Evaluating power grid model hydropower feasibility with a river operations model

Our approach for evaluating hydropower dispatches in a PCM is to drive a detailed hydropower system optimization model with the hourly generation simulated by the PCM. The PCM produces hourly generation for all power plants on the grid, including the hydropower plants studied. The detailed hydropower model accounts for important water-related constraints that are not directly considered or are over-simplified in the PCM, including water balances, river routing and other physical, water-related and power generation characteristics as well as water-related and power-related operating constraints. To perform this exercise, we formulate the objective in the detailed hydropower model to target the PCM generation simulated for each plant in the system. For a given plant, a feasibility error is registered whenever the detailed hydropower model cannot meet the generation schedule from the PCM. The hydropower model is constrained to minimize unrequired spill prior to trying to match PCM generation. The study is conducted using the GV PCM (Yang et al 2003) model of the Western Interconnection and a RiverWare® model (Zagona et al 2001) of the Big 10 system (figure 1).

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2.1.1. The Big 10 hydropower system

The Big 10 includes a fairly large storage project in the Mid-Columbia (Grand Coulee—largest power plant in the United States by nameplate capacity) and nine large run-of-river hydropower plants in the Columbia and Snake Rivers (figure 2). The combined nameplate capacity of the ten projects represents ∼40% of total conventional hydropower capacity of the Western Interconnection. The system of cascading reservoirs operates as a coordinated system, featuring extensive nonpower requirements, including seasonally varying spill and forebay elevation requirements. Grand Coulee is the only plant in the Big 10 with significant reservoir storage capacity, but it is fed by larger upstream reservoir storage. It is drafted and filled on a seasonal basis for flood control and other water-related purposes. The other nine reservoirs operate as run-of-river on a daily basis but have enough storage capacity to allow for shaping of generation within the day. Given the limited storage capacity in the other reservoirs, the releases from Grand Coulee control the amount of water in the Lower Columbia River at a daily timescale, and are often driven by water-related requirements at downstream projects (Leonard et al 2015).

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2.1.2. PCM model: GV-PCM

2.1.3. Detailed hydropower model: RiverWare (RW-B10)

For water operations, RW is typically set up to optimize generation under soft environmental and other water uses constraints. Our hydropower feasibility test is designed to identify periods of hydropower generation in GV-PCM that are not feasible once the more realistic constraints included in RW-B10 are considered. Feasibility error is evaluated by running RW-B10 with soft constraints to match the generation from GV-PCM at each project (p) and at each hour (h)

$$\begin{equation}{\text{Constraint: RiverWareGe}}{{\text{n}}_{{\text{p,h}}}} = {\text{PCMGe}}{{\text{n}}_{{\text{p,h}}}}{\text{,}}\,\,\,\,\,\forall p,\,\forall h .\end{equation} \tag{ 1 }$$

For this study, RW-B10 is formulated such that the constraints to match the target generation from GV-PCM are at a lower priority than all water-related constraints. If it is not possible to fully satisfy the water-related constraints and meet the target generation together, the solution will deviate from GV-PCM generation in order to meet the higher-priority water-related constraints. As a result of this formulation, all feasibility error is represented by deviations from GV-PCM generation. In theory, these deviations can take two forms: over-generation (PCM generation is too high) and under-generation (PCM generation is too low) (equation (2))

$$\begin{align} {\text{PCMOverGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} &= \left\{{\begin{array}{*{20}{l}} {\begin{array}{*{20}{l}} {\begin{array}{*{20}{l}} {{\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} - {\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}},}&{;\,{\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} \leqslant {\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}}}\\ {0,}&{;{\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} > {\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}}} \end{array}} \end{array}}&{,\forall p,\,\forall h} \end{array}} \right. \nonumber \\ {\text{PCMUnderGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} &= \left\{{\begin{array}{*{20}{c}} {\begin{array}{*{20}{l}} {\begin{array}{*{20}{l}} {{\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} - {\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}},}&{;\,{\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} \geqslant {\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}}}\\ {0,}&{;{\text{RiverWareGe}}{{\text{n}}_{{\text{p}},{\text{h}}}} < {\text{PCMGe}}{{\text{n}}_{{\text{p}},{\text{h}}}}} \end{array}} \end{array}}&{,\forall p,\,\forall h} \end{array}\!.} \right. \end{align} \tag{ 2 }$$

Our results contain both over-generation and under-generation. However, in this study the latter happens to be comparatively negligible and so we focus solely on feasibility error as defined by PCM over-generation.

The results of the experiment described above inform on the total feasibility error of GV-PCM relative to a detailed hydropower model (RW-B10) that includes realistic water balance, water storage and transport between dams, and up-to-date policy constraints. These results, however, do not provide quantitative evidence on the relative importance of different causes of feasibility error.

