A General Introduction to Small Hydropower Development:  In Eight Internet Lessons

Lesson 3.  Data requirements – quality and quantity – for hydropower Design.

3.I.   INTRODUCTION

          Basic hydraulic considerations

             Hydroelectric energy technology has been around for a long time.  The basics are rather simple:

  English units-

      where,

           P_kW  is power in kilowatts. 

           Q     is water flow rate in cubic feet per second.

          H     is the net head available to the turbine/generator in feet, and        

           e     is the overall turbine/generator efficiency.

or,       

  Metric units-

         P_{kW  =}  9.81 HQe ,

      where,      

           P_kW    is power in kilowatts

          Q        is in cubic meters per second.

         H         is net head in meters, and

         e         is, as before, efficiency of the system.

        Thus, some of the first things the engineer must determine are (1) how much water is available in a river (and when), and (2) how much head (drop) is potentially available (and when).  From the basic information, he will begin to consider various configurations of dams, penstocks, etc. – including the type and numbers of turbines – in order to minimize the cost while producing the desired amount of power.  He usually conceives a number of possible configurations, each of which must be evaluated in more or less detail.

The turbines that an engineer will consider for modern systems basically fall into two categories:  impulse and reaction.  There are basic differences in their characteristics that should be understood.           

Impulse turbines

 On this kind of turbine, “buckets” on the periphery of a wheel are moved by the force of a jet (or set of jets).  The available (net) head is converted to kinetic energy, of which a portion creates the torque.  Generally, impulse turbines are used for high heads, although at least one modern design is efficiently used for commercial developments in the low-head range.  For mini low-head systems, the Banki turbine has been recommended in many publications.  For higher-head systems, Pelton-type turbines can be efficiently used, as can the Banki.  Figure 3.1 illustrates various impulse turbine runners.

Impulse turbines are enclosed in a case, but operate under atmospheric pressure in air.  There is, therefore, some unused head because they must effectively be set above the tailwater level.  They can be operated below tailwater levels, but then only under positive pressure.                                                                                                 

Reaction turbines

 Reaction turbines are generally of two kinds – mixed flow and axial flow.  Energy is imparted to the turbine from the flowing water by a reduction of pressure and velocity.  On Francis-type turbines, water enters radially, continually impacting the “buckets”, and discharges (usually vertically) down (axially) the center into an expanding draft tube.  Effective head range is quite large, from low- to high-head.  Propeller-type turbines can be serviced by the flow much as a Francis turbine (radially then axially), or in more modern applications (tubular) by designing the water passage purely axially.  In any case, the flow to the propellers is axial.  Effective heads are in the lower to middle ranges.  Reaction turbines take advantage of the total head available to the tailwater level.  As a result, however, the setting of the turbines must be very carefully designed to avoid cavitation.  See Figure 3.2 for illustrations of reaction turbine runners.

          For small installations, the use of propellers and centrifugal pumps run backwards has been found to produce reasonable results.  They have the advantage of being available “off the shelf” throughout the world and thus have a definite importance in development considerations for mini-systems in particular.

     Figure 3.2.  Reaction Turbine Runners.

3.II.  HYDROLOGIC ANALYSES

         The decision to be made concerning the investment in time and money on hydrologic studies is a function of:

·    The kind of study to be done.  Specifically, is it to be a generalized resource study, or is it specific to a development?

·    The level of study to be done.  Is it a reconnaissance, feasibility or design study?

·    The level of project investment. Obviously, the studies that would be made for a 100 MW plant greatly exceed those of a 100 kW or smaller unit.                                                                         

·    Safety considerations. 

         In all cases it should be realized that no level of effort will give 100% hydrological assurance for any investment.  If the studies are done correctly and judiciously they will reduce the margin of possible error.  But it must be realized that we are dealing with analyses of data series that are at best only a small sample of the total population.  Furthermore, we are in most cases forced to assume that the future will, in general, behave like the past.  Although in the short future – which the normal life of investment periods of hydroelectric projects certainly represents – this is probably the most reasonable assumption we can make, there is no proof that that is, in fact, the case.  It only seems reasonable.  In that last word lies what must be a caution to be extended to the person or group doing the studies.  After you have finished your work, step back and ask the simple question:  does it look reasonable?

        I cannot overemphasize this point because too often these days we use computers to do our thinking for us.  There is also a tendency to want to use very sophisticated technologies in all cases – as the expression goes, “using a sledge-hammer to drive a tack.”  Those procedures very often force us to use computers.  And too many people are so in awe of computers that they refuse to believe that anything coming out could be less than perfect – no matter what.  “Garbage in … Gospel out”.  Please remember the accuracy of your streamflow data when you start to run your calculations out to the fourth or fifth decimal place.

        When preparing to do a study, one should ask, is this the best way to do the study?  Is it necessary to do it this way?  Does it really apply to the circumstances?  And, of course, can I base an investment decision on the results?

        If there are special problems in the design of small projects, they certainly involve those of fitting the “mental” approach to the scale of operation.  The economics of small hydro seldom allow the luxury of time and funds characteristic of larger installations.  In small hydro, the feasibility study alone must often be viewed as a significant financial burden warranting an investment-type decision by the potential sponsor. 

        In general, one of two basic questions is to be answered in the hydrologic analysis:

·    How much power/energy can be derived from the development? 

·    Is there sufficient water and head for the amount of power/energy required by the users?

To the first question we must also add the caveat, at what level of installed capacity?  As we all must realize, it is theoretically possible to install almost any size turbine (within reason).  Depending upon the installed capacity, greater or lesser proportions of the available flows will be used for power development.  For extremely large turbines or combinations of turbines of varying capacity, there will be large blocks of time during which some of the equipment will be idle.  For very small installed capacities, there may be large amounts of water that sometimes must be spilled and are thus unavailable for power development.  The design problem is to somehow optimize the level of installed capacity … which in most cases is one involving economic considerations.  That process is discussed later.

