A method is available for estimating the amount of water running through a turbine using a relation between guide vane opening, head and plant discharge. This can be an inexpensive alternative for facilities that are not outfitted with discharge measurement equipment.
By Laufey B. Hannesdottir
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It is important that hydroelectric plant owners know the amount of water used to produce power, as well as how much water is bypassing the hydro plant. A good knowledge of the water resource is vital for planning purposes and, for example, as the basis for a decision on an alternate use of the water. Hydro plant owners need to know how much water is used continuously, every hour of every day, the entire year around. This can only be accomplished by logging these measurements constantly.
To this end, discharge measurement equipment is installed in many of the hydro plants in Iceland that were built after 1990, but such equipment was never installed in many of the plants built earlier than that.
It is common practice to use the power output of a turbine to estimate the water used for power production, by a relation between power output, head and plant discharge. This can be done in power stations where power output and head is recorded continuously. Usually gross head is used because only the water level in the intake pond and the water level downstream is recorded, and so the net head is not known.
But an alternative method is to estimate the amount of water running through a hydroelectric turbine using a relation between guide vane opening, head and plant discharge. This can be done where the guide vane opening is constantly logged. These three parameters already are measured during turbine index testing. This method is not comparable to methods that use precise point measurements of discharge in turbines often used in index and acceptance tests, such as the Winter-Kennedy and Gibson methods. The measurements necessary to calculate precise point measurements of discharge usually are not continuously recorded, and measuring equipment requires much maintenance. This is not the case with the measurement of guide vane opening and gross head.
This methodology has been tested at the 130 MW Sultartangi hydroelectric plant, which began operating in 1998 on the Thjorsa River in Iceland. Ultrasonic discharge measuring equipment supplied by Rittmeyer is installed at this hydro facility, and the discharge calculated using this relationship between guide vane opening, head and plant discharge is compared to the measured discharge. For this plant, a 10 year time series is available for plant discharge, guide vane opening and head in 30 minute resolution. Results from these comparisons show that this method for estimating the plant discharge is acceptably accurate.
Data from index tests performed at two other hydro stations in Iceland also has been analyzed, and a relation between plant discharge, guide vane opening and head has been found, with a good fit between calculated and observed data. This relation can be used to estimate turbine discharge for the available time series of guide vane opening and head.
Francis and Kaplan turbines contain guide vanes that are used to control and regulate discharge through the turbine. These guide vanes regulate the rate of water flow through the turbine by changing the opening between them. Guide vane position often is measured as the servomotor stroke in length units. This measurement has to relate to the actual opening between the vanes. Sometimes the guide vane position is measured indirectly using an electronic governor feedback signal, and this signal is then calibrated to the actual gate positions.
The common form of the relation between guide vane opening, discharge and head is not theoretical, as the hydraulic domain in a reaction turbine is complex and highly dynamic, especially at partial load:
Q = a * GV^b * √H
— Q is discharge in m3/sec;
— GV is guide vane opening in mm;
— H is head in meters; and
— a and b are dimensionless constants.
Results from index tests
Data from an index test performed in July 2000 for the two 65 MW turbines at Sultartangi is used to estimate the relation between guide vane opening and discharge. The testing was performed with both units in operation and with only Unit 2 operating because the relation between discharge and guide vane opening differs depending on how many units are running in the plant. Figure 1, above, shows that the difference in discharge is 0-4% and increases with guide vane opening.
The head change in the index test measurements was only 6 meters. Because a square root is taken on the head, its effect is quite small in the relation. By averaging the measured head for the whole index test, the estimate of the relation changed slightly and the correlation coefficient lowered a fraction. During the operating time of the power station. the head changes have been in the same range as they were in the index test.
The fit of the relation between discharge, guide vane opening and head is good in both cases, when two units are running and when only Unit 2 is running (see Figure 2). The correlation coefficient between observed and calculated data is 0.99 in both cases, explaining 98% of the variance. The standard error for the prediction of flow is 3.6 for Unit 1 and Unit 2 running and 3.2 for only Unit 2 running. For the highest and lowest values of discharge, there is a tendency for calculated discharge to be higher than observed discharge.
Instead of using the proposed form of the relation between discharge, head and guide vane opening, a third degree polynomial can be fitted to the observed discharge and guide vane opening. This gives a very good fit, explaining nearly 100% of the variance and standard error for the prediction of flow of 0.7 for Units 1 and 2 running and an even better fit when only one unit is running. The problem with this method is that only the guide vane opening is used to predict the flow, and not head.
Results of calculated discharge
Data for guide vane opening, discharge and head has been collected at Sultartangi almost continuously since 2000. This gives the opportunity to investigate whether the relation between guide vane opening and discharge changes over a period of time. Results show that the relation has not changed systematically from September 2002 to March 2011.
The accuracy of the ultrasonic equipment used to measure discharge at Sultartangi is ±2%. The accuracy of the head measurements is estimated to be ±1%, but the accuracy of the gate vane openings is not known but is estimated to be about ±2%. Discharge is calculated using all collected data from September 1, 2002, to March 28, 2011, taking out periods when measurements are missing for any of the parameters.
The data is 30 minute average values. The total number of data sets of discharge, guide vane opening and head are about 110,000 for the units. The average observed discharge is 137 m3/sec for Unit 1 and 125 m3/sec for Unit 2.
The water running through the station is from a glacial-fed river with suspended sediments. Despite this, it has not been necessary to replace or repair the guide vanes or turbine blades since they were installed. Although it would be expected for wear of the mechanism that controls the position of the vane gates to show as drift in the difference between calculated and observed discharge, this has not been the case.
