Two-area Test System Research Articles

Damping Torque Analysis of the PMSG-Based WT with Supplementary Damping Control for Mitigating Interarea Oscillations

This study presents a comprehensive analysis of the impact that a supplementary damping controller of the permanent magnet synchronous generator (PMSG)-based wind turbine (WT) has on low-frequency oscillation (LFO) damping. A reduced mathematical model of an interarea system is first established. Then, an auxiliary damping controller is designed using the PMSG active power control loop, enabling the WT to actively support the interarea LFO mitigation. Based on this, the damping torque analysis (DTA) method is applied to explore the contribution of the PMSG-based WT with an auxiliary damping controller to LFO damping enhancement, whose analytical expressions of the damping torque coefficients reveal the impacts of the control parameters and the operation conditions on the system damping characteristics. It is evident that the installation location of the wind power plant (WPP) plays a leading role in determining whether the damping provided by the PMSG controller is positive or negative. Also, the contribution of damping from the PMSG can be improved by tuning the droop coefficient of the PMSG controller properly. The results indicate that the proposed damping control is always helpful in improving the system damping when the wind power penetration increases. Accordingly, analytical conclusions can serve as guidelines for the control design. Case studies of a two-area test system integrated with a PMSG-based wind farm have been conducted to verify the theoretical analysis.

The Impact of Frequency Support by Wind Turbines on the Small-Signal Stability of Power Systems

Rising wind energy integration, accompanied by a decreasing level of system inertia, requires additional sources of ancillary services. Wind turbines based on doubly fed induction generators (DFIGs) can provide inertial and primary frequency support when equipped with specific controls. This paper investigates the effect of frequency support provision by DFIGs on the small-signal stability of power systems. To this end, a modified version of the Kundur two-area test system is employed to analyze different scenarios. Wind energy generation is either added to the existing system or displaces part of the synchronous generation. Simulations show that primary frequency support tends to improve the damping of electromechanical oscillations and deteriorate it for converter control-based ones. On the other hand, the inertial response depends on the control parameters.

A Novel Improved GSA-BPSO Driven PID Controller for Load Frequency Control of Multi-Source Deregulated Power System

In this paper, a novel improved gravitational search algorithm–binary particle swarm optimization (IGSA-BPSO) driven proportional-integral-derivative (PID) controller is proposed to deal with issues of automatic generation control (AGC) of interconnected multi-source (thermal-hydro-gas) multi-area deregulated power systems. The effectiveness and robustness of the proposed controller is compared and analyzed with GSA and PSO-driven PID controllers. The simulated and mathematically formulated results show the superiority of the proposed IGSA-BPSO driven PID controller compared with the other two techniques in settling time, overshoot, and convergence time. The two-area test system considered in this article is integrated with a thermal, hydro, and gas turbine power plant. Integral time multiplied by absolute error (ITAE) is used as the objective function (minimization) by optimization techniques for getting optimum parameters of PID controllers installed in each area. The system’s dynamics are examined using poolco, bilateral, and contract violation cases under a deregulated environment, and the comparative results are shown to analyze the efficacy of the proposed concept. Physical constraints such as generation rate constraints (GRC) and time-delay (TD) have been considered in the system as a realistic approach. This paper considers an accurate AC-DC tie-link model for the proposed AGC mechanism. Dynamic load change condition is tested and verified. The variations of different parameters will be used in the robustness analysis of the proposed system. The comparison shows that the designed controllers are more robust and produce better results than those considered as references.

Influence of Sensor Feedback Limitations on Power Oscillation Damping and Transient Stability

Fundamental sensor feedback limitations for improving rotor angle stability using local frequency or phase angle measurement are derived. Using a two-machine power system model, it is shown that improved damping of inter-area oscillations must come at the cost of reduced transient stability margins, regardless of the control design method. The control limitations stem from that the excitation of an inter-area mode by external disturbances cannot be estimated with certainty using local frequency information. The results are validated on a modified Kundur four-machine two-area test system where the active power is modulated on an embedded high-voltage dc link. Damping control using local phase angle measurements, unavoidably leads to an increased rotor angle deviation following certain load disturbances. For a highly stressed system, it is shown that this may lead to transient instability. The limitations derived in the paper may motivate the need for wide-area measurements in power oscillation damping control.