          The second question is quite often the easier to develop answers for, although because it is very commonly applied to smaller streams, it also presents us with the dilemma of lack of solid data.  It is this approach that is usually involved in considering the installation of mini-hydro units.  In that case, we might take the inverse approach, where we begin by deciding how much power/energy is required.  We often find that only a portion of a river’s flows may be needed (or, for that matter, permitted to be diverted) for generation purposes.  If the flow is available, then the techniques of diverting the required flows become a technical question.

3.III.    DATA REQUIREMENTS

           Although dam safety, including the safe passage of flood flows, is an extremely important part of dam design, it is not being considered in this introductory course.  In this discussion, the interest is primarily on the hydrologic analyses required to determine power and energy potentials.  In fact, however, the system cannot be designed properly without considering all hydrologic factors.

          For simply determining the amount of potential hydropower that is available, all that is required of the hydrologist, as noted in section I, is streamflow and head.  The various techniques for determining streamflows will be discussed later.  The head available can only be approximated initially, with preliminary estimates commonly taken directly from maps.  Actual heads available under different flow conditions are a function of dam/reservoir design and the operation alternatives as well as topography.

          Until the stream regulation scheme is finalized one can only approximate the level of installed capacity and corresponding energy output.  Nevertheless, such approximations are important in giving preliminary assessments (reconnaissance level) as to the advisability of proceeding further into the investigations.  It should also be noted that the reservoir capacities for small hydro installations are usually small, meaning that most such developments will be close to run-of-river operations.

          Other hydrometeorological factors that may be of importance include precipitation, air pressure (obviously related to the elevation of the development), and those other factors related to evaporation.  In some areas of the world, particularly where reservoirs with large surface areas might be involved, the losses due to evaporation may be significant.  The importance of precipitation is greatly increased where flow data is missing or limited.

          Water quality factors may also be important in the design schemes.  Sedimentation of reservoirs must also be carefully considered.  The chemical quality of the water becomes important primarily from the standpoint of erosion and whether or not the water is suitable for bearing lubrication.  Corrosive water can substantially accelerate pitting damage caused by cavitation, as can the effects of erosive materials.

          The existence of topographical maps will greatly facilitate precise location of developments.  They will, in addition, aid in identifying existing transmission lines (where they may exist), gauging station locations, access, interference with roadways, railroads, etc.  Such information may be very valuable in making preliminary subjective economic decisions concerning site selection.

          The value of short records of hydrologic data can often be greatly enhanced if there exists a network of gauges.  Obviously one cannot retroactively create such networks.  It is therefore important that such activities be given serious consideration immediately.

          In its “Guide to Hydrometeorological Practices”[1] the World Meteorological Organization offers many practical guidelines to subjects that will be of interest to hydropower engineers, with reference to the previous discussion of data acquisition networks.  Concerning the development of a minimum network, the Guide states:

     While a minimum plan should be considered as the first step, it will rapidly become insufficient as countries develop. The establishment of an optimum network would be a much greater undertaking.  Also, the gaps which remain even after the establishment of the minimum network would still be sufficiently large to permit the minimum network to become an integral part of the optimum network with very few and only relatively minor changes.  Nearly all of the stations of the first network will be principal or base stations in the ultimate network.

        The two principal data acquisition networks needed for hydropower studies are those of precipitation and river discharge.  The WMO Guide suggests minimum densities.

        Irrespective of the existence or non-existence of a river discharge measurement network, it may be necessary (or at least extremely desirable) to establish a gauge in the proposed development area.  This will probably be almost imperative in the case of mini-hydro systems.  As a matter of economic realism, considering the level of investment, gauging for the mini-hydro systems will tend to be far less sophisticated than that desired for larger developments.

        Although no two water resource surveys will be the same because of the specific questions being asked and the basic information available, nevertheless, general procedures can be suggested.  The following procedure is suggested by Linsley[2]:

       (a)     Assemble the best available maps of the region, piecing together, if              practical, a single master map to the largest possible scale.  Draw on             the map the outlines of the major river basins concerned in the survey. 

(b)     Assemble or at least determine the location of all pertinent hydrological data files.  Locate on the master map the site of all observation stations using appropriate symbols to indicate the nature of the observation.  If printed instructions for observations are in use collect these. If not, determine by interview the methods of observation and types of instruments employed.  As far as possible evaluate the probable reliability of the various items of data available.  Prepare a bar chart showing the actual period of record for each item of data at each station.  If possible indicate on the chart changes and the estimated reliability of the data.

(c)      Survey all existing literature on the hydrology, climatology, geology and geography of the region.  Prepare a bibliography of this material annotated if possible, for further reference during the survey and future use in other studies.  Read as much of the literature as seems useful and note any information or conclusions which are pertinent to the survey.

(d)     Make a field survey of the region, visiting each of the major climatic and topographic regions.  Insofar as possible check the detail of maps, especially the location of divides and the direction of flow of streams which are often in error on inadequate maps.  Use photographs freely to illustrate the various characteristics of stream channels. Note sites which would be suitable for observation stations, especially streamflow, and for dam sites.  Visit as many observation stations as possible noting condition of equipment, techniques of observation, etc., to support the evaluation of data reliability.

(e)      If the available data are very limited and there is a  prospect of collecting information of value before the completion of the survey recommend the immediate installations of stations.  Crude rain gauges can be fabricated of tin cans or oil drums, staff gauges can easily be made by painting scales on existing structures or on planks, and float measurements of streamflow require little equipment.  The type and quality of observation will depend on the local conditions.  However, even limited data on the low flow of streams or on floods, may prove very useful.

(f)       Outline the studies required in the preparation of the survey report.

