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Water Resources Management

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Open Access 07-02-2024

Hydropower Reservoir Optimization with Solar Generation-Changed Energy Prices in California

Authors: Mustafa Sahin Dogan, Josue Medellin-Azuara, Jay R. Lund

Published in: Water Resources Management | Issue 6/2024

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Abstract

Growing solar photovoltaic supply has significantly reshaped energy prices, lowering them during solar generating hours. Large-scale hydropower reservoir operations need to adapt to changes in energy prices to maximize hydropower revenue. This paper evaluates effects of solar generation-changed energy prices on hydropower generation for five multipurpose reservoirs in California using a hydroeconomic optimization model. In California, major solar generation began in 2013, so years 2010–2012 are a pre-solar period, and years 2013–2018 are post-solar. Reservoir operations, hydropower generation and revenue between these periods are compared. Operations in the wet season (January to June), and the dry season (July to December) are evaluated. Results show that releases are more profitable when hydropower is generated twice a day during on-peak hours in the morning and evening in the wet season. When water is scarce, energy is generated only during the higher-price evening peak. Hydropower generation is mostly curtailed between 10am and 6pm due to large solar supplies, and increase during morning and evening peaks when solar generation is unavailable. However, by optimizing hydropower scheduling hours, the new energy price pattern can be more profitable. With increased energy price variability and adaptation, overall daily revenue can increase by about 14% in the wet season and 30% in the dry season.

Highlights

• Effects of solar generation on hydropower operations are evaluated.

• Solar generation increases energy price variability, reducing energy prices during solar generation hours.

• Hydropower releases are less profitable when solar is generated.

• Hydropower generation schedules move to morning and evening on-peak hours.

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

1 Introduction

Reservoirs can serve single or multiple purposes, including water supply, flood control, environmental protection, recreation, and hydropower. Reservoirs store and regulate water releases for various demands, such as irrigation water during the dry season or hydropower during peak energy demands. While some reservoirs operate solely for hydropower, others generate energy as byproduct of water supply releases for agricultural, urban and environmental users. However, reservoir operators’ short-term objective often is to maximize hydropower revenue within larger-scale release schedules for other purposes (Dogan 2019). Martin (1983), Yeh (1985), Wurbs (1993), Labadie (2004), Rani and Moreira (2010), Ahmad et al. (2014), Beiranvand and Ashofteh (2023) review reservoir optimization and compare techniques.

Hydropower with a sizable storage capacity is a dispatchable resource, where water is stored as energy in higher elevation when energy demand is low, and is dispatched later to meet peak demands (Pérez-Díaz and Wilhelmi 2010). Peak energy demands can be seasonal, such as summer demand for long-term operations, or daily peak-hour demands for short-term operations. Hydropower’s lower operating cost (Madani et al. 2014) than most other power sources gives incentive to maximize hydropower generation in a power system with mixed generation sources (Hamlet et al. 2002). Hydropower also can provide operational flexibility by generating power on short notice (Chatterjee et al. 1998; Côté and Leconte 2016) and additional ancillary services, such as peak and frequency regulation, and spinning reserve (Li et al. 2013; Liao et al. 2021). Total electricity demands average less at night and more during daytime. California generates electricity from various sources with most in-State generation from natural gas (California Energy Commission 2018). Nuclear, geothermal, small hydropower provide mostly base load supplies, and thermal (mostly natural gas), large hydropower and imports help meet both peak demands and base load. Although total demand remains substantially unchanged for now, the hourly breakdown of electricity sources has changed significantly since 2013. Natural gas and nuclear generation have been declining, while wind and especially solar generation have been increasing. This is because of California's ambitious clean energy goals called Renewable Portfolio Standard targets that the State wants to achieve 40%, 45%, and 50% of total generation from renewable sources, such as solar, wind, small hydropower, biomass, biogas, and geothermal, by 2024, 2027, and 2030, respectively. Previous targets were 20%, 25% and 33% by 2013, 2016, and 2020, respectively (California Energy Commission 2017). Most of these goals are met by wind and solar photovoltaic (PV) generation. The main limitation of integrating variable wind and solar PV power supplies into power production system is their high intermittency (Margeta and Glasnovic 2011; Chang et al. 2013; Liu et al. 2020). Power supplies from wind and solar fluctuate spatiotemporally depending on climatic variables, mostly wind speed, solar radiation and temperature (François et al. 2016). In an economic equilibrium, supply provided equals demand use. Total supply is the sum ofenergy generation from all sources. The difference between total use and variable supply is net load, and its curve is called a ‘duck curve’ due to its shape (Denholm et al. 2015). With increasing variable supply, especially solar, this shape has notably transformed, lowering net load when solar power production peaks around noon and steeper ramping rates to meet the peak demand in the evening, converting the system from one-daily peak to two-daily peaks. Furthermore, increasing renewable energy supplies are expected to increase volatility in energy systems (Jin et al. 2022). With penetration of large-scale wind and solar PV power, flexible and complementary power sources, such as, hydropower, are needed to maintain power system reliability (Shen et al. 2019; Shan et al. 2020; Xie et al. 2021). Eichman et al. (2013) showed that 50/50 mix of additional solar and wind installation would provide the highest system-wide capacity factor, where large wind farms provide low cost generation and solar provides more predictable generation.

