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This paper presents a novel approach to dynamic phasor-based transient stability simulation. The proposed method is based on the modified nodal analysis (MNA) approach to circuit simulation, which is used to construct continuous differential-algebraic equations (DAEs). The proposed method makes use of the stamp technique, which makes it possible to construct a general purpose MNA-based simulator. Stamp-based models for common power system components are derived in this work. A new MNA-based synchronous machine model is presented, which represents machines as nonlinear inductances instead of subtransient equivalents. The resultant continuous DAEs are numerically solved using the general purpose variable step and variable order library \texttt{IDA}. Simulation results from the IEEE 68 bus test system, a real 400 bus power system, and the IEEE 39 bus test system with an embedded HVdc transmission system demonstrate that the proposed method is suitable for large ac networks with power electronic devices. The results demonstrate good agreement between the proposed method and electromagnetic transient (EMT) simulation. The results also demonstrate that the proposed method is fast and scalable with CPU times that are up to 200 times faster than EMT simulation.

Stability analysis in the power system is becoming more important than ever as more distributed energy resources penetrate in the system. This study presents a novel load pattern voltage stability index (LPVSI) applicable to transmission and distribution systems. By considering the nominal value of voltages, the power network is converted into a two-bus equivalent system. Then, LPVSI is derived by only the real-time measurement of the voltage and deviation of active and reactive power loads. Also, the assessment of distributed generation's penetration level on unbalanced systems, with maximum loadability and power loss reduction constraints, is performed with regard to daily load variations. The accuracy and efficiency of the proposed indicator are tested on an unbalanced 34-node radial distribution system. Obtained results in comparison with some other papers in the literature demonstrate that the proposed voltage stability index is fast and effective in identifying non-trivial instabilities in the power system networks.

This paper utilizes modern statistical and machine learning methodology to predict the oscillation mode of interest in complex power engineering systems. The damping ratio of the electromechanical oscillation mode is formulated as a function of the power of the generators and loads as well as bus voltage magnitudes in the entire power system. The celebrated Lasso algorithm is implemented to solve this high-dimension modeling problem. By the nature of the L1 design, the Lasso algorithm can automatically render a sparse solution, and by eliminating redundant features, it provides desirable prediction power. The resultant model processes a simple structure, and it is easily interpretable. The precision of our sparse modeling framework is demonstrated in the context of an IEEE 50-Generator 145-Bus power network and an online learning framework for the power system oscillation mode prediction is also provided.

The basic concepts of transient rotor angle stability are presented in this chapter. The synchronous machine model with its auxiliary controllers and load models are discussed. The procedure to combine all dynamic models with the transmission network model to perform a dynamic simulation is presented. Although the modelling in this chapter is limited to the synchronous machine and loads, the algorithm of simulation is presented in a general manner to equip the reader with the understanding of how to expand the algorithm to include any dynamic device. A case study is used to demonstrate how to interpret the results of a simulation. The conventional modelling method presented in this chapter is not suitable to simulate faster transients introduced by power electronic devices in modern power systems. The chapter concludes with a short discussion on these limitations and new developments to resolve them.

The absence of complete model data of a power system hinders complete eigenvalue analysis of that system. System identification methods have been used to identify operating-point-dependent equivalent linear model of a power system. Such identified models do not allow a complete eigenvalue analysis. To resolve this, the identification problem can be formulated in such a way to utilize any a-priori knowledge of the system. Model data of a synchronous machine consists of machine data and controller parameters. Methods to determine synchronous machine parameters are well established. In this paper, knowledge of the machine data and knowledge of eigenvalues of the system at multiple distinct operating points, extracted by a system identification method, are used to determine auxiliary controller parameters of the synchronous machine. Model data that are determined by the proposed method is independent of the operating point. Therefore, it can be easily integrated into a complete small signal stability study at any operating point of the synchronous machine.

More and more system operators are interested in calculating transfer capability in real time using real-time power flow models generated from the Energy Management System (EMS). However, in comparing these models with offline study models, the EMS models usually include only a limited portion of the interconnected system. It is not practical to extend the EMS model in order to capture the impact of the external systems and as such using an equivalent network becomes necessary for this purpose. Equivalent circuits derived from the offline models for certain predetermined operating conditions would suffer from invalid results under various real-time operating conditions. Hence, it is necessary to derive an equivalent circuit model that is adaptive to the real-time system conditions. This paper presents a general method of creating an equivalent circuit model based on the measured boundary station parameters such as voltages and power flows. Simulation studies show that such derived equivalent circuit models provide solutions with adequate accuracy.

