arXiv subjects
Publications and source records attributed to Wei Gu.
In this paper we apply two-dimensional supersymmetric gauge theories to directly construct a new Bethe ansatz for the wavefunctions of the q-boson hopping model, and then derive the q-boson algebras from this ansatz.
As an effective emulator of ill-conditioned power flow, continuous Newton methods (CNMs) have been extensively investigated using explicit and implicit numerical integration algorithms. Explicit CNMs are prone to non-convergence issues due to their limited stable region, while implicit CNMs introduce additional iteration-loops of nonlinear equations. Faced with this, we propose a semi-implicit version of CNM. We formulate the power flow equations as a set of differential algebraic equations (DAEs), and solve the DAEs with the stiffly accurate Rosenbrock type method (SARM). The proposed method succeeds the numerical robustness from the implicit CNM framework while prevents the iterative solution of nonlinear systems, hence revealing higher convergence speed and computation efficiency. A new 4-stage 3rd-order hyper-stable SARM, together with a 2nd-order embedded formula to control the step size, is constructed to further accelerate convergence by tuning the damping factor. Case studies on ill-conditioned systems verified the alleged performance. An algorithm extension for MATPOWER is made available on Github for benchmarking.
In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by proving a Nakayama type result for quantum K theory: if the conjectured set of relations deforms a complete set of relations of the classical K theory ring, then they must form a complete set of relations for the quantum K ring. We prove the conjectured presentation in the case of the incidence varieties, and we show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety. Finally, we briefly revisit the change of variables relating the mathematics and physics presentations.
This letter first explores the solution uniqueness of the data-driven modeling of price-responsive flexible loads (PFL). The PFL on the demand side is critical in modern power systems. An accurate PFL model is fundamental for system operations. However, whether the PFL model can be uniquely and correctly identified from operational data remains unclear. To address this, we analyze the structural and practical identifiability of the PFL model, deriving the dataset condition that guarantees the solution uniqueness. Besides, we point out the practical implications of the results. Numerical tests validate this work.
Relying heavily on the secure supply of natural gas, the modern clean electric power systems are prone to the gas disturbances induced by the inherent rupture and leakage faults. For the first time, this paper studies the cross-system propagation speed of these faults using a simulation-based approach. Firstly, we establish the differential algebraic equation models of the rupture and leakage faults respectively. The boundary conditions at the fault locations are derived using the method of characteristics. Secondly, we propose utilizing a semi-implicit approach to perform post-fault simulations. The approach, based on the stiffly-accurate Rosenbrock scheme, possesses the implicit numerical stability and explicit computation burdens. Therefore, the high-dimensional and multi-time-scale stiff models can be solved in an efficient and robust way. Thirdly, to accurately locate the simulation events, which can not be predicted a priori, we propose a critical-time-location strategy based on the continuous Runge-Kutta approach. In case studies, we verified the accuracy and the efficiency superiority of the proposed simulation approach. The impacts of gas faults on gas and power dynamics were investigated by simulation, where the critical events were identified accurately. We found that the fault propagation speed mainly depends on the fault position and is influenced by the pipe frictions. The bi-directional coupling between gas and power may lead to cascading failures.
We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation is obtained by quantum deforming the product of the Hirzebruch $λ_y$ classes of the tautological bundles. In physics, the $λ_y$ classes arise as certain Wilson line operators. The second presentation is obtained from the Coulomb branch equations involving the partial derivatives of a twisted superpotential from supersymmetric gauge theory. This is closest to a presentation obtained by Gorbounov and Korff, utilizing integrable systems techniques. Algebraically, we relate the Coulomb and Whitney presentations utilizing transition matrices from the (equivariant) Grothendieck polynomials to the (equivariant) complete homogeneous symmetric polynomials. Along the way, we calculate K-theoretic Gromov-Witten invariants of wedge powers of the tautological bundles on $\mathrm{Gr}(k;n)$, using the `quantum=classical' statement.
Accurate load forecasting is crucial for maintaining the power balance between generators and consumers,particularly with the increasing integration of renewable energy sources, which introduce significant intermittent volatility. With the advancement of data-driven methods, machine learning and deep learning models have become the predominant approaches for load forecasting tasks. In recent years, pre-trained large language models (LLMs) have achieved significant progress, demonstrating superior performance across various fields. This paper proposes a load forecasting method based on LLMs, offering not only precise predictive capabilities but also broad and flexible applicability. Additionally, a data modeling method is introduced to effectively transform load sequence data into natural language suitable for LLM training. Furthermore, a data enhancement strategy is designed to mitigate the impact of LLM hallucinations on forecasting results. The effectiveness of the proposed method is validated using two real-world datasets. Compared to existing methods, our approach demonstrates state-of-the-art performance across all validation metrics.