Higher net load correlates with higher wholesale energy prices. As renewable supplies, especially solar PV, increases, wholesale energy prices decrease. This new price pattern from renewable expansion significantly affects hourly hydropower operations (Chang et al. 2013). Given significant changes in energy price patterns due to expanded solar generation, reevaluation of hydropower reservoir operations, driven by energy prices and constrained by water availability, becomes important for efficient water and energy management. The review of this subject in the literature is rather scant. This paper quantifies effects of solar generation-changed energy price patterns on short-term dispatchable hydropower operations in California.

Given changes in energy price patterns, this study examines best hours to store and release water to generate hydropower and how much, depending on water availability in wet and dry seasons. Hourly short-term hydropower reservoir operations are analyzed before and after large solar penetration into California’s power supply system with a hybrid linear and nonlinear programming hydroeconomic reservoir optimization model (HERO), with an hourly time-step over a seasonal period from 2010 to 2018. Hydropower storage and release schedules are examined, and generation and revenue results are provided. Furthermore, adaptation strategies on reservoir operations are evaluated with solar generation-changed energy price patterns.

2 Materials and Method

2.1 Study Area

The modeled reservoirs are on the lower foothills of the surrounding mountains, with several low-storage hydropower plants upstream, owned by several agencies and companies including Pacific Gas and Electric Company (upstream of Shasta, Folsom, New Melones, and Pine Flat), Sacramento Municipal Utility District (upstream of Folsom), and Northern California Power Agency (upstream of New Melones). The schematic of the modeled hydropower reservoirs appears in Fig. 1. Nevertheless, these upstream hydropower plants somewhat regulate hourly inflows with hydropower peaking releases to the modeled hydropower plants, as shown in Fig. 2. With large storage capacity, modeled reservoirs can reduce upstream regulation effects, generating energy when it is most valuable. Total hourly average inflows, obtained from California Data Exchange Center (2018) between 2010 and 2018 for dry and wet seasons are used to exclusively evaluate energy price effects on operations, eliminating any hydrologic effects.

Five large reservoirs with varying storage sizes and inflow rates are modeled (Table 1). The model is run for two seasons: wet and dry. The wet season is between January and June, and the dry season is between July and December of each year from 2010 through 2018. The wet season has much higher average reservoir inflows with precipitation and snowmelt runoff, giving operators more flexibility for dispatchable hydropower operations. In the dry season, with lower flows, priorities are given to the most valuable hours in terms of energy prices to maximize overall revenue. For initial and ending storage boundary conditions, half of the reservoir storage capacity is assumed for each season and year, without carryover storage.

