Hao Zhu

Hao Zhu, Georgios B. Giannakis

This paper has been withdrawn by the authors

Hao Zhu, Jia Li, Cuiyun Gao et al. · pku

Large language models (LLMs) have achieved remarkable progress in code understanding tasks. However, they demonstrate limited performance in vulnerability detection and struggle to distinguish vulnerable code from patched code. We argue that LLMs lack understanding of security specifications -- the expectations about how code should behave to remain safe. When code behavior differs from these expectations, it becomes a potential vulnerability. However, such knowledge is rarely explicit in training data, leaving models unable to reason about security flaws. We propose VulInstruct, a specification-guided approach that systematically extracts security specifications from historical vulnerabilities to detect new ones. VulInstruct constructs a specification knowledge base from two perspectives: (i) General specifications from high-quality patches across projects, capturing fundamental safe behaviors; and (ii) Domain-specific specifications from repeated violations in particular repositories relevant to the target code. VulInstruct retrieves relevant past cases and specifications, enabling LLMs to reason about expected safe behaviors rather than relying on surface patterns. We evaluate VulInstruct under strict criteria requiring both correct predictions and valid reasoning. On PrimeVul, VulInstruct achieves 45.0% F1-score (32.7% improvement) and 37.7% recall (50.8% improvement) compared to baselines, while uniquely detecting 24.3% of vulnerabilities -- 2.4x more than any baseline. In pair-wise evaluation, VulInstruct achieves 32.3% relative improvement. VulInstruct also discovered a previously unknown high-severity vulnerability (CVE-2025-56538) in production code, demonstrating practical value for real-world vulnerability discovery. All code and supplementary materials are available at https://github.com/zhuhaopku/VulInstruct-temp.

Hao Zhu, Georgios B. Giannakis

An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In addition to nonconvexity, SE is challenged by data integrity and cyber-security issues. Unfortunately, existing robust (R-) SE schemes employed routinely in practice rely on iterative solvers, which are sensitive to initialization and cannot ensure global optimality. A novel R-SE approach is formulated here by capitalizing on the sparsity of an overcomplete outlier vector model. Observability and identifiability issues of this model are investigated, and neat links are established between R-SE and error control coding. The \emph{convex} semidefinite relaxation (SDR) technique is further pursued to render the nonconvex R-SE problem efficiently solvable. The resultant algorithm markedly outperforms existing iterative alternatives, as corroborated through numerical tests on the standard IEEE 30-bus system.

Hao Zhu, Georgios B. Giannakis

Fast and accurate unveiling of power line outages is of paramount importance not only for preventing faults that may lead to blackouts, but also for routine monitoring and control tasks of the smart grid, including state estimation and optimal power flow. Existing approaches are either challenged by the \emph{combinatorial complexity} issues involved, and are thus limited to identifying single- and double-line outages; or, they invoke less pragmatic assumptions such as \emph{conditionally independent} phasor angle measurements available across the grid. Using only a subset of voltage phasor angle data, the present paper develops a near real-time algorithm for identifying multiple line outages at the affordable complexity of solving a quadratic program via block coordinate descent iterations. The novel approach relies on reformulating the DC linear power flow model as a \emph{sparse} overcomplete expansion, and leveraging contemporary advances in compressive sampling and variable selection using the least-absolute shrinkage and selection operator (Lasso). Analysis and simulated tests on the standard IEEE 118-bus system confirm the effectiveness of lassoing line changes in the smart power grid.

Kaiqing Zhang, Wei Shi, Hao Zhu et al.

In current power distribution systems, one of the most challenging operation tasks is to coordinate the network- wide distributed energy resources (DERs) to maintain the stability of voltage magnitude of the system. This voltage control task has been investigated actively under either distributed optimization-based or local feedback control-based characterizations. The former architecture requires a strongly-connected communication network among all DERs for implementing the optimization algorithms, a scenario not yet realistic in most of the existing distribution systems with under-deployed communication infrastructure. The latter one, on the other hand, has been proven to suffer from loss of network-wide op- erational optimality. In this paper, we propose a game-theoretic characterization for semi-local voltage control with only a locally connected communication network. We analyze the existence and uniqueness of the generalized Nash equilibrium (GNE) for this characterization and develop a fully distributed equilibrium-learning algorithm that relies on only neighbor-to-neighbor information exchange. Provable convergence results are provided along with numerical tests which corroborate the robust convergence property of the proposed algorithm.

