Paulo S.C. Nascimento, Rodrigo M. Novaes, Bruno H. Dias
©SHUTTERSTOCK.COM/ALF RIBEIRO
This article presents a computational tool to calculate some parameters of hydroelectric plants, focusing mainly on microhydroelectric generation; it also evaluates the energy potential of small hydro plants. This computational tool was developed using MATLAB, and it presents a graphical interface that makes it user friendly. The computer program and related knowledge are easy to understand and apply; because the equations implemented are very simple, the tool is not computationally demanding. In fact, although it was developed and designed to help teach undergraduate electrical engineering students attending on classes hydroelectric generation, this tool can be used to estimate the hydroelectric generation potential of a site, which is the first step before starting a hydro plant project.
Hydroelectric generation is one of the most important sources of electrical energy generation; it is considered to be of the utmost importance for many countries. This is especially justifiable since water is a renewable, clean, and efficient resource. According to Paish (2002), modern generators present a conversion rate of approximately 90% or more as well as a low-cost and accessible resource. Hydroelectric plants are generally multipurpose reservoirs being used for irrigation, residential supply, electricity, and even flood control. Therefore, if well planned, they may bring many benefits compared to all of the other energy resources.
According to the International Energy Agency (2015), the world’s hydroelectricity production is equal to 17% of the total generation. Also, there is still a high percentage of unexplored hydro potential in the world, especially in developing countries.
Some countries, such as Norway, New Zealand, and Brazil, have the energy matrix predominantly based on the use of hydroelectric generation. Regarding the Brazilian electricity sector, the hydrogeneration was approximately 65% of all of the electricity production during 2014. Therefore, 407.2 TWh out of the 624.3 TWh of total generation originated from water resources (EPE, 2015), as depicted in Fig. 1.
Fig 1 The electricity generation in Brazil by source in 2015 (EPE, 2015).
Also, it must be highlighted that, in general, the demand for electricity is continuously increasing, so the power systems must be expanded to manage this increase. The growth in demand is generally related to increases in countries’ economic aspects, such as the gross domestic product. Since large amounts of electricity cannot be stored efficiently, electricity should be produced during the time in which it is consumed. Therefore, a significant rise in demand is leading to an increase in electricity generation using renewables, such as wind, solar, and water resources. Some examples can be seen in the European 2020 climate and energy package from the European Union.
These facts and figures clearly highlight the importance of increasing renewables in the energy share; among them are water resources, which have unexplored potential worldwide. It is crucial that engineers understand and estimate the potential of renewable generation.
Support software is of great importance to improve electrical engineering undergraduate students’ learning. Some subjects present topics that cannot be easily seen in practice, so support software can help boost the learning process. Examples can be seen in the work presented by Fortes et al. (2014) and also in the work by Ayasun and Nwankpa (2005), both of which are learning platforms developed in MATLAB.
This article presents a computational tool to calculate some parameters of hydroelectric plants, focusing mainly on microhydroelectric generation; it also evaluates the energy potential of small hydro plants. This computational tool was developed using MATLAB, and it presents a graphical interface that makes it user friendly. The computer program and related knowledge are easy to understand and apply; because the equations implemented are very simple, the tool is not computationally demanding. In fact, although it was developed and designed to help teach undergraduate electrical engineering students attending classes on hydroelectric generation, this tool can be used to estimate the hydroelectric generation potential of a site, which is the first step before starting a hydro plant project.
In practice, the water is collected in the intake and travels through a pipeline (the penstock) to the powerhouse, where the turbine is located. The water turns the turbine, which is attached to a generator. This generator transforms mechanical power into electrical power. Then, the electrical energy generated by this process can be transmitted to consumers via wires that make up the transmission and distribution networks. A general view of a microhydro plant can be seen in Fig. 2.
Fig 2 Simplified hydroelectrical generation scheme (adapted from US Dept. of Energy).
Consequently, the energy potential of a water course is basically estimated by its head and flow. Therefore, in a selected river, stream, or waterfall, the amount of energy that can be generated depends on the difference in the height between the intake and powerhouse and the flow of water deviated into the turbine. The net electrical potential that can be effectively used is actually this gross energy potential multiplied by the efficiency rate as it relates to the conversion of the electromechanical generation components.
Microdistributed generation (micro-DG) is related to an electricity generation plant with an installed capacity of up to 100 kW. DG generally refers to generation units installed near the demand, that is, near the final consumer. Therefore, DG can reduce electrical losses or even, in large scales, transmission congestion. Consequently, numerous microhydroelectric plants exist in some countries, like Brazil, due to their hydrographical characteristics.
