energies

Article A New Optimal Selection Method with Seasonal Flow and Irrigation Variability for Hydro Type and Size

Kiattisak Sakulphan * and Erik L. J. Bohez

Industrial and Manufacturing Engineering Department, School of Engineering of Technology, Asian Institute of Technology, Pathumthani 12120, Thailand; [email protected] * Correspondence: [email protected]

 Received: 19 October 2018; Accepted: 16 November 2018; Published: 20 November 2018 

Abstract: A micro plant of the run-of-river type is considered to be the most cost-effective investment in developing counties. This paper presents a novel methodology to improve flow estimation, without using the flow direction curve (FDC) method, to determine the turbine type and size to operate consistently. A higher precision is obtained through the use of seasonal flow occurrence data, irrigation variability, and fitting the best probability distribution function (PDF) using flow data. Flow data are grouped in classes based on the flow rate range. This method will need a larger dataset but it is reduced to a tractable amount by using the PDF. In the first part of the algorithm, the average flow of each range is used to select the turbine type. The second part of the algorithm determines the optimal size of the turbine type in a more accurate way, based on minimum and maximum flow rates in each class range instead of the average flow rate. A newly developed micro hydropower plant was installed and used for validation at Baan Khun Pae, Chiang Mai Province. It was found, over four years of observation from 2014–2018, that the plant capacity factor was 82%.

Keywords: run-of-river; turbine type and size; streamflow distribution; flow duration curve; hydro turbine; estimation; irrigation demand; energy efficiency

1. Introduction Global installed hydropower capacity has been growing in recent years by an average of 24.2 GW per year. The International Energy Agency has predicted the long-term deployment of hydropower. Installed hydropower capacity will increase to nearly twice the current level of 1947 GW by 2050 [1]. Hydropower plants can be classified based on the installed power generation capacity [2]. When the installed capacity of a hydropower plant is below 10 MW, it is called a small hydropower plant; when the capacity is up to 100 kW, it is called a micro hydropower plant; and when the capacity is below 10 kW, it is called a mini or pico hydropower plant. Micro and pico hydropower plants are usually in the form of run-of-river schemes [3]. Run-of-river hydropower plants are useful in remote areas where there is a need for energy for human development. At the same time, these plants can create sustainable energy with minimal impact to the surrounding area and communities. Electrical production of run-of-river hydropower plants depends on the locally available water resources. In general, the purpose of a hydropower system is to convert the potential energy of the river into mechanical energy in a turbine shaft, which is connected with an electric generator. The output of a hydropower plant is given in terms of power (kW) and electricity production (kWh). The power input is a function of water flow and net head. These variables are needed for evaluating the installed capacity and determining the appropriate turbine type and size.

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Some researchers have presented the advantages of installing several small instead of large ones. Using two or three smaller turbines allows easier control of water usage, although this requires more equipment and carries a higher operational cost [3,4]. Voros et al. [5] presented a short-cut design of small run-of-river hydroelectric plants. The minimum and maximum value of water flow was used in this approach for maximizing economic benefits of investment. Montanri [6] studied the economic compatibility of hydropower plants by regularizing the duration curve and the turbine efficiency. Hosseini et al. [7] determined the optimal installation capacity of existing run-of-river small hydropower plants (SHPs) depending on the amount of annual energy, economy, and reliability. The water flow from the flow duration curve (FDC) was used to calculate the annual energy generated. Anagnostopoulos and Papantonis [8] studied the optimal installation capacity of a run-of-river type SHP to assess the economic benefits of the investment. They optimized two parallel turbines of different types and sizes and found the net present value based on annual energy production. The water flow used in different operating ranges of the turbine is the key to more efficient operation. Santolin [9] presented a techno-economical method for predicting the installed capacity of SHPs. A model was developed on the basis of the flow availability of the site, represented by the FDC. The influence of the design operating conditions based on the FDC was used to determine the turbine size and investment cost. Monterio et al. [10] presented a novel short-term forecasting model of electric power production of existing SHPs. The available water flow was used to determine the power production, economy, and maintenance scheduling of the plants. Bortoni et al. [11] presented a novel methodology for the optimal online operation of hydropower plants provided with a single penstock. This method used the flow rate and head value under several conditions for the optimal distribution of the dispatched power amount. Additionally, Paish [12] presented plans for the future development of run-of-river hydropower plants. Future developments are toward the more accurate and rational sizing of systems to maximize their financial return. Most researchers have focused their attention on the optimal installed capacity and the optimal turbine operation of existing hydropower plants based on the turbine operation flow rate range or the potential energy evaluation from the available water resource, as shown in Table1. They chose the design flow value from the proportion of time a certain streamflow is exceeded which is approximately between 90 to 95% of streamflow occurrence throughout the year from the FDC. Subsequently, the type and size of commercial hydro turbines were considered to optimize the energy production. The results can yield more than one type of turbine for the same operational condition. In general, designs of commercial hydro turbines are standardized, and are not customized for local water resources that are available for all seasons. These commercial turbines are not always operated consistently at the highest efficiency because the design of the turbines is usually determined by the manufacturers. This seems to guarantee that the turbine will operate nearly continuously. However, in reality the operation time is much less than 70%. This could be due to inaccurate FDCs or wrong type and size selection.

Table 1. Research summary of hydropower plant turbine size and type selection.

Turbine Type Selection Turbine Size Selection Author/Reference Comments QHNs FDC PDF TOR EAM Emax Teff PF

√ √ √ √ Investigate the potential Bakis [4] × × × × × × capacity size based on cost estimation √ √ √ √ √ √ √ Maximizing the economic Voros et al. [5] × × × benefits of the plant investment √ √ √ √ √ √ √ √ Method for finding the most Montanari [6] × × economical plant capacity Energies 2018, 11, 3212 3 of 16

Table 1. Cont.

Turbine Type Selection Turbine Size Selection Author/Reference Comments QHNs FDC PDF TOR EAM Emax Teff PF √ √ √ √ √ √ To determine the optimal Hosseini et al. [7] × × × × installation capacity √ √ √ √ √ √ Optimal plant capacity based Anagnostopoulos et al. [8] × × × × on turbine operation

√ √ √ √ √ √ Method for the capacity size Santolin et al. [9] × × × × based on economical parameters

√ √ √ Novel methodology for Monteiro et al. [10] × × × × × × × forecasting the average power production √ √ √ √ √ Novel methodology for the Bortoni et al. [11] × × × × × optimal turbine operation √ √ √ √ √ New method for selecting Rojanamon et al. [13] × × × × × feasible sites

√ √ √ √ To determine the potential Kosa et al. [14] × × × × × × capacity size based on flow and head √ √ √ √ √ √ √ √ √ Novel methodology for the K. Sakulphan et al. × optimal turbine type and size

Notes: Available flow rate (Q), net head (H), specific speed (Ns), flow duration curve (FDC), probability distribution function (PDF), turbine operation range (TOR), economic analysis method (EAM), maximum annual energy production (Emax), turbine efficiency (Teff), plant factor (PF).

