This paper investigates the performance of a microgrid with droop-controlled inverters in terms of the total power losses incurred in maintaining synchrony under persistent small disturbances. The inverters are modeled with variable frequencies and voltages under droop control. For small fluctuations from a steady state, these transient power losses can be quantified by an input-output H2 norm of a linear system subject to distributed disturbances. We evaluate this H2 norm under the assumption of a dominantly inductive network with identical inverters. The results indicate that while phase synchronization, in accordance with previous findings, produces losses that scale with a network's size but only weakly depend on its connectivity, the losses associated with the voltage control will be larger in a highly connected network than in a loosely connected one. The typically higher rate of convergence in a highly interconnected network thus comes at a cost of higher losses associated with the power flows used to reach the steady state.
Distributed cooperative droop control consisting of the primary decentralized droop control and the {secondary} distributed correction control is studied in this paper, which aims to achieve an exact current sharing between generators, worked in the voltage control mode, of DC microgrids. For the DC microgrids with the distributed cooperative droop control, the dynamic stability has not been well investigated although its steady performance has been widely reported. This paper focuses on the stability problem and shows it is equivalent to the semistability problem of a class of second-order ma…
There are tradeoffs between current sharing among distributed resources and DC bus voltage stability when conventional droop control is used in DC microgrids. As current sharing approaches the setpoint, bus voltage deviation increases. Previous studies have suggested using secondary control utilizing linear controllers to overcome drawbacks of droop control. However, linear control design depends on an accurate model of the system. The derivation of such a model is challenging because the noise and disturbances caused by the coupling between sources, loads, and switches in microgrids are under…
This paper investigates transient performance of inverter-based microgrids in terms of the resistive power losses incurred in regulating frequency under persistent stochastic disturbances. We model the inverters as second-order oscillators and compare two algorithms for frequency regulation: the standard frequency droop controller and a distributed proportional-integral (PI) controller. The transient power losses can be quantified using an input-output H2 norm. We show that the distributed PI-controller, which has previously been proposed for secondary frequency control (the elimination of sta…
We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic …
We consider the problem of computing equilibria (steady-states) for droop-controlled, islanded, AC microgrids that are both economic-optimal and dynamically stable. This work is motivated by the observation that classical optimal power flow (OPF) formulations used for economic optimization might provide equilibria that are not reachable by low-level controllers (i.e., closed-loop unstable). This arises because OPF problems only enforce steady-state conditions and do not capture the dynamics. We explain this behavior by using a port-Hamiltonian microgrid representation. To overcome the limitati…
Modeled after the hierarchical control architecture of power transmission systems, a layering of primary, secondary, and tertiary control has become the standard operation paradigm for islanded microgrids. Despite this superficial similarity, the control objectives in microgrids across these three layers are varied and ambitious, and they must be achieved while allowing for robust plug-and-play operation and maximal flexibility, without hierarchical decision making and time-scale separations. In this work, we explore control strategies for these three layers and illuminate some possibly-unexpe…
In this paper, we propose a minimax model predictive control (MPC)-based energy management system that is robust with respect to uncertainties in renewable infeed and load. The MPC formulation includes a model of low-level droop control with saturation at the power and energy limits of the units. Robust MPC-based energy management systems tend to under-utilize the renewable energy sources to guarantee safe operation. In order to mitigate this effect, we further consider droop control of renewable energy sources. For a microgrid with droop-controlled units, we show that enhancing droop feedback…
The voltage received by each customer connected to a power distribution line with local controllers (inverters) is regulated to be within a desired margin through a class of slope-restricted controllers, known conventionally as \emph{droop} controllers. We adapt the design of the droop controllers according to the known bounds of the net power consumption of each customer in each observation time window. A sufficient condition for voltage regulation is provided for each time window, which guides the design of the droop controllers, depending on the properties of the distribution line (line imp…
The power flow is a non-linear problem that requires a Newton's method to be solved in dc microgrids with constant power terminals. This paper presents sufficient conditions for the quadratic convergence of the Newton's method in this type of grids. The classic Newton method as well as an approximated Newton Method are analyzed in both master-slave and island operation with droop controls. Requirements for the convergence as well as for the existence and uniqueness of the solution starting from voltages close to 1pu are presented. Computational results complement this theoretical analysis.