         Although the above suggested procedures were recommended for consideration in reaching conclusions concerning water resources surveys in general, the steps are logical for a thorough analysis of hydropower potential.  In particular, it is too easy to overlook the fact that an adequate hydrologic analysis must include an on-the-ground inspection of the area in question.  It is one thing to analyze data that is both accurate and precise.  It is quite another thing to assume that your data is always so.

3.IV.   DATA QUALITY

         The following tests are some of the ways in which the “goodness” of available data can be determined.  Because not all data is invariable in time and space, it is generally desirable to investigate and, where necessary, adjust the series.  However, adjustments should be made without violating the basic integrity of the data.  As the WMO Guide indicates, adjustments are generally made for one or more of three purposes:

·        To make the record homogeneous with a given environment, an example of which is in fitting a uniform period of record for which a “standard period” mean or normal is to be computed.

·        To eliminate, or at least reduce, the effects of changes or otherwise extraneous conditions, for example to correct for changes in gauge location or exposure.

·        To selectively summarize data for presentation or examination, an example of which is the smoothing of isohyetal maps.

          A very common problem faced by hydrologists when beginning a regional study is that gauging stations will have differing periods of record.  This can be particularly important because some gauges may have operated during periods of high water availability while others may have records representing only low periods.  Others may have overlapped both high and low periods.  Attempts to use the records simultaneously could create confusion and misrepresentation of the actual situation.  By the same token, it is important that any procedure used to fill in data gaps not further confuse the situation.

          Attempts to fill in missing data can create false security if one is not extremely careful.  First, it must be realized that the use of correlation or regression analyses dilutes the value of the data.  The filled-in data can only be considered an approximation of what actually occurred.  Furthermore, if the data are to be used in statistical analyses, the use of simple regression analyses will only produce estimates of the means of the missing values.  In such a case, the natural variations about the mean will be eliminated and the overall variance thus diminished.  It has been suggested that when more than two or three data points are being filled in, a random element based on the unexplained variance of the regression equation be added to the mean value determined by the regression.

          A valuable way to begin any study in which regional data are to be used is to plot the series length as a bar diagram as shown in Figure 3.3  From this plot it is possible to conceptualize the optimum period to which all data series can be related.

          Later in this lesson, a procedure is described for extending the base in flow-duration analyses.  In that case, it is the characteristics of the flows rather than the flows themselves that are being extended.

          Normal or mean precipitation can be estimated approximately with the general equation:

                                   =  

 where,

    N = normal (or mean) precipitation

   P = precipitation during a shorter period

   x = station with unknown normal (or mean)

   r = station with known normal (or mean)

          Use of this equation could result in a substantially-in-error estimate, and thus, in practice, selection of comparable stations should be limited to those in close proximity to that of the short-record station.     

          If the normal (or mean) annual precipitations (N) at three stations (a,b,c) are known, missing precipitation data (P_x) at another station nearby can be reasonably estimated by the following equation:

          Where normal (or mean) precipitation values (N) can be established for all stations (such as for an arbitrarily established period of record overlap), the same equation shown above can be used to estimate missing precipitation events.  Use in this case should be limited to precipitation periods of no less than one month’s duration.

           Double-mass analysis

           The method of applying the technique of double-mass analysis is based on the theory that a graph of the cumulation of one quantity against the cumulation of another quantity during the same period will plot as a straight line, so long as the data are proportional.  It is further assumed that a change in the slope represents a change in the proportionality between the variables.

                                            Year

Lesson 4. Streamflow estimation techniques, flow-duration analysis – for hydropower design.

A General Introduction to Small Hydropower Development:  In Eight Internet Lessons

4 (cont. from 3) Streamflow estimation techniques, flow-

duration analysis – for hydropower design

4.V.   STREAMFLOW ESTIMATION TECHNIQUES[1]

          Even though streamflow records may not be available at a       particular site (in fact, this is probably the first law of hydrology – they won’t be), analytical techniques are available if data are available in the region.  The techniques vary, from those that will estimate mean discharges to more complicated modeling procedures requiring specific competences by very experienced hydrologists.

          In areas in which physical characteristics are common and precipitation relatively uniform across the area, discharge will be found to be highly correlated with drainage area.  In its simplest form, discharges may often be proportioned up or downstream from an existing gauge on a ration of drainage areas. 

          Where several physical or hydrologic characteristics modify the runoff significantly, multiple regression techniques have been used to define the flow statistics.  A general relationship widely used for this purpose is:

 DS_i = a₀ X₁^a1X₂^a2X₃^a3….X_n^an

 where,       

 DS_i = the flow statistic of interest; e.g., mean, standard deviation,                  mean annual flood, etc.

  X_i  =   catchment or hydrologic characteristics.

  ai  =   regional coefficients.

          In regions with large orographic influences, the precipitation distribution with elevation can be usefully applied.  Precipitation maps, in particular, may be used to integrate estimated precipitation over all    or parts of the drainage area. This technique was used in the Idaho   (USA) study of potential hydropower developments.   In another study   (of western Washington, USA)[2] regression equations were developed that successfully described varieties of multiple-peaked annual hydrographs (monthly bases), based principally on a description of the percentages of the watershed areas between elevation bands.

          It is important that the investigation include a search of the       existing literature, for many regional analyses may have already been completed.  Two monumental reports that will provide excellent specific and generalized information that could be of valuable assistance have been produced by UNESCO[3].  The data and maps of worldwide water balances will be particularly useful in areas with minimal data.

          A model developed for use where only precipitation and temperature data are available is discussed in the WMO Guide     previously referenced.  The method is based on a relationship between P/E and R/E, where P is the average annual precipitation, R is the average annual runoff, and E is a temperature factor.  Using tables of T and E, and P/E and R/E, the R value (runoff) may be calculated.  Refinements can be made for regions in which most of the precipitation falls within certain seasons.

