Small Disturbance Voltage Stability Research Articles

A Framework for Analyzing System Loadability With Multiple VSCs Using a Hybrid Model

Due to the increasing number of power electronics-based devices in modern power systems, there are concerns about the impact of higher-frequency interactions on system stability. The typically-used algebraic representation of networks fails to capture these newly emergent issues, but dynamically modelling the entire network with differential equations will lead to a prohibitively long simulation time. This paper proposes a computationally-efficient analysis framework to determine the system loadability in power electronics-rich, large networks with the consideration of multiple types of stabilities. The framework developed in this paper identifies the critical network elements based on the eigenvalue sensitivity in order to exploit a hybrid modelling approach. Within the hybrid model, only the critical network portion is modelled dynamically with the rest of the network represented by algebraic equations. Bifurcation theory is used to simultaneously analyze both small-disturbance rotor angle and small-disturbance voltage stability. The results obtained show that the high-frequency interactions are accurately captured with the proposed framework. Additionally, applying this methodology results in a small dimension for the system matrix and a reduction in the computational burden. Two test networks, a three-bus system and the IEEE 39-bus system, are used to illustrate and verify the analysis framework.

Interconnection of Renewable Energy Resources in the Grid and Study of its Consequences on Small Disturbance Voltage Stability with Phasor Measurement Units

Interconnection of Renewable Energy Resources in the Grid and Study of its Consequences on Small Disturbance Voltage Stability with Phasor Measurement Units

Voltage stability analysis of power systems with a large number of non-synchronous machine sources connected

Compared with synchronous generators, the steady-state and dynamic characteristics of non-synchronous machine sources represented by line commutated converters (LCC) and voltage source converters (VSC) are quite different. The voltage stability of power systems will be changed when a large number of non-synchronous machine sources (NSMS) are connected. The voltage stability of power systems with NSMSs connected is analyzed in this paper. Firstly, based on the relationship between the Jacobian matrix singularity and the small disturbance voltage stability (SDVS), the impact of NSMSs on the SDVS of active systems is analyzed. Secondly, whether there is a reasonable voltage solution in the transient process is taken as a large-disturbance voltage stability (LDVS) criterion, the impact of NSMSs on the LDVS of active systems is studied. Thirdly, for a special scenario where the VSC supplies power to a passive system, the requirements of the voltage stability on load types and VSC parameters are discussed. Finally, based on the Power System Simulator/Engineering (PSS/E), simulations are carried out in the Shanghai power system and a passive power system, and the theoretical analysis results are verified.

Network-based analysis of long-term voltage stability considering loads with recovery dynamics

This study investigates the influence of network structures on long-term voltage stability of power systems considering loads with recovery dynamics. A power system model with load dynamics is established in terms of a network graph and the aggregate nonlinear recovery load model. Stability conditions are proposed for static and small-disturbance voltage stability of power systems, which reveal the interactions between network graph, load demand and load characteristics and sheds new light on the static and small-disturbance voltage stability mechanisms. The impact of the penetration of renewable energy sources is discussed as one illustration. The Monte Carlo method is used for case studies of several widely established IEEE power network test cases. Small-world, scale-free and random networks are considered for the generation of a broad range of network topologies. The simulation results are consistent with the stability conditions. The study in this paper may provide guidance in network planning and operation of power systems.

Small-Disturbance Voltage Stability of Power Systems: Dependence on Network Structure

This paper investigates the impact of network structures on small-disturbance voltage stability of power systems in the long-term. A differential-algebraic model is established in terms of network topology characteristics and the aggregate nonlinear recovery load model. We define the weighted load connectivity (WLC) as an index to indicate the stability of network structures. Then robust stability assessment is used to eliminate the impact of uncertain recovery time of loads. The Monte Carlo method is used to study the relationship between WLC and small-disturbance voltage stability (SDVS) for a broad range of network topologies and parameters. We discover from the simulation results that the network with a larger value of WLC has a stronger ability to maintain SDVS. To further study the impact of renewable energy sources (RESs), we improve the system model by including an inverter-based distributed generator in parallel with each aggregated nonlinear dynamic load. The simulation results of the Hong Kong power grid show that the WLC can still indicate the stability of network structures effectively, and the systems with more stable network structures are less impacted by the penetration of RESs. The proposed WLC appears useful in providing guidance for power network planning and operation.

