Small-signal Stability Studies Research Articles

A new integrated modelling and control of ternary pumped storage hydro power generation for small signal stability studies

Pumped storage hydro power generation (PSHPG), a reliable renewable energy source with an energy storage feature, can impart efficient damping torque to power system oscillations to improve small signal stability with appropriate modelling and additional compensation through the governor. But ternary PSHPG (T-PSHPG) has the unique feature of hydraulic short circuit (HSC) mode, where both pumping and generating modes operate simultaneously. This study presents a novel fourth-order modified Heffron Phillips (MHP) model of T-PSHPG in coordination with a multi-band Power system stabilizer (MB-PSS) employing 2-way penstock, where primary penstock circulates water from the upper reservoir to the lower reservoir through the turbine and secondary penstock divides primary penstock, thereby creating short-circuit path through the pump. Also, this model includes additional reactive power droop control to maintain the voltage profile. A new state space matrix has been developed for coordinating T-PSHPG in HSC mode with MB-PSS. The control parameters of the proposed coordinated model are set by a new multi-objective differential evolution-improved particle swam optimization (DE-IPSO) algorithm. With variable load, random solar and wind source penetrations, it has been found that the proposed model can provide adequate damping actions. The sensitivity of the proposed model has been observed by varying critical model parameters by ±50 %. For all conditions, the settling time of speed variation is within 2.672 s to 5.951 s and the minimum damping ratio lies within 0.105 to 0.455. The minimum damping ratio is 0.32 and the settling time is found to be 3.1 s for system response subject to sudden solar power variation, which has been observed by shifting system eigenvalues toward the left half of the complex plane. Time and frequency domain parameters with sensitivity analysis predict system oscillations being damped effectively with consistency for the proposed modelling and control strategy. The results are verified in real-time with OPAL-RT real-time digital simulator. It has been justified by the present study that appropriate modelling of T-PSHPG along with coordinated control action provided by MB-PSS can handle critical power system oscillations efficiently and effective damping torque can be imparted in HSC mode.

Development of the equivalent Great Britain 36-zone power system for frequency control studies

This paper presents a dynamic model of the equivalent Great Britain (GB) 36-zone power system, which can be used for reliable and realistic assessment of emerging load frequency control mechanisms. Flexible architecture of the presented dynamic test system permits a broad range of security of supply and small-signal stability studies for design of future power grids. It can be particularly useful for academic research, but also for undertaking feasibility studies in power industries. The proposed dynamic test system, which is obtained through network reduction of the original full-scale GB transmission power system developed by National Grid Electricity System Operator (NGESO) Company, provides detailed information about the GB power system. In this regard, the required data and modelling approaches to develop the 36-zone system are provided in detail. The presented dynamic test system represents the system topology, impedance characteristics and electromechanical oscillations of the original GB power system however, it is not an exact equivalent of the master GB system. Illustrative dynamic models of the key system components, including synchronous generators, automatic voltage regulators, power system stabilizers, hydro and steam turbines models along with speed governing systems are presented. Dynamic behavior of 36-zone test system in response to infeed loss contingencies is investigated. Particularly, the impact of changes in the system inertia on the system electromechanical modes is examined using the modal analysis approach. In this context, the mode shape concept is employed to determine dominant generators and contribution of different zones in the low frequency oscillations. Moreover, time-domain simulations are undertaken to validate the modal analysis results. Additionally, the condition of different zones from the viewpoint of frequency nadir and maximum rate of change of frequency for various contingencies and extreme cases are examined.

Design of a Wide-Area Power System Stabilizer resilient to permanent communication failures using bio-inspired algorithms

The operation of power systems requires a set of requirements and studies to ensure the continuous and safe supply of electricity to consumer centers. In small-signal stability studies, low-frequency oscillation modes need to be evaluated as they can compromise the operation of power systems if they are not properly damped. Many structures and control devices have been proposed to mitigate these oscillation modes and the Wide-Area Power System Stabilizers (WAPSSs) have proven to be effective in improving the damping rates of these modes as they use remote system signals from Phasor Measurement Units (PMUs). However, cyber-attacks and communication failures can affect WAPSS communication channels and affect its operation in the power system. This article proposes a method based on a multiobjective optimization model for WAPSS design that is robust to the permanent loss of one WAPSS communication channel. Bio-Inspired Algorithms are applied and compared to solve the optimization problem. A set of case studies were conducted and discussed for the IEEE 68-bus system through modal analysis and time domain simulations. The achieved results showed the need for a fault-robust damping controller and the WAPSS-type controller was able to guarantee good dynamic performance regardless of permanent communication failures. Furthermore, different bio-inspired algorithms provided different results for the closed-loop control system when applied to the proposed optimization model.

