Upgrading the capacity of existing hydropower plants is an important lever to achieve a carbon-neutral power grid. We investigate a hierarchical perspective towards capacity upgrade at a hydropower plant based on work with a European hydropower producer. We develop a nested Markov decision process model that captures both the timing flexibility to delay upgrades and hourly-production flexibility. The former is typically not considered in practice, while the latter is not accurately captured in dynamic upgrade models in academia. Our work bridges this gap. We combine policy and price model structure with options valuation to show that dynamic upgrade policies that capture hourly-production flexibility can be accurately and efficiently valued. We perform extensive numerical experiments on instances calibrated to real market and operational data. We find that our approach allows a hydropower producer to disentangle the value of optimizing the timing of a capacity upgrade versus the value of accurately capturing hourly-production flexibility. Accurately valuing hourly-production flexibility results in more capacity addition, regardless of whether the upgrade timing is optimized. It is thus relevant to NPV models that are popular in practice. Dynamic upgrade policies are viewed as a means of increasing plant value by optimizing upgrade timing. We discover that a significant alternative benefit of optimized upgrade time lies in recovering the upgrade investment cost substantially sooner, even when the increase in market value is marginal.

Hydropower producers estimate the opportunity value of their water, known as a water value, by comparing current prices to future opportunities. When hydropower dominates the energy mix, the system’s hydrological state predominantly governs supply and thus prices. Despite this intuitive relationship, industry practice is to assume that inflow to reservoirs and prices are independent when they establish operational policies 1–2 years ahead. To investigate the impact of this assumption, we formulate the hydropower scheduling problem as a Markov decision process and develop a novel price model that considers the joint dynamics of forward prices and inflows. We find that producers underestimate their water value when they ignore co-movements between price and inflow. The dependency makes producers more willing to postpone generation and tolerate slightly higher spillage risk. This is because high inflow periods tend to observe low prices and the reservoir capacity is limited. Nevertheless, a case study of a hydropower plant with industry data suggests modest economic losses in practice. Our numerical results suggest a potential gain of 0.17% in expected revenue and approximately unchanged revenue variance if producers consider the co-movements when establishing an operational policy.

Hydropower producers need to plan several months or years ahead to estimate the opportunity value of water stored in their reservoirs. The resulting large-scale optimization problem is computationally intensive, and model simplifications are often needed to allow for efficient solving. Alternatively, one can look for near-optimal policies using heuristics that can tackle non-convexities in the production function and a wide range of modelling approaches for the price- and inflow dynamics. We undertake an extensive numerical comparison between the state-of-the-art algorithm stochastic dual dynamic programming (SDDP) and rolling forecast-based algorithms, including a novel algorithm that we develop in this paper. We name it Scenario-based Two-stage ReOptimization abbreviated as STRO. The numerical experiments are based on convex stochastic dynamic programs with discretized exogenous state space, which makes the SDDP algorithm applicable for comparisons. We demonstrate that our algorithm can handle inflow risk better than traditional forecast-based algorithms, by reducing the optimality gap from 2.5 to 1.3% compared to the SDDP bound.

We consider an operator of machinery with deteriorating efficiency, facing the problem of optimally timing of either a minor (maintenance) investment or a major (replacement) investment under price uncertainty. If a maintenance investment is chosen, the efficiency of the machinery will deteriorate more slowly, and replacing later is still possible. The optimal decision rule is expressed in the form of thresholds for long-run prices, indicating that it may be rational to wait to see which of the large and small investment is the better choice. We relate the setting to repowering of green energy facilities, such as hydropower plants and wind farms. Our analysis provides several managerial insights. We characterize the conditions that govern whether the smaller investment should be considered at all, and we quantify the effect of having a replacement option embedded in a maintenance option. Our analysis demonstrates that the large investment may get postponed significantly in expectation, which recognizes maintenance as a temporary alternative to replacement.

Oil and gas companies are facing low output prices and are forced to focus on the development of mature fields. Relevant investment decisions for operators include lifetime-enhancing activities, such as drilling new wells or permanent shutdown. We study the problem of optimal timing of investments in mature oil and gas fields in the presence of price uncertainty, which is an example of a complex real options problem consisting of a portfolio of interdependent options. We formulate a multistage stochastic integer programming model that incorporates a detailed representation of the uncertain oil price, and demonstrate how such a complex real options problem can be efficiently solved using the Stochastic Dual Dynamic Integer Programming algorithm. The paper presents a numerical example based on realistic data and discusses our computational results. We find that only a small number of Markov states are required to represent the uncertain price process, while obtaining convergence of the lower and upper bounds of the objective function. The value of stochastic solution of 11% is considerable in this example. It is concluded that the shutdown decision tends to be postponed as a result of high decommissioning costs, high discount rates, high price uncertainty and low operational expenditures, while it generally is accelerated if the decommissioning costs increase over time.

This paper contributes to forecasting of renewable infeed for use in dispatch scheduling and power systems analysis. Ensemble predictions are commonly used to assess the uncertainty of a future weather event, but they often are biased and have too small variance. Reliable forecasts for future inflow are important for hydropower operation, and the main purpose of this work is to develop methods to generate better calibrated and sharper probabilistic forecasts for inflow. We propose to extend Bayesian model averaging with a varying coefficient regression model to better respect changing weather patterns. We report on results from a case study from a catchment upstream of a Norwegian power plant during the period from 24 June 2014 to 22 June 2015.

In this study, we introduce new Bayesian Model Averaging (BMA) approaches to construct probabilistic discharge forecasts. The approaches are tested for a case study from the Osali catchment in south-western Norway during the period from June, 24 2014 to June 22, 2015, with hydrological deterministic forecasts generated from a HBV-model using ensemble forecasts from European Centre for Medium-Range Weather Forecasts (ECMWF). In the classical BMA approach for postprocessing of ensemble forecasts, a probability density function is associated with each individual ensemble member forecast, and a sliding window training period is used to estimate model parameters, such as the mean and the variance of the individual ensemble member probability density functions. In hydrological forecasting, extreme events caused by snow melting or heavy rainfall, affect the BMA parameters in the following days, resulting in poor predictive performance. We suggest to model the mean in the BMA methodology with a varying coefficient regression (VCR) model to smooth parameter estimates and to better reflect changing weather patterns. Furthermore, we suggest to apply the Climatology Cumulative Probability Regression (CCPR) methodology to construct probabilistic discharge forecasts for each ensemble member, and then combine them with the BMA methodology. The calibration of the probabilistic forecast is assessed using the probability integral transform (PIT) and the predictive performance is assessed according to the continuous rank probability score (CRPS). The results from the case study showed that the predictive performance can be improved by including a varying coefficient regression model and/or the CCPR model in the BMA methodology for postprocessing of hydrological ensemble forecasts.