This paper examines distribution systems with a high integration of distributed energy resources (DERs) and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies where the active and reactive output-powers of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximations of the AC power-flow equations and is network-cognizant; that is, the coefficients of…
As a new type of microgrid structure, AC-DC hybrid microgrid can efficiently consume new energy distributed generator based on photovoltaics, which is very suitable for microgrid systems with electric vehicles as the main load. Unlike the AC microgrid, the DC bus of the AC-DC hybrid microgrid is a low-inertia system. How to improve the DC bus inertia of the AC-DC hybrid microgrid system and the stability of the DC bus voltage become particularly important. Based on this, this paper presents a method for flexible control strategy of microgrid bus voltage based on multi-node droop. By considerin…
In this work we present new distributed controllers for secondary frequency and voltage control in islanded microgrids. Inspired by techniques from cooperative control, the proposed controllers use localized information and nearest-neighbor communication to collectively perform secondary control actions. The frequency controller rapidly regulates the microgrid frequency to its nominal value while maintaining active power sharing among the distributed generators. Tuning of the voltage controller provides a simple and intuitive trade-off between the conflicting goals of voltage regulation and re…
This paper proposes a novel model-free secondary voltage control (SVC) for microgrids using nonlinear multiple models adaptive control. The proposed method is comprised of two components. Firstly, a linear robust adaptive controller is designed to guarantee the voltage stability in the bounded-input-bounded-output (BIBO) manner, which is more consistent with the operation requirements of microgrids. Secondly, a nonlinear adaptive controller is developed to improve the voltage tracking performance with the help of artificial neural networks (ANNs). A switching mechanism is proposed to coordinat…
This paper presents a new distributed control framework to coordinate inverter-interfaced distributed energy resources (DERs) in island microgrids. We show that under bounded load uncertainties, the proposed control method can steer the microgrid to a desired steady state with synchronized inverter frequency across the network and proportional sharing of both active and reactive powers among the inverters. We also show that such convergence can be achieved while respecting constraints on voltage magnitude and branch angle differences. The controller is robust under various contingency scenario…
The ever increasing penetration of Renewable Energy Resources (RESs) in power distribution networks has brought, among others, the challenge of maintaining the grid voltages within the secure region. Employing droop voltage regulators on the RES inverters is an efficient and low cost solution to reach this objective. However, fixing droop parameters or optimizing them only for overvoltage conditions does not provide the required robustness and optimality under changing operating conditions. In this paper, a convex optimization approach is proposed for reconfiguring PV and QV droop regulators d…
In this paper, we compare the transient performance of a multi-terminal high-voltage DC (MTDC) grid equipped with a slack bus for voltage control to that of two distributed control schemes: a standard droop controller and a distributed averaging proportional-integral (DAPI) controller. We evaluate performance in terms of an H2 metric that quantifies expected deviations from nominal voltages, and show that the transient performance of a droop or DAPI controlled MTDC grid is always superior to that of an MTDC grid with a slack bus. In particular, by studying systems built up over lattice network…
Inverter-based microgrids are an important technology for sustainable electrical power systems and typically use droop-controlled grid-forming inverters to interface distributed energy resources to the network and control the voltage and frequency. Ensuring stability of such microgrids is a key issue, which requires the use of appropriate models for analysis and control system design. Full-order detailed models can be more difficult to analyze and increase computational complexity, hence a number of reduced-order models have been proposed in the literature which present various trade-offs betw…
In the field of microgrids with a significant integration of Renewable Energy Sources, the efficient and practical power storage systems requirement is causing DC microgrids to gain increasing attention. However, uncertainties in power generation and load consumption along with the fluctuations of electricity prices require the design of a reliable control architecture and a robust energy management system for enhancing the power quality and its sustainability, while minimizing the associated costs. This paper presents a mixed approach illustrating both simulation and experimental results of a…
Distributed secondary control plays an important role in DC microgrids, since it ensures system control objectives, which are power sharing and DC bus voltage stability. Previous studies have suggested using a control architecture that utilizes a parallel secondary bus voltage and current sharing compensation. However, the parallel controllers have a mutual impact on each other, which degrades the transient performance of the system. This paper reports on an alternative distributed secondary control architecture and controller design process, based on small signal analysis to alleviate the mut…
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. When connecting multiple HVDC lines into a multi-terminal HVDC (MTDC) system, several challenges arise. To ensure safe and efficient operation of MTDC systems, the voltage of all terminals need to be steered to within an operational range. In this paper we study the commonly used decentralized voltage droop controller, and show that it in general does not steer the voltages to within the operational range. We propose a decentralized PI controll…
Microgrids could be the answer to integrating distributed energy resources into our power grid. It promises improved resilience, reliability, efficiency, and decarbonizing of our electric grid. This paper models a low voltage direct current microgrid using a DAE formulation on a complex network. We then offer a novel method to compute a stability metric using the logarithmic norm which can be used to isolate disturbed nodes.
