Multi-machine System Research Articles

Sliding mode control of a Five-Phase Series- Connected Two-Motor Drive

In this work, we study vector control and sliding mode control of series-connected five-phase two asynchronous machines supplied with a three levels inverter. After presentation of multiphase machines, we worked out the mathematical model of five phase asynchronous machine supplied with voltage inverter. Application of Park transformation reduces considerably the mathematical model of machine. After, we applied vector control and sliding mode control to the five-phase induction machine. After that, we study a multi-machine system which comport five-phase two asynchronous machines supplied with a single voltage inverter. In the last, we had the independent vector control and the sliding mode control of series-connected five-phase two asynchronous machines. We observe that an appropriate transposition of phase’s order permits an independent control of two machines.

Performance evaluation of different structures of power system stabilizers

The electric power from the system should be reliable and economical for consumer’s equipment satisfaction. An electric power system consists of many generators, transformers, transmission lines, loads, etc. For the power system network, dynamic performance and stability are important. The system is lost its stability by some disturbances i.e., load variations, generator failure, prime mover failure, transmission line outage, etc. Whenever load variations in the system, generator rotor speed will vary, means oscillations in the rotor speed, which is deviating from rated speed. The excitation system will control the generator rated line voltage. When fault occurs at any equipment in the system, the system will unstable. If fault occurs at generator, the generator oscillates. To reduce the oscillations and to make the system stable used power system stabilizers (PSS’s). Here, three types of PSS’s are used i.e., PSS1B, PSS2B, PSS4B. Comparisons of three PSS’s are on the multi machine system under some disturbance. From the observations, concluding that PSS4B is quickly control the oscillations in the physical parameters of machine in the system than other power system stabilizers.

Dynamic state estimation of multi-machine power system with UPFC using EKF algorithm

Estimation of dynamic state variables in a multi-machine power system connected with UPFC is presented in this paper, using Extended Kalman filter (EKF) algorithm. A two-generator test case is used to estimate the generator rotor angle and rotor speed. The DC link voltage of the UPFC is the additional state variable to be estimated. Dynamic mathematical modeling of the multi-machine system with UPFC is explained in this work. DSE is done under transient condition of three-phase fault.

An Online Wide-Area Direct Coordinated Control Architecture for Power Grid Transient Stability Enhancement Based on Subspace Identification

In this article, by calculating the potential energy of generators, a dynamic real-time energy function based power grid model for the multimachine system is proposed based on available measurement (synchrophasor and prediction). Then, a wide-area optimal control framework that can control multiple generators simultaneously to enhance the transient stability of the system and increase the stability margin is designed and implemented. The main contributions are the proposed dynamic model is dynamic, feasible, and can effectively capture grid dynamics and transients. Furthermore, the architecture provides a dynamic state-space model based on grid events. The proposed approach has been tested on IEEE 68 bus test system and the results are provided. It is observed that the proposed control architecture provides an increased stability margin (up to 60%) and improved critical clearing time by 30%.

Dynamically modelling and locating solid oxide fuel cells and optimally designing fuzzy stabilisers for multi-machine system

Increasing progress in the field of renewable energy, thanks to the low cost of its resources and increasing public awareness of environmental issues, has led to wide use of these resources in power networks. Among various types of renewable sources, Solid Oxide Fuel Cells (SOFC) have the most potential to connect to the grid as a clean source of electricity according to their attributes. This paper presents a new method for mathematical modelling of multi-machine grids including large-scale SOFC. Since the installation location of SOFC in large-scale networks impacts grid dynamics, it is important to dynamically locate it. This study locates SOFC via the objective function of grid dynamics. Grid connected SOFC generation can effectively and efficiently improve small signal stability. Hence, considering the small disturbance fluctuations and the design of an optimal controller is necessary for the stability of a power system. Consequently, the present study investigates the design of a FLPSO-based power system stabiliser to improve the system's small frequency oscillations. The results of the simulation demonstrate that this controller guarantees the stability of the power system during low frequency disturbances.

Research and Analysis of On-Line Optimization Algorithm of Nonlinear Model Predictive Control Based on Hydropower Installation Field

Because of the strong nonlinearity of the controlled system, it cannot be expressed in the form of state space, and the calculation of nonlinear programming is large, so it is difficult to get the analytical solution. At present, it is generally solved by numerical method. The GPC stability theory based on state space analysis and internal model control is difficult to be applied in this case. In this paper, a fast algorithm of online optimization of nonlinear model predictive control based on the field of hydropower installation is presented. A fast algorithm control system of online optimization of nonlinear model predictive control is established and simulated by MATLAB. The simulation results show that the dimension of nonlinear programming solution in rolling optimization is effectively reduced and the feasibility of MPC is improved. Compared with single machine and multi machine systems, the model predictive control method is proved to have strong ability of generator terminal voltage maintenance and electromechanical oscillation damping.

