Trajectory Sensitivity Method Research Articles

Analytic Deep Learning and Stepwise Integrated Gradients-Based Power System Transient Stability Preventive Control

Trajectory sensitivity (TS) is a powerful alternative to linearize strong-nonlinear transient stability patterns. However, due to its incomplete view of an intact power system operational space, it can be readily to drive preventive control to stuck in local stationary solution. To mitigate this issue, an integrated gradient (IG)-based stepwise control method is proposed. The key idea is to develop IG to enable a control sensitivity taking both merits of local and global sensitivity, further help preventive control escape from local stationary points. Particularly, deep belief network (DBN) is firstly utilized to parameterize pattern between transient stability index (TSI) and steady-state dispatches. It is then leveraged to infer IG to linearize transient stability constraints in real-time. Interior point method is employed to solve the linearized model. A stepwise control strategy is finally proposed to adaptively tune the integrated interval of the applied IG, such that the preventive control path can be ensured to follow the trend of improving transient stability. Case studies on two benchmarks show that the proposed method outperforms traditional TS method in terms of efficiency and economy, and provides a promising way to enhance engineering sensitivity methods.

Online correction of the transient voltage security region boundary based on load parameter variations in power systems

The transient voltage security region (TVSR) is an essential part of the dynamic safety region of a power system, which represents the safe operating region of the transient voltage where there is no loss in stability. The power system load significantly affects the transient voltage stability. However, the load model in the existing power systems, which considers the security region of the dynamic process, is too simple to comprehensively characterize the load characteristics of the dynamic process. Furthermore, it neglects the influence of the load model parameters on the dynamic process security region. In this study, a composite load model with distributed photovoltaic power is used as the research object. The main load parameters affecting the voltage stability and the generator nodes that are sensitive to the load parameters are calculated using the trajectory sensitivity method. The TVSR of the system is constructed based on the load and generator’s active powers. The correlations between different load-leading parameter combination scenarios and TVSR boundary points are mined using the CatBoost learning framework. Thus, the TVSR boundary can be promptly corrected online based on the changes in the load parameters, and the system security boundary can be described more accurately. The proposed method is verified using the IEEE39 and IEEE118 node systems. It is observed that the proposed method can correct the TVSR boundary online with high precision corresponding to real-time changes in the load model parameters. This provides a more accurate TVSR boundary for the power system operation scheduler, which helps in guiding it to control the system more accurately.

Parameter Identification of DFIG Converter Control System Based on WOA

The converter is an important component of a wind turbine, and its control system has a significant impact on the dynamic output characteristics of the wind turbine. For the double-fed induction generator (DFIG) converter, the control parameter identification method is proposed. In this paper, a detailed dynamic model of DFIG with the converter is built, and the trajectory sensitivity method is used to study the observation points that are sensitive to the change of control parameters as the observation quantity for control parameter identification; the Whale Optimization Algorithm (WOA) is used to study the converter control system parameters that dominate the output characteristics of DFIG in the dynamic full-process simulation. To validate the proposed method, four classical test functions are used to verify the effectiveness of the algorithm, and the control parameters are identified by setting a three-phase grounded short-circuit fault under maximum power point tracking (MPPT), and the identification results are compared with particle swarm optimization (PSO) and chaotic particle swarm optimization (CPSO) to show the superiority of the proposed method. The final results show that the proposed WOA can identify the control system parameters faster and more accurately.

Study on noise reduction method of main noise transmission path of axial piston pump with new damping material

Axial piston pump is complex fluid machinery with mechanical fluid coupling, and it has the characteristics of multiple noise sources. In order to solve the high noise problem of axial piston pump, this paper proposes a noise reduction method by identifying the main noise sources of axial piston pump and laying new damping materials to reduce noise. It breaks through the existing method of optimizing the parameters of piston pump shell and valve plate structure. A multi-parameter trajectory sensitivity identification and noise reduction method for vibration transmission path of axial piston pump is proposed in this paper. First, the lumped parameter method is used to establish the mathematical model of vibration transmission path of axial piston pump. The sensitivity of structural vibration response to transmission path multi-parameters are analyzed based on trajectory sensitivity method. The most sensitive parameters in the main noise transmission path are determined. Then, the experimental study of radiated noise transmission path of axial piston pump is carried out. A new type of viscous damping material is proposed to reduce the noise on the transmission path of the main noise source. The experimental results show that the noise of piston pump is reduced by 2.32 dB. The research results provide a new method and way for the design and manufacture of low noise piston pump.

