Modeling, Operation, and Analysis of DC Grids: From High Power DC Transmission to DC Microgrids

Contents
List of contributors
1 Introduction
	1.1 The battle of the currents
	1.2 DC grids
	1.3 Power electronics
	1.4 High-power applications
	1.5 Low-power applications
	References
2 HVDC transmission for wind energy
	2.1 Wind energy
	2.2 Slow-dynamics model of the wind turbine
	2.3 HVDC transmission for wind farms
	2.4 Stability of HVDC transmission lines
	2.5 Summary
	References
3 DC faults in HVDC
	3.1 Minimum requirements for the protection system of MTDC
	3.2 Impact of DC faults in VSC
	3.3 Analysis of the MTDC-HVDC during DC faults
		3.3.1 Steady state in MTDC
		3.3.2 Fault transient
		3.3.3 Critical interruption time
		3.3.4 Influence of the DC capacitor on the critical interruption time
		3.3.5 Influence of the DC smoothing inductance on the critical interruption time
		3.3.6 Influence of the short circuit ratio of the AC system
		3.3.7 Influence of the fault resistance on the critical interruption time
		3.3.8 Remark of the section
	3.4 Detection and identification strategies in MTDC
		3.4.1 Selectivity problem
		3.4.2 Proposed detection and location methods for MTDC
			3.4.2.1 Overcurrent protection and undervoltage DC voltage level protection
			3.4.2.2 Differential current protection
			3.4.2.3 Traveling waves
			3.4.2.4 Based on rate of change
			3.4.2.5 Other methods
	3.5 Clearance strategies for MTDC
		3.5.1 Protection system with AC breakers
		3.5.2 Protection system with DC breakers
		3.5.3 Protection system embedded on the power converter
	3.6 HVDC circuit breakers
		3.6.1 Mechanical HVDC circuit breakers
		3.6.2 Solid-state HVDC circuit breakers
		3.6.3 Hybrid HVDC circuit breaker
	3.7 Fault current limiters
		3.7.1 Inductors
		3.7.2 Tuned LC circuit
		3.7.3 Polymer PTC resistor-based FCL
		3.7.4 Liquid metal FCL
		3.7.5 Superconductive FCL
	References
4 Eigenvalue-based analysis of small-signal dynamics and stability in DC grids
	4.1 Introduction
	4.2 Introduction to state-space modeling of electrical systems
		4.2.1 Nonlinear time-invariant state-space models
		4.2.2 Time-invariant representation of three-phase electrical systems
		4.2.3 Linearization
		4.2.4 Eigenvalue-based analysis of small-signal dynamics
	4.3 Synthesis of system-level state-space models of HVDC grids
		4.3.1 Definition of interfaces between sub-systems
		4.3.2 Generic definition of subsystem models
			4.3.2.1 Definition of per-unit scaling and requirements for subsystem interconnection
			4.3.2.2 Models of converter terminals
			4.3.2.3 Cable models
			4.3.2.4 Model of DC nodes
		4.3.3 System model synthesis
			4.3.3.1 Organization of system equations and reduction to state-space form
			4.3.3.2 Calculation of steady-state operating point
			4.3.3.3 Linearization and assembly of the small-signal model
			4.3.3.4 Example of system-level small-signal state-space model
	4.4 Examples of sub-system modeling
		4.4.1 AC–DC converter terminals
			4.4.1.1 Example of AC-power controlled HVDC terminal with two-level voltage source converter
			4.4.1.2 Example of modular multilevel converter-based HVDC terminal
		4.4.2 Modeling of long cables for analysis of HVDC grids
	4.5 Practical considerations for modular and automated generation of system-level small-signal state-space models
		4.5.1 Synthesis of state-space matrices for the system
		4.5.2 Calculation of the steady-state operating point
		4.5.3 Applied procedure for generating system-level state-space models in the presented framework for modular subsystem modeling