According to the Energy Policy and Planning Office, Thailand Ministry of Energy, Thailand has set a target to increase its number of SHPs in 2021 by 20% from the current level. Water resources in many areas of Thailand have been surveyed for the installation of SHPs [13,14]. Additionally, the Provincial Electricity Authority (PEA) has installed run-of-river SHPs in several remote communities in Northern Thailand [15]. There are problems with the hydro turbine currently used by the PEA, as it cannot be operated continuously. The turbine can only work well during the rainy season, which lasts approximately five to six months. In dry seasons, the water flow into the system is quite low and not sufficient to operate the turbine. Average data collected over 25 years for six run-of-river SHPs of the PEA are shown in Table2, and confirm the problem that the average electrical power production value of each hydropower plant is quite different from the installed capacity. This is because the available streamflow value at each site was overestimated from the FDC in order to achieve a high installation capacity in the wet season. However, there is a problem in the dry season. Additionally, the ratio of average electrical power production to installed capacity for each hydropower plant capacity factor is less than 50%, which confirms the above problems and includes the effect of the economic returns from the project.

Table 2. The annual data for hydropower plants under Provincial Electricity Authority (PEA) supervision; Maintenance Production System Division [16].

The Average over 25 Years Mae Tian Mae Jai Mae Ya Mae Pai Mae Thoei Baan Khun Pae 1. Hydro turbine type Francis Francis Turgo Turgo Turgo Turgo 2. Total investment cost (MUSD) 3.13 2.29 1.28 4.47 2.52 0.212 3. Installation capacity (kW) 965 × 2 875 1150 1259 × 2 2,250 90 4. Average annual energy production (kWh) 4,370,199 1,926,524 4,334,214 8,015,167 7,993,557 115,523 5. Average maintenance cost (USD/kWh) 0.000975 0.002064 0.000688 0.000448 0.000614 0.009875 6. Average electrical power production (kW) 498.9 219.9 494.8 915.0 912.5 13.2 7. Plant capacity factor (%) 25.85 25.13 43.02 36.34 40.56 14.67

This paper presents a new way to obtain a more precise flow rate estimation without using the FDC method to determine the optimal turbine type and size, to allow consistent turbine operation throughout the year. This higher precision is obtained using the seasonal flow occurrence data, Energies 2018, 11, 3212 4 of 16 irrigation variability, and fitting a probability distribution function (PDF) using the observed flow data. This approach provides a more precise estimation than the FDC method. Additionally, for the turbine size selection, the use of the minimum and maximum flow rate of operation is used to optimize Energies 2018, 11, x FOR PEER REVIEW 4 of 16 the operation time. The final results of this algorithm are optimal turbine type and size based on the maximum annual energy production. This case study uses actual streamflow data from the Baan Khun the Baan Khun Pae River, Chom Thong District, Chiang Mai Province, Thailand, including Pae River, Chom Thong District, Chiang Mai Province, Thailand, including information from the Baan information from the Baan Khun Pae micro hydropower plant. Khun Pae micro hydropower plant. 2. Potential Energy Estimation 2. Potential Energy Estimation

2.1. Historical Historical Flow Flow Data Historical flow flow data were obtained from the main river gauge station data at the Royal Royal Irrigation Irrigation Department (RID) in Thailand. Historical Historical streamflow streamflow data data were were used used to consider streamflow streamflow trends and variability. Data for the closest gauge statio stationn to the study site, located at the Num Mae Cheam River, were available from 1953 to 2007. The catchm catchmentent area of this gauge station covered the Baan Khun Pae (BKP) River; the distance between the gauge station and the BKP River is approximately 12 km. The The tendency tendency of of streamflow streamflow occurrence occurrence for th thee streamflow streamflow data recorded at this gauge station did not have an exact pattern. The The variance variance of of hist historicalorical streamflow streamflow data data can can be expressed by the standard deviation (SD). (SD). The The SD SD of streamflow streamflow data set in each month are shown in Figure 11.. AA lowlow SD in March shows that the streamflow streamflow data points tended to to be very close to the mean or monthly average value. The The variance variance of of streamflow streamflow occurrence in this month is small, which is more accurate forfor prediction. On On the the other other hand, hand, the the high high SD SD in in September shows shows that that the streamflow streamflow values are spread out over a large range. Therefore, the predic predictiontion of the streamflow streamflow occurrence in this month will be less accurate.

180 /s) 3 160 Mean-STD 140 Mean+STD 120 Mean 100 80 60 40 20 Monthly Average Streamflow (m 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month FigureFigure 1. 1. TheThe average average and and standard standard deviation deviation of monthly streamflow streamflow at gauge station P14.

In order to predict streamflow occurrence in the study area, the variability of monthly streamflow In order to predict streamflow occurrence in the study area, the variability of monthly for various years was plotted, as shown in Figure2. The middle line presents the mean of all values in streamflow for various years was plotted, as shown in Figure 2. The middle line presents the mean the streamflow data set, the upper line indicates the mean value plus the standard deviation, and the of all values in the streamflow data set, the upper line indicates the mean value plus the standard bottom line shows the mean value minus standard deviation; the area of both graphs is the area deviation, and the bottom line shows the mean value minus standard deviation; the area of both between the top and bottom line, and is called the probability area. This area can be used to predict graphs is the area between the top and bottom line, and is called the probability area. This area can the streamflow occurrence. Some data points are outside the probability area, however, most of the be used to predict the streamflow occurrence. Some data points are outside the probability area, data points are within it. This means that in every year, the streamflow can be greater or less than however, most of the data points are within it. This means that in every year, the streamflow can be the monthly average streamflow (middle line), but will not exceed the mean value plus or minus the greater or less than the monthly average streamflow (middle line), but will not exceed the mean value standard deviation. plus or minus the standard deviation.

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512

256

128 /s)

