Contemporary Engineering Sciences, Vol. 7, 2014, no. 22, 1155 - 1162

HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ces.2014.49144

Study on the Power Control Algorithm

Using the Gradient Method

Gyoung-eun Kim

Graduate School of Electrical Engineering

University of Ulsan, 93 Daehak-ro, Ulsan

Republic of Korea

Jae-woo Yoon

Graduate School of Electrical Engineering

University of Ulsan, 93 Daehak-ro

Ulsan, Republic of Korea

Byeong-woo Kim

School of Electrical Engineering

University of Ulsan, 93 Daehak-ro

Ulsan, Republic of Korea

Copyright © 2014 Gyoung-eun Kim, Jae-woo Yoon and Byeong-woo Kim. This is an open

access article distributed under the Creative Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any medium, provided the original work is

properly cited.

Abstract

This paper presents a power control algorithm that will make it possible to apply

a torque assist system (TAS) without reconfiguring the structure of an internal

combustion engine (ICE) vehicle. Several optimal control ideas for hybrid electric

vehicles (HEVs) have been proposed in the literature. In this study, the algorithm

implements a gradient optimization technique. This suggested algorithm considers

the states of the motor starter generator (MSG) and energy storage, as well as the

maximum efficiency of the engine. To optimize the engine efficiency under

various driving conditions, the algorithm considers the driver’s demand outputs. It

will be utilized for optimization based on TAS.

1156 Gyoung-eun Kim, Jae-woo Yoon and Byeong-woo Kim

The use of the proposed algorithm will contribute to the research in this field by

controlling the performance of the engine and MSG at efficient operating points to

match the driver’s demand outputs.

Keywords: Hybrid vehicle, Torque assist system (TAS), Optimal control theory,

Gradient method

1 Introduction

Recently, investments and support have greatly increased in the automobile

industry for the production of highly efficient and environmentally friendly

automobiles due to the depletion of fossil fuels and stricter environmental

regulations [1]. Furthermore, studies are actively progressing on hybrid vehicles

that can achieve high energy efficiency while reducing the load of internal

combustion engines (ICEs) by installing a motor, which is an electric energy

power source, in a conventional system [2]. To obtain excellent energy efficiency,

the performance of the system itself is important, but it is also critical to optimize

the operation performance of the configured system.

Conventional studies have been conducted to increase fuel efficiency by

considering only the state of the electric power source and energy storage devices

of hybrid vehicles [3] [4]. Therefore, further studies are required for a power

distribution control that considers the state of the whole power source as well as

the electric power source and energy storage device.

In this paper, a gradient method, an optimal control theory, is proposed as a

power control method that considers the efficiency and torque of the power source

of an entire hybrid system.

2 Power Control of Torque Assist System

A torque assistance system (TAS) is an optimal torque assistance system that

can assist vehicle engine loads based on a high power density type of motor starter

generator (MSG) in place of a conventional ISA [5]. Fig. 1 shows the system

configuration for the power distribution control that considers the state of the

entire power source. To satisfy the required torque depending on the driver and

driving circumstances, the torque distribution control signal is input to the engine

and motor. Accordingly, a power control algorithm for the vehicle was

constructed for optimal torque assistance; this algorithm can improve fuel

efficiency and increase functionality by adding the torque of the motor to that of

the engine.

Study on the power control algorithm 1157

Fig. 1. Schematic diagram of a power control algorithm based on the TAS

2.1 Efficiency and Torque of Power Source

To apply the power control algorithm that considers the power source of the

entire hybrid system, information is needed for the required torque, depending on

the driver and driving circumstances. When the required torque is specified,

maximum efficiency must be considered. Therefore, an efficiency map is

necessary for the torque demanded by a driver. The efficiency equations for the

engine and motor can be obtained through the calculation process shown below.

The efficiency of engine can be obtained by using brake specific fuel

consumption (BSFC), which measures fuel efficiency, as shown in equation (1)

[6]. Here, the lower heating value (LHV) of a gasoline engine is assumed to be

0.0122225. In equation (2), r is the fuel consumption rate [g/s] and P is the

produced power; P , which is the multiplication of engine speed [rad/s]

and engine torque [Nm].