Table 1

Modeled hydropower plants and observed mean (μ) and standard deviation (σ) of hourly inflows (${m}^{3}/s$) in wet and dry seasons

Plant	Plant ID	Installed capacity (MW)	Storage capacity (MCM)	Wet season¹		Dry season²
Plant	Plant ID	Installed capacity (MW)	Storage capacity (MCM)	μ	σ	μ	σ
Shasta	SHA	714	5615	281	309	134	153
N. bullards bar	BUL	315	1192	71	102	20	47
Folsom	FOL	207	1203	162	240	57	92
New melones	NML	300	2985	64	79	30	33
Pine flat	PNF	165	1233	91	109	34	56

¹January-June, ²July-December

2.2 Demand-Energy Price Relationship

Energy generation from renewable sources, including geothermal, biogas, biomass, small hydropower (< 30 MW), wind, and solar, are now a significant portion of California’s energy portfolio (about 40% when solar generation peaks). Geothermal, biogas, biomass, and small hydro provide about 1500 MW hourly base load, while solar dominates the renewable portfolio mid-day when it peaks, especially in recent years (Fig. 3). Solar and wind generation are intermittent and greatly vary across hours. Wind usually peaks around midnight and solar peaks around noon, somewhat and sometimes complementing each other. Starting 2013, as a part of Renewable Portfolio Standard targets, solar generation has been booming, with modest increases in wind generation, while generation from other renewables is mostly unchanged.

Solar energy converts the sun’s light into electricity (photovoltaics) or heat (thermal) (Labouret and Villoz 2010; Pick 2017). California’s solar generation is predominantly solar PV.

There is a strong relationship between net electricity demand (net load) and energy prices, which are higher for on-peak hours and lower for off-peak hours. These energy prices are more correlated with the net load, the difference between total demand or load and variable supply, shown in Fig. 4. Net load difference in off-peak and on-peak demands are mostly from wind generation, and larger differences are from solar generation. Prices increase with a steeper slope with off-peak demands, then slowly increase with average demand, then steeper increase again with on-peak demands. Around the average energy price and load, the unit increase in price ($\Delta P$) is much greater with net load than the total load. As the variable supply increases, the gap between net load and total load grows, resulting in steeper increases in energy prices, especially in average demands, when solar generation peaks.

2.3 Changed Energy Price Pattern

The California Independent System Operator (CAISO) maintains the power grid and regulates electricity market operations in California. Originally node-based and locational, statewide average of hourly marginal energy prices are used. Hourly energy prices are obtained from CAISO (2018), and reflect the market value of a unit of generation. These wholesale prices differ from retail electricity prices that utility companies charge their customers, where usually fixed plus tier-based tariffs are used (PGE 2019). Also, energy prices were not inflation-adjusted due to low rates in the analysis period (US Bureau of Labor Statistics 2019). Fig. 5-a and b shows hourly average energy prices for each year between 2010 and 2018 and wet and dry seasons. Energy prices depend on variables such as natural gas prices, but usually are higher in the warmer dry season due to air conditioning. Since energy prices change with the net load, as variable supplies, particularly solar, increase, net load decreases, which lowers energy prices between hours 8 to 18 in both seasons, resulting in twice-daily peaks. In the dry season, the price difference between the first and second peaks is much higher, increasing price volatility.

Affected by solar generation, energy prices change considerably and reshape the price scheme. Fig. 5-c and d shows this transformation between 2010 and 2018 for wet and dry seasons with normalized energy prices between 0 and 1. The normalization (Eq. 1) removes the magnitude of prices, which can differ each year, and better show the effects and price trends. Energy prices change significantly during solar generation hours in both seasons. As solar generation increases, energy prices gradually decrease between hours 8 and 20, resulting in two daily peaks. In pre-solar years, 2010–2012, daytime prices are much higher, slightly increasing during the evening peak. Price in these years is higher during hours 8 to 23, and lower the rest of the day. In the wet season (Jan-Jun) of 2016 through 2018, normalized energy prices are even lower during hours 10–18 than prices at night, when total demand is lower. For hydropower plants with sizable storage capacities, this new price scheme gives little incentive to generate hydropower during off-peak hours, focusing operations in a smaller time-frame during on-peak hours, with much increased pulse releases.

$${Price \ Normalized}_{n,s}=\frac{{P}_{n,s}-{\text{min}}({P}_{n,s})}{{\text{max}}({P}_{n,s})-{\text{min}}({P}_{n,s})}, \forall (n,s)$$

(1)

where $P$ is an array of hourly average marginal energy prices in year $n$ between 2010 and 2018 and season $s$ (wet, dry).

