Transient Energy Function Method Research Articles

A robust transient energy function‐based controller for enhancing transient stability of virtual power system

AbstractThis paper offers non‐linear control for enhancing the transient stability in power systems containing a photovoltaic (PV) and doubly fed induction generator (DFIG) by transient energy function (TEF) method and finite‐time observers. At first, the TEF method is utilized to enhance the transient stability in a power system containing a PV, DFIG, and synchronous generator (SG) by constructing a hybrid Lyapunov function. Then, the derivative terms in control are estimated with finite‐time observers. The main contribution of the research is the application of the TEF technique in the transient stability evaluation of a power system consisting of PV, SG, and DFIG. Another innovation of the research is the simultaneous control of DFIG and PV, whose uncertain parameters are estimated with the use of finite‐time observer. The proposed non‐linear control scheme is robust against changes in the configuration of the power system. In order to show the capability of this control scheme, time domain simulations are performed on the IEEE 9‐bus, and the NEW ENGLAND Standard 39‐Bus power system. Using the obtained result, some comparisons are made with the back‐stepping control scheme to clarify the superiority of the proposed method. The comparisons show that the proposed non‐linear control scheme can properly provide extra damping to reduce the first‐swing fluctuations in less time.

Transient stability increase of multi-machine power system by using SSSC and DFIG control with TEF technique and super twisting differentiator

This paper suggests a nonlinear controller of a Static Synchronous Series Compensator (SSSC) and a doubly-fed induction generator (DFIG) for transient stability enhancement by transient energy function (TEF) technique and super-twisting differentiator in the multi-machine power system. Initially, the TEF approach is employed to damping control and stability enhancement in a multi-machine power system including an SSSC, DFIG, and synchronous generator (SG). Then, the signals of time-derivative in the controller with a super-twisting differentiator are estimated. The significance and novelty of this work are the employs of the TEF method obtained for the multi-machine power system containing DFIG and SG. Another novelty is the use of the DFIG and SSSC simultaneous control whose uncertain parameters are estimated with a super-twisting differentiator. The feature of the nonlinear control approach is robust versus modifications in the topology of the system. Simulation is performed on the IEEE 9-bus system to appraise the operation of the nonlinear controller approach compared to back-stepping and sliding mode control. The simulation results demonstrate that the nonlinear controller approach satisfactorily reduces the first swing of oscillations.

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.

Large disturbance stability evaluation of interconnected multi‐inverter power grids with VSG model

The virtual rotor angle stability of interconnected multi-inverter power grids with virtual synchronous generator (VSG) model is studied under large disturbance. According to the VSG regulation scheme, its electromechanical dynamic model is derived. A Lyapunov like energy function candidate of the power system with VSG-controlled inverters is constructed to adopt the transient energy function method. After system large disturbances, the critical clearing times are obtained through potential energy boundary surface method and also verified through time-domain simulations. Furthermore, the impacts of virtual control parameters on system behaviours are also discussed and demonstrated through simulations.

Multi‐objective optimal power flow considering the system transient stability

This study presents a new formulation for optimal power flow (OPF) to enhance the overall transient stability of the power system in addition to the traditional fuel cost minimisation. To overcome the shortcomings of the traditional formulation, this study formulates OPF as a true multi-objective optimisation problem. One objective is to operate the system economically within the system physical bounds. The other objective is to withstand severe contingencies by enhancing the system transient stability. To overcome the inconsistency and sub optimality problems, strength Pareto evolutionary algorithm is developed for solving multi-objective OPF (MOOPF) problem. Time domain simulations (TDSs) are employed for handling transient stability problem that knocks out the numerical inaccuracy and convergence problems. To speed up the transient stability assessment, a hybrid stability classifier is developed that combines TDS and transient energy function methods. To demonstrate the effectiveness of the proposed strategy, two standard test systems have been considered. The results show the effectiveness of the proposed approach to solve the MOOPF and enhance greatly the system transient stability. The results also show the superiority of the proposed approach compared with those reported in the literature.

