arXiv subjects

Junjian Qi

Publications and source records attributed to Junjian Qi.

At least 19 recordsLinked to original sources

arXiv2021

A Stochastic Multi-Agent Optimization Framework for Interdependent Transportation and Power System Analyses

We study the interdependence between transportation and power systems considering decentralized renewable generators and electric vehicles (EVs). We formulate the problem in a stochastic multi-agent optimization framework considering the complex interactions between EV/conventional vehicle drivers, \revi{renewable}/conventional generators, and independent system operators, with locational electricity and charging prices endogenously determined by markets. We show that the multi-agent optimization problems can be reformulated as a single convex optimization problem and prove the existence and uniqueness of the equilibrium. To cope with the curse of dimensionality, we propose ADMM-based decomposition algorithm to facilitate parallel computing. Numerical insights are generated using standard test systems in transportation and power system literature.

math.OC↗

arXiv2020

Generator Parameter Estimation by Q-Learning Based on PMU Measurements

In this paper, a novel Q-learning based approach is proposed for estimating the parameters of synchronous generators using PMU measurements. Event playback is used to generate model outputs under different parameters for training the agent in Q-learning. We assume that the exact values of some parameters in the model are not known by the agent in Q-learning. Then, an optimal history-dependent policy for the exploration-exploitation trade-off is planned. With given prior knowledge, the parameter vector can be viewed as states with a specific reward, which is a function of the fitting error compared with the measurements. The agent takes an action (either increasing or decreasing the parameter) and the estimated parameter will move to a new state. Based on the reward function, the optimal action policy will move the parameter set to a state with the highest reward. If multiple events are available, they will be used sequentially so that the updated $\mathbfcal{Q}$-value can be utilized to improve the computational efficiency. The effectiveness of the proposed approach is validated by estimating the parameters of the dynamic model of a synchronous generator.

eess.SY↗

arXiv2020

Multi-Objective PMU Allocation for Resilient Power System Monitoring

Phasor measurement units (PMUs) enable better system monitoring and security enhancement in smart grids. In order to enhance power system resilience against outages and blackouts caused by extreme weather events or man-made attacks, it remains a major challenge to determine the optimal number and location of PMUs. In this paper, a multi-objective resilient PMU placement (MORPP) problem is formulated, and solved by a modified Teaching-Learning-Based Optimization (MO-TLBO) algorithm. Three objectives are considered in the MORPP problem, minimizing the number of PMUs, maximizing the system observability, and minimizing the voltage stability index. The effectiveness of the proposed method is validated through testing on IEEE 14-bus, 30-bus, and 118-bus test systems. The advantage of the MO-TLBO-based MORPP is demonstrated through the comparison with other methods in the literature, in terms of iteration number, optimality and time of convergence.

eess.SY↗

arXiv2020

Resilience Analysis and Cascading FailureModeling of Power Systems under Extreme Temperatures

In this paper, we propose an AC power flow based cascading failure model that explicitly considers external weather conditions, extreme temperatures in particular, and evaluates the impact of extreme temperature on the initiation and propagation of cascading blackouts. Specifically, load and dynamic line rating changes are modeled due to temperature disturbance, the probabilities for transmission line and generator outages are evaluated, and the timing for each type of events is carefully calculated to decide the actual event sequence. It should be emphasized that the correlated events, in the advent of external temperature changes, could together contribute to voltage instability. Besides, we model undervoltage load shedding and operator re-dispatch as control strategies for preventing the propagation of cascading failures. The effectiveness of the proposed model is verified by simulation results on the RTS-96 3-area system and it is found that temperature disturbances can lead to correlated load change and line/generator tripping, which together will greatly increase the risk of cascading and voltage instability. Critical temperature change, critical area with temperature disturbance, identification of most vulnerable buses, and comparison of different control strategies are also carefully investigated.