Negative energy prices usually occur from excess generation when the demand is low. While shifted slightly to earlier months in recent years, negative prices are mostly in the wet season and wetter years, such as 2011 and 2017, resulting mostly from low-storage (run-of-river) hydropower generation (Fig. 6-a). Another important transformation has occurred in hourly negative price trends. Solar deployment shifts months with negative prices earlier, but more importantly it affects the hourly timing of these prices (Fig. 6-b). In the pre-solar period, negative prices occur during low demand hours, between 0 and 8. As solar generation increases, lowering net hourly load, negative prices shift to hours between 8 and 18 in the post-solar period. Negative prices are not desirable for hydropower plants without much storage capacity. In contrast, hydropower plants with available storage capacities, can store water/energy during those low-valued hours, gaining head, and release water during profitable hours. Negative prices also favor economically pumped-storage hydropower plants, which pumps water to an upper reservoir during low-valued hours to release and generate electricity during higher-valued hours.

2.4 HERO Hydropower Reservoir Optimization Model

HERO (Hydropower Energy Reservoir Optimization) is a hybrid linear and nonlinear programming (LP-NLP) hydroeconomic optimization model for hydropower reservoir operations. Linear programming (LP) has advantages of a fast evaluation and finding a globally optimal solution, but the nonlinear hydropower optimization problem needs to be simplified to fit a LP formulation, reducing the accuracy of results. NLP needs less simplification, and nonlinear hydropower operations can be well-represented. But, computing time increases exponentially with the number of nonlinear decision variables. The HERO model uses the faster LP model to reduce iterations needed in the NLP model. With a hybrid approach, the HERO model first solves the network-flow hydropower reservoir problem with a linear approximation, then in a sequential optimization, LP decision outputs are used to initialize the NLP model (Dogan et al. 2021). Hydropower network-flow models consist of nodes and links, where nodes represent point locations, such as reservoirs or junctions, and links represent connections between nodes, such as streams, canals or tunnels. These type of models require reservoir inflow and energy prices as inputs in addition to plant characteristics. HERO is a deterministic optimization model, so all inputs are known with certainty. The HERO model aims to maximize revenue, where operations are constrained by water availability and physical system capacities, such as turbine and reservoir storage. The current model does not represent load output constraints. HERO is developed with Pyomo (Bynum et al. 2021), a high-level optimization modeling language in Python, and can connect to freely available LP and NLP solvers, such as GLPK (GNU Linear Programming Kit) and IPOPT (Interior Point Optimizer). Dogan et al. (2021) discuss the HERO model in more detail. The objective function (Eq. 2) maximizes overall hydropower revenue and is subject to upper bound (Eq. 3), lower bound (Eq. 4) and mass balance (Eq. 5) constraints.

$${\text{Max}}\;z=\sum_{i}\sum_{j}f\left({X}_{ij}\right)$$

(2)

$${X}_{ij}\le {u}_{ij}, \forall (i,j)\in A$$

(3)

$${X}_{ij}\ge {l}_{ij}, \forall (i,j)\in A$$

(4)

$$\sum_iX_{ji}-\sum_ia_{ij}{\cdot X}_{ij}=0,\forall j\in N$$

(5)

where i and j indices are origin and terminal nodes in space and time. ${X}_{ij}$ is decision variable and represents flow from node $i$ to node $j$. ${u}_{ij}$ and ${l}_{ij}$ are upper and lower bound constraints, respectively. ${a}_{ij}$ is amplitude and represents losses, such as evaporation and seepage.

$f(X)$ can be linear (Eq. 6) or nonlinear (Eq. 7) objective function.

$$f_{LP}=b_F\cdot X+b_S\cdot Y$$

(6)

$$f_{NLP}=\rho\cdot g\cdot\eta\cdot(\alpha\cdot Y^3+\beta\cdot Y^2+\gamma\cdot Y+c)\cdot X\cdot p\cdot\Delta t$$

(7)

where $X$ is flow and $Y$ is storage (decision variables). ${b}_{F}$ and ${b}_{S}$ are optimized unit benefits (slopes) of flow and storage. These unit benefits are fit to the nonlinear hydropower curve (Eq. 7) with a linear approximation. ${f}_{NLP}$ also is a function of constant parameters of water density $\rho (kg/{m}^{3})$, gravitational constant $g (m/{s}^{2})$, overall plant efficiency $\eta$ (constant), unit energy price $p (\$/Wh)$, time step $\Delta t$ (hour), and polynomial parameters $\alpha$, $\beta$, $\gamma$ and $c$ to dynamically calculate water head from storage $Y$. ${f}_{LP}$ and ${f}_{NLP}$ represent total revenue (dollars) from generated energy ($Wh$).

