Abstract-Hydropower producers need to schedule when to release water from reservoirs, and participate in wholesale electricity markets where the day-ahead production is physically traded. A mixed-integer linear stochastic model for bid optimization and short-term production allocation is developed and tested through a simulation procedure implemented for a complex real-life river system. The stochastic bid model sees uncertainty in both spot market prices and inflow to the reservoirs. The same simulation procedure is also implemented for a practicebased deterministic heuristic method similar to what is currently used for bid determination in the industry, and the results are compared. The stochastic approach gives improvements in terms of higher obtained average price and higher total value than the deterministic alternative. It also performs well in terms of startup costs. In the presence of river flow travel delay the practicebased method is even more outperformed by the stochastic model.Index Terms-Bidding, Electricity markets, Hydro Scheduling, Price taker, Simulation, Stochastic programming, Reservoirs NOMENCLATUREThe notation used throughout the paper is stated below. Setsc ∈ C Index for all cuts C for computation of the water value e ∈ E Index for different runs E of the deterministic model h ∈ H Index for all hours in the short-term models and all weeks in the seasonal model, H i ∈ I Index for all bid points in I j ∈ J Index for all turbines J in the system n ∈ N Index for known points on production curves with N breakpoints r ∈ R Index for all reservoirs and belonging stations, R, in the system s ∈ S Index for scenarios all S

In deregulated electricity markets, hydropower producers must bid their production into the day-ahead market. For price-taking producers, it is optimal to offer energy according to marginal costs, which for hydropower are determined by the opportunity cost of using water that could have been stored for future production. At the time of bidding, uncertainty of future prices and inflows may affect the opportunity costs and thus also the optimal bids. This paper presents a model for hydropower bidding where the bids are based on optimal production schedules from a stochastic model. We also present a heuristic algorithm for reducing the bid matrix into the size required by the market operator. Results for the optimized bids and the reduction algorithm are analyzed in a case study showing how uncertain inflows may affect the bids.

We present a literature survey and research gap analysis of mathematical and statistical methods used in the context of optimizing bids in electricity markets. Particularly, we are interested in methods for hydropower producers that participate in multiple, sequential markets for short-term delivery of physical power. As most of the literature focus on day-ahead bidding and thermal energy producers, there are important research gaps for hydropower, which require specialized methods due to the fact that electricity may be stored as water in reservoirs. Our opinion is that multi-market participation, although reportedly having a limited prot potential, can provide gains in exibility and system stability for hydro producers. We argue that managing uncertainty is of key importance for making good decision support tools for the multi-market bidding problem. Considering uncertainty calls for some form of stochastic programming, and we dene a modelling process that consists of three interconnected tasks; mathematical modelling, electricity price forecasting and scenario generation. We survey research investigating these tasks and point out areas that are not covered by existing literature.

We present a model for operational stochastic short-term hydropower scheduling, taking into account the uncertainty in future prices and inflow, and illustrate how the benefits of using a stochastic rather than a deterministic model can be quantified. The solution method is based on stochastic successive linear programming. The proposed method is tested against the solution of the true non-linear problem in a principal setting. We demonstrate that the applied methodology is a first-order approximation to a formal correct head-of-water optimization and achieve good results in tests. How the concept of stochastic successive linear programming has been implemented in a prototype software for operational short-term hydropower scheduling is also presented, and the model's ability is demonstrated through case studies from Norwegian power industry. From these studies, improvements occurred in terms of the objective function value and decreased risk of spill from reservoirs.

Abstract-This work investigates the cost of delivering different types of balancing reserves from a simple hydropower reservoir system. In addition to delivering energy, the fast ramping characteristics of hydropower units makes them suitable for delivery of various balancing products that are needed in order to maintain system security. The price at which these products are offered is determined by the opportunity costs in the dayahead energy market. In a small case study, these opportunity costs are assessed by analyzing the changes from the optimal day-ahead production schedule for various types and volumes of reserve delivery commitments. We find that the requirement of delivering spinning reserves may significantly restrict the production schedule. This type of balancing service is thus found to be costly in our analysis. The special restriction of symmetric up and down regulation for primary reserves also makes this type of service more expensive as the solution space is even more restrained.