With penstock response to transient conditions being critical to the service life and safety of any hydroelectric project, Pacific Gas & Electric Company has engaged in a program to evaluate operating pressures through hydraulic modeling.
By Stephane Lecina and Mohammad Aslam
Pacific Gas & Electric Company (PG&E) operates 68 hydroelectric facilities in the western U.S. PG&E’s hydro facilities have been in service for multiple decades (some more than 100 years), and ensuring their continued safe operation is essential. PG&E has implemented an asset management program to enhance safety, mitigate risks and increase production.
As this program has progressed, the structural capacity and integrity of the penstocks and their response under transient conditions has become an area of interest. Transient conditions, or surges, are among the most severe conditions to occur at hydropower facilities, and the response of turbines, control valves, penstocks, surge shafts and tunnels is critical to the service life and safety of hydroelectric projects.
Within the asset management program for penstocks, PG&E has implemented a process for performing load rejection testing to determine if maximum transient pressures encroach on or exceed rated penstock capacities. Surge pressures are measured at the downstream end of the penstock inside the powerhouse near the turbine shutoff valve, and when possible also at the start of the penstock near the penstock shutoff valve. Load rejection testing is performed for different operating conditions, which typically include load rejection at speed no load, 25%, 50%, 75% and 100% of full load operation. The recorded pressures are compared to the penstock’s operating capacity, which is estimated based on wall thickness and an applied safety factor. If recorded surge pressures exceed the penstock’s rated capacity, mitigation measures are required to bring operation within acceptable limits.
In 2010, PG&E sought advice from Black & Veatch on how to use the recorded pressures at the powerhouses to determine the maximum surge pressures along the entire length of the penstocks. Several of PG&E’s penstocks are greater than 1 mile long, which might result in critical sections being located several thousand feet from the pressure measurement point. Additionally, as part of its pressure relief valve (PRV) replacement program, PG&E was interested in identifying surge pressures along the penstock in the event the PRV failed to open. Most of PG&E’s Francis units are equipped with a PRV, which is set to open for surge relief in the event of a load rejection, when the wicket gates close rapidly to prevent overspeed. Field testing for this extreme event is not acceptable. However, identifying the facilities with the highest exposure for this event would allow PG&E to prioritize the PRV replacement.
To achieve these two objectives, Black & Veatch recommended performing transient analysis through hydraulic modeling. In 2011, PG&E enlisted Black & Veatch to start the analyses, and in 2016 the program was extended to include all PG&E hydro facilities. At the rate of eight transient analyses per year, more than 70 penstocks at 50 hydro facilities (including Francis, Pelton and pump turbine units) have been modeled (see Table 1).
Table 1. Powerhouses and penstocks modeled
The objectives in the hydraulic transient modeling were to simulate a range of operating conditions, including extreme cases, and compute surge pressures along the entire penstock length to identify the sections exposed to the most critical transient conditions. Transient modeling was performed using Black & Veatch’s hydraulic modeling software, which allows modeling of detailed hydraulic components, including closed conduits, surge chambers, stand pipes, air valves and dynamic valves and gates. For Francis units, Black & Veatch used a simplified approach by modeling the wicket gates as valves and the runner as a variable orifice, which is a common practice for determining transient pressures when accurate turbine data and performance curves are not available.
The availability of detailed field data recorded during the load rejection tests — including position vs time of needle valves, wicket gates and PRV in addition to pressure data — allowed for the transient models to be calibrated against field data. Model accuracy was improved by comparing the computed surge pressures against multiple sets of field data, generally covering the full range of turbine operation.
Model calibration consisted of first adjusting the head losses through the system (intake, tunnel, penstocks and turbines for Francis units) to achieve steady-state conditions and then adjusting the flow curves for the PRV and needle valves or wicket gates to match the recorded pressure during the load rejection event. Figure 1 shows the calibration results for the Unit 2 turbine in the Hass Powerhouse, showing computed surge pressures against the recorded field data.
Figure 1. Calibration results for the Unit 2 turbine in the Hass powerhouse for 50% and 100% load rejection.
The analytical model and recorded surge pressures (or hydraulic grade lines, HGL, used in the graph) match not only for maximum and minimum surge values but also for frequency oscillations. Both low-frequency oscillations, controlled by the surge tank characteristics, and high- frequency oscillations, controlled by wave speed through the penstock, relatively closely match the recorded pressures.
The quality and accuracy of model output is proportional to the accuracy of available information for model input. The field measurements PG&E collected during load rejection tests provided an excellent basis for model calibration and, as a result, most of Black & Veatch’s transient model was not subject to significant output errors. The relatively simple geometry of the hydro systems and the availability of comprehensive load rejection tests combined with efficiencies of scale resulted in a streamlined analysis process and reduced costs.
Results and lessons learned
The model output was of great use to PG&E to more precisely estimate the maximum surge pressure in each penstock section, therefore identifying the most at-risk sections. Before developing the transient models, the maximum surge pressure measured at the powerhouse during the tests was used to determine a percentage of pressure increase above static pressure. This value was applied to all the penstock sections to perform the structural analysis. However, the results provided by the transient models showed that this basic approach was inaccurate because it did not account for the penstock profile or the shape of surge envelopes, and in some penstock sections the discrepancy was noticeable.
In several facilities, the maximum surge pressures computed in the upper sections of the penstock exceeded the general tolerance set by PG&E to flag high pressures. As a result, additional structural analyses and/or modified operations were required to allow continued operation.