          Stochastic and deterministic models

          Recognition that the hydrologic cycle is an extremely complex system has led to an increasing awareness that, in the studies of water resource development opportunities, one should maintain a “systems” approach.  Models are a basic element in what has come to be known as “systems analysis” or “operations research.”  The aim of the     process is, of course, to assist in identifying those control measures that will tend to ensure that the planning goals are reached.

          In general, two broad classes of mathematical models can be identified[4] as being of importance from a planning perspective:

(i)               Descriptive simulation models that relate system inputs to outputs by a direct computational procedure and which are usually re-run a number of times to examine the implications of adopting various alternative designs;

(ii)            Analytical optimizing models, particularly of the mathematical programming variety, which seek to determine the optimum manner of achieving an objective.

          Both classes of modeling can be involved in hydropower developments.  The optimization models can be particularly valuable where hydropower is to be added to an existing system in which either (1) thermal systems are reasonable alternatives to be considered, or (2) the existing system contains thermal energy production and (3) the hydropower must be properly valued. 

          In less complex situations, one may be more interested in simulating the hydrologic system than in optimizing the operation, at least during the early stages of investigation.  In mini-hydro investigations, one is probably uninterested, except in a theoretical way, in any simulation whatsoever.

          The classification of simulation models is not all that well defined.  There are those who claim to model the physical processes (in fact, commercial organizations offer this service), while others are presented as being only approximate (based on empiricisms).

          As Diskin[5]  has pointed out:

     The most important problem to the potential user [of models] is probably the choice between the comprehensive model versus the specific model.  The comprehensive model claims that it reproduces all processes that take place in the watershed.  It is thus presented as a tool that can meet the needs of all potential users.  The specific model, as its name implies, is intended to supply one type of design data.  An example of such a model may be one of producing monthly runoff volumes.  Other examples include a model for converting extreme storm rainfalls into design runoff hydrographs.  A specific model also usually produces other data as a by-product, but the accuracy and value of these additional data are inferior to those data for which the model is constructed. 

He concludes:

     Practice gained in the analysis and use of various models appears to be the only tool available to the applied hydrologist for assessing the usefulness of a hydrologic model in the process of planning and management of a water resources project in a given watershed. 

          As a matter of policy, it is probably beneficial to introduce   modeling capabilities early in the planning process, since the   development of capabilities is not without problems inherent in the learning process.  Furthermore, modeling may also assist in guiding the decision to implement data collection networks.  In general two approaches are used in the development of hydrological models:  stochastic or deterministic (and, of course, combination of the two).

          In the stochastic approach, the variables are regarded as being statistical in character, having probability distributions which may be functions of time.  It is important not to be easily deluded by   stochastically generated time-series.  First, the model is absolutely dependent upon historical data for the estimation of the statistical parameters.  The validity of those sample statistics is very much a function of the quality and quantity of the data from which they were determined; however, all suffer from “sample error”.  Second, the basic assumption is that the “world” to be generated synthetically actually is represented by such a model.  Both assumptions can introduce     problems for the conceptualization of the validity (and value) of the results. 

          The main problem in use can often be that referred to earlier:  the computer.  Since it is a very simple matter to program a computer to generate the stochastic data, it is altogether too easy to be misled into      believing that from, say, 10 years of basic data one can generate a 1000-year sequence of more valid events.  The hydrologist should     always keep in mind the length of the historical record upon which his model is based. 

          A final caution in the use of stochastic models:  many series of different lengths can be generated, no one of which will reproduce the historical sequence – in a statistical sense, however, the characteristics    of the generated series will converge to those of the original sample    from which they were derived.  This does not mean anything, except that the model will reproduce the sample.  It should not be used as proof that the extremely long generated series has any inherent greater value.  Nevertheless, there are at least five important values of correctly applied stochastic models:

·        They suggest other (perhaps more critical) orders of equally likely series which can be evaluated for their impact.

·        Even if local data are unavailable, it is possible that a model can be used with statistics determined by regional analyses.

·        It is possible to generate many sequences of possible occurrences from which levels of confidence in their application could be estimated.

·        They can sometimes be used to “fill in” missing data with values that preserve the stochastic nature of the original series.

·        Where they can be applied, as is most often the case, to the rainfall series, and the generated rainfall sequences used with more deterministic rainfall-runoff models in order to generate runoff sequences.

          In hydropower studies we are generally concerned with methods    by which streamflow series can be developed.  Of particular interest     tend to be the rainfall-runoff process models.

          A number of deterministic models exist that variously con-    ceptualize the physical processes within the watershed.  They may be     used with (among others) precipitation data in order to develop the hypothesized streamflow.  One well known example developed by the      US Army Corps of Engineers is the SSARR model.  In this model the precipitation is distributed between runoff and soil moisture recharge.      A soil moisture index and rainfall intensity is required.  Runoff is distinguished between base flow and direct runoff, and the direct runoff    is characterized by subsurface and surface.  Storage zones are fed bythe runoff components, the sum of which is taken as the streamflow for the watershed.  But the model’s accuracy gives satisfactory results only    when sufficient data exist.

          Other more sophisticated models with more complete physical    bases exist.  These models require a great deal more input – rainfall, temperatures, radiation, wind speeds, monthly or daily pan evaporation.  But for the generation of mean monthly data, all of these models tend to    be much too detailed for the level of data commonly available. 

          The choice of model is often guided by the size of the watershed.  Smaller watersheds will probably be more suitable for representation by the more highly detailed physically-based models.  As the area covered increases, there is usually a need to employ larger time units in  the computations, thus the coefficients and parameters tend to depart  from    or can lose their original meaning.

          Finally, there is the natural desire to use models for which the coefficients and parameter values could be easily transferred from a   region of known values to another with insufficient data.  Such       presumed sophistication would be very desirable. 