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation.

This study presents a simple approach to modify the Prony algorithm to extract dominant low-frequency modes present in ring-down oscillations in power systems. The proposed approach is based on the observation that true modes present in the ring-down oscillations appear consistently, irrespective of the order of the Prony model. It is shown that the consistently appearing modes can be extracted using a sorting method. The improved Prony algorithm which has the feature of extracting only the true modes present in the input signal is utilised to propose an oscillation monitoring algorithm in this study. The suitability of the proposed oscillation monitoring algorithm for real-time monitoring of low-frequency inter-area oscillations is demonstrated using synthetic signals and simulated signals of different test systems.

Forced oscillations in a power system are distin-guished from natural oscillations as a rouge oscillatory input to the system. Two examples for sources of these forced oscillations are a malfunctioning governor that has not been modeled or a cyclic load with a low frequency. Power system oscillations are analyzed either by model based methods or by measurement based methods. Several recent papers have studied the impact of forced oscillations in estimating small signal stability of a power system using measurement based methods. When the frequency of the forced oscillation is in the vicinity of natural oscillations in the system, it has been reported that estimating natural and forced oscillatory modes is a challenge. This paper proposes utilizing model data to generate a database of oscillation signatures of the system for different forced oscillations of different frequencies at different origins and, aid measurement based oscillation monitoring methods to determine frequency and damping of natural oscillations and the source of forced oscillations, including at resonant conditions.

This paper presents a novel approach to enable frequent computational cycles in online dynamic security assessment by using the terms of the transient energy function (TEF) as input features to a machine learning algorithm. The aim is to train a single classifier that is capable of classifying stable and unstable operating points independent of the contingency. The network is trained based on the current system topology and the loading conditions. The potential of the proposed approach is demonstrated with the New England 39-bus test power system model using the support vector machine as the machine learning technique. It is shown that the classifier can be trained using a small set of data when the terms of the TEF are used as input features. The prediction accuracy of the proposed scheme was tested under the balanced and unbalanced faults with the presence of voltage sensitive and dynamic loads for different operating points.

In this paper, Power-Voltage Curves obtained from quasi steady state analysis is used to demonstrate the concept of voltage stability. This method is shown to be applicable to analyze the voltage stability when the load consists of constant admittance as well as dynamic induction motor loads. The results obtained from quasi steady state analysis is compared with the results of detailed real time simulations. As expected, the paper confirms that quasi steady state analysis can be used to predict the voltage collapse point of radial power systems with reasonable accuracy even when the loads consist of dynamic loads. The simulations and analysis programs developed in the research can be used as teaching tools.

Detection and analysis of bad data is an important sector of the static state estimation. This paper addresses single and multiple bad data in the modern phasor measurement unit (PMU)-based power system static state estimations. To accomplish this objective, available approaches in the PMU-based state estimation are overviewed, and their advantages and disadvantages are briefly explained. The largest normalized residual test is used to identify bad data. Then, phasor measurements are added by post-processing step in the state estimation. The proposed algorithms of phasor measurements utilization in state estimation can detect and identify single and multiple bad data in redundant and critical measurements. To validate simulations, IEEE 30 bus system are implemented in PowerFactory and Matlab is used to solve proposed state estimation using postprocessing of PMUs and mixed methods. Bad data is generated manually and added in PMU and conventional measurements profile. Finally, the location and analyze of bad data are available by the result of largest normalized residual test.

It has become a common practice of the manufacturers to provide only black-boxed models of devices to their buyers. These black-boxed models are compatible with time domain simulations. In this paper, a black-boxed EMT simulation model of a synchronous generator was connected to a known multi-machine power system, and an improved Prony Analysis method was used to identify the modes of the system from time domain simulations. The machine characteristics of the black-boxed model are assumed to be available to the user while the auxiliary controllers remain unknown. Then, an optimization-based eigenstructure assignment method is used to design a fictitious auxiliary controller for the black-boxed device, and a linearized power system model is realized. Eigenvalue analysis of the realized linear system provides insightful information of the system i.e. participation factors, mode shapes.