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arXiv2020

Robust Dynamic State Estimation of Synchronous Machines with Asymptotic State Estimation Error Performance Guarantees

A robust observer for performing power system dynamic state estimation (DSE) of a synchronous generator is proposed. The observer is developed using the concept of $\mathcal{L}_{\infty}$ stability for uncertain, nonlinear dynamic generator models. We use this concept to (i) design a simple, scalable, and robust dynamic state estimator and (ii) obtain a performance guarantee on the state estimation error norm relative to the magnitude of uncertainty from unknown generator inputs, and process and measurement noises. Theoretical methods to obtain upper and lower bounds on the estimation error are also provided. Numerical tests validate the performance of the $\mathcal{L}_{\infty}$-based estimator in performing DSE under various scenarios. The case studies reveal that the derived theoretical bounds are valid for a variety of case studies and operating conditions, while yielding better performance than existing power system DSE methods.

eess.SY↗

arXiv2019

Dynamic State Estimation of Synchronous Machines Using Robust Cubature Kalman Filter Against Complex Measurement Noise Statistics

Cubature Kalman Filter (CKF) has good performance when handling nonlinear dynamic state estimations. However, it cannot work well in non-Gaussian noise and bad data environment due to the lack of auto-adaptive ability to measure noise statistics on line. In order to address the problem of behavioral decline and divergence when measure noise statistics deviate prior noise statistics, a new robust CKF (RCKF) algorithm is developed by combining the Huber's M-estimation theory with the classical CKF, and thereby it is proposed to coping with the dynamic state estimation of synchronous generators in this study. The simulation results on the IEEE-9 bus system and New England 16-machine-68-bus system demonstrate that the estimation accuracy and convergence of the proposed RCKF are superior to those of the classical CKF under complex measurement noise environments including different measurement noises and bad data, and that the RCKF is capable of effectively eliminating the impact of bad data on the estimation effects.

eess.SY↗

arXiv2019

Robust Cubature Kalman Filter for Dynamic State Estimation of Synchronous Machines under Unknown Measurement Noise Statistics

Kalman-type filtering techniques including cubature Kalman filter (CKF) does not work well in non-Gaussian environments, especially in the presence of outliers. To solve this problem, Huber's M-estimation based robust CKF (RCKF) is proposed for synchronous machines by combining the Huber's M-estimation theory with the classical CKF, which is capable of coping with the deterioration in performance and discretization of tracking curves when measurement noise statistics deviatefrom the prior noise statistics. The proposed RCKF algorithm has good adaptability to unknown measurement noise statistics characteristics including non-Gaussian measurement noise and outliers. The simulation results on the WSCC 3-machine 9-bus system and New England 16-machine 68-bus system verify the effectiveness of the proposed method and its advantage over the classical CKF.

eess.SY↗

arXiv2019

Characterizing the Nonlinearity of Power System Generator Models

Power system dynamics are naturally nonlinear. The nonlinearity stems from power flows, generator dynamics, and electromagnetic transients. Characterizing the nonlinearity of the dynamical power system model is useful for designing superior estimation and control methods, providing better situational awareness and system stability. In this paper, we consider the synchronous generator model with a phasor measurement unit (PMU) that is installed at the terminal bus of the generator. The corresponding nonlinear process-measurement model is shown to be locally Lipschitz, i.e., the dynamics are limited in how fast they can evolve in an arbitrary compact region of the state-space. We then investigate different methods to compute Lipschitz constants for this model, which is vital for performing dynamic state estimation (DSE) or state-feedback control using Lyapunov theory. In particular, we compare a derived analytical bound with numerical methods based on low discrepancy sampling algorithms. Applications of the computed bounds to dynamic state estimation are showcased. The paper is concluded with numerical tests.

