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

Introduction to stochastic programming

Microgrids are now emerging from lab benches and pilot demonstration sites into commercial markets, driven by technological improvements, falling costs, a proven track record, and growing recognition of their benefits. They are being used to improve reliability and resilience of electrical grids, to manage the addition of distributed clean energy resources like wind and solar photovoltaic (PV) generation to reduce fossil fuel emissions, and to provide electricity in areas not served by centralized electrical infrastructure. This review article (1) explains what a microgrid is, and (2) provides a multi-disciplinary portrait of today's microgrid drivers, real-world applications, challenges, and future prospects.

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Microgrids: A review of technologies, key drivers, and outstanding issues

The significant benefits associated with microgrids have led to vast efforts to expand their penetration in electric power systems. Although their deployment is rapidly growing, there are still many challenges to efficiently design, control, and operate microgrids when connected to the grid, and also when in islanded mode, where extensive research activities are underway to tackle these issues. It is necessary to have an across-the-board view of the microgrid integration in power systems. This paper presents a review of issues concerning microgrids and provides an account of research in areas related to microgrids, including distributed generation, microgrid value propositions, applications of power electronics, economic issues, microgrid operation and control, microgrid clusters, and protection and communications issues.

State of the Art in Research on Microgrids: A Review

Microgrids energy management systems: A critical review on methods, solutions, and prospects

This paper presents a model for calculating the optimal size of an energy storage system (ESS) in a microgrid considering reliability criterion. A larger ESS requires higher investment costs while reduces the microgrid operating cost. The optimal ESS sizing problem is proposed which minimizes the investment cost of the ESS, as well as expected microgrid operating cost. Utilizing the ESS, generation shortage due to outage of conventional units and intermittency of renewable units is handled; hence microgrid reliability criterion is satisfied. A practical model for ESS is utilized. Mixed-integer programming (MIP) is utilized to formulate the problem. Illustrative examples show the efficiency of the proposed model.

Reliability-Constrained Optimal Sizing of Energy Storage System in a Microgrid

In this paper, a model for the optimal placement of contingency-constrained phasor measurement units (PMUs) in electric power networks is presented. The conventional complete observability of power networks is first formulated and then, different contingency conditions in power networks including measurement losses and line outages are added to the main model. The communication constraints which would limit the maximum number of measurements associated with each installed PMU is considered as measurement limitations. The relevant formulations are also proposed to make the model more comprehensive. The IEEE standard test systems are examined for the applicability of proposed model. The comparison of presented results with those of other methods is presented which would justify the effectiveness of proposed model with regards to minimizing the total number of PMUs and the execution time. A large-scale system with 2383 buses is also analyzed to exhibit the applicability of proposed model to practical power system cases.

Contingency-Constrained PMU Placement in Power Networks

One of complementary value propositions of microgrids is to improve power system resiliency via local supply of loads and curtailment reduction. This subject is investigated in this paper by proposing a resiliency-oriented microgrid optimal scheduling model. The proposed model aims at minimizing the microgrid load curtailment by efficiently scheduling available resources when supply of power from the main grid is interrupted for an extended period of time. The problem is decomposed to normal operation and resilient operation problems. The normal operation problem solution, i.e., unit commitment states, energy storage schedules, and adjustable loads schedules, is employed in the resilient operation problem to examine microgrid capability in supplying local loads during main grid supply interruption. The schedule is revised via resiliency cuts if a zero mismatch is not obtained. Prevailing operational uncertainties in load, non-dispatchable generation, and the main grid supply interruption time and duration are considered and captured using a robust optimization method. The final solution, which is obtained in an iterative manner, is economically optimal, guarantees robustness against prevailing operational uncertainties, and supports a quick islanding with minimum consumer inconvenience and load curtailment. Numerical simulations demonstrate the effectiveness of the proposed resiliency-oriented microgrid optimal scheduling model applied to a test microgrid.

Resiliency-Oriented Microgrid Optimal Scheduling

This paper presents a model for microgrid optimal scheduling considering multi-period islanding constraints. The objective of the problem is to minimize the microgrid total operation cost which comprises the generation cost of local resources and cost of energy purchase from the main grid. The microgrid optimal scheduling problem is decomposed into a grid-connected operation master problem and an islanded operation subproblem. The microgrid capability in operating in the islanded mode for multiple hours is scrutinized by a T-τ islanding criterion. The integer scheduling decisions determined in the master problem will be examined against the microgrid islanding feasibility in the subproblem. The scheduling decisions will be revised using proper islanding cuts if sufficient generation is not available to guarantee a feasible islanding. Islanding cuts will revise generating units, energy storage systems, and adjustable loads schedules. Any change in the schedule of adjustable loads outside the operating time interval specified by consumers is penalized by an inconvenience factor in the objective. Numerical simulations demonstrate the effectiveness of the proposed microgrid optimal scheduling model and explore its economic and reliability merits.

Amin Khodaei

Papers

State of the Art in Research on Microgrids: A Review

Reliability-Constrained Optimal Sizing of Energy Storage System in a Microgrid

Contingency-Constrained PMU Placement in Power Networks

Resiliency-Oriented Microgrid Optimal Scheduling

Microgrid Optimal Scheduling With Multi-Period Islanding Constraints