3 64

32

16 Discharge (m

8

4

2 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year

P14,March P14,September Mean+STD Mean-STD Mean

Figure 2. The variability of mean streamflow in September and March for various years at gauge Figure 2. The variability of mean streamflow in September and March for various years at gauge station P14. station P14. 2.2. Observed Flow Data 2.2. Observed Flow Data After determining the trend of streamflow occurrence in this area, the actual available streamflow in BaanAfter Khun determining Pae River the is measured trend of to streamflow estimate the occu potentialrrence energy in this production area, the and actual plant available capacity. streamflowSeveral techniques in Baan forKhun measuring Pae River the is flowmeasured in streams to estimate can be the separated potential into energy two production main classes and of planttechniques: capacity. direct Several and techniques indirect measurement for measuring methods the flow [17 in,18 streams]. Direct can measurement be separated methods into two consist main classesof several of methods,techniques: such direct as the and velocity indirect area method,measurement moving methods boat current [17,18]. method, Direct dilution measurement method, methodselectromagnetic consist of method, several andmethods, ultrasonic such method.as the velocity Direct area measurement method, moving methods boat are current conventionally method, dilutionused for method, medium electromagnetic to large rivers. method, Not all and of these ultrasonic methods method. are generally Direct measurement applicable: methods each will are be conventionallyused in the respective used for power medium plant to depending large rivers. on No differentt all of aspectsthese methods including are compatibility, generally applicable: economy, eachand accuracy.will be Thereused arein twothe indirectrespective measurement power plant methods: depending the weir on method different and aspects slope area including method. compatibility,In this study, economy, the weir and method accuracy. is used There to calculate are two water indirect flow ofmeasurement the Baan Khun methods: Pae River the because weir methodit has a smalland slope concrete area weir method. to store water. Some studies have recommended this method for measuring the flowIn this of study, small riversthe weir [19 method–21]. Furthermore, is used to calcul the weirate water method flow is of the the most Baan accurate Khun Pae and River reliable because flow itmeasurement has a small method;concrete the weir accuracy to store should water. be aboutSome ±studies1.7 to ±have3% and recommended the flow condition this method should for not measuringbe more than the 4flow m3/s of [21small]. The rivers principle [19–21]. of Furthe the weirrmore, method the isweir to measuremethod is the the free most surface accurate flow and and reliableto observe flow the measurement head over the method; weir. Frequencythe accuracy of should observation be about is important ±1.7 to ±3% because and the the flow accuracy condition and 3 shouldreliability not ofbe flowmore estimates than 4 m depend/s [21]. The on thisprinciple value. of Therefore, the weir me inthod order is to to check measure the the precision free surface of the flowflow and measurement, to observe the the water head level over over the theweir. concrete Frequency weir shouldof observation be measured is important twice a day because every the day accuracythroughout and the reliability year. Results of flow are shownestimates in Figuredepend3. on this value. Therefore, in order to check the precision of the flow measurement, the water level over the concrete weir should be measured twice a day every day throughout the year. Results are shown in Figure 3.

Energies 2018, 11, x FOR PEER REVIEW 6 of 16 Energies 2018, 11, 3212 6 of 16 Energies 2018, 11, x FOR PEER REVIEW 6 of 16 0.70 /s)

3 0.60 0.70 /s) 0.503 0.60

0.40 0.50

0.30 0.40

0.20 0.30

Availiale Streamflow (m 0.10 0.20

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Date

Date Figure 3. Daily available streamflow of the Baan Khun Pae River, May 2012–April 2013. Figure 3. Daily available streamflow of the Baan Khun Pae River, May 2012–April 2013. Figure 3. Daily available streamflow of the Baan Khun Pae River, May 2012–April 2013. 2.3.2.3. Annual Annual Irrigation Irrigation Demand Demand Estimation Estimation 2.3. Annual Irrigation Demand Estimation 2 TheThe upstream upstream and and downstream downstream irrigation irrigation areas areas are are approximately approximately 56 56km km, including2, including the the 2 2 2 communitycommunityThe area upstream area of 1.1 of 1.1km and km, the 2downstream, theagricultural agricultural areairrigation area of 19 of km 19areas km and 2 areand the approximately theforest forest conservation conservation 56 kmarea2 area, ofincluding 35.9 of 35.9 km km . the2. ThisThiscommunity is the is the total total area area area of used 1.1 used kmin both in2, the both theagricultural the wet wet and and dryarea dry seasons. of seasons.19 km The2 and The dry the dry season forest season conservationis from is from December December area of to 35.9 June to Junekm 2. andandThis the the wetis the wet season total season area is from is used from July in July bothto toNovember. November.the wet and Rice Rice dry is is seasons.the the main main The wet-season wet-season dry season crop, crop, is fromaccounting accounting December for for 70% 70%to June of of thetheand area, area, the whilewet season perennial is from andand July vegetablevegetable to November. cropscrops accountacco Riceunt is for for the 30%. 30%. main Dry Dry wet-season season season cropping cropping crop, accounting will will consist consist for of of 45%70% 45%vegetables,of vegetables, the area, 20%while 20% herbs, herbs, perennial 15%15% ornamentalandornamental vegetable and crops othe other racco upland uplandunt forcrops, crops, 30%. and and Dry 25% 25% season perennials. perennials. cropping The The will schematic schematic consist of simplifiedsimplified45% vegetables, irrigation irrigation 20% demand demandherbs, of 15% the of theornamental Baan Baan Khun Khun and Pae Pae othearea arear isupland shown is shown crops, in Figure in and Figure 25%4. 4The. perennials. The upstream upstream The irrigation irrigation schematic areasareassimplified use use the theinflow irrigation inflow water water demand from from the of thethemountain mountainBaan Khun for forcrop Pae crop growing area growing is shown and and irrigation in irrigation Figure demand. 4. demand.The upstream The The remaining remaining irrigation waterwaterareas flows use flows tothe the to inflow the concrete concrete water weir from weir of the ofthe themountain hydropower hydropower for crop plant. plant. growing The The downstream and downstream irrigation irrigation demand. irrigation areas The areas useremaining use the the waterwaterwater from fromflows the the tailto the tail race concrete race of the of the hydropowerweir hydropower of the hydropower plant plant and and the plant. the water water The over downstream over the the concrete concrete irrigation weir weir (bypass) areas (bypass) use for forthe 2 croppingcroppingwater andfrom and irrigation the irrigation tail race demand. demand. of the Therehydropower There is isalso also aplant acropping cropping and the area area water of of 0.16 0.16 over km the2 thatthat concrete receives weir waterwater (bypass) fromfromthe for theconcrete croppingconcrete weir weirand for irrigationfor vegetable vegetable demand. cropping. cropping. There Thus, Thus, is also the the a water croppingwater flow flow area at at the theof concrete 0.16 concrete km weir2 that weiris receives dividedis divided water into into threefrom threeparts—bypass,the parts—bypass, concrete weir hydropower forhydropower vegetable plant, plant,cropping. and croppingand Thus,croppi area. theng Thewaterarea. water Theflow usedwater at the by used theconcrete croppingby the weir cropping area is divided throughout area into throughoutthethree two-year parts—bypass, the periodtwo-year depends hydropower period on depends the plant, climate on and the and croppiclimate streamflowng and area. streamflow occurrence. The water occurrence. Theused average by the The monthly cropping average water area monthlyflowthroughout requirement water flowthe two-year requirement of the cropping period of thedepends area cropping is shown on areathe in climate Figureis shown5 .and The in streamflowFigure observation 5. The occurrence. data observation of the The streamflow data average of theoccurrence monthlystreamflow water at occurrence the flow concrete requirement atweir the concrete and of the the averageweir cropping and monthly the area average is water shown monthly flow in Figure requirement water 5. Theflow of observation requirement the cropping data of area of theare thecropping usedstreamflow to area estimate are occurrence used the to water estimate at the flow concrete the available water weir forflow and the available the hydropower average for the monthly plant hydropower to water produce flowplant electrical requirement to produce energy. of electricalBasedthe cropping onenergy. the waterarea Based are flow on used the over to water estimate the concreteflow the over water weir the (bypass),flowconcrete available weir it is estimated for(bypass), the hydropower thatit is estimated less than plant onethat to produce percent less thanofelectrical one the percent remaining energy. of the water Based remaining flow on the is availablewater water flow flow to is sustain overavaila theble aquatic concrete to sustain life weir in aquatic the (bypass), area. lifeTherefore, in it the is area.estimated the Therefore, amount that less of theremaining thanamount one ofpercent water remaining at of the the concrete waterremaining at weirthe water concrete will flow be used weir is availa to will estimateble be to used sustain the to maximum estimate aquaticannual lifethe inmaximum the energy area. production annualTherefore, energyofthe the amountproduction hydropower of remaining of the plant. hydropower water at theplant. concrete weir will be used to estimate the maximum annual energy production of the hydropower plant. INFLOW

INFLOW Upstream Irrigation area

Upstream Irrigation area BAAN KHUN PAE RIVER [Concrete weir] BAAN KHUN PAE RIVER [Concrete weir] Cropping area 0.16 km2 BYPASS Hydropower Cropping area Plant 0.16 km2 BYPASS Hydropower Plant

Downstream Irrigation area

Downstream Irrigation area Figure 4. Assumption of water use in the Baan Khun Pae Basin. Figure 4. Assumption of water use in the Baan Khun Pae Basin. Figure 4. Assumption of water use in the Baan Khun Pae Basin.