Power ramp limitation (PRL) is likely to become a requirement for large-scale photovoltaic power plants (LPVPPs) in order to allow the increase of PV penetration levels. Especially in islands with reduced inertia capability, this problem is more stringent: high-power ramp can be caused by either fast irradiance changes or other participant generators for example wind power, or loads. In order to compensate for the power mismatch, LPVPPs must use active power reserve (APR), by either curtailment or auxiliary storage. The paper proposes a PRL control structure for dynamic APR sizing and deployment. The selected test case is the power system of Puerto Rico (PREPA), modeled using the modified IEEE 12 bus benchmark system, with different levels of PV penetration. It is shown that LPVPP with PRL can effectively reduce the ramping rate of the participating generators. Considering that the large area of LPVPPs acts as a filter against fast irradiance changes, the study also reveals the required plant size for which an auxiliary storage is no longer needed in order to comply with PRL requirements—an important economical aspect.

Results of a nonlinear simulation is used in this paper to identify a linear model of a black-boxed synchronous machine. Linear system identification methods such as Prony Analysis, are employed to identify linear models of power system devices when their complete mathematical models are not available to be included in small signal stability studies. While the user lacks the knowledge of the control structure and its parameters, availability of the machine model is practically possible as the models and their parameter estimation methods are well established. Rapidly decaying transients of the machine, such as amortisseur winding transients, usually tend to be missed by available system identification methods. In this work an improved expanding-data-window Prony Analysis method is complemented with an eigenstructure assignment based method to incorporate a-priori knowledge of the generator to determine the highly damped transients of an electromagnetic transient (EMT) simulation model of a synchronous machine with generator controllers.

This paper investigates the impact of different control modes of VSC HVdc to the transient stability of power systems. VSC HVdc offers fast bi-directional power control in addition to fast ac voltage control. This feature is utilized in this study to enhance the transient stability of a conventional generator in a power system. Simulations are carried-out for three scenarios: (i) the generator is connected to the VSC terminal, (ii) the generator is connected at a distance from the VSC terminal, and (iii) the VSC is connected at a distance from the generator terminal. The critical fault clearing time is used as the indicator of the stability of power system. In each scenario, effects of both ac voltage control and reactive power control are studied. This paper shows that the transient stability of power system can be improved by having a VSC with fast ac voltage control near to synchronous generators.

Transient stability of an electrical power system refers to the ability of the system to settle at the stable equilibrium point in the post-fault system subsequent to a specific fault scenario. This stability problem can be studied either as a system stability or a structural stability problem. In this paper, the concept of Lyapunov Exponents (LEs) is used to analyze the transient stability of IEEE 3-generator 9-bus and IEEE 16 generator 69 bus benchmark systems. A spectrum of LEs is calculated from the mathematical models and the Largest Lyapunov Exponent (LLE) being negative implies the exponential stability of the post-fault power system. The system stability regions for specific fault scenarios are determined using the invariance property of the LEs from the initial conditions. Furthermore, the structural stability regions in terms of parameters of the pre-fault system dynamic equations are also determined. This study demonstrates that the concept of LEs can be used as a novel method to determine if the post-fault power system is within the stability region of attraction of the new stable equilibrium point, and hence to determine the stability region. It is also proposed that the largest average exponential rate calculated over a short time window is a sound approach for early prediction of the stability.

This paper utilizes a class of modern machine learning methods for estimating a transient stability boundary that is viewed as a function of power system variables. The simultaneous variable selection and estimation approach is employed yielding a substantially reduced complexity transient stability boundary model. The model is easily interpretable and yet possesses a stronger prediction power than techniques known in the power engineering literature so far. The accuracy of our methods is demonstrated using a 470-bus system.

Summary form only given. This paper presents a comprehensive analysis of sub-synchronous interactions in a wind integrated power system to understand and mitigate them. The proposed procedure has two steps. In the first step, a frequency scan is performed to determine the presence of resonant frequencies in the sub-synchronous range. In the second step, a detailed small signal analysis is performed. Participation factors are used to identify the state variables that are involved in the interaction, and the controllability indices are used to determine the mitigation method. It is shown that the sub-synchronous interaction present in Type 3 wind turbine-generators connected to the grid through series compensated lines is an electrical resonance between the generator and the series compensated line which is highly sensitive to the rotor side converter current controller gains.

