Source-linked AI summary
Decision making under uncertainty in energy systems: state of the art
Alireza Soroudi, Turaj Amraee
TL;DR
Energy-system decisions rely on uncertain inputs, motivating systematic uncertainty modeling. This paper classifies and reviews uncertainty-handling techniques, compares their applications, and concludes that method choice depends on uncertainty severity and type, while identifying future research directions including Z-numbers.
Problem
Energy-system decision making involves uncertain inputs across operating, planning, and policy horizons, creating a need for systematic uncertainty modeling.
Method
The paper proposes a standard classification and comprehensive review of uncertainty-modeling techniques and their power-system applications.
Results
Each uncertainty-modeling method is suitable for a specific uncertainty type, and uncertainty severity dictates the appropriate technique.
Takeaways & Limitations
The review provides a roadmap for uncertainty modeling in power-system studies and highlights Z-numbers as a future possibility.
Takeaways & Limitations
Some research areas remain untouched.
Abstract
from arXiv · showhide
The energy system studies include a wide range of issues from short term (e.g. real-time, hourly, daily and weekly operating decisions) to long term horizons (e.g. planning or policy making). The decision making chain is fed by input parameters which are usually subject to uncertainties. The art of dealing with uncertainties has been developed in various directions and has recently become a focal point of interest. In this paper, a new standard classification of uncertainty modeling techniques for decision making process is proposed. These methods are introduced and compared along with demonstrating their strengths and weaknesses. The promising lines of future researches are explored in the shadow of a comprehensive overview of the past and present applications. The possibility of using the novel concept of Z-numbers is introduced for the first time.
1. Introduction
Energy-system decisions face substantial uncertainty in technical, operational, and economic parameters. The paper reviews uncertainty-handling tools, classifies them by how input uncertainty is described, and maps applications and future research.
- Energy-sector decision makers must address significant uncertainty across short- and long-term decisions.
- Technical parameters include network topology and operating quantities such as demand and generation.
- Economic uncertainty covers factors including fuel supply, production costs, taxes, labor, regulation, and environmental policies.
- Probabilistic, possibilistic, hybrid, information-gap, robust-optimization, and interval methods describe uncertain inputs in different ways.Examples include known PDFs, membership functions, mixed parameter types, information gaps, uncertainty sets, and known intervals.
- Robust optimization produces decisions optimal for the worst-case realization within a specified uncertainty set.
- The review proposes a standard classification, surveys applications, and identifies less explored research areas.
2. Probabilistic approach
The probabilistic approach models uncertain inputs as random variables with known probability distributions. The section describes simulation, moment-based estimation, and scenario methods for propagating uncertainty to outputs.
- Probabilistic modeling represents inputs as random parameters with known PDFs and seeks the distribution of the output.
- Monte Carlo simulation: Monte Carlo simulation repeatedly samples each input from its PDF, evaluates the model, and analyzes the resulting outputs statistically.Latin Hypercube Sampling is cited as a way to reduce Monte Carlo computational burden.
- Point estimate method: The point estimate method uses moments, concentration points, probabilities, and model evaluations to estimate output statistics.The procedure computes the output mean and standard deviation from estimated moments.
- Scenario-based decision making: Scenario-based decision making defines scenarios as probable realizations of uncertain parameters and may reduce a large original set to a smaller representative set.Reduction trades information loss against lower computational burden.
3. Possibilistic approach
The possibilistic approach represents uncertain inputs with membership functions rather than probability distributions. Alpha-cut analysis propagates these descriptions to output bounds before defuzzification produces a crisp value.
- Possibilistic modeling describes uncertain input parameters using membership functions, whose shapes may depend on expert opinion.
- A central problem is determining the membership function of the output from the membership functions of the inputs.
- Alpha-cut analysis: The α-cut method converts fuzzy sets into crisp sets at specified membership levels to compute output bounds.At each α-cut, upper and lower output bounds are determined.
- Defuzzification: Defuzzification translates a fuzzy number into a crisp value using methods such as centroid or weighted average techniques.
4. Hybrid possibilistic-probabilistic approach
Hybrid possibilistic-probabilistic methods address models containing both possibilistic and probabilistic uncertain parameters. The reviewed procedures combine probability-based scenario generation with fuzzy propagation and defuzzification.
- Hybrid models consider objective functions containing possibilistic parameters X and probabilistic parameters Z.
- Mixed possibilistic–Monte Carlo approach: The mixed possibilistic–Monte Carlo approach samples each probabilistic parameter from its PDF and repeats the process to obtain output statistics.The resulting statistics may include PDFs or expected values for output membership functions.
- Scenario-based hybrid approach: A scenario-based hybrid procedure generates scenarios for Z, reduces them to a small set, calculates the hybrid output, and defuzzifies it.
5. Information Gap Decision Theory
Information Gap Decision Theory (IGDT) addresses severe uncertainty when probability distributions may be unavailable, selecting decisions by maximizing robustness against uncertain inputs.