Microgrids consisting of multiple distributed energy resources (DERs) provide a promising solution to integrate renewable energies, e.g., solar photovoltaic (PV) systems. Hybrid AC/DC microgrids leverage the merits of both AC and DC power systems. In this paper, a control strategy for islanded multi-bus hybrid microgrids is proposed based on the Finite-Control-Set Model Predictive Control (FCS-MPC) technologies. The control loops are expedited by predicting the future states and determining the optimal control action before switching signals are sent. The proposed algorithm eliminates the need…
This paper presents a two-layer, four-level distributed control method for networked microgrid (NMG) systems, taking into account the proprietary nature of microgrid (MG) owners. The proposed control architecture consists of a MG-control layer and a NMG-control layer. In the MG layer, the primary and distrib-uted secondary control realize accurate power sharing among distributed generators (DGs) and the frequency/voltage reference following within each MG. In the NMG layer, the tertiary control enables regulation of the power flowing through the point of common coupling (PCC) of each MG in a d…
With the gradual transformation of power generation towards renewables, distributed energy resources are becoming more and more relevant for grid stabilization. In order to involve all participants in the joint solution of this challenging task, we propose a distributed, model-based and unifying controller for frequency and voltage regulation in AC microgrids, based on steady-state optimal control. It not only unifies frequency and voltage control, but also incorporates the classic hierarchy of primary, secondary and tertiary control layers with each closed-loop equilibrium being a minimizer o…
Inverter-interfaced microgrids differ from the traditional power systems due to their lack of inertia. Vanishing timescale separation between voltage and frequency dynamics makes it critical that faster-timescale stabilizing control laws also guarantee by-construction the satisfaction of voltage limits during transients. In this article, we apply a barrier functions method to compute distributed active and reactive power setpoint control laws that certify satisfaction of voltage limits during transients. Using sum-of-squares optimization tools, we propose an algorithmic construction of these c…
Microgrids are increasingly recognized as a key technology for the integration of distributed energy resources into the power network, allowing local clusters of load and distributed energy resources to operate autonomously. However, microgrid operation brings new challenges, especially in islanded operation as frequency and voltage control are no longer provided by large rotating machines. Instead, the power converters in the microgrid must coordinate to regulate the frequency and voltage and ensure stability. We consider the problem of designing controllers to achieve these objectives. Using…
Autonomous droop control PV inverters have improved voltage regulation compared to the inverters without grid support functions, but more flexible control techniques will be required as the number of solar photovoltaic (PV) installations increases. This paper studies three inverter future deployment scenarios with droop control inverters, non-exporting inverters, and coordinated inverter control (CIC). The network operation and the interaction between various inverter control methods are studied by simulating inverter operation on two low-voltage networks. Considering 30% PV penetration as the…
Considering the structure of dc Microgrids (MGs) composed of grid-forming/feeding converters, a hierarchical Plug-and-Play (PnP) voltage/current control architecture for MG clusters is proposed. In the primary level, a PnP voltage/current controller is proposed to achieve simultaneous voltage support and current feeding function according to local references. In addition, stabilizing controller is characterized by explicit inequalities which are only related to local parameters of a MG. In the secondary level, for the system with interconnection of MGs, a leader-based voltage/current distribut…
In the last decade, the integration of Renewable Energy Sources (RES) in distribution networks has been constantly increasing due to their many technical, economical, and environmental benefits. However, the large-scale penetration of RESs is limited by the grid security constraints, e.g., voltage and current limits. The control of inverter-interfaced RESs can guarantee to comply with those constraints while preserving the RESs performance. However, the installation of additional controllable converter units introduces supplementary investment costs and has therefore to be limited. In this pap…
A survey on modeling of microgrids - from fundamental physics to phasors and voltage sources
University of Leeds（利兹大学）；Tufts University（塔夫茨大学）；Siemens AG（西门子股份公司）；Technische Universität Berlin（柏林工业大学）；Max-Planck-Institut für Dynamik komplexer technischer Systeme（马克斯·普朗克复杂技术系统动力学研究所）
Grid-forming inverter-based autonomous microgrids present new operational challenges as the stabilizing rotational inertia of synchronous machines is absent. The design of efficient control policies for grid-forming inverters is, however, a non-trivial problem where multiple performance objectives need to be satisfied, including voltage/frequency regulation, current limiting capabilities, as well as active power sharing and a scalable operation. We propose in this paper a novel control architecture for frequency and voltage control which allows current limitation via an inner loop, active powe…
This article proposes a distributed secondary control scheme that drives a dc microgrid to an equilibrium point where the generators share optimal currents, and their voltages have a weighted average of nominal value. The scheme does not rely on the electric system topology nor its specifications; it guarantees plug-and-play design and functionality of the generators. First, the incremental model of the microgrid system with constant impedance, current, and power devices is shown to admit a port-Hamiltonian (pH) representation, and its passive output is determined. The economic dispatch proble…
