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A survey on modeling of microgrids - from fundamental physics to phasors and voltage sources
Johannes Schiffer, Daniele Zonetti, Romeo Ortega, Aleksandar Stankovic, Tevfik Sezi, Joerg Raisch
TL;DR
The survey addresses the limited explanation of how commonly used reduced microgrid models arise from detailed physical models. It reviews inverter-based microgrids, derives detailed three-phase component models, and shows how time-scale separation and stated assumptions produce reduced models useful for control design and analysis.
Problem
Reduced-order microgrid models are widely used but are often presented without detailed reduction procedures, limiting understanding of the physical phenomena behind them.
Method
The survey reviews power-system concepts, microgrid components, inverter functionality and controls, then derives detailed three-phase inverter-based microgrid models and reduces them using time-scale separation.
Results
The paper shows how detailed physical models can yield commonly used reduced models with controllable voltage-source inverters and static network and load representations under explicit assumptions.
Takeaways & Limitations
The reduced model is a valid approximation for standard applications and can support microgrid control design and system analysis when its assumptions are pertinent.
Takeaways & Limitations
Model selection cannot be established generally; users must assess whether a model's assumptions are pertinent to the intended control design and analysis.
Abstract
from arXiv · showhide
Microgrids have been identified as key components of modern electrical systems to facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure---hampering the understanding of the physical phenomena behind them. Preceded by an introduction to basic notions and definitions in power systems, the present survey reviews key characteristics and main components of a microgrid. We introduce the reader to the basic functionality of DC/AC inverters, as well as to standard operating modes and control schemes of inverter-interfaced power sources in microgrid applications. Based on this exposition and starting from fundamental physics, we present detailed dynamical models of the main microgrid components. Furthermore, we clearly state the underlying assumptions which lead to the standard reduced model with inverters represented by controllable voltage sources, as well as static network and load representations, hence, providing a complete modular model derivation of a three-phase inverter-based microgrid.
1. Introduction
The survey addresses the need for physically grounded microgrid models whose reduction assumptions are explicit, supporting analysis and control design. It reviews microgrid components and inverter operation, then derives a three-phase inverter-based model from detailed dynamics to standard reduced representations.
- 1. Introduction: Microgrids support renewable distributed generation, but their advanced model-based analysis and control create challenging control problems.Renewable generation is commonly connected at LV and MV levels through inverters.
- 1. Introduction: Existing microgrid models are often reduced or linearized without explaining the reduction procedure, limiting understanding of the underlying physical phenomena.Prior work either models individual inverter-interfaced units without explicit network interactions or models network interactions through linearization.
- 1. Introduction: The survey derives detailed three-phase inverter-based microgrid models from fundamental physics and reviews components, inverter functionality, operating modes, and control schemes.Its focus is purely inverter-based networks, while the modeling and reduction techniques can also apply to bulk or mixed-generation systems.
- 1. Introduction: Time-scale separation, dq-transformation, and singular perturbation yield the usual reduced model with controllable AC voltage sources and power-flow equations.The reduction combines dynamic line models with suitable coordinate transformations and recovers the reduced-order model widely used in the literature.
- 1. Introduction: The survey emphasizes that model suitability cannot be established universally and must be decided according to the control-design or analysis application.Users should assess the pertinence and implications of the assumptions embedded in any model-based analysis.
2. Preliminaries and basic definitions
This section introduces three-phase AC signals, symmetry and common system configurations, then presents dq0 coordinates and instantaneous power definitions for power-system analysis.
- Three-phase signals: A three-phase AC signal consists of three AC signals, while a symmetric signal is fully described by its amplitude and phase angle.An asymmetric signal is defined as one that is not symmetric.
- Symmetry: Symmetric operating conditions require both symmetric configuration and symmetric feeding; “balanced” and “unbalanced” are common synonyms for symmetric and asymmetric.The paper illustrates symmetric signals with constant and time-varying amplitudes.
- System configurations: Three-phase systems use either Y- or ∆-configuration, with Y-systems sometimes adding a grounded neutral conductor for transient overvoltages and asymmetric currents.The paper notes that most three-phase power systems are four-wire Y-connected systems with grounded neutral conductors.
- dq0-transformation: The dq0-transformation maps three-phase signals into rotating coordinates and can convert periodic orbits into constant equilibria through an appropriate angle choice.This simplifies power-system control design and analysis and supports the model reduction developed later.
- Instantaneous power: Under symmetric conditions, the paper defines instantaneous active, reactive and apparent power in dq-coordinates; with constant amplitudes and equal frequencies, P, Q and S are constant.The apparent power is defined as S(t) := P(t) + jQ(t), while active power uses Vd(t)Id(t) + Vq(t)Iq(t).
3. The microgrid concept
An AC microgrid is a locally controllable distribution-level network combining generation, loads and storage, with autonomous operation possible for some period and connection through a PCC.
- Definition: An AC microgrid is a connected LV or MV distribution subset with a single connection to the remaining power system, called the PCC.Its definition also includes generation, loads and energy storage elements.
- Main components: Microgrids combine generation units, loads and storage, with enough generation and storage capacity to supply most loads autonomously during at least some period.Typical generation includes photovoltaic, wind, fuel-cell, microturbine and synchronous-generator-based units.
- Loads: Load priorities such as critical and non-critical categories enable load shedding as an operating option in islanded mode.Residential, commercial and industrial loads are identified as typical microgrid loads.
