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

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