arXiv subjects

Zhaojian Wang

Publications and source records attributed to Zhaojian Wang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Stochastic Gradient-based Fast Distributed Multi-Energy Management for an Industrial Park with Temporally-Coupled Constraints

Contemporary industrial parks are challenged by the growing concerns about high cost and low efficiency of energy supply. Moreover, in the case of uncertain supply/demand, how to mobilize delay-tolerant elastic loads and compensate real-time inelastic loads to match multi-energy generation/storage and minimize energy cost is a key issue. Since energy management is hardly to be implemented offline without knowing statistical information of random variables, this paper presents a systematic online energy cost minimization framework to fulfill the complementary utilization of multi-energy with time-varying generation, demand and price. Specifically to achieve charging/discharging constraints due to storage and short-term energy balancing, a fast distributed algorithm based on stochastic gradient with two-timescale implementation is proposed to ensure online implementation. To reduce the peak loads, an incentive mechanism is implemented by estimating users' willingness to shift. Analytical results on parameter setting are also given to guarantee feasibility and optimality of the proposed design. Numerical results show that when the bid-ask spread of electricity is small enough, the proposed algorithm can achieve the close-to-optimal cost asymptotically.

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arXiv2022

Asynchronous Decentralized Federated Learning for Collaborative Fault Diagnosis of PV Stations

Due to the different losses caused by various photovoltaic (PV) array faults, accurate diagnosis of fault types is becoming increasingly important. Compared with a single one, multiple PV stations collect sufficient fault samples, but their data is not allowed to be shared directly due to potential conflicts of interest. Therefore, federated learning can be exploited to train a collaborative fault diagnosis model. However, the modeling efficiency is seriously affected by the model update mechanism since each PV station has a different computing capability and amount of data. Moreover, for the safe and stable operation of the PV system, the robustness of collaborative modeling must be guaranteed rather than simply being processed on a central server. To address these challenges, a novel asynchronous decentralized federated learning (ADFL) framework is proposed. Each PV station not only trains its local model but also participates in collaborative fault diagnosis by exchanging model parameters to improve the generalization without losing accuracy. The global model is aggregated distributedly to avoid central node failure. By designing the asynchronous update scheme, the communication overhead and training time are greatly reduced. Both the experiments and numerical simulations are carried out to verify the effectiveness of the proposed method.

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arXiv2022

On Nash-Stackelberg-Nash Games under Decision-Dependent Uncertainties: Model and Equilibrium

In this paper, we discuss a class of two-stage hierarchical games with multiple leaders and followers, which is called Nash-Stackelberg-Nash (N-S-N) games. Particularly, we consider N-S-N games under decision-dependent uncertainties (DDUs). DDUs refer to the uncertainties that are affected by the strategies of decision-makers and have been rarely addressed in game equilibrium analysis. In this paper, we first formulate the N-S-N games with DDUs of complete ignorance, where the interactions between the players and DDUs are characterized by uncertainty sets that depend parametrically on the players' strategies. Then, a rigorous definition for the equilibrium of the game is established by consolidating generalized Nash equilibrium and Pareto-Nash equilibrium. Afterward, we prove the existence of the equilibrium of N-S-N games under DDUs by applying Kakutani's fixed-point theorem. Finally, an illustrative example is provided to show the impact of DDUs on the equilibrium of N-S-N games.

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arXiv2022

Energy Management Based on Multi-Agent Deep Reinforcement Learning for A Multi-Energy Industrial Park

Owing to large industrial energy consumption, industrial production has brought a huge burden to the grid in terms of renewable energy access and power supply. Due to the coupling of multiple energy sources and the uncertainty of renewable energy and demand, centralized methods require large calculation and coordination overhead. Thus, this paper proposes a multi-energy management framework achieved by decentralized execution and centralized training for an industrial park. The energy management problem is formulated as a partially-observable Markov decision process, which is intractable by dynamic programming due to the lack of the prior knowledge of the underlying stochastic process. The objective is to minimize long-term energy costs while ensuring the demand of users. To solve this issue and improve the calculation speed, a novel multi-agent deep reinforcement learning algorithm is proposed, which contains the following key points: counterfactual baseline for facilitating contributing agents to learn better policies, soft actor-critic for improving robustness and exploring optimal solutions. A novel reward is designed by Lagrange multiplier method to ensure the capacity constraints of energy storage. In addition, considering that the increase in the number of agents leads to performance degradation due to large observation spaces, an attention mechanism is introduced to enhance the stability of policy and enable agents to focus on important energy-related information, which improves the exploration efficiency of soft actor-critic. Numerical results based on actual data verify the performance of the proposed algorithm with high scalability, indicating that the industrial park can minimize energy costs under different demands.

