Searcharxiv⌕ Search

arXiv subjects

Zechun Hu

Publications and source records attributed to Zechun Hu.

At least 19 recordsLinked to original sources
arXiv2026

Reliability-Dependent Scaling Laws of Deterministic Identification over Binary Symmetric Channels

In this paper, we study the asymptotic behavior of deterministic identification (DID) over binary symmetric channels (BSCs) under vanishing error constraints. By introducing a minimum error parameter, we characterize how different error-decay regimes affect the achievable DID rate. General achievability and converse bounds are derived, with explicit asymptotic characterizations in the large-deviation, moderate-deviation, and central-limit regimes. The achievability analysis combines coding-theoretic constructions with probabilistic concentration techniques, while the converse links statistical distinguishability to the minimum-distance structure of DID codes via total variation and Hamming-type bounds. Our results show that the asymptotic behavior of DID over BSCs is governed by a Hamming-shell concentration geometry of channel outputs, offering insights into the finite-blocklength behavior of deterministic identification over discrete-output channels.

cs.IT↗
arXiv2026

Perturbation Power Selection for First-Error Delay Maximization in Enhanced SC Decoding

In this paper, we analyze the effect of perturbation power in delaying the first error position, i.e., the first information bit incorrectly decoded by the successive cancellation (SC) decoding. It is conducted over the finite-length perturbation-enhanced SC (PE-SC) decoding paradigm. We show that the FEP delaying probability exhibits a non-monotonic dependence on the perturbation power \(\sigma_{p}^{2}\). Based on this property, an efficient perturbation power selection algorithm that maximizes the delay probability is proposed to enhance the perturbation efficiency. It results in a more efficient perturbation power selection in finite-length PE-SC decoding.

cs.IT↗
arXiv2026

PolyFormer: learning efficient reformulations for scalable optimization under complex physical constraints

Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric knowledge, i.e., physics-informed machine learning (PIML), offer a promising pathway for efficient solution. Here, we introduce PolyFormer, which opens a new direction for PIML in prescriptive optimization tasks, where physical and geometric knowledge is not merely used to regularize learning models, but to simplify the problems themselves. PolyFormer captures geometric structures behind constraints and transforms them into efficient polytopic reformulations, thereby decoupling problem complexity from solution difficulty and enabling off-the-shelf optimization solvers to efficiently produce feasible solutions with acceptable optimality loss. Through evaluations across three important problems (large-scale resource aggregation, network-constrained optimization, and optimization under uncertainty), PolyFormer achieves computational speedups up to 6,400-fold and memory reductions up to 99.87%, while maintaining solution quality competitive with or superior to state-of-the-art methods. These results demonstrate that PolyFormer provides an efficient and reliable solution for scalable constrained optimization, expanding the scope of PIML to prescriptive tasks in scientific discovery and engineering applications.

cs.LG↗
arXiv2026

Limit behavior of linearly edge-reinforced random walks on the half-line

Motivated by the article [M. Takei, Electron. J. Probab. 26 (2021), article no. 104], we study the limit behavior of linearly edge-reinforced random walks on the half-line $\mathbb{Z}_+$ with reinforcement parameter $\delta>0$, and each edge $\{x,x+1\}$ has the initial weight $x^{\alpha}\ln^{\beta}x$ for $x > 1$ and $1$ for $x = 0, 1$. The aim of this paper is to study the almost sure limit behavior of the walk in the recurrent regime, and extend the results of Takei mentioned above.

math.PR↗
arXiv2025

Favorite sites of one-dimensional asymmetric simple random walk

In this paper, we study favorite sites of one-dimensional asymmetric simple random walks. We show that almost surely, for any fixed integer $r\geq 1$, ``$r$ favorite sites" occurs infinitely often. We also give the asymptotic growth rate of the number of favorite sites.

math.PR↗
arXiv2025

Probabilistic Forecasting Method for Offshore Wind Farm Cluster under Typhoon Conditions: a Score-Based Conditional Diffusion Model

