arXiv subjects

Zhaojian Wang

Publications and source records attributed to Zhaojian Wang.

At least 19 recordsLinked to original sources

arXiv2026

When Can Phasor-Domain Device Models Be Trusted for Electromechanical Stability Analysis of Grid-Forming Converter-Dominated Microgrids?

Grid-forming (GFM) converter-dominated microgrids are often analyzed using reduced-order phasor-domain electromechanical GFM models, but the validity of these models is often taken for granted. Assuming ideal inner-loop tracking (IILT) of terminal-voltage references, these models neglect the inner-loop and filter dynamics at the electromagnetic-transient (EMT) timescale to simplify stability analysis. This paper argues that such neglected dynamics can destabilize the system, invalidating the stability conclusions drawn from the IILT model. To address this cross-timescale stability issue, we formulate the validity of the IILT stability conclusion as a robust-stability certification problem. The EMT-induced model mismatch between the reduced-order converter model and the actual converter model is represented as a structured uncertainty embedded around the IILT feedback loop. This yields a frequency-resolved interaction index and a structured singular-value sufficient certificate for determining when the stability conclusion of the IILT model can be certified with respect to a prescribed EMT uncertainty weight. The uncertainty weight can be obtained from detailed EMT models or terminal reference-response measurements. Case studies confirm that the proposed certificate correctly certifies model validity and identifies the loss of trustworthiness. We also demonstrate that the measurement-based uncertainty weights closely match the model-based ones, which enables deployment without accessing inner-loop models.

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arXiv2026

A Non-Iterative Algorithm for Clearing Two-Layer Energy-Sharing Markets with Voltage Constraints

Real-time hierarchical energy-sharing markets are promising to coordinate large numbers of prosumers. Still, most existing clearing methods rely on linearized or DC power-flow models and do not explicitly handle reactive power or voltage-security constraints. With AC network constraints, the problem becomes a large-scale bilevel Mathematical Program with Equilibrium Constraints (MPEC) that is difficult to solve in real time. This paper develops a non-iterative clearing algorithm for two-layer energy-sharing markets with voltage constraints. We first derive an efficient best-response function for each lower-layer energy-sharing market and reduce the equilibrium search to one dimension by exploiting the pricing-coupling structure. We then embed this function into the upper-layer network-constrained problem and reformulate the bilevel MPEC as a single-level mixed-integer second-order cone program (MISOCP), which is computationally tractable. Case studies on the IEEE 123-bus system with 12,300 prosumers show that the proposed method preserves nodal voltages within prescribed limits and delivers solutions with maximum errors below 0.01\% in 0.829 s.

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arXiv2026

Real-Time Coordinated Operation of Off-Grid Wind Powered Multi-Electrolyzer Systems Considering Thermal Dynamics and HTO Safety

Coordinated operation of alkaline water electrolysis (AWE) systems with multiple electrolyzers under fluctuating renewable power input is challenging due to varying power availability and dynamic safety constraints. Moreover, the conventional separation between optimization and control may result in inconsistent decisions across timescales. To address these issues, this paper proposes a two-layer coordinated operation method integrating feedback optimization (FO) with a projection-based safety layer. The FO layer generates real-time reference inputs to improve renewable energy utilization, while the safety layer corrects these inputs to ensure compliance with operational and safety constraints. To explicitly address the safety constraints arising from the inertial dynamics of AWE systems, discrete-time control barrier function theory is incorporated into the safety layer, thereby enhancing safety assurance and online computational tractability. Theoretical analysis establishes the feasibility and effectiveness of the proposed method. Case studies based on annual wind generation data show that the proposed method achieves high energy utilization, maintains safe operation, and demonstrates online applicability, scalability, and robustness.

