Steady-state Stability Limit Research Articles

Small‐signal rotor angle stability of multi‐virtual synchronous machine (n‐VISMA) microgrid

AbstractAutonomous microgrid is known to lack appropriate inertia and damping for grid stabilization. Due to this, virtual synchronous machine (VISMA) has been introduced to provide necessary ancillary services through control of power converters. In a multi‐VISMA (n‐VISMA) microgrid, relative rotor angle stability of the power system is dependent on the active power balance after small perturbation. Thus, the use of relevant analytical models are essential issues for microgrid stability analysis. This paper presents a comprehensive small‐signal stability analysis to study inherent electromechanical oscillations in the virtual rotors. The subsystems of the microgrid consisting of VISMA, network, load and the outer power control were all modelled in Synchronous Reference Frame. The small‐signal model (SSM) was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines on the network. To validate the developed numerical analytics, dynamic responses of the SSM are compared with those of the non‐linear (NL) system dynamics and the results reveal that the developed linearized SSM is sufficient to accurately characterize behaviour of the VISMA microgrid when operated in autonomous mode. Eigenvalues analysis and parameter sensitivities of the critical modes were investigated. Oscillatory participations of the VISMAs and steady state stability limit of the microgrid have also been investigated.

Steady state characteristics and stability limits of oil lubricated journal bearings using titanium dioxide nanoparticles as lubricant additives

The current work is presented to investigate the impact of titanium dioxide (TiO2) nanoparticle volume fraction and the nanoparticle aggregate sizes on the steady state characteristics and stability limits of journal bearings. A modified Krieger-Dougherty model is used to determine the viscosity of a TiO2 dependent nanolubricant with different TiO2 nanoparticle volume concentration and aggregate particle sizes. Dimensionless couple stress parameter values are calculated based on aggregate particle size and bearing radial clearance. The effects of the couple stress parameter on bearing's steady-state characteristics and dynamic response are studied. The results reveal that increasing the couple stress parameter increases the bearing load capacity as well as the bearing's stability limits. The aggregate TiO2 nanoparticle sizes have sensible effects on bearing characteristics and stability limits of the bearing.

Finite‐element calculation of electromagnetic characteristics and steady‐state stability of dual‐excited synchronous generator

The Dual-Excited Synchronous Generator (DESG) has two sets of field windings. The magnitudes and directions of the two field currents can be regulated, so that the excitation magneto-motive force can be in any direction. The electromagnetic characteristics of the DESG may be different with those of the Traditional Synchronous Generator (TSG) for the different rotor structures of the two generators. To obtain better electromagnetic characteristics, a time-stepping finite element model (T-S FEM) of the DESG is established. The air-gap radial flux density, saturation, active and reactive power of the DESG in single- and dual-axis excitation modes are calculated and compared with those of the TSG. The electromagnetic characteristics affected by the different ratio of q-axis field current to d-axis field current are studied. On this basis, an excitation control strategy that can enhance the steady-state stability is proposed, and the steady-state stability limits with and without excitation control are calculated by the T-S FEM. A 10-kW DESG is developed to verify the correctness of the simulation results. The results show that the DESG with dual-axis excitation has better electromagnetic characteristics and stronger reactive power ability, and the steady-state stability limit of the DESG is increased obviously through the excitation control.

Power and energy system oscillation damping using multi-verse optimization

Power system oscillations are the primary threat to the stability of a modern power system which is interconnected and operates near to their transient and steady-state stability limits. Power system stabilizer (PSS) is the traditional controller to damp such oscillations, and flexible AC transmission system (FACTS) devices are advised for the improved damping performance. This paper suggests a technique for controller parameters tuning of PSS and a shunt connected FACTS device to be operated in coordination. A static synchronous compensator (STATCOM) connected in a two-machine system is considered as a test power system for the system studies. A recent meta-heuristic algorithm, Multi-Verse optimizer (MVO) has been suggested and compared with the other state-of-the-art algorithms. Improvement in system damping has been achieved by minimizing the oscillating nature of the system states by framing the objective function as a function of damping ratio and location of poles of the system. The Phillips-Heffron model of the test system has been designed by considering the system dynamics. The coordinated system behavior under the perturbation in system parameters has been observed satisfactory with the tuned controller parameters obtained from the suggested algorithm.