Mechanism analysis and mitigation strategies for oscillatory instability of synchronous generators affected by voltage source converters

The electric power systems are experiencing a transformation to be characterized by power electronic devices, for example, voltage source converters (VSCs). However, the large-capacity VSC will interact with the synchronous generators (SGs) and could lead to low-frequency oscillation (LFO). It becomes a hurdle for the secure and stable operation of modern electric power systems. Therefore, this paper analyses the oscillatory instability mechanism of the SG with the penetration of grid-forming (GFM) and grid-following (GFL) VSC. The distinctive transfer function model of the SG-VSC system is first developed. Then, through parameter sensitivity and transfer function analysis, the impact of three types of VSC is investigated, encompassing GFM-VSC and GFL-VSCs with two conventional reactive control schemes. It proves that the voltage control of the VSC can be detrimental to the damping torque of the SG. According to the theoretical analysis, a supplementary compensator is proposed to suppress the LFO induced by the VSC. Finally, case studies in a two-area test system validate the analytical results and robustness of the proposed enhancement method.

The performance analysis of type-2 fuzzy fractional-order tilt integral derivative controller with enhanced Harris hawks optimization

Modern Alternating Current (AC) microgrids (ACMGs) are highly complex because of the indeterminate nature of distributed energy generation and load causes frequency fluctuations. It is essential to maintain the constant power amongst load and generations by the proper design of an efficient controller to stabilize frequency fluctuations. In this paper, the type-2 fuzzy fractional-order tilt integral derivative controller structure is designed and analyzed for frequency control of an ACMG by using an enhanced Harris hawks optimization (EHHO). The modified optimization technique is analyzed employing test functions and compared with similar methods. It is noticed that the modified optimization technique is outperforming the other methods in most of the test functions. The frequency control performance of an ACMG is demonstrated and compared with the original Harris hawks optimization (HHO) and other optimization methods. The proposed type-2 fuzzy fractional-order tilt integral derivative controller tuned with EHHO technique is demonstrated to be effective and superior to any of the alternatives by application to a typical two-area test system.

Application of a simplified Grey Wolf optimization technique for adaptive fuzzy PID controller design for frequency regulation of a distributed power generation system

A Simplified Grey Wolf Optimizer (SGWO) is suggested for resolving optimization tasks. The simplification in the original Grey Wolf Optimizer (GWO) method is introduced by ignoring the worst category wolves while giving priority to the better wolves during the search process. The advantage of the presented SGWO over GWO is a better solution taking less execution time and is demonstrated by taking unimodal, multimodal, and fixed dimension test functions. The results are also contrasted to the Gravitational Search Algorithm, the Particle Swarm Optimization, and the Sine Cosine Algorithm and this shows the superiority of the proposed SGWO technique. Practical application in a Distributed Power Generation System (DPGS) with energy storage is then considered by designing an Adaptive Fuzzy PID (AFPID) controller using the suggested SGWO method for frequency control. The DPGS contains renewable generation such as photovoltaic, wind, and storage elements such as battery and flywheel, in addition to plug-in electric vehicles. It is demonstrated that the SGWO method is superior to the GWO method in the optimal controller design task. It is also seen that SGWO based AFPID controller is highly efficacious in regulating the frequency compared to the standard PID controller. A sensitivity study is also performed to examine the impact of the unpredictability in the parameters of the investigated system on system performance. Finally, the novelty of the paper is demonstrated by comparing with the existing publications in an extensively used two-area test system.

Stabilization of inter-area oscillations in two-area test system via centralized interval type-2 fuzzy-based dynamic brake control

Inter-area oscillations are, by far, the most detrimental oscillation category to the integrity of synchronously interconnected power systems. Inter-area oscillations are characterized by the inherent weak damping. The inherent poor damping associated with the inter-area oscillations leaves open wide probabilities for irrevocable widespread blackouts with the consequent eventual devastating outcomes measured in terms of the huge economic casualties and the possible human fatalities. The main purpose of this work is to mitigate inter-area power oscillations. This article explores the effectiveness of dual thyristor controlled braking resistor units with Interval Type-2 fuzzy-based centralized architecture for neutralizing the jeopardy of inter-area power oscillations in Kundur’s two-area test system using MATLAB™/Simulink environment. The effectiveness of the proposed scheme is examined by considering four case studies with different degrees of severity. The simulation results show that the proposed scheme is simple yet effective in treating the inter-area oscillations appropriately under the considered case studies.