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arXiv2018

Optimal distributed generation planning in active distribution networks considering integration of energy storage

A two-stage optimization method is proposed for optimal distributed generation (DG) planning considering the integration of energy storage in this paper. The first stage determines the installation locations and the initial capacity of DGs using the well-known loss sensitivity factor (LSF) approach, and the second stage identifies the optimal installation capacities of DGs to maximize the investment benefits and system voltage stability and to minimize line losses. In the second stage, the multi-objective ant lion optimizer (MOALO) is first applied to obtain the Pareto-optimal solutions, and then the 'best' compromise solution is identified by calculating the priority memberships of each solution via grey relation projection (GRP) method, while finally, in order to address the uncertain outputs of DGs, energy storage devices are installed whose maximum outputs are determined with the use of chance-constrained programming. The test results on the PG&E 69-bus distribution system demonstrate that the proposed method is superior to other current state-of-the-art approaches, and that the integration of energy storage makes the DGs operate at their pre-designed rated capacities with the probability of at least 60% which is novel.

math.OC↗

arXiv2018

Robust Control for Renewable-Integrated Power Networks Considering Input Bound Constraints and Worst-Case Uncertainty Measure

Uncertainty from renewable energy and loads is one of the major challenges for stable grid operation. Various approaches have been explored to remedy these uncertainties. In this paper, we design centralized or decentralized state-feedback controllers for generators while considering worst-case uncertainty. Specifically, this paper introduces the notion of $\mathcal{L}_{\infty}$ robust control and stability for uncertain power networks. Uncertain and nonlinear differential algebraic equation model of the network is presented. The model includes unknown disturbances from renewables and loads. Given an operating point, the linearized state-space presentation is given. Then, the notion of $\mathcal{L}_{\infty}$ robust control and stability is discussed, resulting in a nonconvex optimization routine that yields a state feedback gain mitigating the impact of disturbances. The developed routine includes explicit input-bound constraints on generators' inputs and a measure of the worst-case disturbance. The feedback control architecture can be centralized, distributed, or decentralized. Algorithms based on successive convex approximations are then given to address the nonconvexity. Case studies are presented showcasing the performance of the $\mathcal{L}_{\infty}$ controllers in comparison with automatic generation control and $\mathcal{H}_{\infty}$ control methods.

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arXiv2017

Model-Free MLE Estimation for Online Rotor Angle Stability Assessment with PMU Data

Recent research has demonstrated that the rotor angle stability can be assessed by identifying the sign of the system maximal Lyapunov exponent (MLE). A positive (negative) MLE implies unstable (stable) rotor angle dynamics. However, because the MLE may fluctuate between positive and negative values for a long time after a severe disturbance, it is difficult to determine the system stability when observing a positive or negative MLE without knowing its further fluctuation trend. In this paper, a new approach for online rotor angle stability assessment is proposed to address this problem. The MLE is estimated by a recursive least square (RLS) based method based on real-time rotor angle measurements, and two critical parameters, the Theiler window and the MLE estimation initial time step, are carefully chosen to make sure the calculated MLE curves present distinct features for different stability conditions. By using the proposed stability assessment criteria, the developed approach can provide timely and reliable assessment of the rotor angle stability. Extensive tests on the New-England 39-bus system and the Northeast Power Coordinating Council 140-bus system verify the effectiveness of the proposed approach.

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arXiv2016

EV Dispatch Control for Supplementary Frequency Regulation Considering the Expectation of EV Owners

Electric Vehicles (EVs) are promising to provide frequency regulation services due to their fast regulating characteristics. However, when EVs participate in Supplementary Frequency Regulation (SFR), it is challenging to simultaneously achieve the dispatch of the control center and the expected State of Charge (SOC) levels of EV batteries. To solve this problem, in this paper we propose a Vehicle-to-Grid (V2G) control strategy, in which an uncertain dispatch is implemented in the control center without detailed EV charging/discharging information. The regulation from the control center is achieved by allocating the regulation task within the frequency regulation capacity (FRC) of EVs. The expected SOC levels of EV batteries are guaranteed by a real-time correction of their scheduled V2G power in EV charging stations. Simulations on an interconnected two-area power system validate the effectiveness of the proposed V2G control in achieving both the frequency regulation and the expected SOC levels of EVs.

math.OC↗

arXiv2016

Interval Estimation for Conditional Failure Rates of Transmission Lines with Limited Samples