Once a model is calibrated, analyzing other scenarios can be done relatively efficiently and yield powerful information. In most facilities, the transient model was used to evaluate extreme conditions, which are unsafe to test (PRV failure, rapid valve closure, blockage, etc.). In several large facilities, the model was used to evaluate conditions under which test data could not be obtained, such as load rejection events without bypass flows (to other units in the same powerhouse or to instream releases). Bypass flows generally provide surge relief, reducing the overall magnitude of surge.
The transient models were used to estimate the extreme surge pressures resulting from a PRV failure and to identify the most at-risk penstocks to prioritize PRV replacement. Figure 2 presents the surge envelopes developing along the Wise 1 penstock with and without the PRVs. It illustrates the severity of the surge if the PRVs failed to open, showing a significant increase in maximum pressures and with low pressures reaching full vacuum conditions at all the high points, exposing the penstock to potential damages.
Figure 2. These surge envelopes for the Wise 1 penstock show the severity of the surge if the PRVs failed to open.
In 2015, a transient model (built by Black & Veatch in 2013) of the Cresta hydro facilities was used to investigate the impact of blockage inside the lateral surge tunnel, where routine inspections discovered sediment accumulation. Simulation with the transient model revealed that the impact on surge pressures was minor inside the penstocks and supply tunnel, even when assuming full blockage, because of the relatively small size of the surge shaft inlet/outlet ports. Their capacity was barely reduced by the restriction in the lateral tunnel. Furthermore, the tunnels and surge shaft are oversized as they were designed for the operation of three units but only two units were installed. Additional field testing was performed, including load rejections and load-on/load-off cases, with pressures being recorded at the powerhouse and at the valve house located near the surge lateral tunnel. This test data was then input to the transient model and used to estimate the magnitude of the actual hydraulic restriction and to better estimate its impact on surge pressures. The results of the updated transient analyses provided useful input for the team evaluating the justification of continued operation.
The transient model was also used to identify a means of monitoring the level of blockage/restriction inside the lateral surge tunnel, resulting in a recommendation to monitor the differential head between the two sides of the zone of blockage during load-on transient events.
Figure 3 shows surge HGL vs time, computed at the Cresta powerhouse, when assuming various levels of blockage in the lateral surge tunnel. For all cases, including full blockage, the model shows that the maximum surge pressure occurs about 1 second after the load rejection and reaches a magnitude that is independent of the blockage. The maximum surge is controlled by the transfer of flow from the rapidly closing wicket gates to the rapidly opening PRV. When the pressure peak occurs so rapidly, the surge shaft cannot provide much dampening due to its remote location.
Figure 3. The maximum surge recorded at the Cresta powerhouse was not impacted by the blockage.
Figure 3 also shows that the steady pressure rise coincident with closure of the PRV (from 5 to 40 seconds) is sensitive to the level of blockage inside the lateral surge tunnel. However, the magnitude of this second pressure peak (t = 40s) remains lower than the maximum value reached within seconds of the load rejection.
The load rejection tests were used to calibrate and validate the analytical hydraulic models, which were then used to expand the level of understanding of transient conditions from the initial test data. Reciprocally, the models could be used to improve test data collection during the field tests. For example, the models helped to identify key locations to take pressure measurements. Models were also instrumental in determining the initial operating conditions, which are likely to yield the most useful tests results, such as low bypass flow to produce higher surge pressures during load rejection. As described in the example of the Cresta lateral surge tunnel, the transient model could also be used to develop a monitoring and operation strategy during transient conditions to limit future sediment accumulation. The transient simulations could be used to identify the delay required to allow system pressures to stabilize between two consecutive load rejection tests to improve overall test integrity. Hydro facilities that include long tunnels and large surge shafts that are not equipped with energy dissipation systems might take more than one hour to stabilize after a load rejection at 100% load.
Finally, the in-depth review of load rejection test data helped to identify erroneous field data due to faulty sensors, further eliminating concerns for “out of tolerance” values.
Identifying the initial steady state flow rate and system head losses was critical to efficient model calibration. PG&E hydro facilities are typically not equipped with flowmeters, so the availability of index testing data was critical. The steady state flow rate defines the momentum of the moving mass of water in the system, which is directly linked to the maximum surge reached at the end of the slow closure of needle valves (Pelton) or PRVs (Francis).
Accurate modeling of the surge shaft geometry is essential to obtain a good match of low-frequency oscillations after interruption of flow at the powerhouse. The transient models appeared particularly sensitive to the flow coefficient used for the inlet and outlet ports of the surge shaft. The high-frequency oscillations are very sensitive to the penstock wave speed and to the time-step used in the transient simulation. Each penstock section, defined by a change in diameter or wall thickness, was modeled independently to account for every change in wave speed and increase accuracy. However, in addition to precise input of wave speed, it was essential for the time-step used in the simulation to be small enough to not alter the time characteristics of the system. This was a challenging requirement because the use of a small time-step resulted in long computation times.
The PG&E penstock assessment program is unique and large in scope and, although not complete yet, it has allowed PG&E to gain a high level of understanding of the integrity of its most important assets and optimize production while limiting risks. The hydraulic models developed remain available to PG&E for providing in-depth analyses of operating conditions, which may arise at these facilities in the coming years of operation.
Through the development and calibration of transient models for more than 70 penstocks and turbines, Black & Veatch has developed a high level of understanding of the operational constraints of these facilities that regularly operate under complex transient conditions. Through this large-scale program, Black & Veatch was able to streamline the analysis process and reduce modeling costs. This modeling approach has also been applied to hydropower facilities for the evaluation of performance under transient conditions for other owners.
Stephane Lecina P.E., is a hydraulics engineer at Black & Veatch. Mohammad Aslam Ph.D., P.E., S.E., is a senior consulting engineer at Pacific Gas & Electric Company.