One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural networks to estimate players' cost functions. Depending on the availability of data, we propose two approaches (a) the two-stage approach: we need the data pair of players' strategy and relevant function value to first learn the players' cost functions by monotonic neural networks or graph neural networks, and then solve the Nash equilibrium with the learned neural networks; (b) the joint approach: we use the data of partial true observation of the equilibrium and contextual information (e.g., weather) to optimize and learn Nash equilibrium simultaneously. The problem is formulated as an optimization problem with equilibrium constraints and solved using a modified Backpropagation Algorithm. The proposed methods are validated in numerical experiments.
The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear partial differential equations (PDE), making the dispatch problem of the EG-IES a complicated optimization model constrained by nonlinear PDE. To address it, we propose a globally linearized gas network model based on the Koopman operator theory, avoiding the commonly used local linearization and spatial discretization. Particularly, we propose a data-driven Koopman operator approximation approach for the globally linearized gas network model based on the extended dynamic mode decomposition, in which a physics-informed stability constraint is derived and embedded to improve the generalization ability and accuracy of the model. Based on this, we develop an optimal dispatch model for the EG-IES that first considers the nonlinear gas dynamics in the NGS. The case study verifies the effectiveness of this work. Simulation results reveal that the commonly used locally linearized gas network model fails to accurately capture the dynamic characteristics of NGS, bringing potential security threats to the system.
We utilize physics arguments, and the nonabelian/abelian correspondence, to relate the Givental and Lee's quantum K theory ring of Grassmannians to a twisted variant of the quantum cohomology ring. Furthermore, the quantum K pairing is related to correlators arising from supersymmetric localization. We state some mathematical conjectures, which we illustrate in several examples.
The district heating network (DHN) is essential in enhancing the operational flexibility of integrated energy systems (IES). Yet, it is hard to obtain an accurate and concise DHN model for the operation owing to complicated network features and imperfect measurements. Considering this, this paper proposes a physical-ly informed data-driven aggregate model (AGM) for the DHN, providing a concise description of the source-load relationship of DHN without exposing network details. First, we derive the analytical relationship between the state variables of the source and load nodes of the DHN, offering a physical fundament for the AGM. Second, we propose a physics-informed estimator for the AGM that is robust to low-quality measurements, in which the physical constraints associated with the parameter normalization and sparsity are embedded to improve the accuracy and robustness. Finally, we propose a physics-enhanced algorithm to solve the nonlinear estimator with non-closed constraints efficiently. Simulation results verify the effectiveness of the proposed method.
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained voltage-stability-constrained optimal power flow (CC-VSC-OPF) problem, which is hindered by the implicit voltage stability index and intractable chance constraints Leveraging a neural network (NN)-based surrogate model, the stability constraint is explicitly formulated and directly integrated into the model. To perform uncertainty propagation without relying on presumptions or complicated transformations, an advanced data-driven method known as adaptive polynomial chaos expansion (APCE) is developed. To extend the scalability of the proposed algorithm, a partial least squares (PLS)-NN framework is designed, which enables the establishment of a parsimonious surrogate model and efficient computation of large-scale Hessian matrices. In addition, a dimensionally decomposed APCE (DD-APCE) is proposed to alleviate the "curse of dimensionality" by restricting the interaction order among random variables. Finally, the above techniques are merged into an iterative scheme to update the operation point. Simulation results reveal the cost-effective performances of the proposed method in several test systems.
The thermal inertia of buildings brings considerable flexibility to the heating and cooling load, which is known to be a promising demand response resource. The aggregate model that can describe the thermal dynamics of the building cluster is an important interference for energy systems to exploit its intrinsic thermal inertia. However, the private information of users, such as the indoor temperature and heating/cooling power, needs to be collected in the parameter estimation procedure to obtain the aggregate model, causing severe privacy concerns. In light of this, we propose a novel privacy-preserved parameter estimation approach to infer the aggregate model for the thermal dynamics of the building cluster for the first time. Using it, the parameters of the aggregate thermal dynamic model (ATDM) can be obtained by the load aggregator without accessing the individual's privacy information. More specifically, this method not only exploits the block coordinate descent (BCD) method to resolve its non-convexity in the estimation but investigates the transformation-based encryption (TE) associated with its secure aggregation protocol (SAP) techniques to realize privacy-preserved computation. Its capability of preserving privacy is also theoretically proven. Finally, simulation results using real-world data demonstrate the accuracy and privacy-preserved performance of our proposed method.
