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One Dimensional Penstock Flow Models for Hydropower Digital Twin

This report details the inelastic, unsteady, one-dimensional flow equations that are used to model flow through a penstock in a hydropower facility. The flow model is coupled to a mechanistic turbine model to compute the rotation rate of the turbine, which is dependent on the flow rate, gravitational head, and various parameters of the machine, such as inlet vane angle. Results are given for an example hydropower facility in which the turbine is subjected to a specified time-varying load, and the results on the flow rate are shown. Future applications for the flow model are also briefly reviewed.

13 HYDRO ENERGY↗

Hybridization Assessment of Trybrid Pumped Storage Hydropower System—Part 1: A Case Study of Corral Summit

This report is a part of the deliverables for technical assistance provided to Cat Creek Energy for the Coral Summit Trybrid (Triple Hybrid-Pumped Storage Hydropower, Battery Energy Storage System, and photovoltaic solar energy) energy project. This report explores the operational benefits and challenges of hybridizing an open loop PSH (200MW) located at Mackay, Custer County, Idaho with solar PV (Ground mount 300MW and floating 40MW) and battery (720MWhr). This document reports two activities performed as a part of the hybridization assessment task 1) optimal resource allocation and energy management strategy, and 2) power quality and reliability assessment. From optimal resource allocation and energy management strategy (activity 1), the following key findings can be observed: • Conventional PSH (CPSH) with two reversible pump turbines and separate penstocks can provide required flexibility equivalent to that from two ternary PSH with separate penstock. With single unit CPSH, upper reservoir head cannot be maintained accurately, the variation of water level is rapid and pump mode flexibility is not available. These disadvantages can be overcome by single unit TPSH. However, using two CPSH units with separate penstocks also overcome these disadvantages with the formation of the hydraulic short circuit between two conventional units. • Flooding of the lower reservoir is a severe concern when considering continuous operation for black start. This limits the duration of continuous operation from PSH alone to around 50 hours. Due to the complementary PV and battery action, the duration of continuous operation and smooth power output can be extended. • An optimization problem is framed that maximizes the power output on an hourly basis while minimizing constraint violations and respecting seasonal variations of solar PV and load profiles . Two value streams, arbitrage and baseload generation are served by this profile. It was uncovered that for smooth power output during regular operation, PV curtailment will be required, or the battery capacity needs to be increased above 90MW to accommodate additional PV. From power quality and reliability assessment (activity 2) the following takeaway points can be observed: • The Trybrid, when integrated at the Lost River bus, and limited to 250MW in generation mode and -150MW in the pump mode, causes no violation of voltage or flow.

13 - HYDRO ENERGY↗

Control Co-Design Framework for Joint Optimization of PID Governor and Hydraulic Dynamics for a Hydropower Plant

This paper presents a control co-design (CCD) framework tailored to the hydraulic and mechanical subsystems of hydropower systems, aimed at enhancing their dynamic performance and responsiveness to grid demands. Conventional sequential design approaches often fall short in capturing the coupled interactions between plant dynamics and control objectives. The proposed CCD methodology enables simultaneous optimization of key hydro plant parameters - such as governor settings, penstock characteristics, and valve control - with the control system architecture. Results indicate that both CCD and sequential design approaches achieve comparable transient and steady-state performance, with minor discrepancies arising from differences in their optimized parameters. However, CCD demonstrates a distinct advantage by tripling the water time constant (Tw) while maintaining similar dynamic performance to the sequential approach. This increase in Tw enables optimization of penstock dimensions, as it is directly influenced by penstock design, thereby contributing to overall cost optimization.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Update on Model Specification Development of Ternary Pumped Storage Technologies [Slides]

T-PSH is an innovative structure of C-PSH that features two turbines, one for pumping and one for generation, replacing the single turbine in C-PSH. These turbines are housed in separate chambers, with an additional set of penstocks connecting the pump turbine to the hydraulic system. This structure enables T-PSH to operate in an HSC mode, allowing for simultaneous pumping and generation, which provides greater operational flexibility compared to C-PSH. To model T-PSH's HSC mode, a user defined turbine and governor system model is required, including the shared penstock model and additional pump turbine model. This specification will focus on the details of the user-defined turbine and governor model, which leverages the HYGOV model.