The estimation of the conditional failure rate (CFR) of an overhead transmission line (OTL) is essential for power system operational reliability assessment. It is hard to predict the CFR precisely, although great efforts have been made to improve the estimation accuracy. One significant difficulty is the lack of available outage samples, due to which the law of large numbers is no longer applicable and no convincing statistical result can be obtained. To address this problem, in this paper a novel imprecise probabilistic approach is proposed to estimate the CFR of an OTL. The imprecise Dirichlet model (IDM) is applied to establish the imprecise probabilistic relation between a single conditional variable and the failure rate of an OTL. Then a credal network is constructed to integrate the IDM estimation results corresponding to different conditional variables and infer the CFR. Instead of providing a single-valued estimation result, the proposed approach predicts the possible interval of the CFR in order to explicitly indicate the uncertainty of the estimation and more objectively represent the available knowledge. The proposed approach is illustrated by estimating the CFRs of two LGJ-300 transmission lines located in the same region; the test results validate its effectiveness.

stat.AP↗

arXiv2016

An SQP Method Combined with Gradient Sampling for Small-Signal Stability Constrained OPF

Small-Signal Stability Constrained Optimal Power Flow (SSSC-OPF) can provide additional stability measures and control strategies to guarantee the system to be small-signal stable. However, due to the nonsmooth property of the spectral abscissa function, existing algorithms solving SSSC-OPF cannot guarantee convergence. To tackle this computational challenge of SSSC-OPF, we propose a Sequential Quadratic Programming (SQP) method combined with Gradient Sampling (GS) for SSSCOPF.At each iteration of the proposed SQP, the gradient of the spectral abscissa unction is randomly sampled at the current iterate and additional nearby points to make the search direction computation effective in nonsmooth regions. The method can guarantee SSSC-OPF is globally and efficiently convergent to stationary points with probability one. The effectiveness of the proposed method is tested and validated on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system.

math.OC↗

arXiv2016

Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance

In this paper, the empirical controllability covariance (ECC), which is calculated around the considered operating condition of a power system, is applied to quantify the degree of controllability of system voltages under specific dynamic var source locations. An optimal dynamic var source placement method addressing fault-induced delayed voltage recovery (FIDVR) issues is further formulated as an optimization problem that maximizes the determinant of ECC. The optimization problem is effectively solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The proposed method is tested on an NPCC 140-bus system and the results show that the proposed method with fault specified ECC can solve the FIDVR issue caused by the most severe contingency with fewer dynamic var sources than the Voltage Sensitivity Index (VSI) based method. The proposed method with fault unspecified ECC does not depend on the settings of the contingency and can address more FIDVR issues than VSI method when placing the same number of SVCs under different fault durations. It is also shown that the proposed method can help mitigate voltage collapse.

math.OC↗

arXiv2016

Nonlinear Model Reduction in Power Systems by Balancing of Empirical Controllability and Observability Covariances

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods, the external system does not need to be linearized but is directly dealt with as a nonlinear system. A transformation is found to balance the controllability and observability covariances in order to determine which states have the greatest contribution to the input-output behavior. The original system model is then reduced by Galerkin projection based on this transformation. The proposed method is tested and validated on a system comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system. The results show that by using the proposed model reduction the calculation efficiency can be greatly improved; at the same time, the obtained state trajectories are close to those for directly simulating the whole system or partitioning the system while not performing reduction. Compared with the balanced truncation method based on a linearized model, the proposed nonlinear model reduction method can guarantee higher accuracy and similar calculation efficiency. It is shown that the proposed method is not sensitive to the choice of the matrices for calculating the empirical covariances.

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arXiv2016

Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.

physics.soc-ph↗

arXiv2016

Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter with Enhanced Numerical Stability

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is proposed and compared with five existing approaches, including UKF-schol, UKF-$κ$, UKF-modified, UKF-$ΔQ$, and the square-root unscented Kalman filter (SR-UKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is found that UKF-schol, UKF-$κ$, and UKF-$ΔQ$ do not work well in some estimations while UKF-GPS works well in most cases. UKF-modified and SR-UKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.

math.OC↗