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The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequency’s nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of thermal plants that are needed to provide frequency response (FR) and inertia. Additional consideration of fast FR, a dynamically reduced largest loss and under frequency load shedding (UFLS) allows frequency security to be achieved more cost effectively. This paper derives a novel constraint from the swing equation to contain the frequency nadir using all of these services. The expected cost of UFLS is found probabilistically to facilitate its comparison to the other frequency services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone (SOC), resulting in highly tractable convex problems. Case studies performed on a Great Britain 2030 system demonstrate that UFLS as an option to contain single plant outages can reduce annual operational costs by up to $\pounds $ 559 m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored. [ABSTRACT FROM AUTHOR]

The foreseen development of large-scale Offshore Windfarms (OWFs) further from the shore dictates that the OWF transmission system must be optimally designed based on Dynamic Thermal Rating (DTR) in order to fully utilize the intermittent nature of the wind and to keep the offshore wind cost-competitive. In this paper, a comprehensive, DTR-based, two-stage stochastic model is presented, which has been developed for investment decision support for OWF size and HVAC transmission systems. Complex DTR models for all the critical HV components are made fit for the mixed-integer linear programming problem, while accounting for the stochasticity in wind generation and component availability. The main decisions incorporate the discrete size of OWFs, HV subsea export cable cross-sections and ratings for transformers and shunt reactors. For validation, an actual testcase OWF off the east coast of U.K. has been used. Results indicate that DTR-based iterative design of OWF and its transmission components can significantly improve the business case, even though transmission efficiency and energy delivered are not maximum for the optimal design [ABSTRACT FROM AUTHOR]

Capital cost is a practical limitation in distributed energy resources (DER) system sizing and the optimal size may lead to high capital investment. This calls for the development of a framework that provides alternate system sizing with the ability to address capital cost constraints. A framework for sizing microgrid DER considering capital cost constraints and inclusion of manufacturer catalog ratings is introduced in this article. This framework uses a system-wide, composite, cost metric that combines capital costs and operating costs per month. This per-month optimization results are transformed to evaluate the feasible DER ratings and annual savings possible with imposed capital and operating cost constraints. The formulated framework is demonstrated using two microgrid case studies in peak shaving applications at industrial facilities located in the U.K. and USA. This article also introduces development of hardware-in-loop (HIL) system as a tool to validate microgrid sizing results demonstrating that real-time operation can provide the savings projected by the optimized assets. The HIL simulation, with a microgrid controller and the plant sized per the optimization verifies the annual savings. This HIL confirmed that the sizing did not result in violations of state of charge limits of battery energy storage. Traditional optimal sizing approaches do not verify for violations and can result in suboptimal or oversized designs. [ABSTRACT FROM AUTHOR]