16 TIDAL AND WAVE POWER↗

Structured Neural Network Modeling for Developing Digital Twins Models of Hydropower Generation Units

Dynamic modeling is a key part in the development of digital twin (DT) for dynamic systems. This is true for hydropower systems, where whole system modeling including penstock, turbine and generators, etc is important in realizing actuate modeling for the real systems. On the other hand, in response to the large variations of the power demand due to increased penetration of renewables such as wind and solar, hydropower systems are now required to operate in a large power generation range. This situation triggers the nonlinear characteristics of the generation unit with respect to its models. As such, it is imperative to use data driven modeling such as neural networks to learn the nonlinear dynamics of the hydropower generation unit. To achieve this objective, this study constructs a modeling and learning algorithm integrated with multiple structured neural network models for the modeling of turbine shaft speed, penstock pressure, and generator power output based on the generator power control setpoint, field current, and field voltage. In addition, the study uses the hydropower data from Tacoma Public Utilities to train and validate the proposed neural network algorithm. The results have shown that this structured neural network modeling approach can learn the system dynamics effectively by using the real-time data collected from the hydropower system with the desired modeling results.

Wang, Hong↗

DT-HYDRO

The software solves the time dependent, one dimensional (1D) coupled mass and momentum balance equations governing the elastic flow of water through the penstock, turbine and draft tube in a hydroelectric facility using a high order finite volume based method. The numerical method is based on the Kurganov-Tadmor central method paired with the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL). This solution method accurately resolves the fast transient behavior of the flow, including water hammer. Additionally, the software estimates the full 3D flow field within the turbine chamber in real time, a feat that is made possible by leveraging pre-computed CFD results by utilizing a reduced order modeling method based on an efficient randomized singular value decomposition (SVD) driven proper orthogonal decomposition (POD) with POD-mode weight regression. The reduced order model of the 3D flow is directly coupled to the 1D elastic flow model so the entire flow field through the penstock and turbine system is resolved quickly and with high fidelity.

Gurecky, William [Oak Ridge National Laboratory (O↗

Construction Support for New Slab Creek Powerhouse Project (Final Technical Report)

The Sacramento Municipal Utility District (SMUD) has constructed a new powerhouse and Boating Flow Release Facility (BFRF) ¼ mile downstream of the existing Slab Creek Dam with the assistance of grant funding from the Department of Energy in the amount of $1.5 million. Slab Creek Dam impounds 16,600 acre-feet of storage and has a normal full pool elevation of 1850ft. Water is conveyed from Slab Creek Reservoir through a 4.9 mile power tunnel to the 224 MW White Rock Powerhouse which discharges into Chili Bar Reservoir. A small 450 kW powerhouse located at Slab Creek Dam utilizes the original license in-stream flow requirement. The new license (FERC Project No. 2101-084) requires significantly more instream flows immediately below the dam for aquatic preservation and recreational flows over the original license. The terms of the new license allow the Slab Creek Powerhouse to utilize the original required dam releases, while the new South Fork Powerhouse will use the new instream flow requirements above the original license requirement. The South Fork Powerhouse routes flows back to the South Fork of the American River via a new penstock that is tied into the White Rock Tunnel at Adit #3. This new penstock bifurcates at the Adit #3 portal with one leg going to the BFRF and the other to the new powerhouse. The South Fork Powerhouse is a single generating unit with a capacity of 2.98 kVA. The BFRF is valve house with an energy dissipation chamber for a 60” fixed cone valve capable of passing 1,300 cfs for meeting the recreational flow requirements of the license.