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arXiv2026

Matrix-Valued Passivity Indices: Foundations, Properties, and Stability Implications

The passivity index, a quantitative measure of a system's passivity deficiency or excess, has been widely used in stability analysis and control. Existing studies mostly rely on scalar forms of indices, which are restrictive for multi-input, multi-output (MIMO) systems. This paper extends the classical scalar indices to a systematic matrix-valued framework, referred to as passivity matrices. A broad range of classical results in passivity theory can be naturally generalized in this framework. We first show that, under the matrix representation, passivity indices essentially correspond to the curvature of the dissipativity functional under a second-variation interpretation. This result reveals that the intrinsic geometric structure of passivity consists of its directions and intensities, which a scalar index cannot fully capture. For linear time-invariant (LTI) systems, we examine the structural properties of passivity matrices with respect to the Loewner partial order and propose two principled criteria for selecting representative matrices. Compared with conventional scalar indices, the matrix-valued indices capture the passivity coupling among different input-output channels in MIMO systems and provide a more comprehensive description of system passivity. This richer information leads to lower passivation effort and less conservative stability assessment.

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arXiv2025

Extreme Scenario Characterization for High Renewable Energy Penetrated Power Systems over Long Time Scales

Power systems with high renewable energy penetration are highly influenced by weather conditions, often facing significant challenges such as persistent power shortages and severe power fluctuations over long time scales. This paper addresses the critical need for effective characterization of extreme scenarios under these situations. First, novel risk indices are proposed to quantify the severity of continuous power shortages and substantial power fluctuations over long-term operations. These indices are independent of specific scheduling strategies and incorporate the system's resource regulation capabilities. By employing a filtering-based approach, the proposed indices focus on retaining key characteristics of continuous power shortages and fluctuation events, enabling the identification of extreme scenarios on long time scales. Secondly, an extreme scenario generation method is developed using Gaussian mixture models and sequential Monte Carlo simulation. Especially, this method periodically evaluates the severity of generated scenarios based on the defined risk indices, retaining extreme scenarios while discarding less critical ones. Finally, case studies based on real-world data demonstrate the efficacy of the proposed method. The results confirm that integrating the identified extreme scenarios significantly enhances the system's ability to ensure long-term security and reliability under high renewable energy penetration.

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arXiv2024

Co-Scheduling of Energy and Production in Discrete Manufacturing Considering Decision-Dependent Uncertainties

Modern discrete manufacturing requires real-time energy and production co-scheduling to reduce business costs. In discrete manufacturing, production lines and equipment are complex and numerous, which introduces significant uncertainty during the production process. Among these uncertainties, decision-dependent uncertainties (DDUs) pose additional challenges in finding optimal production strategies, as the signature or the shape of the uncertainty set cannot be determined before solving the model. However, existing research does not account for decision-dependent uncertainties (DDUs) present in discrete manufacturing; moreover, current algorithms for solving models with DDUs suffer from high computational complexity, making them unsuitable for the real-time control requirements of modern industry. To this end, we proposed an energy-production co-scheduling model for discrete manufacturing, taking into account decision-dependent uncertainties (DDUs). Subsequently, we devised a method for transforming the constraints associated with DDUs into linear form ones. Finally, we designed a novel algorithm based on the column-and-constraint generation (C&CG) algorithm and undertook a theoretical analysis of its performance of convergence and algorithmic complexity. A real-world engine assembly line was used to test our model and algorithm. Simulation results demonstrate that our method significantly reduces production costs and achieves better frequency regulation performance.

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arXiv2024

Optimal Hardening Strategy for Electricity-Hydrogen Networks with Hydrogen Leakage Risk Control against Extreme Weather

Defense hardening can effectively enhance the resilience of distribution networks against extreme weather disasters. Currently, most existing hardening strategies focus on reducing load shedding. However, for electricity-hydrogen distribution networks (EHDNs), the leakage risk of hydrogen should be controlled to avoid severe incidents such as explosions. To this end, this paper proposes an optimal hardening strategy for EHDNs under extreme weather, aiming to minimize load shedding while limiting the leakage risk of hydrogen pipelines. Specifically, modified failure uncertainty models for power lines and hydrogen pipelines are developed. These models characterize not only the effect of hardening, referred to as decision-dependent uncertainties (DDUs), but also the influence of disaster intensity correlations on failure probability distributions. Subsequently, a hardening decision framework is established, based on the two-stage distributionally robust optimization incorporating a hydrogen leakage chance constraint (HLCC). To enhance the computational efficiency of HLCC under discrete DDUs, an efficient second-order-cone transformation is introduced. Moreover, to address the intractable inverse of the second-order moment under DDUs, lifted variables are adopted to refine the main-cross moments. These reformulate the hardening problem as a two-stage mixed-integer second-order-cone programming, and finally solved by the column-and-constraint generation algorithm. Case studies demonstrate the effectiveness and superiority of the proposed method.