Research and Analysis of Step Intelligent Model Predictive Control of Generator Excitation System Based on the Field of Building Installation

The traditional hydroelectric unit control system mostly adopts proportional integral derivative (PID) control strategy, which has simple control algorithm structure and is easy to understand and realize by the operation and maintenance personnel of the power station. However, its control objective is single, and the dynamic process and internal state information of the system water machine electricity coupling are less considered, especially the lack of the ability to constrain the system state variables In order to meet the increasingly complex operating environment in the regulation system of hydropower units high-quality control needs. Therefore, a step intelligent model predictive control method for synchronous generator excitation system based on tree algorithm is proposed. The step control and intelligent optimization algorithm are introduced into the rolling optimization of model predictive control, which effectively reduces the dimension of nonlinear programming solution in the rolling optimization and improves the feasibility of the control algorithm. In order to ensure the closed-loop stability of the control system, the concept of "quasi infinite time domain optimization" is introduced into the design process of the model predictive control of the excitation system of synchronous generator. The terminal penalty term and the terminal inequality domain are added in the rolling optimization link, and the "virtual" local linear feedback controller outside the prediction domain is designed. Compared with the traditional excitation control method in single machine and multi machine systems, it is proved that the predictive control method has stronger ability of generator terminal voltage maintenance and electromechanical oscillation damping than the conventional excitation control method.

Frequency-constrained Co-planning of Generation and Energy Storage with High-penetration Renewable Energy

Large-scale renewable energy integration decreases the system inertia and restricts frequency regulation. To maintain the frequency stability, allocating adequate frequency-sup-port sources poses a critical challenge to planners. In this context, we propose a frequency-constrained coordination planning model of thermal units, wind farms, and battery energy storage systems (BESSs) to provide satisfactory frequency supports. Firstly, a modified multi-machine system frequency response (MSFR) model that accounts for the dynamic responses from both synchronous generators and grid-connected inverters is constructed with preset power-headroom. Secondly, the rate-of-change-of-frequency (ROCOF) and frequency response power are deduced to construct frequency constraints. A data-driven piecewise linearization (DDPWL) method based on hyperplane fitting and data classification is applied to linearize the highly nonlinear frequency response power. Thirdly, frequency constraints are inserted into our planning model, while the unit commitment based on the coordinated operation of the thermal-hydro-wind-BESS hybrid system is implemented. At last, the proposed model is applied to the IEEE RTS-79 test system. The results demonstrate the effectiveness of our co-planning model to keep the frequency stability.

An Original Educational Algorithm Assessing the Behaviours of Angular Frequency Deviations of a Multimachine System in Small Signal Analysis

The paper presents a fully self-implementable algorithm that has demonstrated to be an effective tool for power education at the University of Padova-Department of Industrial Engineering. It deals with the small signal analysis of the electromechanical transients of a multimachine system. The algorithm allows analytically building both the state matrix and the input matrix. Moreover, by exploiting the matrix exponential, the angular frequency deviations of synchronous generators can be computed and plotted so to help students to evaluate transient stability. Besides the full exposition of the algorithm, the paper presents a comparison between a self-implemented linearized dynamic in Matlab environment and the dynamic simulation obtained by the commercial software DIgSILENT PowerFactory.

Transient Energy of an Individual Machine PART I: Stability Characterization

The individual-machine-equal-area-criterion method already shows potential in the transient stability assessment of multimachine systems. This two-paper series systematically analyzes the transient characteristics of the system trajectory from a genuine individual-machine transient energy perspective. In the first paper, the stability property that characterizes a critical machine is investigated by defining the residual kinetic energy, which only occurs at the maximum individual-machine potential energy point. We indicate that the transient energy conversion inside a critical machine can delineate the trajectory stability of the machine. In this way, the mapping between individual-machine kinetic energy and individual-machine trajectory can hence be established. Simulation results show that the individual-machine transient energy describes the system trajectory more precisely than the superimposed global transient energy in terms of transient stability analysis, and we also demonstrate that the conjecture in early individual-machine studies might fail in special simulation cases.

Multi-machine system "Synchronous generator - steam turbine"

In this article, we will consider the problems of controlling multidimensional phase systems described by nonlinear differential equations. These mathematical models describe processes in complex systems consisting of many turbines and generators and are used for their analysis. The relevance of these models lies in the fact that they allow simulating different pre-emergency, emergency, and post-emergency situations. The controllability of the model under consideration is determined by studying the global asymptotic stability of dynamical systems in cylindrical phase systems. The results obtained are demonstrated by a numerical example.

