*One or two new runners for the units at the 355-MW Brazeau Power Station in Alberta, Canada, would allow owner TransAlta Corp. to better optimize revenue and provide valuable ancillary services. Modeling of the various upgrade options allowed the utility to arrive at the most valuable solution.*

**By David Elwood, Robert Sherrick, Rick Jones and German Mojica**

*This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.*

TransAlta Corp. (TAC) is evaluating options for replacement runners in the two Francis units at its 355-MW Brazeau Power Station on the Brazeau River in Alberta, Canada. Unit 1 has a nominal capacity of 163 MW and Unit 2 192 MW. Based on a 2006 index test, Unit 1 exhibits a relatively small rough operation in the middle range, while a 2011 index test revealed Unit 2 exhibits a wider rough zone. Operation of both units within these ranges is avoided. The Brazeau plant has been in operation since 1965. TAC executed many overhaul works and has tried to reduce these rough zones. Both units have similar minimum and best efficiency points (BEP), potentially limiting the station’s overall dispatch flexibility.

TAC desires a replacement runner (or runners) with a spread of generating ranges and efficiencies, with a goal of optimizing revenue potential for the station, given its water-limited nature and opportunity for revenue in energy and ancillary services markets, as administered by the Alberta Electric System Operator (AESO). In most years, there are periods where sufficient water exists to run both units for energy during the wetter season and one or both units for energy, regulating range and reserves during the drier season.

In 2011, HDR Engineering Inc. completed a hydromechanical upgrade analysis of the units that included preliminary evaluation of a runner upgrade for Unit 2. This analysis was updated in 2012 to incorporate Voith Hydro data on the potential efficiency of an upgraded Unit 2 runner. Runner upgrade options for Unit 1 were also developed, providing 16 potential combinations of runners to consider for these two units. The preliminary hydraulic analysis considered the potential benefits of adjusting the BEP of both turbines such that the rough zones would no longer overlap. TAC has been exploring options for eliminating these rough operating zones in parallel to the runner optimization study to increase operational flexibility. (The rough zones were not included as constraints for the optimization model.)

The complexity of the trade-offs between efficiency differences at various operating points, minimum and maximum generating points, and a dynamic market for energy and ancillary services results in an inability to make direct inferences on the incremental value of one type of turbine runner upgrade when compared to a set of alternatives. Thus, TAC determined that an hourly, optimization-based model should be developed to predict operating strategies and expected revenue at Brazeau. The model was calibrated with the existing unit performance data, historical hydrology and market conditions to establish a reasonable baseline for comparison.

The model was developed in Microsoft Excel 2010, using the standard Data Tables and Solver to perform a two-pass optimization over an 11-year period of record provided by TAC.

The two-pass approach was necessary because the fundamental objective function and associated variables exhibit largely non-linear behavior and are significantly linked in time, which results in a tendency toward multiple local maxima that can confuse an optimization algorithm. The first pass was designed to make several key deterministic assumptions about the “blocked” operation of the units during light load and heavy load hours. This blocked operation provided a more stable set of initial conditions that allowed the second-pass Solver optimization to land on or near the global maximum solution (i.e., effectively eliminating large sections of the solution space that were unnecessary to search).

Several factors in the modeling approach lead to (generally subtle) differences in operating decisions between historical and modeled hourly operations. These include perfect foreknowledge of hourly energy prices in the model, a long-term average assumption of the proportion of regulating range that will be deployed as energy (as directed by AESO) and a lack of “rough zones” in the model. The model revealed about 9% additional revenue over the 11-year period when compared to historic revenue data.

These two figures show the assumed system efficiencies for the existing and upgraded units at the Brazeau plant. |

Three upgrade alternatives were evaluated for each unit, representing what is expected to be the full range of hydromechanical performance trade-offs between low-end and high-end operating capabilities and efficiencies. These three alternatives, coupled with the existing runners as a fourth alternative, result in 16 unique scenarios. Sensitivity analyses suggest that the economics of the station are most sensitive to changes in energy prices and relatively insensitive to changes in regulating range deployment magnitude.

## Modeling methods

The assumptions used for the Brazeau plant can be classified as physical, operational and environmental. Physical assumptions are required when the existing or planned configuration of critical project features is uncertain. Assumptions must also be made concerning current and future project operations. Finally, uncertainty in hydrology and market conditions make up the primary environmental assumptions (in this case, the plant’s “environment” represents factors outside of TAC’s control).

Physical assumptions are primarily related to the flow capacity of the existing turbines and efficiency and flow capacity of upgraded runner options. Assumptions for the existing turbines are based on data provided by TAC. For the runner upgrades, HDR made assumptions related to the turbine efficiencies, minimum flows and maximum flows based on experience with similar machines. HDR understands TAC’s desire to maximize the turbine operating range with potential runner upgrades. However, without detailed design studies including model testing, it is difficult to determine these values with certainty.

