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1. Quadratically Constrained Quadratic Programming Formulation of Contingency Constrained Optimal Power Flow with Photovoltaic Generation

   https://doi.org/10.3390/en13133310  

   Leon, Luis M. ; Bretas, Arturo S. ; Rivera, Sergio ( July 2020 , Energies)

   null (Ed.)

   Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective. 

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2. Inexactness of Second Order Cone Relaxations for Calculating Operating Envelopes

   https://doi.org/10.1109/SmartGridComm57358.2023.10333939  

   Moring, Hannah ; Mathieu, Johanna L. ( October 2023 , IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids)

   As the number of distributed energy resources participating in power networks increases, it becomes increasingly more important to actively manage network constraints to ensure safe operation. One proposed method that has gained significant attention and implementation, particularly in Australia, is the use of dynamic operating envelopes. Operating envelopes represent net export limits set by the system operator on every node in the distribution network that change as system conditions change. They are calculated using an optimal power flow problem, frequently using a linearization or relaxation of the nonlinear power flow equations. This paper presents two case studies and some numerical analysis to explain why a second order cone relaxation of the power flow equations will lead to ineffective operating envelopes. A modification to the objective function which allows the second order cone relaxation to nearly recover the solution to the nonlinear formulation is also presented. 

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3. Two-Stage Robust Quadratic Optimization with Equalities and Its Application to Optimal Power Flow

   https://doi.org/10.1137/22M1469651  

   Kuryatnikova, Olga ; Ghaddar, Bissan ; Molzahn, Daniel K. ( December 2023 , SIAM Journal on Optimization)

   In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed, and the rest of the optimization variables (state variables) are set up as a solution to a known system of possibly nonlinear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems as well as gas and water networks. We propose a convergent iterative algorithm to build a sequence of approximately robustly feasible solutions with an improving objective value. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the nonlinearity of other constraints. We implement our approach and demonstrate its performance on Matpower instances of AC optimal power flow. Although this paper focuses on quadratic problems, the approach is suitable for more general setups. 

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4. Learning Solutions for Intertemporal Power Systems Optimization with Recurrent Neural Networks

   https://doi.org/10.1109/PMAPS53380.2022.9810638  

   Mohammadian, Mostafa ; Baker, Kyri ; Dinh, My H. ; Fioretto, Ferdinando ( January 2022 , International Conference on Probabilistic Methods Applied to Power Systems (PMAPS))

   Learning mappings between system loading and optimal dispatch solutions has been a recent topic of interest in the power systems and machine learning communities. However, previous works have ignored practical power system constraints such as generator ramp limits and other intertemporal requirements. Additionally, optimal power flow runs are not performed independently of previous timesteps - in most cases, an OPF solution representing the current state of the system is heavily related to the OPF solution from previous timesteps. In this paper, we train a recurrent neural network, which embeds natural relationships between timesteps, to predict the optimal solution of convex power systems optimization problems with intertemporal constraints. In contrast to traditional forecasting methods, the computational benefits from this technique can allow operators to rapidly simulate forecasts of system operation and corresponding optimal solutions to provide a more comprehensive view of future system states. 

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5. Power control and beamforming design for SWIPT in AF two-way relay networks

   https://doi.org/10.1109/ICCS.2016.7833632  

   Wang, Wei ; Wang, Rui ; Mehrpouyan, Hani ; Zhang, Guoan ( December 2016 , IEEE International Conference on Communication Systems (ICCS), 2016)

   In this paper, we study the problem of joint power control and beamforming design for simultaneous wireless information and power transfer (SWIPT) in an amplify-and-forward (AF) based two-way relaying (TWR) network. The considered system model consists of two source nodes and a relay node. Two single-antenna source nodes receive information and energy simultaneously via power splitting (PS) from the signals sent by a multi-antenna relay node. Our objective is to maximize the weighted sum energy at the two source nodes subject to quality of service (QoS) constraints and the transmit power constraints. However, the joint optimization of the relay beamforming matrix, the source transmit power and PS ratio is intractable. To find a closed-form solution of the formulated problem, we decouple the primal problem into two subproblems. In the first problem, we intend to optimize the beamforming vectors for given transmit powers and PS ratio. In the second subproblem, we optimize the remaining parameters with obtained beamformers. It is worth noting that although the corresponding subproblem are nonconvex, the optimal solution of each subproblem can be found by using certain techniques. The iterative optimization algorithm finally converges. Simulation results verify the effectiveness of the proposed joint design. 

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