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Register a new userOptimal Scheduling of Frequency Services Considering a Variable Largest-Power-Infeed-Loss
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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 in 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.
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We derive the branch ampacity constraint associated to power losses for the convex optimal power flow (OPF) model based on the branch flow formulation. The branch ampacity constraint derivation is motivated by the physical interpretation of the transmission line {Pi}-model and practical engineering considerations. We rigorously prove and derive: (i) the loop constraint of voltage phase angle, required to make the branch flow model valid for meshed power networks, is a relaxation of the original nonconvex alternating current optimal power flow (o-ACOPF) model; (ii) the necessary conditions to recover a feasible solution of the o-ACOPF model from the optimal solution of the convex second-order cone ACOPF (SOC-ACOPF) model; (iii) the expression of the global optimal solution of the o-ACOPF model providing that the relaxation of the SOC-ACOPF model is tight; (iv) the (parametric) optimal value function of the o-ACOPF or SOC-ACOPF model is monotonic with regarding to the power loads if the objective function is monotonic with regarding to the nodal power generations; (v) tight solutions of the SOC-ACOPF model always exist when the power loads are sufficiently large. Numerical experiments using benchmark power networks to validate our findings and to compare with other convex OPF models, are given and discussed.
The scheduling utility plays a fundamental role in addressing the commuting travel behaviours. In this paper, a new scheduling utility, termed as DMRD-SU, was suggested based on some recent research findings in behavioural economics. DMRD-SU admitted the existence of positive arrival-caused utility. In addition, besides the travel-time-caused utility and arrival-caused utility, DMRD-SU firstly took the departure utility into account. The necessity of the departure utility in trip scheduling was analysed comprehensively, and the corresponding individual trip scheduling model was presented. Based on a simple network, an analytical example was executed to characterize DMRD-SU. It can be found from the analytical example that: 1) DMRD-SU can predict the accumulation departure behaviors at NDT, which explains the formation of daily serious short-peak-hours in reality, while MRD-SU cannot; 2) compared with MRD-SU, DMRD-SU predicts that people tend to depart later and its gross utility also decrease faster. Therefore, the departure utility should be considered to describe the travelers scheduling behaviors better.
Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model gives an efficient way to find the global optimal solution of ACOPF but suffers from the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gap and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.
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, demonstrating 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.
It is likely that electricity storage will play a significant role in the balancing of future energy systems. A major challenge is then that of how to assess the contribution of storage to capacity adequacy, i.e. to the ability of such systems to meet demand. This requires an understanding of how to optimally schedule multiple storage facilities. The present paper studies this problem in the cases where the objective is the minimisation of expected energy unserved (EEU) and also a form of weighted EEU in which the unit cost of unserved energy is higher at higher levels of unmet demand. We also study how the contributions of individual stores may be identified for the purposes of their inclusion in electricity capacity markets.
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