A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation. Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. Experimental results on a IEEE 6-bus system are presented, showing that without any tunings of parameters, the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general, and our method also enjoys higher reliability of dispatch operation

Information-Driven Path Planning for UAV with Limited Autonomy in Large-scale Field Monitoring

This paper presents a novel information-based mission planner for a drone tasked to monitor a spatially distributed dynamical phenomenon. For the sake of simplicity, the area to be monitored is discretized. The insight behind the proposed approach is that, thanks to the spatio-temporal dependencies of the observed phenomenon, one does not need to collect data on the entire area. In fact, unmeasured states can be estimated using an estimator, such as a Kalman filter. In this context the planning problem becomes the one of generating a flight path that maximizes the quality of the state estimation while satisfying the flight constraints (e.g. flight time). The first result of this paper is to formulate this problem as a special Orienteering Problem where the cost function is a measure of the quality of the estimation. This approach provides a Mixed-Integer Semi-Definite formulation to the problem which can be optimally solved for small instances. For larger instances, two heuristics are proposed which provide good sub-optimal results. To conclude, numerical simulations are shown to prove the capabilities and efficiency of the proposed path planning strategy. We believe this approach has the potential to increase dramatically the area that a drone can monitor, thus increasing the number of applications where monitoring with drones can become economically convenient

The Next Generation of Beam Hopping Satellite Systems: Dynamic Beam Illumination with Selective Precoding

peer reviewe

Despacho ótimo de potência reativa com controladores discretos usando o algoritmo branch and bound : uma abordagem por relaxação semidefinida

Orientador: Marcos Julio Rider FloresDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente, vários relaxamentos convexos foram aplicados com sucesso para resolver o problema do fluxo de potência ótimo de CA (OPF), o que chamou a atenção da comunidade científica. Dentre esses relaxamentos, destaca-se um relaxamento baseado em programação semidefinida (SDP). Nesse sentido, neste trabalho é proposta uma metodologia para resolver o despacho ótimo de potência reativa (ORPD) em sistemas elétricos de potência(SEP), considerando controladores discretos. Controladores discretos, como a posição de tap dos transformadores de comutação em carga (OLTC) e compensação de shunt reativa comutável, são otimizados pelo método proposto. Uma relaxação semidefinida(SDR) do problema ORPD e um algoritmo branch-and-bound (B&B) foram totalmente implementados. O algoritmo B&B personalizado lida com a natureza discreta das variáveis de controle binárias. Além disso, a fim de melhorar a convexificação, desigualdades válidas chamadas de cortes não lineares elevados (LNCs) são implementadas no SDR. Além disso, uma técnica de decomposição de cordas é usada para melhorar o desempenho computacional. Finalmente, o algoritmo B&B é usado para resolver o problema de programação semidefinida inteira mista. Vários sistemas de referência foram usados para mostrar a precisão e escalabilidade do método proposto, e a análise de convergência mostraque soluções ótimas quase globais são geradas com pequenas brechasAbstract: Recently, several convex relaxations has been successfully applied to solve the AC optimal power flow (OPF) problem, which has caught the attention of the research community. Among these relaxations, a relaxation based on semidefinite programming (SDP) stands out. Accordingly, in this work a methodology to solve the optimal reactive power dispatch (ORPD) in electric power systems (EPS), considering discrete controllers, is proposed. Discrete controllers, such as the tap position of on-load tap changing (OLTC) transformers and switchable reactive shunt compensation, are optimized by the proposed method. A semidefinite relaxation (SDR) of the ORPD problem and a branch-and-bound (B&B) algorithm has been fully deployed. The customized B&B algorithm deals with the discrete nature of the binary control variables. Moreover, in order to enhance the convexification, valid inequalities called lifted non-linear-cuts (NLC) are implemented in the SDR. Addition-ally, a chordal decomposition technique is used to improve the computational performance. Finally, the B&B algorithm is used to solve the mixed-integer semidefinite programming problem. Several benchmarks have been used to show the accuracy and scalability of the proposed method, and convergence analysis shows that near-global optimal solutions are generated with small relaxation gapsMestradoEnergia ElétricaMestre em Engenharia Elétrica88882.329400/2019-1CAPE

Low Voltage Distribution Networks Modeling and Unbalanced (Optimal) Power Flow: A Comprehensive Review

The rapid increase of distributed energy resources (DERs) installation at residential and commercial levels can pose significant technical issues on the voltage levels and capacity of the network assets in distribution networks. Most of these issues occur in low-voltage distribution networks (LVDNs) or near customer premises. A lack of understanding of the networks and advanced planning approaches by distribution network providers (DNSPs) has led to rough estimations for maximum DERs penetration levels that LVDNs can accommodate. These issues might under- or over-estimate the actual hosting capacity of the LVDNs. Limited available data on LVDNs' capacity to host DERs makes planning, installing, and connecting new DERs problematic and complex. In addition, the lack of transparency in LVDN data and information leads to model simplifications, such as ignoring the phase imbalance. This can lead to grossly inaccurate results. The main aim of this paper is to enable the understanding of the true extent of local voltage excursions to allow more targeted investment, improve the network's reliability, enhance solar performance distribution, and increase photovoltaic (PV) penetration levels in LVDNs. Therefore, this paper reviews the state-of-the-art best practices in modeling unbalanced LVDNs as accurately as possible to avoid under- or over-estimation of the network's hosting capacity. In addition, several PV system modeling variations are reviewed, showing their limitations and merits as a trade-off between accuracy, computational burden, and data availability. Moreover, the unbalanced power flow representations, solving algorithms, and available tools are explained extensively by providing a comparative study between these tools and the ones most commonly used in Australia. This paper also presents an overview of unbalanced optimal power flow representations with their related objectives, solving algorithms, and tools