Identifiability Analysis for Power Plant Parameter Calibration in the Presence of Collinear Parameters

A good quality stability model is a key factor for accurate power system operations.Inaccurate parameters of the stability models affect the decision making which paves the way for serious consequences. Thus, it is necessary to calibrate the stability model parameters in a regular manner. There are several calibration methods in the literature which are based on simultaneous estimation of the parameters and states. However, not all of the model parameters are well estimable simultaneously. Simultaneous estimation of parameters with high collinearity may result in biased calibration results. In this paper, the trajectory sensitivity method is used to detect the sensitive parameters and construct the sensitivity matrix. Then, parameters with high linear dependency are identified using the sensitivity matrix. It is shown that, despite the high sensitivity of a parameter, its estimability degrades as the collinearity with other parameters increase. In this paper an identifiability analysis that detects the collinearity among the sensitive parameters is proposed. The proposed method is validated using WSCC 9-Bus System.

Parameter Sensitivity Analysis of a Brake Pressure Control System in Aviation Using an Electro-Hydraulic Servo Valve

The landing gear system has the task of bearing the weight of the aircraft, bearing the impact load, and providing the braking function in the process of the aircraft taxiing, take-off, and landing. There are many parameters in the aviation brake pressure servo valve-controlled cylinder system (ABPSVCS) which will have a significant influence on the dynamic behavior of the system. Sensitivity analysis is an effective method to analyze the influence of system parameters on system characteristics, especially for nonlinear systems. The trajectory sensitivity method based on the description of system state space is used for the parameter sensitivity analysis of the ABPSVCS. By grouping various parameters for sensitivity analysis, the law of parameter sensitivity of each group is obtained, and the results are verified by experiments. The results can lay a theoretical and experimental foundation for the related research work of the aviation brake pressure servo valve.

An analysis of structural and practical identifiability applied to a transient generator model

This article addresses issues of the structural and practical identifiability of a transient model of a synchronous generator. A structural identifiability analysis was conducted for nonlinear models of differential-algebraic equations (DAEs) and then applied to the DAE model of the synchronous generator, whose parameters were estimated by a practical identifiability analysis employing a trajectory sensitivity method. An optimal time window of measurement data was selected for improving the accuracy of the estimated parameters, which were validated from different sets of measurements collected in two different experiments.

Galerkin method‐based model predictive control for mid‐long term voltage stability enhancement

Mid-long term voltage stability refers to voltage stability concerning the dynamics of the slow dynamic elements and protection devices in power systems. To improve the mid-long term voltage stability, this paper proposes a scheme of model predictive control (MPC) based on Galerkin method. The basic principle of MPC is to solve the optimization problem regarding voltage stability control based on the prediction model periodically. By applying the optimal control scheme to power systems, the mid-long term voltage stability can be enhanced. The Galerkin method-based polynomial approximation approximates the relationship between mid-long term trajectories and control parameters by a polynomial function. The polynomial function acts as a prediction model to predict future system trajectories under different values of control parameters in MPC. The advantage of the proposed method is that its prediction accuracy is relatively high and thus the control efficiency of MPC is improved, as the polynomial function can embody the non-linear characteristics of the power system. In the case study, the 3-machine 10-bus system and the New England 39-bus system are taken as examples to compare the MPC based on the proposed method and the trajectory sensitivity method in terms of prediction accuracy, computation time and control results.

A Data-Driven Multi-Scale Online Joint Estimation of States and Parameters for Electro-Hydraulic Actuator in Legged Robot

In order to satisfy the real-time need of model-based controllers for model parameters and full states feedback, this paper has conducted in-depth research on the states and parameters estimation of electro-hydraulic actuator in legged robot with three problems for time-varying parameters estimation (including system parameters and external load force), non-measurable states estimation and measurable states filtering. The first-order trajectory sensitivity method based on the dynamic model is used to determine the parameter set to be estimated, and the parameter fast and slow characteristics are analyzed in detail to obtain the generalized states and slow-varying parameters. Then, the combined algorithm with a fast-varying time scale (composed of a fusion kalman filter and a fast-varying time scale extended kalman filter) and a slow-varying time scale (composed of a slow-varying time scale extended kalman filter) is innovatively proposed to realize the data-driven multi-scale online joint estimation of states and parameters for the actuator system. Finally, the results of three comparative experiments show that the proposed algorithm has better stability, faster convergence speed and more accurate estimation than the dual extended kalman filter algorithm, and the states and parameters estimated by the proposed algorithm accurately reflect the actual characteristics of actuator. Moreover, the algorithm has strong adaptability and robustness in different actuator hardware environment and strong convergence ability for different initial values of states and parameters.

