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International Journal of Advanced Research in Engineering and Technology IN ENGINEERING
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 7, November - December 2013, pp. 109-119
© IAEME: www.iaeme.com/ijaret.asp
Journal Impact Factor (2013): 5.8376 (Calculated by GISI)
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IJARET
©IAEME

DEMAND BASED OPTIMAL PERFORMANCE OF A HYDROELECTRIC
POWER PLANT
Shambhu Ratan Awasthi1, Vishnu Prasad2, Saroj Rangnekar3
1

Department of Energy, Maulana Azad National Institute of Technology, Bhopal, India
2
Department of Civil Engineering, Maulana Azad National Institute of Technology,
Bhopal, India
3
Department of Energy, Maulana Azad National Institute of Technology, Bhopal, India

ABSTRACT
Climate change is emerging as one of the greatest challenges of 21st century for which fossil
fuels are mainly responsible which emit green house gases. In order to meet this challenge, it is
necessary to adopt alternative sources of energy and make optimum use of natural resources,
predominantly water. The paper presents a concept for regulating the release of water so as to
achieve optimal performance of the units in a of hydro power plant while meeting the load demand.
Present work considers all the hydraulic and electrical losses in a hydro power plant and meets the
load demand with minimum quantity of water. The concept is applied to an operational 8x125 MW
Indira Sagar hydroelectric power plant in India and conservation of water is computed in three cases
viz. near rated head, below rated head and above rated head.
Keywords: Optimal Performance, Head Loss in Starts/Stops, Hydro Power Plant, Tail Race Level,
Turbine Efficiency, Water Conservation.
1. INTRODUCTION
In order to mitigate the challenges imposed by the climate change, it is necessary to minimize
dependency of power on fossil fuels and make optimum use of natural resources in a sustainable
manner. The reduction in per capita availability of water necessitates meticulous attention on water
management. In view of this, efficient operation of hydro power plants is drawing more attention of
the researchers in the 21st century.
Variation in turbine efficiency play an important role in the optimum generation scheduling.
Polynomial functions of 2nd and 4th degree are used to model the efficiency of turbine-generator.
109

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

Difference in efficiency obtained from these two models is found to be negligible[1]. In generation
scheduling of hydro power plants, it is observed that all the hydraulic and electrical losses are not
considered [2, 3]. The concept of start-up and shut-down for hydro power plants is presented from
cost considerations due to wear and tear caused by start-ups and shut-downs [4, 5]. The start-up and
shut-down processes are phased out and loss of water is modeled mathematically [6]. Strategic
planning for enhanced generation with same quantity of water is presented [7] which is achieved by
optimal operation of large hydroelectric power plants [7].
This paper presents a concept of running the optimum number of units at maximum turbine
efficiency to meet the load demand in a short term scheduling of 24-hours so that water required is
minimised. The concept is demonstrated by applying to an operational 8x125 MW hydroelectric
power plant under three conditions, namely, near rated head, below rated head and above rated head.
2. PROBLEM FORMULATION
In this work, the load demand is met by optimizing the quantity of water used. This is
achieved by optimum selection of turbine units and their operation at maximum efficiency.
2.1 Objective function

(1)
subject to constraints :

(2)
m ≤ n
2.2 Bounds

(3)

Reservoir level
Turbine discharge
Unit output
Head

: MDDL ≥ Hlh ≤ FRL
: Qmin < Q
< Qmax
: Pgmin < Pgeach < Pgmax
: Hmin < Hnet < Hmax

3. COMPUTATION OF PARAMETERS
3.1 Turbine output
It is computed in kW as:
Pt

= 9.8*Q*Hnet*Et

(3)

3.2 Turbine efficiency
In a Francis turbine, variation in efficiency with output is large as shown in Fig. 1 and plays
an important role in optimum generation scheduling. Turbine efficiency is read from hill curves of a
prototype.

