Combining the scaling principles traditionally used in physical models with numerical modeling software frequently utilized for flood routing led to an innovative solution for studying load rejection in a power canal.
By Liaqat A. Khan, Charles E. Sweeney, and Roger L. Raeburn
In April 2002, a power canal failed at the 78-MW Swift No. 2 hydroelectric project on the Lewis River in Washington. The 5-kilometer-long power canal carried water from an upstream facility, PacifiCorp’s 240-MW Swift No. 1 project, to the Swift No. 2 powerhouse, which is owned by Public Utility District (PUD) No. 1 of Cowlitz County. As a result of the failure, the Swift No. 2 powerhouse was out of service until February 2006. During this period, Swift No. 1 continued to operate, but the discharge that would normally have been conveyed to the Swift No. 2 powerhouse was diverted to a bypass channel through an existing wasteway in the power canal embankment, upstream of the failure site.
PacifiCorp retained ENSR Corporation’s Redmond, Washington, office to conduct a hydraulic investigation to determine the effects of Cowlitz PUD’s reconstruction plan on the operational flexibility of Swift No. 1. The reconstruction plan included reconfiguring a 1.8-kilometer length of the canal, increasing the hydraulic capacity of the Swift No. 2 powerhouse to 255 cubic meters per second (cms) to match the Swift No. 1 powerhouse, and adding a surge arresting structure at the Swift No. 2 powerhouse. Although the design was expected to improve the overall operation of the system, the power canal reconfiguration created new concerns about the potential for hydraulic transients resulting from load rejections at the Swift No. 2 powerhouse. Detailed hydrodynamic information was necessary to evaluate the possible effects of these conditions and to identify design and operational strategies for managing them.
Modeling approach and model selection
The proposed configuration would reduce the canal volume by 40 percent and increase flow velocity significantly in the reconfigured reach. In addition, PacifiCorp was concerned about possible regulatory restrictions on wasteway flows in the future. The proposed surge arresting structure would have a capacity of 127.5 cms and could be opened or closed completely in one minute. Still, the utility was concerned that, under some circumstances, load rejection could result in overtopping of the canal embankments and adverse effects on the operation of the Swift No. 1 powerhouse. The challenge was to develop an analytical approach to assessing wave heights, wave speeds, and response times at various locations in the power canal for a range of operational scenarios.
To perform the analysis, PacifiCorp and ENSR chose the U.S. Army Corps of Engineers’ UNET, a one-dimensional unsteady flow routing model contained within the HEC-RAS river modeling package. The model allows the user to define spatially variable cross section data; set time-dependent inflows, outflows, and gate operations; and review detailed results at various points in time and space. It also can accommodate reversals in flow – an important feature for the load rejection problem. Furthermore, HEC-RAS offered the advantage of having wide recognition among regulatory reviewers. Many regulatory agency personnel have experience with and confidence in the model and readily understand the interface and outputs.
However, the model’s graphical user interface offers a minimum time step size of one minute for user-input time series, such as the closing of control gates. Therefore, the eight-second load rejection period at Swift No. 2 could not be represented as such in a prototype-scale model. The solution was to construct a scaled numerical model, following the rules of Froude scaling just as they would be applied to a physical model of the system. The modeling was performed on a 56.25:1 (length) scale model. Unlike a typical physical modeling study, in which the model is considerably smaller than the prototype to meet size limitations of the test facility, the scaled numerical model was 56.25 times larger than the prototype. In the following paragraphs, all of the numerical modeling input and results are expressed at the prototype scale.
Model building and testing
To simulate flow in the existing power canal, ENSR constructed a HEC-RAS model with 42 cross sections representing the spatially variable canal geometry. The sections were derived from construction drawings and a digital terrain model of the canal that was developed for this study. To represent the proposed configuration, the original sections within 1.83 kilometers of Swift No. 2 were replaced by the newly designed trapezoidal sections with appropriate invert elevations. The turbine intakes at Swift No. 2 were represented in the model by sluice gates, which could be set to close over a specified time period. Another sluice gate represented the surge arresting structure. The gates representing the turbine intakes and surge arresting structure were sized in the model to match the conduit diameter in the prototype.
We calibrated the numerical model by adjusting the Manning’s roughness and sluice gate discharge coefficients and comparing the model results to historical records of flows and water surface elevations. The calibrated Manning’s “n” value and discharge coefficient were 0.017 and 0.45, respectively, based on calibration at a flow of 73.4 cms. For the calibration run, the error in the computed head loss in the 5-kilometer canal was 1.3 percent. The model was then verified for a historical discharge of 226.5 cms, which is approximately 90 percent of the maximum hydraulic capacity of Swift No. 1 and the proposed maximum capacity of Swift No. 2. The error in head loss for the verification run was 6.3 percent.
Wave propagation in the canal
To represent the effects of load rejections at Swift No. 2, the model was set to simulate a sluice gate closure having an eight-second duration. The internal computational time step was 0.8 second, allowing closure of the gate over ten time steps. The surge arresting structure gate opened in 60 seconds (75 time steps), immediately following load rejection at Swift No. 2. The model was allowed to develop the initial conditions using a steady-state water surface profile calculation. A steady inflow of 255 cms was assumed at the upstream boundary, representing continuous, full-capacity operation at Swift No. 1.