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0.035 0.035 Dry Season Wet Season 0.030 Dry Season Wet Season

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Average demand Average demand (m 0.005 0.005 0.000 0.000 DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAYMonth JUN JUL AUG SEP OCT NOV Month

FigureFigure 5.5. Average monthlymonthly waterwater requirementrequirement forfor cropcropproduction. production. Figure 5. Average monthly water requirement for crop production. 2.4.2.4. EstimationEstimation ofof thethe AvailableAvailable StreamflowStreamflow 2.4. Estimation of the Available Streamflow ThereThere isis nono availableavailable flowflow recordrecord andand thethe measuredmeasured streamflowstreamflow forfor onlyonly oneone yearyear isis notnot accurateaccurate enoughenoughThere to evaluateis evaluate no available the the available availableflow record energy. energy. and The the The measmeasured measurementurement streamflow error error and for andsome only some missing one missingyear flow is not data, flow accurate when data, whenenoughheavy heavy rain to evaluate occurred, rain occurred, the affect available affect the theaccuracyenergy. accuracy The of the ofmeas the energyurement energy estimation. estimation. error and This some This problem problemmissing can canflow be be data, solved when byby usingheavyusing aarain PDF.PDF. occurred, VariousVarious distributionaffectdistribution the accuracy functionsfunctions of havehavethe energy beenbeen usedused estimation. toto increaseincrease This thethe problem reliabilityreliability can ofof be observationobservation solved by data,usingdata, such sucha PDF. asas Variousthethe WeibullWeibull distribution distribution,distribution, functions lognormallognormal have been distribution,distribution, used to andincreaseand GammaGamma the reliability distribution.distribution. of observation OneOne ofof thethe distributiondata,distribution such as functions functions the Weibull will will bedistribution, be used used to to obtain obtain lognormal the the probability probability distribution, of theof theand observed observed Gamma values. divalues.stribution. Many Many textbooks One textbooks of andthe researchersdistributionand researchers have functions recommendedhave willrecommended be used a good to obtaina estimate good the estimate of probability the distribution of the of distributionthe parameters observed parameters values. by using Many the bymaximum textbooksusing the likelihoodandmaximum researchers methodlikelihood have [22 method–recommended24]. This [22–24]. study a This considersgood study estimate three considers of different the three distribution probability different parameters probability distributions bydistributions whichusing arethe widelymaximumwhich are used widelylikelihood in hydrology used method in distributionhydrology [22–24]. distribution analysis.This study analysis.considers three different probability distributions which are widely used in hydrology distribution analysis. TheThe threethree differentdifferent distributionsdistributions areare fittedfitted toto thethe observationobservation values,values, andand parametersparameters ofof distributionsdistributionsThe three areare different estimatedestimated distributions usingusing thethe maximummaximum are fitted likelihoodlikelihood to the observation method.method. TheThe values, “statistic“statistic and toolbox”toolbox” parameters functionfunction of indistributionsin MATLABMATLAB isisare usedused estimated forfor thisthis using purpose.purpose. the ResultsmaximumResults areare likelihood shownshown inin Tablemethod.Table3 .3. The TheThe estimated estimated“statistic parameters toolbox”parameters function of of the the distributionsindistributions MATLAB is basedbased used onon for thethe this maximummaximum purpose.likelihood likelihoodResults are methodmeth shownod showshowin Table thatthat 3. thethe The GammaGamma estimated distributiondistribution parameters performsperforms of the betterdistributionsbetter thanthan the thebased other other on distributions. the distributions. maximum Figure likelihood Figure6 shows 6 meth ashows comparisonod showa comparison betweenthat the Gamma thebetween fitted distribution Gamma the fitted distribution performs Gamma andbetterdistribution the than frequency andthe theother of thefrequency distributions. observation of the values observationFigure from 6 shows Figure values 5.a from Thecomparison observedFigure 5. flowThebetween observed rates the were flowfitted grouped rates Gamma were into distribution and the frequency of the observation values from Figure 5. The observed flow rates were 20grouped classes into with 20 a rangeclasses of with 0.05 a m range3/s. of 0.05 m3/s. grouped into 20 classes with a range of 0.05 m3/s.

(m3/s) (m3/s) Figure 6. Comparison of fitted distributions with the observation flow data grouped into 20 classes. Figure 6. Comparison of fitted distributions with the observation flow data grouped into 20 classes. Figure 6. Comparison of fitted distributions with the observation flow data grouped into 20 classes. Table 3. Estimated parameters for selecting distributions. Table 3. Estimated parameters for selecting distributions. DistributionTable 3. Estimated parameters Weibull for selecting Lognormal distributions. Gamma Distribution Weibull Lognormal Gamma DistributionScale parameters Weibullα = 0.1023 µ Lognormal= −2.9144 α = 0.8682Gamma ScaleShape parameters parameters α β= 0.1023= 0.9157 σμ= = 1.3641 −2.9144 β = 0.1228α = 0.8682 Scale parameters α = 0.1023 μ = −2.9144 α = 0.8682 ShapeMax. likelihoodparameters estimation β = 459.1460.9157 437.749σ = 1.3641 459.386β = 0.1228 Shape parameters β = 0.9157 σ = 1.3641 β = 0.1228 Max. likelihood estimation 459.146 437.749 459.386 Max. likelihood estimation 459.146 437.749 459.386

Energies 2018, 11, 3212 8 of 16

Energies 2018, 11, x FOR PEER REVIEW 8 of 16 The scale (mean) and shape (variance) parameters of the Gamma distribution function were used The scale (mean) and shape (variance) parameters of the Gamma distribution function were used to generateto generate the streamflowthe streamflow data data set set based based on on the the observedobserved flow flow data data in in one one year. year. The The streamflow streamflow data data set forset each for each day day within within one one year year (365 (365 samples)samples) is is us useded to toestimate estimate the thepotential potential energy energy production production of of thethe BKP BKP micro micro hydropower hydropower plant.plant. The comparison of of observation observation data data in one in one year year and andgenerated generated streamflowstreamflow data data set fromset from the the Gamma Gamma distribution distribution functionfunction is is shown shown in in Table Table 4. 4The. The probability probability of the of the generatedgenerated streamflow streamflow data data set set is representedis represented by by thethe histogramshistograms shown shown inin Figure Figure 7. 7Note. Note that that there there is is less variabilityless variability of the of the data data compared compared with with Figure Figure6 .6.