Placing Grid-Forming Converters to Enhance Small Signal Stability of PLL-Integrated Power Systems

The modern power grid features the high penetration of power converters, which widely employ a phase-locked loop (PLL) for grid synchronization. However, it has been pointed out that PLL can give rise to small-signal instabilities under weak grid conditions. This problem can be potentially resolved by operating the converters in grid-forming mode, namely, without using a PLL. Nonetheless, it has not been theoretically revealed how the placement of grid-forming converters enhances the small-signal stability of power systems integrated with large-scale PLL-based converters. This paper aims at filling this gap. Based on matrix perturbation theory, we explicitly demonstrate that the placement of grid-forming converters is equivalent to increasing the power grid strength and thus improving the small-signal stability of PLL-based converters. Furthermore, we investigate the optimal locations to place grid-forming converters by increasing the smallest eigenvalue of the weighted and Kron-reduced Laplacian matrix of the power network. The analysis in this paper is validated through high-fidelity simulation studies on a modified two-area test system and a modified 39-bus test system. This paper potentially lays the foundation for understanding the interaction between PLL-based (i.e., grid-following) converters and grid-forming converters, and coordinating their placements in future converter-dominated power systems.

On Area Control Errors, Area Injection Errors, and Textbook Automatic Generation Control

We reexamine and critique the classical area control error concept used in automatic generation control, and propose a new error signal termed the area injection error. Unlike the ACE, the AIE uses direct measurement of generator power levels, yielding improved AGC performance in the presence of bias uncertainty and nonlinearity in generator turbine-governor responses. As a by-product of our analysis, we conclude that the effective frequency biasing found in a common textbook implementation of AGC is larger than intended, resulting in unintended interaction between control areas. Our theory is validated via simulations on a detailed two-area test system.

Event‐triggered load frequency control for multi‐area power systems based on Markov model: a global sliding mode control approach

In this study, a new method is put forward for the stability and stabilisation analysis of the event-triggered load frequency control (LFC) with interval time-varying delays, considering the global sliding mode controller. To lighten the network bandwidth and save more limited networked resources, the event-triggered scheme is optimised through quantum genetic algorithm, according to different circumstances. Additionally, global sliding mode control (GSMC) scheme is proposed to provide stronger robustness performance, which against the frequency deviation caused by power unbalance or transmission time delays better. Based on the proposed schemes, multi-area LFC for the power system model is formulated as a Markov jump linear system model, considering transmission time delays and external disturbances. By applying improved Lyapunov stability theory, criteria about the stability and stabilisation conditions for multi-area power system can be deduced in terms of linear matrix inequality. Finally, to validate a more realistic LFC application, the proposed event-triggered GSMC is also deployed on Kundur's two-area test system. Simulation studies are carried out to illustrate the effectiveness and superiority of the developed schemes.

A Novel Wide-Area Control Strategy for Damping of Critical Frequency Oscillations via Modulation of Active Power Injections

This article proposes a novel wide-area control strategy for modulating the active power injections to damp the critical frequency oscillations in power systems, this includes the inter-area oscillations and the transient frequency swing. The proposed method pursues an efficient utilization of the limited power reserve of existing distributed energy resources (DERs) to mitigate these oscillations. This is accomplished by decoupling the damping control actions at different sites using the oscillation signals of the concerned mode as the power commands. A theoretical basis for this decoupled modulating control is provided. Technically, the desired sole modal oscillation signals are filtered out by linearly combining the system-wide frequencies, which is determined by the linear quadratic regulator based sparsity-promoting (LQRSP) technique. With the proposed strategy, the modulation of each active power injection can be effectively engineered considering the response limit and steady-state output capability of the supporting device. The method is validated based on a two-area test system and is further demonstrated based on the New England 39-bus test system.