Functioning of back-to-back high voltage direct current link model in Tomsk electric power system

In this article the research results of steady-state and dynamic performance of asynchronous back-to-back HVDC link in Tomsk electric power system are presented. It is proposed to use the back-to-back HVDC link to provide an asynchronous link for parallel operation of the North and South parts of Tomsk electric power system. The steady-state stability limit and maximum allowed power flow were defined. Based on this the more effective location and power of back-to-back HVDC link were determined. Therefore, it is shown the application of back-to-back HVDC link decreases the level of short-circuit current, power fluctuations and increases the stability of load operation, especially of motor load at substation.

Optimal Design and Control of SSSCs for TLs Considering Technical and Economic Indices Using GA and SAMPE-JAYA Algorithms

Improving transmission lines (TL) steady-state stability limit can be achieved by Static Synchronous Series Compensators (SSSC) that work as a converter-based compensator. The modification of the SSSC function to inject both active and reactive power into the TL improves its performance according to different indices. The TL improvement indices include the reduction of TL losses, the enhancement of dynamic stability margin and the improvement of voltage profile along the TL. The economic index is considered a vital factor in the design of SSSC devices installed in TLs. This paper proposes an objective function to design and control SSSC devices by considering various technical and economical indices. The formulation of the objective function requires power flow analysis in the compensated transmission line under different loading conditions and compensation levels. The proposed multi-objective function includes the transmission line losses, the dynamic stability span, and the cost of SSSC device. The Genetic Algorithm (GA) and Self-adaptive Multi-population Elitist Jaya Algorithm (SAMPE-JAYA) are proposed as optimization techniques to obtain the minimized value of the multi-objective function. This paper proposes the installation of two SSSC devices in TL that leads to the improvement of the design and control indexes. The proposed objective function and the optimization techniques are applied for tie-line (400kV, 400km) that connects between two networks.

Steady-State Stability of Sending-End System with Mixed Synchronous Generator and Power-Electronic-Interfaced Renewable Energy

Coupled with the power system through power-electronic interfaces, renewable energies including wind power and photovoltaic can control the power quickly and flexibly. In the steady-state stability analysis, by neglecting the fast dynamics of power-electronic interfaces, the renewable energy power is simplified to a static power injection model and can be described as an algebraic equation in the dynamic process. Based on this simplified model, the steady-state stability of sending-end system with mixed synchronous generator and power-electronic-interfaced renewable energy is studied. By proposing a triangular transformation model based on the classical model of power system, the steady-state stability analysis becomes feasible. The mechanism of steady-state stability is revealed, and the influence of renewable energy on the steady-state stability limit is quantitatively investigated. When the renewable energy power increases, the steady-state stability limit of the sending-end system first increases and then decreases. Reducing the power output of synchronous generator can change for a higher integration limit of renewable energy. Simulation results validate the conclusion.

Implementation of graphical user interface to observe and examine the frequency and rotor angle stability of a power system due to small disturbances

<span lang="EN-GB">The aim of this research is to anticipate the stability status of a power system when the system is exposed to a change in frequency and rotor angle due to small disturbances. The proposed study was implemented on the IEEE Reliability Test System 1979 (IEEE RTS-79) which contains 24 buses, 38 transmission lines and 32 generators. Steady state stability limit of a system refers to the maximum amount of power that is permissible through the system without loss of its steady state stability. This research proposes the development of a Graphical User Interface (GUI) to observe the frequency and rotor angle stability due to the effect of small disturbances using the One Machine Infinite Bus (OMIB) technique. This proposed technique could ease the power system utility especially the power system operation to observe and examine the system frequency and rotor angle stability due to small disturbances. The findings from this research has proven that the proposed technique to observe the frequency and rotor angle stability due to small disturbances has successfully been developed using a GUI.</span>

Estimating the Wind Power Integration Threshold Considering Electro-Thermal Coupling of Overhead Transmission Lines

With regard to wind farms connected to the main system via dedicated overhead transmission lines, the available wind power absorbed by the system relies on not only the power generation capacity but also the power transmission threshold. Thus, this study centers on the close relationship between environmental conditions and power transfer limits that involve the thermal limit and steady-state stability limit. Simultaneous equations representing both overhead conductors’ heat balance and power transmission operation are established. In addition, formulations of the maximum transmission power for the steady-state stability limit are derived and then expressed as functions of environmental factors and the line length. The presented approach allows one to analyze the threshold considering not only the thermal limit but also the steady-state stability limit, which could be remarkably different under certain environmental and transmission distance conditions. Then, a scheme to identify the primary limitation and obtain the corresponding threshold value is proposed. Moreover, a simple treatment of wind speed correlation is deployed because of the close distance between a wind farm and its tie-line. Case studies demonstrate that, for a certain wind speed level, the process of transmission rather than generation could become the key factor determining the threshold value.

