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DEMAND BASED OPTIMAL PERFORMANCE OF A HYDROELECTRIC
POWER PLANT
Shambhu Ratan Awasthi1, Vishnu Prasad
2,
Saroj Rangnekar3
1Department of Energy, Maulana Azad National Institute of Technology, Bhopal, India
2Department of Civil Engineering, Maulana Azad National Institute of Technology,
Bhopal, India 3Department 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.
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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 (3)
2.2 Bounds Reservoir level : MDDL ≥ Hlh ≤ FRL
Turbine discharge : Qmin < Q < Qmax
Unit output : Pgmin < Pgeach < Pgmax
Head : 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.
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
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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 m3
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.
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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
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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
capacity 12.22 Billion m
3
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 = 259.855 m
Average plant discharge = 498.25 cumecs
Cumulative volume of water released in 24 h = 43.0488 million m3
No. of start-ups =10
No. of shut-downs = 9
Water loss in start-ups = 10 x 5700 = 57,000 m3
Water loss in shut-downs = 9 x 7000 = 63,000 m3
Water utilized in generation = 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).
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Table 2 : Plant Discharge and Duration of Operation
Units in
operation
(No.)
Tail water
level (m)
Net head
(m)
Maximum
turbine
efficiency
Plant
discharge
(cumecs)
Duration of
operation
(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
operation
(No.)
Output of
each unit
(MW)
Total output
of units
(MW)
Duration of
operation
(hr)
Total water
required
(million m3)
Total water
conserved,
(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
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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
Energy transfer efficiency = 0.98842%
Average reservoir elevation = 255.375 m
Average plant discharge = 168.98 cumecs
Cumulative volume of water released in 24-hr = 14.599872, say 14.6 million m3
No. of start-ups = 6
No. of shut-downs = 6
Water loss in start-ups = 6 x 5700 = 34200 m3
Water loss in shut downs = 6 x 7000 = 42000 m3
Water utilized in generation = 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.
Table 4 : Plant Discharge and Duration of Operation
Units in
operation
(No.)
Tail water
level (m)
Net head
(m)
Maximum
turbine
efficiency
Plant
discharge
(cumecs)
Duration of
operation
(hr)
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 3.44
6 195.507 58.995 0.95075 1406.87 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.
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Table 5 : Water Conservation in Power Generation of 2.15 MU
Units in
operation
(No.)
Output of
each unit
(MW)
Total output
of units
(MW)
Duration of
operation
(hr)
Total water
required
(million m3)
Total water
conserved
(million m3)
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
Energy transfer efficiency = 0.97888%
Average reservoir elevation = 248.72 m
Average plant discharge = 446 cumecs
Cumulative volume of water released in 24 h = 38.5344 million m3
No. of start-ups = 6
No. of shut-downs = 5
Water loss in start-ups = 6 x 5700 = 34200 m3
Water loss in shut-downs = 5 x 7000 = 35000 m3
Total water loss in start-ups and shut-downs = 69200 m3
= 0.0692 million m3
Water utilized in generation = 38.5344 – 0.0692 = 38.4652 million m3
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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.
Table 6 : Plant Discharge and Duration of Operation
Units in
operation
(No.)
Tail water
level (m)
Net head
(m)
Maximum
turbine
efficiency
Plant
discharge
(cumecs)
Duration of
operation
(hr)
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
Units in
operation
(No.)
Output of
each unit
(MW)
Total
output of
units (MW)
Duration of
operation
(hr)
Total water
required,
(million m3)
Total water
conserved,
(million m3)
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.
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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 efficiency of turbine
Etmax max. turbine efficiency
FRL Full Reservoir Level (m)
Hlh Elevation of reservoir (m)
Hmax maximum head limit (m)
Hmin minimum head limit (m)
Hnet net head (m)
LD load demand (MW)
MDDL Minimum Draw Down Level
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m no. of units in operation
n no. of units in power plant
Pgeach output of each generator (MW)
Pgmax unit maximum output limit (MW)
Pgmin unit minimum output limit (MW)
Pi output of ith
unit (MW)
Pt output of turbine (MW)
POL part/over load (MW)
PTLi power transfer loss
Q discharge (cumecs)
Qi discharge of ith
turbine (cumecs)
Qmax maximum discharge limit of a turbine (cumecs)
Qmin minimum discharge limit of a turbine (cumecs)
Qrated minimum discharge limit of a turbine (cumecs)
ti time of operation of ith
turbine (s)
T1 time to achieve 90% of rated speed from standstill (30 s)
T2 time to reach synchronous speed and synchronizing (60 s)
T3 time to load the unit after synchronizing (30 s)
T4 stopping time (60 s)
Vstart_los loss of water in one start-up (m3)
Vstop_los loss of water in one shut-down (m3)
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