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 enabling of ac microgrids in distribution networks allows delivering distributed power and providing grid support services during regular operation of the grid, as well as powering isolated islands in case of faults and contingencies, thus increasing the performance and reliability of the electrical system. The high penetration of distributed generators, linked to the grid through highly controllable power processors based on power electronics, together with the incorporation of electrical energy storage systems, communication technologies, and controllable loads, opens new horizons to the effective expansion of microgrid applications integrated into electrical power systems. This paper carries out an overview about microgrid structures and control techniques at different hierarchical levels. At the power converter level, a detailed analysis of the main operation modes and control structures for power converters belonging to microgrids is carried out, focusing mainly on grid-forming, grid-feeding, and grid-supporting configurations. This analysis is extended as well toward the hierarchical control scheme of microgrids, which, based on the primary, secondary, and tertiary control layer division, is devoted to minimize the operation cost, coordinating support services, meanwhile maximizing the reliability and the controllability of microgrids. Finally, the main grid services that microgrids can offer to the main network, as well as the future trends in the development of their operation and control for the next future, are presented and discussed.

Control of Power Converters in AC Microgrids

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

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 chapter discusses leading problems linked to energy that the world is now confronting and to propose some ideas concerning possible solutions. Oil deserves special attention among all energy sources. Since the beginning of 1981, it has merely been continuing and enhancing the downward movement in consumption and prices caused by excessive rises, especially for light crudes such as those from Africa, and the slowing down of worldwide economic growth. Densely-populated oil-producing countries need to produce to live, to pay for their food and their equipment. If the economic growth of the industrialized countries were to be 4%, even if investment in the rational use of energy were pushed to the limit and the development of nonpetroleum energy sources were also pursued actively, it would be extremely difficult to prevent a sharp rise in prices. It is evident that it is absolutely necessary to pursue actively the development of coal, natural gas, and nuclear power if a physical shortage of energy is not to block economic growth.

World energy outlook

About The Authors. Preface. Acknowledgements. List of Symbols. PART I: INTRODUCTION TO POWER SYSTEMS. 1 Introduction . 1.1 Stability and Control of a Dynamic System. 1.2 Classification of Power System Dynamics. 1.3 Two Pairs of Important Quantities: Reactive Power/Voltage and Real Power/Frequency. 1.4 Stability of Power System. 1.5 Security of Power System. 1.6 Brief Historical Overview. 2. Power System Components. 2.1 Structure of the Electrical Power System. 2.2 Generating Units. 2.3 Substations. 2.4 Transmission and Distribution Network. 2.5 Protection. 2.6 Wide Area Measurement Systems. 3. The Power System in the Steady-State. 3.1. Transmission Lines. 3.2. Transformers. 3.3. Synchronous Generators. 3.4. Power System Loads. 3.5. Network Equations. 3.6. Power Flows in Transmission Networks. PART II: INTRODUCTION TO POWER SYSTEM DYNAMICS. 4. Electromagnetic Phenomena. 4.1. Fundamentals. 4.2. Three-Phase Short-Circuit on a Synchronous Generator. 4.3. Phase-to-Phase Short-Circuit. 4.4. Synchronization. 4.5. Short Circuit in a Network and its Clearing. 5. Electromechanical Dynamics - Small Disturbances. 5.1. Swing Equation. 5.2. Damping Power. 5.3. Equilibrium Points. 5.4. Steady-State Stability of Unregulated System. 5.5. Steady-State Stability of the Regulated System. 6. Electromechanical Dynamics - Large Disturbances. 6.1. Transient Stability. 6.2. Swings in Multi-Machine Systems. 6.3. Direct Method for Stability Assessment. 6.4. Synchronization. 6.5. Asynchronous Operation and Resynchronization. 6.6 Out-Of-Step Protection Systems. 6.7. Torsional Oscillations in the Drive Shaft. 7. Wind Power. 7.1 Wind Turbines. 7.2 Induction Machine Equivalent Circuit. 7.3 Induction Generator Coupled to the Grid. 7.4 Induction Generators with Slightly Increased Speed Range Via External Rotor Resistance. 7.5 Induction Generators with Significantly Increased Speed Range: DFIGs. 7.6 Fully Rated Converter Systems: Wide Speed Control. 7.7 Peak Power Tracking Of Variable Speed Wind Turbines. 7.8 Connections of Wind Farms. 7.9 Fault Behaviour of Induction Generators. 7.10 Influence of Wind Generators on Power System Stability. 8. Voltage Stability. 8.1. Network Feasibility. 8.2. Stability Criteria. 8.3. Critical Load Demand and Voltage Collapse. 8.4. Static Analysis. 8.5. Dynamic Analysis. 8.6. Prevention of Voltage Collapse. 8.7. Self-Excitation of a Generator Operating on a Capacitive Load. 9. Frequency Stability and Control. 9.1. Automatic Generation Control. 9.2. Stage I - Rotor Swings in the Generators. 9.3. Stage II - Frequency Drop. 9.4. Stage III - Primary Control. 9.5. STAGE IV - Secondary Control. 9.6. FACTS Devices in Tie-Lines. 10. Stability Enhancement. 10.1. Power System Stabilizers. 10.2. Fast Valving. 10.3. Braking Resistors. 10.4. Generator Tripping. 10.5. Shunt FACTS Devices. 10.6. Series Compensators. 10.7. Unified Power Flow Controller . PART III: ADVANCED TOPICS IN POWER SYSTEM DYNAMICS. 11. Advanced Power System Modelling. 11.1 Synchronous Generator. 11.2. Excitation Systems. 11.3. Turbines and Turbine Governors. 11.4. FACTS Devices. 12. Steady-State Stability of Multi-Machine System. 12.1. Mathematical Background. 12.2. Steady-State Stability of Unregulated System. 12.3. Steady-State Stability of The Regulated System. 13. Power System Dynamic Simulation. 13.1. Numerical Integration Methods. 13.2. The Partitioned-Solution. 13.3. The Simultaneous Solution Methods. 13.4. Comparison Between the Methods. 14. Power System Model Reduction - Equivalents. 14.1. Types of Equivalents. 14.2. Network Transformation. 14.3. Aggregation of Generating Units. 14.4. Equivalent Model of External Subsystem. 14.5. Coherency Recognition. 14.6. Properties of Coherency-Based Equivalents. Appendix. References. Index.

