Stability Margin Of System Research Articles

Frequency stability analysis of power system with photovoltaic frequency regulation considering communication delay

Photovoltaic (PV) grid-connected will reduce the inertia of the system, which has an effect on power system frequency reliability. In order to clarify the frequency stability situation of power system when photovoltaic participates in frequency regulation, this paper first establishes the load frequency control (LFC) model of the power system with photovoltaic based on the analysis of the traditional LFC model of the power system. Secondly, based on the Pade approximation method, the communication delay in the control loop is linearized. The frequency stability of power system with photovoltaic participation in frequency regulation is characterized by system frequency steady-state error, feedback system sensitivity, and closed-loop system stability margin. According to the index calculation and theoretical derivation, the influence of system frequency regulation related parameters on frequency characteristics is analyzed. Finally, on the matlab/simulink simulation environment, the frequency stability methodological approach presented in this research is validated. The results of the simulations demonstrate the effectiveness of this analytical approach in assessing the frequency stability of a power system with photovoltaic frequency regulation while taking communication latency into account. It can provide guidance for the power grid’s secure operation and control when photovoltaics participate in frequency regulation.

Nonlinear adaptive flight control system: Performance enhancement and validation

The problem of decreasing stability margins in L1 adaptive control systems is discussed and an out-of-loop L1 adaptive control scheme based on Lyapunov’s stability theorem is proposed. This scheme enhances the effectiveness of the adaptation, which ensures that the system has sufficient stability margins to achieve the desired performance under parametric uncertainty, additional delays, and actuator faults. The stability of the developed control system is demonstrated through a series of simulations. Compared with an existing control scheme, the constant adjustment of the stability margins by the proposed adaptive scheme allows their range to be extended by a factor of 4–5, bringing the stability margin close to that of variable gain PD control with adaptively scheduled gains. The engineered practicability of adaptive technology is verified. A series of flight tests verify the practicability of the designed adaptive technology. The results of these tests demonstrate the enhanced performance of the proposed control scheme with nonlinear parameter estimations under insufficient stability margins and validate its robustness in the event of actuator failures.

Stability analysis of load frequency control for power systems with interval time-varying delays

This study investigates the stability problem of load frequency control (LFC) for power systems with interval time-varying delays. The two categories of time delays, the lower bound being zero and non-zero, are considered. The systems can be described as time delay systems of load disturbances. First, an augmented Lyapunov–Krasovskii functional (LKF) is constructed. Some delay-dependent nonintegral terms and single integral terms are additionally introduced to make full use of the information on the system state variables and the time-varying delays. Second, to overcome the problem of nonlinear inequalities caused by the augmented LKF, the nonlinear inequalities are converted into linear matrix inequalities (LMIs) by applying the new negative definite inequality equivalence transformation lemma, which can be solved easily by the MATLAB LMI toolbox. A new stability criterion is presented by applying the Lyapunov stability theory. The stability criterion is less conservative than some existing literature studies, which further improves the stability margin for the power systems based on LFC. Finally, some numerical examples are given to show the effectiveness of the proposed method and the superiority of the results.

Inertia compensation of power grid with flywheel-integrated synchronous condenser

<abstract><p>This paper studies the integration of flywheel energy storage system (FESS) to a synchronous condenser (SC) and its effect on the stability margin of the power system. To show the applicability of FESS-integrated SC in mitigating sudden power loss and sudden load implementation, the experimental and simulation results are presented.</p></abstract>

Stability assessment and parametric sensitivity analysis based on extended Gershgorin Theorem for multiple grid-connected converters