A comparative validation of a synchronous generator by trajectory sensitivity and offline methods

Summary This paper addresses a comparison between online and offline methods to estimate parameters of a synchronous generator. The main aim of this comparison is to validate the results of a new online method based on trajectory sensitivity method against offline method. Steady-state, sudden short circuit, and voltage recovery tests were selected among the offline methods to serve of comparison for trajectory sensitivity method. The online method has the following features: It uses only terminal voltages and currents and field voltage measurements, it does not need the power angle, and it estimates the power angle using an auxiliary algebraic equation. Tests were conducted in a 2-kVA salient pole machine, and the differences in parameter values obtained from each approaches were analyzed. Eventually, it is concluded that technique based on trajectory sensitivity provides more reliable generator parameters of estimation process.

Unified Analysis of Single Machine Equivalent and Trajectory Sensitivity to Formulate a Novel Transient Stability-constrained Optimal Power Flow Approach

—This article proposes a new transient stability constraint that permits quantifying the degree of instability of a power system from the active power dispatched by generators. Based on this constraint, which is derived from both single machine equivalent and trajectory sensitivity methods, a new transient stability-constrained optimal power flow is formulated in the Euclidian space to preventively control the transient stability in realistic power systems. The validity and the effectiveness of the proposed method are numerically demonstrated in the WSCC 3-machine, 9-bus and Mexican 46-machine, 190-bus systems.

Selective transient stability-constrained optimal power flow using a SIME and trajectory sensitivity unified analysis

A novel approach based on both single machine equivalent (SIME) and trajectory sensitivity methods is proposed to formulate a transient stability-constrained optimal power flow (TSC-OPF) in the Euclidian space, where only one single stability constraint is necessary in the optimization problem to represent all dynamic and transient stability constraints of the multi-machine system. This formulation remarkably reduces the dimension of the optimization problem to one similar to a conventional OPF, resulting in a tractable approach to the preventive control of transient stability in realistic power systems. A unified framework of time domain analysis is proposed, where the transient stability, trajectory sensitivity and SIME analyses are all combined to assess the system's stability and to compute the sensitivity coefficients of the proposed transient stability constraint. Based on these sensitivity coefficients, three non-heuristic selection criteria are proposed to perform the preventive control by rescheduling only a selected number of generators, which is the commonly accepted practice followed by the system's operators. The validity and the effectiveness of the proposed method are numerically demonstrated in the 10-machine 39-bus New England system and Mexican 46-machine 190-bus system.

Determination of Transient Stability Constrained Interface Real Power Flow Limit Using Trajectory Sensitivity Approach

Fast determination of the transient stability constrained interface power transfer limit is a critical problem in power system real time operation. Conventional methods normally require repeated time domain simulations to determine this interface transfer limit; therefore, they are computationally burdensome and time consuming. This paper presents an application of the trajectory sensitivity method to determine the transient stability constrained interface transfer limit. For a specified contingency, the trajectory sensitivity method is used to determine the stability constrained maximum output of the key generators that affect the power flow of the interface. Then using the power transfer distribution factors (PTDFs) of those key generators on the tie-lines constituting the interface, the maximum interface transfer increment can be determined. The advantage of this method is that it requires much less computation compared to the conventional methods while having the same level of accuracy. An application of the proposed method to the WECC test system is presented in detail. The results obtained demonstrate the efficiency and accuracy of the proposed method.

Pelton Turbine Needle Control Model Development, Validation, and Governor Designs

Underspeed needle control of two Pelton turbine hydro units operating in a small power system has caused many incidents of partial system blackouts. Among the causes are conservative governor designs with regard to small signal stability limits, nonminimum phase power characteristics, and long tunnel-penstock traveling wave effects. A needle control model is developed from “water to wires” and validated for hydro-turbine dynamics using turbine test data. Model parameters are tuned using a trajectory sensitivity method. In the governor design proposed here the needle regulation gains are distributed into the power and frequency governor loops with a multi-timescale approach. Elements of speed loop gain scheduling and a new inner-loop pressure stabilization circuit are devised to improve the frequency regulation and to damp the traveling wave effects. Simulation studies show the improvements of the proposed control designs.

