Three-machine Power System Research Articles

Distributed finite-time fault estimation and fault-tolerant control for cyber-physical systems with matched uncertainties

This paper is concerned with finite-time distributed fault estimation (DFE) and fault-tolerant control (DFTC) for cyber-physical systems (CPSs) with actuator faults and matched uncertainties. First, in order to deal with the partly unmeasurable states, matched uncertainties and actuator faults with the loss of effectiveness and bias, a distributed fault estimation observer (DFEO) is designed based on the functional observer with an adaptive compensator. Then, a distributed fault-tolerant controller (DFTCr) is designed to compensate faults effect on the interconnected CPSs based on the integral sliding mode control (SMC) technique, which ensures that the closed-loop systems reach a given boundedness in a predefined finite time. Moreover, some sufficient conditions in the form of linear matrix inequalities are proposed to guarantee the finite-time boundedness with H∞ performance (FTB-H∞). Due to introducing more degrees of freedom of the functional observer, the designed finite-time distributed fault-tolerant controller is more flexible and less conservative. Finally, a numerical simulation on the three-machine power systems is acquired to show the validity of the proposed method.

The Extension of the Method for the Out-of-step Condition Prediction using Post-disturbance Voltage Fluctuations in a Three-machine Power System

The Extension of the Method for the Out-of-step Condition Prediction using Post-disturbance Voltage Fluctuations in a Three-machine Power System

Resilient decentralized sampled-data [formula omitted] filter design for linear interconnected systems subject to denial-of-service attacks

This paper investigates the design problem of the resilient decentralized sampled-data H∞ filter for linear interconnected systems subject to the denial-of-service attacks. A piecewise Lyapunov function-based method is first developed to determine the filter parameters and the sampled-data communication schemes. Then the obtained results are utilized to facilitate the design of the resilient decentralized sampled-data H∞ filter against the denial-of-service attacks. Compared with the existing results, the communication channels from the subsystems of interconnected systems to the filters are allowed to be independent and be compromised by different adversaries. Finally, numerical simulations on the double-inverted pendulums system and the three-machine power system are provided to illustrate the efficacy of the proposed method.

Decentralized observer-based optimal control using two-point boundary value successive approximation approach application for a multimachine power system

In this paper, we present a new decentralized observer for a class of nonlinear interconnected systems, based on an optimal control law using the two-point boundary value (TPBV) successive approximation approach. This technique, used previously to develop a nonlinear decentralized suboptimal control for a multimachine power system, inspired us to develop a new method to design a decentralized observer-based suboptimal control law for the same system. The TPBV approach is characterized by the transformation of each high order coupling nonlinear TPBV problem into a sequence of linear decoupling TPBV problems that uniformly converge to the optimal control for nonlinear interconnected large-scale systems. Sufficient conditions for the asymptotic stability of the developed feedback control scheme are proposed in terms of linear matrix inequalities (LMIs) constraints, which can be efficiently solved by the LMI optimization techniques, to compute the control and the observation gains of the overall system. We applied this approach to a three-machine power system which generators are nonlinear systems strongly interconnected. We demonstrated clearly, via advanced simulations, that this approach was able to bring good performances, improving effectively transient stability of this power system in few iterative sequences while allowing the reconstruction of its non-measurable state variables.

Mitigation of power oscillations using hybrid DE-PSO optimization-based SSSC damping controller

This paper presents an optimal design of a static synchronous series compensator (SSSC)-based controller for damping of low-frequency oscillations in multi-machine power systems. The proposed controller design problem is formulated to the optimization problem. The tuning of controller parameters can be obtained by employing a new hybrid differential evolution and particle swarm optimization (hDE-PSO) algorithm. To justify the effectiveness of the proposed SSSC-based damping controller, three-machine and four-machine power systems have been considered. The hDE-PSO algorithm outperforms in the damping of oscillations over DE and PSO algorithms. Various simulation results are presented and compared for different load disturbances like three-phase fault, load rejection and tripping of one parallel transmission line. The simulation results ensure the robustness of the proposed controller.