• A multiple grid-connected converters is modeled as a medium and high dimensional negative feedback system with a stable open-loop function in unified dq frame, which fills in the limitations of traditional impedance ratios for the small disturbance stability analysis of multiple grid-connected converters system. • In terms of estimating eigenvalues for the multiple grid-connected converters system, a stability assessment method based on extended Gershgorin Theorem is proposed in frequency domain. Moreover, the algebraic form of the criterion is further simplified to quantify the oscillatory stability, which has the lower complexity compared with generalized nyquist criterion. The proposed method is of great potential in analyzing the stability issue for large-scale new energy power systems. • The reshaped eigenvalue estimation area based on extended Gershgorin Theorem is smaller than traditional Gershgorin Theorem, which can reduce its conservatism to improve system stability margin. • Compared to observe the changed trend of system stability by the change of the related parameters, the parameter sensitivity analysis based on equivalent impedance network model is used to quantify the impact factors on stability, which can be given to guide the parameter optimization of the multiple grid-connected converters system. The large-scale integration of power electronic based systems is bringing new oscillatory stability issues, further threatening the safe and stable operation of power system. Early researches are focused on stability analysis of single grid-connected converters to simple networks. Instead, there have been growing interests in studying the small signal stability of multiple grid-connected converters nowadays, whose main method is to apply traditional stability assessment with high complexity and conservatism. To address this problem, a simplified criterion based on extended Gershgorin Theorem to assess the stability of multiple grid-connected converter. The proposed method has less conservatism than tradition Gershgorin Theorem-based criteria, and has the lower computational complexity with simple algebraic operation compared to generalized nyquist criteria. Moreover, the parametric sensitivity analysis is used for analyzing the impact factors to promote system stability based on the proposed criteria. Theoretical results as well as electromagnetic transient simulations have verified the validity. The proposed method has the potential to assess the high-order system, and provides guidance on system parameters optimization based on the sensitivity.

Adaptive fuzzy-based stability control and series impedance correction for the grid-tied inverter

The regenerative braking in the tram allows the energy to be returned to the power grid through a power inverter. Since the inverter location between the tram and the power grid is not fixed, resulting in a wide variety of impedance networks at grid coupling points, posing a severe threat to the stable operation of the grid-tied inverter (GTI). By independently changing the loop characteristics of the GTI, the adaptive fuzzy PI controller (AFPIC) can adjust according to different impedance network parameters. It is challenging to fulfill the stability margin requirements of GTI under high network impedance since the PI controller has phase lag characteristics. A correction method of series virtual impedance is proposed, which connects the inductive link in a series configuration with the inverter output impedance, correcting the inverter equivalent output impedance from resistance-capacitance to resistance-inductance and improving the system stability margin. Feedforward control is adopted to improve the system's gain in the low-frequency band. Finally, the specific series impedance parameters are obtained by determining the maximum network impedance and setting the minimum phase margin of 45°. The realization of virtual impedance is simulated by conversion to an equivalent control block diagram, and the effectiveness and feasibility of the proposed method are verified by simulation and a 1 kW experimental prototype.

Optimal Coordination of TCSC and PSS2B Controllers in Electric Power Systems Using MOPSO Multiobjective Algorithm

Oscillations are an intrinsic phenomenon in interconnected power systems, leading to steady-state stability, safety decline, transmission power limitation, and electric power systems’ ineffective exploitation by developing power systems, particularly by connecting these systems to low-load lines. In addition, they affect the economic performance of the systems. In this study, PSS2B power system stabilizers and TCSC compensators are used to improve the stability margin of power systems. In order to coordinate TCSC compensators, the MOPSO multiobjective algorithm with integral of the time-weighted absolute error (ITAE) and figure of demerit (FD) objective functions was used. The MOPSO algorithm optimization results are compared with nondominated sorting genetic algorithm (NSGAII) and multiobjective differential evolution (MODE) algorithms. The optimization results indicated a better performance of the proposed MOPSO algorithm than NSGAII and MODE. The simulations were iterated in two scenarios by creating different loading conditions in generators. The results indicated that the proposed control system, where the coordination between PSS2B power system stabilizers and TCSC compensators using the MOPSO algorithm, is better than power systems in which PSS2B Stabilizers or TCSC compensators are utilized solely. All criteria, e.g., ITAE, FD, maximum deviation range, and the required time for power oscillation damping in hybrid control systems, have been obtained. This means more stability and accurate and proper performance.