Trajectory Sensitivity Based Preventive Control of Voltage Instability Considering Load Uncertainties

This paper presents an application of the trajectory sensitivity method to the voltage stability problem considering load uncertainty. The trajectory sensitivity method can be used to determine the system stability bound based on the base case system response and the various load parameter sensitivities calculated along the base case. Based on the evaluated stability bound, the size of various preventive control actions to maintain system voltage stability will exist within a specific range instead of being a fixed amount. The trajectory sensitivity method is also utilized to determine the various optimal preventive control strategies in terms of shunt compensation and generation rescheduling, for all potential operating points that are deemed to be unstable. The computational efficiency problem is also addressed. A new Jacobian matrix updating strategy is developed for the very dishonest Newton (VDHN) method. Using this Jacobian updating mechanism, the computation time is significantly reduced. The proposed method is applied to a large WECC test system.

Multi-parameter Uncertainty Analysis in Power System Dynamic Simulation: A New Solution Based on the Stochastic Response Surface Method and Trajectory Sensitivity Method

Power system simulations are greatly affected by uncertainties arising from models and parameters. The conventional methods of uncertainty analysis involve many thousand rounds of computation, which are both time and effort demanding. Based on the stochastic response surface method and the trajectory sensitivity method, this article proposes a new solution to reduce the number of uncertain inputs and to expedite the calculation of uncertainty. The trajectory sensitivity method is first applied to narrow down a set of parameters with high sensitivity, and the stochastic response surface method is then applied on this set to analyze the uncertainties, which can greatly speed up the computation process. The uncertainties estimated this way are close to those by 105 Monte Carlo simulations in case studies of the NE power grid of China.

Cluster Computing-Based Trajectory Sensitivity Analysis Application to the WECC System

This paper presents an application of the trajectory sensitivity method to a large realistic power system. A cluster computing platform is utilized to solve the trajectory sensitivity equations in parallel when multiple sensitivity element calculations are performed. The results show great efficiency improvement with this platform. Another important issue addressed is the error associated with the perturbation size for linear trajectory approximations. When the perturbation size varies, it is critical to ascertain the accuracy of the trajectory approximation. A technique to characterize the error and quantify it is developed. A transient stability constrained preventive control application of generation rescheduling involving trajectory sensitivity analysis, parallel computing, and accuracy evaluation is presented for a large WECC test system. This demonstration highlights the efficacy of the parallel computing capability and accuracy of the calculated preventive control.

Trajectory Sensitivity Method and Master‐Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master‐slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master‐slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz′s and Chua′s systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples.

Wide area measurements-based model validation and its application

Simulation veracity is very important to the plan and operation of a power system. Too optimistic a simulation will put the system at risk whereas too pessimistic a simulation will waste investments. Wide area measurements (WAMs), one of the fast developing technologies in recent years, could record the synchronized phasors in the whole power grid, which provides the possibility for simulation validation work. Recent contingency reproduction work worldwide has shown the inaccuracy of current digital simulation. Therefore simulation validation and model calibration are necessary to enhance simulation veracity. However, because of the complexity of the power system, it is difficult to find the erroneous ones among a large amount of components, which makes the simulation validation a very challenging problem. A new approach for WAMs-based simulation validation work is proposed. The proposed method is very simple and easy to be implemented in the available power system simulation software. Then, the trajectory sensitivity method is applied to the parameter calibration work. Real applications via the proposed methods in the big NE power grid of China are studied, which fully show the efficiency of the proposed methods.

Determination of Effectiveness of Transient Stability Controls Using Reduced Number of Trajectory Sensitivity Computations

This paper presents a new approach for determining the effectiveness of preventive generation rescheduling and shunt/series compensation in improving transient stability using trajectory sensitivity (TS) method. It is shown that the effectiveness of changes in parameter values can be judged by evaluating the TS of certain variables with respect to clearing time. Therefore, the need to evaluate a host of sensitivities with respect to many parameters is obviated. This heuristic is motivated by the fact that for simple models and small changes, controllability of trajectories using certain parameters can be inferred from observability in certain output signals. An example of such a parameter and signal pair is shunt susceptance at a bus and the square of voltage at that bus, respectively. Case studies are carried out on a 10-machine 39-bus system with detailed models and 17-machine system to validate this method.