TableTable 4. Comparison 4. Comparison of observation of observation data data and and streamflow streamflow data form form the the Gamma Gamma distribution distribution function. function. Observation Data in Gamma Distribution Description Description Observation DataOne Year in One Year GammaFunction Distribution Function Total numberTotal of samples number of samples 365365 365 365 Average streamflowAverage (m streamflow3/s) (m3/s) 0.10670.1067 0.1041 0.1041 3 Minimum streamflowMinimum (m streamflow/s) (m3/s) 0.00480.0048 0.0001 0.0001 3 Maximum streamflowMaximum (m streamflow/s) (m3/s) 0.60240.6024 0.6314 0.6314 Standard deviation 0.1132 0.1117 Standard deviation 0.1132 0.1117

0.275 0.250 0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 Probability of occurrence 0.025 0.000

Flow rate range (m3/s)

FigureFigure 7. Probability 7. Probability of of occurrence occurrence ofof 365 samples in in 20 20 flow flow rate rate ranges. ranges. 3. Turbine Type Selection 3. Turbine Type Selection The selectionThe selection of the of the turbine turbine depends depends upon upon thethe sitesite characteristics. The The main main characteristics characteristics that that shouldshould be considered be considered to selectto select the th turbinee turbine type type areare thethe head and and flow flow available, available, the thedesired desired running running speedspeed of the of generator, the generator, and whether and whether the turbine the turbine will be wi expectedll be expected to operate to operate in variable in variable flow conditions. flow Hydroconditions. turbines Hydro can be turbines classified can be into classified two main into two groups main based groups on based the on flow the pattern flow pattern in the in the turbine and theturbine specific and speed.the specific Based speed. on theBased flow on pattern,the flow pattern, hydro turbineshydro turbines are categorized are categorized into into three three groups: high,groups: medium, high, and medium, low head. and Theselow head. are These grouped are intogrouped two into categories: two categories: impulse impulse and reaction and reaction turbines. The differenceturbines. The between difference impulse between and impulse reaction and turbines reaction can turbines be explained can be explained by water by pressure. water pressure. When the When the water pressure applies a force on the face of the runner blades, which decreases as it water pressure applies a force on the face of the runner blades, which decreases as it proceeds through proceeds through the turbines, these are called reaction turbines. A reaction turbine needs a higher the turbines, these are called reaction turbines. A reaction turbine needs a higher volume flow rate to volume flow rate to operate than an impulse turbine. There are three main types of reaction turbine operateused: than the an propeller, impulse Kaplan, turbine. and There Francis are turbines. three main For typesimpulse of reactionturbines, turbineall the water used: pressure the propeller, is Kaplan,converted and Francis into kinetic turbines. energy For before impulse entering turbines, the runner. all theKinetic water energy pressure is in the is form converted of a high-speed into kinetic energyjet beforethat strikes entering the buckets, the runner. mounted Kinetic on the energy periph isery in of the the form runner. of aThere high-speed are three jet main that types strikes of the buckets,impulse mounted turbines on used: theperiphery the Pelton, ofTurgo, therunner. and cros Theres-flow areturbines. three All main variables types are of impulserelated toturbines the used:turbine the Pelton, specific Turgo, speed. and The cross-flow specific speed turbines. of turbine All variablestypes is the are most related suitable to theparameter turbine on specific which to speed. The specificbase the speed selection of turbine of a turbine. types is In the general, most suitablelow turbine parameter specific on speed which of to an base impulse the selection turbine of a turbine.corresponds In general, to lowlow turbineflow rates specific and high speed heads, of an whereas impulse high turbine turbine corresponds specific speed to low of flowa reaction rates and turbine corresponds to high flow rates and low heads. The turbine specific speed is given by the high heads, whereas high turbine specific speed of a reaction turbine corresponds to high flow rates dimensionless parameter [25]: and low heads. The turbine specific speed is given by the dimensionless parameter [25]: √ N Q N = R D S 3/4 (1) (gHN) Energies 2018, 11, 3212 9 of 16

3 where NS is the turbine specific speed, NR is the angular velocity (rad/s), QD is a design flow (m /s), and HN is an effective head (m). Commonly, the turbine should be operated at the normal speed of a standard generator. Therefore, the specific speed equation is used in this algorithm for selecting turbine type by fixing the turbine shaft speed. The normal operating ranges for the turbine specific speed and the effective head for each turbine type are shown in Table5.

Table 5. Operating ranges of hydraulic turbines; Dixon and Hall [19].

Turbine Type Turgo Pelton Francis Kaplan Specific speed 0.02–0.8 0.05–0.4 0.4–2.2 1.8–5.0 Effective Head (m) 50–250 50–1300 10–350 2–40

4. Annual Energy Production Estimation The energy potential of a run-of-river power plant is proportional to the flow and the head. Here, the operation range is used to estimate the annual energy production. The operation range of each turbine type is different. The turbine can operate when the water flow rate is between a minimum (Qmin) and a maximum (Qmax) value. Penche [3] presented the minimum technical flow for different types of turbines. The minimum flow for each turbine type is given as a percentage of design flow as shown in Table6. The design flow (QD) or water flow rate through the turbine is determined by the following relationship as a function of the available streamflow (Qav):  0 Q < Q  av min QD = Qav Qmin < Qav < Qmax (2)   Qmax Qmax < Qav

If the available streamflow is less than the minimum flow rate of the turbine, the turbine will shut down. On the other hand, if the available flow rate is more than the maximum flow rate of the turbine, the maximum flow rate or design flow will be used to operate the turbine because the intake gate and the difference of water level at the small weir of run-of-river will not affect the turbine performance. Therefore, the decision to select the design flow of each turbine type and size will be limited by Equation (2). In order to increase the reliability of micro hydro turbine operation and increase the accuracy of the potential energy estimation, the probability of streamflow occurrence is used to evaluate the maximum annual energy production, given by

nc E = ∑[ρgQD,i HN Prih] (3) i=1

3 where E is the maximum annual energy production (kWh/year), QD is the design flow (m /s), HN is the effective head or net head (m), Pri is the probability of streamflow occurrence within the range, h is the number of operation hours within a year (h/year), i is the sequence of streamflow range, and n is the total number of streamflow ranges.

Table 6. Minimum operating flow of turbines; Penche [3].