This paper presents a probabilistic approach to evaluate the reliability of a synchrophasor-based multi-input damping controller. Considering the probabilities of losing input signals to the controller, expected damping for the critical electromechanical oscillatory modes are determined. A two input power system stabilizer that uses a local and a remote signal is considered as a test system to evaluate the expected damping. Different probabilities of failures are considered for different controller inputs and the resultant expected damping values are compared. The importance of using a probabilistic index in the design stage of a controller is highlighted.

Analysis of the impact of communication network infrastructure performance on critical power system applications that rely on wide area synchrophasor measurements can be realistically achieved only through co-simulation of the power system and the synchrophasor communication network. In this paper, a single simulation platform, an electromagnetic transient (EMT) simulation program - PSCAD/EMTDC, was used to implement the detailed models of the components in a wide area synchrophasor network. Using the developed components models, a simple wide area damping control application was co-simulated to demonstrate the impact of communication latency, packet losses, and bit flip errors on the controller performance. It was shown that with the aid of co-simulations, application specific issues can be diagnosed and appropriate solutions can be investigated.

Matrix Pencil (MP) and Hankel Total Least Squares (HTLS) algorithms approximate an input signal as a sum of decaying sinusoidal oscillations. This paper presents a simple technique to improve these algorithms for extracting only the true oscillations present in the input signal. The rationale behind the improvement is the observation that the true modes present in the input signal appear consistently irrespective of the order of the linear approximation used in MP and HTLS algorithms. It is shown that the modes appearing consistently can be extracted using a sorting method. The improved MP and HTLS algorithms presented in this paper are used for monitoring the low-frequency oscillations in power system in an online environment. The performances of the proposed algorithms are demonstrated using synthetic signals and simulated signals of different test systems.

In this paper, an artificial neural network (ANN) based method is developed for quickly estimating the long-term voltage stability margin. The investigation presented in the paper showed that node voltage magnitudes and the phase angles are the best predictors of voltage stability margin. Further, the paper shows that the proposed ANN based method can successfully estimate the voltage stability margin not only under normal operation but also under N-1 contingency situations. If the voltage magnitudes and phase angles are obtained in real-time from phasor measurement units (PMUs) using the proposed method, the voltage stability margin can be estimated in real time and used for initiating stability control actions. Finally, a suboptimal approach to determine the best locations for PMUs is presented. Numerical examples of the proposed techniques are presented using the New England 39-bus test system and a practical power system which consists of 1844 buses, 746 load buses, and 302 generator buses.

The paper applies the method of eigenstructure assignment for the design of a controller for a wind generation scenario in Northern Scotland based on doubly-fed induction generators (DFIGs). The designed controller serves the combined purpose of a conventional power system stabilizer (PSS) and an active damping controller and provides a contribution to both network and shaft damping. This novel approach is superior because all available degrees of freedom are fully exploited by selecting not only the new eigenvalue locations but also certain elements of the left eigenvectors. These elements are obtained by solving a multiobjective nonlinear optimization problem (MONLOP). Examples are presented to demonstrate that optimizing the eigenvectors yields a better performing controller in comparison with one designed using mere eigenvalue relocation.

Transient rotor angle stability assessment and oscillatory rotor angle stability assessment subsequent to a contingency are integral components of dynamic security assessment (DSA) in power systems. This study proposes a hybrid algorithm to determine whether the post-fault power system is secure due to both transient rotor angle stability and oscillatory rotor angle stability subsequent to a set of known contingencies. The hybrid algorithm first uses a new security measure developed based on the concept of Lyapunov exponents (LEs) to determine the transient security of the post-fault power system. Later, the transient secure power swing curves are analysed using an improved Prony algorithm which extracts the dominant oscillatory modes and estimates their damping ratios. The damping ratio is a security measure about the oscillatory security of the post-fault power system subsequent to the contingency. The suitability of the proposed hybrid algorithm for DSA in power systems is illustrated using different contingencies of a 16-generator 68-bus test system and a 50-generator 470-bus test system. The accuracy of the stability conclusions and the acceptable computational burden indicate that the proposed hybrid algorithm is suitable for real-time security assessment with respect to both transient rotor angle stability and oscillatory rotor angle stability under multiple contingencies of the power system.

