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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]

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]

Recent long term planning studies have demonstrated the important role of variable renewables (VRE) in decarbonising our energy system. However, cost-optimising models do not capture the visual impact of VREs on the landscape which can act to undermine their public acceptability. Here, we use crowd-sourced scenicness data to derive spatially explicit wind energy capacity potentials for three scenarios of public sensitivity to this visual impact. We then use these scenarios in a cost-optimising model of Great Britain's power system to assess their impact on the cost and design of the electricity system in 2050. Our results show that total system costs can increase by up to 14.2% when public sensitivity to visual impact is high compared to low. It is thus essential for policy makers to consider these cost implications and to find mechanisms to ameliorate the visual impact of onshore wind in local communities. [ABSTRACT FROM AUTHOR]

This letter analyzes the difficulty of estimating power system inertia under ambient conditions using the Center-of-Inertia (CoI) system model. We show that the main obstacle to doing this is a difficulty in detecting a peak in the Power Spectral Density (PSD) of the frequency trace. This is due to a combination of two factors: (i) the Ornstein-Uhlenbeck (OU) process with a high mean-reversion time, which models the load disturbance and is mathematically equivalent to a low-pass filter with a high time constant; (ii) the CoI dominant mode is highly damped. This observation also explains why it is possible to estimate system inertia under ambient conditions using wide-area PMU measurements by exploiting information about inter-area oscillations which have lower damping than the dominant mode of the CoI model. We validated those findings by using the PSD of the actual 2-hour frequency trace for Great Britain from 00:00 to 02:00 of January 01, 2019. [ABSTRACT FROM AUTHOR]