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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]

In Part I of this paper we have introduced the closed-form conditions for guaranteeing regional frequency stability in a power system. Here we propose a methodology to represent these conditions in the form of linear constraints and demonstrate their applicability by implementing them in a generation-scheduling model. This model simultaneously optimises energy production and ancillary services for maintaining frequency stability in the event of a generation outage, by solving a frequency-secured Stochastic Unit Commitment (SUC). We consider the Great Britain system, characterised by two regions that create a non-uniform distribution of inertia: England in the South, where most of the load is located, and Scotland in the North, containing significant wind resources. Through several case studies, it is shown that inertia and frequency response cannot be considered as system-wide magnitudes in power systems that exhibit inter-area oscillations in frequency, as their location in a particular region is key to guarantee stability. In addition, securing against a medium-sized loss in the low-inertia region proves to cause significant wind curtailment, which could be alleviated through reinforced transmission corridors. In this context, the proposed constraints allow to find the optimal volume of ancillary services to be procured in each region. [ABSTRACT FROM AUTHOR]

This paper presents a fault tree analysis (FTA) method for the unavailability of supply of gas networks. The method is based on the automatic generation of fault trees, which estimate the probability of disruption of the gas delivery from terminals/storages to the demand nodes. Moreover, it allows probabilistic analyses of the availability of gas supply to individual demand nodes and to the overall gas network. To assess the importance of each network component, the risk achievement worth and the risk reduction worth importance measures are utilized. The developed method can identify weakness in the gas network and can guide expansion planning and maintenance scheduling activities. Furthermore, the developed framework is enriched by steady-state analysis of the gas network operations performed using a physical flow/pressure model. The impact of a component failure on the gas supply interruption at different demand nodes is assessed by the physical model in retrospective to the FTA results. The framework is exemplified with reference to the reduced gas network of Great Britain. The results provide insights to support a robust reliability assessment of the gas network. Moreover, the probability mapping of the most important components in the gas network informs optimal strategies for maintenance scheduling as well for prioritizing improvements of the gas network aimed at significant risk reduction. Remarkably, the failure of components identified as most important according to the FTA importance measures may not have significant effects on the gas supply. A discussion on the range of applicability and limitations of the two methodologies is provided. [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]