- Storage: Storage elements help balance fluctuations from intermittent renewable sources and contribute to network control; examples include batteries, flywheels and supercapacitors.The combination of renewable distributed generation and storage is an assumption for the inverter models derived in the paper.
- Inverter interfacing: DC sources and variable- or high-speed-frequency units require AC or DC/AC inverters to connect to an AC network.The paper therefore uses “inverters” as a general label for these devices.
- Operating modes: Microgrids can operate in grid-connected or islanded mode, whereas true island power systems cannot be frequently connected to and disconnected from a larger network.Island power systems are nevertheless sometimes called microgrids because they face similar renewable-integration challenges.
4. Modeling of inverter-based microgrids
This section develops a modular modeling framework for inverter-based microgrids, beginning with inverter functionality and operation modes before combining component models into an overall representation.
- Microgrid components: AC microgrids rely on inverter-interfaced units for fundamental frequency and voltage control because most renewable generation and storage units connect through inverters.This motivates model-based analysis of inverter behavior within the network.
- Network representation: The modeling framework partitions inverter nodes into grid-forming and grid-feeding subsets and represents the network as a graph whose nodes are voltage buses and edges are dynamic power lines.The incidence matrix fully describes network topology, after which inverter, load, line, and transformer models are combined.
- Inverter functionality: DC/AC inverters use semiconductor switching to produce AC, while an LC filter attenuates harmonics and yields an approximately sinusoidal output voltage.The unfiltered power-electronics output is not sinusoidal; filtering reduces its harmonic content.
- Inverter operation modes: Grid-forming inverters regulate a designer-specified output voltage through cascaded current and voltage control, whereas grid-feeding inverters deliver prescribed active and reactive power.Grid-feeding operation is also called grid-following or PQ control; grid-forming operation is also called VSI control.
- Inverter control: Both inverter modes commonly use inner current control to reject high-frequency disturbances, enhance output-filter damping, and provide harmonic compensation.Grid-forming inverters may omit the inner current loop, although it is often retained to improve control performance.
- Overall model: The paper derives a suitable generic dynamical model for grid-forming inverters and combines component equations into differential equations for the overall inverter-based microgrid.The derivation is intended for control design and stability analysis and uses assumptions including fast-reacting storage for fluctuating renewable sources.
5. To phasors and voltage sources via time-scale separation
The survey derives the standard reduced microgrid model by applying time-scale and coordinate reductions to detailed inverter, load, and network dynamics. The resulting formulation represents grid-forming inverters as controllable voltage sources and expresses network interactions in phasor-like coordinates.
- Static loads and sources: Assumption 5.2 neglects load and grid-feeding-unit dynamics, allowing loads and injections to be represented algebraically, including constant-impedance, constant-current, constant-power, or ZIP models.Under this assumption, the load state satisfies ẋℓ,k(t) = 0.
- Voltage-source inverter model: Assumption 5.1 treats inner current and voltage controllers as tracking references instantaneously and exactly, reducing each grid-forming inverter to an AC voltage-source model.The reported controller bandwidths are 400–600 Hz for inner controls and 2–10 Hz for the next control level.
- Voltage-source inverter model: The inverter output is parameterized by controllable voltage amplitude and frequency, with active and reactive power commonly measured and low-pass filtered for feedback.The filter time constant limits the overall control bandwidth when filtered power signals are used in the controls.
- Static network representation: Assumption 5.3 makes the electrical network static because line dynamics are faster than generation-source dynamics, yielding algebraic current–voltage relations.The line reactances are evaluated at the constant synchronous frequency ωs, typically in 2π rad/s.
- Coordinate transformation and phasors: A dq-coordinate transformation and complex-plane representation reconcile inverter variables in abc coordinates with network variables in common dq coordinates.Local dq voltages are related to common-frame quantities through a rotation, such as ˆVqd,i = e^jδiVqd,i.
- Final reduced model: The reformulated equations complete the standard overall microgrid model, combining inverter dynamics, algebraic network relations, and node power-balance equations.The survey notes that this model is widely used in microgrid analysis and control, sometimes with additional assumptions such as constant voltage amplitudes or small phase-angle differences.
6. Conclusions and topics of future research
The survey concludes that its reduction procedure provides a useful approximation for inverter-based microgrid analysis while requiring careful attention to neglected phenomena and numerical simulation choices. It identifies asymmetric operation and detailed load modeling as important directions for future work.
- 6.1. Summary: The derived reduced model is a valid approximation when its reduction assumptions are satisfied and can support microgrid control design and system analysis.The same reduction techniques can also be applied to standard bulk power-system models.
- 6.1. Summary: The model neglects asymmetric operation, DC-side dynamics of distributed-generation units, and line capacitances, which must be considered when interpreting analysis results.These omissions define important boundaries on the model’s applicability.
- 6.1. Summary: The detailed model is stiff because it contains dynamics on widely separated time scales, whereas the reduced model eliminates fast dynamics and permits simpler integration methods.Standard integration methods can become numerically unstable on the detailed model unless extremely small step sizes are used.
- 6.2. Future research: Reliable, safe, and efficient microgrid operation remains an open research area spanning theoretical and application-oriented control problems.The survey highlights frequency and voltage stability, secondary control, and optimal dispatch among relevant objectives.
- 6.2. Future research: Future modeling work should assess dynamic phasors and symmetric components for asymmetric microgrid operation while preserving analytical tractability.More detailed but generically valid load models are another open challenge because microgrids contain many different load types.