This paper proposes an image-based algorithm for detecting and cleaning the wind turbine abnormal data based on wind power curve (WPC) images. The abnormal data are categorized into three types, negative points, scattered points, and stacked points. The proposed algorithm includes three steps, data pre-cleaning, normal data extraction, and data marking. The negative abnormal points, whose wind speed is greater than cut-in speed and power is below zero, are first filtered in the data pre-cleaning step. The scatter figure of the rest wind power data forms the WPC image and corresponding binary image. In the normal data extraction step, the principle part of the WPC binary image, representing the normal data, is extracted by the mathematical morphology operation (MMO). The optimal parameter setting of MMO is determined by minimizing the dissimilarity between the extracted principle part and the reference WPC image based on Hu moments. In the data mark step, the pixel points of scattered and stacked abnormal data are successively identified. The mapping relationship between the wind power points and image pixel points is built to mark the wind turbine normal and abnormal data. The proposed image-based algorithm is compared with k-means, local outlier factor, combined algorithm based on change point grouping algorithm and quartile algorithm (CA). Numerous experiments based on 33 wind turbines from two wind farms are conducted to validate the effectiveness, efficiency, and universality of the proposed method.
Is there a statistical difference between Naive Bayes and Random Forest in terms of recall, f-measure, and precision for predicting software defects? By utilizing systematic literature review and meta-analysis, we are answering this question. We conducted a systematic literature review by establishing criteria to search and choose papers, resulting in five studies. After that, using the meta-data and forest-plots of five chosen papers, we conducted a meta-analysis to compare the two models. The results have shown that there is no significant statistical evidence that Naive Bayes perform differently from Random Forest in terms of recall, f-measure, and precision.
With the sustained attention on carbon neutrality, the personal carbon trading (PCT) scheme has been embraced as an auspicious paradigm for scaling down carbon emissions. To facilitate the simultaneous clearance of energy and carbon allowance inside the energy community while hedging against uncertainty, a joint trading framework is proposed in this article. The energy trading is implemented in a peer-to-peer (P2P) manner without the intervention of a central operator, and the uncertainty trading is materialized through procuring reserve of conventional generators and flexibility of users. Under the PCT scheme, carbon allowance is transacted via a sharing mechanism. Possible excessive carbon emissions due to uncertainty balance are tackled by obliging renewable agents to procure sufficient carbon allowances, following the consumption responsibility principle. A two-stage iterative method consisting of tightening McCormick envelope and alternating direction method of multipliers (ADMM) is devised to transform the model into a mixed-integer second-order cone program (MISOCP) and to allow for a fully decentralized market-clearing procedure. Numerical results have validated the effectiveness of the proposed market model.
We show how a Heisenberg spin chain emerges from the two-dimensional ${\mathcal N}$=(2,2) gauge theory at an intermediate scale, which relies on the renormalization group flow guided by the global symmetries and the dynamics of domain walls. The discussion of higher-dimensional gauge theories with four supercharges is similar by compactifying them into two dimensions. Instead of utilizing the bosonic fields solely in the literature, adopting the fermionic degrees of freedom of gauge theory is a crucial step in our construction. From the perspective of the spin chain, we observe that the Seiberg(-like) duality between two gauge theories is manifest since it is a finite symmetry in the closed spin chain. Based on this, we further conjecture gauge theories with the same global symmetries could be unified into a single system: the Heisenberg spin chain. At least, we prove this conjecture at the intermediate scale. Finally, we also comment on other formulations of an integrable system centered on the Heisenberg spin chain.
Quasi-dynamic energy flow calculation is an indispensable tool for the heat and electricity integrated energy system (HE-IES) analysis. One solves the nonlinear partial differential algebraic equations to obtain thermal, hydraulic and electric variations. However, mainstream iteration solvers face the challenges of inefficiency and bad robustness. For one thing, the frequent update and factorization of Jacobian matrices utilize high CPU time. For another, the per-step iteration numbers grow exponentially as the system loading level creeps up. This paper presents a novel non-iterative algorithm for the quasi-dynamic energy flow calculation. The kernel of the proposed algorithm is to transform these nonlinear equations into linear recursive ones, by solving which, we obtain explicit closed-form solutions of unknown variables. In each step, the proposed algorithm requires only one matrix factorization and fixed times of arithmetic operations regardless of the loading levels, so that it achieves small and consistent per-step time costs. A semi-discrete scheme is used in PDE solution to avoid dissipative and dispersive errors that are often overlooked in previous literature. To ensure convergence, we also propose to control the temporal step sizes adaptively by estimating the simulation errors. Case studies showed that the proposed method manifested efficient and robust time performance compared with the iterative algorithms, and meanwhile preserved high accuracy.