Distributed event-triggered scheduling in networked interconnected systems with sparse connections

This paper is concerned with the problem of distributed event-triggered scheduling for a class of interconnected systems with limited coupling connections. Different from the existing studies, in the considered interconnected system, each remote control station is allowed to retrieve event-triggered sampled-data from interacting control stations, while the number of coupling communication connections is upper bounded in a κ-sparse sense rather than permanently fixed. The distributed event-triggered scheduling problem subject to such a cardinality constraint is nontrivial due to its combinatorial nature. Different from the existing l1 norm based iterative convexification approach, a direct design approach based on mixed-integer programming is proposed to handle the cardinality constraint. Furthermore, an explicit κ-sparse distributed scheduling algorithm is designed for the networked interconnected system via the Lyapunov functional method and some matrix manipulations. The proposed approach is finally applied to a three-machine power system to illustrate its effectiveness.

Analysis on Nonlinear Dynamic Characteristic of Synchronous Generator Rotor System

This paper focuses on the swing oscillation process of the synchronous generator rotors in a three‐machine power system. With the help of bifurcation diagram, time history, phase portrait, Poincaré section, and frequency spectrum, the complex dynamical behaviors and their evolution process are detected clearly in this power system with varying perturbation related parameters and different system parameters. Furthermore, combining the qualitative and quantitative characteristics of the chaotic motion, different paths leading to chaos coexisting in this system have been found. The Wolf method has been introduced to calculate the corresponding largest Lyapunov exponent, which is used to verify the occurrence of chaotic motion. These results obtained in this paper will contribute to a better understanding of nonlinear dynamic behaviors of synchronous generator rotors in a three‐machine power system.

Proportional integral observer-based decentralized stabilization design scheme for nonlinear complex interconnected systems

For a class of complex interconnected nonlinear disturbed systems, a proportional integral (PI) decentralized observer-based feedback robust decentralized controller technique is proposed, relying on H∞ synthesis for disturbance mitigation and linear matrix inequality (LMI) tools to achieve asymptotic stabilization and stability analysis within the Lyapunov framework. The proposed design method draws on a prominent optimization problem that can be tackled in terms of LMI constraints to evaluate the decentralized controller and PI observer gain matrices jointly, to maximize the nonlinearity coverage tolerated by the system without destabilization and to improve the robustness of the proposed control strategy by minimizing an H∞ criterion despite exogenous disturbances and strong nonlinear interconnections affecting the subsystems. The efficacy and high performance of the proposed control approach, compared with a renowned decentralized guaranteed cost control strategy from the literature, are validated by numerical simulations on a greatly interconnected three-machine power system.

Sliding-mode perturbation observer-based sliding-mode control design for stability enhancement of multi-machine power systems

This paper presents the design of a sliding-mode perturbation observer-based sliding-mode control for stability enhancement of multi-machine power systems. The combinatorial effect of nonlinearities, parameter uncertainties, unmodelled dynamics and time-varying external disturbances is aggregated into a perturbation, which is rapidly estimated by a sliding-mode state and perturbation observer and then fully compensated by a sliding-mode controller in real time. The attractiveness of the sliding surface is analysed theoretically in the context of the Lyapunov criterion. The proposed control does not require an accurate system model and only one state measurement is needed. In addition, an over-conservative control effort can be effectively avoided via perturbation compensation. Simulation results for a three-machine power system and the New England power system verify the effectiveness of the proposed approach.

A mathematical model of SOFC power plant for dynamic simulation of multi-machine power systems

Modern power networks are complex multi-component dynamic system with many operational levels made up of a wide range of renewable energy resources. The low frequency oscillations may undergo and sustain to cause system separation if adequate damping is not provided. This research work presents the mathematical model of Solid Oxide Fuel Cells (SOFC) within transmission network in order to dynamic stability analysis and control. The main contribution is to propose the new linearized Heffron-Philips model of the system under consideration the SOFC power plant to studying of low frequency oscillations. The eigenvalue-based objective function is used to search optimal multi-machine power system stabilizer (PSS) with the Particle Swarm Optimization (PSO) technique under various operating conditions. The effectiveness of the proposed model is tested on three-machine power system integrated with the single SOFC power plant. The time-domain simulation results are promising and illustrate the effectiveness of the proposed stabilizers. It can be damp the low frequency oscillations in the best possible procedure and significantly improves the stability performance of the case study system.