          Since this series of lessons is not intended to be used as a field manual, the details of streamflow measurement will not be discussed.  Many books (e.g., Inversin[6] would be an excellent choice) and      manuals give excellent advice on various methods by which the flow       can be measured.   For large installations a stream-gauging procedure    will probably involve considerable care and effort by technically trained individuals.  For mini hydro installations the process will more than     likely be undertaken by relatively inexperienced persons.  The guides referred to above will serve to instruct such individuals satisfactorily in    the techniques required.

          It is important that individuals interested in a mini-hydro      installation be aware of the inevitable fluctuations in flow from day to    day and season to season.  In general, these installations will be   concerned with the minimum flows that will be available.  But whether minimum flow or flows during specific seasons are of concern, it is important that the individuals familiarize themselves with the typical patterns of flow in the stream.  This may require measurements over a prolonged period of time.

          One must also determine, as quantitatively as possible, whether     the period during which the measurements were made was wet or dry.     In general, the procedures mentioned before for correlation with other areas will apply; however, this level of sophistication will probably not occur with most mini-hydro developers.  In fact, it is probably     unnecessary since the question most frequently being asked is the availability of firm power during periods of critical streamflow.  For      that estimate only a lower limit is required – and in many cases the   amount of flow in a stream will exceed that which the developer would wish to divert for power.  On the other hand, high flow periods may be equally important for simple run-of-river type projects since during those periods the effective head for small impoundments may prove to be so low as to be of no value in generating electricity.  This point should not be overlooked and may be important in considering installation designs.

          What if you have no data?

          Because the title of this section is one which is raised regularly, in particular by those interested in developing mini-hydro units, it needs careful consideration. First of all, in the absence of any data     (quantitative or qualitative), one would be well advised not to invest any      funds whatsoever.  On the other hand, it would be a rare situation that would preclude any investigation that could provide some guidance.  The point is, if no specific data exist at your site, you should apply the   type of techniques described earlier.  Site visitation is always required – one should never consider a hydrologic study complete without site verification. 

·        Would it not be a professional waste of time (not to mention a personal embarrassment) to find that months of regional     correlation, etc., were valueless because the basic map      erroneously showed the stream flowing in the wrong direction?

·        Furthermore, site visitations should be used to verify office calculations.  And site visitations can provide considerable  qualitative information concerning the history of flow variation: 

·        Flood plain location, vegetative growth variations, material      lodged in trees from previous high flows, etc.  The guesses as to     the true ground contours – trees often grow much better (and     taller) in the low areas – can give erroneous hints.  Maps (and     even aerial photographs) will sometimes suggest smooth     transitions in areas with extreme relief.

4.VI.    FLOW-DURATION ANALYSES

          The characterization of flows at a specific site can be made with varying degrees of sophistication, dictated to a great extent by the availability and type of data.  In general, the only “given” in hydrology      is that there will almost never have been data accumulated precisely  where it is needed.  Thus, almost any hydrologic analysis will require transposition, regionalization, statistical generalization or some other technique for deriving information at a specific site from data gathered at other locations.

          The ultimate goal in the hydrologic analysis would be to develop an appropriate time series of flows at the specific site.  From that time series will ultimately be determined the potential installed capacity and    the energy which can be developed therefrom.       

          Although not the only way the time series can be used, the flow-duration approach is perhaps the most easily understood.  It is     widely used in practice.  In this procedure the data must be condensed      in order to provide working curves.  The very act of condensing can influence the annual energy values calculated.

          In a flow-duration analysis the time series is rank-ordered by   annual, monthly, weekly or daily mean flows according to magnitude.    The use to which the information is to be put determines the choice of   time interval.  The rank-ordered values are then assigned order     numbers, the largest beginning with order 1.   As an alternative approach the series can be ordered by class intervals, with the number in each class interval used in further calculations.  The order numbers are then divided by the total number in the record and multiplied by 100 – thus  representing the percent of time intervals (days, weeks, etc.) that a particular mean flow has been equaled or exceeded during the period of record analyzed.  The flow value is then plotted versus the respective “exceedance percentage”.  As in any statistical analysis, the value of the information contained is a function of the length of record.  References to flow-duration curves are usually made as Q₅₀,  Q₃₀, Q₁₀, etc., indicating the flow values at the percentage point subscripted. 

          As noted before, the choice of time interval or analysis procedure will be governed by the use to which the results will be put.   A very     simple energy model, used for preliminary potential analysis, can be    made on the basis of the daily flow observations over the period of record (approximately 365 x n days, where n is the number of years of record). It must be realized, however, that this ‘daily’ method of analysis submerges low-flow years and low-flow within-year periods in  one overall record.  The percentages indicate the average relative frequency over the period   of record only.  It is helpful when using such a procedure to show typical annual hydrographs as well so that critical within-year periods will be identified (see Figure 4.5).

          The same procedure, with the same limitations, can be done       using monthly mean values. The record in that case will consist of 12n items of data.  Because the monthly mean values will camouflage within-month variations, the flow-duration curve will look somewhat different from a daily flow analysis and, as a result, will be somewhat less useful in design considerations. Of course, the same arguments would   hold for flow-duration curves developed from annual mean values.

          Because flows at specific sites generally follow cyclical variations     as a function of within-year periods, greater value can be derived if the analysis is based on monthly flow-durations.  This may be done in at     least two manners – in one, all data series of n years are used, and the analysis made.  The monthly averages used, however, can mask within-month variations.  Thus, an analysis of all the daily January      flows (in this example) will provide a better basis for design     consideration.  Depending upon the purpose of the analysis, it may         only be necessary to evaluate the critical monthly periods (which for small hydro should include the high-flow as well as the obvious low-flow   months).