power tunnel↗

1D Modeling for the Development of a Digital Twin for Hydropower Systems with Applications for a Testing Rig

Modeling and simulation constitute two important parts in constructing a sensible digital twin to mimic the dynamics of hydropower systems. Because of the physical nature of a hydropower system, the basic modeling should cover the water flow systems from the reservoir to the penstock (inlet water pipes), penstock to hydro turbine, and hydro turbine to generator and from the linkage of the hydropower systems to the grid. This report describes initial attempts to model these dynamic components, including the formulation of the linearized state space model for hydro turbine systems using the well-known six-coefficients linearization method and the formulation of the voltage and power dynamical models of a synchronous generator. To validate the accuracy of the proposed model, data collected from Norwegian University of Science and Technology were used to obtain relevant parameters for the model, and the desired simulation results were obtained. Additionally, neural network modeling and learning were also developed and applied to model the generation torque and water flow rate subsystems to demonstrate a potential learning scheme, which can be used in the development of a digital twin.

13 HYDRO ENERGY↗

Elastic Flow Modeling for Hydropower Digital Twins

This report details the elastic, unsteady, one-dimensional flow equations that are used to model flow through a penstock in a hydropower facility. The elastic flow model is accurate even in cases of fast transients, long penstock length, and high gravitation head. The compressibility of the water and elasticity of the pipe walls are explicitly accounted for in the developed models so that the water hammer phenomena can be accurately captured. The elastic flow model is coupled to a mechanistic turbine model to resolve the dynamic feedbacks between the elastic water column and the turbine rotation rate. A finite volume method is employed to solve the governing equations, and the method is shown to have low numerical diffusion in sharp gradient phenomena, such as those encountered when simulating water hammer. The method is applied to single dimensional linear advection benchmark problem and numerical results are compared with analytic results. This is followed on by an application to a full hydropower system with a coupled turbine. The elastic flow model results are compared against an inelastic model.

13 HYDRO ENERGY↗

Hybrid renewable pumped storage hydropower energy storage system

A pumped storage hydroelectric system may include a reservoir system including an upper reservoir system and a lower reservoir system. At least one of the upper reservoir system and the lower reservoir system may include a modular reservoir arrangement. A penstock may be coupled with the upper reservoir system. A pump/turbine may be coupled with the penstock and with the lower reservoir system. The pump/turbine may be configured to receive water flowing from the upper reservoir system to the lower reservoir system for generating electrical power, and to pump water from the lower reservoir system to the upper reservoir system for storing energy.

Medina, Hector Eduardo↗

FAST Equipment Lease with Liberty University, Inc. (Cooperative Research and Development Final Report)

Liberty University, Inc. (Participant) will receive government owned equipment from NREL to evaluate and perform fatigue testing of bladders in use for small scale pumped storage hydropower. NREL is providing technical support to advance Liberty University's pumped storage hydropower (PSH) concept towards commercialization. The concept creates modular upper and lower watertight enclosures (tanks or reservoirs) connected by a series of modular pipe lengths (penstock).

13 HYDRO ENERGY↗

Financial Analysis of the Smallmouth Bass Flows implemented at the Glen Canyon Dam during Water Year 2024

