Representing Energy Price Variability in Long- and Medium- term Hydropower Optimization

Representing peak and off-peak energy prices is often difficult in hydropower modeling because the time scale of price variability (hours or less) is much shorter than that needed for many operations planning models (days to months). This work extends and examines the reliability of an existing approximate method to incorporate hourly energy price information into revenue functions used in hydropower reservoir optimization models with larger time steps (weekly, monthly, etc). The method assumes constant head, an exogenously known frequency distribution for hourly prices during each modeled time period (day, week, month) and a revenue-maximizing operational strategy that allocates hydropower releases in order of decreasing hourly price. The method is extended to the case with minimum instream flows requirements. The reliability of the method was tested for the cases with and without minimum instream flow requirements. Revenue estimates for a hypothetical hydropower site were compared with the exact optimal revenue from solving the hourly optimization problem within one week, showing less than 1% error using a finely discretized price frequency curve. INTRODUCTION Optimization models are commonly used for hydropower reservoir operations planning, with time horizons ranging from weeks to years and time steps ranging from days to months. In this modeling, it is often important to represent energy price variability (peak vs. off-peak prices) which occurs on short time scales (minutes to hours) in models using longer (daily to monthly) time steps. These models are almost always based on maximization of hydropower revenues, with essentially fixed operational costs for hydropower production (Labadie, 2004; Pereira & Pinto, 1991; Kelman et al., 1990; Faber & Stedinger, 2001; Fleten & Kristoffersen, 2008). Some models also include coordination of hydropower and thermal power assets (Jacobs and Schultz, 2002). The output of each hydropower plant is usually small relative to the overall energy market and so typically has almost no effect on energy prices, allowing energy prices to be considered exogenous from the perspective of individual hydropower facilities. Because energy prices usually vary on short (e.g., hourly) time scales, much hydropower modeling on longer (daily to monthly) time steps can be misleading if it relies on a single representative price for each time step (e.g. week, month), especially if an average energy price is used. Using an average price in most cases underestimates revenues for a given level of power production, because reservoir releases will be allocated preferentially for