A Hybrid Modular Cascade Machines System for Electric Vehicles Using Induction Machine and Permanent Magnet Synchronous Machine

Modular Cascade Machines (MCM) system is a multi-machine system for the traction systems of electrified vehicles. Currently, MCM is composed of several machines of the same type, generally, several Permanent Magnet Synchronous Machines (PMSM). This paper proposes a hybrid MCM system, which is composed of a PMSM and an Induction Machine (IM). This combination aims to fully benefit the properties of different machines. This hybrid MCM is compared with other traction systems, namely, PMSM-based MCM and single PMSM drive. For a fair comparison, the design specifications of all the traction systems are optimally sized by a specific sizing method, which can maximize the system high-efficiency area. Then, different traction systems are designed by Finite Element Method (FEM), in order to have accurate material consumptions and efficiency maps. The comparison study shows that the proposed hybrid MCM is competitive for energy saving. Therefore this new drive saves about 5% of energy in comparison with a single PMSM derive. The hybrid MCM energy saving is very close to the one of a PMSM-based MCM. Moreover, the hybrid MCM system reduces the PM volume (reduced by 53%) while increases the usage amount of winding copper, steel and aluminum, due to the existence of IM. Fortunately, the cost estimation proves that the hybrid MCM (not include inverters) has almost the same cost as the single PMSM. Hence the proposed hybrid MCM is a competitive alternative of the single PMSM than the PMSM-based MCM.

An Analytical Model for Small Signal Stability Analysis in Unbalanced Electrical Power Systems

This paper presents a general model to carry out a small signal stability analysis in electrical power systems (EPSs) that operate in unbalanced conditions. The classic traditional approach is based on a phase representation where it is supposed that the triphasic electric grid does not suffer any variations during its operation. With the presence of unbalances in transmission lines and loads, it is necessary to develop a general model that allows answering the needs and challenges with which modern electric systems must deal. The present work firstly intends to address the three-phase representation of an EPS, including the controllers. The proposed model is applied to a classical test system, a three machine-nine bus system, considering all the dynamic and algebraic variations associated with angular stability analysis. The proposed approach to small signal stability analysis shows results that differ from the classical analysis. The results are backed up with time domain simulations, and therefore, these results could be used in the calculation of the controllers that operate in unbalanced multimachine systems.

Islanding detection of distributed generation systems using hybrid technique for multi-machine system

Due to depletion of conventional fuels and increase in power demand, many renewable energy sources are being integrated into the electrical grid. One of the major concerns with this integration of these renewable sources with utility grid is unintentional islanding. Many techniques have been proposed to detect unintentional islanding, all of them trying to comply with the IEEE standard 1547. This paper presents an analysis of the hybrid technique to detect the islanding condition of the power system with multi-machine systems. This work aims at analysing the technique against increasing size of the system with increasing number of distributed generators by including practical voltage unbalance formula. The validity of this detection technique is verified using IEEE standard test power systems in MATLAB platform. This method can be used to identify multiple islanding conditions effectively. The simulation results show the effectiveness of the technique to detect islanding condition for multi-machine systems.

Sweeping power system stabilisation with a parametric fuzzy predictive control of a generalised energy storage device

A control oriented approach is adopted for the implementation of a parametric fuzzy-predictive control on a compact model of a generalised energy storage device implanted in a multi-machine system. It is realised using a combination of a heuristic fuzzy logic control (HFLC) and a predictive step ahead control (PSAC) for energy storage reactive and real power modulation, respectively. While PSAC overcomes the computational burden innate to model predictive control, the HFLC with paramount simplicity lays down the design template for fuzzy control. Local bus measurements are translated into rate of change of frequency and voltage errors, while accommodating a second-order dynamics of a phase locked loop. To emphasise the computational simplicity and implementation speed of the proposed technique, all parameters of the problem are solved explicitly. These parameters account for the input–output mapping structure consisting of membership spreads and rule base in fuzzy domain. In predictive control, while approximating the storage-converter dynamics by a second-order system, relevant expressions are derived for the parameters involved in the loop. Umbrella power system stabilisation, viz., high oscillation damping with quicker settling times, frequency-nadir curtailment, power and voltage smoothing is assured with the parametric fuzzy-predictive controlled energy storage.

Transient stability analysis of power grids with admissible and maximal robust positively invariant sets

Abstract The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid’s bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.