A Review of Generator Loss of Excitation Protection Schemes

Loss of excitation (LOE) on synchronous machine is an abnormal operating condition which, if not detected, can have severe consequence. This paper aims at providing an in-depth analysis of the phenomenon, factors and the impact of LOE. It discusses the various protection schemes and provides the basis for selection of settings. The philosophy for coordinating loss of excitation protection with generator capability and steady-state stability limits is discussed. The performance of impedance and admittance schemes is analysed with the help of simulation. A case where loss of excitation protection is prone to incorrect operation for stable power swings is studied, which suggests the importance of dynamic studies for setting loss of excitation relay. The results suggest the need for intelligent relaying techniques for improving the reliability of LOE protection schemes. Finally, it discusses the latest advancements in the area of LOE protection.

Models of Closest Marginal States of Power Systems in <italic>p-</italic>Norms

In order to maintain power system security at the appropriate level and low cost, it is essential to accurately assess steady-state stability limits and power flow feasibility boundaries, i.e., power system marginal states (MS). This paper is devoted to researching the closest MS models in the p -norms. The theoretical studies have revealed that the model of the closest MS in the weighted max-norm, which considers errors of the power change forecast by means of the weighted Euclidean norm, corresponds most closely to requirements of the system operator (SO) for an assessment of the steady-state stability reserve and for the preventive control. At the same time the model of the closest MS in the one - norm best satisfies SO requirements for the corrective and emergency control, and for moving a system state into the power flow feasibility region. This model gives a control action to a critical bus, adding others only in the case of a dosage lack. As a result minimum number of buses will be affected, and minimum loads will be shed.

Determination of Generator Steady State Stability Limit for Multimachine System based on Network Losses Concept

In the multimachine circumstances, it is difficult to analyze the steady state stability of each generator. In previous research, analysis of the steady state stability limit has been carried out but only look at the stability of the overall system. Therefore, to analyze the stability of each generator, the multimachine system must be changed into a Single Machine to Infinite Bus (SMIB) system by collecting all the loads into one central load in the infinite bus. The method to change from the multimachine system to SMIB system is presented in this paper. The multimachine system is converted into an equivalent impedance (req and xeq) and an equivalent load based on losses concept. After req and xeq is calculated, then by using steady state stability limit concept, the value of the maximum generation of each generator units can be determined. By means of maximum generation is the maximum output power limit that can be generated without causing unstability. ETAP simulation is used to validate the calculation results of the proposed method. The method was applied to units generator in Java Bali system 500 kV.

Reactualization of a Modified Single Machine to Infinite Bus Model to Multimachine System Steady State Stability Analysis Studies Using Losses Network Concepts and Radial Basis Function Neural Network (RBFNN)

To analyze the stability of each generator, the multimachine system must be changed into a Modified Single Machine to Infinite Bus (M-SMIB ) system. This paper proposes a method to change the multimachine system into a M-SMIB system with an equivalent impedance and an equivalent load by determining the contribution of each generator to a loading value using a simple technique. After the M-SMIB system is obtained, a steady-state stability analysis can be performed on each generator unit. In this paper, the maximum generation value which is the generator steady state stability limit, is determined. The Radial Basis Function Neural Network (RBFNN) is applied to determine the range area of generator steady state stability with the variable load to observe the influence of load variation in the generator steady state stability area. Thus, the area of safe operation of the generator can be directly observed without causing instability of the system. Therefore, the steady state stability limits of each generator unit can be directly determined every time there is a change of loading and recognize the operation limit of each generator during disturbances occurring on the bus. This method will be applied to a 4-bus IEEE system with 2 generators.

Effective Micro Grid Stability Under Excitation Limiters in Islanded and Connected Modes

In this paper the authors tried to design a under excitation limiter and a power system stabilizer which can operate without any kind of interaction. The under excitation limiter (UEL) is intended to prevent reduction of generator excitation to a level where the steady state stability limit or the stator core end-region heating limit is exceeded. The power system stabilizer (PSS) uses auxiliary stabilizing signals to control the excitation system so as to improve power system dynamic performance.

