Stein-Erik Fleten

Stochastic Programming Models in Energy

We give the reader a tour of good energy optimization models that explicitly deal with uncertainty. The uncertainty usually stems from unpredictability of demand and/or prices of energy, or from resource availability and prices. Since most energy investments or operations involve irreversible decisions, a stochastic programming approach is meaningful. Many of the models deal with electricity investments and operations, but some oil and gas applications are also presented. We consider both traditional cost minimization models and newer models that reflect industry deregulation processes. The oldest research precedes the development of linear programming, and most models within the market paradigm have not yet found their final form.

Short-term hydropower production planning by stochastic programming

Within the framework of multi-stage mixed-integer linear stochastic programming we develop a short-term production plan for a price-taking hydropower plant operating under uncertainty. Current production must comply with the day-ahead commitments of the previous day which makes short-term production planning a matter of spatial distribution among the reservoirs of the plant. Day-ahead market prices and reservoir inflows are, however, uncertain beyond the current operation day and water must be allocated among the reservoirs in order to strike a balance between current profits and expected future profits. A demonstration is presented with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.

Constructing bidding curves for a price-taking retailer in the norwegian electricity market

We propose a stochastic linear programming model for constructing piecewise-linear bidding curves to be submitted to Nord Pool, which is the Nordic power exchange. We consider the case of a price-taking power marketer who supplies electricity to price-sensitive end users. The objective is to minimize the expected cost of purchasing power from the day-ahead energy market and the short-term balancing market. The model is illustrated using a case study with data from Norway.

Renewable energy investments under different support schemes: A real options approach

This paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes. The main purpose is to examine investment behavior under the most extensively employed support schemes, namely, feed-in tariffs and renewable energy certificate trading. We consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme, and we obtain both analytical (when possible) and numerical solutions. In a Nordic case study based on wind power, we find that the feed-in tariff encourages earlier investment. Nevertheless, as investment has been undertaken, renewable energy certificate trading creates incentives for larger projects. In our baseline scenario and taking the fixed feed-in tariff as a base, the revenue required to trigger investments is 61% higher with renewable certificates. At the same time, investment capacity is 61% higher.

Hedging Electricity Portfolios via Stochastic Programming

Electricity producers participating in the Nordic wholesale-level market face significant uncertainty in inflow to reservoirs and prices in the spot and contract markets. Taking the view of a single risk-averse producer, we propose a stochastic programming model for the coordination of physical generation resources with hedging through the forward and option market. Numerical results are presented for a five-stage, 256 scenario model that has a two year horizon.

Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer

From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.

Constructing forward price curves in electricity markets

We present and analyze a method for constructing approximated high-resolution forward price curves in electricity markets. Because a limited number of forward or futures contracts are traded in the market, only a limited picture of the theoretical continuous forward price curve is available to the analyst. Our method combines the information contained in observed bid and ask prices with information from the forecasts generated by bottom-up models. As an example, we use information concerning the shape of the seasonal variation from a bottom-up model to improve the forward price curve quoted on the Nordic power exchange.

The performance of stochastic dynamic and fixed mix portfolio models

The purpose of this paper is to demonstrate how to evaluate stochastic programming models, and more specifically to compare two different approaches to asset liability management. The first uses multistage stochastic programming, while the other is a static approach based on the so-called constant rebalancing or fixed mix. Particular attention is paid to the methodology used for the comparison. The two alternatives are tested over a large number of realistic scenarios created by means of simulation. We find that due to the ability of the stochastic programming model to adapt to the information in the scenario tree, it dominates the fixed mix approach.

Medium term power planning with bilateral contracts

This paper addresses the optimal management of hydropower resources on medium term. The objective is to maximize the expected revenue of a producer, and the decision variables are generation and forward contracts in each period for each scenario. Stochastic linear and nonlinear programming has been used as a framework for modeling and solution. Results are exposited for a Norwegian power producer participating in Nord Pool, the Nordic power exchange.

Day-ahead market bidding for a Nordic hydropower producer: taking the Elbas market into account

In many power markets around the world the energy generation decisions result from two-sided auctions in which producing and consuming agents submit their price-quantity bids. The determination of optimal bids in power markets is a complicated task that has to be undertaken every day. In the present work, we propose an optimization model for a price-taker hydropower producer in Nord Pool that takes into account the uncertainty in market prices and both production and physical trading aspects. The day-ahead bidding takes place a day before the actual operation and energy delivery. After this round of bidding, but before actual operation, some adjustments in the dispatched power (accepted bids) have to be done, due to uncertainty in prices, inflow and load. Such adjustments can be done in the Elbas market, which allows for trading physical electricity up to one hour before the operation hour. This paper uses stochastic programming to determine the optimal bidding strategy and the impact of the possibility to participate in the Elbas. ARMAX and GARCH techniques are used to generate realistic market price scenarios taking into account both day-ahead price and Elbas price uncertainty. The results show that considering Elbas when bidding in the day-ahead market does not significantly impact neither the profit nor the recommended bids of a typical hydro producer.