Synergy of adaptive super-twisting method (ASTM) and game-theory algorithm (GTA) for dynamic stability improvement of interconnected grids

In this research work, a proposed technique of adaptive super-twisting method (ASTM) and game-theory algorithm (GTA) is presented. The proposed technique is applied to improve the dynamic stability of UPFC-based tidal energy resource. The impact of UPFC-based tidal energy resource on the power network is significantly recognized to support the demands supply and to enhance the dynamic performance. UPFC is able to control and enhance the power flow, voltage profile, power angle profile, and transmission lines loadability. The proposed technique has been optimally tuned to control the operational parameters of UPFC-based tidal energy resource. Both scenarios of single machine connected to infinite-bus grid, and multi-machine system are considered. The dynamic modelling of underlined system is done by d–q axis reference modelling. The analysis of steady-state stability is represented by the dynamic response specifications with stability discussion to evaluate the system performance. The simulations, including modelling, analysis and results, are carried out to confirm the entire stability of underlined systems. It has been confirmed the superb characteristics of proposed technique on interconnected UPFC-based tidal energy resource to power systems. The results of concerned scenarios have been emphasized that the proposed technique outperforms other well-established techniques. It is consolidated that UPFC-based tidal energy resource with proposed technique achieves significant performance and strengthened response. Therefore, the proposed solution can be offered as a favourable technique for enhancing the dynamic performance of power systems.

Decentralised design of robust multi‐objective PSSs: D ‐decomposition approach

This study addresses the problem of determining the set of all robust three-parameter power system stabilisers having the form . Graphical characterisation of stabilising power system stabilisers (PSSs) is carried out using D-decomposition, whereas the controller–parameter space is subdivided into root-invariant regions. Rather than Hurwitz stability, D-decomposition can parameterise D-stabilising PSSs that enforce pole-clustering in a pre-specified region D to ensure better time-domain specifications. The convex region of D-stabilising PSSs is sketched by mapping the contours from the s-plane onto the controller–parameter plane by two parametric functions and with fixed . The frequency range considered for mapping is initially computed to avoid sweeping over unnecessary frequencies. Based on the geometry of the D-stability region, analytical expressions are derived to compute optimal σ − ζ PSSs for an arbitrary operating point. Parametric uncertainties are captured by an image-set polynomial where the region guarantying robust D-stability of the family is investigated. A computationally effective approach based on stabilising two vertex plants is concluded from the D-stability region. Extension to multi-machine systems is treated where decentralised PSSs are synthesised. An iterative algorithm is suggested to modify a set of initial feasible PSSs sequentially while maximising damping indices. Simulation results confirm the efficacy of the suggested method.

Amended GWO approach based multi-machine power system stability enhancement

The conception of electromechanical oscillations initiates in the power network when there is an installation of the generator in parallel with the existent one. Further, the interconnection of multiple areas, extension in transmission, capricious load characteristics, etc. causes low-frequency oscillations in the consolidated power network. This paper proposes variants of a booming population-based grey wolf optimization (GWO) algorithm in the tuning of power system stabilizer parameters of a multi-machine system in damping low-frequency oscillations. The parameters have been tuned by framing an objective function considering the improving damping ratios for the system states with lesser damping ratios and shifting the system eigenvalues towards the left-hand side of s-plane for the improved settling characteristics for the oscillations in the system. The requisites of stabilizer strategy are mapped with the hallmarks of prevalent algorithms and designed hybrid versions of GWO for the enhancement of the multi-machine power system stability. Four variants of GWO technique are nominated based on the competent stabilizer performance namely, modified grey wolf optimization (MGWO), hybrid MGWO particle swarm optimization (MGWOPSO), hybrid MGWO sine cosine algorithm (MGWOSCA) and hybrid MGWO crow search algorithm (MGWOCSA) for the designed multi-machine power network. The proposed methods have been realized with the statistical analysis on the 23 benchmark functions. Nonparametric statistical tests, namely, Feidman test, Anova test and Quade tests, have been performed on the test system, further analysed in detail. A detailed comparative analysis under the self-clearing fault is presented to illustrate the suitability of the proposed techniques. For the analysis purpose, the location of system eigenvalues has been observed along with their oscillating frequencies and corresponding damping ratios. Further, the damping nature offered with considered system uncertainty for the system states also presented with the PSS parameters obtained by the proposed algorithms.

Adequacy of the Single-Generator Equivalent Model for Stability Analysis in Wind Farms With VSC-HVDC Systems

Due to the complexity of detailed models, the single-generator equivalent model (SEM) of a wind farm is commonly used to facilitate the stability analysis. However, the adequacy of the SEM for stability analysis in direct-drive wind farms with VSC-HVDC systems is still uncertain. Therefore, this article analyzes the SEM adequacy in two aspects: the oscillation modes analysis and the sub-synchronous oscillation (SSO) stability enhancement by optimizing wind farm parameters. Firstly, various critical oscillation modes are characterized according to the frequency, and a comparison of these modes between the two-generator equivalent model and the SEM is presented. The effect of single-generator aggregation on the critical oscillation modes is discussed. Then, the impact of permanent magnet synchronous generator (PMSG) parameters on the inside-wind-farm/wind-farm-grid SSO modes is explored. It is revealed that with the change of PMSG parameters, the damping effect of the two SSO modes is identical. This implies that the SEM can be used to improve the SSO stability of the multi-machine system by optimizing the PMSG parameters. PSCAD/EMTDC simulations are further performed to verify the theoretical analysis.