Critical Generation Evaluation Using Hybrid Energy Function Method

SUMMARYIt is well known that the transient energy function (TEF) method is useful for an efficient transient stability assessment as represented by the estimation of the critical clearing time (CCT). However, there still remains an issue for practical use: most of the TEF methods adopt the classical model of a synchronous machine in which the internally generated voltage is assumed to be constant. Moreover, critical generated output can be a more practical stability index instead of the CCT used in the conventional TEF methods. In this paper, a conventional hybrid TEF method is developed in order to estimate the transient stable critical generated power by using an improved hybrid simulation. The proposed method can handle the detailed model for a synchronous machine and can estimate the critical generated power with higher accuracy. Experimental results for a large network model are given in order to verify the practicability of the proposed method.

Hybridエネルギー関数法を用いた過渡安定限界発電出力の推定法

SUMMARY It is well known that the transient energy function (TEF) method is useful for an efficient transient stability assessment as represented by the estimation of the critical clearing time (CCT). However, there still remains an issue for practical use: most of the TEF methods adopt the classical model of a synchronous machine in which the internally generated voltage is assumed to be constant. Moreover, critical generated output can be a more practical stability index instead of the CCT used in the conventional TEF methods. In this paper, a conventional hybrid TEF method is developed in order to estimate the transient stable critical generated power by using an improved hybrid simulation. The proposed method can handle the detailed model for a synchronous machine and can estimate the critical generated power with higher accuracy. Experimental results for a large network model are given in order to verify the practicability of the proposed method.

Transient Stability Analysis of Grid-connected Wind Turbines with Front-end Speed Control via Information Entropy Energy Function Method

According to the characteristics like time-consuming and can not be quantitatively analyzed of time domain simulation in power system transient stability analysis, a direct method using information entropy combined with transient energy function method is proposed in this paper to analyze the transient stability of wind power system equiped with front-end speed controlled wind turbines (FSCWT) with synchronous generators. In which, the system kinetic energy and potential energy are used as information source to makeup information entropy function, then, a theoretical analysis of system transient stability is conducted. Based on this, simulations are carried out in IEEE 5-machine 14-bus system compared with the time domain’s, which verified the consistency of information entropy energy function (IEEF) method and time domain analysis. Results show that it is more intuitively and effectively to use IEEF method for wind power system transient analysis equiped with FSCWT. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3379

Determination of Dynamic Available Transfer Capability Using Potential Energy Boundary Surface Based Transient Energy Function

This paper proposes the application of potential energy boundary surface (PEBS) based transient energy function (TEF) method to evaluate fast and dynamically secured real time available transfer capability (DATC ) for the effective power transactions in the deregulated electricity market. With the involvement of various power transactions in this electricity market at the same time, the system may subject to severe disturbances. Transient stability analysis is a valuable tool for the system operator to maintain the system operating conditions under severe disturbances. In this paper, PEBS method of transient energy function is used to avoid the computational complexities in the transient stability analysis for the highly stressed power systems. The proposed method involves in assessing maximum Dynamic ATC at the critical point of energy margin. The prescreening of line outages using energy margin values is also carried out to reduce the computational burden in determining DATC. The proposed approach has been analyzed and tested on WSCC 3-machine 9-bus system and New England 10-machine 39-bus system.

Phasor measurement units for out of step detection

Synchronized phasor measurements have become an important technology with several international manufacturers offering commercial phasor measurement units (PMUs) which meet the prevailing industry standard for synchrophasors. With the occurrence of major blackouts in many power systems around the world, the value of data provided by PMUs has been recognized, and installation of PMUs on power transmission networks of most major power systems has become an important current activity . This paper presents a transmission line protection scheme based on synchronized phasor measurement units to detect (predict) out of step condition using equal-area criterion which is consistent with transient energy function method for single machineinfinite bus system or two machines system. This scheme uses the measured values of voltages and currents, as complex values, at the generator bus and at the infinite bus. These values of voltage and current are measured in time domain and transformed into phasor domain by using Discrete Fourier Transform to calculate the required areas. The proposed scheme can be used for the detection of out of step condition using equal area criterion with different types of faults at different locations and different models of transmission lines.