It is necessary, at times, to estimate the amount of electrical energy generation at a chosen location. The platform presented here aims at estimating this potential and helping electrical engineering students better understand hydroelectricity generation. It combines theoretical studies with a practical, real-world application, making it easier for students to grasp the knowledge and discuss some practical aspects of this subject.
Based on information on the head and flow, the generator power can be determined by considering the generator’s and turbine’s efficiencies. After those basic calculations are made, it is possible to determine the main characteristics and equipment of the microhydropower plant.
The preliminary sizing seeks to present, in a simplified manner, the main components of a hydroelectric generator. In addition, it describes the steps in the estimation of plant dimensioning. The sizing estimation may be considered the first step, as it allows one to determine whether the hydromechanical power will be sufficient to justify further studies concerning the investment.
Many other aspects must be taken into account in a final project. Environmental factors play an important role and determine many significant aspects; for instance, they might determine whether the plant can be installed in a given location or if some operation characteristics must be imposed, such as the minimum flow that the river must maintain. Environmental issues are essential aspects that constrain our economic feasibility and vary not only from country to country but also from region to region. Other constraints include equipment costs, the construction cost of the dams and powerhouse (especially when related to some specific regional characteristic), difficulties in the transportation of the equipment to the site, and costs to connect the power plant to the system.
Some data necessary for the preliminary analysis include the available head, or net head, which is the height of the water resource, discounting the losses in the intake and penstock. Also, it is critical that the flow must be continuously provided. Therefore, the intake and penstock are constructed to regularize the water flow. With these data in hand, the available power can be estimated by (1) in watts and (2) in cheval vapeur (CV). \[{P}_{{\text{H}}_{\left({\text{W}}\right)}} = {\gamma}\times{Q}\times{H} \tag{1} \] \[{P}_{{\text{H}}_{\left({\text{CV}}\right)}} = \frac{1,000}{75}\times{Q}\times{H}, \tag{2} \] where ${\gamma}$ is the specific weight of the water, Q is the flow, and H is the head.
After calculating the net head, the type of turbine can be chosen. The net head is not the only variable that affects the turbine choice, but it is the main decision variable. Table 1 shows the main kinds of turbines and specific velocity characteristics related to the available head.
Table 1. The main kinds of turbines and specific speeds.
The most important part of the hydroelectric plant is the turbine, as it converts hydraulic energy to mechanical energy that is then transformed into electrical energy by the generator. A large variety of turbines are available, generally divided into two main kinds: impulse and reaction turbines.
Impulse turbines basically convert the available kinetic energy into mechanical energy. This group is mainly represented by Pelton wheels. Fig. 3 provides a historical picture that shows the original patent drawings of the Pelton wheels.
Fig 3 The Pelton wheel (L.A. Pelton, U.S. Patent 233 692). (Source: http://www.google.com/patents/US233692.)
The Francis turbine shown in Fig. 4 and Kaplan turbine in Fig. 5 represent the main reaction turbines, in which the static pressure diminishes between the rotor input and its output. In the Francis models, the flow is radial. The water enters through a circular duct with a decreased section and then moves a central rotor. The main difference between the Kaplan and Francis turbine is the rotor design.
Fig 4 The Francis turbine. (Source: Wikicommons [https://commons.wikimedia.org/wiki/File:M_vs_francis_schnitt_1_zoom.jpg].)
Fig 5 The Kaplan turbine. (Source: Wikicommons [http://commons.wikimedia.org/wiki/File:Water_turbine.svg].)
The computational platform can be used to estimate either the large hydroelectric power station (LHPS) or the microhydroelectric power station (MHPS).
The input data are composed of the following:
The output data include the following:
In Fig. 6, the screen of the proposed platform is presented, showing the dimensioning of a large hydro plant (LHPS).
Fig 6 The LHPS screen.
For an MHPS, the program simulates a case using a Pelton wheel with one injector.
The variables to be provided are the following:
The outputs provide the following:
Figure 7 shows the screen of the MHPS dimensioning.
Fig 7 The MHPS screen.
To choose the LHPS, one must click on “Calculate”; then, the program will estimate the output parameter. If the “Automatic” button is pressed, the program will choose one or two types of turbines that may be applied to that water resource. If the user wants to choose a different kind of turbine than those proposed, he or she can press the “Manual” button and then press “Calculate.”