Chaitra Niddodi, Shanny Lin, Sibin Mohan et al.

This paper focuses on the secure integration of distributed energy resources (DERs), especially pluggable electric vehicles (EVs), with the power grid. We consider the vehicle-to-grid (V2G) system where EVs are connected to the power grid through an aggregator. In this paper, we propose a novel Cyber-Physical Anomaly Detection Engine that monitors system behavior and detects anomalies almost instantaneously. This detection engine ensures that the critical power grid component (viz.,aggregator)remains secure by monitoring(a)cyber messages for various state changes and data constraints along with (b)power data on the V2G cyber network using power measurements from sensors on the physical/power distribution network. Since the V2G system is time-sensitive, the anomaly detection engine also monitors the timing requirements of the protocol messages to enhance the safety of the aggregator. To the best of our knowledge, this is the first piece of work that combines(a)the EV charging/discharging protocols, the(b)cyber network and(c)power measurements from physical network to detect intrusions in the EV to power grid system.

Shaohui Liu, Weiqian Cai, Hao Zhu et al.

The growing prevalence of inverter-based resources (IBRs) for renewable energy integration and electrification greatly challenges power system dynamic analysis. To account for both synchronous generators (SGs) and IBRs, this work presents an approach for learning the model of an individual dynamic component. The recurrent neural network (RNN) model is used to match the recursive structure in predicting the key dynamical states of a component from its terminal bus voltage and set-point input. To deal with the fast transients especially due to IBRs, we develop a Stable Integral (SI-)RNN to mimic high-order integral methods that can enhance the stability and accuracy for the dynamic learning task. We demonstrate that the proposed SI-RNN model not only can successfully predict the component's dynamic behaviors, but also offers the possibility of efficiently computing the dynamic sensitivity relative to a set-point change. These capabilities have been numerically validated based on full-order Electromagnetic Transient (EMT) simulations on a small test system with both SGs and IBRs, particularly for predicting the dynamics of grid-forming inverters.

Zhaiming Shen, Menglun Wang, Guang Cheng et al.

Being able to successfully determine whether the testing samples has similar distribution as the training samples is a fundamental question to address before we can safely deploy most of the machine learning models into practice. In this paper, we propose TOOD detection, a simple yet effective tree-based out-of-distribution (TOOD) detection mechanism to determine if a set of unseen samples will have similar distribution as of the training samples. The TOOD detection mechanism is based on computing pairwise hamming distance of testing samples' tree embeddings, which are obtained by fitting a tree-based ensemble model through in-distribution training samples. Our approach is interpretable and robust for its tree-based nature. Furthermore, our approach is efficient, flexible to various machine learning tasks, and can be easily generalized to unsupervised setting. Extensive experiments are conducted to show the proposed method outperforms other state-of-the-art out-of-distribution detection methods in distinguishing the in-distribution from out-of-distribution on various tabular, image, and text data.

Yuqi Zhou, Jeehyun Park, Hao Zhu

Effective and timely responses to unexpected contingencies are crucial for enhancing the resilience of power grids. Given the fast, complex process of cascading propagation, corrective actions such as optimal load shedding (OLS) are difficult to attain in large-scale networks due to the computation complexity and communication latency issues. This work puts forth an innovative learning-for-OLS approach by constructing the optimal decision rules of load shedding under a variety of potential contingency scenarios through offline neural network (NN) training. Notably, the proposed NN-based OLS decisions are fully decentralized, enabling individual load centers to quickly react to the specific contingency using readily available local measurements. Numerical studies on the IEEE 14-bus system have demonstrated the effectiveness of our scalable OLS design for real-time responses to severe grid emergency events.