Stabilization of Inter-Area Oscillations in a Two-Area Test System via Interval Type-2 Fuzzy Based Dynamic Brake Control

Inter-area oscillations are, by far, the most detrimental to the synchronous integrity of interconnected power systems. This detriment comes from their wide frequency spectrum and the large numbers of the participant generators. The inherent poor damping associated with the inter-area oscillations leaves open wide probabilities for irrevocable widespread blackouts with the consequent eventual devastating outcomes measured in terms of the huge economic casualties and the possible human fatalities. This article explores the influences of the Interval Type-2 fuzzy logic-based strategized dynamic braking interventions of dual brake models, namely Thyristor Controlled Braking Resistors (TCBRs), for neutralizing the jeopardy of negatively damped inter-area power oscillations in Kundur’s two-area test system, using MATLAB™/Simulink environment. The relative inner generator's speed deviation is employed in this work as a control signal to the proposed controller. The effectiveness of the proposed scheme is authenticated by considering four case studies with different severity degrees. By analyzing the performance repercussions due to four disturbances, without the implementation of the proposed scheme, the unstable nature of the system responses is clearly noticed. With the implementation of the proposed scheme, the system oscillatory behavior is stabilized in an appropriate manner. The performed comparative non-linear time-domain simulation results emphasize the great potential of the proposed scheme in mitigation of inter-area power oscillations according to the considered disturbances. The proposed scheme is simple yet effective in treating the inter-area oscillations appropriately under the considered case studies.

A Modified Moth Swarm Algorithm-Based Hybrid Fuzzy PD–PI Controller for Frequency Regulation of Distributed Power Generation System with Electric Vehicle

This paper presents a modified moth swarm algorithm (mMSA) to solve the frequency control of distributed power generation system (DPGS). The DPGS contains renewables like wind, solar photovoltaic as well as storage devices like the battery and flywheel along with electric vehicles. At the first stage, the superiority of the proposed mMSA over moth swarm algorithm is compared by considering benchmark unimodal, multimodal and fixed-dimension test functions. The outcomes are also compared with some recently suggested optimization algorithms to validate the superiority of the suggested mMSA method. In the next step, the hybrid fuzzy PD–PI (hFPD–PI) controller is proposed for the frequency regulation of DPGS. To authenticate the feasibility of the proposed method, experimental validation employing hardware-in-the-loop real-time simulation based on OPAL-RT has been carried out. Further, to study the effect of uncertainties in the parameters of the studied system, sensitivity analysis is performed. Finally, the proposed approach is compared with some newly proposed frequency regulation methods in a standard two-area test system. It is noticed that mMSA-based hFPD–PI controller provides better frequency regulation compared to some recent approaches.

Robust control of automatic voltage regulator (AVR) with real structured parametric uncertainties based on [formula omitted] and [formula omitted]-analysis

Within this work, a novel controller in terms of H infinity (H∞) and structured singular value decomposition has been presented to provide the robust performance of the Automatic Voltage Regulator (AVR) system Six real structured uncertainties in actuator, exciter and generator have been assumed for the linear transfer functions of the AVR system. Each uncertain parameter varies between a minimum and a maximum value due to the load variations in a period of time and aging effects over the life time. The efficiency of the presented design lies on two main reasons. The first is the simultaneous considering of the output disturbances, sensor noises and system uncertainties in the controller design approach. The second is the non-conservative modeling of all six structured parameters in the required μ-synthesis P−Δ−K configuration. By suboptimal H∞ control design technique and μ-analysis theorem, a single input single output (SISO) controller comprising a closed loop system with μ<1 is obtained. The offered controller’s supremacy is represented through comparison of its performance with some other optimized PID, PIDD fractional order PID (FOPID), fuzzy + PID and Interval Type-2 fuzzy logic controllers by heuristic optimization algorithms. The simulation outcomes indicate that the provided robust controller for the AVR system has the better performance than the other optimized and fuzzy controllers in a wide range of the uncertainties. Also, the better behavior of the intended robust controller was shown in two benchmarks: a single machine connected to a 230kV network, and a four-machine two-area test system.

