Mathematical Modeling, Simulation and Optimization for Power Engineering and Management (Mathematics in Industry, 34)

✍ Scribed by Simone Göttlich (editor), Michael Herty (editor), Anja Milde (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 333
• Category: Library

✦ Synopsis

This edited monograph offers a summary of future mathematical methods supporting the recent energy sector transformation. It collects current contributions on innovative methods and algorithms. Advances in mathematical techniques and scientific computing methods are presented centering around economic aspects, technical realization and large-scale networks.

Over twenty authors focus on the mathematical modeling of such future systems with careful analysis of desired properties and arising scales. Numerical investigations include efficient methods for the simulation of possibly large-scale interconnected energy systems and modern techniques for optimization purposes to guarantee stable and reliable future operations.

The target audience comprises research scientists, researchers in the R&D field, and practitioners. Since the book highlights possible future research directions, graduate students in the field of mathematical modeling or electrical engineeringmay also benefit strongly.

✦ Table of Contents

Preface
About KoMSO e.V.
Contents
Contributors
Part I Economic Aspects
1 Modeling the Intraday Electricity Demand in Germany
1.1 The ENets-Project—Modeling the Microstochastics of Intraday Electricity Demand and Intraday Electricity Prices
1.2 Introduction—Demand and Electricity Prices
1.3 Basics on the Electricity Markets and Models
1.3.1 German Spot Electricity Markets
1.3.2 Structural Models for Electricity Prices
1.3.3 The Jacobi Process as a New Modeling Ingredient
1.4 Data Analysis—Stylized Facts of German Electricity Demand
1.5 Case Study: Modeling the Intraday Electricity Demand
1.6 Challenges and Future Work Packages
References
2 Application of Continuous Stochastic Processes in Energy Market Models
2.1 Introduction
2.2 Application I: Economics Behind Energy Markets
2.2.1 Temperature
2.2.2 Solar Infeed
2.2.3 Wind Infeed
2.2.4 Total Energy Demand
2.2.5 Modelling Routine
2.3 Application II: Risk Management on the Electricity Market
2.3.1 Price Models
2.3.2 Industrial Application
References
3 Probabilistic Analysis of Solar Power Supply Using D-Vine Copulas Based on Meteorological Variables
3.1 Introduction
3.2 Data
3.2.1 Data Description
3.2.2 Empirical Data Analysis
3.3 Methodology
3.3.1 Modeling Approach
3.3.2 D-Vine Copulas
3.3.3 Fitting Procedure
3.4 Results and Discussion
3.4.1 Model Fitting and Validation
3.4.2 Conditional Means of Solar Power Supply
3.4.3 Validation Scores for Conditional Level-Crossing Probabilities
3.5 Conclusion
References
Part II Technical Applications
4 GivEn—Shape Optimization for Gas Turbines in Volatile Energy Networks
4.1 Introduction
4.2 Areas of Mathematical Research and Algorithmic Development
4.2.1 Aerodynamic Shape Optimization
4.2.2 Heat Transfer and the Thermal Loop
4.2.3 Probabilistic Objective Functionals for Material Failure
4.2.4 Shape Optimization for Probabilistic Structure Mechanics
4.2.5 Multiobjective Optimization
4.3 Applications
4.3.1 German Aerospace Center (DLR)
4.3.2 Siemens
References
5 Using the Stein Two-Stage Procedure to Calculate Uncertainty in a System for Determining Gas Qualities
5.1 Introduction
5.2 Monte Carlo Method for Gas Quality Reconstruction
5.2.1 Simple Examples
5.2.2 Example with Reversal of the Flow Direction
5.3 Accuracy and Reliability
5.3.1 Standard Deviation and Uncertainty
5.3.2 Estimated Uncertainty
5.3.3 Number of Monte Carlo Runs
5.3.4 Excess Not Equal to Null
5.4 Stein's Two-Stage Procedure
5.4.1 Determining the Uncertainty (Batch Design)
5.4.2 Dependency on the Batch Size
5.4.3 Comparison with Earlier Estimation
5.4.4 Numerical Tests
5.5 Summary and Outlook
References
6 Energy-Efficient High Temperature Processes via Shape Optimization
6.1 Motivation
6.1.1 Industrial Background
6.1.2 Mathematical Background
6.2 The Multiphysics Problem
6.2.1 Geometric Setup
6.2.2 Energy Equation
6.2.3 Radiative Transfer Equation
6.2.4 The Flow Model
6.2.5 Reaction and Vaporization
