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Page 1
Utilisation of Electrical Energy
Electric Traction-II,
INTRODUCTION
The movement of trains and their energy consumption can be most conveniently
studied by means of the speed–distance and the speed–time curves. The motion of
any vehicle may be at constant speed or it may consist of periodic acceleration and
retardation. The speed–time curves have significant importance in traction. If the
frictional resistance to the motion is known value, the energy required for motion of the
vehicle can be determined from it. Moreover, this curve gives the speed at various time
instants after the start of run directly. TYPES OF SERVICES
There are mainly three types of passenger services, by which the type of
traction system has to be selected, namely:
1. Main line service.
2. Urban or city service.
3. Suburban service.
Main line services
In the main line service, the distance between two stops is usually more than 10 km. High
balancing speeds should be required. Acceleration and retardation are not so important.
Urban service
In the urban service, the distance between two stops is very less and it is less than 1
km. It requires high average speed for frequent starting and stopping.
Suburban service
In the suburban service, the distance between two stations is between 1 and 8 km. This service
requires rapid acceleration and retardation as frequent starting and stopping is required.
SPEED–TIME AND SPEED–DISTANCE CURVES FOR DIFFERENT SERVICES
The curve that shows the instantaneous speed of train in kmph along the ordinate and time in
seconds along the abscissa is known as ‘speed–time’ curve. The curve that shows the distance
between two stations in km along the ordinate and time in seconds along the abscissa is known as
‘speed–distance’ curve. The area under the speed–time curve gives the distance travelled during,
given time internal and slope at any point on the curve toward abscissa gives the acceleration and
retardation at the instance, out of the two speed–time curve is more important.
Page 2
Utilisation of Electrical Energy
Electric Traction-II,
INTRODUCTION
The movement of trains and their energy consumption can be most conveniently
studied by means of the speed–distance and the speed–time curves. The motion of
any vehicle may be at constant speed or it may consist of periodic acceleration and
retardation. The speed–time curves have significant importance in traction. If the
frictional resistance to the motion is known value, the energy required for motion of the
vehicle can be determined from it. Moreover, this curve gives the speed at various time
instants after the start of run directly. TYPES OF SERVICES
There are mainly three types of passenger services, by which the type of
traction system has to be selected, namely:
1. Main line service.
2. Urban or city service.
3. Suburban service.
Main line services
In the main line service, the distance between two stops is usually more than 10 km. High
balancing speeds should be required. Acceleration and retardation are not so important.
Urban service
In the urban service, the distance between two stops is very less and it is less than 1
km. It requires high average speed for frequent starting and stopping.
Suburban service
In the suburban service, the distance between two stations is between 1 and 8 km. This service
requires rapid acceleration and retardation as frequent starting and stopping is required.
SPEED–TIME AND SPEED–DISTANCE CURVES FOR DIFFERENT SERVICES
The curve that shows the instantaneous speed of train in kmph along the ordinate and time in
seconds along the abscissa is known as ‘speed–time’ curve. The curve that shows the distance
between two stations in km along the ordinate and time in seconds along the abscissa is known as
‘speed–distance’ curve. The area under the speed–time curve gives the distance travelled during,
given time internal and slope at any point on the curve toward abscissa gives the acceleration and
retardation at the instance, out of the two speed–time curve is more important.
Utilisation of Electrical Energy
Speed–time curve for main line service Typical speed–time curve of a train running on
main line service is shown in Fig. 10.1. It mainly consists of the following time periods:
1. Constant accelerating period.
2. Acceleration on speed curve.
3. Free-running period.
4. Coasting period.
5. Braking period.
Fig. 10.1 Speed–time curve for mainline service
Constant acceleration
During this period, the traction motor accelerate from rest. The curve ‘OA’ represents
the constant accelerating period. During the instant 0 to T1, the current is maintained
approximately constant and the voltage across the motor is gradually increased by
cutting out the starting resistance slowly moving from one notch to the other. Thus,
current taken by the motor and the tractive efforts are practically constant and
therefore acceleration remains constant during this period. Hence, this period is also
called as notch up accelerating period or rehostatic accelerating
period. Typical value of acceleration lies between 0.5 and 1 kmph. Acceleration is
denoted with the symbol ‘a’.