Evaluation of Operating Domains in Power Systems

This paper presents the results of a recent major industry-supported study with the aim to provide power system operators with more meaningful and effective means to quickly identify feasible operating boundaries as well as more flexibility to select alternate operating scenarios. In this regard, the paper outlines the main theoretical basis and computational framework for the development of innovative computerized schemes capable of identifying and processing various system integrity domains. The novel framework allows system operators to determine – in a fast and reliable manner – the most favorable operating scenarios which maintain system security, reliability and operating performance quality. For demonstration purposes, and without loss of generality, an emphasis is given to the dynamic system security problem where the Transient Energy Function (TEF) method is used to define quantitative measures of the level (degree) of system security for a given operating scenario. Nonetheless, the framework presented is applicable quite as well to other system performance functions and criteria that may be considered. A demonstrative application is presented for a 9-bus benchmark system, widely used in the literature. In addition, a practical application is also presented for the Saudi Electricity Company (SEC) power system where the operating security domain was evaluated in the operating parameter space spanned by two major interface flows in the system.

Allocating the cost of transient stability constraint relief in bilateral electricity markets

In this study, the issue of allocating the cost of transient stability relief in a bilateral electricity market is investigated. The results of a constrained generation scheduling problem can be utilised in two ways to price the cost of a constraint. In the first method, which is the basis of nodal pricing, the Lagrange multipliers of the nodal power balance constraint are used as the price of electricity at various buses. In the second method, which is used in this study, the constraint relief scheme is based on a bid-based adjustment market of increments and decrements offered by generators to be involved in the constraint relief process. In the scheme used in this study, the cost of transient stability relief is first allocated to the individual constraints by different methods and the allocated costs are then allocated to the transactions in proportion to the degree of involvement in that constraint. Three methods are proposed and discussed for allocation of cost to the constraints and the results are compared and commented. The transient energy function (TEF) method is used to calculate the contribution of transactions in the constraints.

Determination of Critical Generator Group Using Accelerating Power and Synchronizing Power Coefficient in the Transient Energy Function Method

This paper proposes an algorithm for determining critical generator lists using accelerating power and synchronizing power coefficient (SPC), and critical generator group (CGG) from CGG candidates, which is a combination of critical generators. The accurate determination of CGG provides a more accurate energy margin while providing system operator with information of possible unstable generator group. Classical transient energy function (TEF) method selects the critical generators with big corrected kinetic energy of each generator at the moment of fault removal. However, the generator with small acceleration after fault, that is, the generator with small corrected kinetic energy, is also likely to belong to CGG if the generator has small synchronizing power. The proposed algorithm has been verified to be effective compared with the classical TEF method. We utilized the power system of Korean Electric Power Corporation(KEPCO) as a test system.

Rescheduling of power systems constrained with transient stability limits in restructured power systems

This paper investigates various approaches to relieve the transient stability constraint in restructured power systems. The approaches adopted fall into two broad categories: those based on eliminating the constraint in the least-cost way and those based on eliminating with the least possible rescheduling. The latter group can, on the other hand, emerge in the form of a pool-protected policy in which the bilateral contracts are rescheduled to maintain the stability or in the form of a contract-protected policy in which the realizable bilateral contracts are maximized while minimizing the rescheduling in pool market. Transient energy function (TEF) method is used as a tool to calculate the sensitivity of energy margin to the variations in the magnitude of generation and load. The effectiveness of the method is illustrated by case studies on Western System Coordinating Council (WSCC) 3-machine 9-bus power system and on the 10-machine 39-bus New England test system and the results are compared. The results are also verified by time domain simulations.