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arXiv2024

Flexible Operation of Electricity-HCNG Networks with Variable Hydrogen Fraction: A Distributionally Robust Joint Chance-Constrained Approach

Hydrogen-enriched compressed natural gas (HCNG) is a promising way to utilize surplus renewable energy through hydrogen electrolysis and blending it into natural gas. However, the optimal hydrogen volume fraction (HVF) of HCNG varies following the daily fluctuations of renewable energy. Besides, facing the rapid volatility of renewable energy, ensuring rapid and reliable real-time adjustments is challenging for electricity-HCNG (E-HCNG) coupling networks. To this end, this paper proposes a flexible operation framework for electricity-HCNG (E-HCNG) networks against the fluctuations and volatility of renewable energy. Based on operations with variable HVF, the framework developed an E-HCNG system-level affine policy, which allows real-time re-dispatch of operations according to the volatility. Meanwhile, to guarantee the operational reliability of the affine policy, a distributionally robust joint chance constraint (DRJCC) is introduced, which limits the violation probability of operational constraints under the uncertainties of renewable energy volatility. Furthermore, in the solving process, to mitigate the over-conservation in DRJCC decomposition, an improved risk allocation method is proposed, utilizing the correlations among violations under the affine policy. Moreover, to tackle the non-convexities arising from the variable HVF, customized approximations for HCNG flow formulations are developed. The problem is finally reformulated into a mix-integer second-order cone programming problem. The effectiveness of the proposed method is validated both in small-scale and large-scale experiments.

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arXiv2024

Optimal Control in Both Steady State and Transient Process with Unknown Disturbances

The scheme of online optimization as a feedback controller is widely used to steer the states of a physical system to the optimal solution of a predefined optimization problem. Such methods focus on regulating the physical states to the optimal solution in the steady state, without considering the performance during the transient process. In this paper, we simultaneously consider the performance in both the steady state and the transient process of a linear time-invariant system with unknown disturbances. The performance of the transient process is illustrated by the concept of overtaking optimality. An overtaking optimal controller with known disturbances is derived to achieve the transient overtaking optimality while guaranteeing steady-state performance. Then, we propose a disturbance independent near-optimal controller, which can achieve optimal steady-state performance and approach the overtaking optimal performance in the transient process. The system performance gap between the overtaking optimal controller and the proposed controller proves to be inversely proportional to the control gains. A case study on a power system with four buses is used to validate the effectiveness of the two controllers.

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arXiv2024

On the Equilibrium of a Class of Leader-Follower Games with Decision-Dependent Chance Constraints

In this paper, we study the existence of equilibrium in a single-leader-multiple-follower game with decision-dependent chance constraints (DDCCs), where decision-dependent uncertainties (DDUs) exist in the constraints of followers. DDUs refer to the uncertainties impacted by the leader's strategy, while the leader cannot capture their exact probability distributions. To address such problems, we first use decision-dependent ambiguity sets under moment information and Cantelli's inequality to transform DDCCs into second-order cone constraints. This simplifies the game model by eliminating the probability distributions. We further prove that there exists at least one equilibrium point for this game by applying Kakutani's fixed-point theorem. Finally, a numerical example is provided to show the impact of DDUs on the equilibrium of such game models.

