Arild Helseth

Long-term hydro-thermal scheduling including network constraints

This paper presents a method for treating transmission network bottlenecks in a stochastic hydro-thermal scheduling model. The model is designed for long- and medium-term scheduling of hydro-thermal power system operation, where decisions are made for aggregated regional subsystems or areas. The aggregate area representation allows simulation of large hydro systems with a relatively high degree of detail, thus making the model well suited for comprehensive studies on a national and international scale.

Reliability modeling of gas and electric power distribution systems; similarities and differences

Due to the introduction of alternative energy carriers, such as district heating and natural gas, the Norwegian energy system is becoming more complex. Assessing the reliability of electrical distribution systems is a mature field of research, but limited work has been carried out concerning the reliability of distribution systems for alternative energy carriers. This paper proposes a methodology for assessing the reliability of natural gas distribution systems based on experiences drawn from similar analysis of electrical power distribution systems. A simple test case is presented for illustrative purposes and the basic load-point reliability indices of average interruption rate, average outage time and average annual outage time are found

Optimal Medium-Term Hydropower Scheduling Considering Energy and Reserve Capacity Markets

This paper describes a method for optimal scheduling of hydropower systems for a profit maximizing, price-taking, and risk neutral producer selling energy, and capacity to separate and sequentially cleared markets. The method is based on a combination of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP), and treats inflow to reservoirs and prices for energy and capacity as stochastic variables. The proposed method is applied in a case study for a Norwegian watercourse, quantifying the expected changes in schedules, and water values when going from an energy-only market to a joint treatment of energy and reserve capacity markets.

A linear optimal power flow model considering nodal distribution of losses

This paper presents a method for accurately treating active power losses in linear (DC) optimal power flow models. Quadratic nodal losses are approximated by iteratively adding linear constraints. In each iteration a linear programming problem is solved, and constraints on the nodal loss functions are built as linearizations around the current system operating state. The performance of the proposed model - in terms of computational time and convergence properties - is demonstrated on the IEEE 118 bus test system.

Hydropower scheduling in day-ahead and balancing markets

We present a stochastic mixed-integer model for the optimization of joint trade in the day-ahead and balancing markets. The model takes the perspective of a risk-neutral price-taking hydropower producer for a one-day planning horizon. The model is used to study the value of trading in both markets as opposed to day-ahead trades only. In particular we study how this value is affected by the flexibility in the production system. The results indicates a small added value from balancing market participation which is increasing as the production flexibility increases.

Handling balancing power in a power market with a large share of hydropower

This paper presents a model well suited for analysis of power systems with a large share of new renewable in combination with hydropower and pumped-storage hydro. The model is designed for a detailed hydropower representation and can be used with hourly time resolution. The model solves the detailed dispatch of hydropower in two steps. First it uses a heuristic model for weekly decisions where the goal is to find the target for end reservoir levels. Then the problem is re-solved as a formal optimization problem where the goal is to fully utilize the flexibility in the hydropower system within the week.

Hydrothermal scheduling in Norway using stochastic dual dynamic programming; a large-scale case study

We test the stochastic dual dynamic programming (SDDP) approach on a system an order of magnitude larger than previously published studies. The analysis shows that the SDDP-approach can be applied to very large system sizes to solve the hydropower scheduling problem through formal optimisation and obtain individual decision variables for every reservoir. However, this can be very time-consuming compared to other existing models based on other principles. The results from our SDDP-based model compare favorably to an aggregation-disaggregation model which is in operational use in the power market when using statistical inflow series as input to the models.

Impact of Energy End Use and Customer Interruption Cost on Optimal Allocation of Switchgear in Constrained Distribution Networks

The introduction of new energy carriers, such as natural gas and district heating, to energy systems dominated by electrical power will certainly relieve stress on the power system. Some of the end uses initially served by the power system will be gradually decoupled and served by alternative energy carriers. As a result, the specific customer interruption costs and load profiles will change. In this paper, we analyze how the optimal level of switchgear in electric power distribution systems is affected by such changes. The proposed optimization method is based on a genetic algorithm and takes into account the constrained network capacity.

Co-optimizing sales of energy and capacity in a hydropower scheduling model

This paper describes a model for optimal scheduling of hydroelectric systems for a price-taking producer selling energy and capacity to separate markets. The model is based on a combination of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP), and treats inflow to reservoirs and energy prices as stochastic variables. It allows sales of capacity at a deterministic sequence of capacity reserve prices. Thus, the sales of energy and capacity is co-optimized within the SDDP framework. The presented model is tested on a Norwegian watercourse where the producer sells energy to the day-ahead market and capacity to the primary reserve markets. When adding the possibility to sell capacity in the model, the results show that less water is used during winter and more during summer/autumn in order to sell capacity.

Combined SDDP and simulator model for hydropower scheduling with sales of capacity

In following work, we investigate the importance of detailed hydropower scheduling modelling when including sales of capacity, which adds complexity that is not easily incorporated in a Linear Programming (LP) problem. In the proposed approach, we use the profit-to-go function obtained from a Stochastic Dual Dynamic Programming (SDDP) scheduling-model in a Simulator Model, based on Mixed Integer Programming (MIP), and perform detailed simulations. The Simulator Model allows a more complex problem description, than by the LP formulation in the SDDP model. The Simulator Model may therefore be used to give an estimate of the LP approximation, which is used for providing the opportunity cost in short-term hydropower scheduling models or conceivably for making investment decisions. For the given case study, the expected profit from selling capacity was 29.2% higher than the linear SDDP Model to the Simulator Model. The overall profit loss was reduced by 0.93%, quantifying the overestimation of profit in the SDDP Model. This illustrates the importance of detailed modelling when considering sales of capacity.