Identification and improvement of probabilistic voltage instability modes of power system with wind power integration

A probabilistic-based approach is presented to identify and improve small-disturbance voltage stability of power systems incorporating a wind farm, taking into consideration the stochastic uncertainty of system loads, output of wind turbine generators and synchronous generators. The whole system model is based on plug-in modeling technology (PMT) with detailed representation of doubly-fed induction generator (DFIG) dynamic model. The probabilistic distribution of state-matrix eigenvalues is obtained for analyzing the small-disturbance stability of power systems. Voltage stability correlation ratio and voltage instability mode coefficient are proposed for identifying voltage modes and improving voltage stability. The proposed approach is tested on a three-machine system and a nine-machine system. The simulation results show that the approach can quantify the well-known observation that wind farm integration may increase the voltage instability of the power system. The stochastic variations can induce a higher probability of system instability when compared with the one that does not have wind generation. Besides, with wider eigenvalues distributing after the wind generation installation, it makes more difficult for stability improvement. In this paper, static VAR compensator (SVC) is installed at the weakest point which is determined by the voltage instability mode coefficient to improve the system probabilistic voltage stability. The final results validate the efficiency and feasibility of the proposed approach.

Studying Voltage Stability in Power System Considering Load Dynamics

This paper investigates on-load tap changer OLTC effect on voltage stability. Chaos theory used in this analysis is via the calculation of the maximum power transmission. Resulted chaotic behavior is exhibited by singular induced bifurcation which clearly shows the voltage stability of the power system with OLTC from a singular induced bifurcation point of view. The paper is organized as follows: 1) increasing in the maximum reactive power via increasing the ratio of OLTC and the possibility of voltage collapse decrease under the same load command. 2) Noting that the voltage instability is directly affected by the load characteristics, shown via the effect of OLTC on the voltage instability under different static load models. 3) Studying voltage stability in state space and the effects of the generator excitation current limit, the OLTC and load dynamics on voltage collapse. In addition, a small-disturbance voltage stability region of a power system is constructed. The voltage stability of the system is determined by the dynamic characteristics of both the OLTC and the load.

Studying Voltage Stability in Power System Considering Load Dynamics

This paper investigates on-load tap changer OLTC effect on voltage stability. Chaos theory used in this analysis is via the calculation of the maximum power transmission. Resulted chaotic behavior is exhibited by singular induced bifurcation which clearly shows the voltage stability of the power system with OLTC from a singular induced bifurcation point of view. The paper is organized as follows: 1) increasing in the maximum reactive power via increasing the ratio of OLTC and the possibility of voltage collapse decrease under the same load command. 2) Noting that the voltage instability is directly affected by the load characteristics, shown via the effect of OLTC on the voltage instability under different static load models. 3) Studying voltage stability in state space and the effects of the generator excitation current limit, the OLTC and load dynamics on voltage collapse. In addition, a small-disturbance voltage stability region of a power system is constructed. The voltage stability of the system is determined by the dynamic characteristics of both the OLTC and the load.

Review of Electric Load Modeling Research

The effect of load model on the analyses of load flow, transient stability, small disturbance stability and voltage stability is analyzed. The importance of the load modeling research is emphasized. The development of component-based method and measurement-based method is reviewed. The advances on the load model research including the select ion of load model structure, model parameters identification, load model with the voltage stability analysis and the sensitivity of load model to the transient stability is summarized.

The Probabilistic Collocation Method for Power-System Damping and Voltage Collapse Studies in the Presence of Uncertainties

This paper explores the feasibility of using the Probabilistic Collocation Method (PCM) in power-system studies in the presence of uncertainties. The application of the PCM is illustrated on small disturbance stability studies and voltage stability studies. First, the PCM is used to determine the effects of a supplementary power oscillation damping (POD) controller installed on a VSC-HVDC line in the presences of parameter and operational uncertainties. Second, it is used to calculate the probabilistic distance to voltage collapse in a distribution system based on measurement errors. The PCM is shown to produce accurate statistical results whilst drastically reducing the computational time of the studies in both cases. Additionally, a ranking process based on eigenvalue sensitivity is presented alongside the small disturbance analysis as an appropriate method for reduction of system complexity for extension to large power systems. This technique is validated through the application of the PCM on a large power-system model, yielding accurate probabilistic results.

On-line dynamic voltage instability prediction based on decision tree supported by a wide-area measurement system

In this study, a new decision tree-based method is proposed to assess the small disturbance (limited to load disturbance) voltage stability of power systems by only using synchronised phasors (synchrophasors) measured by phasor measurement units in a wide-area measurement system. To properly predict the voltage instability considering various load increase directions as well as load increase step sizes, a mathematical morphology algorithm is used to extract appropriate features from synchronised measured voltage phasors during the few seconds just after the disturbance. These features along with the pre-disturbance ones are then applied to a trained decision tree to predict the voltage instability of the power system. The proposed method is applied and tested on the Nordic32 test system. To examine the efficiency and accuracy of the proposed method, the dynamic behaviours of on-load tap changing transformers as well as the stator current limiters of synchronous generators are considered. The simulation results demonstrate that this method effectively predicts the voltage instability of the power system during the first two seconds just after the disturbance, for the test system.

