This paper proposes a cyber-physical cooperative mitigation framework to enhance power systems resilience under extreme events, e.g., earthquakes and hurricanes. Extreme events can simultaneously damage the physical-layer electric power infrastructur
e and the cyber-layer communication facilities. Microgrid (MG) has been widely recognised as an effective physical-layer response to such events, however, the mitigation strategy in the cyber lay is yet to be fully investigated. Therefore, this paper proposes a resilience-oriented centralised-to-decentralised framework to maintain the power supply of critical loads such as hospitals, data centers, etc., under extreme events. For the resilient control, controller-to-controller (C2C) wireless network is utilised to form the emergency regional communication when centralised base station being compromised. Owing to the limited reliable bandwidth that reserved as a backup, the inevitable delays are dynamically minimised and used to guide the design of a discrete-time distributed control algorithm to maintain post-event power supply. The effectiveness of the cooperative cyber-physical mitigation framework is demonstrated through extensive simulations in MATLAB/Simulink.
Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open proble
m that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.
The reduced inertia levels in low-carbon power grids necessitate explicit constraints to limit frequencys nadir and rate of change during scheduling. This can result in significant curtailment of renewable energy due to the minimum generation of ther
mal 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 nadir constraint from the swing equation that, for the first time, provides a framework for the optimal comparison of all these services. We demonstrate that this constraint can be accurately and conservatively approximated for moderate UFLS levels with a second order cone, 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}559m, 52% of frequency security costs. The sensitivity of this value to wind penetration, abundance of alternative frequency services, UFLS amount and cost is explored.
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.
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are discussed, demonst
rating that the post-fault frequency evolution in any given region is equal to the frequency evolution of the Centre Of Inertia plus certain inter-area oscillations. This finding leads to the deduction of conditions for guaranteeing frequency stability in all regions of a power system, a deduction performed using a mixed analytical-numerical approach that combines mathematical analysis with regression methods on simulation samples. The proposed stability conditions are linear inequalities that can be implemented in any optimisation routine allowing the co-optimisation of all existing ancillary services for frequency support: inertia, multi-speed frequency response, load damping and an optimised largest power infeed. This is the first reported mathematical framework with explicit conditions to maintain frequency stability in a power system exhibiting inter-area oscillations in frequency.
Accurate inertia estimates and forecasts are crucial to support the system operation in future low-inertia power systems. A large literature on inertia estimation methods is available. This paper aims to provide an overview and classification of iner
tia estimation methods. The classification considers the time horizon the methods are applicable to, i.e., offline post mortem, online real time and forecasting methods, and the scope of the inertia estimation, e.g., system-wide, regional, generation, demand, individual resource. Shortcomings of the existing inertia estimation methods have been identified and suggestions for future work have been made.
The need for Enhanced Frequency Response (EFR) is expected to increase significantly in future low-carbon Great Britain (GB) power system. One way to provide EFR is to use power electronic compensators (PECs) for point-of-load voltage control (PVC) t
o exploit the voltage dependence of loads. This paper investigates the techno-economic feasibility of such technology in future GB power system by quantifying the total EFR obtainable through deploying PVC in the urban domestic sector, the investment cost of the installment and the economic and environmental benefits of using PVC. The quantification is based on a stochastic domestic demand model and generic medium and low-voltage distribution networks for the urban areas of GB and a stochastic unit commitment (SUC) model with constraints for secure post-fault frequency evolution is used for the value assessment. Two future energy scenarios in the backdrop of 2030 with `smart and `non-smart control of electric vehicles and heat pumps, under different levels of penetration of battery energy storage system (BESS) are considered to assess the value of PEC, as well as the associated payback period. It is demonstrated that PVC could effectively complement BESS towards EFR provision in future GB power system.
Most renewable energy sources (RES) do not provide any inertial response. Their integration in a power grid implies a highly reduced level of system inertia, which leads to a deteriorated frequency performance. Then, the requirement for frequency res
ponse is significantly increased in order to maintain frequency security. Alternatively, enhanced provision of inertia from auxiliary sources may alleviate this problem. However, the benefits of inertia provision are not yet fully understood. In this paper, an inertia-dependent Stochastic Unit Commitment (SUC) tool is applied to quantify the economic value of inertia. The results demonstrate that enhanced provision of inertia would lead to significant economic savings, although these savings vary under different system conditions. These results should be brought to the attention of both market operators and investors, in order to inform the design of an ancillary-services market for inertia and the investment in auxiliary provision of inertia.
Low levels of inertia due to increasing renewable penetration bring several challenges, such as the higher need for Primary Frequency Response (PFR). A potential solution to mitigate this problem consists on reducing the largest possible power loss i
n the grid. This paper develops a novel modelling framework to analyse the benefits of such approach. A new frequency-constrained Stochastic Unit Commitment (SUC) is proposed here, which allows to dynamically reduce the largest possible loss in the optimisation problem. Furthermore, the effect of load damping is included by means of an approximation, while its effect is typically neglected in previous frequency-secured-UC studies. Through several case studies, we demonstrate that reducing the largest loss could significantly decrease operational cost and carbon emissions in the future Great Britains grid.
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by the curren
tly best-performing worker (leader). Our method differs from the parameter-averaging scheme EASGD in a number of ways: (i) our objective formulation does not change the location of stationary points compared to the original optimization problem; (ii) we avoid convergence decelerations caused by pulling local workers descending to different local minima to each other (i.e. to the average of their parameters); (iii) our update by design breaks the curse of symmetry (the phenomenon of being trapped in poorly generalizing sub-optimal solutions in symmetric non-convex landscapes); and (iv) our approach is more communication efficient since it broadcasts only parameters of the leader rather than all workers. We provide theoretical analysis of the batch version of the proposed algorithm, which we call Leader Gradient Descent (LGD), and its stochastic variant (LSGD). Finally, we implement an asynchronous version of our algorithm and extend it to the multi-leader setting, where we form groups of workers, each represented by its own local leader (the best performer in a group), and update each worker with a corrective direction comprised of two attractive forces: one to the local, and one to the global leader (the best performer among all workers). The multi-leader setting is well-aligned with current hardware architecture, where local workers forming a group lie within a single computational node and different groups correspond to different nodes. For training convolutional neural networks, we empirically demonstrate that our approach compares favorably to state-of-the-art baselines.