Investigation of the initial results revealed that a spill policy change that was not reflected in the PCM input data was a major source of error in PCM results. The 2020 spill policies included in RW-B10 require significantly more spill for fish passage than was required in 2009—meaning the 2009 monthly hydropower generation targets used to constrain GV-PCM likely request too much energy from the Lower Columbia and Lower Snake plants during spring months. It is important to note that there was no a-priori reason to expect that the PCM data was lacking any significant policy change. Only the use of a detailed water model was able to determine a policy change was not reflected in the PCM data and to pinpoint it to a change in spill policy. With this posterior knowledge, future PCM runs for this area could use data that reflected the spill policy change by using data only from years after the change was made. (The PCM cannot directly model spill policy.)

These initial results led us to extend our initial RW experiment to perform an additional simulation of RW-B10 designed to isolate the influence of the 2020 spill policies on feasibility error. We determine the impact of spill policy on feasibility error by running RW-B10 with observed 2009 hourly generation as the target. Any feasibility error arising from this experiment can be attributed to two sources: 2020 spill policy and error in RW-B10 representation of the hydropower. Any feasibility error in the GV-PCM experiment that is residual to this may be assumed to arise due to other limitations of the PCM discussed in the following sections.

Comparing GV-PCM generation against RW-B10 generation reveals substantial feasibility error (figure 3). Over the full simulation period of one year, the total non-feasible generation exposed by RW-B10 is approximately 6000 GWh—9% of hydropower generation in GV-PCM for the Big 10 projects. This feasibility error is distributed non-uniformly throughout the year, with the three-month spring period April through June accounting for almost two-thirds of total annual feasibility error. Approximately 20% of GV-PCM hydropower generation in April and May is infeasible in RW-B10. Lowest relative (and absolute) feasibility error occurs in September—which is also the month of lowest total hydropower generation in both models. January, in contrast, features high overall generation and low feasibility error.

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Feasibility error is also distributed non-uniformly across plants in the Big 10 system (figure 4). Grand Coulee is the largest plant analyzed, contributing ∼30% of total Big 10 generation in GV-PCM. However, Grand Coulee contributes only 16% of total feasibility error. The eight run-of-river plants in the Lower Snake and Lower Columbia account for 78% of feasibility error. In the Lower Columbia (∼42% of total feasibility error) we observe a clear contrast between spring (April, May, June) and the remainder of the year. Winter GV-PCM generation is relatively high, but—in the most part—matched in RW-B10. In contrast, the high and relatively stable daily GV-PCM generation through spring cannot be sustained in RW-B10.

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A significant portion of GV-PCM feasibility error arises because RW-B10 includes contemporary spill policies. Our additional RW-B10 simulation using observed 2009 generation (section 2.3) allows us to estimate the contribution of increased fish spill requirements on total feasibility error. We find that two-thirds of total feasibility error is caused by contemporary spill policy (primary cause) and RW-B10 error (figure 5).

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It is common for the water-related requirements of a hydropower system to change over time due to updated biological opinions, environmental assessments, or other updates to legal obligations. When such a significant policy shift occurs, it warrants an adjustment to the parameters in the PCM (energy totals, minimum and maximum generation) for the affected hydropower projects. In the case of the modifications to Big 10 spill requirements, it may be possible to convert the additional spill flow required to the corresponding reduction in energy and maximum generation to provide a reasonable representation of the updated operating limits. The appropriate adjustments for other policy changes would be specific to the nature of the policy modification and would vary by river system.

The residual feasibility error after accounting for the effects of spill policy equals approximately 3% of total GV-PCM Big 10 generation (red portion of feasibility error in figure 5). This residual error is due to the interaction of river system dynamics and policy constraints at a finer time scale, such as minimum and maximum flow, reservoir elevation limits, spill requirements, and lag times, that are not captured by GV-PCM. One cause of much of this error is the distribution of energy within each month by the PCM, which cannot account for the finer time scale interactions of river system dynamics and policy. One example of constraints at a finer time scale is a daytime maximum flow limit of 120 kcfs (3398 m³ s⁻¹) at Bonneville dam, at the downstream end of the system, to support chum salmon spawning in November and December. Due to the limited storage capacity at the Lower Columbia projects, this effectively limits flows, and subsequently generation, throughout the cascading system. Figure 4 shows very high GV-PCM generation for a period in early December (about one week) at most of the projects, much of which is infeasible in RW-B10 due to the Bonneville flow limits, then relatively low generation the following week. The total generation across the two weeks may be feasible, but the constraints in RW-B10 would require it to be more evenly distributed. In other cases, the opposite may occur. The PCM generation distribution may be relatively constant across a month, whereas rapidly evolving flow conditions, such as during spring runoff, may require generation to be concentrated in shorter time periods. Possible reasons for inability of RW-B10 to match observed generation during months outside spring include planned and forced unit outage, special operations, other one-time considerations, and responses to real time information like flow forecasts or hydropower curtailment needs to integrate wind generation resources.