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arXiv2021

Approaching the Transient Stability Boundary of a Power System: Theory and Applications

Estimating the stability boundary is a fundamental and challenging problem in transient stability studies. It is known that a proper level set of a Lyapunov function or an energy function can provide an inner approximation of the stability boundary, and the estimation can be expanded by trajectory reversing methods. In this paper, we streamline the theoretical foundation of the expansion methodology, and generalize it by relaxing the request that the initial guess should be a subset of the stability region. We investigate topological characteristics of the expanded boundary, showing how an initial guess can approach the exact stability boundary locally or globally. We apply the theory to transient stability assessment, and propose expansion algorithms to improve the well-known Potential Energy Boundary Surface (PEBS) and Boundary of stability region based Controlling Unstable equilibrium point (BCU) methods. Case studies on the IEEE 39-bus system well verify our results and demonstrate that estimations of the stability boundary and the critical clearing time can be significantly improved with modest computational cost.

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arXiv2021

Convergence Analysis of Dual Decomposition Algorithm in Distributed Optimization: Asynchrony and Inexactness

Dual decomposition is widely utilized in distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet drop. In addition, computational errors also exist when individual agents solve their own subproblems. In this paper, we analyze the convergence of the dual decomposition algorithm in distributed optimization when both the asynchrony in communication and the inexactness in solving subproblems exist. We find that the interaction between asynchrony and inexactness slows down the convergence rate from $\mathcal{O} ( 1 / k )$ to $\mathcal{O} ( 1 / \sqrt{k} )$. Specifically, with a constant step size, the value of objective function converges to a neighborhood of the optimal value, and the solution converges to a neighborhood of the exact optimal solution. Moreover, the violation of the constraints diminishes in $\mathcal{O} ( 1 / \sqrt{k} )$. Our result generalizes and unifies the existing ones that only consider either asynchrony or inexactness. Finally, numerical simulations validate the theoretical results.

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arXiv2021

Robust Scheduling of Virtual Power Plant under Exogenous and Endogenous Uncertainties

Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel model for determining the optimal offering strategy in the day-ahead energy-reserve market and the optimal self-scheduling plan. It considers exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind power generation, as well as the endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution method based on strong duality theory, McCormick relaxation, and the Benders' decomposition to solve the proposed stochastic adaptive robust optimization with DDUs formulation is developed. Simulation results demonstrate the applicability of the proposed approach.

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arXiv2020

Asynchrony-Resilient and Privacy-Preserving Charging Protocol for Plug-in Electric Vehicles

The proliferation of plug-in electric vehicles (PEVs) advocates a distributed paradigm for the coordination of PEV charging. Distinct from existing primal-dual decomposition or consensus methods, this paper proposes a cutting-plane based distributed algorithm, which enables an asynchronous coordination while well preserving individual's private information. To this end, an equivalent surrogate model is first constructed by exploiting the duality of the original optimization problem, which masks the private information of individual users by a transformation. Then, a cutting-plane based algorithm is derived to solve the surrogate problem in a distributed manner with intrinsic superiority to cope with various asynchrony. Critical implementation issues, such as the distributed initialization, cutting-plane generation and localized stopping criteria, are discussed in detail. Numerical tests on IEEE 37- and 123-node feeders with real data show that the proposed method is resilient to a variety of asynchrony and admits the plug-and-play operation mode. It is expected the proposed methodology provides an alternative path toward a more practical protocol for PEV charging.

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arXiv2020

Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called "prosumers", i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we convert the GNG into an equivalent optimization problem. A Krasnosel'ski{ǐ}-Mann iteration type algorithm is thereby devised to solve the problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 123 prosumers.