Coordinated Design of Under-Excitation Limiters and Power System Stabilizers

In this paper the authors tried to design a under excitation limiter and a power system stabilizer which can operate without any kind of interaction. The under excitation limiter (UEL) is intended to prevent reduction of generator excitation to a level where the steady state stability limit or the stator core end-region heating limit is exceeded. The power system stabilizer (PSS) uses auxiliary stabilizing signals to control the excitation system so as to improve power system dynamic performance.

Об анализе пределов по апериодической устойчивости электроэнергетических систем

The article considers the possibility of finding a correspondence between the electric power system (EPS) aperiodic steady-state stability limit and the reaching of an extreme value of some physical variable(s). It is shown that for EPSs satisfying the conditions under which the Jacobian of the steady-state equation system has the sign coinciding with the sign of the EPS characteristic equation’s absolute term, the aperiodic steady-state stability limit corresponds to the extreme value of the variable in which the operating mode is aggravated (and, consequently, to the extreme values of the active power outputs of the generators being loaded/unloaded and consumed loads in the operating mode aggravation scenario). It is also shown that in the general case one cannot judge about reaching the EPS aperiodic steady-state stability limit based on reaching an extreme value of power transmitted through one of the aggravated power system cut sets.

Fast and Reliable Method of SearchingPower System Marginal States

In order to maintain power system security at the appropriate level and low cost, it is essential to accurately assess steady-state stability limits and power flow feasibility boundaries, i.e., power system marginal states (MS). This paper is devoted to a robust realization of the MS model based on nonlinear programming in a given direction of power change. Considering peculiar properties of this model has allowed proposing a simple, robust and computationally efficient method of the MS search that uses only standard blocks of the load flow solution and can be easily realized in the existing load flow programs. The technique developed on this basis allows considering errors of power change forecast quite easily. Tests on IEEE and Russian systems showed effectiveness of the proposed methods.

Design and Implementation of Voltage Source Converter Excitation System to Improve Power System Stability

This paper presents the design of the voltage source converter (VSC) excitation system and an integrated prototype using digital signal processor (DSP) as the core of the excitation controller is developed. Compared with the static excitation systems with thyristor, the VSC excitation system owns one more channel offering positive damping to power system by controlling reactive power of VSC on its ac side, and this approach is approved much faster than field voltage regulation. To design the prototype, the VSC excitation system has to meet the practical condition of the selected synchronous generator (SG) set such as generator capacity, terminal voltage, field voltage and field current. The designed VSC excitation system consists of converters containing a front-end three-phase VSC and a back-end H-bridge chopper, a step-down transformer, and a coordinate excitation controller. Through a series of experiments, it is demonstrated that the VSC excitation system is able to improve both transient stability and steady-state stability limit of power systems. It is a prospective substitute to the conventional thyristor-based static excitation system and an attractive solution to strengthen power system stability as well as increase the capability of long-distance transmission systems.

Analysis of power transfer limit considering thermal balance of overhead conductor

Series resistances of overhead transmission lines (OTLs) are largely dependent on the corresponding conductor temperature. The electric current heats the conductor, and the environmental conditions affect the thermal exchange. Therefore, multiple factors related to the thermal balance codetermine the conductor temperature and resistance. However, the traditional power flow analysis neglects the thermal balance effects by treating those related factors as invariables, which may introduce some errors because of the change of the factors. Therefore, in this study, new power flow formulations, which allow for the relationship between the transmission power flow and the thermal balance, are derived. This study demonstrates the errors by applying the new formulations to calculate the power transfer limit (PTL). Moreover, the PTL of the OTL is defined either by encountering the thermal rating (TR) or the steady-state stability limit. A case study based on an equivalent 2-bus test system was used to illustrate the efficacy of the thermal balance that affects the PTLs of both types. In this analysis, this study also reveals the relationship between the TR and steady-state stability limit with various physical and environmental conditions.

Study on the Steady-State Stability Margin of a Weak Section by Using the Online Data of WAMS

To realize the on-line quick analysis of the steady-state stability margin for the weak section of a power grid, a method of dividing the important generator groups according to the impact of the system equivalent impedance on the static stability limits of the section is presented. By using the dynamic information provided by the Wide Area Measurement System (WAMS), the center of inertia (COI) of the section of the two sides system is determined. Then the steady-state stability limits of the transmission section and the static stability margin can be calculated. The algorithm is verified by taking the out-play cross-section of West Inner Mongolia as an example, the results show that the static stability power limit and the steady-state stability margin of the section can be obtained accurately according to the presented algorithm. This algorithm can provide an effective analytical method for the online static stability security analysis of a power system.