While the chum spawning flow limits are specific to Bonneville, many hydropower projects have similar flow restrictions for specific days or times of day that restrict generation in those time periods. Other possible reasons for residual inability of RW-B10 to match observed generation during months outside spring include planned and forced unit outage, special operations, other one-time considerations, and responses to real time information like flow forecasts or hydropower curtailment needs to integrate wind generation resources.

There are two other potential PCM deficiencies—not observed in our study—which could cause feasibility error in a PCM representation of a cascade hydropower system: monthly parameters and lag times between reservoirs with limited storage. The prospect of these deficiencies means that our finding of approximately 9% feasibility error in this system could be small relative to other systems or PCM configurations that have these additional deficiencies.

The first deficiency is the monthly specification of parameters (minimum, maximum, and total generation) that constrain the PCM scheduling of hydropower may allow too much latitude for the PCM to move a single project's generation within a month. For example, a project that has adequate storage available and high flexibility in the timing of generation could shift generation by days or weeks within a month while a downstream project relying on water from the upstream project may not have that flexibility. To illustrate, in the Big 10 system the Lower Columbia projects do not have sufficient storage to shift significant energy across weeks. Their generation is limited primarily by what is released from Grand Coulee and, to a lesser extent, what comes from the Snake River. In other words, allowing the Lower Columbia projects to generate in a way that is inconsistent with releases at Grand Coulee would over-estimate their operational flexibility. The GV_PCM in this study constrained projects to load following at an hourly level. This prevented substantial load shifting at an hourly level and therefore prevented inconsistent shifts of energy for projects at larger time scales. Specifically, the issue is avoided for the Big 10 in GV-PCM because load following behavior coded into the GV–PCM scheduling for the Big 10 dams forces them to ramp up and down in unison at the hourly time scale—guaranteeing that consistency across plants is preserved at longer time scales. If the load following behavior were removed from our study, as may be the case for other PCM models, an even larger feasibility error would occur.

The second deficiency can occur as a result of extreme and correlated peaking by individual plants, including extreme load following, which can lead to infeasibility at short time scales due to lag times needed to deliver water between plants with limited storage. The water generated on peak by one plant may not arrive until much later at a downstream plant, but the PCM does not recognize this physical water conveyance constraint; instead, the PCM is allowed to dispatch all resources in the cascade system at maximum generating capacity at the same time, resulting in unrealistic flexibility when the generation at a downstream plant is constrained due to lack of water, and may only reach maximum after a time lag following generation and release at an upstream plant. This potential issue is avoided in GV-PCM through the imposition of tight constraints on maximum and minimum hourly generation at each plant. This prevents the problem because less extreme generation leads to smaller water storage requirements. The trade-off is that these plants may often be over-constrained—leading to an underestimation of the operational flexibility of the system in the PCM.

The major source of feasibility error (over generation) in our study is the updated spill policy. This inconsistency between PCM generating targets and realistic, up-to-date operations applies to any PCM study for which (a) historical, plant-level generation profiles for a particular year are used for energy targets (whether monthly or sub-monthly), and (b) the operations at those plants have changed since the historical year adopted in the PCM study. The policies that changed in our specific case study relate to spill requirements, but there are other possible constraints on a river system that could impinge on hydropower generation (e.g. environmental flows, flood control, recreation, new water demands, new infrastructure). For the BPA Columbia River System projects (including the ten studied here), a new environmental impact statement has been issued that is leading to development of new monthly hydropower targets (USACE 2020). Its impact on monthly hydropower generation targets and further onto power flow modeling has also been evaluated, albeit not from a power grid reliability perspective. Further testing of the impact of updated river and reservoir policies at higher resolution would be required to gain more insight into the associated impacts on feasibility error and PCM performance. However, our results demonstrate that reservoir policies can be a major source of feasibility error (over and under generation) in a PCM. Updating reservoir policies across a large fleet of hydropower plants (such as the ∼500 hydropower plants serving the U.S. Western Interconnect) presents a significant challenge for PCM users. The PCMs do not directly model water policies and instead must rely on historical data for operation of the hydropower plants. The PCM users generally do not know when policy changes have taken place that may cause the historical data to incorrectly characterize the capability of the data to reflect hydropower operations.

Another potential source of feasibility error is related to the selection of 2009 as the year used to project hydrology into the future decade. As explained in section 2.1.2, this study has adopted the common WECC 2028 Anchor dataset projection practice of selecting the year in the past decade that is closest to average with respect to hydropower generation; this year will also likely reflect hydrologic conditions that are closest to average over the Western Interconnect. Selection of a different year would likely result in different feasibility error results, and likely that the results would be greater feasibility errors since more extreme hydrologic conditions in either direction result in greater constraints on the system. Our purpose is to investigate the results for the typical application of this PCM methodology.