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

The analysis of the small-signal stability of conventional power systems is well established, but for inverter based microgrids there is a need to establish how circuit and control features give rise to particular oscillatory modes and which of these have poor damping. This paper develops the modeling and analysis of autonomous operation of inverter-based microgrids. Each sub-module is modeled in state-space form and all are combined together on a common reference frame. The model captures the detail of the control loops of the inverter but not the switching action. Some inverter modes are found at relatively high frequency and so a full dynamic model of the network (rather than an algebraic impedance model) is used. The complete model is linearized around an operating point and the resulting system matrix is used to derive the eigenvalues. The eigenvalues (termed "modes") indicate the frequency and damping of oscillatory components in the transient response. A sensitivity analysis is also presented which helps identifying the origin of each of the modes and identify possible feedback signals for design of controllers to improve the system stability. With experience it is possible to simplify the model (reduce the order) if particular modes are not of interest as is the case with synchronous machine models. Experimental results from a microgrid of three 10-kW inverters are used to verify the results obtained from the model

Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid

The increasing interest in integrating intermittent renewable energy sources into microgrids presents major challenges from the viewpoints of reliable operation and control. In this paper, the major issues and challenges in microgrid control are discussed, and a review of state-of-the-art control strategies and trends is presented; a general overview of the main control principles (e.g., droop control, model predictive control, multi-agent systems) is also included. The paper classifies microgrid control strategies into three levels: primary, secondary, and tertiary, where primary and secondary levels are associated with the operation of the microgrid itself, and tertiary level pertains to the coordinated operation of the microgrid and the host grid. Each control level is discussed in detail in view of the relevant existing technical literature.

Trends in Microgrid Control

This paper presents a review of advanced control techniques for microgrids. This paper covers decentralized, distributed, and hierarchical control of grid-connected and islanded microgrids. At first, decentralized control techniques for microgrids are reviewed. Then, the recent developments in the stability analysis of decentralized controlled microgrids are discussed. Finally, hierarchical control for microgrids that mimic the behavior of the mains grid is reviewed.

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Advanced Control Architectures for Intelligent Microgrids—Part I: Decentralized and Hierarchical Control

Advanced control strategies are vital components for realization of microgrids. This paper reviews the status of hierarchical control strategies applied to microgrids and discusses the future trends. This hierarchical control structure consists of primary, secondary, and tertiary levels, and is a versatile tool in managing stationary and dynamic performance of microgrids while incorporating economical aspects. Various control approaches are compared and their respective advantages are highlighted. In addition, the coordination among different control hierarchies is discussed.

Hierarchical Structure of Microgrids Control System

This work is concerned with the control strategy for the parallel operation of distributed generation systems (DGS) in a standalone ac power supply. The proposed control method uses only low-bandwidth data communication signals between each generation system in addition to the locally measurable feedback signals. This is achieved by combining two control methods: droop control method and average power control method. The average power method with slow update rate is used in order to overcome the sensitivity about voltage and current measurement errors. In addition, a harmonic droop scheme for sharing harmonic content of the load currents is proposed based on the voltages and currents control algorithm. Experimental and simulation studies using two parallel three-phase pulsewidth modulation (PWM) inverters are presented to show the effectiveness of the proposed control.

Control of distributed generation systems - Part II: Load sharing control

This paper presents a photovoltaic (PV) model estimation method from the PV module data. The model is based on a single-diode model of a PV cell. The cell model of a module is extended to estimate the parameters of arrays. The variation of the parameters with change in temperature and irradiance is also studied. Finally, estimation of the maximum power point from the estimated parameters under varying environmental conditions is presented.

Identification of Photovoltaic Source Models

This paper discusses a digital control strategy for three-phase pulse-width modulation voltage inverters used in a single stand-alone ac distributed generation system. The proposed control strategy utilizes the perfect robust servomechanism problem control theory to allow elimination of specified unwanted voltage harmonics from the output voltages under severe nonlinear load and to achieve fast recovery performance on load transient. This technique is combined with a discrete sliding mode current controller that provides fast current limiting capability necessary under overload or short circuit conditions. The proposed control strategy has been implemented on a digital signal processor system and experimentally tested on an 80-kVA prototype unit. The results showed the effectiveness of the proposed control algorithm.

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Control of distributed generation systems-Part I: Voltages and currents control

This paper presents an analytical method of modeling permanent magnet (PM) motors. The model is dependent only on geometrical and materials data which makes it suitable for insertion into design programs, avoiding long finite element analysis (FEA) calculations. The modeling procedure is based on the calculation of the air gap field density waveform at every time instant. The waveform is the solution of the Laplacian/quasi-Poissonian field equations in polar coordinates in the air gap and takes into account slotting. The model allows the rated performance calculation but also such effects as cogging torque, ripple torque, back-EMF form prediction, some of which are neglected in commonly used analytical models.