3 Results and Discussion

3.1 Hydropower Generation

Hydropower generation is controlled by water storage and release decisions, driven by present and future energy prices. Hydropower generation helps meet demand since energy price and demand are highly correlated. As storage increases, the potential energy difference between storage elevation and tailwater (head) increases. Increased storage also sustains hydropower generation for longer periods. However, hydropower is not generated until water is released through turbines. So, the decision becomes how much to store and release and when to do so.

Operations vary for plants as each has different storage and turbine capacities and inflow rates (Fig. 7). Shasta and Folsom generate small amounts in morning peak hours, while remaining plants generate for both morning and evening peaks with large amounts in the post-solar period in the wet season. New Bullards Bar generates hydropower during most hours because its head does not change significantly with storage, so it does not have to wait long to store water and gain head. New Melones and Pine Flat generate hydropower during both peaks with similar morning and evening peak generation. All plants in the wet season reduce hydropower generation between hours 9 to 18 in the post-solar period.

Generation focuses mostly on evening peak hours in the dry season due to less water availability and much higher energy prices during the evening peak, as shown in Fig. 8. All plants significantly reduce pre-solar period hydropower generation during solar generation hours, with small morning peak generation, and extend the duration of evening peak generation. Hydropower plants can start operations faster than thermal plants, but increased ramping rates in the post-solar period can cause environmental harm downstream. In addition, minimum in-stream flow requirements downstream of these plants often affect optimized releases. Most large reservoirs, such as Shasta, New Bullards Bar, and Folsom, have smaller reservoirs downstream, which can act as afterbays to alleviate negative impacts of pulse releases and help meet environmental flows (Olivares 2008). Water availability, storage capacity and storage-head relationship result in different plant operations. The average reservoir operating rule for large-scale hydropower plants becomes to generate hydropower first during evening peak, and only if there is enough water, release during the morning peak, with reduced hydropower generation during solar generation hours (9–18).

3.2 Reservoir Storage and Release

Reservoir storage increases with inflows and decreases with generation releases. The slope of the rising limb of the storage curve gives average net inflow rate, and similarly the slope of the recession limb equals the average net turbine discharge rate (Fig. 9). Spills are penalized to minimize foregone energy, and no significant spills occur during any hourly time-step with overall average inflows. In the pre-solar period storage peaks earlier in the day in the wet season, around hours 6 and 10 (Fig. 9-a). Storage slightly decreases during hours around 7–8 with morning peak releases in the post-solar period in the wet season, but a much greater daily storage peak occurs at hour 18 and falls with evening peak generation releases. In the dry season (Fig. 9-b), normalized storage does not change significantly with solar development. Peak storage of the post-solar period shifts about 3 h later, occurring around hour 18.

Since overall average inflows are used for pre- and post-solar periods to eliminate inter- annual hydrologic variability, total release volume does not change (the area under the release curve is the same for both periods shown in Fig. 10). In the wet season of the pre-solar period, some releases on hours 9 to 18 move to earlier hours, forming the morning peak releases. The remaining releases move to later hours, extending the duration and amount of evening peak releases in the post-solar period. Plants make little releases during morning peak hours in the dry season, and concentrate operations to evening peak hours. Some pre-solar period releases, from 13 to 18 h shift to later hours, increasing evening peak releases in the post-solar period.

