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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 reduced level of system inertia in low-carbon power grids increases the need for alternative frequency services. However, simultaneously optimizing the provision of these services in the scheduling process, subject to significant uncertainty, is a complex task given the challenge of linking the steady-state optimization with frequency dynamics. This paper proposes a novel frequency-constrained stochastic unit commitment model which, for the first time, co-optimizes energy production along with the provision of synchronized and synthetic inertia, enhanced frequency response, primary frequency response and a dynamically-reduced largest power infeed. The contribution of load damping is modeled through a linear inner approximation. The effectiveness of the proposed model is demonstrated through several case studies for Great Britain's 2030 power system, which highlight the synergies and conflicts among alternative frequency services, as well as the significant economic savings and carbon reduction achieved by simultaneously optimizing all these services. [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]