Offshore wind power (OWP) exhibits significant fluctuations under typhoon conditions, posing substantial challenges to the secure operation of power systems. Accurate forecasting of OWP is therefore essential. However, the inherent scarcity of historical typhoon data and stochasticity of OWP render traditional point forecasting methods particularly difficult and inadequate. To address this challenge and provide grid operators with the comprehensive information necessary for decision-making, this study proposes a score-based conditional diffusion model (SCDM) for probabilistic forecasting of OWP during typhoon events. First, a knowledge graph algorithm is employed to embed historical typhoon paths as vectors. Then, a deterministic network is constructed to predict the wind power under typhoon conditions based on these vector embeddings. Finally, to better characterize prediction errors, a denoising network is developed. At the core of this approach is a mean-reverting stochastic differential equation (SDE), which transforms complex error distributions into a standard Gaussian, enabling the sampling of forecasting errors using a reverse-time SDE. The probabilistic forecasting results are reconstructed by combining deterministic forecasts with sampled errors. The proposed method is evaluated using real-world data from a cluster of 9 offshore wind farms. Results demonstrate that under typhoon conditions, our approach outperforms baseline models for both deterministic and probabilistic metrics, verifying the effectiveness of the approach.

eess.SY↗
arXiv2024

A study on the $F$-distribution motivated by Chv\'{a}tal's theorem

Let $X_{d_1, d_2}$ be an $F$-random variable with parameters $d_1$ and $d_2,$ and expectation $E[X_{d_1, d_2}]$. In this paper, for any $\kappa>0,$ we investigate the infimum value of the probability $P(X_{d_1, d_2}\leq \kappa E[X_{d_1, d_2}])$. Our motivation comes from Chv\'{a}tal's theorem on the binomial distribution.

math.PR↗
arXiv2024

Quantifying and Optimizing the Time-Coupled Flexibilities at the Distribution-Level for TSO-DSO Coordination

The flexibilities provided by the distributed energy resources (DERs) in distribution systems enable the coordination of transmission system operator (TSO) and distribution system operators (DSOs). At the distribution level, the flexibilities should be optimized for participation in the transmission system operation. This paper first proposes a flexibility quantification method that quantifies the costs of providing flexibilities and their values to the DSO in the TSO-DSO coordination. Compared with traditional power-range-based quantification approaches that are mainly suitable for generators, the proposed method can directly capture the time-coupling characteristics of DERs' individual and aggregated flexibility regions. Based on the quantification method, we further propose a DSO optimization model to activate the flexibilities from DER aggregators in the distribution system for energy arbitrage and ancillary services provision in the transmission system, along with a revenue allocation strategy that ensures a non-profit DSO. Numerical tests on the IEEE test system verify the proposed methods.

eess.SY↗
arXiv2024

Multiple Joint Chance Constraints Approximation for Uncertainty Modeling in Dispatch Problems

Uncertainty modeling has become increasingly important in power system decision-making. The widely-used tractable uncertainty modeling method-chance constraints with Conditional Value at Risk (CVaR) approximation, can be overconservative and even turn an originally feasible problem into an infeasible one. This paper proposes a new approximation method for multiple joint chance constraints (JCCs) to model the uncertainty in dispatch problems, which solves the conservativeness and potential infeasibility concerns of CVaR. The proposed method is also convenient for controlling the risk levels of different JCCs, which is necessary for power system applications since different resources may be affected by varying degrees of uncertainty or have different importance to the system. We then formulate a data-driven distributionally robust chance-constrained programming model for the power system multiperiod dispatch problem and leverage the proposed approximation method to solve it. In the numerical simulations, two small general examples clearly demonstrate the superiority of the proposed method, and the results of the multiperiod dispatch problem on IEEE test cases verify its practicality.

math.OC↗
arXiv2023

DC-based Security Constraints Formulation: A Perspective of Primal-Dual Interior Point Method