The efficiency of the motor is calculated by the power of the motor and

electric power loss, as shown in equation (3) [7]. Furthermore, the efficiency of

the motor is determined by the operating torque and rotation speed, like those of

the engine.

)/( LHVBSFCengine 1

(1)

PrBSFC / (2)

100

lossMSG

MSGMSG

WP

P

(3)

0

1

0

MSGMSGMSGMSGMSG

MSGMSGMSGMSGMSG

MSG TifT

TifT

P

(4)

1158 Gyoung-eun Kim, Jae-woo Yoon and Byeong-woo Kim

In the power source control strategy algorithm, the required power of the

vehicle is determined by the pedal input from the driver. The final power of the

engine, depending on the required power, is determined by the assistance power

of the MSG, which considers the maximum efficiency of the engine. For the

required power of the vehicle depending on the pedal input of the driver, the

engine’s torque map was used based on a conventional ICE. The efficiency and

torque maps of the core power source for the TAS system, depending on vehicle

speed, are shown in Figs. 2–4.

Fig. 2. Efficiency map of the engine

Study on the power control algorithm 1159

Fig. 3. Torque map of the engine

Fig. 4. Efficiency and torque map of the motor

1160 Gyoung-eun Kim, Jae-woo Yoon and Byeong-woo Kim

2.2 Optimal Control Algorithm

To determine the maximum efficiency point of the engine, a gradient method,

which is an optimal theory, was used [8] [9]. This method determines the most

optimized point, i.e., the maximum point, by repeatedly finding the direction of

the gradient dropping most radically from the current position, then finding a new

location by moving in that direction. Fig. 5 shows the gradient method.

As shown in Fig. 6, assuming that the efficiencies of the engine depending

on the vehicle speed and driver’s required power are constant values, kc (k = 0,

1 , 2,… ), several level sets can be obtained by connecting the corresponding

values. The maximum value for the efficiency function of the engine is found by

repeating equation (5) for obtaining the level set for the engine efficiency value

depending on the driving state of the vehicle.

,,)( )()()( 2111 kxftxx kk

kk (5)

(a) Typical sequence level set (b) Engine efficiency level set

Fig. 5. Typical sequence resulting from the gradient method

Fig. 6. Constructing level set corresponding to level ck (k = 0, 1 , 2,… ) for engine efficiency function f

Study on the power control algorithm 1161

Fig. 7. Required power based on engine and the maximum engine efficiency

Once the required torque is determined depending on the required speed of

the driver, the maximum efficiency of the engine for the required torque can be

obtained through the maximum efficiency point of the engine by using the

gradient method. Fig. 7 shows the result. Once the maximum efficiency point is

determined for the required torque in the entire power system, MSG assists the

torque within the proper efficiency range to allow the engine’s efficiency to reach

its maximum point. In this way, the gradient method, which is an optimal control

theory, can be applied as a torque power control method for an entire power

system depending on the driving state.

3 Conclusion In this study, we proposed a power control method to apply TAS without

modifying the structure of conventional ICE vehicles. Through the power control

algorithm that considers the efficiencies of two power sources, we proposed a

power torque distribution algorithm for an entire vehicle. The gradient method

was used to determine the maximum efficiency of the engine depending on the

driving state of the vehicle. If the control method proposed in this study is used,

the engine and electric power source can be controlled and operated at their

efficient operation points according to the required power of the driver. The

proposed method is expected to contribute to studies on hybrid power controls

that consider a vehicle’s overall efficiency. In a future study, we plan to analyze

1162 Gyoung-eun Kim, Jae-woo Yoon and Byeong-woo Kim

the overall efficiency and fuel efficiency of vehicles in various driving

environments.

Acknowledgements. Foundation item: This research was supported by the MSIP

(Ministry of Science, ICT&Future Planning), Korea, under the C-ITRC

(Convergence Information Technology Research Center) support program

(NIPA-2013-H0401-13-1008) supervised by the NIPA (National IT Industry

Promotion Agency).

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Received: August 11, 2014