There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper presents a review of control strategies, stability analysis, and stabilization techniques for dc microgrids (MGs). Overall control is systematically classified into local and coordinated control levels according to respective functionalities in each level. As opposed to local control, which relies only on local measurements, some line of communication between units needs to be made available in order to achieve the coordinated control. Depending on the communication method, three basic coordinated control strategies can be distinguished, i.e., decentralized, centralized, and distributed control. Decentralized control can be regarded as an extension of the local control since it is also based exclusively on local measurements. In contrast, centralized and distributed control strategies rely on digital communication technologies. A number of approaches using these three coordinated control strategies to achieve various control objectives are reviewed in this paper. Moreover, properties of dc MG dynamics and stability are discussed. This paper illustrates that tightly regulated point-of-load converters tend to reduce the stability margins of the system since they introduce negative impedances, which can potentially oscillate with lightly damped power supply input filters. It is also demonstrated that how the stability of the whole system is defined by the relationship of the source and load impedances, referred to as the minor loop gain. Several prominent specifications for the minor loop gain are reviewed. Finally, a number of active stabilization techniques are presented.

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DC Microgrids—Part I: A Review of Control Strategies and Stabilization Techniques

DC microgrids (MGs) have been gaining a continually increasing interest over the past couple of years both in academia and industry. The advantages of dc distribution when compared to its ac counterpart are well known. The most important ones include higher reliability and efficiency, simpler control and natural interface with renewable energy sources, and electronic loads and energy storage systems. With rapid emergence of these components in modern power systems, the importance of dc in today's society is gradually being brought to a whole new level. A broad class of traditional dc distribution applications, such as traction, telecom, vehicular, and distributed power systems can be classified under dc MG framework and ongoing development, and expansion of the field is largely influenced by concepts used over there. This paper aims first to shed light on the practical design aspects of dc MG technology concerning typical power hardware topologies and their suitability for different emerging smart grid applications. Then, an overview of the state of the art in dc MG protection and grounding is provided. Owing to the fact that there is no zero-current crossing, an arc that appears upon breaking dc current cannot be extinguished naturally, making the protection of dc MGs a challenging problem. In relation with this, a comprehensive overview of protection schemes, which discusses both design of practical protective devices and their integration into overall protection systems, is provided. Closely coupled with protection, conflicting grounding objectives, e.g., minimization of stray current and common-mode voltage, are explained and several practical solutions are presented. Also, standardization efforts for dc systems are addressed. Finally, concluding remarks and important future research directions are pointed out.

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DC Microgrids—Part II: A Review of Power Architectures, Applications, and Standardization Issues

Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. This paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

https://ieeexplore.ieee.org/ielaam/5165411/8075182/7990560-aam.pdf

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

In recent researches on inverter-based distributed generators, disadvantages of traditional grid-connected current control, such as no grid-forming ability and lack of inertia, have been pointed out. As a result, novel control methods like droop control and virtual synchronous generator (VSG) have been proposed. In both methods, droop characteristics are used to control active and reactive power, and the only difference between them is that VSG has virtual inertia with the emulation of swing equation, whereas droop control has no inertia. In this paper, dynamic characteristics of both control methods are studied, in both stand-alone mode and synchronous-generator-connected mode, to understand the differences caused by swing equation. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results are verified by simulations and experiments. It is suggested that VSG control and proposed inertial droop control inherits the advantages of droop control, and in addition, provides inertia support for the system.

Comparison of Dynamic Characteristics Between Virtual Synchronous Generator and Droop Control in Inverter-Based Distributed Generators

LCL filters are used in grid-connected voltage source inverters (GC-VSIs) due to their lower cost and higher efficiency. These filters attenuate high order harmonics effectively; however, the grid impedance fluctuations (GIFs) may cause resonance and system instability. The GIF can reduce the resonance frequency to lower than a permissible threshold, then, the resonance may happen and prevent some nonlinear loads from being fed. On the other hand, very high resonance frequencies cause capacitor of the filter being actually short circuited. Consequently, the nature of the filter changes and reduces the power quality of the network. In this paper, considering the possible range for GIFs and using Kharitonov control theorem (KCT), the coefficients of the PI controller and the current feedback of the filter capacitor are obtained simultaneously to ensure safe and desired operation of the GC-VSI against the GIFs. As a result, the proposed closed loop system shows optimal response to variation of the reference current. Genetic algorithm (GA) is used to determine optimal values of the coefficients and the gain. Simulation results carried out in MATLAB/SIMULINK show accuracy and effectiveness of the proposed method.

