Stochastic Optimization Model for Detailed Long-term Hydro Thermal Scheduling Using Scenario-tree Simulation

AbstractThe paper presents a case study comparing two models for hydro-thermal scheduling. Both models are tools that can be applied for forecasting and planning in electricity markets, taking into account inter-connected power markets and using detailed hydro modelling. The first model, which is used as the reference, is in operative use by most market players in the Nordic power market. The second model is a new prototype which is expected to give better utilization in systems with large shares of hydro power because it to a larger extent is based on formal optimization. The case study compares the models with regard to differences in hydropower scheduling, market prices and socio-economic surplus

Hydropower Aggregation by Spatial Decomposition – an SDDP Approach

The balance between detailed technical description, representation of uncertainty and computational complexity is central in long-term scheduling models applied to hydro-dominated power system. The aggregation of complex hydropower systems into equivalent energy representations (EER) is a commonly used technique to reduce dimensionality and computation time in scheduling models. This work presents a method for coordinating the EERs with their detailed hydropower system representation within a model based on stochastic dual dynamic programming (SDDP). SDDP is applied to an EER representation of the hydropower system, where feasibility cuts derived from optimization of the detailed hydropower are used to constrain the flexibility of the EERs. These cuts can be computed either before or during the execution of the SDDP algorithm and allow system details to be captured within the SDDP strategies without compromising the convergence rate and state-space dimensionality. Results in terms of computational performance and system operation are reported from a test system comprising realistic hydropower watercourses.Hydropower Aggregation by Spatial Decomposition – an SDDP ApproachacceptedVersio

Modelling uncertainty in gas and CO2 prices – consequences for electricity price

A hydro-thermal market model is applied to a description of the north-European electricity system. The paper describes how modelling uncertain gas and CO 2 prices affects uncertainty in calculated electricity prices. Gas and CO 2 price uncertainty are modelled using historic price variations. With this new uncertainty modelling, the resulting electricity price uncertainty increases significantly compared to the deterministic modelling of thermal marginal costs that is standard in these types of models. Changes in electricity price uncertainty are shown using visual and quantitative measures for some representative price areas in the modelled system. Price forecasts from hydro-thermal models are among others used for hydro investment analysis. An underestimation of the future price uncertainty leads to less investment in flexibility which is much needed in the future electricity system with large shares of new renewables.Modelling uncertainty in gas and CO2 prices – consequences for electricity priceacceptedVersio

Approximating Ramping Constraints in Hydropower Scheduling

This work concerns the modeling of ramping constraints on discharge in medium-term hydropower scheduling models applied in a liberalized market context. Such models often apply a coarse time discretization to ensure reasonable computation times. Consequently, ramping constraints at a fine time-resolution are challenging to represent. To address this challenge, we derive a quadratic transition-cost term capturing the power production shifted to time periods with less favorable prices due to ramping constraints. We approximate the quadratic term by linearization so that it can be embedded in an existing hydropower scheduling tool based on stochastic linear programming. A prototype hydropower scheduling model, including the approximated transition-cost term, was tested on a realistic hydropower system in Norway. We demonstrate that the improved modeling of ramping constraints significantly impacts discharge patterns and comes at a significant, but not prohibitive, increase in computation time.Approximating Ramping Constraints in Hydropower SchedulingacceptedVersio

Methodology for forecasting in the Swedish–Norwegian market for el-certificates

In this paper we describe a novel methodology for forecasting in the Swedish-Norwegian el-certificate market, which is a variant of a tradable green certificate scheme. For the forecasting, the el-certificate market is integrated in the electricity-market model EMPS, which has weekly to hourly time-step length, whereas the planning horizon can be several years. Strategies for the certificate inventory are calculated by stochastic dynamic programming, whereas penalty-rates for non-compliance during the annual settlement of certificates are determined endogenously.In the paper the methodology is described, and we show the performance of the model under different cases that can occur in the el-certificate market. The general results correspond to theoretical findings in previous studies for tradable green certificate markets, in particular that price-scenarios spread out in such a way that the unconditional expected value of certificates is relatively stable throughout the planning period. In addition the presented methodologies allows to assess the actual dynamics of the certificate price due to climatic uncertainty. Finally, special cases are indentified where the certificate price becomes excessively high respectively zero, due the design-specific dynamics of the penalty rate. © 2015 Elsevier Ltd.Methodology for forecasting in the Swedish–Norwegian market for el-certificatesacceptedVersio

