, taking into account the thermal state (TS on) of the engine reduces the fuel consumption when compared to the base case. Experimental measurements confirmed those gains in both cycles. The 4.1% and 3% accumulated fuel reductions were obtained for the WLTC and RDE cycles, respectively. This is because when the control strategy considered the thermal state of the engine, the engine was turned on only when its warming-up time was going to be the fastest and the engine operated at maximum times at higher temperatures. This contributes to decreasing power losses and increasing ICE fuel consumption.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EV | electric vehicles |

EMS | energy management system |

DP | dynamic programming |

PMP | Pontryagin’s minimum principle |

ECMS | equivalent consumption management strategy |

MPC | model predictive control |

BSFC | brake specific fuel consumption |

ICE | internal combustion engine |

ICEV | internal combustion engine vehicle |

PHEVS | plug-in hybrid electric vehicles |

SOC | state of charge |

PID | proportional–integral–derivative controller |

FMU | functional mock-up unit |

RDE | real driving emission |

WLTC | worldwide harmonized light vehicle test cycle |

HSG | high-voltage starter generator |

EM | electric motor |

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**Figure 4.**$h(n,\alpha ,{\theta}_{c})$ 3D Map of fuel consumption ratio with the engine coolant temperature.

**Figure 5.**Evolution of the coolant temperature in a RDE with the ICE. Comparison between experimental results and control-oriented model.

**Figure 9.**Example of non-convexity in Equation (26) leading to strongly different torques minimizing the cost functions at two similar engine speeds.

**Figure 10.**Scheme of the extension of the ECMS to integrate several (N) modes and the corresponding torque and speed demands of the j engines and electric machines.

**Figure 11.**Simulation results for both control strategies during the WLTC cycle. (

**a**) Vehicle velocity. (

**b**) State of Charge of the Battery (SOC). (

**c**) ICE switch.

**Figure 12.**Comparison between both strategies for ICE simulation results (left plots) and experimental measurements (right plots) during the WLTC cycle. (

**a**) Model torque. (

**b**) Experimental torque. (

**c**) Model fuel consumption. (

**d**) Experimental fuel consumption. (

**e**) Model coolant temperature. (

**f**) Experimental coolant temperature.

**Figure 13.**Simulation results for both control strategies during the RDE cycle. (

**a**) Vehicle velocity. (

**b**) State of charge of the battery (SOC). (

**c**) ICE switch.

**Figure 14.**Comparison between both strategies for ICE simulation results (left plots) and experimental measurements (right plots) during the RDE cycle. (

**a**) Model torque. (

**b**) Experimental torque. (

**c**) Model fuel consumption. (

**d**) Experimental fuel consumption. (

**e**) Model coolant temperature. (

**f**) Experimental coolant temperature.

Parameter | Value |
---|---|

Displacement | 999 cm${}^{3}$ |

Diameter | $81.3$ mm |

Stroke | $72.2$ mm |

Number of cylinders | 3 in line |

Number of valves | 4 per cylinder |

Max torque @ speed | $182.3$ Nm @ 2250 rpm |

Max power @ speed | $83.0$ kW @ 5250 rpm |

Variable | Instrument | Range | Accuracy |
---|---|---|---|

Engine speed | Dynamometer | 0–7500 rpm | $\pm 1$ rpm |

Torque | Dynamometer | 0–400 Nm | ±0.5% |

Fluid temperature | k-type thermocouple | 70–1520 K | $\pm 2$ K |

Air mass flow | Flowmeter | 0–1700 kg/h | ±2% |

In-cylinder pressure | AVL GH13P | 0–200 bar | ±0.3% |

Coolant flow | OPTIFLUX 4000 | 4.5–90 lpm | ±0.5% |

Oil pressure | Piezoresistive transducer | 0–10 bar | $\pm 25$ mbar |

Emissions | Horiba MEXA @ AVL Smoke meter |

**Table 3.**Variable definitions of Equation (17).

Variable | Definition |
---|---|

${M}_{wheel}$ | Net torque applied at the wheels |

${m}_{Veh}$ | Vehicle mass |

${J}_{pwt}$ | Global powertrain inertia |

${r}_{wheel}$ | Wheel effective radius |

v | Vehicle linear speed |

$\dot{v}$ | Vehicle linear acceleration |

${\dot{\omega}}_{wheel}$ | Wheel angular acceleration |

g | Gravity acceleration |

$\beta $ | Track slope |

$\mu $ | Dynamic coefficient of rolling friction |

$\rho $ | Environment air density |

S | Vehicle frontal area |

${C}_{x}$ | Longitudinal aero drag coefficient |

**Table 4.**Transcription of the energy management problem to the mathematical framework of the optimal control.

Symbol | Description | Variable in the Energy Management Strategy |
---|---|---|

u | Control action vector | Power split |

x | State vector | State of Charge of the Battery (SOC), engine thermal state (coolant temperature) |

w | Disturbance vector | Vehicle speed profile, route height profile, wind velocity and direction |

L | Lagrangian cost | Fuel consumption, energy consumption, weighted average between energy consumption and pollutants |

$\psi $ | Terminal cost | Deviation of a target SOC, emissions exceeding certain limit |

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## Share and Cite

**MDPI and ACS Style**

Broatch, A.; Olmeda, P.; Plá, B.; Dreif, A.
Novel Energy Management Control Strategy for Improving Efficiency in Hybrid Powertrains. *Energies* **2023**, *16*, 107.
https://doi.org/10.3390/en16010107

**AMA Style**

Broatch A, Olmeda P, Plá B, Dreif A.
Novel Energy Management Control Strategy for Improving Efficiency in Hybrid Powertrains. *Energies*. 2023; 16(1):107.
https://doi.org/10.3390/en16010107

**Chicago/Turabian Style**

Broatch, Alberto, Pablo Olmeda, Benjamín Plá, and Amin Dreif.
2023. "Novel Energy Management Control Strategy for Improving Efficiency in Hybrid Powertrains" *Energies* 16, no. 1: 107.
https://doi.org/10.3390/en16010107