The model results without the surge arresting structure showed that if load rejection occurred at Swift No. 2 when both powerhouses were operating at full capacity, significant spilling could occur through the wasteway. The effects of the load rejection are presented in Figure 1 as a time series of water level at the two powerhouses and water level and outflow at the wasteway. The amplitude of the waves is smaller near the wasteway than it is at either powerhouse. Wave energy decays between Swift No. 2 and the wasteway as a result of frictional energy losses and the wasteway outflows. However, as the wave approaches the upstream boundary (Swift No. 1), the amplitude increases again due to reflection of the wave energy at the upstream boundary.
Figure 1 also shows how spill through the wasteway would develop, and eventually stabilize at the power canal inflow rate of 255 cms. The time for spill to begin following load rejection is consistent with the travel time computed from the wave propagation speed, c:
c = (gD)1/2
g is the acceleration of gravity; and
D is hydraulic depth.
The travel time from the Swift No. 2 powerhouse to the wasteway computed from the wave speed formula is 8.6 minutes. The travel time given by the model is 9.3 minutes, and is slightly longer than the time given by the wave-speed formula as a result of frictional effects and storage in the canal. The model also computed a wave travel time of 11 minutes from Swift No. 2 to Swift No. 1, which agrees with the ten-minute travel time observed in the field.
Developing operational strategies
ENSR also made model runs to identify operational measures that would mitigate or prevent spilling at the wasteway. To prevent spill at the wasteway, a complete shutdown of Swift No. 1 would be necessary with the old power canal configuration. A reduction in flow to 127.5 cms (the surge arresting structure capacity) would be necessary with the new configuration. Even with these reductions, there is a possibility of transient wasteway discharges as the wave caused by the load rejection propagates upstream from the Swift No. 2 powerhouse.
The time available to shut down or ramp down the Swift No. 1 powerhouse is related to the speed and height of the wave. The time available was determined using a trial and error process. Figure 2 shows the temporal variations in water level at the two powerhouses and the wasteway, as well as wasteway flow, for the existing canal, assuming that the response at Swift No. 1 would begin one minute after the load rejection at Swift No. 2, reaching complete shutdown at the end of the second minute. In this simulation, a peak wasteway flow of 6.7 cms occurred about 17 minutes after load rejection. The figure shows that Swift No. 1 could be shut down within two minutes with a very small wasteway overflow. To avoid any spill at all, it would be necessary to initiate shutdown 15 seconds earlier, still assuming that the shutdown process lasted one minute from beginning to end. Alternatively, spill could be avoided by raising the wasteway crest elevation by 10 centimeters.
Figure 3: In the proposed condition, which includes a surge arresting bypass having a 127.5 cms capacity, the wave amplitude is diminished to the point that spill at the wasteway is negligible (0.3 cms).
Adding the surge arresting structure outlet at Swift No. 2 would provide improved control of transients in the power canal. Figure 3 shows the temporal variations in water surface elevation and the wasteway outflow when the Swift No. 1 discharge is ramped down to 127.5 cms (the capacity of the surge arresting structure) over a five-minute period, beginning one minute after the load rejection at Swift No. 2. These results suggest that incorporating the surge arresting structure in the design would permit a much longer response time than the one-minute shutdown period needed with the original configuration. The wave amplitudes shown in Figure 3 also are much smaller than those in Figure 2, and the wasteway outflow under the proposed conditions would be about 0.3 cms.
Practical benefits of an unorthodox approach
Designers and operators of hydro plants frequently face the problem of handling surges in power canals. In the case of the Swift No. 2 canal study, the project managers were able to identify an effective strategy for controlling surges. The analytical results also provided a scientific rationale for adding the surge arresting bypass at Swift No. 2.
The methodology applied to the Swift No. 2 project is conceptually transferable to other projects. In many cases, designers need to understand the full dynamic effects of a rapid change in operating status. Possible applications include: turbine operation or upgrades; synchronizing load acceptances at adjacent plants; reconfiguring power canals; upgrading or operating forebay control structures or fish passage facilities; and in embankment overtopping studies. The software used in this study is free and is widely accepted for dynamic modeling in rivers and canal systems. Like all computer models, it has limitations. In this study, those limitations were overcome by returning to traditional physical modeling principles without sacrificing the benefits of digital analysis.
Dr. Khan and Mr. Sweeney may be contacted at ENSR, 9521 Willows Road N.E., Redmond, WA 98052; (1) 425-881-7700; E-mail: firstname.lastname@example.org. com or email@example.com. Mr. Raeburn may be contacted at PacifiCorp, 825 N.E. Multnomah, Suite 1500, Portland, OR 97232; (1) 503-813-6667; E-mail: firstname.lastname@example.org.
Liaqat Khan, senior technical specialist at ENSR, developed and conducted the model study described in this article. Charles “Chick” Sweeney, ENSR’s hydraulic engineering program manager, provided input to the modeling strategy and reviewed study results. Roger Raeburn, asset planning manager for PacifiCorp, reviewed the possible effects of the proposed reconstruction of Swift No. 2 on the Swift No. 1 plant.
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