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arXiv2020

Exponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions

In this paper, we investigate the continuous time partial primal-dual gradient dynamics (P-PDGD) for solving convex optimization problems with the form $ \min\limits_{x\in X,y\inΩ}\ f({x})+h(y),\ \textit{s.t.}\ A{x}+By=C $, where $ f({x}) $ is strongly convex and smooth, but $ h(y) $ is strongly convex and non-smooth. Affine equality and set constraints are included. We prove the exponential stability of P-PDGD, and bounds on decaying rates are provided. Moreover, it is also shown that the decaying rates can be regulated by setting the stepsize.

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arXiv2020

A Distributed Incremental Update Scheme for Probability Distribution of Wind Power Forecast Error

Due to the uncertainty of distributed wind generations (DWGs), a better understanding of the probability distributions (PD) of their wind power forecast errors (WPFEs) can help market participants (MPs) who own DWGs perform better during trading. Under the premise of an accurate PD model, considering the correlation among DWGs and absorbing the new information carried by the latest data are two ways to maintain an accurate PD. These two ways both require the historical and latest wind power and forecast data of all DWGs. Each MP, however, only has access to the data of its own DWGs and may refuse to share these data with MPs belonging to other stakeholders. Besides, because of the endless generation of new data, the PD updating burden increases sharply. Therefore, we use the distributed strategy to deal with the data collection problem. In addition, we further apply the incremental learning strategy to reduce the updating burden. Finally, we propose a distributed incremental update scheme to make each MP continually acquire the latest conditional PD of its DWGs' WPFE. Specifically, we first use the Gaussian-mixture-model-based (GMM-based) joint PD to characterize the correlation among DWGs. Then, we propose a distributed modified incremental GMM algorithm to enable MPs to update the parameters of the joint PD in a distributed and incremental manner. After that, we further propose a distributed derivation algorithm to make MPs derive their conditional PD of WPFE from the joint one in a distributed way. Combining the two original algorithms, we finally achieve the complete distributed incremental update scheme, by which each MP can continually obtain its latest conditional PD of its DWGs' WPFE via neighborhood communication and local calculation with its own data. The effectiveness, correctness, and efficiency of the proposed scheme are verified using the dataset from the NREL.

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arXiv2019

Distributed Stability Conditions for Power Systems with Heterogeneous Nonlinear Bus Dynamics

This paper derives distributed conditions that guarantee the system-wide stability for power systems with nonlinear and heterogeneous bus dynamics interconnected via power network. Our conditions require each bus dynamics should satisfy certain passivity-like conditions with a large enough passivity index, a sufficient requirement of which is dictated by the steady-state power flow. The passivity indices uniformly quantify the impacts on the system-wide stability of individual bus dynamics and the coupling strength from the power network. Furthermore, taking three typical bus dynamics as examples, we show that these conditions can be easily fulfilled via proper control design. Simulations on a rudimentary 3-bus example and the IEEE 39-bus system well verify our results under both small and large disturbances.

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arXiv2019

Asynchronous Distributed Voltage Control in Active Distribution Networks

With the explosion of distributed energy resources (DERs), voltage regulation in distribution networks has been facing a great challenge. This paper derives an asynchronous distributed voltage control strategy based on the partial primal-dual gradient algorithm, where both active and reactive controllable power of DERs are considered. Different types of asynchrony due to imperfect communication or practical limits, such as random time delays and non-identical sampling/control rates, are fitted into a unified analytic framework. The asynchronous algorithm is then converted into a fixed-point problem by employing the operator splitting method, which leads to a convergence proof with mild conditions. Moreover, an online implementation method is provided to make the controller adjustable to time-varying environments. Finally, numerical experiments are carried out on a rudimentary 8-bus system and the IEEE-123 distribution network to verify the effectiveness of the proposed method.

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arXiv2019

Toward Distributed Stability Analytics for Power Systems with Heterogeneous Bus Dynamics

The stability issue emerges as a growing number of diverse power apparatus connecting to the power system. The stability analysis for such power systems is required to adapt to heterogeneity and scalability. This paper derives a local passivity index condition that guarantees the system-wide stability for lossless power systems with interconnected, nonlinear, heterogeneous bus dynamics. Our condition requires each bus dynamics to be output feedback passive with a large enough index w.r.t. a special supply rate. This condition fits for numerous existing models since it only constrains the input-output property rather than the detailed dynamics. Furthermore, for three typical examples of bus dynamics in power systems, we show that this condition can be reached via proper control designs. Simulations on a 3-bus heterogeneous power system verify our results in both lossless and lossy cases. The conservativeness of our condition is also demonstrated, as well as the impact on transient stability. It shows that our condition is quite tight and a larger index benefits transient stability.