Structure and stylized facts of a deregulated power market

Dramatic changes to the structure of the power sector have taken place over the past few decades. The major structural change being the introduction of competitive markets and power exchanges. In this paper, we conduct a detailed empirical study of the statistical properties of the Nordic power (Nord Pool) spot market. The aim of this study is to identify so-called stylized facts of the market. We address the structure of the market, and in particular, describe in detail the spot price forming process (equilibrium point trading). A collection of stylized facts is identified and discussed for the hourly system spot price, based on the entire 12 year history of available Nord Pool data. In particular we analyze: seasonallity, weather effects, the human factor, return distributions, volatility, spikes, and mean-reversion (anticorrelation). The empirical study presented in this paper shed new light on the mechanisms, features and structures of these new commodity markets. The market features that distinguish them from more classic financial and commodity markets are pointed out.Electricity markets; Spot price; Stylized facts; Deregulation; Econophysics

Detailed long-term hydro-thermal scheduling for expansion planning in the Nordic power system

acceptedVersio

Hydropower Scheduling with State-Dependent Discharge Constraints: An SDDP Approach

Environmental constraints in hydropower systems serve to ensure sustainable use of water resources. Through accurate treatment in hydropower scheduling, one seeks to respect such constraints in the planning phase while optimizing the utilization of hydropower. However, many environmental constraints introduce state-dependencies and even nonconvexities to the scheduling problem, making them challenging to represent in stochastic hydropower scheduling models. This paper describes how the state-dependent maximum discharge constraint, which is widely enforced in the Norwegian hydropower system, can be embedded within the stochastic dual dynamic programming (SDDP) algorithm for hydropower scheduling without compromising computational time. In this work, a combination of constraint relaxation and time-dependent auxiliary lower reservoir volume bounds is applied, and the modeling is verified through computational experiments on two different systems. The results demonstrate that the addition of an auxiliary lower bound on reservoir volume has significant potential for improved system operation, and that a bound based on the minimum accumulated inflow in the constraint period is the most efficient.Hydropower Scheduling with State-Dependent Discharge Constraints: An SDDP ApproachpublishedVersio

A Comprehensive Simulator for Hydropower Investment Decisions

Due to a higher share of power production from renewable sources with high short-term variation, hydro systems must more often operate closer to their components' physical limits. To simulate system behaviour, a hydropower system simulator must therefore include most physical details. We present a simulator for hydropower investment analysis that combines a medium-term production planning model based on stochastic dual dynamic programming principles with a detailed and deterministic short-term hydro scheduling model. To reduce computation times, the system description for the short-term model may include only a snipped subset of the plants and reservoirs without deteriorating the results. The simulator is verified in a case study where an investment decision has been analysed for a Norwegian hydropower producer. The combination of medium-term optimization and short-term, detailed simulation is a useful decision support tool and provides both economic results and detailed physical information about the system behaviour.A Comprehensive Simulator for Hydropower Investment DecisionsacceptedVersio

Measuring the Impact of Environmental Constraints on Hydropower Flexibility

Implementation of EU’s Water Framework directive, meant to ensure sustainability of the hydropower production, may lead to new environmental constraints on hydropower systems. This can result in loss of production, reduced operational flexibility and consequently reduced income from production. Flexibility is here defined as the ability to adapt production to variations in power prices, whereas the production income is strongly influenced by the price level and sum production. This paper presents and evaluates two different measures that are used to quantify how new constraints affect system flexibility in the Norway and Sweden. These measures are the established Flexibility Factor, comparing achieved price with average price, and an imaginary equivalent electrical storage unit, which is parametrized by the equivalent storage and power capacity needed to compensate for the lost flexibility. The calculation and evaluation of the two measures are exemplified using two Norwegian water courses.Measuring the Impact of Environmental Constraints on Hydropower FlexibilityacceptedVersio