An empirical analysis of scenario generation methods for stochastic optimization

Löhndorf, Nils

doi:10.1016/j.ejor.2016.05.021

Cited by 76 publications

(38 citation statements)

References 35 publications

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“…Through clustering analysis, the scenarios with similar daily net load shapes will be assigned to the same cluster, then we can intuitively produce a representative scenario set by sampling few scenarios in each cluster. In addition, to ensure the effectiveness of scenario reduction, we carry out the scenario sampling and determine the weight coefficient of each scenario by solving an optimization problem of minimizing the Kantorovich distance between the raw scenario set and the reduced scenario set, a detailed description of which can be found in [24].…”

Section: Scenario Reductionmentioning

confidence: 99%

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Investment optimization of grid-scale energy storage for supporting different wind power utilization levels

Wang

et al. 2019

J. Mod. Power Syst. Clean Energy

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With the large-scale integration of renewable generation, energy storage system (ESS) is increasingly regarded as a promising technology to provide sufficient flexibility for the safe and stable operation of power systems under uncertainty. This paper focuses on grid-scale ESS planning problems in transmission-constrained power systems considering uncertainties of wind power and load. A scenario-based chance-constrained ESS planning approach is proposed to address the joint planning of multiple technologies of ESS. Specifically, the chance constraints on wind curtailment are designed to ensure a certain level of wind power utilization for each wind farm in planning decision-making. Then, an easy-to-implement variant of Benders decomposition (BD) algorithm is developed to solve the resulting mixed integer nonlinear programming problem. Our case studies on an IEEE test system indicate that the proposed approach can co-optimize multiple types of ESSs and provide flexible planning schemes to achieve the economic utilization of wind power. In addition, the proposed BD algorithm can improve the computational efficiency in solving this kind of chance-constrained problems.

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Section: Scenario Reductionmentioning

confidence: 99%

“…It is subject to (2), (3), (21), (23), (24), (43) and (44). Equations (43) and (44) can be solved by using commercial MILP solvers.…”

Section: Investment Master Problemmentioning

confidence: 99%

Investment optimization of grid-scale energy storage for supporting different wind power utilization levels

Wang

et al. 2019

J. Mod. Power Syst. Clean Energy

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“…Then generated scenarios are reduced into an optimal subset that represents well enough the uncertainties using the k-means clustering technique [30]. Finally, the scenarios are combined to construct the whole set of scenarios based on a scenario tree [31]. Each branch in scenario tree corresponds to one scenario in scheduling horizon with a probability calculated as follows: There are several operating constraints for DG units that represent the relationship between active power productions of DGs and upward/downward regulation capacities as follows:…”

Section: B Proposed Solution Methodologymentioning

confidence: 99%

Optimal scheduling of distributed energy resources and responsive loads in islanded microgrids considering voltage and frequency security constraints

Vahedipour‐Dahraie

Najafi

Anvari‐Moghaddam

et al. 2018

Journal of Renewable and Sustainable Energy

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Low inertia of distributed energy resources (DERs), high penetration levels of renewable energy sources (RESs) and load demand variations put the islanded microgrids (MGs) security at risk of instability. This paper proposes a twostage stochastic model for coordination of DERs and responsive loads in islanded MGs with regard to voltage and frequency security constraints. Based on the proposed model, scheduling of the controllable units in both supply and demand sides is done in a way not only to maximize the expected profit of MG operator (MGO), but also to minimize the energy payments of customers under the premise of security and stability of MG. An AC optimal power flow (AC-OPF) procedure is also used to study operating condition of the system under uncertainties and to guarantee acceptable nodal voltages and system frequency during different scenarios. The proposed stochastic optimization model is then applied to a typical autonomous MG and its effectiveness is demonstrated through different scenarios under uncertainties in load consumption and renewable energy resources (RESs) productions. Simulation results demonstrate that customers' participation in DR programs have significant effect on the system's performance in terms of voltage and frequency stability. Moreover, optimal coordination of DERs and responsive loads can increase the expected profit of MGO significantly. The effectiveness of the proposed scheduling approach is verified on an islanded MG test system over a 24-h period.Index Terms-Demand response (DR), microgrid (MG), distributed energy resource (DER), voltage and frequency security, renewable energy sources (RESs). DR t j D BIncome of group j of customer at period t after implementing DR programs. ,t j BIncome of group j of customer at period t when the demand is at nominal value. Energy bid submitted by wind unit w (PV v) in period t (cents/kWh).Bid of the up (down)-spinning reserve submitted by DG i in period t (cents/kWh).Bid of the non-spinning reserve submitted by DG i in period t (cents/kWh).Bid of the up (down)-spinning reserve submitted by load j in period t (cents/kWh).Demand of load j in period t (and scenario s) (kW).Demand of load group j after implementing DR programs in period t (kW).Self-elasticity (Cross-elasticity) of load group j. LFMaximum power flow from node n to r (kW). 2I. Introduction Recently, microgrid (MG) idea has been introduced to transform the conventional power systems to a more reliable, economic and environmentally friendly system. The diversified load consumption pattern and availability of power from green distributed energy resources (DERs) cause supply-demand mismatch in MGs. Optimal operation of MGs both technically and economically mainly relies on the coordination between different components including DERs, energy storage systems (ESSs), and responsive loads [1]- [2]. In grid-connected MGs, normally the economic operation is the main objective as there is a stiff-grid on upstream to support the system frequency and voltage at the point of ...

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“…A multitude of techniques have been proposed in literature [27,28]. In this paper, importance sampling, as presented in [29], in combination with a random walk (see [28]) was applied and will be debated below.…”

Section: Appendix B Scenario Generationmentioning

confidence: 99%

Hydro Power Reservoir Aggregation via Genetic Algorithms

Löschenbrand

Korpås

2017

Energies

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Electrical power systems with a high share of hydro power in their generation portfolio tend to display distinct behavior. Low generation cost and the possibility of peak shaving create a high amount of flexibility. However, stochastic influences such as precipitation and external market effects create uncertainty and thus establish a wide range of potential outcomes. Therefore, optimal generation scheduling is a key factor to successful operation of hydro power dominated systems. This paper aims to bridge the gap between scheduling on large-scale (e.g., national) and small scale (e.g., a single river basin) levels, by applying a multi-objective master/sub-problem framework supported by genetic algorithms. A real-life case study from southern Norway is used to assess the validity of the method and give a proof of concept. The introduced method can be applied to efficiently integrate complex stochastic sub-models into Virtual Power Plants and thus reduce the computational complexity of large-scale models whilst minimizing the loss of information.

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An empirical analysis of scenario generation methods for stochastic optimization

Cited by 76 publications

References 35 publications

Investment optimization of grid-scale energy storage for supporting different wind power utilization levels

Investment optimization of grid-scale energy storage for supporting different wind power utilization levels

Optimal scheduling of distributed energy resources and responsive loads in islanded microgrids considering voltage and frequency security constraints

Hydro Power Reservoir Aggregation via Genetic Algorithms

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