          Another procedure might be to attempt to provide “index” years.    In this procedure, the yearly average flow-duration curve is prepared    first.  From this, the K-th percentile index year may be identified.  By   using the historic monthly and daily flows occurring during the selected index year, the capacity and energy characteristics can be determined.  Although this procedure has been called “probabilistic”, it is only the   index year that has any true probabilistic inference.  There is nothing certain about the probability of that year’s within-year distribution of   flow.  Thus, it is very important to inspect that year for any perceived anomalies and, since the acceptance of an “index” year concept is a subjective decision, there may be some advantage to purposely “normalizing” the within-year distribution.  By ordering the index year daily flows, a more realistic and useful flow-duration curve for     determining capacity and annual energy will be available for the      selected year.  It has been suggested that the Q₅₀ index year can offer a good estimate of primary energy, anything above that value being secondary.  Figures 4.6 through 4.8 show some other of the various flow-duration techniques by example.  Experience has shown that the Q₂₀  or Q₃₀  values are good starting places for sizing.

Figure 4.5.  Daily, Monthly and Annual Flow Analysis; Salmon

                                       River at Whitebird, Idaho, USA

Figure 4.6.  Daily Flow Duration Curves for

                    June and January; Salmon River

                    at Whitebird, Idaho, USA.

 Figure 4.7.  Monthly Flow Values from 50% Index     Year and Monthlylow Duration Curve Analyses.

  Figure 4.8.  Correlation Between Kankakee River and

                    Iroquois River, USA, Based on Discharge

                    of Equal Percent Duration (see Table 4.1).

          In some areas of the world, experience may have shown or hydrologic studies may suggest that average annual flows can be    estimated based on some key variables.  In New England (USA), for example, it has been found that the precipitation varies between 20"      and 30" per year.   A useful rule of thumb assumes that 2 cfs per         square mile drainage area as the corresponding 20 to 30 percent exceedance flows.

          More often than not in developing countries the data for site hydrologic analyses will be quite limited.  Even in the United States, a country that by general standards could be considered to have a wealth     of data, it is almost always necessary to adjust remote information.

          A study completed several years ago at the Idaho Water     Resources Research Institute (Idaho, USA) had as one of its goals a complete hydroelectric potential analysis of the Pacific Northwest region   of the United States[7].   In that study it was decided to use the daily flow-duration procedure with accompanying average annual hydrographs.  Since it appeared evident that such a task would greatly exceed the capability to depend upon nearby gauges, a regionalized approach was developed that included availability of an estimate of  mean annual precipitation values. The procedures used permitted the development of synthetic flow-duration curves at any point on any stream in the region, within the constraints of the process.  This, in combination with the site physical data allowed the calculation of the potential energy under a series of assumed installed capacity levels.

          If records are to be compared with each other or used in regional analyses, they should, of course, represent concurrent periods.  It is important that the differences in records reflect those of climate and/or drainage basin characteristics and not simply those of different time periods.  Even if no regional studies are contemplated, it is important to extend the records carefully, and it is possible to add information by so doing.  Techniques were discussed earlier concerning the general     subject of extending records and filling gaps.

          A method for directly extending flow-duration curves has been suggested.  In this procedure, called the Index-Station Method, a relationship is established between two stations.  The procedure begins    by using the data of the overlapping time period to derive two flow-duration curves.  The pairs of discharges corresponding to given exceedance percentages are then plotted against each other (as shown in Figure 3.8).  The graph of equal exceedance for this short period is assumed to represent the relationship between the two stations and,     thus, would correspond for the longer period.  If this can be accepted,    one can enter the graph with the known discharge value at its specified exceedance level in the flow-duration curve of the long-record station and determine the corresponding value (for the same exceedance percentage) of the short-record station.  Table 4.1 illustrates the procedure, the last column representing the short record (Iroquois River) adjusted to comparable long-record values.  Reasonable approximations appear to be possible using this procedure.

          As will be seen later, flow-duration curves can be used (with       other data) to determine optimal installed capacity and the energy    derived therefrom.   However, in its originally calculated form this      method represents conditions without storage.  Its use also assumes that flow sequences are of little importance.

          If it is important that flows not be permitted to drop below some arbitrary but reasonable value, then clearly storage may be required.       In that case the flow below the reservoir will have flow-duration characteristics as indicated in the regulated flow-duration curve shown in Figure 4.9.

Such flow regulation would obviously make the turbines’ use more effective by storing the higher flows when they appear and making them available during times when the flows would have normally been lower.  In Figure 4.9 the volume of flows represented by a-b-c-d must equal that of e-f-g-c-d.   The shaded area represents flow from storage.  As a practical matter, it means that if, for example, we had installed a turbine with flow capacity equal to level f-g, then with the regulated flows it would run for 100% of the time (presumably).  With unregulated flows, it would run under partial loads for periods of time.

ASSIGNMENT:

1.     For a selected watershed in your region find and plot the existing precipitation gauges (see Problem 3 in Lesson 3).

2.     On the map, for Problem 1, locate the possible small hydro plant

     of your interest.  Describe the site hydraulics and geology of the

     site.  What kind of flow regulation do you think might be required

     of the source stream?

3.     *What social, economic and environmental impacts would your

     new power plant cause?  How many people would be affected?

4.     *Locate a stream gauge with at least 20 years of record.  Perform a daily “Index Year” analysis, on the basis of Q₅₀  daily flows. 

 Table 4.1.   Discharge of equal percent duration on two river                        in Illinois, USA

 Figure 4.9.   Regulated and Unregulated Flow-Duration Curve.

A General Introduction to Small Hydropower Development:  In Eight Internet Lessons

Lesson 5 (cont. from 3 and 4).   Determining hydroelectric capacity and energy.

5.VII.        SITE HYDRAULIC AND PHYSICAL   CHARACTERISTICS

          It should be understood that the hydrologic, hydraulic and physical characteristics referred to in this paper are limited in general to those directly influencing the hydroelectric energy generation.   Considerable engineering work will also be necessary for dam design and general safety considerations – including safe and economic flood-flow passage.  Where an existing dam is being considered, it is particularly important that a satisfactory safety inspection be made by a competent engineer.

