California’s high elevation hydropower system with more than 150 power plants provides 74% of the US state’s hydropower. Given that studying such a large system with conventional hydropower modelling methods would be tedious and costly, Kaveh Madani and Jay Lund have developed a new model (EBHOM) that can be used for large-scale hydropower planning studies in California with reasonable computational effort and time.


Figure 1

California relies on hydropower for 15% of the electricity used in the state, on average, and as much as 30% in wet years. More than 150 hydropower plants at high elevations (above 300m) supply about 75% of in-state hydropower. High elevation reservoirs are mostly single-purpose built mainly for hydropower production for private owners, but sometimes have secondary benefits such as flood control. The high elevation hydropower reservoirs in California are generally small with high turbine heads and no year-to-year carry-over storage. The systems have been designed to take advantage of snowpack, which is considered as the ‘largest seasonal surface water reservoir’ in the state. These man-made and natural storage systems have combined for many years to supply hydropower to Californians.

Hydropower and climate change

Given its low cost, near-zero greenhouse gas emissions, and ability to respond quickly to peak loads, hydroelectric power is a valuable resource in California. However, expected climatic changes put the reliability of this resource in question. Climate change can affect hydropower supply through hydrological changes and affect hydropower demand through temperature changes and other unknown consumers’ responses. Climate change could reduce revenues for hydropower generators, increase electricity costs for the consumers, and increase demand for new electricity sources in California.

To adapt to the possible effects of climate change and also other future expected changes such as population and electricity demand growth on hydropower systems, hydropower operators and governmental planning agencies first need to evaluate such effects. Evaluation of the effects of external changes on the systems’ operations and hydropower revenues can help answering questions such as:

• Are hydropower systems sensitive to climate change and other future changes?

• What is the magnitude of future hydropower generation and revenue losses?

• Which attributes of climate change (changed flow timing of the flow, changed flow levels, changed demand patterns, etc.) are most problematic for the hydropower systems?

• How effective are the changes in the operation policies and rule curves in minimising the losses?

• Are structural changes such as storage and energy generation capacity expansion needed to increase the reliability of hydropower systems?

Models can help answer these questions, evaluate the effects of external changes on the system operations, and find promising strategies to minimise losses. When dealing with large systems like the high elevation hydropower systems in California, the challenge is to develop a model that provides reliable information about the system without requiring extensive computational, cost and time efforts. Determining the required level of details in the model is tricky, especially when there is uncertainty about the future changes such as climate change.


Following the interest of the California Energy Commission in understanding the climate change effects on high elevation hydropower in California, researchers Kaveh Madani and Jay Lund developed an innovative model. The Energy-Based Hydropower Optimization Model (EBHOM) is a non-linear optimisation model that finds the reservoir operations and hydropower generation which maximises hydropower revenues.

EBHOM provides planning and management insights about hydropower systems with minimal computational effort. The run time of the model is low and its application to different systems is not costly. EBHOM has been tested through a collaborative study between research teams from the University of California at Davis and the University of California at Berkeley, comparing against a detailed hydropower model developed based on conventional methods. The results suggested that EBHOM often can reliably find the optimal operation, for broad policy studies, without detailed conventional modelling.

The effects of on-peak and off-peak pricing on the hydropower operations are considerable. EBHOM uses a novel method to incorporate the effects of variable pricing on the operations. This is important for hydropower systems that are operated with fluctuating hourly prices.

EBHOM uses energy units instead of volumetric units for the inflows and outflows to the reservoirs. Through an innovative method (no spill method) EBHOM estimates the energy storage capacity of high elevation reservoirs with no carry-over storage in energy units once the distribution of the water inflows and generation outflows are known. Therefore, EBHOM does not need some details about the hydropower systems such as effective energy head and storage capacity, without which modelling is impossible with conventional method. This capability makes EBHOM valuable for modelling systems for which reliable information is not readily available.

Like any other model, EBHOM has limitations. However, depending on the desired accuracy level and the needs of the study, most limitations can be addressed with additional effort. The existing EBHOM is often pessimistic in estimating the storage capacities of reservoirs. This is not important when storage capacities are available. So far, EBHOM has been used in studies in which hydrologic scenarios are given and the operator has seasonal foresight. However, in practice, decisions involve uncertainty. When consideration of uncertainty is crucial, the optimisation formulation of EBHOM can be improved.

Despite these limitations, EBHOM has been found to be a reliable tool to perform large-scale hydropower studies for the purpose of long-term planning and policy making with the top-bottom approach. Under such an approach, the modeller will first get familiarised with the system and discover the general changes in the system under different changes. Then the modeller can identify the critical parts of the system and perform detailed studies on them. This approach will be cost-effective as detailed models will not be developed unless serious problems are identified.

EBHOM’s contribution to hydro studies

EBHOM has been used in several state-wide hydropower planning and management studies in California with the climate change adaptation objective. The first applications of EBHOM (EBHOM 1.0) only considered the effects of climate change on the supply side of the hydropower systems, ie how changes in runoff timing and quantity affect hydropower generation and revenues. Results of these studies suggested that due to the limited storage capacities of the high elevation hydropower systems, the operations are highly sensitive to the runoff timing. Generally, lower revenues are expected under dry climate warming, due to decreased water quantities.

However, the level of reduction in generation was found to be less than the level of revenue losses due to the non-linear nature of the hydropower market. On the other hand, given the limited generation and storage capacities that result in spills, California will be unable to benefit from increased runoff under wet climate warming. Also, due to the non-linear nature of the market the level of increase in hydropower revenues is far less than the level of increase in hydropower generation under the wet warming scenario.

Recently, EBHOM has been improved to also consider the climate change effects on hydropower demand and pricing. The improved EBHOM (EBHOM 2.0) benefits from an Artificial Neural Networks (ANN) module that estimates the changes in hourly hydropower pricing in response to temperature changes. In California, with a Mediterranean climate, higher average prices in hotter summer months and lower prices in warmer winter months are expected with climate warming. Simultaneous consideration of climate warming effects on hydropower supply and demand has suggested that revenue losses under the dry climate warming are not as significant as when the pricing changes are ignored. This is due to higher average prices with dry climate warming. On the other hand, hydropower revenues are not expected to increase even with increased generation under wet climate warming. This is because increased generation will be expected in months that will have lower average prices with warming.

Dr. Kaveh Madani ( is the Founding Coordinator of the Hydro-Environmental and Energy Systems Analysis (HEESA) Research Group and an assistant professor in the Department of Civil, Environmental and Construction Engineering at the University of Central Florida.

Dr. Jay R. Lund ( is the Director of the Center for Watershed Sciences and a Ray B. Krone Professor in the Department of Civil and Environmental Engineering at the University of California at Davis.


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