The DC network security constraints have been extensively studied in numerous power system problems, such as optimal power flow (OPF), security-constrained economic dispatch (SCED), and security-constrained unit commitment (SCUC). Linear shift factors, i.e., power transfer distribution factors (PTDFs), are widely applied to replace DC power flow constraints. However, the PTDF matrix is extremely dense, making it difficult to solve security-constraint optimization problems. This paper analyzes/investigates the computational inefficiency of PTDF-based security constraints from the sparse structure perspective of the primal-dual interior point method(IPM). Additionally, a matrix transformation method is proposed for restoring the sparsity of the linear system during IPM iterations. It turns out that the transformation method is equivalent to solving the original optimization problem expressed in pure voltage angle, which preserves the sparsity structure but introduces additional variables and constraints proportional to one to two times the total number of buses. The regular B-$\theta$ formulation is also a variant of the proposed transformation. Numerical studies show that sparsity rather than the size of variables and constraints is the key factor impacting the speed of solving convex quadratic problems (QP), i.e., OPF and SCED problems. In contrast, sparsity is less desirable when solving a mixed integer problem (MIP), such as the SCUC problem, where reoptimization techniques are significantly more critical and the dual simplex method is typically employed rather than IPM.

math.OC↗
arXiv2023

Improved Inner Approximation for Aggregating Power Flexibility in Active Distribution Networks and its Applications

Concise and reliable modeling for aggregating power flexibility of distributed energy resources in active distribution networks (ADNs) is a crucial technique for coordinating transmission and distribution networks. Our recent research has successfully derived an explicit expression for the exact aggregation model (EAM) of power flexibility at the substation level under linearized distribution network constraints. The EAM, however, is impractical for decision-making purposes due to its exponential complexity. In this paper, we propose an inner approximation method for aggregating flexibility in ADNs that utilizes the properties of the EAM to improve performance. Specifically, the geometric prototype of the inner approximation model is defined according to a subset of the coefficient vector set of the EAM, which enhances the accuracy. On the other hand, the computation efficiency of the inner approximation is also significantly improved by exploiting the regularity of coefficient vectors in the EAM in the parameter calculation process. The inner approximated flexibility model of ADNs is further incorporated into the security-constrained unit commitment problem as an application. Numerical simulations verify the effectiveness of the proposed method.

eess.SY↗
arXiv2021

Aggregated Feasible Region of Heterogeneous Demand-Side Flexible Resources -- Part I: Theoretical Derivation of the Exact Model

In the first part of the two-part series, the model to describe the exact aggregated feasible region (AFR) of multiple types of demand-side resources is derived. Based on a discrete-time unified individual model of heterogeneous resources, the calculation of AFR is, in fact, a feasible region projection problem. Therefore, the Fourier-Motzkin Elimination (FME) method is used for derivation. By analyzing the redundancy of all possible constraints in the FME process, the mathematical expression and calculation method for the exact AFR is proposed. The number of constraints is linear with the number of resources and is exponential with the number of time intervals, respectively. The computational complexity has been dramatically simplified compared with the original FME. However, the number of constraints in the model is still exponential and cannot be simplified anymore. Hence, In Part II of this paper, several approximation methods are proposed and analyzed in detail.

eess.SY↗
arXiv2021

Modeling of Frequency Security Constraints and Quantification of Frequency Control Reserve Requirements for Unit Commitment

The high penetration of converter-based renewable energy sources has brought challenges to the power system frequency control. It is essential to consider the frequency security constraints and frequency control reserve requirements in unit commitment (UC). Considering that the risk of frequency insecurity varies under the changeable operational condition, we propose to optimize the PFC droop gains and reserve capacities in the UC model to provide diverse control efforts in different risk levels adaptively. Copula theory is used to establish the joint distribution model among frequency control performance, secondary frequency control (SFC) reserve capacities, and power fluctuations. Then the distributionally robust optimization technique is utilized in the SFC reserve requirement determination to handle the possible error in the probability model. The UC simulation is conducted on IEEE 118-bus system to test the proposed optimal PFC droop gain strategy and SFC reserve requirement quantification method. Simulation results show that the proposed optimal PFC droop gain strategy is better than the traditional fixed PFC droop gain setting on economic efficiency and operational flexibility. Besides, the SFC reserve requirement calculated by the proposed method is more appropriate than the actual SFC reserve capacity in the historical operation.