Transient stability output margin estimation based on the energy function method

AbstractIn this paper, a new method of estimating the critical generation margin (CGM) in power systems is proposed based on transient stability diagnostics. The proposed method can directly compute the stability limit output for a given fault based on the transient energy function method (TEF). Since CGM can be directly obtained by the limit output using estimated P‐θ curves and is easy to understand, it is more useful than the conventional critical clearing time (CCT) of the energy function method. The proposed method can also estimate CGM as a negative value, which means instability in the present load profile, and so a negative CGM can be directly used as a restriction on generator output.The accuracy and fast solution ability of the proposed method are verified by applying it to a simple 3‐machine model and IEEJ EAST10‐machine standard model. Furthermore, the usefulness of the method for severity ranking of transient stability for various fault cases is discussed by using CGM. 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(3): 10–19, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ eej.21035

Study on power system transient instability detection based on wide area measurement system

AbstractIn this paper, a method, which is essential in initiating emergency control measures, is proposed for fast and accurate online detection of transient instability based on real‐time measurement. Under a certain disturbance, the candidate critical cluster (CC) of power system is predicted and refreshed at each sampling step. The method identifies the loss of synchronism at each time step by observing the geometric characteristic of the post‐fault trajectory of the generalized one‐machine equivalent system. Unlike the previous extended equal‐area criterion method, it is unnecessary to calculate the unstable equilibrium point (UEP) during instability detection in this method and some limitations caused by the time‐invariant assumption are also eliminated. Simulations are carried out on the IEEE 50 generator test system and a real power system. The simulation results indicate that the proposed method has the features of reliability and effectiveness in identifying the loss of synchronism with inter‐area mode. Copyright © 2008 John Wiley & Sons, Ltd.

Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.

エネルギー関数法に基づく過渡安定度発電余力推定手法

In this paper, a new method of estimating critical generation margin (CGM) in power systems is proposed from the viewpoint of transient stability diagnostic. The proposed method has the capability to directly compute the stability limit output for a given contingency based on transient energy function method (TEF). Since CGM can be directly obtained by the limit output using estimated P-θ curves and is easy to understand, it is more useful rather than conventional critical clearing time (CCT) of energy function method. The proposed method can also estimate CGM as its negative value that means unstable in present load profile, then negative CGM can be directly utilized as generator output restriction.The proposed method is verified its accuracy and fast solution ability by applying to simple 3-machine model and IEEJ EAST10-machine standard model. Furthermore the useful application to severity ranking of transient stability for a lot of contingency cases is discussed by using CGM.

Best location of SVC to improve first swing stability limit of a power system

While the primary purpose of a static var compensator (SVC) is to regulate bus voltage, it can also improve stability and damping of a power system if located appropriately. This paper proposes a method of determining the location index of a SVC in a multi-machine system to improve the first swing stability limit of the system. Based on the concept of transient energy function method, the location index of a SVC is considered to be the additional critical energy supported by the SVC and is computed through controlling unstable equilibrium point and potential energy boundary surface methods. In computing the critical energy, the SVC is represented by its susceptance at the verge of stability and which can be justified by carefully observing a recent control strategy of SVC used to improve the first swing stability limit of a power system. The effectiveness of the proposed location index of SVC is then tested on the 10-machine New England system and the 20-machine IEEE test system. Results obtained by the proposed method are then verified by comparing the critical clearing time obtained through time domain simulations of system dynamic equations.

Application of energy function to assess the first-swing stability of a power system with a SVC

The transient energy function method is usually used to assess the stability of a power system without considering the effect of control devices. A modification of the method is proposed to determine the first-swing stability limit of a power system in the presence of a static VAR compensator (SVC). The effect of the SVC is carefully incorporated in determining the value of critical energy needed for system separation. The unstable equilibrium point at which the critical energy is to be evaluated is determined by considering that the SVC operates at its full capacitive rating. A recent control strategy of SVC proposed to maximise the first-swing stability limit can justify the use of such an unstable equilibrium point. The above technique of determining the first-swing stability limit of a power system in the presence of a SVC is tested on both single- and multimachine systems. The results obtained by the proposed technique are also compared with the corresponding actual values found through repetitive time-domain simulations of system dynamic equations.