Acceleration on speed-curve
During the running period from T1 to T2, the voltage across the motor remains constant and
the current starts decreasing, this is because cut out at the instant ‘T1’. According to the
characteristics of motor, its speed increases with the decrease in the current and finally the
Page 3
Utilisation of Electrical Energy
Electric Traction-II,
INTRODUCTION
The movement of trains and their energy consumption can be most conveniently
studied by means of the speed–distance and the speed–time curves. The motion of
any vehicle may be at constant speed or it may consist of periodic acceleration and
retardation. The speed–time curves have significant importance in traction. If the
frictional resistance to the motion is known value, the energy required for motion of the
vehicle can be determined from it. Moreover, this curve gives the speed at various time
instants after the start of run directly. TYPES OF SERVICES
There are mainly three types of passenger services, by which the type of
traction system has to be selected, namely:
1. Main line service.
2. Urban or city service.
3. Suburban service.
Main line services
In the main line service, the distance between two stops is usually more than 10 km. High
balancing speeds should be required. Acceleration and retardation are not so important.
Urban service
In the urban service, the distance between two stops is very less and it is less than 1
km. It requires high average speed for frequent starting and stopping.
Suburban service
In the suburban service, the distance between two stations is between 1 and 8 km. This service
requires rapid acceleration and retardation as frequent starting and stopping is required.
SPEED–TIME AND SPEED–DISTANCE CURVES FOR DIFFERENT SERVICES
The curve that shows the instantaneous speed of train in kmph along the ordinate and time in
seconds along the abscissa is known as ‘speed–time’ curve. The curve that shows the distance
between two stations in km along the ordinate and time in seconds along the abscissa is known as
‘speed–distance’ curve. The area under the speed–time curve gives the distance travelled during,
given time internal and slope at any point on the curve toward abscissa gives the acceleration and
retardation at the instance, out of the two speed–time curve is more important.
Utilisation of Electrical Energy
Speed–time curve for main line service Typical speed–time curve of a train running on
main line service is shown in Fig. 10.1. It mainly consists of the following time periods:
1. Constant accelerating period.
2. Acceleration on speed curve.
3. Free-running period.
4. Coasting period.
5. Braking period.
Fig. 10.1 Speed–time curve for mainline service
Constant acceleration
During this period, the traction motor accelerate from rest. The curve ‘OA’ represents
the constant accelerating period. During the instant 0 to T1, the current is maintained
approximately constant and the voltage across the motor is gradually increased by
cutting out the starting resistance slowly moving from one notch to the other. Thus,
current taken by the motor and the tractive efforts are practically constant and
therefore acceleration remains constant during this period. Hence, this period is also
called as notch up accelerating period or rehostatic accelerating
period. Typical value of acceleration lies between 0.5 and 1 kmph. Acceleration is
denoted with the symbol ‘a’.
Acceleration on speed-curve
During the running period from T1 to T2, the voltage across the motor remains constant and
the current starts decreasing, this is because cut out at the instant ‘T1’. According to the
characteristics of motor, its speed increases with the decrease in the current and finally the
Utilisation of Electrical Energy
current taken by the motor remains constant. But, at the same time, even though train
accelerates, the acceleration decreases with the increase in speed. Finally, the
acceleration reaches to zero for certain speed, at which the tractive effort excreted by
the motor is exactly equals to the train
resistance. This is also known as decreasing accelerating period. This period is shown
by the curve ‘AB’.
Free-running or constant-speed period
The train runs freely during the period T2 to T3 at the speed attained by the train at the
instant ‘T2’. During this speed, the motor draws constant power from the supply lines.
This period is shown by the curve BC.
Coasting period
This period is from T3 to T4, i.e., from C to D. At the instant ‘T3’ power supply to the
traction, the motor will be cut off and the speed falls on account of friction, windage
resistance, etc. During this period, the train runs due to the momentum attained at that
particular instant. The rate of the decrease of the speed during coasting period is
known as coasting retardation. Usually, it is denoted with the symbol ‘ßc’.
