Multi-machine Power System Research Articles

Fully Adaptive Recurrent Neuro-Fuzzy Control for Power System Stability Enhancement in Multi Machine System

Voltage instability in a power system produces low-frequency oscillations (LFOs), causing adverse effects in power distribution. Intelligent control schemes can overcome the limitations of fixed-parameter structures in power system stabilizers (PSS). Flexible alternating current transmission system (FACTS) control along with some supplementary control have remarkable potential in damping the oscillations. This paper proposes an adaptive neurofuzzy based recurrent wavelet control (ANRWC) scheme to enhance the power system stability. The proposed scheme utilizes recurrent Gaussian as antecedent part’s membership function and recurrent wavelet function in consequent parts. Our scheme uses gradient descent, adadelta, adaptive moment estimation (ADAM) and proximal gradient descent algorithms for optimization in which parameters of the scheme are updated using a back-propagation algorithm. A multi-machine power system is used for testing the controller. We evaluate the proposed control scheme in comparison to conventional lead-lag control and an adaptive neurofuzzy takagi sugeno kang (ANFTSK) control scheme. For comparison, we calculate the performance indices (PIs) for different controllers. Both quantitative and qualitative evaluations assert the effectiveness of the proposed control as compared to other schemes.

On the Equality of Modal Damping Power and the Average Rate of Transient Energy Dissipation in a Multimachine Power System

This letter establishes a relationship between the concepts of damping torque and the dissipation of transient energy in a multimachine power system with constant power loads. To that end, we present a mathematical proof showing that, for a poorly-damped mode, the total damping power stemming from the interaction of electromagnetic torques and rotor speeds is approximately equal to the average rate of transient energy dissipation in the system corresponding to the modal oscillation. This is verified with numerical studies on the IEEE 2-area 4-machine and 5-area 16-machine test systems.

Connection Between Damping Torque Analysis and Energy Flow Analysis in Damping Performance Evaluation for Electromechanical Oscillations in Power Systems

The damping performance evaluation for electro-mechanical oscillations in power systems is crucial for the stable operation of modern power systems. In this paper, the connection between two commonly-used damping performance evaluation methods, i.e., the damping torque analysis (DTA) and energy flow analysis (EFA), are systematically examined and revealed for the better understanding of the oscillatory damping mechanism. First, a concept of the aggregated damping torque coefficient is proposed and derived based on DTA of multi-machine power systems, which can characterize the integration effect of the damping contribution from the whole power system. Then, the pre-processing of measurements at the terminal of a local generator is conducted for EFA, and a concept of the frequency-decomposed energy attenuation coefficient is defined to screen the damping contribution with respect to the interested frequency. On this basis, the frequency spectrum analysis of the energy attenuation coefficient is employed to rigorously prove that the results of DTA and EFA are essentially equivalent, which is valid for arbitrary types of synchronous generator models in multi-machine power systems. Additionally, the consistency between the aggregated damping torque coefficient and frequency-decomposed energy attenuation coefficient is further verified by the numerical calculation in case studies. The relationship between the proposed coefficients and the eigenvalue (or damping ratio) is finally revealed, which consolidates the application of the proposed concepts in the damping performance evaluation.

Improved Squirrel Search Algorithm Driven Cascaded 2DOF-PID-FOI Controller for Load Frequency Control of Renewable Energy Based Hybrid Power System

Renewable energy-based hybrid power systems are being increasingly deployed across the globe to reduce carbon emissions. The system frequency and tie-line power tend to fluctuate due to system operating conditions. These fluctuations can be maintained within the desired limits using optimally designed controllers. In this article, the recently developed improved squirrel search algorithm (ISSA) is used to tune the parameters of different controllers, such as the proportional-integral-differential (PID), two degrees of freedom PID (2DOF-PID), three degrees of freedom PID (3DOF-PID), and a cascaded 2DOF-PID fractional order integral (FOI) to improve the performance of the system. The effectiveness of the best controller tuned with ISSA is compared with other optimization techniques such as Particle Swarm Optimization (PSO) and Squirrel Search Algorithm (SSA). A two-area multi-machine hybrid power system is considered to demonstrate the robustness of the proposed concept. The first area consists of a thermal, a hydro, and a wind power plant, while the second area consists of a thermal, a hydro, and a diesel power plant. Comparative performance analysis is carried out to obtain the best controller, tuned with the best optimization technique. Various case studies have been developed to check the system’s robustness, flexibility, and reliability.