Turbine Type Qmin (% of QD) Francis 30 Kaplan 15 Cross-flow 15 Pelton 10 Turgo 20 Propeller 65 Energies 2018, 11, 3212 10 of 16

5. Optimal Turbine Type and Size Selection Algorithm The selection algorithm is separated into two main processes. The first process is selecting the turbine type and minimum flow variable for the operation of each hydro turbine type, as shown in Figure8. The results of the first process will be used for the second process, which is to find the optimal turbine size after type selection, as shown in Figure9. The first two steps of the first process are the collection and analysis of observation flow data, including the irrigation demand. The Gamma distribution function is used to generate the streamflow data set for one year (365 samples). Thence, the streamflow data set are arranged from larger values to smaller values. The next steps in the flowchart are finding the maximum streamflow (Qmax) and minimum streamflow (Qmin) from the generated streamflow data (Qav) (365 samples). The class range index is used to select the streamflow range (SR) to calculate the number of class ranges (nc). In each class range (i) the mean streamflow (Qmean) is used to count the streamflow occurrence number of days to evaluate the probability of occurrence (Pr,i). Then, each streamflow range is associated with this probability to evaluate the annual energy production and turbine specific speed. The first iteration starts from the minimum flow rate value (Qmin), and it has a high probability of occurrence. This iteration process continues until the last class range (nc). After that, the turbine specific speed at maximum annual energy production (Equation (3)) is used to select the turbine type and minimum flow rate to operate. If the turbine specific speed value is lower than 0.02 the algorithm is stopped because the lowest streamflow and net head are not suitable; otherwise, it will recommend the best type. The type results in the first process are then used in the second process to select the size (Figure9). The second process finds the turbine size based on a more accurate way of calculating maximum potential energy production. The streamflow data (Qav), mean flow rate (Qmean), probability of streamflow occurrence (Pr,i), and number of class ranges (nc) are used. Especially, the minimum flow rate variable of the turbine type is used to check the operation condition of the turbine. The first iteration begins from the mean streamflow (Qmean) in the first-class range. The streamflow data between mean streamflow (Qmean) and turbine minimum streamflow (Qturbine min flow) are used to check the operation condition before computing the annual energy production. If the available streamflow is lower than the minimum streamflow, the turbine will be shut down and the energy is equal to zero. Energies 2018, 11, 3212 11 of 16 Energies 2018, 11, x FOR PEER REVIEW 11 of 16

Start

Collection the available streamflow data (Qav), twice a day and everyday throughout the year

Fitting the observation streamflow data by Gamma distribution function and generate the streamflow data set (Qav = Qav,k ); k= 365

Find the minimum streamflow (Qmin) and maximum streamflow (Qmax) from the generated streamflow data (Qav)

Identify of streamflow Calculate the streamflow range (SR) data in each range SR = Qmin × Class range index

Calculate the number of class ranges (nc) nc = [Qmin+Qmax]/SR

Calculate the mean flow rate (Qmaen) in each range

Evaluate the annual Count the number of days of the flow rate energy production occurs in each range (Qmean)

Calculate the occurrence probability (Pr,i) of flow rate for each range

Calculate the annual energy production (E) and turbine specific speed (Ns) for each range

Find the turbine specific speed at maximum annual energy production

Hydro turbine cannot operate under the flow Ns < 0.02 Yes Stop rate and net head of this case No Turgo turbine minimum flow rate variable Ns ≤ 0.3 Yes (Qturbine min flow = 0.2 × Qmean) No Pelton turbine minimum flow rate variable Ns ≤ 0.4 Yes (Qturbine min flow = 0.1 × Qmean) No Fancis turbine minimum flow rate variable Ns ≤ 2.5 Yes (Qturbine min flow = 0.3 × Qmean) No minimum flow rate variable Next process for Ns > 2.5 Yes (Qturbine min flow = 0.15 × Qmean) Turbine size selection

Figure 8. Optimal turbine type selection algorithm.

Energies 2018, 11, 3212 12 of 16 Energies 2018, 11, x FOR PEER REVIEW 12 of 16

Turbine type Available Number of Probability selection streamflow class range (Pr) process data (Qav) (nc) in each range

Turbine minimum Mean flow rate flow rate variable for (Qmean) type selected before in each range

i = i+1 For i = 1 : 1 : nc

j = j+1 N = number of available For j = 1 : 1: Nav av streamflow data (365)

Qavj ≤ Qturbine min flow Yes Power = 0

No

Qavj ≤ Qmean, i Yes Power = ρgHNQav,j

No

Qavj ≥ Qmean, i Yes Power = ρgHNQmean,i

Calculate the average power capacity (Pavg,j)

Calculate the annual energy production (Ej, i)

Find the maximum annual energy i = nc production (Emax)

Calculate the payback period

Final results Turbine type and size, design flow, plant capacity, payback period, and maximum annual energy production

Stop

FigureFigure 9. Optimal9. Optimal turbine turbine size size selection selection algorithm. algorithm.

On the other hand, if the available streamflow (Q ) is less than or equal to the mean streamflow On the other hand, if the available streamflow (avQav) is less than or equal to the mean streamflow (Q ) of the turbine condition, the available streamflow is used to evaluate the power capacity. If the (meanQmean) of the turbine condition, the available streamflow is used to evaluate the power capacity. If the available streamflow (Q ) is more than the mean streamflow (Q ) of the turbine condition, the mean available streamflow av(Qav) is more than the mean streamflow mean(Qmean) of the turbine condition, the mean streamflowstreamflow is usedis used to calculate to calculate the power the power capacity. capaci Thisty. loop This stops loop with stops the last with sequence the last of streamflowsequence of data (j = 365). After that, the average power capacity (P ) in this range is used to compute the annual streamflow data (j = 365). After that, the average poweravg capacity (Pavg) in this range is used to compute energythe annual production energy ( Eproduction). The mean (E streamflow). The mean is streamflow changed to is thechanged next class to the range next untilclass therange last until class the rangelast (classi = nc range) is reached. (i = nc) The is reached. maximum The annual maximum energy annual production energy is production used to determine is used turbine to determine size. Theturbine last process size. The is to last check process the cost–benefitis to check the ratio cost–b of theenefit proposed ratio of turbine the proposed type and turbine size and type calculate and size theand design calculate flow. the Information design flow. about Information the maintenance about the costs maintenance of the hydro costs turbines of the under hydro supervision turbines under of supervision of PEA, the average annual income from electricity sales of PEA, and the investment

Energies 2018, 11, 3212 13 of 16

Energies 2018, 11, x FOR PEER REVIEW 13 of 16 PEA, the average annual income from electricity sales of PEA, and the investment costs of turbines are costsused of for turbines this step. are The used final for outputsthis step. of The this final algorithm outputs are of athis turbine algorithm type andare a size, turbine maximum type and annual size, maximumenergy production, annual energy design production, flow, plant design capacity, flow, and plant payback capacity, period. and The payback design period. flow value The design is then flowused value to design is then the used detailed to design turbine the geometry. detailed turbine geometry.