Vector-controlled Y-connected three-phase induction motor drives: small-signal stability study during IGBT short-circuit fault

<p>The stability analysis is one of the most important elements to describe the performance of AC drive systems under both dynamic and steady-state operating circumstances. This is particularly essential because electric motors operate over a wide range of speeds and utilize complex control systems such as field-oriented control (FOC). This study establishes a small-signal stability analysis (SSSA) in a 1-horsepower vector-controlled Y-connected three-phase induction motor (YCTPIM) drive during an insulated gate bipolar transistor short-circuits failure (IGBT-SCF). In the beginning, a vector control system that is based on the indirect rotor FOC (IRFOC) method is described for post-fault functioning of the YCTPIM while the IGBT-SCF is taking place. After that, a small-signal model of the system that has been provided is explored. This model is based on a voltage-current model, and it is constructed by linearizing the non-linear dynamic equations of the system. During IGBT-SCF, an IRFOC strategy as well as SSSA operations are carried out on the 1-HP, 380 V, and YCTPIM. In this research, both analytical and simulation-based methodologies are applied.</p>

A simplified model of flexible power point tracking algorithms in double-stage photovoltaic systems

Traditionally, photovoltaic (PV) systems have been operated using maximum power point tracking algorithms, which force the PV arrays to produce the maximum available power at all times. Nevertheless, distribution system operators are increasingly asking for flexible power point tracking (FPPT) algorithms, which allow the regulation of the PV power to a predefined reference value. FPPTs are difficult to tune and often have non-linear behavior. It complicates the modeling of PV systems for power system stability studies. This paper proposes a simplified model that reproduces the dc-side dynamics of a double-stage FPPT-controlled PV system. In addition to its simple tuning, the key advantage of the proposed model is that it can be easily translated into differential equations, which can be used in stability analyses. The proposed model is validated on a temporal simulation as well as a small-signal stability study.

Revamped Sine Cosine Algorithm Centered Optimization of System Stabilizers and Oscillation Dampers for Wind Penetrated Power System

The mapping of damping ratios and damping factors by Sine-Cosine Algorithm (SCA) is significant in the analysis of low frequency oscillations generated in an integrated network having multiple conventional and renewable energy sources. Multiple random models with unknown search spaces and uncertain conditions and constraints, which incorporate the fluctuation of solutions towards or outwards at the initial stage for solving real-time problems can be analyzed by a revamped sine-cosine algorithm (RSCA) model. In this paper, the SCA has been revamped to explore the stability threshold for a stable system under dynamic nonlinear operating conditions. It is achieved with the infusion of suitable mathematical functions for optimizing the parameters of Power System Stabilizers (PSSs) and Doubly Fed Induction Generator (DFIG) system-based oscillation dampers to enhance the Small Signal Stability of power systems through effective damping of low-frequency oscillations (LFOs). These LFOs weaken the effective power generation and demand management cycle in conventional power systems when the system faces conditions like intermittent renewable energy sources, overloading conditions, impulsive faults etc. The small-signal and transient stability studies for various disturbances and different operating conditions are investigated, and the performance of the proposed RSCA for optimized parameter tuning of system stabilizers and oscillation dampers are analyzed on the modified benchmarking systems with wind generators using MATLAB Ⓡ simulations. The efficiency and robustness of the proposed algorithm has been verified under selective critical operating conditions, line outages, and load uncertainties to prove that the low frequency modes are damped with an elevated positive damping ratio and rapid settling time with reduced oscillations. The application of system stabilizers and oscillation dampers optimized through the proposed RSCA shows a reduced settling time in the LFOs created and improved damping ratio of 0.22 for an increase in 20% loading and 50% of wind power generation in the case study of Two Area Four Machine System.