Power System Voltage Stability Margin Estimation Using Adaptive Neuro-Fuzzy Inference System Enhanced with Particle Swarm Optimization

In the current era of e-mobility and for the planning of sustainable grid infrastructures, developing new efficient tools for real-time grid performance monitoring is essential. Thus, this paper presents the prediction of the voltage stability margin (VSM) of power systems by the critical boundary index (CBI) approach using the machine learning technique. Prediction models are based on an adaptive neuro-fuzzy inference system (ANFIS) and its enhanced model with particle swarm optimization (PSO). Standalone ANFIS and PSO-ANFIS models are implemented using the fuzzy ‘c-means’ clustering method (FCM) to predict the expected values of CBI as a veritable tool for measuring the VSM of power systems under different loading conditions. Six vital power system parameters, including the transmission line and bus parameters, the power injection, and the system voltage derived from load flow analysis, are used as the ANFIS model implementation input. The performances of the two ANFIS models on the standard IEEE 30-bus and the Nigerian 28-bus systems are evaluated using error and regression analysis metrics. The performance metrics are the root mean square error (RMSE), mean absolute percentage error (MAPE), and Pearson correlation coefficient (R) analyses. For the IEEE 30-bus system, RMSE is estimated to be 0.5833 for standalone ANFIS and 0.1795 for PSO-ANFIS; MAPE is estimated to be 13.6002% for ANFIS and 5.5876% for PSO-ANFIS; and R is estimated to be 0.9518 and 0.9829 for ANFIS and PSO-ANFIS, respectively. For the NIGERIAN 28-bus system, the RMSE values for ANFIS and PSO-ANFIS are 5.5024 and 2.3247, respectively; MAPE is 19.9504% and 8.1705% for both ANFIS and PSO-ANFIS variants, respectively, and the R is estimated to be 0.9277 for ANFIS and 0.9519 for ANFIS-PSO, respectively. Thus, the PSO-ANFIS model shows a superior performance for both test cases, as indicated by the percentage reduction in prediction error, although at the cost of a higher simulation time.

Coupled single-port method based voltage stability assessment with inverter-based generators

With the increase of inverter-based generators in the power system, the proportion of traditional generators is decreasing, and their voltage support ability to the power system is weakening, the power system operation is approaching to its voltage stability limit. It is of great significance to study on-line analysis of power system voltage stability under different control manners of inverter-based generators. Firstly, impedance matching theory and coupled single-port circuit theory are introduced. Secondly, coupled single-port method based voltage stability assessment method with inverter-based generators is proposed. Then, use the impedance matching condition and proposed method to analyze the influence of inverter-based generators on voltage stability in different control manners. The proposed method can reveal the voltage stability margin of power system with inverter-based generators in the current running state, and is suitable as an on-line voltage stability approach to evaluate the proximity of voltage collapse in real time. The various scenario simulations experiment validate the effectiveness and accuracy of the proposed method. Meanwhile, experimental analysis results show that different control manners of inverter-based generators not only affect voltage stability margin but also change the weakest bus of power system.

Structure-Informed Graph Learning of Networked Dependencies for Online Prediction of Power System Transient Dynamics

Online transient analysis plays an increasingly important role in dynamic power grids as the renewable generation continues growing. Traditional numerical methods for transient analysis not only are computationally intensive but also require precise contingency information as input, and therefore, are not suitable for online applications. Existing online transient assessment studies focus on the determination of post-contingency system stability or stability margin. This paper develops a novel graph-learning framework, Deep-learning Neural Representation or DNR, for online prediction, of the time-series trajectories of the system states using initial system responses that can be measured by phasor measurement units (PMUs). The proposed DNR framework consists of two sequential modules: a Network Constructor that captures network dependencies among generators, and a Dynamics Predictor that predicts the system trajectories. The key to improved prediction performance is the introduction of the spatio-temporal message-passing operations into graph neural networks with structural knowledge. Its effectiveness and scalability are validated through comparative studies, demonstrating the prediction performance under different contingency scenarios for systems of different sizes. This framework provides a solution to online predicting post-fault system dynamics based on real-time PMU measurements. Additionally, it can also be applied to facilitate the offline transient simulation without simulating the entire trajectories.