Optimal Robust Control of LCL-type Grid-Connected Voltage Source Inverters against Grid Impedance Fluctuations

In this article, we propose an optimal decentralized robust $H_\infty $ control system for the voltage control problem of autonomous uncertain dc microgrids consisting of multiple distributed generations (DGs) with general topology. The one-degree-of-freedom (DoF) structure of the developed control system guarantees the robust performance of the system as well as its robust stability against various sources of uncertainty, such as plug-and-play (PnP) operation of the DGs, topology changes, large load perturbations, different subsequent system changes, and the presence of constant power loads (CPLs). To that end, the uncertain dc microgrid is modeled as a Linear Time-Invariant (LTI) polytopic state-space system. Then, a state-feedback control technique based on linear matrix inequality (LMI) with linearly parameter-dependent (LPD) Lyapunov matrices is implemented on the uncertain dc microgrids. The proposed controller does not require any sort of communications, and the robust performance property of the controller eliminates the need for prefilter design. The efficiency of the proposed controller is analyzed by simulating different case studies through SimPowerSystems Toolbox in MATLAB. Finally, the performance of the proposed control method is validated via experimental studies.

Decentralized Voltage Control of Autonomous DC Microgrids With Robust Performance Approach

In DC microgrids, classical generators in traditional power grid are replaced by converter-interfaced distributed generation (DG) or energy storage systems (ESSs) and rotating inertia cannot be directly connected. This causes a reduction of the total inertia of the system. Therefore, the DC microgrid voltage becomes more sensitive under load variations and power fluctuation from the intermittent distributed energy sources. In this paper a virtual-impedance control is designed for DC microgrids, which provides the system with synthetic inertia. In proposed strategy, the rate of change of voltage (RoCoV) can be decreased by virtual-capacitor part, transient and steady-state behavior of the converter under load variations can be defined by varying the virtual-inductance and virtual-resistance, respectively. Stability of the proposed strategy is analyzed by looking at the dominant eigenvalues of the small-signal model. The simulation results indicate that the proposed method with virtual impedance improves the transient response.

Dynamic Performance Improvement of DC Microgrids Using Virtual Impedance

Dynamic modeling, stability analysis and control of interconnected microgrids: A review

Microgrids (MGs) the building blocks of the smart grid are local grids comprise di erent technologies such as power electronics converters, distributed renewable and non-renewable energy sources, energy storage systems, and telecommunications which can operate either in islanded mode or connected to the main grid. Apart from the obvious bene ts of MGs, their introduction into the traditional distribution network raises many new challenges, thus, a hierarchical control concept has been introduced for these systems. While the decentralized primary control of this hierarchy ensures the system stability and adjusts the frequency and voltage according to the active and reactive powers, the secondary control level is often used to regulate the system frequency and voltage to the rated values, eliminating deviations produced by primary level. The tertiary control is in charge of regulating power exchange with external grid or/and with other MGs and includes functions related to e ciency and economic enhancement. This thesis is focused on development of distributed control strategies for secondary control of autonomous ac and dc MGs to avoid a central controller and complex communication network, thus o ering improved reliability and expandability. The special emphasis has been given to consensusbased protocols where the mathematical analysis has been also studied and presented. The proposed methodologies based on this approach are fully distributed meaning that each MG source requires to exchange information with only its direct neighbours through a sparse communication network. Loss of sources and communication links do not a ect system operation as long as the communication graph remains connected. Moreover, they are scalable, for that prior knowledge of the system is not required, as a new component enters the MG. The proposed control frameworks for ac MGs include two modules, namely, voltage regulator, and reactive power regulator. The voltage regulator boosts the voltage across the MG to satisfy the global voltage regulation, while the reactive power regulator handles the proportional reactive power sharing considering transmission line impedances. Moreover, the proposed controllers are able to proportionally share the load power even at the presence of di erent control parameters and initial values. This thesis also proposes a distributed hierarchical control framework for dc MG clusters to ensure smooth connection and reliable operation of these systems. A decentralize adaptive droop method is introduced for primary

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Qobad Shafiee

Papers

Optimal Robust Control of LCL-type Grid-Connected Voltage Source Inverters against Grid Impedance Fluctuations

Decentralized Voltage Control of Autonomous DC Microgrids With Robust Performance Approach

Dynamic Performance Improvement of DC Microgrids Using Virtual Impedance

Dynamic modeling, stability analysis and control of interconnected microgrids: A review

Multi-Functional Distributed Secondary Control for Autonomous Microgrids