Braking period
Braking period is from T4 to T5, i.e., from D to E. At the end of the coasting period, i.e., at ‘T4’
brakes are applied to bring the train to rest. During this period, the speed of the train decreases
rapidly and finally reduces to zero. In main line service, the free-running period will be more, the
starting and braking periods are very negligible, since the distance between the stops for the main
line service is more than 10 km. Speed–time curve for suburban service In suburban service, the
distance between two adjacent stops for electric train is lying between 1 and 8 km. In this service,
the distance between stops is more than the urban service and smaller than the main line service.
The typical speed–time curve for suburban service is shown in Fig. 10.2.
Page 4
Utilisation of Electrical Energy
Electric Traction-II,
INTRODUCTION
The movement of trains and their energy consumption can be most conveniently
studied by means of the speed–distance and the speed–time curves. The motion of
any vehicle may be at constant speed or it may consist of periodic acceleration and
retardation. The speed–time curves have significant importance in traction. If the
frictional resistance to the motion is known value, the energy required for motion of the
vehicle can be determined from it. Moreover, this curve gives the speed at various time
instants after the start of run directly. TYPES OF SERVICES
There are mainly three types of passenger services, by which the type of
traction system has to be selected, namely:
1. Main line service.
2. Urban or city service.
3. Suburban service.
Main line services
In the main line service, the distance between two stops is usually more than 10 km. High
balancing speeds should be required. Acceleration and retardation are not so important.
Urban service
In the urban service, the distance between two stops is very less and it is less than 1
km. It requires high average speed for frequent starting and stopping.
Suburban service
In the suburban service, the distance between two stations is between 1 and 8 km. This service
requires rapid acceleration and retardation as frequent starting and stopping is required.
SPEED–TIME AND SPEED–DISTANCE CURVES FOR DIFFERENT SERVICES
The curve that shows the instantaneous speed of train in kmph along the ordinate and time in
seconds along the abscissa is known as ‘speed–time’ curve. The curve that shows the distance
between two stations in km along the ordinate and time in seconds along the abscissa is known as
‘speed–distance’ curve. The area under the speed–time curve gives the distance travelled during,
given time internal and slope at any point on the curve toward abscissa gives the acceleration and
retardation at the instance, out of the two speed–time curve is more important.
Utilisation of Electrical Energy
Speed–time curve for main line service Typical speed–time curve of a train running on
main line service is shown in Fig. 10.1. It mainly consists of the following time periods:
1. Constant accelerating period.
2. Acceleration on speed curve.
3. Free-running period.
4. Coasting period.
5. Braking period.
Fig. 10.1 Speed–time curve for mainline service
Constant acceleration
During this period, the traction motor accelerate from rest. The curve ‘OA’ represents
the constant accelerating period. During the instant 0 to T1, the current is maintained
approximately constant and the voltage across the motor is gradually increased by
cutting out the starting resistance slowly moving from one notch to the other. Thus,
current taken by the motor and the tractive efforts are practically constant and
therefore acceleration remains constant during this period. Hence, this period is also
called as notch up accelerating period or rehostatic accelerating
period. Typical value of acceleration lies between 0.5 and 1 kmph. Acceleration is
denoted with the symbol ‘a’.
Acceleration on speed-curve
During the running period from T1 to T2, the voltage across the motor remains constant and
the current starts decreasing, this is because cut out at the instant ‘T1’. According to the
characteristics of motor, its speed increases with the decrease in the current and finally the
Utilisation of Electrical Energy
current taken by the motor remains constant. But, at the same time, even though train
accelerates, the acceleration decreases with the increase in speed. Finally, the
acceleration reaches to zero for certain speed, at which the tractive effort excreted by
the motor is exactly equals to the train
resistance. This is also known as decreasing accelerating period. This period is shown
by the curve ‘AB’.
Free-running or constant-speed period
The train runs freely during the period T2 to T3 at the speed attained by the train at the
instant ‘T2’. During this speed, the motor draws constant power from the supply lines.
This period is shown by the curve BC.
