Page 99 - IJEEE-2022-Vol18-ISSUE-1

Al-Flehawee & Al-Mayyahi | 95

? The block of powertrain and vehicle dynamic:-This block ???? Motor torque Nm
includes the dynamic equations that express the vehicle ???? Generator torque Nm
and the powertrain, as the powertrain includes the engine,
motor, generator, batteries, and a planetary gear set. In the dynamic equations of powertrain and vehicle, the
Engine torque, motor torque, and generator torque are the
entries of this block that come from the control unit. following assumptions are made:-
While the state variables are transmitted from this block
to the control unit, the outputs of this block are the vehicle 1. The carrier inertia, the ring inertia, and the sun inertia are
speed and the battery charge state.
neglected.

2. Only the longitudinal dynamics of the vehicle are

considered.

Thus, the dynamic equations of powertrain and vehicle

III. DYNAMIC EQUATIONS OF A SERIES-PARALLEL HEV are[13]:
AND FUEL FLOW RATE EQUATION
??????? ?? = ???? - ??(?? + ??) (5)
In general, the dynamic equations of the series-parallel ????????? = ???? + ???? (6)
hybrid electric vehicle can be divided into:-
??????? ?? = ???? + ???? - ???????? (7)

?? ???? ???h = {((???????????? + ????????)/????) - 0.5?????????????2???h

A. The Powertrain and Vehicle Dynamic Equations -????(????cos?? + sin??)} (8)

In the planetary gear set, the rotational speed of the ring From (1)-(8) we obtain:

gear ??? , the sun gear ??? and the carrier gear ??? are =??? ?? ??? ??1 - ??? ??2 + ??? ??3 + ??? ??4 (9)
governed by the constraints of kinematic equality at all times
??? ??1 = ((??1????)/(??1??1 - ??2??2))

by the following relationship[12]:- ??? ??2 = ((??2????)/(??1??1 - ??2??2))

?????? + ?????? = (?? + ??)???? (1) ??? ??3 = ((????(??1??3 - ??3??2))/(??1??1 - ??2??2))

The rest of the abbreviations used in the equations are found ??? ??4 = (??1/(??1??1 - ??2??2){((-0.5?????????????3? ???2?)/???3? )

in Table I. The above equation can be written in terms of the -(????????) + (????????/????)}

engine speed ???? (rad/sec), the motor speed ???? (rad/sec),

and the engine speed ????(rad/sec). ??? ?? = ??? ??1 + ??? ??2 + ??? ??3 - ??? ??4 - ??? ??5 (10)

Where: ???? = ???? ??? ??1 = (????/??1)

???? = ????}, (2) ??? ??2 = ((??3????)/??1) - ((??2????)/(??1??1 - ??2??2))

???? = ???? ??? ??3 = ((??2??2????)/(??1(??1??1 - ??2??2)))

Then (1) becomes: ??? ??4 = (??2????/??1)((??1??3 - ??3??2)/(??1??1 - ??2??2))

?????? + ?????? = (?? + ??)???? (3) ??? ??5 = (??2/(??1??1 - ??2??2){((-0.5?????????????3? ???2?)/???3? )

The another constraint of the kinematic equality between -(????????) + (????????/????)}

the planetary gear set and the vehicle speed is that the Where:-

rotational speed of the ring gear is a function of the vehicle ??1 = ???? + ((?? + ??)/??)2????

speed and is represented by the following relationship:- ??2 = -(??(?? + ??)/??2)????

V????h = ???? ???? , ? ???? = ???? V????h (4) ??3 = (?? + ??)/??
???? ???? ??1 = ???? + (??2/??2)???? + (????/????)2??

TABLE I ??2 = -??(?? + ??/??2)????

LIST OF ABBREVIATIONS AND THEIR VALUE ??3 = -??/??

Abbr. Definition Units

???? Vehicle frontal area 2.16m2 B. Battery Dynamic Equations

?? Gravitational constant 9.81m/s2

?? Air density 1.18kg/m2 One of the most important parameters in the energy

???? Drag coefficient 0.26 management of hybrid electric vehicles is the battery state of

?? Total mass of the vehicle 1200Kg charge (SOC), which represents a measure of the remaining

???????? Speed of the vehicle m/s electric energy in the battery, it is determined by[14]:

?? The slope of the road 0radians ?????? = ??????????-?????0 ??????????(??)???? (11)

???? Wheel rolling friction coefficient 0.01 ??????????
Nm
???????? Friction brake torque 30 The battery current ?????????? can be found after solve this

?? Number of teeth of the sun gear equation[15]:

?? Number of teeth of the ring gear 78 ?????????? = ???????????????? - ???2??????? ?????????? (12)

???? Final gear ratio 1.3 Then
???? wheel radius 0.3m
?????????? 8.1A.h ?????????? = - ?????? - v?????? 2 - 4????????????????????
?????????? Capacity of the battery watt 2??????????
?????????? Battery power 0.246Ohm
?????? Volt The dynamic equation of the state of charge (SOC) can
???? Internal resistance of the battery Nm
Battery voltage be obtained by taking the time derivative of (11)[16]:
Engine torque
????? ?? = - ??????-v??????2-4???????????????????? (13)

2????????????????????