          The net hydraulic head available for generation of hydro power is, of course, related closely to the development scheme devised.  Where high heads are being developed, the tailwater variations may be minimally important.  However, in lower head systems, it is important to study the site and proposed development scheme carefully to determine the relationship of head to discharge both in the reservoir (where used) and in the tailwater area.  In this case, the maximum head will generally be available at lowest flows, whereas it is quite possible for the available head to be so small at extremely high flows as to make negligible the amount of power produced.

          Although most small hydro developments will tend toward run-of-river, it is quite possible that a reservoir produced may be of sufficient volume to offer some regulation capability.  It is, in any case, necessary to study the reservoir characteristics to determine the area to be inundated.  Characteristics to be determined will include stage-capacity and area-capacity relationships, areal extent, and backwater effects.  The physical characteristics of the dam/reservoir site should also include groundwater and permeability characteristics to ensure the “tightness” of the reservoir.

          Numerous site factors may control the eventual consideration of the potential development scheme.  Many of these deal not so much with the specific site as they do with its relationship to other considerations.  In the previously mentioned University of Idaho study the following were considered in attempting to preliminarily rank the sites according to their potential feasibility: 

·        Transmission line characteristics.

·        Local load characteristics.

·        Land use restrictions.

·        Utility and building displacement.

·        Fish problems.

          The factors considered will vary depending upon the country or region, but a list of considerations should definitely be developed.

5.VIII.   DETERMINING HYDROELECTRIC CAPACITY

          After completion of the basic hydrologic studies, alternative development arrangements can be investigated.  One of the basic considerations is the impoundment or diversion scheme to be used.  If reservoir storage capacity is to be involved, then operation studies may be carried out.  Reservoir operation studies are no more than accounting for water inflows and outflows, probably under some assumed operating schedules, to allow for safe flood passage, energy production, etc.  A proper operation study will consider, where appropriate, reservoir volume loss due to sediment accumulation and water losses due to evaporation.

          The information series available will, to a great extent, control the detail of the analysis.  The availability of computers for calculation will greatly facilitate the handling of the data and will permit the investigation of a variety of alternative schemes.

          A means of estimating the reservoir size that will be required to satisfy specified flow demand is Mass Curve Analysis.  The details of this basic procedure, which are surely known to all civil engineers, will not be described here.  However, it should be noted that there are many variations of the basic approach, a number of which are included in an excellent book by McMahon and Mein[1].

          The flow-duration approach to power and energy basically assumes no storage for flow regulation.  It does permit, however, the incorporation of variable efficiencies of electric energy production as well as the relationship between effective head and discharge rate.  A number of alternative installations can be analyzed and cost comparisons made for eventual use in optimizing the system design.

          The typical development will probably consider variable pitch propellers (Kaplan turbines) very carefully because of the increased cost, in spite of the vastly superior maintained efficiency.  The problem is that the efficiency curve for a fixed-blade system will show a peak at which point the best use of the water occurs.  A hydro plant with a single non-adjustable turbine will then have only one flow with peak efficiency.  For a situation where there is some storage, it is possible that a single unit may be acceptable.

          Where no storage exists, better use of the flow may sometimes be made if multiple turbine units are incorporated.  Multiple units may be of equal size or, for greater overall efficiency, of unequal size.  As Purdy explains[2]:

      A plant with two unequal size turbines has three peak efficiency points; a plant with three unequal size units has seven peak efficiency points.  The ideal sizing is approximately 70-30 and 57-28-15, respectively.

          As he notes, the important advantage is the much improved operation during low flow.  Also, because a large portion of the flow-duration curve is used, the system can be operated much closer to run-of-river with little reservoir draw-down and, consequently, a high average head.

          Figures 5.10 and 5.11 show a simplified example of four equally sized turbines, the operation of which is superimposed first on a typical annual hydrograph, and second on a flow-duration curve[3]. In periods of high water flow, the full capacity of all four units is exceeded – and presumably excess water is being discharged via spillways.  On the other hand, during the period of low flows one unit is used, and then only partially.  Where the flow-duration curve is used (Figure 5.11) it can be seen that (in the example shown) one unit will operate 70 percent of the time at full capacity, two units will operate 40 percent of the time at full capacity, three units will operate 30 percent of the time at full capacity, and four units will operate only 20 percent of the time at full capacity.  In this example, for 20 percent of the time, the flows exceed the turbine capacity and are not available for energy production.  As noted previously, the efficiency curve is considerably flattened with three unequally-sized turbines.

                    Figure 5.10.   Monthly average flows at site, showing

                                              use of multiple turbines.

            Figure 5.11.   Typical presentation of flow-duration data with

                                    multiple turbines.

          It has also been pointed out that, principally for economic purposes, to allow the use of small high speed generators rather than large slow speed generators, speed increasers have often been used between the turbines and the generators.  The speed increaser can also be advantageously applied at sites where large variations in head exist.  It is quite possible under such circumstances that efficiencies may be so low at the extremes that the unit must be shut down.  A suggested way of improving this situation is to provide for a change in turbine speed by installing more than one gear ratio in the speed increaser.  In the synchronous generator arrangement, in which generator speed remains relatively constant, the variable gear ratio will then force a change in turbine speed, thus permitting the turbine to operate more efficiently.

5.IX.  EXAMPLE OF CALCULATING POWER AND ENERGY USING THE FLOW-DURATION METHOD

            Let us assume we are to look at the hydrology of a site for a run-of-river project using a reaction turbine.  We will use the flow-duration curve approach this time.  Other approaches could be used.

          Before beginning, we will need to know the ways in which head losses can occur.  Figure 5.12 illustrates some typical head/flow relationships.

Figure 5.12.   Typical head/flow relationships.