Stability Analysis and Performance Improvement of Power Sharing Control in Islanded Microgrids

Due to the requirement of synchronism and power sharing, droop control and its variations have become one essential component for distributed generator (DG)-powered microgrids. However, the power sharing accuracy and system stability margin may be threatened by the randomness from the load demand and renewable generation. In this paper, a dynamic stability analysis is first performed on a DG-powered microgrid through a produced system frequency response model (SFR). The results point out that (i) the critical system eigenvalues directly vary with the system operating condition; (ii) a fixed-gain power sharing control is prone to be less damped and loses stability easily under some operating conditions. Then, the heuristic adaptive dynamic programming (HDP) strategy is used for power sharing control with the benefit of adapting to real-time disturbances and uncertainties. Through Lyapunov theorem, stability analysis is provided to demonstrate the reliability of the HDP-based power sharing control in islanded microgrids. Finally, simulation tests verify the analysis results and demonstrate the favorable performance of the HDP-based power sharing control under uncertain load disturbances.

An Improved Frequency-Adaptive Virtual Variable Sampling-Based Repetitive Control for an Active Power Filter

To eliminate the harmonics caused by nonlinear loads, repetitive controllers are widely applied as current controllers for active power filters (APF). In practice, a variation in grid frequency leads to the appearance of a fractional-order delay filter. As a result, the resonant frequency of the repetitive controller will deviate from the fundamental frequency and the controller cannot compensate for harmonics accurately. To solve this problem, an improved frequency-adaptive repetitive controller based on virtual variable sampling (IMFA-VVS-RC) for APF is proposed in this paper. To enhance the system stability margin, the proposed RC introduces an infinite impulse response (IIR) low-pass filter. The proposed RC has a high stability margin at high frequencies due to the low gain of the IIR low-pass filter in the region above the cutoff frequency. In this way, the influence of model uncertainty and parameter uncertainty on system stability are reduced at high frequencies. At the same time, compared with the conventional repetitive controller (CRC), the proposed RC for APF has a better harmonic suppression ability when the frequency varies. Experiments have verified the effectiveness of the scheme adopted for APF.

Estimation of dominant power oscillation modes based on ConvLSTM approach using synchrophasor data and cross-validation technique

This paper proposes a deep neural network approach considering performance-based cross-validation and confidence interval analysis to estimate a power system’s dominant power oscillation modes. Due to increased electricity demands, power utilities implement various generation sources in their power systems. Accordingly, a modern power system is increasingly complex as a multi-area and multi-machine power system. The electromechanical oscillation modes arise inevitably. Moreover, a major-unexpected event could excite weakly damped power oscillation modes and cause power system instability. The estimation of dominant power oscillation modes is significant for power system monitoring and control. A fast computing time of such modes estimation is essential for further actions. This paper applies the convolutional long short-term memory 2-dimension (ConvLSTM2D) approach to estimate dominant oscillation modes based on synchrophasor data. The proposed ConvLSTM2D approach provides precise estimation with a great opportunity to avoid a forced power system outage. The simulation results of the ConvLSTM2D approach show better accuracy of the dominant power oscillation modes estimated in comparison with the state-of-the-art algorithms (SOTA), i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and hybrid convolutional neural networks-long short-term memory (CNN-LSTM) algorithms. The proposed approach is a systematic approach that can be adaptively improved over time. In addition, the proposed approach can be further applied to wide-area monitoring considering the stability margin of a transmission system. • A ConvLSTM approach is proposed to estimate multiple dominant power oscillation modes. • The proposed approach using time-series cross-validation provides a promising performance. • The performance of proposed approach is robust proved by confidence interval analysis. • The proposed approach can reduce model parameters and training time.