An analytical approach for LQR design for improving damping performance of multi-machine power system

In a multi-machine environment, the inter-area low-frequency oscillations induced due to small perturbation(s) has a significant adverse effect on the maximum limit of power transfer capacity of power system. Conventionally, to address this issue, power systems were equipped with lead-lag power system stabilizers (CPSS) for damping oscillations of low-frequency. In recent years the research was directed towards optimal control theory to design an optimal linear-quadratic-regultor (LQR) for stabilizing power system against the small perturbation(s). The optimal control theory provides a systematic way to design an optimal LQR with sufficient stability margins. Hence, LQR provides an improved level of performance than CPSS over broad-range of operating conditions. The process of designing of optimal LQR involves optimization of associated state (Q) and control (R) weights. This paper presents an analytical approach (AA) to design an optimal LQR by deriving algebraic equations for evaluating optimal elements for weight matrix ‘Q’. The performance of the proposed LQR is studied on an IEEE test system comprising 4-generators and 10-busbars.

Improved Salp Swarm Optimization Algorithm for Damping Controller Design for Multimachine Power System

This paper proposes an improved salp swarm algorithm (ISSA) as an effective metaheuristic method for tackling global optimization issues and damping power system oscillations. In the suggested ISSA, new equations are introduced to update the location of the leader and followers. This modification improves the method’s exploration possibilities while also preventing it from converging prematurely. Benchmark test functions are used to confirm the proposed algorithm’s performance, and the results are compared to SSA and other effective optimization algorithms. According to the extensive comparisons, the enhanced ISSA algorithm has higher convergence accuracy and stability than the original SSA and other researched algorithms. Furthermore, the feasibility and efficiency of the proposed method were demonstrated by the simultaneous coordinated design of UPFC based damping controllers. For the two-area, four-machine system, the experimental findings are provided. Simulation experiments reveal that ISSA designed controllers outperform those created using other methods.

Decentralized Hybrid Fuzzy-Sliding Mode Control of Multi-machine Power System

Decentralized Hybrid Fuzzy-Sliding Mode Control of Multi-machine Power System

Tuning the Parameters of Power System Stabilizer Using Runge Kutta Algorithm

Low-frequency oscillations due to unpredictable disturbances in an interconnected power grid are a serious threat to the stability of the power system. Reliable operation of a modern power system, when exposed to sudden disturbances, is crucial, and the safe operation of the system is directly related to success in damping oscillations. Power System Stabilizer (PSS) devices have been used to reduce fluctuations caused by short-time disturbances in power systems. These devices provide additional damping torque components to the generators as an auxiliary control device of the excitation system. Due to the non-linearity of electrical power systems, it is significant to design multi-machine power systems with optimum PSS parameters under critical conditions. In this paper, the PSS design problem was solved using the Runge Kutta Algorithm (RUN). The PSS design problem was considered an optimization problem in which an eigenvalue-based objective function has developed, and the proposed RUN method was tested in a WSCC 3-machine 9-bus test system using the linearized Heffron-Phillips model. In the linearized model, system stability has been enhanced by shifting the eigenvalues to the stability regions. When the results obtained from the test system are examined, it has seen that the proposed RUN is the most effective method in terms of system stability.

Modified Transient Stability Evaluation Methodology of a Multi-Machine Power System Incorporating Renewable Energy Resources

This paper investigates the effect of integrating Renewable Energy Sources (RESs) into a system on the Critical Clearing Time (CCT) as a direct transient stability measure. The developed methodology quantifies the stability margin based on the fault clearing time. Moreover, the methodology considers the dynamic system performance under fault conditions as a worst-case scenario to determine the CCT. The proposed technique is a novel numerical methodology presented to study the transient stability of a multi-machine power system with the existence of a RES. Different from the typical solution of the swing equation of a two-machine power system, the proposed methodology numerically solves the swing equation of a multi-machine system. From this, accurate solutions are obtained to determine the optimal penetration level of the RES. Moreover, this work aims to derive an explicit relationship between the rotor angle deviation of the synchronous generator and the penetration level of the RES. Consequently, the CCT associated with the maximum power angle deviation can be determined. The proposed methodology is validated by comparing the results with dynamic simulations using the power-system-simulator (PSS®E) software package developed by Siemens. The IEEE 9-bus system is considered as a benchmark, with the results exhibiting great agreement with the PSS®E results, thus confirming the effectiveness of the proposed methodology.

