## Abstract

The purpose of the present paper is to investigate what significance, if any, inclusion of uncertainties has for the conclusions of the modelling and analysis, i.e., whether the policy recommendations implicit in the results of the analysis depend on the inclusion or not of uncertainties. We do this within the context of a model of the Northern European electricity sector.

The paper considers uncertainties about future states of nature. More specifically, we consider the inflow of water into a hydropower production system, where the states of nature are represented by a "dry", a "normal" and a "wet" year.

The problems may be formulated as non-linear optimisation models where the objective function basically consists of the expected value of the-sum of consumers', producers', and authorities' surplus. The models take into account that there are losses in the transmission and distribution of electricity and that the consumers pay an energy tax on their use of electricity. The consumers are divided into two groups, households and industry. Also, complementarity formulations are used, as these are shown to be more adequate for certain aspects, in particular where risk aversion within a liberalised market context is modelled.

For each of eight Northern European countries, the basic results of the models are the installation of new production capacities, the production on old and new production capacities, the electricity prices, and the interchange between the countries. The investment in new production capacity is represented by a single Value for each country, while the productions differ in that they depend on natural phenomena, which we refer to as the state of nature and represent by stochastic variables.

It was found that in this context it was relatively easy to include stochastic elements in the model. Second, complementarity formulations are preferable to optimisation based modelling for some problem types. Third, results of the stochastic model have natural interpretations, also compared to one or several versions of a deterministic model. And fourth, we have seen that the quantitative results, and hence the implied policy recommendations, may differ significantly from those of deterministic models. We therefore conclude that increased attention should be given to the inclusion of stochastic elements into the modelling of energy systems.

The paper considers uncertainties about future states of nature. More specifically, we consider the inflow of water into a hydropower production system, where the states of nature are represented by a "dry", a "normal" and a "wet" year.

The problems may be formulated as non-linear optimisation models where the objective function basically consists of the expected value of the-sum of consumers', producers', and authorities' surplus. The models take into account that there are losses in the transmission and distribution of electricity and that the consumers pay an energy tax on their use of electricity. The consumers are divided into two groups, households and industry. Also, complementarity formulations are used, as these are shown to be more adequate for certain aspects, in particular where risk aversion within a liberalised market context is modelled.

For each of eight Northern European countries, the basic results of the models are the installation of new production capacities, the production on old and new production capacities, the electricity prices, and the interchange between the countries. The investment in new production capacity is represented by a single Value for each country, while the productions differ in that they depend on natural phenomena, which we refer to as the state of nature and represent by stochastic variables.

It was found that in this context it was relatively easy to include stochastic elements in the model. Second, complementarity formulations are preferable to optimisation based modelling for some problem types. Third, results of the stochastic model have natural interpretations, also compared to one or several versions of a deterministic model. And fourth, we have seen that the quantitative results, and hence the implied policy recommendations, may differ significantly from those of deterministic models. We therefore conclude that increased attention should be given to the inclusion of stochastic elements into the modelling of energy systems.

Original language | English |
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Journal | Annals of Operations Research |

Volume | 97 |

Pages (from-to) | 213-229 |

ISSN | 0254-5330 |

DOIs | |

Publication status | Published - 2000 |