The user has the option to save the report as a .txt file that contains the result of the simulation. As presented in Fig. 8, two options are available: the file can be saved as an LHPS or an MHPS case.
Fig 8 The file menu.
The user can choose either LHPS or MHPS, as presented in Fig. 9.
Fig 9 The power stations menu.
This example is used to describe some basic steps for implementing a hydroelectric plant. Specifically, it explains ways to determine the most adequate kind of turbine, available electrical and mechanical power, angular speed of the turbine’s axis, and number of poles in the electricity generator. Given the availability of a hydroelectricity source with a gross head of ${\text{H}}_{BR} = {132}\,{\text{m}}$, the intake losses are evaluated by $\Delta{\text{H}}_{\text{TA}} = {11}{\%}\cdot{\text{H}}_{BR},$ where the efficiency of the penstock can be considered to be approximately ${\eta}_{C} = {85}{\%}$. The flow of this source is ${\text{Q}} = {4}\,{\text{m}}{/}{\text{s}}$.
The intake losses can be calculated based on available data: $\Delta{\text{H}}_{\text{TA}} = \left({{11}{/}{100}}\right)\cdot{132} = {14.52}\,{\text{m}}$; the penstock losses are calculated using the given efficiency: $\Delta{\text{H}}_{\text{CA}} = {(}{\text{H}}_{BR}{-}\Delta{\text{H}}_{\text{TA}}{)}\cdot\left({{1}{-}{\eta}_{C}}\right) = \left({{132}{-}{14.52}}\right)\cdot\left({{1}{-}{0.85}}\right) = {17.62}\,{\text{m}}$.
The available (net) head can be measured by discounting the estimate losses from the gross head: ${\text{H}} = {\text{H}}_{BR}{-}\left({\Delta{\text{H}}_{\text{TA}} + \Delta{\text{H}}_{\text{CA}}}\right) = {132}{-}\left({14.52} + {17.62}\right) = {99.86}\,{\text{m}}$.
To choose the type of turbine, it is necessary to determine the turbine’s specific speed. This step uses a set of empirical equations and makes some prior assumptions.
Supposing that a Pelton wheel is used, the specific speed may be calculated by ${n}_{s} = \sqrt{{R}_{o}}\cdot\left({{{A}_{PE}}{/}{\sqrt{{H}_{BR}}}}\right) = {1}\cdot\left({{510}{/}{\sqrt{132}}}\right)\approx{44}{\text{r}}{/}{\min}$, where ${R}_{o}$ is the number of rotors of the turbine, and ${A}_{PE}$ is an empirical measure that is considered to be 510 in the present work.
Supposing that a Francis turbine is used, the specific speed is calculated as ${n}_{s} = {2,300}{/}{\sqrt{{\text{H}}_{BR}}} = {2,300}{/}{\sqrt{132}}\approx{200}\,{\text{r}}{/}{\min}$. Table 1 reveals that the Francis turbine is the most appropriate, with a specific speed of ${132}\,{\text{r}}{/}{\min}\leq{n}_{s}\leq{200}\,{\text{r}}{/}{\min}$ and an available head between 50 and 100 m.
As the available head is near 100 m, a simple change from $\Delta{\text{H}}_{\text{TA}} = {14.52}\,{\text{m}}$ to $\Delta{\text{H}}_{\text{TA}} = {14.3}\,{\text{m}}$ would make ${\text{H}} = {100.045}\,{\text{m}}$, changing the turbine to a two-nozzle Pelton with ${36}\,{\text{r}}{/}{\min}\leq{n}_{s}\leq{50}\,{\text{r}}{/}{\min}$ and ${100}\,{\text{m}}\leq{\text{H}}\leq{400}\,{\text{m}}{.}$ Therefore, for the same resource, there may be more than one kind of turbine that can be chosen, as the values are approximate.
