The document discusses developing a formula to assign a water value to hydroelectric generation reservoirs that accounts for various factors. The proposed formula assigns a water value as a complex number, with the real part representing present water availability and the imaginary part representing future water availability. It aims to make the water value inversely proportional to present storage and future inflow. The formula is designed to generate a contour graph with characteristics including inversely proportional relationships between water value and both present storage and future availability. It also aims to reduce the effect of future inflows on water value as present storage decreases.

1. Water Value for Hydro Generation Reservoirs
S.P.S.M. Sandagiri
070286R
Level 4
Department of electrical engineering
Sri Lanka.
Abstract – Water is a basic need of all human But as the maximum capacities of the reservoirs are
beings. The demand for the water is very large and different to each other the reservoirs can’t be
drastically increasing. But the availability of the compared directly with their amount of water
water to fulfill these needs is not sufficient. Time to available. Such issue is illustrated below.
time this scarcity increased to considerable value. Maximum capacity of the A and B reservoirs are
Hence the value of the water changes with time. As 721MCM and 218MCM. Then consider a situation B
water is considered to a free resource this value is filled with 200 MCM and A to 300 MCM without
variation doesn’t taken in to consideration when having the fact of their maximum capacity those two
most of the decisions are taken. When dispatching can’t be compared. In this occasion although amount
the hydro power plants this value variation makes of water in the A is high the risk of spilling is high in
a considerable effect. The purpose of this research is to the B.
investigate and propose a proper algorithm which In order to address this issue in this analysis all
provides a water value for hydro power plant reservoirs. values are divided from their maximum capacity of
the reservoir. Then the information of the risk of
I INTRODUCTION spilling is embedded there. Same thing should be
done for the Future inflow. Therefore simply water
For thermal power generation the fuel cost is the value can be taken as
most dominant factor which effects to the variable
cost. When there is a scarcity or uncertainty for fuel
that is directly represented by its fuel price. Therefore
the uncertainty factor should not be considered as
separate for thermal power plants. But hydro power
plants are totally different from that. The fuel of Although the behavior of the future inflow function
hydro power is water which can be taken free of is needed to calculate water value it can’t be directly
charge. But scarcity of water can be occurred.. express mathematically. Hence another method
Above mentioned scarcity, changes with time and should be used to convert this pattern change in to
sometimes it add higher value for water. From area to mathematical number.
area reservoir to reservoir this value can be different. Main important things should be considered when
To identify this added value, it is necessary to introducing a method are
introduce a value for water. Pattern of future inflow varies with the time
It is necessary that introduced water Most recent future inflow is more important
value, either represents a value in rupees which can than subsequent future inflow.
directly compare with fuel cost or a value which can This example will illustrate its importance. Consider
be used to compare each reservoir’s water value. In two power plants, one has a good inflow within next
this study more attention is focused to introduce a two three weeks but other has a huge inflow larger
value to compare the hydro power plants reservoirs’ than first one, after 4 months. But first plant should
water. be given a higher priority than second because the
II Objective first one should be used its present water to prepare
Build up a formula for water value which gives a to take that immediate future inflow water. Then take
value to compare the reservoirs. that information into account more weight should be
given to most recent future.
III Investigation Inflow most probably repeats during period of one
Factors which affects the water availability of the year. Hence it is reasonable to consider one year as
reservoirs. time horizon for future inflow.
Present water capacity of the reservoir Below mention equation will covert the pattern into a
Future inflow number as well provides more weight to most recent
Change Rate of the inflow with given time inflow of future.
horizon.(behavior of future inflow function)

2. dispatch that plant although the future
inflow gives an appraisal to the water value.
Hence the effect to the water value from
future inflow should gradually decrease with
Here the f(t) is forecasted future inflow graph of the the storage.
reservoir and the integration time horizon is 12 Then the water value can be given in a 3D graph
months. where x and y axis represents above mentioned real
and imaginary part and the z value represents the
Here weighting function is and
water value. Expected contour curve graph is shown
below. This graph satisfies the all four above mention
Then the value of k=.9999938553 characteristics.
But future inflow can’t be simply added to the
present storage. Because effect to the water value Contour
may not be same from present storage and future curves
inflow. Therefore a constant is defined.
But if it is possible to give these two parameters
separately it will give more detailed idea of the Inflow
reservoir. Therefore the water value can be given as a
complex number.
q
Real part = present water availability
Imaginary part = future water availability. p
Storage
Although this formula provides a detailed idea of the
reservoir it is not comparable. The comparability is
more important for water value. Because it is used to Figure 4
prepare the merit order. Other weakness of this Contour curves of water value
formula is it increase with the water availability. But
more priority is given for lower water values when
dispatch schedule is prepared. Hence this should be Above mention four characteristics has four different
improved. This water value definition can be used in features. There are individual functions which
computer program based analysis where the compare contains these features. Using combination of these
can be done using an algorithm. functions expected function was derived.
As we are interested in a formula which provides a
value to compare the reservoirs it is more Water value=
advantageous if a single value can be given as a
water value. Before going to define such value it is Here a,b,c,d and g are constant. Introducing the
more important to analyze and find what appropriate values for them expected graph can be
characteristics of a water value. obtained.
Characteristics of water value according to above For a=1 and b= 1, c=.8 d=.1 e=2 the graph is shown
defined function, in figure 2. These values give the expected contour
1. It should inversely proportional to the per curve graph. But from power system to power system
unit present storage (Real part). and country to country the there can small changes of
2. It should inversely proportional to future the constants. But the basic shape should identical to
water availability(imaginary part) figure 2.
3. For a constant water value when the future
inflow increase the storage should be
decrease to keep the water value fixed.
4. But when the storage is reduced to a
significant lower level it is impossible to

3. Figure 2
Contour curve graph of the water value
Figure 3
Water value graph