6.6. Results Results and and Discussion Discussion BasedBased on on the histogram of of probability probability of of streamflow streamflow occurrence occurrence from from Figure Figure 77,, thethe streamflowstreamflow rangerange is is 0.0175 0.0175 m m3/s3/s for for a total a total of 20 of class 20 class ranges. ranges. Therefore, Therefore, the first-class the first-class range of range flow ofrate flow is 0.0001– rate is 0.01750.0001–0.0175 m3/s, which m3/s, encompasses which encompasses the flow the rate flow values rate for values 289 days. for 289 The days. mean The flow mean rate flow of this rate range, of this 0.0088range, m 0.00883/s, has m 3a/s, high has probability a high probability of occurrence of occurrence of approximately of approximately 80%. The 80%. power The capacity, power capacity, annual energyannual energyproduction, production, and turbine and turbine specific specific speed speed in th inis thisrange range are are6.73 6.73 kW, kW, 39,015 39,015 kWh, kWh, and and 0.0567, 0.0567, respectively.respectively. ForFor thethe nextnext classclass range, range, the the flow flow rate rate range range is greateris greater than than that that of theof the first first class, class, and and will willbe used be used to calculate to calculate the the next next annual annual energy energy production production until until the the last last class class rangerange withwith the lowest probability of occurrence. TheThe class class range range index index (see (see Figure Figure 8)8) does does change change th thee flow flow range range in in each each class. class. A Ahigher higher value value of classof class range range index index will willresult result in a lower in a lower number number of classes. of classes. The class The range class index range was index selected was selectedto be as smallto be as possible small as so possible that further so that increases further did increases not change did not the changeresulting the maximum resulting energy maximum production energy inproduction the turbine in thetype turbine selection type algorithm. selection algorithm.This was obtained This was with obtained 200 classes with 200 for classes a class for range a class index range of 36index through of 36 trial through and trialerror. and The error. comparison The comparison of annual of energy annual production energy production results and results turbine and specific turbine speedsspecific for speeds 200 classes for 200 are classes shown are in shownFigure 10. in FigureHigh flow 10. Highrates have flow ratesa lower have probability a lower probabilityof occurrence of andoccurrence produce and low produce annual low energy. annual On energy. the other On the hand, other low hand, flow low rates flow rateshave havea high a high probability probability of occurrence,of occurrence, and and allow allow the the turbines turbines to toproduce produce larger larger amounts amounts of of annual annual energy. energy. The The impulse impulse turbine turbine isis more more popular popular in in micro micro hydropower hydropower plant plant selection selection than than the the reaction reaction turbine turbine because because it it is is cheaper cheaper andand easiereasier toto maintain. maintain. Moreover, Moreover, impulse impulse turbines turbines have have lower lower frictional frictional losses thanlosses reaction than turbines,reaction turbines,which affects which the affects flow ratethe flow range rate to operaterange to the operate turbine. the Fromturbine. the From results, thethe resu turbinelts, the specificturbine speedspecific is speed0.2051 is at 0.2051 maximum at maximum annual energy annual production, energy production, which is which in the rangeis in the of range the Turgo of the and Turgo Pelton and turbines. Pelton turbines.Both turbines Both areturbines suitable are in suitable this case inbecause this case of be thecause low of flow the ratelow andflow high rate effective and high head. effective The Turgohead. Theturbine Turgo will turbine have awill smaller have diametera smaller thandiameter the Pelton than the turbine. Pelton Therefore,turbine. Therefore, it can be it concluded can be concluded that the thatTurgo the turbine Turgo isturbine a better is choicea better for choice thiscase for this study case than study the than Pelton the turbine. Pelton turbine.

0.500 250,000 0.450 225,000 193,251 kWh 0.400 200,000 0.350 175,000 0.300 Specific Speed 150,000 0.250 0.2051 Annual Energy 125,000 0.200 100,000 0.150 75,000 Turbine specific speed specific Turbine 0.100 50,000

0.050 25,000 AnnualEvaluation Energy(kWh) 0.000 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 Streamflow occurrence (m3/s)

Figure 10. Results of annual energy evaluation and turbine type selection from the first phase of the Figure 10. Results of annual energy evaluation and turbine type selection from the first phase of the algorithm (Figure9) in 200 classes. algorithm (Figure 9) in 200 classes. As shown in Figure8, the optimal turbine type selection algorithm uses the mean flow rate in eachAs range shown to compute in Figure the 8, estimationthe optimal of turbine power type capacity selection and annualalgorithm energy uses production.the mean flow As shownrate in each range to compute the estimation of power capacity and annual energy production. As shown in in Figure 10, the optimal turbine size selection algorithm will use the Qmin cut of values to calculate Figurethe power 10, the of the optimal turbine turbine operation. size selection Considering algorithm the maximum will use annualthe Qmin energy cut of productionvalues to calculate (Figure the11), powerthe probability of the turbine of streamflow operation. occurrence Considering is approximately the maximum 30%,annual which energy can production produce a power(Figure capacity 11), the probabilityof 87.95 kW. of streamflow occurrence is approximately 30%, which can produce a power capacity of 87.95 kW.

Energies 2018, 11, x 3212 FOR PEER REVIEW 1414 of of 16 16 Energies 2018, 11, x FOR PEER REVIEW 14 of 16

1.000 500 1.000 500 0.900 450 0.900 450 0.800 400 0.800 400 0.700 350 0.700 350 0.600 300 0.600 300 0.500 250 0.500 Power Capacity 250 0.400 Power Capacity 200 0.400 0.3041 200 0.300 0.3041 Probability of Occurrence 150 0.300 Probability of Occurrence 150 0.200 100 Probability of Occurrence 0.200 100 Probability of Occurrence 0.100 50 0.100 87.95 kW 50 (kW) Power Capacity Evaluation