The mechanical power available to the generator (in CV) is ${\text{P}}_{{\text{MG}}_{\left({\text{CV}}\right)}} = {\eta}_{\text{t}}\cdot{1,000}{/}{75}\cdot{Q}\cdot{\text{H}}{.}$ If one considers the turbine efficiency as ${\eta}_{\text{t}} = {85}{\%}$, then ${\text{P}}_{{\text{MG}}_{\left({\text{CV}}\right)}} = {0.85}\cdot{1},{000}{/}{75}\cdot{4}\cdot{99.86} = {4,526.9}\,{\text{CV}}$. To estimate the electrical power, one can apply the generator’s efficiency: ${\text{P}}_{{\text{E}}_{\left({\text{W}}\right)}} = {75}\cdot{9.81}\cdot{\eta}_{\text{G}}\cdot{\text{P}}_{{\text{MG}}_{\left({\text{CV}}\right)}} = {75}\cdot{9.81}\cdot{0.98}\cdot\,{4,526.9} = {3,264.05}\,{\text{kW}}$, or ${\text{P}}_{{\text{E}}_{\left({\text{VA}}\right)}} = {(}{\text{P}}_{{\text{E}}_{\left({\text{W}}\right)}}{/}{\text{power factor}}{)} = {(}{3,264.05}{/}{0.9}{)} = {3,626.72}\,{\text{kVA}}{.}$
The angular speed of the turbine is calculated as a function of the specific speed, mechanical power, and available head, as presented in the equation ${n}_{\text{T}} = {n}_{s}\cdot{(}{\text{H}}^{1.25}{/}{\text{P}}_{{\text{MT}}_{\text{CV}}}{}^{0.5}{)} = {200}\cdot\,{(}{99.86}^{1.25}{/}{4,526.9}^{0.5}{)} = {938.36}\,{\text{r}}{/}{\min}{.}$
The turbine’s axis is attached to a synchronous generator, so the actual speed depends on the system’s electrical frequency and number of poles in the generator. In the case of the Brazilian system, the frequency is 60 Hz. The number of poles is calculated using ${\text{P}} = {120}\cdot{f}{/}{n}_{\text{T}} = {120}\cdot{60}{/}{938.36} = {7.67}$ poles. As this must be an integer, it can be rounded to eight poles, resulting in a rotation speed of ${900}\,{\text{r}}{/}{\min}{.}$
This example illustrates a real case of a Brazilian power system hydro plant. To calculate this example, we considered some real official data, like the total generated output and kind of turbine utilized. This 50-MW installed capacity plant is located in the southeastern region of Brazil; it has a gross head of 127.9 m and 21.54 m³/s. This example is shown in Fig. 10; clearly, to achieve the correct output of electrical power, a high efficiency is needed. This is due to the fact that this software presents a first forecast for the energy potential, but it must be highlighted that, even with many approximations, the results are well estimated.
Fig 10 Estimating the potential of a real Brazilian hydroelectric generator.
This work presents the dimensioning of a hydroelectric power plant and software to size the plant’s main parameters in a simplified manner. The objective of this computational tool is to verify the amount of electrical energy that can be generated in a selected water resource—more specifically, to implement microhydro generation. This software is especially important to electrical engineering undergraduate students learning hydro generation, as it gives them real-world examples of the evaluation of potential sites for implementing hydroelectric projects and exploring water resources.
The basic knowledge involved in this work, together with the use of this program, contributes to the learning process. It may be used to show novice students some basic information about hydro generation estimation. This platform can be adapted to include more detailed equations to present a more precise model.
Paulo S.C. Nascimento (castro.paulo@engenharia.ufjf.br) earned his B.Sc. degree in electrical engineering from the Federal University of Juiz de Fora, Brazil, in 2015. He is an engineer at ONS the Brazilian ISO and a Ph.D. candidate at the Federal University of Juiz de Fora, 36036-330, Brazil. His research interests include modeling and simulation of electric power systems and energetic systems.
Rodrigo M. Novaes (rodrigo.novaes@engenharia.ufjf.br) earned his B.Sc. degree in electrical engineering from the Federal University of Juiz de Fora, Brazil, in 2017. He is an energy analyst at PSR Energy Consulting and Analytics, Rio de Janeiro, 22250-040, Brazil. His research interests include computer programming and power system operation planning.
Bruno H. Dias (bruno.dias@ufjf.edu.br) earned his B.Sc. degree in electrical engineering from the Federal University of Juiz de Fora, Brazil, in 2005 and his M.Sc. and D.Sc. degrees from Pontifical Catholic University of Rio de Janeiro in 2006 and 2010, respectively. He is a professor in the Electrical Energy Department, Federal University of Juiz de Fora, Juiz de Fora, 36036-330, Brazil. His research interests include applied optimization, hydrothermal systems operation planning, and electrical engineering education. He is a Member of IEEE.
Digital Object Identifier 10.1109/MPOT.2015.2478635