Assumptions regarding plant operation and in particular the unit dispatch strategy also affect model results. For the block optimization routine, HDR assumed each unit will be committed for ancillary services in eight-hour light load hour (LLH) and a 16-hour heavy load hour (HLH) blocks consistent with off-peak and on-peak energy consumption. The LLH block is only used when the HLH block is completely used and additional flow is available. This assumption reduces the level of computational effort required. The hourly optimization routine uses the block dispatch as its initial condition and then uses Excel’s Solver to redispatch flows to maximize revenue from energy and ancillary services. AESO market caps ancillary services that can be sold at 80 MW per product, 190 MW per unit and 270 MW per plant. The market depth assumptions are included in the model as constraints on the quantity of ancillary services that can be bid for each block.

Finally, based on direction from TAC, HDR assumed there are no zones of rough operation that will need to be avoided during normal operations. (With an appropriate runner design, it may be possible to operate across the rough zones that exist in all hydraulic turbines, without damage.)

Environmental assumptions will affect results of the optimization model. The model uses time series inputs for the historical daily-average inflow and forebay elevation to calculate the initial allocation of unit flows throughout the day and as constraints on the solution of the optimization routine.

## Optimization approach

Optimization algorithms maximize an objective function by systematically choosing input values while meeting constraints. For Brazeau, the objective function for each day is the plant’s overall revenue potential from sales of energy and ancillary services. The “best” or optimal value of the objective function determined by an optimization algorithm depends on the initial conditions, constraints, numerical precisions and convergence tolerances. Selecting appropriate initial conditions, constraints and settings is vital to obtaining results that maximize revenue. HDR used a two-pass optimization approach for the Brazeau model that first generates an optimum dispatch table for the two units and then optimizes the allocation of water within a day to maximize revenue using the Solver add-in.

Initially, HDR attempted to optimize operations using a one-pass approach that allowed the Solver to vary unit flows within a day to maximize overall revenue potential for the plant. During testing of the prototype model, it became clear that the complexity of the optimization problem was beyond the capability of the Solver.

To address this, a two-pass optimization approach was devised. During the first pass, operations are “block optimized” with fixed operations in the HLH and LLH blocks, based on block-averaged energy and ancillary services pricing. The resulting flows are used as initial conditions to redispatch hourly flows in a second-pass optimization, based on hourly energy and ancillary services products. The first-pass optimization provides a starting point that is relatively close to the hourly optimum solution, which improves the efficiency and stability of the Solver’s algorithm. Certain pricing and flow combinations result in less than a “maximized” revenue solution due to the algorithm’s limitations, but HDR believes these conditions are rare and result in revenues that approach maximum potential.

The block optimization routine calculates the best dispatch for a given set of units using the unit characteristics, market rules, day-ahead average flow, day-ahead gross head, day-ahead energy price, and day-ahead ancillary services premiums. The calculations used to determine the best dispatch for the two units consist of Excel tables that iterate all combinations, seeking the optimum dispatch in an empirical fashion. For each day in a simulation, the deployed power is calculated over the range of potential unit dispatch options based on unit efficiencies, day-ahead plant flow and day-ahead gross head. Base power, regulation range and spinning reserve are calculated based on the deployed power and ancillary service market constraints and assuming that a set percentage of the regulation is deployed within any hour. The best dispatch for the two units in the HLH and LLH blocks, along with the best dispatch to maximize energy revenue without considered ancillary services, are calculated and referenced by named ranges. The user can manually run the block optimization for a given day within the period of record.

Block optimization results in 95% to 98% of the revenue predicted by the two-pass optimization over a multi-year period, with a small fraction of the run time necessary. The block optimization performs best when one or more of the ancillary service products are relatively valuable. When energy is the only valuable product, the optimum operation moves directly to an hourly maximization of total generation, which the block approach is inherently incapable of producing.

After the initial flows are set, the Solver is used to further optimize flows on an hourly basis within the day. The objective function for the Solver is to maximize the daily revenue with the following constraints:

- Daily average plant flow must be less than or equal to the input daily flow;
- Hourly plant flow must be less than the maximum combined unit capacity;
- Minimum hourly plant flow must be greater than the input minimum flow; and
- Market constraints for ancillary services are captured in the calculation of regulating range, spinning reserve, supplemental reserve and daily ancillary services revenue. The minimum ancillary services available during the LLH and HLH blocks is assumed to be the day-ahead bid used in the hourly ancillary services revenue calculation.

## Summary results

HDR completed model runs for each of the 16 combinations of runner upgrades. Figure 1 on page 28 shows the assumed system efficiencies for the existing and upgraded units, based on the runner upgrade study completed by HDR1 and head loss measurements from Voith Hydro index tests,2,3 and assuming a peak generator efficiency of 98%. The scenarios were run using daily flow and forebay elevation data provided by TAC for Jan. 1, 2002, to Dec. 31, 2012.4 Hourly energy prices and ancillary services premiums were used as inputs to the model.