Event-triggered distributed robust model predictive control for a class of nonlinear interconnected systems

In this work, we develop an event-triggered distributed robust model predictive control algorithm to stabilize the origin of a class of interconnected systems with nonlinear coupling terms and additive bounded disturbances. Each subsystem is assumed to be able to exchange information with its neighboring subsystems. The transmitted information between neighbors is used to estimate their future behaviors. Then, a robust distributed model predictive control algorithm for each subsystem is developed by integrating the estimations of its neighbors and each subsystem executes a local model predictive control law after solving its optimization problem. Furthermore, a distributed event-triggered mechanism is designed to trigger a series of asynchronous computations of the optimization problems, which achieves a trade-off between communication resource usage and control performance. Theoretical conditions on ensuring feasibility and closed-loop stability are provided. Finally, a practical example of the multi-machine power system with governor controllers is provided to show the effectiveness of the proposed algorithm.

Identification of topology changes in power grids via reduced admittance matrix

Frequent changes in power grid topology bring risks to the stable operation of power systems. It is essential to identify changes in the power grid topology quickly and accurately. This paper presents a novel method named network reduction-based topology change identification (NR-TCI) algorithm to identify topology changes in multi-machine power systems. The proposed algorithm can quickly identify power grid topology changes using only phasor measurement unit (PMU) data sampled during the system’s transient process. The NR-TCI algorithm uses the network order reduction method to reduce the order of a bus admittance matrix and then uses PMU measurement data to estimate the reduced admittance matrix by least square method. Finally, the reduced admittance matrix is adopted to find topological information, and the Sherman–Morrison formula is utilized to identify the topology changes. The effectiveness of the proposed NR-TCI algorithm is verified with a case study of a 3 machine 9 bus system in Matlab. In addition, the influence of PMU sampling frequency on the effectiveness of the proposed algorithm is also studied.

A Novel Approach Using TCSR FACTS Controller for Mitigation of Congestion in a Multi-machine Power System

A Novel Approach Using TCSR FACTS Controller for Mitigation of Congestion in a Multi-machine Power System

Multimachine stability enhancement with hybrid PSO-BFOA based PV-STATCOM

The article explores the mitigating capabilities of a large PV-farm as a PV-STATCOM (Static synchronous compensator) in quenching the power system oscillations in a multimachine power system. Power system oscillations include fluctuation in the rotor dynamics (generator speed and angle), coupling voltage, and shaft torsions. At dusk, the PV-farm starts operating as VSC (Voltage Source Converter)-STATCOM deploying its entire inverting capabilities for suppressing the oscillations. While at the full sun during the faults, the solar-farm instantly ceases the real power generation and, operating as a PV-STATCOM until the normal operating states are resumed. The paper demonstrates the optimizing capabilities of a Bacterial Swarm Optimization (BSO), a hybrid of particle swarm and bacterial foraging optimizations in controlling the power flow of PV-STATCOM deployed in the literature. Kundur’s modified two-area model integrated with a largescale PV-farm is designed in Matlab to probe the rotor swings with torsional deviations in the interconnected shaft segments. The results for several test cases including without-with and BSO-tuned PV-STATCOM reveal the optimizing capabilities of the proposed BSO-based controller in alleviating the power system oscillations in the multi-machine power system.

LMI approach-based sampled-data control for uncertain systems with actuator saturation: application to multi-machine power system

LMI approach-based sampled-data control for uncertain systems with actuator saturation: application to multi-machine power system

Extended Equal Area Criterion Revisited: A Direct Method for Fast Transient Stability Analysis

For transient stability analysis of a multi-machine power system, the Extended Equal Area Criterion (EEAC) method applies the classic Equal Area Criterion (EAC) concept to an approximate One Machine Infinite Bus (OMIB) equivalent of the system to find the critical clearing angle. The system-critical clearing time can then be obtained by numerical integration of OMIB equations. The EEAC method was proposed in the 1980s and 1990s as a substitute for time-domain simulation for Transmission System Operators (TSOs) to provide fast, transient stability analysis with the limited computational power available those days. To ensure the secure operation of the power system, TSOs have to identify and prevent potential critical scenarios through offline analyses of a few dangerous ones. These days, due to increased uncertainties in electrical power systems, the number of these critical scenarios is increasing, substantially, calling for fast, transient stability analysis techniques once more. Among them, the EEAC is a unique approach that provides not only valuable information, but also a graphical representation of system dynamics. This paper revisits the EEAC but from a modern, functional point of view. First, the definition of the OMIB model of a multi-machine power system is redrawn in its general form. To achieve fast, transient stability analysis, EEAC relies on approximate models of the true OMIB model. These approximations are clarified, and the EAC concept is redefined with a general definition for instability, and its conditions. Based on the defined conditions and definitions, functions are developed for each EEAC building block, which are later put out together to provide a full-resolution, functional scheme. This functional scheme not only covers the previous literature on the subject, but also allows to introduce several possible new EEAC approaches and provides a detailed description of their implementation procedure. A number of approaches are applied to the French EHV network, and the approximations are examined.