An Approximate Aggregated Impedance Model of a Grid-Connected Wind Farm for the Study of Small-Signal Stability

In this paper, an approximate aggregated impedance model (AAIM) of a grid-connected wind farm with multiple wind turbine generators (WTGs) for the small-signal stability study is derived. The derivation is conducted under the condition that the WTGs inside the wind farm are of the same type and from the same manufacturer. The AAIM derived can be seen as the impedance model (IM) of a grid-connected aggregated WTG. The IM of the aggregated WTG is the weighted average of the IMs of the individual WTGs in the wind farm and hence is simple to be built. The reactance of the line connecting the aggregated WTG to the external AC grid is the maximum eigenvalue of the network reactance matrix of the grid-connected wind farm. In addition, the derivation justifies the representation of a wind farm by an aggregated WTG in the IM-based small-signal stability analysis. Finally, two example grid-connected wind farms are used to evaluate and demonstrate the effectiveness of the AAIM proposed in the small-signal stability analysis. It is also shown that the computational burden of the stability analysis of a large-scale wind farm could be effectively reduced when the AAIM is used.

Linear quadratic regulator design via metaheuristics applied to the damping of low-frequency oscillations in power systems

This paper proposes the application of control by state feedback using the linear quadratic regulator (LQR) optimized by metaheuristics to damp low-frequency electromechanical oscillations in electrical power systems. The current sensitivity model was used to represent the single machine infinite bus (SMIB) system in the time domain. The weighting matrices of the LQR were adjusted using four different algorithms: (i) the genetic algorithm, (ii) the differential evolution algorithm, (iii) the particle swarm optimization algorithm, and (iv) the gray wolf optimization (GWO) algorithm. In the cases considered, disturbances were applied to the electrical power system and, then, performances comparisons associated with each metaheuristic were statistically analyzed, in which the number of iterations, error, and time to achieve convergence of each algorithm were compared. From the results, it was possible to conclude that the algorithms were efficient in adjusting the weighting matrices of the LQR, providing additional damping to the poles of interest of the system. It was also possible to conclude that the GWO algorithm presented the best performance, accrediting it as a powerful tool in the study of small-signal stability for the analyzed case.

Large-Signal Stability Analysis and Control for Small-Scale AC Microgrids With Single Storage

Small-signal stability studies of ac microgrids have obtained abundant results, however, the large-signal stability is still a great challenge and this topic is little studied. In this article, the nonlinear reduced-order model of small-scale ac microgrids with single storage is established considering the structure changes of converters under large disturbances. Then, the large-signal stability is analyzed and the unstable mechanism is revealed. It is found that the structural changes caused by the limitation links have a great influence on the system stability. Based on the unstable mechanism, the virtual synchronous damping control is proposed to enhance the large-signal stability of ac microgrids. The effectiveness of the proposed analysis and control methods is validated through related case studies.

An approach for the aggregation of power system controllers with different topologies

This paper proposes an approach to aggregate non-structured power system controllers preserving the dynamical characteristics of the original devices. The method is based on linear operations that use the frequency response of the elements, resulting in an accurate input–output description of the equivalent controller when compared to the original ones. The developed method was applied to a model of the future interconnected Paraguayan-Argentinean power system to produce a dynamic equivalent used in a real-time simulator to test the special protection scheme needed for the safe operation of the this future system. Transient and small-signal stability studies presented matching simulation results in the time domain with significantly reduced computational burden and processing time.

Mayfly Optimization Algorithm Applied to the Design of PSS and SSSC-POD Controllers for Damping Low-Frequency Oscillations in Power Systems

In this paper, it is proposed to apply the mayfly optimization algorithm (MOA) to perform the coordinated and simultaneous tuning of the parameters of supplementary damping controllers, i.e., power system stabilizer (PSS) and power oscillation damping (POD), that actuate together with the automatic voltage regulators of the synchronous generators and the static synchronous series compensator (SSSC), respectively, for damping low-frequency oscillations in power systems. The performance of the MOA is compared with the performances of the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm for solving this problem. The dynamics of the power system is represented using the current sensitivity model, and, because of that, a current injections model is proposed for the SSSC, which uses proportional-integral (PI) controllers and the residues of the current injections at the buses, obtained from the Newton–Raphson method. Tests were carried out using the New England system and the two-area symmetrical system. Both static and dynamic analyses of the operation of the SSSC were performed. To validate the proposed optimization techniques, two sets of tests were conducted: first, with the purpose of verifying the performance of the most effective algorithm for tuning the parameters of PSSs, PI, and POD controllers, and second, with the purpose of performing studies focused on small-signal stability. The results have validated the current injections model for the SSSC, as well as have indicated the superior performance of the MOA for solving the problem, accrediting it as a powerful tool for small-signal stability studies in power systems.