Dynamic synchrophasor estimation by Taylor–Prony method in harmonic and non‐harmonic conditions

Dynamic phasor is suitable for analysis of non-stationary signals (such as power swings) in phasor measurement unit. In this study, dynamic phasor of the generated signals during power swing is analysed by a classical signal processing technique known as Prony. The Prony analysis is a useful technique to model a linear sum of damped complex exponential signals. In this study, a combination of the least square-based Prony analysis and Taylor expansion called as Taylor–Prony is proposed to estimate the dynamic phasor. Zeroth-order Taylor–Prony, i.e. static phasor is compared with the second-order Taylor–Prony, i.e. dynamic phasor for illustrating the dynamic phasor capability. Sinusoidal and step changes of amplitude and phase, harmonic condition, frequency tracking tests, noise infiltration and computation time are different tests which are used to validate the proposed method. First, the method is explained theoretically, and then its potential is demonstrated by simulating various numerical signals in MATLAB and measured signals during power swing from three-machine power system simulated in PSCAD. Simulation results show that the proposed method can estimate the dynamic phasor during power swing accurately. Ultimately, the proposed method is compared with six methods which have already presented to verify the capability of the proposed method.

Fuzzy-PSS and fuzzy neural network non-linear PI controller-based SSSC for damping inter-area oscillations

In this paper, a new approach is recommended for damping out power system oscillations. In this approach, a new fuzzy neural proportional–integral (PI) controller (FNPIC) based static synchronous series compensator (SSSC) and a fuzzy-power system stabilizer (fuzzy-PSS) with a new structure are simultaneously employed. Adaptive learning rates based on the Lyapunov stability theory to enhance the convergence speed of the proposed controller are obtained. In the structure of fuzzy-PSS, a pattern search algorithm is used to adjust four gains. A two-area four-machine power system and a three-area, three-machine power system are employed to investigate the efficiency of the proposed method. Simulations results confirm the capabilities of proposed controller in suppressing the power system oscillations.

An Efficient Decentralized Control Strategy Applied to an Interconnected Multi-Machine Electric Power Grid

Background/Objectives: It is essential to design an efficient decentralized control strategy to deal with the stability against various disturbances in a practical electric power interconnection with nonlinearities and uncertainties. Methods: This paper presents theoretically a decentralized control strategy which is appropriately applied to an interconnected power system. Such an electric power grid is mathematically modeled first, then the design of an efficient control scheme for a stabilized solution will be presented. Finally, the feasibility and superiority of the proposed approach will be verified through various simulation cases using MATLAB/Simulink platform for a typical three-machine electric power system. Findings: It should be obviously found that a practical multi-area electric power network, which is considered to be a typical example of large-scale systems, composes of many synchronous generators. These machines are strongly interconnected via a number of nonlinearities such as parameters of transmission lines, thereby this feature brings a big challenge to the modeling of the network and the design of an efficient control strategy for an electric power interconnection in order to ensure its stability and reliability. Decentralized control strategies have been applied to be more suitable for tackling the stabilization problem of such an interconnected power grid in comparison with the centralized control scheme. In the present paper, an efficient linear decentralized control methodology based on a number of modified Riccati equations to calculate a proper feedback control law will be studied as a typically feasible candidate to this issue. The promising simulation results obtained in a three-machine interconnected power system model with various cases of initial conditions are quite able to demonstrate the superiority of the proposed control methodology. Application/Improvements: The proposed decentralized control strategy is successfully applied to a three-machine electric power interconnection model as a typical case study. Hence, this control methodology can afford to be efficiently adopted to a practical power network.

Decentralized Disturbance Attenuation Control for Multi-Machine Power System

This paper proposes a decentralized control scheme for multi-machine power system with nonlinear interconnections. The decentralized control law is constructed by a backstepping method. The proposed controller is robust with regard to the parameter uncertainties and also attenuates persistent disturbances in the sense of L2-gain. Simulation results on a three-machine power system clearly show the effectiveness of the proposed decentralized control scheme.