	4.6 Example of small-signal analysis
		4.6.1 Case description
		4.6.2 Linearized state-space model
		4.6.3 Small-signal stability analysis
		4.6.4 Analysis of participation factors and system interaction
		4.6.5 Analysis of parametric sensitivity
	4.7 Conclusion
	References
5 Inertia emulation with HVDC transmission systems
	5.1 Introduction
	5.2 Basis for a need of virtual inertia with VSC HVDC systems
	5.3 VSC HVDC control approaches for inertia emulation
	5.4 Fast frequency response service by VSC HVDC systems
		5.4.1 Inertia emulation with offshore wind power plants
		5.4.2 Inertia emulation using the capacitor of the HVDC VSC link
		5.4.3 Frequency support through MTDC based in (RCH)
	5.5 Summary
	Acknowledgment
	References
6 Real-time simulation of a transient model for HVDC cables in SOC-FPGA
	6.1 Introduction
		6.1.1 What is a SoC-FPGA?
	6.2 Frequency domain model formulation
	6.3 Cable model with difference equations
	6.4 VHDL conceptual design of the HVDC cable model
		6.4.1 Floating to fixed point conversion and arithmetic
		6.4.2 Blocks architecture of the HVDC cable with VHDL
		6.4.3 Description of the blocks used in the HVDC cable
			6.4.3.1 Delay feedback: delay component
			6.4.3.2 Delay feed-forward: delay_1 component
			6.4.3.3 Inner product: Producto_afloop component
			6.4.3.4 Product vector and scalar: Producto_vecscalar component
			6.4.3.5 Product vector and matrix: producto_vecmatr component
			6.4.3.6 Sum: Suma component
			6.4.3.7 Module ss_siso
	6.5 Integration and development of the HVDC cable in VHDL
		6.5.1 Model for the characteristic admittance
		6.5.2 Model for the propagation function
		6.5.3 Model for the half side cable
		6.5.4 Cable full model
		6.5.5 Communication of the cable with the software
	6.6 Conclusions
	References
7 Probabilistic analysis in DC grids
	7.1 Introduction
	7.2 DC power grid model
	7.3 Probabilistic power flow analysis in DC grids
		7.3.1 Monte Carlo simulation
		7.3.2 Point estimate methods
		7.3.3 Data-driven approaches
	7.4 Bayesian modeling of DC grids
		7.4.1 Bayes theorem and its interpretation
		7.4.2 Likelihood-based Bayesian modeling using Laplace approximation
		7.4.3 Likelihood-free Bayesian modeling
	7.5 Experimental validation
		7.5.1 PPF analysis for DC microgrids
		7.5.2 PPF analysis for an MT-HVDC grid
	7.6 Conclusions
	References
8 Stationary-state analysis of low-voltage DC grids
	8.1 Introduction
	8.2 Modeling the grid
		8.2.1 Exact nonlinear formulation
		8.2.2 Linear successive approximations
			8.2.2.1 Method based on Newton–Raphson formulation
			8.2.2.2 First Taylor-based method: hyperbolic lineatization
			8.2.2.3 Second Taylor-based method: product linearization
		8.2.3 Convex reformulations
			8.2.3.1 Semidefinite programming model
			8.2.3.2 Second-order cone programming model
	8.3 Results
	8.4 Conclusions
	References
9 Stability analysis and hierarchical control of DC power networks
	9.1 Literature review and scope of the chapter
		9.1.1 Introduction
		9.1.2 Contents of the chapter
	9.2 Power system and control system overview
		9.2.1 Microgrid description
		9.2.2 Microgrid control system structure
		9.2.3 Local and primary controllers
		9.2.4 Secondary controller
		9.2.5 Supervisor model predictive controller
	9.3 Small-signal modeling of the DC microgrid
		9.3.1 Model of the grid-connected VSC
		9.3.2 Battery-system VSC
		9.3.3 Railway and auxiliary-network VSCs
		9.3.4 DC-capacitor modeling
		9.3.5 Aggregated model of the DC microgrid
	9.4 Case study and prototype description
	9.5 Validation of the model predictive controller