110


Fig. 1. Variation in turbine efficiency with output at rated head

3.3 Electrical losses in transfer of power from generator to switchyard are computed as the
difference between generated power and dispatched power
3.4 Turbine output is obtained from generator efficiency curve
3.5 Head water level is read from the level measuring instrument
3.6 Hydraulic losses in water conductor system are directly proportional to the square of discharge.
It is calculated as equivalent head loss to obtain net head
3.7 Start–up/Shut down : Water required till loading of the units during start-up and then during
shut-down do not contribute in generation of power. This loss of water is taken into account
using empirical formulae given below :
3.7.1 Loss of Water in each Start-up
(4)
In case of Indira Sagar Project, it works out to be 5700 m3
3.7.2 Loss of water in each shut-down
(5)
In case of a Indira Sagar Project, it works out to be 7000 m

3

4. COMPUTATION OF OPTIMUM PERFORMANCE
The computation is carried out in three stages:
Stage-I : computation of initial net head
For a given load demand, compute gross head, plant discharge, maximum turbine efficiency. Obtain
net head by subtracting head loss from gross head.
111


Stage-II : Computation of final net head
Compute plant discharge, tail water level, head loss and net head iteratively to obtain final value of net
head. Compute number of units to operate.
Stage-III : Optimization and optimality check
The development of computer program is shown in the form of a flow chart in Fig. 2.

Fig. 2. Flow – chart for computation of optimal performance
112


5.

APPLICATION TO A HYDROELECTRIC POWER PLANT

The concept is applied to a 8x125 MW Indira Sagar hydroelectric power plant situated in the
state of Madhya Pradesh in India. Relevant project data are given in Table 1.
Table 1: Relevant Data of Indira Sagar Project
Description
Data
Reservoir gross storage
12.22 Billion m3
capacity
Reservoir area at FRL
913 km2
Rated head
60 m
Turbine output
125 MW + 10% overload
Rated discharge
229.5 cumecs
The optimisation is carried out for 24-h in different seasons of a year for different head
conditions. The optimisation is applicable when number of units in operation are two or more. Water
requirement on a typical day under following two situations are computed :
(i) on the basis of ‘Daily Report’ of Indira Sagar Project
(ii) as per the proposed methodology for same generation by operating turbines at maximum
efficiency
Above two water requirements are compared to obtain water conservation.
Case-I : Operation at above rated head
Following data on a typical day in November is taken from ‘Daily Report’.
Energy generated
= 6.7183 MU
Energy dispatched
= 6.6982 MU
Energy transfer efficiency
= 0.997%
Average reservoir elevation
Average plant discharge
Cumulative volume of water released in 24 h

= 259.855 m
= 498.25 cumecs
= 43.0488 million m3

No. of start-ups
No. of shut-downs
Water loss in start-ups
Water loss in shut-downs
Water utilized in generation

=10
=9
= 10 x 5700 = 57,000 m3
= 9 x 7000 = 63,000 m3
= 43.0488 – 0.12 = 42.9288 million m3

The units are operated in different time periods as per ‘Load Dispatch Schedule’. As a
general practice, units are equally loaded without any consideration of turbine efficiency. For each
head there is a maximum turbine efficiency. Tail water elevation, net head and plant discharge are
computed while operating the turbines at maximum efficiencies as given in Table 2. Duration of
operation is computed for total quantity of water i.e. 42.9288 million m3. For example, duration of
operation of 2 units is calculated as 25.17 hr (42928800 x 3600/473.72).
113


Table 2 : Plant Discharge and Duration of Operation
Units in Tail water Net head Maximum
Plant
Duration of
operation level (m)
(m)
turbine
discharge
operation
(No.)
efficiency
(cumecs)
(hr)
2
194.163
64.621
0.94991
473.72
25.17
3
194.499
64.287
0.95004
710.11
16.79
4
194.838
63.949
0.95015
946.19
12.60
5
195.181
63.608
0.95026
1181.96
10.09
6
195.520
63.271
0.95036
1417.45
8.41
7
195.854
62.937
0.95044
1652.66
7.22
8
196.190
62.603
0.95052
1887.59
6.32
As per the optimization methodology i.e. by operating the units at maximum turbine
efficiency, duration of operation for same generation is obtained. For example, to generate 6.7183
MU of energy, 2 units will operate for 24.43 hr (6.7183 MWh/275 MW) as given in Table 3.
Table 3 : Water Conservation in Power Generation of 6.7183 MU
Units in Output of Total output Duration of Total water Total water
of units
operation
required
conserved,
operation each unit
(No.)
(MW)
(MW)
(hr)
(million m3) (million m3)
2
137.50
275.00
24.43
41.6630
1.2658
3
137.50
412.50
16.29
41.6355
1.2933
4
137.50
550.00
12.22
41.6081
1.3207
5
137.50
687.50
9.77
41.5807
1.3481
6
137.01
822.06
8.17
41.7029
1.2259
7
136.21
953.49
7.05
41.9208
1.0080
8
135.41
1083.32
6.20
42.1418
0.7870
Upto 5 units, power output of each unit at maximum turbine efficiency is more than
permissible maximum output limit of 137.5 MW. Hence, it is desirable to maximize generation by
operating the units at their maximum output limits irrespective of turbine efficiency. In the present
case, as per Table 3, the load demand will be met by operating 3 units at maximum output limit of
137.5 MW which will result in water conservation of 3.01%. For different number of units in
operation, water conservation from 1.83% to 3.14% will be achieved for same generation as shown
in Fig. 3.