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arXiv2019

Towards Distributed Stability Analytics of Dynamic Power Systems: A Phasor-Circuit Theory Perspective

With the rapid development of renewable and distributed energies, the underlying dynamics of power systems are no longer dominated by large synchronous generators, but by numerous dynamic components with heterogeneous characteristics. In such a situation, the traditional stability analysis method may fail due to the challenges of heterogeneity and scalability. In this paper, we handle this issue by fundamental circuit theory. Inspired by the work of Brayton and Moser in the nonlinear RLC circuit, we extend the concept of the voltage potential to phasor circuits and offer new results into the distributed stability analytics in power systems. We show that under certain distributed passivity-like conditions the system-wide stability can be ensured. The simulation of a 3-bus system is also provided to verify our results.

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arXiv2019

Distributed Optimal Load Frequency Control Considering Nonsmooth Cost Functions

This work addresses the distributed frequency control problem in power systems considering controllable load with a nonsmooth cost. The nonsmoothness exists widely in power systems, such as tiered price, greatly challenging the design of distributed optimal controllers. In this regard, we first formulate an optimization problem that minimizes the nonsmooth regulation cost, where both capacity limits of controllable load and tie-line flow are considered. Then, a distributed controller is derived using the Clark generalized gradient. We also prove the optimality of the equilibrium of the closed-loop system as well as its asymptotic stability. Simulations carried out on the IEEE 68-bus system verifies the effectiveness of the proposed method.

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arXiv2019

Asynchronous Distributed Power Control of Multi-Microgrid Systems Based on the Operator Splitting Approach

Forming (hybrid) AC/DC microgrids (MGs) has become a promising manner for the interconnection of various kinds of distributed generators that are inherently AC or DC electric sources. This paper addresses the distributed asynchronous power control problem of hybrid microgrids, considering imperfect communication due to non-identical sampling rates and communication delays. To this end, we first formulate the optimal power control problem of MGs and devise a synchronous algorithm. Then, we analyze the impact of asynchrony on optimal power control and propose an asynchronous iteration algorithm based on the synchronous version. By introducing a random clock at each iteration, different types of asynchrony are fitted into a unified framework, where the asynchronous algorithm is converted into a fixed-point problem based on the operator splitting method, leading to a convergence proof. We further provide an upper bound estimation of the time delay in the communication. Moreover, the real-time implementation of the proposed algorithm in both AC and DC MGs is introduced. By taking the power system as a solver, the controller is simplified by reducing one order and the power loss can be considered. Finally, a benchmark MG is utilized to verify the effectiveness and advantages of the proposed algorithm.

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arXiv2018

Distributed Load-Side Control: Coping with Variation of Renewable Generations

This paper addresses the distributed frequency control problem in a multi-area power system taking into account of unknown time-varying power imbalance. Particularly, fast controllable loads are utilized to restore system frequency under changing power imbalance in an optimal manner. The imbalanced power causing frequency deviation is decomposed into three parts: a known constant part, an unknown low-frequency variation and a high-frequency residual. The known steady part is usually the prediction of power imbalance. The variation may result from the fluctuation of renewable resources, electric vehicle charging, etc., which is usually unknown to operators. The high-frequency residual is usually unknown and treated as an external disturbance. Correspondingly, in this paper, we resolve the following three problems in different timescales: 1) allocate the steady part of power imbalance economically; 2) mitigate the effect of unknown low-frequency power variation locally; 3) attenuate unknown high-frequency disturbances. To this end, a distributed controller combining consensus method with adaptive internal model control is proposed. We first prove that the closed-loop system is asymptotically stable and converges to the optimal solution of an optimization problem if the external disturbance is not included. We then prove that the power variation can be mitigated accurately. Furthermore, we show that the closed-loop system is robust against both parameter uncertainty and external disturbances. The New England system is used to verify the efficacy of our design.

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