Development of a Computational Interface for Hydropower Plants

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2.1.3. The Turbine Types Interface

This interface is responsible for accepting the user input of the type of turbine used, it has six radio buttons for the following types of turbine: Francis, Kaplan, Propeller, Pelton, Turgo and Cross flow Turbines. It also has a textbox for accepting manual efficiency which is enabled if the user decides not to use the model calculated efficiency and checks the enter efficiency manually radio button, the form also has a textbox that accepts the generator efficiency and a combo box for number of Jets which is used in the efficiency computation of Pelton and Turgo turbines.

2.2. Design Calculations
2.2.1. Turbine Efficiency

The Formulae for calculating the efficiency of the turbines are as given below ^[2]:

Reaction turbine runner size

(2)

where: d = runner throat diameter in m

Q_d = Design flow (flow at rated head and full gate opening in m³/s)

Specific speed

(3)

where:

n_q = specific speed on flow

k = 800 for Kaplan and propeller turbines

k = 600 for Francis turbine

H = rated head on turbine in m

for Francis turbine:

Specific speed adjustment to peak efficiency:

(4)

Runner size adjustment to peak efficiency:

(5)

Turbine peak efficiency:

(6)

where:

R_m = turbine manufacture/design coefficient

Peak efficiency flow:

(7)

Efficiencies at flows below peak efficiency flow:

(8)

Drop in efficiency at full load:

(9)

Efficiency at full load:

(10)

Efficiencies at flows above peak efficiency flow:

(11)

for Kaplan and Propeller turbines:

Specific speed adjustment to peak efficiency:

(12)

Runner size adjustment to peak efficiency:

(13)

Turbine peak efficiency:

(14)

where:

R_m = turbine manufacture/design coefficient

for Kaplan turbines:

Peak efficiency flow:

(15)

Efficiencies at flows above and below peak efficiency flow:

(16)

for Propeller turbines:

Peak efficiency flow:

(17)

Efficiencies at flows below peak efficiency flow:

(18)

for Pelton turbines:

Rotational speed:

(19)

i = number of jets (user – selected value from 1-6)

Outside diameter of runner:

(20)

Turbine peak efficiency:

(21)

Peak efficiency flow:

(22)

Efficiencies at flows above and below peak efficiency flow:

(23)

for Turgo turbines:

(24)

for Cross flow turbines:

Peak efficiency flow:

Efficiency:

(25)

All these formulae were written into codes and during runtime the values they generate are sent to the home form for them to be accessed by other forms, the generator efficiency is stored as well.

2.2.2. The Plant Capacity

The computed capacity of the plant is done using the following equations ^[2]:

(26)

where:

The power duration values are computed using each available flow duration value in the equation as Q

(27)

where:

(28)

l_hydr,max = maximum hydraulic losses specified by the user

(29)

The renewable energy available is the area under the power duration curve and it is computed using the 21 values of power duration in the formula ^[2]:

(30)

where: l_dt is the is annual downtme losses.

3. Results and Discussion

The program interface requires real data from a functioning hydropower plant to ascertain its correctness. At this stage of the development of this interface program, data from Small Hydropower Plants (SHPs) would have been appropriate, however data from SHPs in Nigeria are either difficult to come by or are not available at all. The data of Jebba hydropower plant, Nigeria were obtained and used for the testing ^[9]. Although Jebba power plant is a large hydropower plant, using its data for testing is safe because the formulae for calculating the output of other sizes of hydropower plants are similar to that of small hydropower plant but additional losses need to be considered in the computation.

Figure 2. The loaded flow form

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The input data used for the testing are:

i. The monthly flow data of the river Niger from 1984-2008

ii. Design flow of 380m³/s ^[10]

iii. Head of 27.6m ^[11]

iv. Generator efficiency of 91%

v. Fixed blade (propeller) type turbine

vi. Latitude = 9.138, Longitude = 4.7883 ^[12].

The losses, residual flow and percentage specified for firm flow were however not available. Nonetheless the program interface was however tested without these values because although they are necessary for accuracy, estimation can be made without them, moreover subsequently assumptions of the unavailable values within acceptable range was used to show that if the values were known, the result would have been closer to the actual value.

With all the necessary input obtained, the program was run and tested. From the flow form shown in Figure 2 below, it can be seen that a flow of 3275 m³/s is obtainable from the site only at 1% of the time in a year; also a flow of 1880 m³/s is obtainable at 5% of the time and so on.

It can be seen from the Figure 3 that the flow values have been arranged in 5% increment of percentage equaled or exceeded, these are the values needed for further computation.

Figure 3. The flow duration values

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Because residual flow was not entered it was passed as 0 to the application and that was what was subtracted from the flow duration values, hence the same values for the flow duration are for the available flow duration as well.

3.1. Flow Duration Curve

The flow duration and available flow duration have the same line because they share the same value. The flow duration curve obtained is depicted in Figure 4 below.

The following data were assumed with restriction to their range.

Percentage specified = 50%

Residual flow = 200m³/s

Transformer losses = 0.0125

Parasitic electricity losses = 0.02021

Maximum hydraulic losses = 0.07

Maximum tail water effect = 1

Annual downtime losses = 0.04

Figure 4. The flow duration curve

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3.2. The Power Duration Curve

The power values were equal except the last value because any value larger than the design flow will not be used, rather the design flow will be used in its stead, this is because the turbine cannot utilize more than it is designed to use. This application plotted the curve using the power duration values as shown in Figure 5, and the area under this curve is the renewable energy available.

Figure 5. Power duration curve

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Figure 6. Plant capacity

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