The Glen Canyon Dam (GCD) is a Colorado River Storage Project (CRSP) power resource that is a component of the Salt Lake City Area Integrated Projects (SLCA/IP). The 2016 record of decision (ROD) for the GCD long-term experimental and management plan (LTEMP) final Environmental Impact Statement (EIS) specifies criteria for GCD monthly water releases, daily and hourly operating limits, and experimental releases. This report presents a financial analysis of the Smallmouth bass (Micropterus dolomieu) (SMB) flows implemented at GCD during Water Year (WY) 2024. These bypass flows were introduced by the U.S. Bureau of Reclamation (USBR) as an emergency response to the growing threat posed by invasive SMB in the Colorado River ecosystem downstream of the dam. SMB are a non-native predatory species that pose a significant threat to native fish populations, including the endangered humpback chub (Gila cypha). The thermal regime below GCD, typically cold due to hypolimnetic releases from Lake Powell, has historically served as a thermal barrier limiting SMB establishment. However, persistently low reservoir levels in recent years have reduced stratification in Lake Powell, allowing warmer water to be released downstream. This has enabled SMB to spawn successfully below the dam, prompting urgent ecological concerns. To mitigate the risk of SMB proliferation, the USBR implemented a series of bypass flows in WY 2024. Drawn from a lower elevation than the penstocks, the bypass structures released cooler water downstream. These short-duration bypass flows aimed to keep temperatures cool enough to prevent SMB from spawning, thereby reducing the ecological threat posed by this invasive species. Although motivated by ecological objectives, these bypass flows came with financial tradeoffs. Releasing water through the bypass structures instead of the turbines at GCD reduced hydropower generation, resulting in a significantly lower financial position for Western Area Power Administration (WAPA), which is responsible for marketing the electricity produced by the GCD Powerplant. This report analyzes the financial impact of the SMB flows implemented from July to November 2024. These experimental releases led to an estimated financial cost of approximately $18.9 million, primarily driven by the substantial volume of water diverted through the bypass structures. This study applies an integrated set of tools to estimate WAPA financial impacts by simulating GCD under two types of cases; namely, (1) a “With Experiment” case that mimics the water operations that actually occurred, including the SMB bypass flows, and (2) a “Without Experiment” case that simulates operations under the assumption that the SMB flows did not occur. Both cases comply with LTEMP hourly and daily operating criteria, and the monthly water release volumes are assumed to be identical under both cases. The Colorado River Storage Project Python-based model (CRiSPPy) model was the main modeling tool used to simulate the dispatch of the GCD hydropower plant and associated water releases from Lake Powell. In the modeling process, the research team used extensive data sets and historical information on SLCA/IP power plant characteristics, hydrologic conditions, and WAPA’s power purchases and sales prices.

13 HYDRO ENERGY↗

Digital Twin User Guide for Chelan County Public Utility District

This user manual offers a comprehensive guide for developing a Digital twin (DT) of a Kaplan turbine at Chelan County Public Utility District (Chelan PUD) using neural networks. As variable renewable generation expands, hydropower units must operate with optimal efficiency and stability. For Kaplan machines, this flexibility is achieved through coordinated control of guide vane (wicket gates) opening and runner blade pitch, which amplifies the plant’s inherent nonlinear behavior and challenges traditional physics-only modeling. The efficiency of the Kaplan turbine varies with different combinations of the guide vans (wicket gate) opening and the blade angle. Each guide van opening and blade angle has a corresponding highest efficiency point, forming a cam relationship that represents the optimal combination.The discharge of a hydraulic turbine is controlled by the opening angle of the guide vans. Therefore, for each value of head, there is a certain guide van opening and blade angle that corresponds to the highest efficiency. For a given head, different combinations of the guide van opening and blade angle have different efficiencies. Therefore, coordinate cam curves are used to describe the relationship between the wicket gate opening and blade angle with different water head. To address these challenges, the manual details a data-driven modeling and learning workflow centered on structured neural networks. The approach is designed to forecast critical operational variables—discharge flow, net head, penstock (or scroll-case) pressure, and generator electrical outputs—by leveraging real-time inputs such as the generator power control setpoint, exciter field current and field voltage, together with hydromechanical commands (e.g., gate position and, when available, runner blade-pitch angle). The neural models are trained and validated on operational data from a Kaplan unit operated by Chelan PUD, demonstrating that the structured NN architecture can learn the coupled gate–blade–electrical dynamics. The result is a robust DT that improves situational awareness and supports data-informed decision-making for Chelan PUD’s Kaplan turbine operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Adaptively Learned Modeling for a Digital Twin of Hydropower Turbines with Application to a Pilot Testing System

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained.

13 HYDRO ENERGY↗