Coasting period
This period is from T3 to T4, i.e., from C to D. At the instant ‘T3’ power supply to the
traction, the motor will be cut off and the speed falls on account of friction, windage
resistance, etc. During this period, the train runs due to the momentum attained at that
particular instant. The rate of the decrease of the speed during coasting period is
known as coasting retardation. Usually, it is denoted with the symbol ‘ßc’.
Braking period
Braking period is from T4 to T5, i.e., from D to E. At the end of the coasting period, i.e., at ‘T4’
brakes are applied to bring the train to rest. During this period, the speed of the train decreases
rapidly and finally reduces to zero. In main line service, the free-running period will be more, the
starting and braking periods are very negligible, since the distance between the stops for the main
line service is more than 10 km. Speed–time curve for suburban service In suburban service, the
distance between two adjacent stops for electric train is lying between 1 and 8 km. In this service,
the distance between stops is more than the urban service and smaller than the main line service.
The typical speed–time curve for suburban service is shown in Fig. 10.2.
Utilisation of Electrical Energy
Fig. 10.2 Typical speed–time curve for suburban service
The speed–time curve for urban service consists of three distinct periods. They are:
1. Acceleration.
2. Coasting.
3. Retardation.
For this service, there is no free-running period. The coasting period is comparatively
longer since the distance between two stops is more. Braking or retardation period is
comparatively small. It requires relatively high values of acceleration and retardation.
Typical acceleration and retardation values are lying between 1.5 and 4 kmphp and 3 and
4 kmphp, respectively. Speed– time curve for urban or city service The speed–time curve
urban or city service is almost similar to suburban service and is shown in Fig. 10.3.
Fig. 10.3 Typical speed–time curve for urban service
In this service also, there is no free-running period. The distance between two stop is less about 1
km. Hence, relatively short coasting and longer braking period is required. The relative values of
acceleration and retardation are high to achieve moderately high average between the stops. Here,
the small coasting period is included to save the energy consumption. The acceleration
Page 5
Utilisation of Electrical Energy
Electric Traction-II,
INTRODUCTION
The movement of trains and their energy consumption can be most conveniently
studied by means of the speed–distance and the speed–time curves. The motion of
any vehicle may be at constant speed or it may consist of periodic acceleration and
retardation. The speed–time curves have significant importance in traction. If the
frictional resistance to the motion is known value, the energy required for motion of the
vehicle can be determined from it. Moreover, this curve gives the speed at various time
instants after the start of run directly. TYPES OF SERVICES
There are mainly three types of passenger services, by which the type of
traction system has to be selected, namely:
1. Main line service.
2. Urban or city service.
3. Suburban service.
Main line services
In the main line service, the distance between two stops is usually more than 10 km. High
balancing speeds should be required. Acceleration and retardation are not so important.
Urban service
In the urban service, the distance between two stops is very less and it is less than 1
km. It requires high average speed for frequent starting and stopping.
Suburban service
In the suburban service, the distance between two stations is between 1 and 8 km. This service
requires rapid acceleration and retardation as frequent starting and stopping is required.
SPEED–TIME AND SPEED–DISTANCE CURVES FOR DIFFERENT SERVICES
The curve that shows the instantaneous speed of train in kmph along the ordinate and time in
seconds along the abscissa is known as ‘speed–time’ curve. The curve that shows the distance
between two stations in km along the ordinate and time in seconds along the abscissa is known as
‘speed–distance’ curve. The area under the speed–time curve gives the distance travelled during,
given time internal and slope at any point on the curve toward abscissa gives the acceleration and
retardation at the instance, out of the two speed–time curve is more important.
Utilisation of Electrical Energy
Speed–time curve for main line service Typical speed–time curve of a train running on
main line service is shown in Fig. 10.1. It mainly consists of the following time periods:
1. Constant accelerating period.
2. Acceleration on speed curve.
3. Free-running period.
4. Coasting period.
5. Braking period.
Fig. 10.1 Speed–time curve for mainline service
Constant acceleration
During this period, the traction motor accelerate from rest. The curve ‘OA’ represents
the constant accelerating period. During the instant 0 to T1, the current is maintained
approximately constant and the voltage across the motor is gradually increased by
cutting out the starting resistance slowly moving from one notch to the other. Thus,
current taken by the motor and the tractive efforts are practically constant and
therefore acceleration remains constant during this period. Hence, this period is also
called as notch up accelerating period or rehostatic accelerating
period. Typical value of acceleration lies between 0.5 and 1 kmph. Acceleration is
denoted with the symbol ‘a’.