Fig. 3. Variation in water conservation above rated head
114


It is observed from Fig. 3 that there is a rising trend in water conservation upto 5 units when
each of them operate at their maximum output limit of 137.5 MW though at sub-optimal turbine
efficiencies. When 6th unit onwards are added, they operate below maximum output limit but at
maximum turbine efficiency. Effect of reduction in net head caused by rise in tail race level is
visible with the addition 6th unit onwards, resulting in reduced water conservation.
Case-II : Operation near to rated head
Following data on a typical day in the month of February is taken from ‘Daily Report’.
Energy generated
= 2.15 MU
Energy dispatched
= 2.1251 MU
= 0.98842%
= 255.375 m
= 168.98 cumecs
Cumulative volume of water released in 24-hr = 14.599872, say 14.6 million m3
No. of start-ups
No. of shut-downs
Water loss in shut downs

= 6
= 6
= 6 x 5700 = 34200 m3
= 6 x 7000 = 42000 m3
= 14.6 – 0.0762 = 14.5238 million m3

Tail water elevation, net head and plant discharge are computed while operating the turbines at
maximum efficiencies. Duration of operation for total quantity of water i.e. 14.5238 million m3 is
computed on the basis of plant discharges given in Table 4.
Net head
Maximum
Plant
Duration of
Units in Tail water
turbine
discharge
operation
operation level (m)
(m)
efficiency
(cumecs)
(hr)
(No.)
1

193.835

60.487

0.95079

235.06

17.16

2

194.171

60.326

0.95080

470.01

8.58

3

194.513

59.985

0.95080

704.60

5.73

4

194.838

59.661

0.95079

938.96

4.30

5

195.172

59.328

0.95078

1173.04

6

195.507

58.995

0.95075

1406.87

3.44
2.87

7

195.837

58.666

0.95072

1640.46

2.46

8

196.170

58.334

0.95068

1873.80

2.15

It is observed from Table 4 that net head available is near rated head of 60 m. Power output,
duration of operation and water conservation are computed at maximum turbine efficiency as given
in Table 5.

115


Table 5 : Water Conservation in Power Generation of 2.15 MU
Units in Output of Total output Duration of Total water Total water
operation each unit
of units
operation
required
conserved
(No.)
(MW)
(MW)
(hr)
1
130.17
130.17
16.517
13.9768
0.5470
2
129.99
259.98
8.270
13.9929
0.5309
3
129.18
387.54
5.548
14.0724
0.4514
4
128.41
513.63
4.186
14.1494
0.3744
5
127.62
638.08
3.369
14.2291
0.2947
6
126.82
760.94
2.825
14.3102
0.2136
7
126.04
882.29
2.437
14.3911
0.1327
8
125.25
1002.01
2.146
14.4741
0.0497
It is observed from Table 5 that generation required is so small that it is met by operating
only 1 unit at maximum turbine efficiency which results in water conservation of 3.77% as shown in
Fig. 4. As the number of units are increased, there is decrease in conservation of water.

Fig. 4. Variation in water conservation near rated head
Case-III : Operation below rated head conditions
Following data on a typical day in the month of May is taken from ‘Daily Report’.
Energy generated
= 4.976 MU
Energy dispatched
= 4.8709 MU
= 0.97888%
Cumulative volume of water released in 24 h

= 248.72 m
= 446 cumecs
= 38.5344 million m3

No. of start-ups
No. of shut-downs
Water loss in shut-downs
Total water loss in start-ups and shut-downs

=6
=5
= 6 x 5700 = 34200 m3
= 5 x 7000 = 35000 m3
= 69200 m3 = 0.0692 million m3
= 38.5344 – 0.0692 = 38.4652 million m3
116