6.2.6 Simulation Results
6.3 Shape Optimization
6.3.1 The Radiation Model
6.3.2 The Optimal Design Problem
6.3.3 Basic Concepts in Shape Optimization
6.3.4 Numerical Results
6.4 Conclusions
References
7 Power-to-Chemicals: A Superstructure Problem for Sustainable Syngas Production
7.1 Introduction
7.1.1 Reactor-Separator-Recycle Superstructure
7.1.2 Contribution
7.2 Mathematical Model
7.2.1 Connectivity of Unit Operations
7.2.2 Reactors
7.3 Forward Simulation
7.3.1 Discretization and DAE-System
7.3.2 Simulation Results
7.3.3 Parareal for DAEs
7.3.4 Model Order Reduction
7.4 Outlook and Challenges
References
Part III Energy Networks
8 Optimization and Stabilization of Hierarchical Electrical Networks
8.1 Introduction
8.2 Modeling of the Electrical Power Grid
8.3 Distributed Optimization in Low-Voltage Smart Grids
8.3.1 Modelling Microgrids
8.3.2 Distributed Optimization via ALADIN
8.3.3 Surrogate Models in Optimization of Coupled Microgrids
8.3.4 Outlook
8.4 Safety Sets for Transient Stability in Power Networks
8.4.1 Decomposition of Model for Synchronization Problems
8.4.2 Safety Sets
8.4.3 Future Research: Interaction Between the Distribution and Transmission Levels
8.5 Clustering-Based Model Order Reduction for the Synchronous Machine Model
8.5.1 Structure-Preserving
8.5.2 POD-Based Clustering
8.5.3 Numerical Results
8.5.4 Summary
8.6 Optimal Power Flow for Future Power Networks
8.7 Conclusion
References
9 New Time Step Strategy for Multi-period Optimal Power Flow Problems
9.1 Introduction
9.2 Methodology
9.2.1 Measuring the Change in Residual Load
9.2.2 Different Δt for Different Changes
9.2.3 Segmenting the Optimisation Period
9.2.4 Temporal Resolution Profile
9.2.5 Interpolation Operator
9.2.6 Estimating the Error
9.3 Results
9.4 Conclusion and Outlook
References
10 Reducing Transmission Losses via Reactive Power Control
10.1 Introduction
10.2 Power Flow Equation
10.3 Optimization Problem
10.4 Numerical Simulations
10.4.1 Details on Implementation
10.4.2 Results
10.5 Conclusions and Outlook
References
11 MathEnergy – Mathematical Key Technologies for Evolving Energy Grids
11.1 Overview
11.2 Modeling and Model Order Reduction
11.2.1 Modeling
11.2.2 Model Order Reduction
11.3 State Estimation Using Reduced-Order Models
11.3.1 Problem Setting
11.3.2 State Estimation
11.3.3 Numerical Results and Discussion
11.4 Efficient MSO for Gas Networks with Hydrogen Injection
11.4.1 MYNTS
11.4.2 partDE-Hy Demonstrator
11.4.3 Gas Laws - Comparisons and Results of a First Ensemble Analysis
11.5 Coupled Transient Modeling and Simulation of Power and Gas Networks
11.5.1 Transient Modeling of Gas Networks
11.5.2 Transient Modeling of Power Networks
11.5.3 Model Coupling of Gas and Power Networks
11.5.4 Transient Co-Simulation for Coupled System
11.6 State Estimation of the Power Grid
11.6.1 Observability
11.6.2 Switch Observer for Mode Detection
11.6.3 Example Switch Observer
11.7 Outlook
References
12 Modeling and Simulation of Sector-Coupled Energy Networks: A Gas-Power Benchmark
12.1 Introduction
12.2 Model and Algorithm
12.2.1 Model of the Gas Network
12.2.2 Other Edges
12.2.3 Nodes
12.2.4 Model of the Power Grid
12.2.5 Gas-Power-Conversion
12.3 Network Data
12.3.1 Gas Network
12.3.2 Power Network
12.4 Numerical Results
12.4.1 Comparison of Coupling Conditions
12.4.2 Gas-Power-Conversion
12.5 Conclusion
References
13 Coupling of Two Hyperbolic Systems by Solving Half-Riemann Problems
13.1 Introduction
13.2 Riemann Problems for Coupled Conservation Laws
13.3 Fluid-Structure Coupling: Linear Elastic and Compressible Euler Equations
13.3.1 Modelling of the Fluid-Structure Coupling Problem
13.3.2 Riemann Problem for the Fluid-Structure Coupling
13.3.3 Entropy Solutions of the Riemann Problem for the Fluid-Structure Coupling
13.4 A Numerical Example
13.5 Conclusions
References
14 District Heating Networks – Dynamic Simulation and Optimal Operation
14.1 Introduction
14.2 Model
14.2.1 Water Properties
14.2.2 Non-pipe Devices
14.2.3 Pipes
14.3 Analytic Solutions
14.3.1 Preheating
14.3.2 Flow Reversal
14.4 Simulation
14.4.1 Method of Characteristics
14.4.2 Automatic Differentiation
14.4.3 Initialization
14.5 Optimization
14.6 Results
14.7 Conclusion
References