- IGDT is used to make robust decisions against severe uncertainty in input parameters.
- IGDT defines robustness as immunity of a predefined constraint’s satisfaction under uncertainty.The constraint reflects a decision maker’s requirement, such as an acceptable risk or minimum revenue.
- IGDT formulates constraint satisfaction using equality and inequality constraints over input parameters and decision variables.Here, x is the input parameter, d̄ is the decision-variable vector, and H and G denote equality and inequality constraints.
- Uncertainty is represented by an envelope-bound set containing values whose deviation from the forecast does not exceed α times the forecast.α denotes the uncertainty level, while the decision maker does not know the values of x and α.
- Robustness is the maximum uncertainty level α for which the required constraints are always satisfied.
- The decision policy chooses decision variables that maximize robustness rather than only optimizing the objective function.
6. Robust optimization
Robust optimization handles uncertain parameters without requiring a specified probability distribution by optimizing over an uncertainty set and solving a robust counterpart.
- The robust optimization concept was first introduced by Soyster.
- Robust optimization addresses optimization problems affected by uncertainty, especially when full information about uncertainty is unavailable.
- For z = f(x, y), x is uncertain while y is known, with z linear in x and nonlinear in y.
- The method assumes uncertain parameters lack a specified probability distribution and models them with an uncertainty set U(x).
- The uncertainty set U(x) contains the values that the uncertain parameter x can take.
- The robust solution seeks to maximize z while maintaining optimality with high probability despite prediction errors in x.
- A robust counterpart is constructed and solved, with the formulation involving two nested optimization problems and a dual form for linear subproblems.
7. Interval analysis
Interval analysis represents each uncertain input by bounded intervals and computes lower and upper bounds for the objective function.
- Each uncertain input parameter is assigned a range of values represented by an interval.
- For f = f(x1, ..., xn), each parameter satisfies lbi ≤ xi ≤ ubi, where lbi and ubi are its lower and upper bounds.
- The goal is to find the lower and upper bounds of the objective function f.
- Software has been developed to solve interval-analysis-based problems.
8. Applications
The reviewed uncertainty-modeling techniques are applied across diverse energy-system domains, including network operation, generation planning, markets, renewable energy, and reliability.
- The context demonstrates applications of the uncertainty analyses described in the paper.
- Applications are categorized into several fields, with uncertainty-modeling attributes summarized in separate tables.
- Other application areas include plug-in hybrid electric vehicles, available transfer capability, renewable-energy operation and planning, and load-flow or optimal-power-flow calculations.
- Reliability evaluation and distribution-network operation and planning include network reconfiguration, phase balancing, and cost-benefit analysis.
- Transmission and generation applications include planning, operation, control, self-scheduling, fault location, dispatch, maintenance, voltage control, and stability.
- Electricity-market applications include real-time demand-side management, bidding, energy-hub management, and electricity procurement.
9. Promising lines of future researches
Future research should improve uncertainty modeling for increasingly complex energy-system inputs, reduce computational burden, select techniques appropriately, and explore hybrid or heuristic approaches.
- Future research directions: Future work should address uncertainties arising from financial, societal, environmental, and technical factors in evolving energy systems.Examples include policy incentives, carbon emissions, smart-grid information architecture, demand response, and market conditions.
- Future research directions: Reducing computational burden is identified as important for large-scale power systems and real-time applications.
- Future research directions: Future studies should focus on choosing uncertainty-handling techniques appropriate to the uncertain environment.
- Future research directions: Hybridizing existing techniques and using heuristic methods are proposed to improve uncertainty description and soften computation procedures.
- Exploring new methods: Z-numbers are presented as a new uncertainty-handling direction that represents both a restriction and its certainty degree.A Z-number is expressed as Z = (A, B), where A describes behavior and B describes certainty.
- Exploring new methods: For load modeling, a Z-number can represent a possibility distribution over probability distributions, with G(Prob) indicating membership in the low-load set.The example uses L = (A1, B2), where A1 denotes low demand and B2 its certainty level.
10. Conclusion
The paper classifies and compares uncertainty-handling methods, introduces Z-numbers for load-value modeling, and concludes that method choice should match the uncertainty being modeled.
- Contribution: The paper proposes a standard classification of uncertainty-handling methods and identifies promising future research directions.
- Novelty: Z-numbers are introduced for uncertainty modeling of load values for the first time.
- Methods reviewed: The assessed methodologies include probabilistic, possibilistic, hybrid, robust-optimization, interval-based, and Z-number approaches.
- Comparison: The methods are compared, and their strengths and shortcomings are investigated.
- Conclusion: Each uncertainty-handling method is suitable for a specific type of uncertainty.
- Conclusion: The severity of uncertainty dictates the choice of an appropriate uncertainty-modeling technique.
- Scope boundary: Some research areas remain untouched.