Shanny Lin, Hao Zhu

Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the accuracy of line parameter estimation. Inspired by the sparse changes in residential loads, we advocate to regularize the group sparsity of the unobservable injections in a bi-linear estimation problem. The alternating minimization scheme of guaranteed convergence is proposed to take advantage of convex subproblems with efficient solutions. Numerical results using real-world load data on the single-phase equivalent of the IEEE 123-bus test case have demonstrated the accuracy improvements of the proposed solution over existing work for both parameter estimation and voltage modeling.

Shaohui Liu, Chengyang Wu, Hao Zhu

Solving the optimal power flow (OPF) problem in real-time electricity market improves the efficiency and reliability in the integration of low-carbon energy resources into the power grids. To address the scalability and adaptivity issues of existing end-to-end OPF learning solutions, we propose a new graph neural network (GNN) framework for predicting the electricity market prices from solving OPFs. The proposed GNN-for-OPF framework innovatively exploits the locality property of prices and introduces physics-aware regularization, while attaining reduced model complexity and fast adaptivity to varying grid topology. Numerical tests have validated the learning efficiency and adaptivity improvements of our proposed method over existing approaches.

Shanny Lin, Hao Zhu

Enhancing the spatio-temporal observability of distributed energy resources (DERs) is crucial for achieving secure and efficient operations in distribution grids. This paper puts forth a joint recovery framework for residential loads by leveraging the complimentary strengths of heterogeneous measurements in real time. The proposed framework integrates low-resolution smart meter data collected at every load node with fast-sampled feeder-level measurements from limited number of distribution phasor measurement units. To address the lack of data, we exploit two key characteristics for the loads and DERs, namely the sparse changes due to infrequent activities of appliances and electric vehicles (EVs) and the locational dependence of solar photovoltaic (PV) generation. Accordingly, meaningful regularization terms are introduced to cast a convex load recovery problem, which will be further simplified to reduce the computational complexity. The load recovery solutions can be utilized to identify the EV charging events at each load node and to infer the total behind-the-meter PV output. Numerical tests using real-world data have demonstrated the effectiveness of the proposed approaches in enhancing the visibility of grid-edge DERs.

Vassilis Kekatos, Gang Wang, Hao Zhu et al.

This chapter aspires to glean some of the recent advances in power system state estimation (PSSE), though our collection is not exhaustive by any means. The Cram{é}r-Rao bound, a lower bound on the (co)variance of any unbiased estimator, is first derived for the PSSE setup. After reviewing the classical Gauss-Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. A disciplined paradigm for distributed and decentralized schemes is subsequently exemplified under linear(ized) and exact grid models. Novel bad data processing models and fresh perspectives linking critical measurements to cyber-attacks on the state estimator are presented. Finally, spurred by advances in online convex optimization, model-free and model-based state trackers are reviewed.

Hao Jan Liu, Wei Shi, Hao Zhu

Voltage control in power distribution networks has been greatly challenged by the increasing penetration of volatile and intermittent devices. These devices can also provide limited reactive power resources that can be used to regulate the network-wide voltage. A decentralized voltage control strategy can be designed by minimizing a quadratic voltage mismatch error objective using gradient-projection (GP) updates. Coupled with the power network flow, the local voltage can provide the instantaneous gradient information. This paper aims to analyze the performance of this decentralized GP-based voltage control design under two dynamic scenarios: i) the nodes perform the decentralized update in an asynchronous fashion, and ii) the network operating condition is time-varying. For the asynchronous voltage control, we improve the existing convergence condition by recognizing that the voltage based gradient is always up-to-date. By modeling the network dynamics using an autoregressive process and considering time-varying resource constraints, we provide an error bound in tracking the instantaneous optimal solution to the quadratic error objective. This result can be extended to more general \textit{constrained dynamic optimization} problems with smooth strongly convex objective functions under stochastic processes that have bounded iterative changes. Extensive numerical tests have been performed to demonstrate and validate our analytical results for realistic power networks.