Hydropower Estimation#

Hydrogenerate canculates hydropower potential using

\[P = \eta \times \gamma \times Q \times H\]

where,

  • \(P\) is the hydropower potential (watt),

  • \(\eta\) is the overall system efficiency (dimensionless),

  • \(\gamma\) is the specific weight of water (9,810 N/m^3),

  • \(Q\) is the flow (m^3/s), and

  • \(H\) is the net hydraulic head (m).

HG uses a simplified configuration, consisting of one penstock, turbine, and generator. The turbine type is selected based on head and design flow. Penstock, turbine diamter and other element are sized for a design flow that can be entered by the user or computed in HG, using flow data. The overall efficiency of the system is calculated as \(\eta = e_{turb}*e_{gen}\), where \(e_{turb}\) and \(e_{gen}\) are turbine and generator efficiencies. Turbine efficiencies at flows below or above the design flow are computed using a set of empirical equations for each turbine type (CANMET, 2004), while considering constant generator efficiency.

HG considers the streamflow provided by the user to be the flow routed through the hydropower plant. In some instances, e.g., multi-purpose operation reservoir, the amount of flow routed through the power system, and its operation, obey different priorities and must be analyzed outside HG to compute the flow available for hydropower generation. The considerations and analyses needed to generate the available-for-hydropower flow are outside the scope of the current version of HG.

HG Workflow#

HG can currently compute hydropower under three hydropower types: Basic, Diversion, and Hydrokinetic. The User Guide section includes multiple examples that illustrate each of these hydropwoer types as well as additional funcitionality.

Basic hydropower calculation:#

Required inputs: Hydraulic head, flow, rated power. In the basic calculation mode, users can input two of these three variables and HG will calculate the third.

Diversion#

Required inputs: Hydraulic head, flow. Optional inputs: all the inputs listed in Table 1 in the User Guide section, except those used only for hydrokinetic estimations.

Computation Steps:#

  1. Compute head losses using the method described in the Theory Section - Head Loss Estimation.

  2. Calculate the design flow as described in the Theory Section - Design Flow Estimation (\(Q_d\)).

  3. Select the turbine type based on the net hydraulic head and design flow folowing the graph included in the Theory Section - Turbine Selection.

  4. Calculate turbine efficiency using the corresponding turbine equation included in the Theory Section - Turbine Efficiency for flows above and below the design flow. Turbine efficiency is calculated following the methodology presented in the Clean Energy Project Analysis electronic textbook (CANMET Energy Technology Center, 2004)

  5. Estimate estimate power for the value (s) of flow provided the user implementing any contraint selected. Flow constraints are discussed in the Theory Section - Flow Constraints

  6. Compute the overall efficiency of the system. The overall efficiency of the system is computed as the turbine efficiency (calculated in step 4) times the Generator efficiency.

  7. Compute estimated power potential using the hydropower euqation at the top of this document.

  8. Compute all economic parameters as described in the Theory Section - Cost, O&M, and Revenue Calculation.

Output: the list of outputs will depend on the inputs used. In the most complete case, the output list includes all the variables listed in Table 2 in the User Guide section, except for those resulting from hydrokinetic calculations.

Hydrokinetics#

For hydrokinetic generation, HG will estimate the potential of installing a single turbine. Users can use this single turbine estimate as a reference value for single installations or understand the type of setup needed to meet their energy needs. For hydrokinetic assessments the only required input is the average velocity in the river section. Additionally, the users can select among different hydrokinetic turbine types and vary the dimensions to evaluate energy potential.

For hydrokinetic estimations, when replacing the net hydraulic head by the velocity head, we obtain:

\[P=\eta \ast\rho\ast Q\ast\ \frac{V^2}{2}\]

Replacing \(Q=V\times\ A_b\), we obtain:

\[P=\frac{1}{2}\eta \ast\rho\ast A_b\ast V^3\]

Where

  • \(\rho\) is the density of water, in Kg/m^3,

  • \(A_b\) is the swept area of blades, in m^2, and

  • \(V\) is the velocity of water, in m/s.

The maximum energy that can be extracted from flow is limited to approximately 59%; this value is commonly known as the Betz limit (Betz, 2014). Replacing \(\eta\) with 0.59 allow us to compute the maximum energy that could be generated for a turbine of a given area:

\[P=0.295\ast\rho\ast A_b\ast V^3\]

The average channel velocity value introduced by the user is directly used in this equation. The swept area of blades is computed for each turbine type and dimensions given. Niebuhr et al., (2019) provides a review of existing hydrokinetic turbine types. The turbine types and default sizes included in HG were derived from Niebuhr et al., (2019) and brochures of existing hydrokinetic turbines.

Required inputs: Average cross sectional velocity. Optional inputs: type of blade, height and diameter of blade.

References#

DOE. (2023). Types of Hydropower Plants | Department of Energy. https://www.energy.gov/eere/water/types-hydropower-plants

Hadjerioua, Boualem, Wei, Yaxing, and Kao, Shih-Chieh. An Assessment of Energy Potential at Non-Powered Dams in the United States. United States: N. p., 2012. Web. https://doi.org/10.2172/1039957

U.S. Bureau of Reclamation. (2011). Hydropower Resource Assessment at Existing Reclamation Facilities. https://www.usbr.gov/power/AssessmentReport/USBRHydroAssessmentFinalReportMarch2011.pdf

U.S. DOI. (2007). Potential Hydroelectric Development at Existing Federal Facilities For Section 1834 of the Energy Policy Act of 2005. https://www.usbr.gov/power/data/1834/Sec1834_EPA.pdf

CANMET Energy Technology Center. (2004). Clean Energy Project Analysis: Retscreen Engineering & Cases Textbook. https://www.ieahydro.org/media/1ccb8c33/RETScreen®-Engineering-Cases-Textbook–-PDF.pdf

Betz, A. (2014). Introduction to the theory of flow machines. Elsevier. eBook ISBN: 9781483180908. https://shop.elsevier.com/books/introduction-to-the-theory-of-flow-machines/betz/978-0-08-011433-0

Niebuhr, C.M., Van Dijk, M., Neary, V.S. and Bhagwan, J.N., 2019. A review of hydrokinetic turbines and enhancement techniques for canal installations: Technology, applicability and potential. Renewable and Sustainable Energy Reviews, 113, p.109240. https://doi.org/10.1016/j.rser.2019.06.047