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Analytical model for permanent magnet motors with surface mounted magnets

FOREWORD. PREFACE. ACKNOWLEDGMENTS. 1 ENERGY AND CIVILIZATION. 1.1 Introduction. 1.2 Fossil Fuel. 1.3 Depletion of Energy Resources. 1.4 An Alternative Energy Source: Nuclear Energy. 1.5 Global Warming. 1.6 The Age of the Electric Power System. 1.7 Green and Renewable Energy Sources. 1.8 Energy Units and Conversions. 1.9 Estimating the Cost of Energy. 1.10 Conclusion. 2 POWER GRIDS. 2.1 Introduction. 2.2 Electric Power Grids. 2.3 The Basic Concepts of Power Grids. 2.4 Load Models. 2.5 Transformers in Electric Power Grids. 2.6 Modeling a Microgrid System. 2.7 Modeling Three-Phase Transformers. 2.8 Tap Changing Transformers. 2.9 Modeling Transmission Lines. 3 MODELING CONVERTERS IN MICROGRID POWER SYSTEMS. 3.1 Introduction. 3.2 Single-Phase DC/AC Inverters with Two Switches. 3.3 Single-Phase DC/AC Inverters with a Four-Switch Bipolar Switching Method. 3.3.1 Pulse Width Modulation with Unipolar Voltage Switching for a Single-Phase Full-Bridge Inverter. 3.4 Three-Phase DC/AC Inverters. 3.5 Pulse Width Modulation Methods. 3.6 Analysis of DC/AC Three-Phase Inverters. 3.7 Microgrid of Renewable Energy Systems. 3.8 The DC/DC Converters in Green Energy Systems. 3.9 Rectifiers. 3.10 Pulse Width Modulation Rectifiers. 3.11 A Three-Phase Voltage Source Rectifier Utilizing Sinusoidal PWM Switching. 3.12 The Sizing of an Inverter for Microgrid Operation. 3.13 The Sizing of a Rectifi er for Microgrid Operation. 3.14 The Sizing of DC/DC Converters for Microgrid Operation. 4 SMART POWER GRID SYSTEMS. 4.1 Introduction. 4.2 Power Grid Operation. 4.3 The Vertically and Market-Structured Utility. 4.4 Power Grid Operations Control. 4.5 Load-Frequency Control. 4.6 Automatic Generation Control. 4.7 Operating Reserve Calculation. 4.8 The Basic Concepts of a Smart Power Grid. 4.9 The Load Factor. 4.10 A Cyber-Controlled Smart Grid. 4.11 Smart Grid Development. 4.12 Smart Microgrid Renewable Green Energy Systems. 4.13 A Power Grid Steam Generator. 4.14 Power Grid Modeling. 5 MICROGRID SOLAR ENERGY SYSTEMS. 5.1 Introduction. 5.2 The Solar Energy Conversion Process: Thermal Power Plants. 5.3 Photovoltaic Power Conversion. 5.4 Photovoltaic Materials. 5.5 Photovoltaic Characteristics. 5.6 Photovoltaic Effi ciency. 5.7 The Design of Photovoltaic Systems. 5.8 The Modeling of a Photovoltaic Module. 5.9 The Measurement of Photovoltaic Performance. 5.10 The Maximum Power Point of a Photovoltaic Array. 5.11 A Battery Storage System. 5.12 A Storage System Based on a Single-Cell Battery. 5.13 The Energy Yield of a Photovoltaic Module and the Angle of Incidence. 5.14 The State of Photovoltaic Generation Technology. 5.15 The Estimation of Photovoltaic Module Model Parameters. 6 MICROGRID WIND ENERGY SYSTEMS. 6.1 Introduction. 6.2 Wind Power. 6.3 Wind Turbine Generators. 6.4 The Modeling of Induction Machines. 6.5 Power Flow Analysis of an Induction Machine. 6.6 The Operation of an Induction Generator. 6.7 Dynamic Performance. 6.8 The Doubly-Fed Induction Generator. 6.9 Brushless Doubly-Fed Induction Generator Systems. 6.10 Variable-Speed Permanent Magnet Generators. 6.11 A Variable-Speed Synchronous Generator. 6.12 A Variable-Speed Generator with a Converter Isolated from the Grid. 7 LOAD FLOW ANALYSIS OF POWER GRIDS AND MICROGRIDS. 7.1 Introduction. 7.2 Voltage Calculation in Power Grid Analysis. 7.3 The Power Flow Problem. 7.4 Load Flow Study as a Power System Engineering Tool. 7.5 Bus Types. 7.6 General Formulation of the Power Flow Problem. 7.7 The Bus Admittance Model. 7.8 The Bus Impedance Matrix Model. 7.9 Formulation of the Load Flow Problem. 7.10 The Gauss Seidel YBus Algorithm. 7.11 The Gauss Seidel ZBus Algorithm. 7.12 Comparison of the YBus and ZBus Power Flow Solution Methods. 7.13 The Synchronous and Asynchronous Operation of Microgrids. 7.14 An Advanced Power Flow Solution Method: The Newton Raphson Algorithm. 7.15 The Fast Decoupled Load Flow Algorithm. 7.16 Analysis of a Power Flow Problem. 8 POWER GRID AND MICROGRID FAULT STUDIES. 8.1 Introduction. 8.2 Power Grid Fault Current Calculation. 8.3 Symmetrical Components. 8.4 Sequence Networks for Power Generators. 8.5 The Modeling of a Photovoltaic Generating Station. 8.6 Sequence Networks for Balanced Three-Phase Transmission Lines. 8.7 Ground Current Flow in Balanced Three-Phase Transformers. 8.8 Zero Sequence Network. 8.9 Fault Studies. APPENDIX A COMPLEX NUMBERS. APPENDIX B TRANSMISSION LINE AND DISTRIBUTION TYPICAL DATA. APPENDIX C ENERGY YIELD OF A PHOTOVOLTAIC MODULE AND ITS ANGLE OF INCIDENCE. APPENDIX D WIND POWER. INDEX.

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Ali Keyhani

Papers

Control of distributed generation systems - Part II: Load sharing control

Identification of Photovoltaic Source Models

Control of distributed generation systems-Part I: Voltages and currents control

Analytical model for permanent magnet motors with surface mounted magnets

Design of Smart Power Grid Renewable Energy Systems