Performance Evaluation of Hybrid Power System Incorporating Electric-Vehicles

State-of-the-art: The present study broadly addresses the performance analysis of a hybrid power system with the inclusion of modern day electric vehicles (EV) and renewable energy sources. Generations in the form of conventional-thermal, diesel-plant, solar-thermal for the hybrid power system as well as EVs establish a concurrent regulation of system frequency, voltage and corresponding tie-lie power. The effective power management for the power system is established in such a way that EV realizes the battery management system integrated with the utility grid. The instantaneous control and management capability of a grid-connected EV are the main attractive features that are highlighted in this work. Small signal stability study of the developed hybrid power system is investigated through Eigen-value analysis.
 Methods & Outcomes: For anticipated performance enhancement for the developed hybrid power system, the parameters are adjusted using a dominant magnetotactic-bacteria optimization (MBO) technique. The performance of MBO optimized controller for effective control of system dynamic responses are validated in this study. Sensitivity tests involving large deviations beyond nominal values of system components validate the reliability of the hybrid power system. The role of EV in terms of power control and management has been successfully demonstrated. The stability of the controlled power system is verified using Eigen-value analysis. The role of EVs help to improve system stability is also proved.

Enhancing Transient Response and Voltage Stability of Renewable Integrated Microgrids

Integration of renewable generation coupled with an energy storage system (ESS) in a power system increases the complexity of networks’ stability analysis and control. Therefore, an accurate stability assessment of power networks is expected to become a big challenge in the future. In this work, an effective approach to prevent power outage by controlling the source voltage of the power network is formulated to mitigate the effects of grid faults. Small signal stability studies are conducted on a renewable integrated IEEE 9 bus system as a case study with optimized size and allocation of ESS for reducing output power variability of renewables. An assessment is performed to study the effects of load-sharing devices on parallel generators under 6-cycle three-phase fault disturbances. The damping of the power network is increased at nominal and light loading conditions with 6-cycle three-phase fault disturbances through coordinated power system stabilizer (PSS) and static VAR compensator (SVC) at bus 9. The developed framework is extensively analyzed in steady-state conditions using a load flow program. Based on the results obtained, the proposed coordinated PSS-SVC device proves to possess comparatively better performance in terms of enhancing most of the system response rate under various load conditions with overall improved stability.

Recommendations of Optimal Sampling Rates for Periodic Output Feedback Based Discrete Mode PSS

In this paper, an attempt is made to recommend the optimal sampling time period for Periodic Output Feedback (POF) based discrete mode power system stabilizer (DPSS). Various collection of input and output sampling time interval has been used in the designing of POF based DPSS. The Particle Swarm Optimization (PSO) technique is used to obtain the optimal gain matrix of the POF controller as well as the optimal sampling time intervals. The effectiveness of POF based DPSS over continuous mode lead-lag PSS is certified using small-signal stability studies. The parameters of lead-lag type continuous mode PSS is also tuned using the PSO technique. The PSS is designed using POF technique for single machine infinite bus (SMIB) system, considering a variety of sampling time intervals at input-output port. Finally, a trial is made to propose an optimum input and output sampling time period for SMIB test power system, through simulation studies.

Comparative Study of Small-Signal Stability Under Weak AC System Integration for Different VSCs

Voltage source converters (VSCs) with self-commutation ability are suitable for interconnecting weak ac systems. This article conducts a comparative study of the small-signal stability characteristics for three typical VSCs, namely, the two-level VSCs (TL-VSCs), the half-bridge modular multilevel converters (HB-MMCs), and the hybrid MMCs (HY-MMCs), under weak ac system integration with special consideration on both inverter and rectifier operation. The frequency responses based on impedance models are compared using the frequency-domain analysis. The oscillation frequencies and mainly participated state variables of the unstable modes are compared using root locus and participation factor analysis in the time domain. Proper parameter retuning approaches for stability enhancement are proposed. The above analysis is adequately validated by electromagnetic simulations.