The left side of Figure 3, overleaf, shows observed and calculated discharge from April 4, 2003, to April 20, 2003, for Unit 1. The discharge is calculated using the proposed relation between guide vane opening and head and a polynomial of the relation between guide vane opening and discharge. The values calculated using the first method are similar to those observed, and the biggest difference is about 1.5 m3/sec, or ±1%. The values calculated using the polynomial deviate more from the observations, about 2.5 m3/sec or ±1.5%.
The right side of Figure 3 provides another example of observed and calculated discharge from March 7, 2011, to March 17, 2011, for Unit 1. Part of the time, no discharge was observed through the turbine, but calculated discharge for that time was 3-4 m3/sec. The guide vane opening was observed as 0.5 mm, not completely closed, giving this small amount of calculated discharge. This discrepancy can be attributed to measurement error in discharge and guide vane opening.
When the observed discharge is 86 m3/sec, discharge calculated using the first method is 95 m3/sec. The difference is 9 m3/sec, or about 10% of observed discharge. The difference is not so great for discharge calculated using the polynomial method, 5 m3/sec. When observed discharge is greater than 100 m3/sec, observed and calculated discharge is similar and the difference is about 1%.
The best results can be expected for discharge from 100 to 170 m3/sec because this falls within the range of calibration (see Figure 2).
For observed discharge >170 m3/sec, the difference between observed and calculated discharge is high, in many cases >10 m3/sec, and calculated discharge is higher than the observed discharge. The reason for this can be seen in the data from the index test where the calculated discharge deviates from the measurements for the highest values of discharge (see Figure 2).
For observed discharge <100 m3/sec, the difference between observed and calculated discharge is often high. This could be explained as arising from the fact that no attempt is made to estimate a relation between discharge, guide vane opening and head outside the discharge range of the index test. The most frequent operational load of Unit 1 is within the discharge range of the index test, and so for 96% of the time Unit 1 is within that range.
A histogram of the difference between discharge calculated using the first method and observed discharge in Unit 1 for 30 minute values in the range of 100-170 m3/sec reveals that the difference is concentrated around zero. Values of the difference are between ±4 m3/sec 83% of the time and between ±6 m3/sec 90% of the time. This range of difference can be used to estimate the accuracy of the method to be about ±5% or 6 m3/sec. Average differences for all the data is 1.09 m3/sec, which equates to about 1% of mean discharge.
A histogram of the data for Sultartangi Unit 2 is very similar to that for Unit 1. The observed discharge is only in the range of 100-170 m3/sec 76% of the time because it is run at part load to regulate fluctuations in the power distribution system.
Figure 4 shows the daily averages of the difference between calculated and observed discharge for Unit 1 for the whole period of data. The difference fluctuates and is for long periods of time below or above the zero line, but no apparent systematic change in the difference is seen in the data, and during 2005, the difference was below zero for a long time, and in 2007 and 2008 it was above zero.
It is difficult to determine reasons why the difference is above or below the zero line for a long period of time. During the time of observation, no calibrations were done on the measuring equipment for discharge and guide vane opening.
The data for Unit 2 is similar to that for Unit 1. Only data for discharge of 100-170 m3/sec is displayed, and the difference between observed and calculated discharge does not fluctuate as much as for Unit 1.
Index tests from other stations
This method has been tested on two other hydro plants in Iceland. The first, 150 MW Sigalda, began operating in 1977 with three 50 MW Francis turbines. The second is 210 MW Hrauneyjafoss, which began operating in 1981 with three 70 MW Francis turbines.
For these sites, the relation has been found between discharge, guide vane opening and head. Figure 5 show results from data analysis for these sites. In both cases, the fit is good, the correlation coefficient is about 0.995 and the standard error for the production of flow is <1 m3/sec. The fitted relation enables owner Landsvirkjun to calculate water used for the time when continuous measurements of guide vane opening and head are available.
As has been shown, a fairly accurate and inexpensive method to estimate discharge in hydropower turbines is available. If a continuous measurement of guide vane opening is recorded and data from an index test is available, the cost to estimate discharge involves only the cost of performing the required calculations. By comparison, the cost to install discharge measuring equipment varies with the type of generating equipment and situation at the hydropower station and would in most cases exceed $10,000.
The average difference between estimated and observed discharge at the Sultartangi plant is 1% for the whole period of data. Within this period of data, a good fit between observed and estimated discharge is found where the difference is less than 1%. But a bad fit is also found where the difference in estimated and observed discharge is high. Taking the most frequent differences between estimated and observed discharge as an estimate of the accuracy of the method gives a value of ±5% or 6 m3/sec.
The data does not show that the relation between discharge, guide vane opening and head changes with time. This could be expected because of wear of the mechanism that controls this position on the blade angle measurements. The estimate is only good within the discharge values in the index test and not good at the highest and lowest values of discharge.
Finally, it cannot be overlooked that inaccuracy in the observations of discharge, guide vane opening and head can be responsible for apparent discrepancies in estimated discharge and that the measurements have not been controlled in order to secure good results.
Hannesdottir, Laufey B., "Wicket Gate Opening as a Discharge Meter," Proceedings of HydroVision International 2011, PennWell Corporation, Tulsa, Okla., 2011.
Laufey Hannesdottir is a project manager of hydrology in the resources department of Landsvirkjun. Her primary responsibility is to maintain the utility's hydrometric database.