## Model validation

HDR tried to validate that the existing units were being appropriately represented by the assumed efficiency curves. To do this, power was computed using historic plant flow, gross head and the efficiency curves developed by HDR. The calculations were then filtered to find times when flow was relatively stable and only one unit was running. Figure 2 on page 34 shows that the model calculation for power does not exhibit any bias toward high or low flows and therefore the shape of the efficiency curves appears to be correct.

However, the modeled values come out slightly lower than the historical power over the range of flows. This could be due to two factors. First, the historic data is based on hourly average flow and power. It is likely that during each hour the flow through the units was fluctuating, potentially moving the operating point into a zone of higher efficiency for a portion of the hour. The second source of the discrepancy could be the way flow is measured during hourly operations, particularly when deployment of regulating range under actual operations is dynamic. Flow is generally measured with a greater degree of accuracy during an index test than during normal operations, and the data is not averaged over an hour.

Plant operations are validated by examination of hourly results. The model is limited by rules to stay within the realm of possible operations, and usually it represents probable operations as well. When the value of ancillary services is low, the model can deviate significantly from historic operations by using perfect foresight of the hourly pricing. When ancillary services are very valuable, the model often earns more revenue than historic due to maximizing ancillary services in the first-pass optimization, as well as the 50% regulation range deployment assumption. Plant operations are represented adequately to compare the revenue of various runner alternatives over a range of flow and pricing conditions during the 11-year period of record.

## Expected revenue

Table 1 on page 29 shows the potential increase in revenue for each combination of runners using a block optimization approach. An increase of 4.7% to 9.9% per year can be achieved with upgraded runners. Table 2 on page 29 shows the potential increase in revenue for each combination of runners using a two-pass optimization approach. The revenue predicted by the model with the existing runners was about 4.1% higher using the two-pass optimization approach than using the block optimization. As can be seen in the table, the modeled increase in revenue with runner upgrades ranges from 2.7% to 8.1%.

The model calculation for power does not exhibit any bias toward high or low flows and therefore the shape of the efficiency curves appears to be correct. |

## Ranking of options by revenue improvement

The 16 options were ranked based on their estimated annual revenue potential using the two-pass optimization routine (see Table 3 on page 29). The most attractive scenario is the combination of Options 1B and 2C, where revenue would increase by 8% per year. The most attractive scenarios upgrading one runner would be Options 1B or 2A, where revenue would grow by 5% per year.

Most of the overall incremental revenue potential (about 70% in the case of Unit 1) can be achieved through the upgrade of a single runner. However, a cost-benefit analysis of the remaining incremental revenue potential should be performed before making a final decision. It is also important to note that, with the selection of Unit 1 Option “B,” each of the Unit 2 runner upgrades result in favorable incremental conditions.

## Discussion

All the upgrade options showed the potential for increased revenue. Block optimization is more computationally efficient (about 10 times faster) but results in 2% to 4% lower projected revenues. The most attractive upgrade options using the two approaches are consistent, with hourly optimization predicting less benefit with the upgraded units. The hourly optimization approach benefits the existing runner combination most because of the steep nature of the efficiency curves, which gives the hourly optimization more valuable tradeoffs in changes to hourly releases. The upgraded efficiency curves are flatter, resulting in less incremental gain in the hourly optimization mode. This impact is a worthwhile consideration for real-world operation of the Brazeau plant.

HDR recommended hourly optimization as the most refined approach for comparing runner combinations. The results allowed TAC to create a business case for further execution and to add value that TAC can achieve the expected benefits by reducing capital expenditures.

## Acknowledgments

The authors would like to acknowledge the work of Dr. Juliusz Kirejczyk, who provided efficiency estimates for the proposed runner upgrade options, and TransAlta Corp. for its input and permission to publish this article.

## Notes

^{1}“Draft Brazeau U1 and U2 Turbine Upgrade Potential Report,” HDR Engineering, York, Pa., 2012.

^{2}“TransAlta Brazeau Hydroelectric Plant Unit 1 Index and Signature Test Report,” Voith Hydro, York, Pa., 2003.

^{3}“Brazeau (TransAlta) Unit 2 Technical Report Index Tests and Vibration Recording,” Voith Hydro, York, Pa., 2011.

^{4}“Brazeau Plant Log – 2002 to 2012,” TransAlta Utilities, Calgary, Alberta, Canada, 2012.

## Reference

Elwood, David, et al., “An Optimization Model of the Brazeau Power Plant to Evaluate the Value of Potential Turbine Upgrades,” Proceedings of HydroVision International 2014, PennWell Corp., Tulsa, Okla., 2014.

**David Elwood, P.E., formerly a mechanical engineer with HDR Engineering Inc., is now a mechanical engineer with Public Utility District No. 1 of Douglas County. Robert Sherrick, EIT, is a hydrologist and Rick Jones, P.E., is water resources engineer and managing principal with HDR. German Mojica, P.E., is senior engineer, water management with TransAlta Corporation in Canada.**

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