3.3 Hydropower Revenue

The hybrid LP-NLP hydropower optimization model maximizes hydropower revenue across all plants $i$ and time-steps $t$. Hydropower revenue $R$ is obtained by multiplying hydropower generation $G$ with unit energy prices $p$. To maximize revenue, the model generates hydropower during the most profitable hours. Generation in less profitable hours are only made when enough water is available. Revenue changes linearly with energy prices and hydropower generation (Eq. 8).

$$R_{i,t}=p_{i,t}\cdot G_{i,t}$$

(8)

Table 2 shows hourly average modeled revenue in wet and dry seasons between 2010 and 2018, denoting how revenue changes with solar induced energy price changes. Overall, hydropower revenue increases proportionally with increased (mean) energy prices and are higher in the wet season and lower in the dry season. As solar development increases between 2010 and 2018, price range increases significantly, causing twice-daily peaks. This range is measured as the energy price difference between hours 20 (evening peak demand and price hour) and 13 (solar generation peak hour). Given those changes and similar amounts of hydropower generation on average, with seasonal average reservoir inflows, hydropower revenue increases in the post-solar period. For example, wet season of 2016 and 2012 have the same average price (21 $/MWh), but hourly average revenues in these years are 2,842 and 2,706 $/h, respectively. Similarly, the dry seasons of 2016 and 2011 have the same average price (31 $/MWh), but price range and hourly revenue of 2016 (23 $/MWh and 1,846 $/h) is much more than in 2011 (6 $/MWh and 1,765 $/h). Similar comparisons can be made for other years and seasons between pre- and post-solar periods, showing the effect of the new price pattern on hydropower revenue. Years from 2013 to 2015 are transitioning years from 1-daily to 2-daily energy price peaks, so revenue comparison in these years may not give the same results (for example 2010 and 2013 wet seasons).

Table 2

Average energy price, price range and hourly average modeled revenue

Period	Year	Season	Energy price ($/MWh)		Average revenue ($/h)
Period	Year	Season	Average	Range¹	Average revenue ($/h)
Pre-solar	2010	Wet	34	1	4585
	2010	Dry	31	3	1665
	2011	Wet	24	4	3490
	2011	Dry	31	6	1765
	2012	Wet	21	5	2706
	2012	Dry	28	5	1653
Post-solar	2013	Wet	37	10	4447
	2013	Dry	41	10	2190
	2014	Wet	43	16	5724
	2014	Dry	40	15	2209
	2015	Wet	29	16	3708
	2015	Dry	30	15	1636
	2016	Wet	21	13	2842
	2016	Dry	31	23	1846
	2017	Wet	25	33	3891
	2017	Dry	36	43	2550
	2018	Wet	27	30	3933
	2018	Dry	43	37	2761

¹Energy price range (difference) between hours 13 and 20, which are mid-day solar generation peak and evening energy price peak hours

Figure 11 shows hourly revenue differences between pre-solar (2010–2012) and post- solar (2013–2018) period averages. Although a total of roughly 18.2 $K revenue per day is lost due to less hydropower generation during solar generation hours between 11 and 17, roughly 30.1 $K of revenue per day is gained in the other hours in the wet season, with a net increase of 11.9 $K per day, corresponding to about 14% increase in overall revenue. The dry season has less operational flexibility, when roughly 12.9 $K of revenue per day is lost between hours 12 and 17, but a total of 25 $K per day is gained during hours between 18 and 22, totaling the net difference to 12.1 $K per day. Overall revenue increase in the dry season is about 30%. The adaptation to new conditions of the post-solar period results in an additional net daily benefit of 24 $K per plant per day.

3.4 Summary and Adaptations

The new energy price pattern increases overall hydropower revenue with adaptations, although most hours between 10 and 18 are less profitable due to solar generation, especially in wet seasons with more water availability. Fig. 12 summarizes annual average hydropower operations with normalized values (between 0 and 1) for pre-solar and post-solar periods and wet and dry seasons. The normalized values of energy prices were much lower due to less net load during hours between 9 and 18 in the post-solar period, creating two daily peaks occurring hours 7–9 in the morning and 19–21 in the evening in both seasons. The magnitude of the latter is much greater. Since the model is driven by energy prices, subject to water availability, operations significantly adapt to these new energy price conditions. Reservoir storage peaks daily during hours 6–9 in the wet season and 13–14 in the dry season in the pre-solar period, then decreases with hydropower releases. These storage peaks shift to hours 16–18 in the wet season and 15–17 in the dry season in the post-solar period, before evening peak releases start. Peak releases of the post-solar period concentrate to shorter evening peak hours with greater release intensities. Plants generate some hydropower during the morning peak hours in the post-solar period, mostly in the wet period, but most generation and revenue is from hours between 19 and 21.