Decentralized Robust Control for Multi-Machine Power System

This paper proposes a new decentralized output feedback control scheme for three-machine power system. The decentralized controller synthesis problem is formulated as a scaled H∞ control problem, and an LMI-based algorithm is developed to synthesize the decentralized controller. The proposed controller provides robustness with regard to parametric uncertainties and also attenuates bounded exogenous disturbances in the sense of L2-gain. Simulation results clearly show the effectiveness of the developed decentralized output feedback control scheme.

Wide-Area Measurement-Based Backup Protection for Power Network With Series Compensation

This paper presents a synchronized phasor measurement-based wide-area backup protection scheme which compares the magnitude of sequence voltages of buses at a system protection center to identify the bus closest to the fault. Then, the sign of cosine of the angle between voltage and current at both ends of all lines connected to this bus are compared to identify the faulted branch. The technique is tested for various faults resulting in voltage/current inversion in a series-compensated line and during load encroachment and power swing conditions using data simulated through EMTDC/PSCAD for a nine-bus, three-machine power system. The scheme is found to be accurate and fast. With today's synchronized phasor measurement technology and communication system, the proposed scheme can overcome the limitations of the conventional backup protection scheme.

Modeling UPFC into Multi-Machine Power Systems

Modeling of unified power flow control (UPFC) into multi-machine power systems by Wang, published by IET, has been widely quoted by many researchers. However, the correctness of the derivation of its equations has not been strictly scrutinized. The model cannot properly represent power system networks in its current form and need to be corrected. In this paper, the model proposed by Wang is revisited and the equations re-derived obtaining different results. The corrected model was developed and tested on three-machine and New England power systems installed with a UPFC. The DC link capacitor voltage is controlled in UPFC by modulating the phase angle of the excitation transformer voltage. The effect of the controller in damping of the low-frequency oscillations is demonstrated by using the proposed correct model and the results are compared with model presented by Wang.

Wide-area nonlinear robust voltage control strategy for multi-machine power systems

This paper presented a novel wide-area nonlinear excitation control strategy for multi-machine power systems. A simple and effective model transformation method was proposed for the system’s mathematical model in the COI (center of inertia) coordinate system. The system was transformed to an uncertain linear one where deviation of generator terminal voltage became one of the new state variables. Then a wide-area nonlinear robust voltage controller was designed utilizing a LMI (linear matrix inequality) based robust control theory. The proposed controller does not rely on any preselected system operating point, adapts to variations of network parameters and system operation conditions, and assures regulation accuracy of generator terminal voltages. Neither rotor angle nor any variable’s differentiation needs to be measured for the proposed controller, and only terminal voltages, rotor speeds, active and reactive power outputs of generators are required. In addition, the proposed controller not only takes into account time delays of remote signals, but also eliminates the effect of wide-area information’s incompleteness when not all generators are equipped with PMU (phase measurement unit). Detailed tests were conducted by PSCAD/EMTDC for a three-machine and four-machine power systems respectively, and simulation results illustrate high performance of the proposed controller.

Power System Oscillations Damping Using Unified Power Flow Controller-Based Stabilizer

Problem statement: The Phillips-Heffron model of a power system with UPFC published by AJAS, demonstrates the effect of the UPFC in improving power system oscillation stability. Unfortunately, some of the equations have not been correctly derived and so working with this model in its existing form is misleading. Approach: In this study, the model is revisited and the equations are re-derived obtaining correct results. Three-machine power system installed with a UPFC is used to investigate the validity of these equations. Results: The simulation results demonstrated that the corrected model with an effective controller is active on damping of the low-frequency oscillations under different operating conditions. Conclusion: The corrected model works properly with power system networks for enhancing power system stability.

Adaptive fuzzy decentralized control for interconnected MIMO nonlinear subsystems

This paper describes an adaptive fuzzy control strategy for decentralized control for a class of interconnected nonlinear systems with MIMO subsystems. An adaptive robust tracking control schemes based on fuzzy basis function approach is developed such that all the states and signals are bounded. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds. The resultant adaptive fuzzy decentralized control with multi-controller architecture guarantees stability and convergence of the output errors to zero asymptotically by local output-feedback. An extensive application example of a three-machine power system is discussed in detail to verify the effectiveness of the proposed algorithm.