Power system dynamics : stability and control

Continuing trend towards deregulation and unbundling of transmission services has resulted in the need to assess what the impact of a particular generator or load is on the power system. A new method of tracing the flow of electricity in meshed electrical networks is proposed which may be applied to both real and reactive power flows. The method allows assessment of how much of the real and reactive power output from a particular station goes to a particular load. It also allows the assessment of contributions of individual generators (or loads) to individual line flows. A loss-apportioning algorithm has also been introduced which allows the break down of the total transmission loss into components to be allocated to individual loads or generators. The method can be useful in providing additional insight into power system operation and can be used to modify existing tariffs of charging for transmission loss, reactive power and transmission services.

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Tracing the flow of electricity

The drastic reduction of carbon emission to combat global climate change cannot be realized without a significant contribution from the electricity sector. Renewable energy resources must take a bigger share in the generation mix, effective demand response must be widely implemented, and high-capacity energy storage systems must be developed. A smart grid is necessary to manage and control the increasingly complex future grid. Certain smart grid elements-renewables, storage, microgrid, consumer choice, and smart appliances-increase uncertainty in both supply and demand of electric power. Other smart gird elements-sensors, smart meters, demand response, and communications-provide more accurate information about the power system and more refined means of control. Simply building hardware for renewable generators and the smart grid, but still using the same operating paradigm of the grid, will not realize the full potential for overall system efficiency and carbon reduction. In this paper, a new operating paradigm, called risk-limiting dispatch, is proposed. It treats generation as a heterogeneous commodity of intermittent or stochastic power and uses information and control to design hedging techniques to manage the risk of uncertainty.

Smart Operation of Smart Grid: Risk-Limiting Dispatch

This paper introduces a simple novel method of transmission supplement charge allocation based on topological analysis of power flows in the network. The method uses the MW-MILE methodology but analyses the share, not the impact of, individual loads and generators in line flows. This results in positive contributions from all the users hence rescinding the problem of counterflows.

Topological generation and load distribution factors for supplement charge allocation in transmission open access

Power System Components. The Power System in the Steady-State. Electromagnetic Phenomena. Electromechanical Dynamics - Small Disturbances. Electromechanical Dynamics - Large Disturbances. Voltage Stability. Frequency Variations. Stability Enhancement. Advanced Power System Modelling. Power System Model Reduction - Equivalents. Steady-State Stability of Multi-Machine System. Power System Dynamic Simulation. Appendix. References. Index.

Janusz Bialek

Papers

Power system dynamics : stability and control

Tracing the flow of electricity

Smart Operation of Smart Grid: Risk-Limiting Dispatch

Topological generation and load distribution factors for supplement charge allocation in transmission open access

Power system dynamics and stability