Acceleration on speed-curve
During the running period from T1 to T2, the voltage across the motor remains constant and
the current starts decreasing, this is because cut out at the instant ‘T1’. According to the
characteristics of motor, its speed increases with the decrease in the current and finally the
Utilisation of Electrical Energy
current taken by the motor remains constant. But, at the same time, even though train
accelerates, the acceleration decreases with the increase in speed. Finally, the
acceleration reaches to zero for certain speed, at which the tractive effort excreted by
the motor is exactly equals to the train
resistance. This is also known as decreasing accelerating period. This period is shown
by the curve ‘AB’.
Free-running or constant-speed period
The train runs freely during the period T2 to T3 at the speed attained by the train at the
instant ‘T2’. During this speed, the motor draws constant power from the supply lines.
This period is shown by the curve BC.
Coasting period
This period is from T3 to T4, i.e., from C to D. At the instant ‘T3’ power supply to the
traction, the motor will be cut off and the speed falls on account of friction, windage
resistance, etc. During this period, the train runs due to the momentum attained at that
particular instant. The rate of the decrease of the speed during coasting period is
known as coasting retardation. Usually, it is denoted with the symbol ‘ßc’.
Braking period
Braking period is from T4 to T5, i.e., from D to E. At the end of the coasting period, i.e., at ‘T4’
brakes are applied to bring the train to rest. During this period, the speed of the train decreases
rapidly and finally reduces to zero. In main line service, the free-running period will be more, the
starting and braking periods are very negligible, since the distance between the stops for the main
line service is more than 10 km. Speed–time curve for suburban service In suburban service, the
distance between two adjacent stops for electric train is lying between 1 and 8 km. In this service,
the distance between stops is more than the urban service and smaller than the main line service.
The typical speed–time curve for suburban service is shown in Fig. 10.2.
Utilisation of Electrical Energy
Fig. 10.2 Typical speed–time curve for suburban service
The speed–time curve for urban service consists of three distinct periods. They are:
1. Acceleration.
2. Coasting.
3. Retardation.
For this service, there is no free-running period. The coasting period is comparatively
longer since the distance between two stops is more. Braking or retardation period is
comparatively small. It requires relatively high values of acceleration and retardation.
Typical acceleration and retardation values are lying between 1.5 and 4 kmphp and 3 and
4 kmphp, respectively. Speed– time curve for urban or city service The speed–time curve
urban or city service is almost similar to suburban service and is shown in Fig. 10.3.
Fig. 10.3 Typical speed–time curve for urban service
In this service also, there is no free-running period. The distance between two stop is less about 1
km. Hence, relatively short coasting and longer braking period is required. The relative values of
acceleration and retardation are high to achieve moderately high average between the stops. Here,
the small coasting period is included to save the energy consumption. The acceleration
Utilisation of Electrical Energy
for the urban service lies between 1.6 and 4 kmphp. The coasting retardation is about
0.15 kmphp and the braking retardation is lying between 3 and 5 kmphp. Some typical
values of various services are shown in Table. 10.1.
Table 10.1 Types of services
SOME DEFINITIONS
Crest speed
The maximum speed attained by the train during run is known as crest speed. It is
denoted with ‘Vm’.
Average speed
It is the mean of the speeds attained by the train from start to stop, i.e., it is defined as the ratio
of the distance covered by the train between two stops to the total time of rum. It is denoted
with ‘Va’.
where Va is the average speed of train in kmph, D is the distance between stops in
km, and T is the actual time of run in hours.
Schedule speed
The ratio of the distance covered between two stops to the total time of the run
including the time for stop is known as schedule speed. It is denoted with the symbol
‘Vs’. where Ts is the schedule time in hours.
Schedule time
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