arXiv subjects

Yue Song

Publications and source records attributed to Yue Song.

85 records · Page 5Linked to original sources

arXiv2022

Convex Relaxation of AC Optimal Power Flow with Flexible Transmission Line Impedances

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.

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arXiv2022

Formulating Connectedness in Security-Constrained Optimal Transmission Switching Problems

This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed with the principle of preserving NC as much as possible within reasonable limits. By extending the electrical flow based NC constraints, a proposition is derived to associate different cases of NC with the optimum of a linear program, yielding the mathematical formulation of the NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further transformed into a tractable version which can be incorporated with existing SCOTS models without affecting the applicability of original solution approaches. Finally, case studies on various networks and SCOTS models demonstrate the efficacy of the proposed approach.

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arXiv2022

Disentangle Saliency Detection into Cascaded Detail Modeling and Body Filling

Salient object detection has been long studied to identify the most visually attractive objects in images/videos. Recently, a growing amount of approaches have been proposed all of which rely on the contour/edge information to improve detection performance. The edge labels are either put into the loss directly or used as extra supervision. The edge and body can also be learned separately and then fused afterward. Both methods either lead to high prediction errors near the edge or cannot be trained in an end-to-end manner. Another problem is that existing methods may fail to detect objects of various sizes due to the lack of efficient and effective feature fusion mechanisms. In this work, we propose to decompose the saliency detection task into two cascaded sub-tasks, \emph{i.e.}, detail modeling and body filling. Specifically, the detail modeling focuses on capturing the object edges by supervision of explicitly decomposed detail label that consists of the pixels that are nested on the edge and near the edge. Then the body filling learns the body part which will be filled into the detail map to generate more accurate saliency map. To effectively fuse the features and handle objects at different scales, we have also proposed two novel multi-scale detail attention and body attention blocks for precise detail and body modeling. Experimental results show that our method achieves state-of-the-art performances on six public datasets.

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arXiv2022

Fast Differentiable Matrix Square Root

Computing the matrix square root or its inverse in a differentiable manner is important in a variety of computer vision tasks. Previous methods either adopt the Singular Value Decomposition (SVD) to explicitly factorize the matrix or use the Newton-Schulz iteration (NS iteration) to derive the approximate solution. However, both methods are not computationally efficient enough in either the forward pass or in the backward pass. In this paper, we propose two more efficient variants to compute the differentiable matrix square root. For the forward propagation, one method is to use Matrix Taylor Polynomial (MTP), and the other method is to use Matrix Padé Approximants (MPA). The backward gradient is computed by iteratively solving the continuous-time Lyapunov equation using the matrix sign function. Both methods yield considerable speed-up compared with the SVD or the Newton-Schulz iteration. Experimental results on the de-correlated batch normalization and second-order vision transformer demonstrate that our methods can also achieve competitive and even slightly better performances. The code is available at \href{https://github.com/KingJamesSong/FastDifferentiableMatSqrt}{https://github.com/KingJamesSong/FastDifferentiableMatSqrt}.

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arXiv2021

Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling?

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 Padé 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.

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arXiv2020

Ensuring Network Connectedness in Optimal Transmission Switching Problems

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.

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arXiv2020

Chance-Constrained OPF in Droop-Controlled Microgrids with Power Flow Routers

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.

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arXiv2020

A Hierarchical Framework for Ambient Signals based Load Modeling with Exploring the Hidden Quasi-convexity

Load modeling is an important issue in modeling a power system. The approach of ambient signals-based load modeling (ASLM) was recently proposed to better track the time-varying changes of load models. To improve computation efficiency and model structure complexity, a hierarchical framework for ASLM is proposed in this paper. Through this framework, the hidden quasi-convexity of load modeling problem is explored for the first time, and more complicated static load model structures can be applied. In the upper stage, the identification of dynamic load parameters is regarded as an optimization problem. In the lower stage, the optimal static load parameters are obtained through linear regression for a given group of dynamic load parameters. Afterwards, the regression residuals are regarded as the objective function (OF) of the upper stage optimization problem. The proposed method is validated by the case study results in Guangdong Power Grid. The results have shown that the OF is mostly quasi-convex after the transformation of induction motor model, which provides the basis for the application of gradient-based optimization algorithm. The case study results also validate that the proposed approach has better computation efficiency and model structure complexity compared with the previous ASLM approach.