  The following values are first taken from a river flow-duration curve and selected turbine characteristics, assuming the turbine Full-Gate Discharge is 10,000 cfs at 15.50 ft. (at the 0% exceedance).  The head, H, is the net head available when the head difference between the reservoir level and the tailwater level is modified by an estimated head loss in the plant unit and piping.  We then proceed to calculate:  

*    Determined from a stage-discharge relationship and hydraulic losses to the turbine

** Estimated from the manufacturer’s information

### Cumulative Energy beginning with the rightmost column, 1000 kWh

            So, under the assumption that our run-of-the-river plant could use all of the river flow, our scheme would apparently produce 56,576 kWh[4] of energy. 

          What if our turbine full-gate capacity were set at the 20 percent value of the river flow-duration curve, or 4700 cfs at 21 foot head?  The river flow-duration curve would be the same, but because of the differences between reservoir and tailwater levels (note that this is typical of reservoirs and run-of-river plants using reaction turbines) the plant discharge would decrease above the 20% value.  The plant discharges beyond the capacities of the installed turbine are calculated using the following equation: 

            For a presentation describing the ‘why’ of the above equation, look to the last page of this lesson.

where,

Q_i = plant discharge at the 10% and 0% exceedance selected, cfs

Q_c = plant discharge at the 20 % design full-gate capacity, cfs (in this case 4700 cfs)

H_i = net head corresponding to Q_i , ft

H_c = net head corresponding to Q_c , which in this case is 4700 cfs. ft.

   # in this case, the plant and natural discharges and generated power (and energy) from 100% to 20% are identical to the calculations of the first case.

            So, were the turbine full-gate capacity to have been set at the 20% value, the following calculations show what the generated energy would have been.

            A plotting of the power produced against the percent of time it is exceeded (the Power-Duration curve)[5] for a run-of-river development would be as presented in Figure 5.13. 

Fiure 5.13.   Power-duration curve for a run-of-river        hydroelectric plant with the turbine full-gate set at 20%.

          All of this is interesting, but is it merely a mathematical game?  No, certainly not.  It can be used to help find the maximum net benefit from the installation of the most efficient equipment.  The process, which would benefit from a computer program, is as follows:

1.     Obtain the river flow data, and headwater and tailwater elevations for each flow level.

2.     Under the assumption of the required generation equipment, estimate the head loss throughout the hydraulic system, then calculate the net head.

3.     Choose a plant capacity flow, and estimate the plant efficiency.

4.     Calculate the plant discharge at all of the flow values.

5.     Calculate the generated power and energy.

6.     Repeat steps 1 – 5 for several different plant installed turbine capacities.

7.     Estimate the annual plant costs for each of the installed turbine capacities for which you have made these calculations.

8.     Calculate the average expected benefits based on the sale of the energy developed for each installed turbine capacity for which you have made the previous estimates based on the expected value of that energy.                                                                                                                                                                                                                                                                                                                                                                                    

9.     Plot annual costs and benefits against plant turbine capacity power, and find the optimum plant by noting where the maximum net benefit is or where the benefit equals cost (see Figure 5.14, as an example). 

            This procedure is probably more relevant for larger hydroelectric developments, but it does illustrate one of the values of the use of flow-duration curves.  It is important, even for mini or small developments, that a determination is made of the potential capacity and annual energy production.  The hydrologic analysis is the key for calculating the output and benefits for a proposed project.    

Before using historic hydrologic data it is important to know if there have been any changes in the river system during the period of record.  For example, have there been dams constructed, have the reservoirs been used to regulate flow, or have there been diversions for whatever purposes.  If so, of course, the historic flows should be modified (reconstituted) so that the record to be used in the analyses that will follow represents that which the proposed project will face after construction. 

Figure 5.14.   Benefits and Costs Versus Plant Capacity.        

ASSIGNMENT:

1.     *Find a potential site for a mini hydro project.  Then consider and discuss the following aspects as possible restrictions to its development:

·        Transmission line characteristics.

·        Local load characteristics.

·        Land use restrictions.

·        Utility and building displacement.

·        Fish problems.

2.     Locate a dam with data on flow vs. reservoir elevation, and flow versus tailwater elevation.  Plot the data.

3.     Locate a reasonably long historical record of flow (without modifications).  Construct a flow-duration curve.  Assume a hydro plant is to be developed on an existing dam.  Calculate the energy that could be developed if a turbine were installed with a full-gate setting at the 30% flow.  [If you cannot find all the data required, assume some values – e.g., no head losses in the hydraulic system, available overall head variable, but no greater than 50 ft., plant efficiency 90% at all flows.]

4.     *Find a river with an historical flow data series.  Have the flows been modified by man?  Describe what has been done, and how you might go about rectifying the situation.

****Determination of the equation shown on page 78****

1.     At the design point of the turbine, Q = Q_c ,  and in the case of a run-of-the-river design for a reaction turbine,  the turbine is designed to take advantage of the entire river flow at point c.

2.     Since the total flow at this point is going through the turbine, Q_c =  AV_c or,  Q_c = A (2gH_c)^½ = k(H_c)^½, where H_c is, of course, the net head available to the turbine at the design point.

3.     At a point i we need to know the flow through the turbine, Q_i .  But we must do some calculations. Since A is the same, and as a result Q_i is a function, k, which is a function of the turbine design (A exists, but it is not known directly, only indirectly as shown in step 2, above).

4.     Whatever Q_i is, we know it must equal k(H_i)^½ . 

5.     Then, Q_i / Q_c = (H_i)^½/(H_c)^½, or as shown in step 6 (next) and on page 79 (in a slightly different format),

6.     Q_i = Q_c [H_i /H_c]^½      

for each of the 18 major drainage basins (see earlier discussion) were used in a regression analysis to develop equations of the form:   Qi = Ai[QAA] to the Bi        

where,

 A and B are constants determined by regression analysis, and

i  represents the 10, 30, 50, 80 and 95 exceedance percentages.