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This paper incorporates a continuous-type network flexibility into chance constrained economic dispatch (CCED). In the proposed model, both power generations and line susceptances are continuous variables to minimize the expected generation cost and guarantee a low probability of constraint violation in terms of generations and line flows under renewable uncertainties. From the analytical form of CCED, we figure out the mechanism of network flexibility against uncertainties -- while renewable uncertainties shrink the usable line capacities and aggravate transmission congestion, network flexibility mitigates congestion by re-routing the base-case line flows and reducing the line capacity shrinkage caused by uncertainties. Further, we propose an alternate iteration solver for this problem. By duality theory, we set up a master problem in the form of second-order cone programming to optimize generation dispatch scheme and a subproblem in the form of linear programming to optimize line susceptances. A satisfactory solution can be obtained efficiently by alternately solving these two problems. The proposed method applies to both Gaussian uncertainty and non-Gaussian uncertainty by means of Gaussian mixture model. The case studies on the IEEE 14-bus system and IEEE 118-bus system suggest that network flexibility can significantly improve operational economy while ensuring security under uncertainties., Comment: 12 pages, 8 figures

Global covariance pooling (GCP) aims at exploiting the second-order statistics of the convolutional feature. Its effectiveness has been demonstrated in boosting the classification performance of Convolutional Neural Networks (CNNs). Singular Value Decomposition (SVD) is used in GCP to compute the matrix square root. However, the approximate matrix square root calculated using Newton-Schulz iteration \cite{li2018towards} outperforms the accurate one computed via SVD \cite{li2017second}. We empirically analyze the reason behind the performance gap from the perspectives of data precision and gradient smoothness. Various remedies for computing smooth SVD gradients are investigated. Based on our observation and analyses, a hybrid training protocol is proposed for SVD-based GCP meta-layers such that competitive performances can be achieved against Newton-Schulz iteration. Moreover, we propose a new GCP meta-layer that uses SVD in the forward pass, and Pad\'e Approximants in the backward propagation to compute the gradients. The proposed meta-layer has been integrated into different CNN models and achieves state-of-the-art performances on both large-scale and fine-grained datasets., Comment: Accepted by ICCV21 as poster presetation

High penetration of renewable generation poses great challenge to power system operation due to its uncertain nature. In droop-controlled microgrids, the voltage volatility induced by renewable uncertainties is aggravated by the high droop gains. This paper proposes a chance-constrained optimal power flow (CC-OPF) problem with power flow routers (PFRs) to better regulate the voltage profile in microgrids. PFR refer to a general type of network-side controller that brings more flexibility to the power network. Comparing with the normal CC-OPF that relies on power injection flexibility only, the proposed model introduces a new dimension of control from power network to enhance system performance under renewable uncertainties. Since the inclusion of PFRs complicates the problem and makes common solvers no longer apply directly, we design an iterative solution algorithm. For the subproblem in each iteration, chance constraints are transformed into equivalent deterministic ones via sensitivity analysis, so that the subproblem can be efficiently solved by the convex relaxation method. The proposed method is verified on the modified IEEE 33-bus system and the results show that PFRs make a significant contribution to mitigating the voltage volatility and make the system operate in a more economic and secure way., Comment: 8 pages

Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification method for the AC optimal power flow with flexible line impedances. First, it is discovered that a flexible-impedance line is equivalent to a constant-impedance line linking a pair of transformers with correlated and continuously adjustable tap ratios. Then, with this circuit equivalent, the original optimization problem is reformulated into a semi-definite program under the existing convex relaxation framework, which improves the solution tractability and optimality in an easy-to-implement manner. The proposed method is verified by numerical tests on the IEEE 118-bus system., Comment: 4 pages, 2 figures

The impasse surface is an important concept in the differential-algebraic equation (DAE) model of power systems, which is associated with short-term voltage collapse. This paper establishes a necessary condition for a system trajectory hitting the impasse surface. The condition is in terms of admittance matrices regarding the power network, generators and loads, which specifies the pattern of interaction between those system components that can induce voltage collapse. It applies to generic DAE models featuring high-order synchronous generators, static loads, induction motor loads and lossy power networks. We also identify a class of static load parameters that prevent power systems from hitting the impasse surface; this proves a conjecture made by Hiskens that has been unsolved for decades. Moreover, the obtained results lead to an early indicator of voltage collapse and a novel viewpoint that inductive compensation to the power network has a positive effect on preventing short-term voltage collapse, which are verified via numerical simulations., Comment: 8 pages, 5 figures

Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching (OTS) to ensure network connectedness strictly. To fill this gap, this paper proposes a set of linear connectedness constraints by leveraging the equivalence between network connectedness and feasibility of the vertex potential equation of an electrical flow network. The proposed constraints are compatible with any existing OTS models to ensure topology connectedness. Furthermore, we develop a reduction version for the proposed connectedness constraints, seeking for improvement of computational efficiency. Finally, numerical studies with a DC OTS model show the deficiency of OTS formulations without full consideration of network connectedness and demonstrate the effectiveness of the proposed constraints. The computational burden caused by the connectedness constraints is moderate and can be remarkably relieved by using the reduced version., Comment: 6 pages, 5 figures

Widespread utilization of renewable energy sources (RESs) in subtransmission systems causes serious problems on power quality, such as voltage violations, leading to significant curtailment of renewables. This is due to the inherent variability of renewables and the high R/X ratio of the subtransmission system. To achieve full utilization of renewables, battery energy storage systems (BESSs) are commonly used to mitigate the negative effects of massive fluctuations of RESs. Power flow router (PFR), which can be regarded as a general type of network-side controller, has also been verified to enhance the grid flexibility for accommodating renewables. In this paper, we investigate the value of PFR in helping BESSs for renewable power accommodation. The performance of PFR is evaluated with the minimum BESS capacity required for zero renewable power curtailment with and without PFRs. The operational constraints of BESSs and the terminal voltage property of PFRs are considered in a multi-period optimization model. The proposed model is tested through numerical simulations on a modified IEEE 30-bus subtransmission system and a remarkable result shows that 15% reduction of BESS capacity can be achieved by installing PFRs on a single line., Comment: 5 pages, 5 figures

This paper proposes a robust transient stability constrained optimal power flow problem that addresses renewable uncertainties by the coordination of generation re-dispatch and power flow router (PFR) tuning.PFR refers to a general type of network-side controller that enlarges the feasible region of the OPF problem. The coordination between network-side and generator-side control in the proposed model is more general than the traditional methods which focus on generation dispatch only. An offline-online solution framework is developed to solve the problem efficiently. Under this framework the original problem is significantly simplified, so that we only need to solve a low-dimensional deterministic problem at the online stage to achieve real-time implementation with a high robustness level. The proposed method is verified on the modified New England 39-bus system. Numerical results demonstrate that the proposed method is efficient and shows good performance on economy and robustness., Comment: 10 pages, 8 figures