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arXiv2020

Robust Transient Stability Constrained Optimal Power Flow with Power Flow Routers Considering Renewable Uncertainties

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.

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arXiv2020

Reducing BESS Capacity for Accommodating Renewables in Subtransmission Systems with Power Flow Routers

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.

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arXiv2019

On Extension of Effective Resistance with Application to Graph Laplacian Definiteness and Power Network Stability

This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the traditional definitions that only apply to a pair of nodes. The monotonicity and convexity properties are preserved by the extended definitions. The extended definitions provide new insights into graph Laplacian definiteness and power network stability. It is proved that the Laplacian matrix of a signed graph is positive semi-definite with only one zero eigenvalue if and only if the effective conductances between some specific pairs of node sets are positive. Also the number of Laplacian negative eigenvalues is upper bounded by the number of negative weighted edges. In addition, new conditions for the small-disturbance angle stability, hyperbolicity and type of power system equilibria are established, which intuitively interpret angle instability as the electrical antagonism between certain two sets of nodes in the defined active power flow graph. Moreover, a novel optimal power flow (OPF) model with effective conductance constraints is formulated, which significantly enhances power system transient stability. By the properties of extended effective conductance, the proposed OPF model admits a convex relaxation representation that achieves global optimality.

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arXiv2019

Radiality Constraints for Resilient Reconfiguration of Distribution Systems: Formulation and Application to Microgrid Formation

Network reconfiguration is an effective strategy for different purposes of distribution systems (DSs), e.g., resilience enhancement. In particular, DS automation, distributed generation integration and microgrid (MG) technology development, etc., are empowering much more flexible reconfiguration and operation of the system, e.g., DSs or MGs with flexible boundaries. However, the formulation of DS reconfiguration-related optimization problems to include those new flexibilities is non-trivial, especially for the issue of topology, which has to be radial. That is, existing methods of formulating radiality constraints can cause underutilization of DS flexibilities. Thus, this work proposes a new method for radiality constraints formulation fully enabling the topological and some other related flexibilities of DSs, so that the reconfiguration-related optimization problems can have extended feasibility and enhanced optimality. Graph-theoretic supports are provided to certify its theoretical validity. As integer variables are involved, we also analyze the tightness and compactness issues. The proposed radiality constraints are specifically applied to post-disaster MG formation, which is involved in many DS resilience-oriented service restoration and/or infrastructure recovery problems. The resulting new MG formation model, which allows more flexible merge and/or separation of sub-grids, etc., establishes superiority over the models in the literature. Case studies are conducted on two test systems.

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arXiv2019

Distributed Inter-Area Oscillation Damping Control for Power Systems by Using Wind Generators and Load Aggregators

This paper investigates the potential of wind turbine generators (WTGs) and load aggregators (LAs) to provide supplementary damping control services for low frequency inter-area oscillations (LFOs) through the additional distributed damping control units (DCUs) proposed in their controllers. In order to provide a scalable methodology for the increasing number of WTGs and LAs, a novel distributed control framework is proposed to coordinate damping controllers. Firstly, a distributed algorithm is designed to reconstruct the system Jacobian matrix for each damping bus (buses with damping controllers). Thus, the critical LFO can be identified locally at each damping bus by applying eigen-analysis to the obtained system Jacobian matrix. Then, if the damping ratio of the critical LFO is less than a preset threshold, the control parameters of DCUs will be tuned in a distributed and coordinated manner to improve the damping ratio and minimize the total control cost at the same time. The proposed control framework is tested in a modified IEEE 39-bus test system. The simulation results with and without the proposed control framework are compared to demonstrate the effectiveness of the proposed framework.

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