		9.5.1 Local, primary, and secondary controllers
		9.5.2 Prediction horizon set to Np=24 hours
		9.5.3 Prediction horizon set to Np=6 hours
		9.5.4 Prediction horizon set to Np=3 hours
	9.6 Validation of the small-signal modeling approach
		9.6.1 Stability analysis of the DC microgrid
		9.6.2 Experimental results
	9.7 Conclusion
	References
10 Digital control strategies of DC–DC converters in automotive hybrid powertrains
	10.1 Introduction
	10.2 Analysis of the DC–DC power converters
		10.2.1 Buck converter model
		10.2.2 Boost converter model
	10.3 Digital current control strategies
		10.3.1 Average current control based on passivity
		10.3.2 Discrete-time sliding-mode current control
		10.3.3 Digital proportional-integral current control
		10.3.4 Predictive digital current programmed control
	10.4 Simulation results
		10.4.1 Average current control based on passivity simulation results
		10.4.2 Discrete-time sliding-mode current control simulation results
			10.4.2.1 Double-loop DSMCC results
		10.4.3 Digital proportional-integral current control simulation results
			10.4.3.1 Double-loop PICC results
		10.4.4 Predictive digital current programmed control results
	10.5 Summary
	Acknowledgments
	References
11 Adaptive control for second-order DC–DC converters: PBC approach
	11.1 Introduction
	11.2 DC–DC converter modeling
		11.2.1 Buck converter
		11.2.2 Boost converter
		11.2.3 Buck-boost converter
		11.2.4 Noninverting buck-boost converter
	11.3 Passivity-based control method
		11.3.1 PI-PBC design
	11.4 Control design for DC–DC converters
		11.4.1 Adaptive control using I&I conductance estimator
	11.5 Simulation results
		11.5.1 Test system
		11.5.2 Numerical validation
			11.5.2.1 Buck converter
			11.5.2.2 Boost converter
			11.5.2.3 Buck-boost converter
			11.5.2.4 Noninverting buck-boost converter
	11.6 Conclusions
	Acknowledgments
	References
12 Advances in predictive control of DC microgrids
	12.1 Introduction
	12.2 Predictive control of DC microgrids
		12.2.1 Primary control of DC microgrids
			12.2.1.1 Finite control set model predictive control
			12.2.1.2 Modulated model predictive control
			12.2.1.3 Decentralized model predictive control
			12.2.1.4 Hybrid finite control set model predictive control/deadbeat predictive control
		12.2.2 Secondary control of DC microgrids
			12.2.2.1 Model predictive-based self-adaptive inertia control
			12.2.2.2 Centralized model predictive control
	12.3 Conclusion
	Acknowledgment
	References
13 Modeling and control of DC grids within more-electric aircraft
	13.1 Introduction to more-electric aircraft
	13.2 Modeling of aircraft EPS
		13.2.1 Modeling paradigm
			13.2.1.1 Multilevel modeling paradigm
			13.2.1.2 Studies of functional models
		13.2.2 Modeling of power generation system
			13.2.2.1 Permanent magnet synchronous generators
			13.2.2.2 AC/DC power converters
		13.2.3 Energy storage system
			13.2.3.1 Battery
			13.2.3.2 Bidirectional DC/DC converter
		13.2.4 DC link modeling
		13.2.5 Load modeling
			13.2.5.1 Environmental control system
			13.2.5.2 Flight controls
			13.2.5.3 Fuel pumps
			13.2.5.4 Wing ice protection
			13.2.5.5 General load model
	13.3 Control development
		13.3.1 Single PMSG control
			13.3.1.1 Current control loop
			13.3.1.2 DC link control and flux weakening control
		13.3.2 ESS control
		13.3.3 Power sharing control
			13.3.3.1 Centralized control
			13.3.3.2 Distributed control
			13.3.3.3 Decentralized control
				Voltage-mode approach
				Current-mode approach
	13.4 Summary
	References
Index