Tail water elevation, net head and plant discharge are computed while operating the turbines
at maximum efficiencies. Duration of operation for the total quantity of water i.e. 38.4652 million
m3 is computed on the basis of plant discharges given in Table 6.
Units in Tail water Net head Maximum
Plant
Duration of
(m)
operation
operation level (m)
discharge
turbine
(cumecs)
(hr)
(No.)
efficiency
2

194.162

53.528

0.94902

464.94

22.98

3

194.495

53.197

0.94884

697.06

15.33

4

194.823

52.871

0.94866

928.96

11.50

5

195.152

52.544

0.94847

1160.63

9.21

6

195.483

52.216

0.94827

1392.07

7.68

7

195.812

51.890

0.94808

1623.29

6.57

8

196.140

51.567

0.94787

1854.29

5.76

Power output and duration of operation are computed at maximum turbine efficiency. Water
conservation achieved is given in Table 7.
Table 7 : Water Conservation in Actual Power Generation of 4.976 MU
Duration of Total water Total water
Units in Output of
Total
operation each unit output of
operation
required,
conserved,
(MW) units (MW)
(No.)
(hr)
2

113.84

227.68

21.86

36.5907

1.8745

3

113.05

339.15

14.67

36.8203

1.6449

4

112.28

449.10

11.08

37.0475

1.4177

5

111.50

557.50

8.93

37.2924

1.1728

6

110.71

664.28

7.49

37.5425

0.9227

7

109.94

769.55

6.47

37.8577

0.6075

8

109.16

873.30

5.70

38.0254

0.4398

It is seen from Table 7 that unit output decreases with the increase in number of units. It is
due to reduction in net head with increase in plant discharge. Hence, it is most advantageous to
operate minimum number of units. In this case, operation of 2 units as above will meet the load
demand efficiently with water conservation of 4.87%. Variation in water conservation from 1.14%
to 4.87% with number of units in operation is shown in Fig. 7.

117


Fig. 5. Variation in water conservation below rated head
6. CONCLUSION
The concept of demand based optimal generation of a hydroelectric power plant is developed
on the basis of operation of turbines at maximum efficiency and applied to a multi-unit hydroelectric
power plant. It is found that variation in water conservation varies with the head and number of units
to be operated. Maximum upto 4.87% saving in water is achieved when head is below the rated
head. Towards the end of summer season, water level in reservoir is low and hence conservation of
water becomes crucial. It is also found that in all the cases, saving in water is maximum with lesser
number of units in operation.
Using above information, the utilities may coordinate with river control authorities and Load
Dispatch Centre for operation of the units at maximum turbine efficiencies. In summer when
scarcity of water is more and demand of electricity is increased, the role of water management
becomes critical to ensure its optimum utilization. The operation of turbines at maximum efficiency
minimizes vibrations and cavitation which reduces wear-tear and in-turn maintenance cost.
7. ACKNOWLEDGEMENT
The authors gratefully acknowledge Dr. Appu Kuttan K. K., Director, Maulana Azad
National Institute of Technology, Bhopal, India for his encouragement in carrying out research work.
The authors are thankful to NHDC Ltd. for cooperation and sharing of data on Indira Sagar
Hydroelectric Project.
NOMENCLATURE
Et
Etmax
FRL
Hlh
Hmax
Hmin
Hnet
LD
MDDL

efficiency of turbine
max. turbine efficiency
Full Reservoir Level (m)
Elevation of reservoir (m)
maximum head limit (m)
minimum head limit (m)
net head (m)
load demand (MW)
Minimum Draw Down Level
118


m
n
Pgeach
Pgmax
Pgmin
Pi
Pt
POL
PTLi
Q
Qi
Qmax
Qmin
Qrated
ti
T1
T2
T3
T4
Vstart_los
Vstop_los

no. of units in operation
no. of units in power plant
output of each generator (MW)
unit maximum output limit (MW)
unit minimum output limit (MW)
output of ith unit (MW)
output of turbine (MW)
part/over load (MW)
power transfer loss
discharge (cumecs)
discharge of ith turbine (cumecs)
maximum discharge limit of a turbine (cumecs)
minimum discharge limit of a turbine (cumecs)
minimum discharge limit of a turbine (cumecs)
time of operation of ith turbine (s)
time to achieve 90% of rated speed from standstill (30 s)
time to reach synchronous speed and synchronizing (60 s)
time to load the unit after synchronizing (30 s)
stopping time (60 s)
loss of water in one start-up (m3)
loss of water in one shut-down (m3)

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