Equivalent Multiple $dq$-Frame Model of the MMC Using Dynamic Phasor Theory in the $\alpha \beta z$-Frame

This article introduces an equivalent multiple dq-frame model of the modular multilevel converter (MMC) that is derived from a dynamic phasor based small-signal state-space MMC model in the stationary αβz frame. When compared to a model in the stationary ABC frame, the order of the model in the αβz frame can be reduced for balanced operation, during which some voltage, and current harmonics are inherently separated in an αβz representation. The proposed method enables further model order reduction through a generalized transformation towards multiple dq-frames. The development of the model, and the generalized transformation are explained in detail, and the obtained equivalent multiple dq-frame models are verified against a nonlinear averaged model in MATLAB/Simulink. An eigenvalue-based small-signal stability analysis highlights the effect of higher-order harmonics in system-level small-signal stability studies, and two case studies of active harmonic suppression illustrate how the presented model allows an in-depth investigation of the impact of extended control functionalities on the small-signal stability.

Coordinated Voltage and Frequency Control in Hybrid AC/MT-HVDC Power Grids for Stability Improvement

In this paper, an adaptive coordinated voltage and frequency control scheme is proposed for hybrid AC/ multi-terminal high voltage direct current (MT-HVDC) power networks for stability improvement. The coordinated control strategy is realised using a multi-dimensional droop approach, which can also be implemented as a distributed control strategy in hybrid AC/MT-HVDC networks without a communication link between voltage source converters (VSCs). Moreover, the controller parameters are adaptive to the fault condition to improve the stability and suppress post-fault oscillations. A state-space model of the VSC is built while explicitly representing the phase-locked loop (PLL) dynamics. An oscillation index is proposed to quantitatively assess the oscillation severity of the AC voltage, frequency and the DC voltage. The proposed strategy is implemented in the CIGRE test system developed in DIgSILENT Power Factory. According to the small-signal stability study, the proposed multi-dimensional control scheme improves the frequency stability and maintains the AC voltage stability of the hybrid AC/MT-HVDC power network. Under severe fault conditions, the adaptive multi-dimensional control scheme improves the system stability while adjusting the controller parameters based on the severity of the fault. Therefore, the proposed scheme can improve and optimise the overall stability of the hybrid AC/DC power grid.

Analysis of the dynamics and topology dependencies of small perturbations in electric transmission grids.

We study the phase dynamics in power grids in response to small disturbances and how this depends on the grid topology. To this end, we consider the swing equations in linear order in phase disturbances and solve the resulting linear wave equation, deriving the eigenmodes of the weighted graph Laplacian. A linear response expression for the deviation of frequency is given in terms of these eigenvalues and eigenvectors, which it is argued to be the basis for future power system stabilizers and other control measures in power systems. As an example, we present results for random networks based on the Watts-Strogatz model, where we observe a transition to localized eigenstates as the randomness in the degree distribution grows. Moreover, it is found that localization leads to faster decay rates. Thereby, disturbances are found to remain localized on a few nodes where they decay faster. Finally, we also consider the German transmission grid topology, where the eigenstate of the lowest eigenfrequency, the Fiedler vector, is found to be extended, with large intensities at the northwestern and southern boundaries.

Small signal stability analysis of power systems integrated with wind power using sensitivity-based index

To know the inherent property of the power system connected with a wind farm along with its associated controllers, a small signal stability study is required. For this, a linearized system model has to be developed. The small signal model of the system with wind farm along with its controllers is discussed here. The eigenvalues of system matrix are computed from the linearized model of the power system. The absolute value of the real part of eigenvalues indicates distance from instability. The sensitivity of this minimum real part of eigenvalues with respect to small changes of wind power injection is used as an index to assess the small signal stability under various operating conditions. The optimum value of the wind power can also be determined with the help of the proposed eigenvalue sensitivity index. The systems used for the study are WSCC 3-machine 9-bus system and IEEE 16-machine 68-bus system.

Parameter Preserving Model Order Reduction of Large Sparse Small-Signal Electromechanical Stability Power System Models

This paper proposes a method for the model order reduction (MOR) of large scale power system models that produces reduced order models (ROM) which preserve the access to selected parameters exactly like the original full order model (FOM). The preserved parameters are related to decentralized power system devices, including, but not limited to, power system stabilizers that are used for the damping control of system electromechanical oscillations. The problem formulation of this parametric MOR (PMOR) is described, as well as the implementation details regarding efficiency and flexibility. Test results are described for large practical power system models used in small-signal electromechanical stability studies. The ROM produced sufficiently accurate responses following parameters changes, when equivalently compared to the original FOM results. The proposed method allows preserving specified nonlinearities in chosen devices of the parameterized ROMs. It can also be applied to the reduction of differential algebraic equation models related to other areas of engineering.