Active vibration control of smart beam by μ -synthesis technology: modeling via finite element method based on FSDT

This article proposes an efficient strategy for the active vibration control of smart beam that combines the Finite Element Method (FEM) and advanced robust control to suppress vibration. The piezoelectric actuator and sensor are coupled as part of the smart structure by using the 2D First-order Shear Deformation (FSDT) plate theory. The accurate modeling of the mechanical displacement field and electric potential field is achieved by approximating the sub-layered coupling of the piezoelectric potential field in the z-axis direction. In practice, most active controls of smart structures do not take into account the influence of the piezoelectric itself and the piezoelectric effect on the natural frequency of the smart structures, and they do not emphasize the internal stability and stability margin of the control system. Regarding the above questions, a modeling method of a generalized uncertain plant for the piezoelectric smart beam is proposed in this article. Fully considering the uncertainty of the system model caused by parameter perturbation and modeling error, a dynamic controller is designed with the μ-Synthesis technology. The proposed approach is numerically verified to have good robust performance on piezoelectric smart beam, which can effectively enhance the performance of smart structure control in other scenarios.

Fixed-Point Theorem-Based Voltage Stability Margin Estimation Techniques for Distribution Systems With Renewables

The future distribution systems expose to an unprecedented level of uncertainties due to renewable resources, nontraditional loads, aging infrastructure, etc., posing potential risks to secure operation of the system.This article proposes a new technique to estimate the voltage stability margin of the distribution systems with high penetration of renewables.Its convergence and robustness under complex and stressed working conditions are guaranteed in theory. This technique is handy for the operation as it features self-adaptive step size and is applicable to general system topology. It leverages a newly derived analytical solvability certificate based on the Kantorovich fixed-point theorem. A fast version of the proposed technique is duly proposed to speed up the computation up to 8 times while maintaining high accuracy, which lends itself to online and time-sensitive emergency tasks. Numerical simulations with various IEEE test feeders verify the performance of the techniques.

A Stochastic Model for Determining Static Stability Margins in Electric Power Systems

This paper aims to develop a method for determining margins of static aperiodic stability for electric power systems equipped with distributed generation plants. To this end, we used generalized equations of limiting modes in a stochastic formulation. Computer simulation showed that the developed methodology can be used in solving problems of operational control of the modes of electric power systems. On the basis of the results obtained, we arrived at the following conclusions: the modified equations do not allow the iterative process to converge to a trivial solution and, therefore, they ensure high reliability of results when determining stability margins in a stochastic statement; a technique based on the introduction of an additional variable can be used to improve the convergence of computational processes when determining the stability margins in a deterministic statement; the parameters of the limiting modes obtained in the deterministic and stochastic formulations may significantly differ; with an increase in the variance of the load graphs, the risk of stability violation significantly increases; at the same time, the amount of the margin determined on the basis of the Euclidean norm remains overly optimistic; in the illustrative example, a significant increase in the risk of stability violation takes place during planned and emergency shutdowns of the EPS elements.

Impact of control system on the DC impedance characteristics of low-medium frequency bands and stability of modular multilevel converter based HVDC system

The resonance in modular multilevel converter based high voltage direct current (MMC-HVDC) system poses a potential threat to the safe and stable operation of the power grid. The mechanism of the resonance phenomenon is complicated, which is closely related to the impedance characteristics of MMC system. By establishing the DC impedance model of MMC-HVDC system at both ends, the influence of parameters of control system in converter stations on the DC impedance characteristics of MMC system was analyzed, revealing the main influencing frequency bands and effect of each control parameter. The DC impedance characteristics of low and medium frequency bands could be shaped in a targeted manner by adjusting the control parameters, the stability margin of the system will be improved as well. The correctness of the results was verified by time domain simulation. The analysis results of this article can provide reference for the selection of the parameters of control system and the improvement of stability margin of MMC-HVDC system.