0.000 87.95 kW 0 (kW) Power Capacity Evaluation 0.0000.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0 0.00 0.05 0.10 0.15 0.20Streamflow 0.25 0.30 occurrence 0.35 0.40 (m3/s) 0.45 0.50 0.55 0.60 0.65 3 Streamflow occurrence (m /s) Figure 11. Relationship between probability of occurrence and power capacity evaluation based on Figure 11.11. RelationshipRelationship betweenbetween probability probability of of occurrence occurrence and and power power capacity capacity evaluation evaluation based based on theon the first phase of the algorithm (Figure 9) in 200 classes. firstthe first phase phase of the of algorithmthe algorith (Figurem (Figure9) in 9) 200 in classes.200 classes. In order to increase the accuracy, the operation range of the Turgo turbine, as calculated using In orderorder toto increaseincrease thethe accuracy,accuracy, thethe operationoperation rangerange ofof thethe TurgoTurgo turbine,turbine, asas calculatedcalculated usingusing Equation (2), was used to estimate the annual energy production. The minimum flow rate for Equation (2),(2), was was used used to estimateto estimate the annualthe annual energy energy production. production. The minimum The minimum flow rate flow for operating rate for operating the hydro turbine (Table 6) and information regarding the maintenance costs of the Turgo theoperating hydro the turbine hydro (Table turbine6) and (Table information 6) and informat regardingion regarding the maintenance the maintenance costs of the costs Turgo of the turbines Turgo turbines under supervision of the PEA are used in the optimal turbine size selection algorithm, as underturbines supervision under supervision of the PEA of the are PEA used are in theused optimal in the optimal turbine sizeturbine selection size selection algorithm, algorithm, as shown as shown in Figure 9. The average annual income from electricity sales of the PEA is around 0.105 USD inshown Figure in9 Figure. The average9. The average annual annual income income from electricity from electricity sales ofsales the of PEA the isPEA around is around 0.105 0.105 USD USD per per kW. The investment cost determined in this study does not include civil work, only mechanical kW.per kW. The investmentThe investment cost cost determined determined in this in studythis study does does not includenot include civil civil work, work, only only mechanical mechanical and and electrical works of the Turgo turbine type, the cost of which is approximately 1250 USD per kW. electricaland electrical works works of the of the Turgo Turgo turbine turbine type, type, the the cost cost of of which which is is approximately approximately 12501250 USDUSD per kW. kW. The condition of turbine operation based on turbine minimum flow rate is very important to The conditioncondition of of turbine turbine operation operation based based on turbine on turbine minimum minimum flow rate flow is very rate important is very important to accurately to accurately estimate the precise turbine size, since if the available flow rate is lower than the minimum estimateaccurately the estimate precise the turbine precise size, turbine since ifsize, the since available if theflow available rateis flow lower rate than is lower the minimum than the minimum flow rate flow rate value the turbine will be shut down. In contrast, if the available flow rate is higher than the valueflow rate the value turbine the will turbine be shut will down. be shut In down. contrast, In cont if therast, available if the available flow rate flow is higher rate is thanhigher the than design the design flow value, the turbine will use the design flow rate value to produce electricity. The accuracy flowdesign value, flow thevalue, turbine the turbine will use will the use design the design flow rate flow value rate to value produce to produce electricity. electricity. The accuracy The accuracy of this of this algorithm will depend on the amount of available streamflow data. If there is a large amount algorithmof this algorithm will depend will depend on the amounton the amount of available of available streamflow streamflow data. If data. there If is there a large is amounta large amount of data, of data, the accuracy of the result will be higher. Furthermore, energy production depends on the theof data, accuracy the accuracy of the result of the will result be higher. will be Furthermore, higher. Furthermore, energy production energy production depends on depends the operational on the operational turbine performance. The final results show that the Turgo turbine can produce a turbineoperational performance. turbine performance. The final results The show final thatresu thelts Turgoshow turbinethat the can Turgo produce turbine a maximum can produce annual a maximum annual energy of 0.1771 GWh with a payback period of 1197 days. The minimum flow rate energymaximum of 0.1771 annual GWh energy with of a 0.1771 payback GWh period with of a 1197payb days.ack period The minimum of 1197 days. flow The rate minimum required to flow operate rate required to 3operate is 0.0105 m3/s, with a design3 flow of 0.0526 m3/s at a net head of 98 m and a turbine isrequired 0.0105 mto operate/s, with is a 0.0105 design m flow3/s, with of 0.0526 a design m /sflow at of a net0.0526 head m3 of/s 98at a m net and head a turbine of 98 m shaft and a speed turbine of shaft speed of 1000 rpm. The plant capacity is 50 kW. It is possible to compare the more accurate 1000shaft rpm.speed The of plant1000 rpm. capacity The is plant 50 kW. capacity It is possible is 50 kW. to compare It is possible the more to compare accurate the maximum more accurate energy maximum energy estimate by comparing Figures 10 and 11 with the results from the second phase estimatemaximum by energy comparing estimate Figures by compar 10 anding 11 Figureswith the 10 results and 11 from with the the second results phasefrom the of thesecond algorithm phase of the algorithm (Figure 12). (Figureof the algorithm 12). (Figure 12).

100 200,000 100 200,000 90 177,100 kWh 180,000 90 177,100 kWh 180,000 80 160,000 80 160,000 70 140,000 70 140,000 60 120,000 60 50.530 kW 120,000 50 50.530 kW 100,000 50 100,000 40 80,000 40 80,000 30 Power Capacity 60,000

Power Capacity (kW) 30 60,000 20 Power Capacity 40,000 Power Capacity (kW) Annual Energy Production 20 40,000 10 Annual Energy Production 20,000 10 20,000 AnnualProduction Energy (kWh) 0 0 AnnualProduction Energy (kWh) 00.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 0 0.000 0.010 0.020 0.030 0.040Design 0.050 flow (m3 0.060/s) 0.070 0.080 0.090 0.100 3 Design flow (m /s) Figure 12. 12. ComparisonComparison between between the the power power capacity capacity and and an annualnual energy energy production production of the result result of the the Figure 12. Comparison between the power capacity and annual energy production of the result of the secondsecond phase phase of the algorithm (Figure 10)10) in 200 classes. second phase of the algorithm (Figure 10) in 200 classes.

Energies 2018, 11, 3212 15 of 16

7. Conclusions A novel methodology for estimating the energy production of a hydro plant based on observation, irrigation demand, and historical flow data was developed and implemented. The results were used to determine optimal turbine type and size. Streamflow was measured and fitted with the best PDF. The flow data were grouped into classes based on flow rate range. Flow occurrence curves were used to compute the total annual energy production for various turbine parameters. An algorithm was developed to find the optimal turbine type and size based on the maximum annual energy production. In the first part of the algorithm the average flow of each range was used. The average flow of the class that gives the highest annual energy was used to select the turbine type. The number of classes used is important: the higher the number of classes, the more accurate the results. The class number was selected to be as small as possible so that a further increase did not change the resulting maximum energy production. This was obtained for 200 classes with a class index of 36. The second part of the algorithm starts with the resulting turbine type as an outcome of the first part of the algorithm. Instead of using the class average flow range, the minimum and maximum flow rate of the selected nominal size was used to compute a more accurate estimate of the annual energy production. Additionally, the information of the maintenance cost, investment cost, and average income for electricity sales from the PEA was used to estimate the payback period. This algorithm was validated by a real case study of the Baan Khun Pae micro hydropower plant in Chiang Mai Province, Thailand. The result of the algorithm showed that the Turgo turbine is a better choice for this case study than other turbines; it can produce a maximum annual energy of 0.1771 GWh with a payback period of 3.28 years. The minimum flow rate needed to operate the turbine is 0.0105 m3/s, with a design flow of 0.0526 m3/s, at a maximum power capacity of 50 kW. The final turbine design was manufactured and installed to replace the existing turbine, the size of which was selected based on the standard FDC method. The average annual energy production of the new Turgo turbine for four years (2014–2018) was 0.146 GWh at a plant capacity of 82%. Comparing this result to the historical data of the Baan Khun Pae micro hydropower plant, as shown in Table2, it can be seen that the new Turgo turbine produced electricity similar to the prediction of our algorithm and the plant capacity is better than for the previous turbine. Although the maximum power of the new Turgo turbine is lower than that of the existing turbine, it can produce more annual energy. Therefore, this algorithm is more accurate than others at determining the type and size of hydro turbine to install in the run-of-river micro hydropower plants with highly variable flow conditions. In case the flow rate is deterministic there will be no need to use the PDF but the two-phase type and size selection can still be used to maximize the annual energy production.

Author Contributions: K.S. contributed to the conceptualization, methodology, validation, and data collection, and wrote the paper; E.L.J.B. made corrections to the paper and gave some useful recommendations. Funding: This research was funded by the Department of Research Funding and Technology Development, Provincial Electricity Authority (PEA), Thailand. Acknowledgments: The authors would like to thank the Royal Project Foundation at Baan Khun Pae branch for their annual cropping report in this area. The authors also express their gratitude to the Hydrology and Water Management Center for upper northern region, Royal Irrigation Department for the historical flow data.

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