Study of Modified Flux-Coupling-Type SFCLs For Stability Improvement of a Multi-Machine Power System Based On Energy Function

This paper investigates modified flux-coupling-type superconducting fault current limiters (SFCLs) for enhancing the transient stability of a multi-machine power system (MMPS). The clustering architecture of the MMPS with the modified SFCLs is presented, and the transient energy function (TEF) of the MMPS is established. Through clarifying the potential influence of the modified SFCLs, theoretical analysis signifies that the modified SFCLs can reduce the transient energy accumulation during the fault-feeding period, and increase the transient stability margin of the MMPS. Using MATLAB/Simulink, a benchmark IEEE 9-bus system with the SFCLs is modeled, and the simulation analysis of the generator rotor swing behaviors is carried out. Varying the resistive-inductive parameters and altering the positions of the SFCLs are considered, and the TEF method is applied to gain quantitative effects. The simulation findings in different scenarios testify the correctness of the theoretical analysis. The presence of the SFCLs can availably reduce the generator rotor oscillating and restrain the transient energy changing, and meanwhile, an extension of the critical clearance time is achieved for the MMPS.

Robust Design of Power System Stabilizers Using Improved Harris Hawk Optimizer for Interconnected Power System

In this present work, a new metaheuristic method called a Harris hawk optimizer (HHO) is applied to achieve the optimal design of a power system stabilizer (PSS) in a multimachine power system. Several well-known chaos maps are incorporated into the HHO to form a chaotic HHO (CHHO) with the aim of improving static operators and enhancing global searching. To assess the CHHO performance, exhaustive comparison studies are made between anticipated chaotic maps in handling unconstrained mathematical problems. At this moment, The PSS design problem over a wide permutation of loading conditions is formulated as a non-linear optimization problem. The adopted objective function defines the damping ratio of lightly damped electromechanical modes subject to a set of constraints. The best PSS parameters are generated by the proposed CHHO. The applicability of the proposed CHHO based on PSS is examined and demonstrated on a 10-generator and 39-bus multimachine power system model. The performance assessments of the CHHO results are realized by a comparative study with HHO through extensive simulations along with further eigenvalue analysis to prove its efficacy. The simulation results convincingly demonstrate the high performance of the proposed CHHO-PSS under various operating scenarios.

Strong Excitation Control and Stabilization of Operating Modes in a Multi-Machine Power System

Strong Excitation Control and Stabilization of Operating Modes in a Multi-Machine Power System

Primary frequency control of large-scale PV-connected multi-machine power system using battery energy storage system

<span lang="EN-US">Large-scale grid-tied photovoltaic (PV) station are increasing rapidly. However, this large penetration of PV system creates frequency fluctuation in the grid due to the intermittency of solar irradiance. Therefore, in this paper, a robust droop control mechanism of the battery energy storage system (BESS) is developed in order to damp the frequency fluctuation of the multi-machine grid system due to variable active power injected from the PV panel. The proposed droop control strategy incorporates frequency error signal and dead-band for effective minimization of frequency fluctuation. The BESS system is used to consume/inject an effective amount of active power based upon the frequency oscillation of the grid system. The simulation analysis is carried out using PSCAD/EMTDC software to prove the effectiveness of the proposed droop control-based BESS system. The simulation result implies that the proposed scheme can efficiently curtail the frequency oscillation. </span>

Decentralized robust state estimation of multimachine power systems

The problem of online estimating the states of nonlinear (NL) Multimachine Power Systems (MPSs) is addressed within a constructive framework that combines notions and tools from electrical engineering and nonlinear estimation theory. First, the standard NL centralized model is realized as a set of linear decentralized robustly observable models, with augmented states that capture nonlinearity, parameter error, and intermachine state interaction. Then, based on the observability property of the decentralized model, a robustly convergent linear Geometric (Luenberger-like with integral action) estimator with simple tuning is constructed. With respect to previous MPS estimation techniques, the novelties are: (i) from a theoretical perspective, the comprehensiveness of the methodology, with model design, solvability in terms of observability, and robust functioning criteria coupled with a simple tuning scheme, and (ii) from an industrial applicability viewpoint, an online computation load considerably smaller than the one of the NL Extended Kalman Filter (EKF), and a tuning scheme appreciably simpler than the one of the NL sliding mode perturbation observer (SMPO). The proposed design methodology is illustrated through numerical simulation with a representative case example.