eess.SY↗
arXiv2021

Automatic Generation Control Considering Uncertainties of the Key Parameters in the Frequency Response Model

The highly fluctuated renewable generations and electric vehicles have undergone tremendous growth in recent years. The majority of them are connected to the grid via power electronic devices, resulting in wide variation ranges for several key parameters in the frequency response model (FRM) such as system inertia and load damping factor. In this paper, an automatic generation control (AGC) method considering the uncertainties of these key parameters is proposed. First, the historical power system operation data following large power disturbances are used to identify the FRM key parameters offline. Second, the offline identification results and the normal operation data prior to the occurrence of the disturbance are used to train the online probability estimation model of the FRM key parameters. Third, the online estimation results of the FRM key parameters are used as the input, and the model predictive-based AGC signal optimization method is developed based on distributionally robust optimization (DRO) technology. Case studies conducted on the IEEE 118-Bus System show that the proposed AGC method outperforms the widely utilized PI-based control method in terms of performance and efficiency.

eess.SY↗
arXiv2021

An Extreme Learning Machine-Based System Frequency Nadir Constraint Linearization Method

Large-scale integration of converter-based renewable energy sources (RESs) into the power system will lead to a higher risk of frequency nadir limit violation and even frequency instability after the large power disturbance. Therefore, it is essential to consider the frequency nadir constraint (FNC) in power system scheduling. Nevertheless, the FNC is highly nonlinear and non-convex. The state-of-the-art method to simplify the constraint is to construct a low-order frequency response model at first, and then linearize the frequency nadir equation. In this letter, an extreme learning machine (ELM)-based network is built to de-rive the linear formulation of FNC, where the two-step fitting process is integrated into one training process and more details about the physical model of the generator are considered to reduce the fitting error. Simulation results show the superiority of the proposed method on the fitting accuracy.

eess.SY↗
arXiv2021

Data-Driven Scheduling of Electric Boiler with Thermal Storage for Providing Power Balancing Service

The rapid development of renewable energy has increased the peak to valley difference of the netload, making the netload following being a new challenge to the power system. Electric boiler with thermal storage (EBTS) occupies a non-negligible part of the load in the winter season in Northern China. EBTS operation optimization can not only save its own energy cost but also reduce the peak shaving and valley filling pressure of the system. To this end, the operation optimization of EBTS for providing the power balancing service is studied in this paper, which mainly includes three parts: First, the joint probability distribution between the predicted and actual temperatures is built by utilizing the Copula theory; Secondly, the actual temperatures are sampled based on the predicted temperatures of the next day, and the scenario set is generated by clustering these samples, where K-means clustering method are used; Thirdly, the stochastic operation optimization model of EBTS considering the uncertainty of outdoor temperature is constructed. Through the case study, it is found that the proposed method can save the total operation cost of the EBTS compared with the deterministic EBTS operation optimization model.

eess.SY↗
arXiv2021

Data-Driven Distributionally Robust Optimization for Real-Time Economic Dispatch Considering Secondary Frequency Regulation Cost

With the large-scale integration of renewable power generation, frequency regulation resources (FRRs) are required to have larger capacities and faster ramp rates, which increases the cost of the frequency regulation ancillary service. Therefore, it is necessary to consider the frequency regulation cost and constraint along with real-time economic dispatch (RTED). In this paper, a data-driven distributionally robust optimization (DRO) method for RTED considering automatic generation control (AGC) is proposed. First, a Copula-based AGC signal model is developed to reflect the correlations among the AGC signal, load power and renewable generation variations. Secondly, samples of the AGC signal are taken from its conditional probability distribution under the forecasted load power and renewable generation variations. Thirdly, a distributionally robust RTED model considering the frequency regulation cost and constraint is built and transformed into a linear programming problem by leveraging the Wasserstein metric-based DRO technique. Simulation results show that the proposed method can reduce the total cost of power generation and frequency regulation.

eess.SY↗