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arXiv2024

Data-driven Power Flow Linearization: Simulation

Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations stems from the theoretical analysis's inherent limitations, particularly the challenge of identifying the differences in real-world performance among DPFL methods with overlapping theoretical capabilities and/or limitations. The absence of a comprehensive numerical comparison of DPFL approaches in the literature also motivates this paper, especially given the fact that over 95% of existing DPFL studies have not provided any open-source codes. To bridge the gap, this paper first reviews existing DPFL experiments, examining the adopted test scenarios, load fluctuation settings, data sources, considerations for data noise/outliers, and the comparison made so far. Subsequently, this paper evaluates a total of 44 methods, containing over 30 existing DPFL approaches, some innovative DPFL techniques, and several classic physics-driven power flow linearization methods for benchmarking. The evaluation spans various dimensions, including generalizability, applicability, accuracy, and computational efficiency, using various different test cases scaling from 9-bus to 1354-bus systems. The numerical analysis identifies and examines significant trends and consistent findings across all methods under various test cases. It also offers theoretical insights into phenomena like under-performance, failure, excessive computation times, etc. Overall, this paper identifies the differences in the performances of the wide range of DPFL methods, reveals gaps not evident from theoretical discussions, assists in method selection for real-world applications, and provides thorough discussions on open questions within DPFL research, indicating ten potential future directions.

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arXiv2024

Data-driven Power Flow Linearization: Theory

This two-part tutorial dives into the field of data-driven power flow linearization (DPFL), a domain gaining increased attention. DPFL stands out for its higher approximation accuracy, wide adaptability, and better ability to implicitly incorporate the latest system attributes. This renders DPFL a potentially superior option for managing the significant fluctuations from renewable energy sources, a step towards realizing a more sustainable energy future, by translating the higher model accuracy into increased economic efficiency and less energy losses. To conduct a deep and rigorous reexamination, this tutorial first classifies existing DPFL methods into DPFL training algorithms and supportive techniques. Their mathematical models, analytical solutions, capabilities, limitations, and generalizability are systematically examined, discussed, and summarized. In addition, this tutorial reviews existing DPFL experiments, examining the settings of test systems, the fidelity of datasets, and the comparison made among a limited number of DPFL methods. Further, this tutorial implements extensive numerical comparisons of all existing DPFL methods (40 methods in total) and four classic physics-driven approaches, focusing on their generalizability, applicability, accuracy, and computational efficiency. Through these simulationmethodss, this tutorial aims to reveal the actual performance of all the methods (including the performances exposed to data noise or outliers), guiding the selection of appropriate linearization methods. Furthermore, this tutorial discusses future directions based on the theoretical and numerical insights gained. As the first part, this paper reexamines DPFL theories, covering all the training algorithms and supportive techniques. Capabilities, limitations, and aspects of generalizability, which were previously unmentioned in the literature, have been identified.

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arXiv2024

Sharing Energy in Wide Area: A Two-Layer Energy Sharing Scheme for Massive Prosumers

The popularization of distributed energy resources transforms end-users from consumers into prosumers. Inspired by the sharing economy principle, energy sharing markets for prosumers are proposed to facilitate the utilization of renewable energy. This paper proposes a novel two-layer energy sharing market for massive prosumers, which can promote social efficiency by wider-area sharing. In this market, there is an upper-level wide-area market (WAM) in the distribution system and numerous lower-level local-area markets (LAMs) in communities. Prosumers in the same community share energy with each other in the LAM, which can be uncleared. The energy surplus and shortage of LAMs are cleared in the WAM. Thanks to the wide-area two-layer structure, the market outcome is near-social-optimal in large-scale systems. However, the proposed market forms a complex mathematical program with equilibrium constraints (MPEC). To solve the problem, we propose an efficient and hierarchically distributed bidding algorithm. The proposed two-layer market and bidding algorithm are verified on the IEEE 123-bus system with 11250 prosumers, which demonstrates the practicality and efficiency for large-scale markets.

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arXiv2022

Online Optimization in Power Systems with High Penetration of Renewable Generation: Advances and Prospects

Traditionally, offline optimization of power systems is acceptable due to the largely predictable loads and reliable generation. The increasing penetration of fluctuating renewable generation and Internet-of-Things devices allowing for fine-grained controllability of loads have led to the diminishing applicability of offline optimization in the power systems domain, and have redirected attention to online optimization methods. However, online optimization is a broad topic that can be applied in and motivated by different settings, operated on different time scales, and built on different theoretical foundations. This paper reviews the various types of online optimization techniques used in the power systems domain and aims to make clear the distinction between the most common techniques used. In particular, we introduce and compare four distinct techniques used covering the breadth of online optimization techniques used in the power systems domain, i.e., optimization-guided dynamic control, feedback optimization for single-period problems, Lyapunov-based optimization, and online convex optimization techniques for multi-period problems. Lastly, we recommend some potential future directions for online optimization in the power systems domain.