Water management evolves as policies, operating rules, environmental regulations, and hydroclimatic conditions change. Adaptive management is key for robust, reliable, and resilient water systems, including flood, water supply, ecosystem, and hydropower, and to use limited resources efficiently (Medellín-Azuara et al. 2008; Connell-Buck et al. 2011; Hanak and Lund 2012; Lund and Moyle 2013; Ahmadi et al. 2014; Hui et al. 2018). When hydropower and other renewables are implemented cooperatively, existing hydro-only reservoir operating rules may become less effective and require adaptations (Ming et al. 2019). Adapting short-term hydropower reservoir operations to the new price scheme increases overall hydropower revenue.

Useful adaptations include:

Hydropower releases are less valuable or optimal in hours when solar generation is high.
If water availability is greater in the wet season, releases are made twice a day to generate during on-peak hours in the morning and evening with lower solar generation.
If water is scarcer, energy is generated only during the most valuable hours (the evening peak).
Storing water during less profitable hours and energy generation during the evening peak for extended durations increases overall hydropower revenue.

4 Conclusions

This paper shows effects of new energy price patterns from renewable generation, particularly solar energy, on short-term hydropower operations, using a hybrid LP-NLP hydropower optimization model. The expansion of solar generation, as part of California’s renewable goals, decreased energy prices significantly during daylight hours, when solar generation peaks, resulting in a two-peak net demand and energy price pattern. The first peak occurs around 8 in the morning, and the second peak occurs around 20 in the evening. This new energy price pattern considerably affects dispatchable hydropower operations. The new price pattern, if adapted to, is more profitable for short-term hydropower operations. In the wet season, twice-daily hydropower pulse releases, without much generation between 10 and 18, increase hydropower revenue. In the dry season, the evening price peak is much greater than the morning. With more limited water availability in the dry season, operations concentrate on the evening peak hours with a shorter duration. Large hydropower pulse releases for a shorter duration can potentially harm downstream ecosystems, but most reservoirs have afterbays to reduce impacts from these pulses. California will increase renewable generation to meet its Renewable Portfolio Standard target of 50% by 2030. Given most of this target is from solar generation, the State might double current solar generation. This will continue to lower energy prices during solar hours and reshape energy price pattern, giving more opportunities for operational optimization of dispatchable hydropower. Changes in electricity demands from electric vehicles, heat pumps and other technologies are likely to further affect electricity price patterns. Hydropower plants with sizable storage capacities are more adaptable to changing conditions. However, run-of-river plants or plants with small storage capacities are negatively affected from climatic and energy prices changes.

Declarations

Ethical Approval

This research did not involve human or animal subjects and therefore did not require ethical approvals.

The research did not involve human subjects. Therefore, there were no requirements of consent to participate.

The authors grant full rights to publish and freely distribute the content of this paper once it is accepted for publication in the Water Resources Management Journal.

Competing Interests

The authors have no competing interests to declare in relation to the content of this manuscript.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Title: Hydropower Reservoir Optimization with Solar Generation-Changed Energy Prices in California
Authors: Mustafa Sahin Dogan
Josue Medellin-Azuara
Jay R. Lund
Publication date: 07-02-2024
Publisher: Springer Netherlands
Published in: Water Resources Management / Issue 6/2024
Print ISSN: 0920-4741
Electronic ISSN: 1573-1650
DOI: https://doi.org/10.1007/s11269-024-03747-6

Springer Professional

Abstract

Highlights

Publisher's Note

1 Introduction

2 Materials and Method

2.1 Study Area

2.2 Demand-Energy Price Relationship

2.3 Changed Energy Price Pattern

2.4 HERO Hydropower Reservoir Optimization Model

3 Results and Discussion

3.1 Hydropower Generation

3.2 Reservoir Storage and Release

3.3 Hydropower Revenue

3.4 Summary and Adaptations

4 Conclusions

Declarations

Ethical Approval

Consent to Participate

Consent to Publish

Competing Interests

Publisher's Note

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