Optimum location of R-SFCL in an IEEE bench-marked four-machine, two-area test system

Optimum location of R-SFCL in an IEEE bench-marked four-machine, two-area test system

Damping of low-frequency oscillation in power systems using hybrid renewable energy power plants

Global warming, increase in environmental pollution, and high cost of electrical power generation using fossil fuels are considered the most important reasons for the application of renewable energy power plants (REPPs) around the world. In recent years, a new generation of REPPs called hybrid renewable energy power plants (HREPPs) has been implemented in order to have higher efficiency and reliability than conventional REPPs such as wind power plants and photovoltaic power plants. The HREPPs include two or more renewable energy generation units such as wind turbine generation units, and PV generation units. In case of high penetration of these types of power plants, the most common tasks of synchronous generators should be supported by them. One of these tasks is the ability to reduce the low-frequency oscillation (LFO) risk through power oscillation damper such as the power system stabilizers of synchronous generators. In this paper, a novel method is proposed for LFO damping by HREPPs, which is based on the design of an optimal power oscillation damper (OPOD) implemented in the generic HREPP controller model. The structure of the proposed OPOD is a 2nd-order single-input lead-lag controller, and its performance is investigated in a modified two-area test system. The simulation results show the proper performance of the HREPP for LFO damping using the proposed OPOD in the various loading levels and different short circuit ratio values.

New signal subspace approach to estimate the inter‐area oscillatory modes in power system using TLS‐ESPRIT algorithm

The authors propose here a new low-frequency oscillatory (LFO) modes estimation scheme by applying Karhunen–Loeve transform (KLT) with total least square estimation of signal parameter employing rotational invariance technique (TLS-ESPRIT). The proposed KLT provides the perfect decorrelation of the signal from the noise at low signal-to-noise ratio and for both white and coloured noise. KLT also maximally compress the energy of the estimated signal. KLT helps to estimate the signal subspace perfectly for any non-stationary ambient power signal with the fastest computational time. First, the authors applied the KLT denoise to the filtered signal buried with highly correlated coloured Gaussian noise through the first eigenvectors of the correlation matrix and estimated the signal subspace. Finally, TLS-ESPRIT is applied to estimate the modes of the power system. A comparative analysis of the KLT-TLS-ESPRIT with the modified TLS-ESPRIT, multi-channel wavelet transform, data driven-stochastic subspace identification, TLS-ESPRIT, Root-MUSIC, and improved Prony method is presented. To explore the real-time application of the KLT-TLS-ESPRIT, the authors considered Kundur's two-area test system and 16-machine 68-bus system using 50,000 Monte-Carlo simulations. The obtained results show that the KLT-TLS-ESPRIT accurately estimates the LFO with least mean and standard deviation as compared to the remaining six methods.

Damping Low-Frequency Oscillations Through VSC-HVdc Stations Operated as Virtual Synchronous Machines

With proper control methods, grid-connected power converters can mimic the dynamics of conventional synchronous generators (SGs), i.e., acting as virtual synchronous machines (VSMs), for improving the grid frequency stability and ensuring a smooth transition toward converter-dominated power systems. However, the integration of VSMs will inevitably influence the low-frequency oscillations (LFOs) in power grids which are usually caused by the interactions among SGs. This influence should be of concern especially when the VSM's capacity is similar to that of SG, e.g., operating voltage-source converter (VSC)-HVdc stations as VSMs. This paper investigates how the VSM affects LFOs in power systems by analyzing its equivalent damping torque. We show that with proper control design, VSMs can provide considerable positive damping torque to effectively damp LFOs in power grids. Particularly, using the damping torque analysis, the influences of virtual impedance and grid frequency detector (i.e., phase-locked loop) are elaborately studied so as to provide design guidelines for better damping LFOs. Finally, case studies of a two-area test system with integration of a VSM-based VSC-HVdc station verify the validity of the analysis.

Study of Resistive SFCL and UPFC for Transient Behavior Enhancement of Multi-Machine Power System

Based on a resistive-type superconducting fault current limiter (SFCL) as well as a unified power flow controller (UPFC), this paper researches the combined utilization of them to improve a multi-machine power system’s transient stability. The SFCL is firstly to provide a fault current-limitation. Then, the UPFC is to realize an efficient power flow adjustment and a precise stabilizing control. Related modeling and control are presented, and a four-machine two-area test system including a SFCL and a UPFC is simulated in MATLAB. Different simulation conditions are applied, and it can be concluded that: (i) The SFCL-UPFC enables to more directly and powerfully refrain the fault current surge, mitigate the bus voltage sag and alleviate the inter-area oscillation. (ii) As the increase of fault clearance time, the power system’s demand for the SFCL-UPFC’s stabilizing effect would be very critical. (iii) Compared to the asymmetric fault, the SFCL-UPFC owns a better ability to handle the symmetric fault.