Impact of wind generation uncertainty on power system small disturbance voltage stability: A PCM-based approach

The connection of wind generators with electric power system influences the system stability and nodal voltages. This paper performs uncertainty analysis to investigate the impact of wind generation variation on the small disturbance voltage stability. The probabilistic collocation method (PCM) is presented as a computationally efficient method to conduct the uncertainty analysis. It has been implemented in a simple system to demonstrate its applicability in analyzing wind generation uncertainty. More case studies on a larger system are conducted to obtain a deeper understanding of how the system voltage stability is affected by the integration of DFIG-based wind farms. As compared with the traditional Monte Carlo simulation method, the collocation method could provide a quite accurate approximation for the eigenvalue probabilistic distribution with fewer simulation runs.

Small disturbance voltage stability assessment of power systems by modal analysis and dynamic simulation

The introduction of liberalized electricity markets in many countries has resulted in more highly stressed power systems. On the other hand, operating points of a power system are acceptable in the feasible region, which is surrounded by the borders of different stabilities. Power system instability is critical for all participants of the electricity market. Determination of different stability margins can result in the optimum utilization of power system with minimum risk. This paper focuses on the small disturbance voltage stability, which is an important subset of the power system global stability. This kind of voltage stability is usually evaluated by static analysis tools such as continuation power flow, while it essentially has dynamic nature. Besides, a combination of linear and nonlinear analysis tools is required to correctly analyze it. In this paper, a hybrid evaluation method composed of static, dynamic, linear, and nonlinear analysis tools is proposed for this purpose. Effect of load scenario, generation pattern, branch and generator contingency on the small disturbance voltage stability are evaluated by the hybrid method. The test results are given for New England and IEEE68 bus test systems.

Small-Disturbance Voltage Stability of Distribution Systems With Induction Generators

This letter presents an investigation about the small-disturbance voltage stability of distribution systems with induction generators by using time-domain nonlinear dynamic simulations. Results show that the presence of induction generators may decrease the system voltage stability margin. It was verified that at the maximum loading point, if the system loading is increased even more, then the induction generator accelerates to a high speed, becoming unstable and leading the system to a voltage collapse.

Analysis of voltage-collapse mechanisms in state space

The effects of the generator excitation current limit, the on-load tap changer (OLTC) and load dynamics on voltage stability are analysed in state space. The variation of the number and coordinates of the equilibrium points with parameters of the system are discussed. In addition, a small-disturbance voltage stability region of a simple system is constructed. When the dynamic aspect of voltage collapse is considered, it is more convenient to analyse it in the state space rather than in the input/output parameter space. The voltage stability of a system is determined by the dynamic characteristics of both the OLTC and the load. The generator excitation current limit affects the voltage stability by changing the small-disturbance voltage stability region and the equilibrium points of the system. After a small disturbance, the mode of voltage instability, fast instability or longer-term instability depends on the composition of the load as well as the value of the system reactance.

A dynamic interpretation of the load-flow Jacobian singularity for voltage stability analysis

In voltage stability analysis, both static and dynamic approaches are used to evaluate the system critical conditions. The static approach is based on the standard load flow equations. For small-disturbance analysis, the dynamic approach is based on the eigenvalue computation of the linearized system, while for large-disturbance analysis a complete time-domain simulation is required. However, both the equilibrium point around which linearization is performed and the initial conditions for the simulation are computed by a procedure which uses the standard load-flow equations. The standard load-flow equations make some implicit assumptions on the steadystate behaviour of dynamic components (generator control systems, loads). These assumptions are not satisfied by the usual dynamic models, and this discrepancy leads to different results in the voltage stability assessment using static and dynamic methods. In the framework of bifurcation theory, this paper discusses the relationships between static and small-disturbance dynamic approaches to find the voltage stability critical condition, with emphasis on system component modelling. A set of hypotheses on generator control systems and load models is given for a multimachine system, according to which the same critical conditions are obtained both from the load flow equations and from the full eigenvalue analysis. These hypotheses are less restrictive than those previously proposed in the literature and make it possible to obtain equivalence between the singularity of the load flow Jacobian and a null eigenvalue of the linearized dynamic system. Following a dynamic argumentation based on small-disturbance analysis, this result may justify the use of simple and fast static methods for voltage stability assessment and shows that the smalldisturbance voltage stability limit depends only on the steady-state characteristics of the dynamic components of the system.

On-line detection of power system small disturbance voltage instability

Small disturbance (SD) voltage stability (or instability) deals with a system's ability to maintain satisfactory voltages following a small disturbance. For an operating condition, a system's SD voltage stability depends on the proximity of the condition to the critical point (or voltage collapse point). A Q angle and Q directional derivatives are proposed for SD voltage instability detection and weak bus identification, respectively. The Q angle index can handle different kinds of loads, e.g., constant P and Q, constant impedance, and constant current, or a combination of them, and is effective in dealing with generator VAr limits. Moreover, the computation speed of the Q angle is fast, which makes it suitable for on-line application. Simulation results using two power systems are provided.