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arXiv2022

Distributed Emergency Frequency Control Considering Transient Stability Constraints in Multi-Infeed Hybrid AC-DC System

Due to possible emergency faults and frequency regulation reserve shortage in the multi-infeed hybrid AC-DC (MIDC) system, the emergency frequency control (EFC) with LCC-HVDC systems participating is important for system frequency stability. Nevertheless, the existing decentralized EFC strategies cannot guarantee the transient stability constraints of lines and cannot meet the frequency restoration requirement. To fill this gap, this paper proposes a complementary distributed EFC strategy. By selecting the semi-distributed or fully-distributed control law according to the state of AC system control center, the proposed distributed EFC can improve the control performance with a normal control center and enhance the control reliability in case of control center failure. Then, to derive the semi-distributed and fully-distributed control laws, a general design method is proposed by formulating an optimal EFC problem. Both of these two control laws can guarantee transient stability constraints, restore system frequency and achieve the defined optimal control objective. Moreover, the optimality of the closed-loop equilibrium is proven, and a Lyapunov analysis shows the asymptotic stability of the closed-loop system with the discontinuous control dynamics. A case study verifies the effectiveness of the proposed distributed EFC strategy.

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arXiv2022

Distributed Online Generalized Nash Equilibrium Tracking for Prosumer Energy Trading Games

With the proliferation of distributed generations, traditional passive consumers in distribution networks are evolving into "prosumers", which can both produce and consume energy. Energy trading with the main grid or between prosumers is inevitable if the energy surplus and shortage exist. To this end, this paper investigates the peer-to-peer (P2P) energy trading market, which is formulated as a generalized Nash game. We first prove the existence and uniqueness of the generalized Nash equilibrium (GNE). Then, an distributed online algorithm is proposed to track the GNE in the time-varying environment. Its regret is proved to be bounded by a sublinear function of learning time, which indicates that the online algorithm has an acceptable accuracy in practice. Finally, numerical results with six microgrids validate the performance of the algorithm.

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arXiv2022

Incentive Mechanism Design for Emergency Frequency Control in Multi-Infeed Hybrid AC-DC System

In multi-infeed hybrid AC-DC (MIDC) systems, the emergency frequency control (EFC) with LCC-HVDC systems participating is of vital importance for system frequency stability. Nevertheless, when regional power systems are operated by different decision-makers, the LCC-HVDC systems and their connected AC systems might be unwilling to participate in the EFC due to the costs and losses. In this paper, to incentivize the LCC-HVDC systems and their connected adjacent AC systems to participate in the droop-based EFC, a novel control-parameter-based incentive mechanism is proposed, which can deal with various possible emergency frequency faults. Then, a non-cooperative-based incentive game model is formulated to implement the incentive mechanism in the MIDC system. An algorithm for seeking the Nash equilibrium is designed, and the uniqueness of Nash equilibrium is proven. Moreover, the individual rationality, incentive compatibility and social optimality of the proposed mechanism are analyzed and proven. The effectiveness of the proposed incentive mechanism is verified through a case study.

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arXiv2022

Fast Distributed Stochastic Scheduling for A Multi-Energy Industrial Park

The multi-energy management framework of industrial parks advocates energy conversion and scheduling, which takes full advantage of the compensation and temporal availability of multiple energy. However, how to exploit elastic loads and compensate inelastic loads to match multiple generators and storage is still a key problem under the uncertainty of demand and supply. To solve the issue, the energy management problem is constructed as a stochastic optimization problem. The optimization aims are to minimize the time-averaged energy cost and improve the energy efficiency while respecting the energy constraints. To achieve the distributed implementation in real time without knowing any priori knowledge of underlying stochastic process, a distributed stochastic gradient algorithm based on dual decomposition and a fast scheme are proposed. The numerical results based on real data show that the industrial park, by adopting the proposed algorithm, can achieve social welfare maximization asymptotically.

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