Harmonic Current Suppression for AMB System via the Finite Dimension Repetitive Controller

The harmonic current in active magnetic bearing (AMB) system usually results from rotor unbalance and sensor runout. It not only causes considerable harmonic vibration, but also brings about the power saturation and the instability of AMB system especially for the high-speed rotor. Therefore, a novel parallel finite dimension repetitive controller (PFDRC) is proposed to restrain the harmonic current in this paper. Compared with the conventional repetitive controller (RC), PFDRC only introduces the limited imaginary poles, so that the problem that the infinite imaginary poles of RC endanger the stability and instantaneous characteristic of the closed-loop system is solved. In order to realize the harmonic current suppression, the power amplifier system is taken as the controlled object, and the proposed PFDRC is parallel with the original equivalent main controller. Then the root reclus method is adopted to design the parameters and to analyze the closed-loop system stability. Based on the phase-frequency characteristic of the system function, the compensators are introduced to improve the system stability margin. Meanwhile, the low-pass property of power amplifier system is sufficiently taken into consideration in the parameters design. Finally, the simulations and experiments are implemented to validate the effectiveness of the proposed PFDRC, and the results demonstrate that the harmonic current is dramatically restrained by the proposed method.

A composite voltage stability index for integrated energy systems based on L-index and the minimum eigenvalue of reduced Jacobian matrix

The closer interdependency of subsystems in integrated energy systems (IESs) and the continuous increase of electricity/gas/heat loads have brought great challenges to the stable operation of IESs. In response to the static voltage stability problem of IESs, this paper proposes a composite voltage stability index (CVSI) based on the minimum eigenvalue of a reduced Jacobian matrix and the known L-index. First, a unified multi-energy flow model for integrated electrical, natural gas and heating system is established, which comprises the steady-state modeling of each energy subsystem and coupling components in IESs. Then, an integrated multi-energy flow calculation method based on the Newton–Raphson algorithm is developed to solve the unified steady-state model of IESs. On the basis, the unified Jacobian matrix after multi-energy flow convergence can be obtained. Moreover, a reduced Jacobian matrix considering the impacts of multi-energy state variables on the reactive power of electrical power system (EPS) is constructed. Afterward, the CVSI is proposed, which combines the minimum eigenvalue of the constructed reduced Jacobian matrix and the L-index derived from bus voltage calculation formula. The proposed CVSI takes both the voltage stability margin of whole system and the voltage stability of electrical buses into consideration. Finally, numerical simulations are exploited to verify the effectiveness and applicability of the proposed voltage stability index.

Mechanism Analysis of a Subsequent Commutation Failure and a DC Power Recovery Speed Control Strategy

A subsequent commutation failure (SCF) of the Line-Commutated Converter–High-Voltage Direct Current (LCC-HVDC) may occur during the recovery after the clearance of an AC fault, seriously threatening the safe and stable operation of the LCC-HVDC and the entire post-fault AC/DC hybrid power system. In this study, the mechanism of an SCF as affected by the transient stability was analyzed, and a DC power recovery speed control strategy is proposed as an additional form of control to prevent the occurrence of SCFs. First, the sending-end and receiving-end power systems were modeled as synchronous generators instead of ideal voltage sources, and the mechanism of an SCF as affected by the transient stability was analyzed and verified. Second, the ramp function was adopted to describe the recovery characteristic of DC power, and a model of its recovery was established. Then, the recovery speed control strategy is presented based on the mechanism analysis of SCFs, which can not only be used to avoid the occurrence of SCFs but also increase the transient stability margin of the sending-end power system. Finally, the effectiveness and robustness of the proposed control strategy were validated by using a hybrid electromechanical–electromagnetic model and the full electromagnetic model of the IEEE 39-bus asynchronous interconnection test power system. With the implementation of the proposed control strategy, the safe and stable operation of the LCC-HVDC and AC/DC hybrid power system can be guaranteed. The adaptive DC power recovery speed control strategy will be further investigated in future research work.