This paper summarizes the work done by the Task Force on Assessing the Need to Include Higher Order Terms for Small-Signal (Modal) Analysis. This Task Force was created by the Power System Dynamic Performance Committee to investigate the need to include higher order terms for small signal (modal) analysis. The focus of the work reported here is on establishing and documenting the practical significance of these terms in stability analysis using the method of Normal Forms. Special emphasis was placed on determining and describing conditions when higher order terms need to be included to accurately describe modal interactions. Test cases were developed on a standard test system to demonstrate the application of appropriate indices to detect the occurrence of nonlinear interaction and hence the need for higher order terms in stability analyzes. The use of the higher order terms in the site selection for a damping controller is also documented.

This paper deals with modelling induction motor loads for voltage stability analysis. A simple first order induction motor load model and a detailed third order induction motor load model suitable for this purpose are derived in terms of real power, reactive power and slip. It is shown analytically that the generic dynamic load models (GDLM) proposed in the literature, in their present form, are incapable of capturing induction motor characteristics. The generic dynamic load model is modified to capture the dynamics represented by the proposed induction motor load models. The appropriateness of the proposed dynamic load models in analysing the transient and steady state stabilities of induction motor loads are evaluated. It is shown that the first or third order induction motor models can be used for studying the power system voltage stability, with different degrees of accuracy.

This paper presents a case where the design of a Power System Stabilizer (PSS) to achieve desired damping using local speed feedback signals is difficult using the conventional design technique. It is shown that synchrophasor based two input power system stabilizer can be designed without much difficulty to achieve the desired damping. Eigenanalysis is performed on the reduced equivalent of New England New York power system. One controller location was found as the best location to improve damping of three inter-area modes. Residue analysis reveals the presence of a remote signal which has better sensitivity to the same controller location. The procedure of designing a two input PSS that uses a local signal and a remote signal is presented and it is shown that the required performance is achieved.

This paper discusses the real time digital simulation of a Static VAr Compensator (SVC) with fuzzy logic based supervisory control to damp the oscillations seen in the voltage after disturbances. The main controller is a traditional PI-controller and the auxiliary control path is made using fuzzy logic controller to provide the damping action. Therefore, the resultant is a non-linear controller, which performs better than the linear PI-controller. The controller performance is tested by connecting the SVC to a multi-machine power system, which is modeled in RSCAD software. The Real Time Digital Simulator (RTDS) is used to simulate the test system and the results are presented to show the improved performance of the proposed non-linear controller.

The paper presents a novel FACTS concept to improve the dynamic stability of an ac power system. The concept of parallel ac/dc transmission between two ac systems has been exploited in the scheme presented, using one ac line for both the ac and the dc transmission. A small unit of power is extracted from the system, converted to dc and injected into the ac line through the transformer, neutrals at the two ends to enhance the dynamic stability. The objective of the paper is to introduce the new concept and prove its feasibility. To demonstrate the validity of the proposed method, computer simulated dynamic responses of an ac power system, with and without the controlled dc injection are presented. It has been shown that by using about 2% of ac power transfer, as modulated dc power, substantial system of damping could be achieved.

Design of a fuzzy logic controller needs qualitative knowledge about the system under consideration. This knowledge is usually obtained from experienced human controllers, or using analytical/heuristical techniques. However, with large/complex interconnected power systems, it is extremely difficult to obtain the necessary knowledge from human controllers or using conventional analytical/heuristical techniques. An approach to ascertain the relationships among variables to generate fuzzy rules is presented in this paper. The proposed method is based on system response to pulse input signals applied at appropriate instances. Use of this approach, along with sequential decentralised control design techniques for developing DC current and generator excitation modulation controllers to improve damping of oscillations in an AC-DC interconnected power systems, is presented in this paper. Simulation results reveal the successful application of the proposed rule base derivation approach along with sequential decentralised control techniques to design fuzzy logic modulation controllers for damping improvement of power systems.

This paper presents a fuzzy logic controller for improving the frequency regulation of the rectifier side AC system of an HVDC scheme interconnecting two power systems. The controller coordinates the modulation of, the current in the DC scheme and the generator excitation of the rectifier side AC system, in response to rectifier side AC system frequency deviation. The fuzzy logic controller is designed without using any precise system model. Only the qualitative knowledge about the system is used in designing the controller. An iterative technique using steepest descent gradient search method is proposed in this paper for further tuning of the output gains of the controller to optimise a chosen objective function. Simulation results reveal that, a fuzzy logic controller can be successfully implemented to realise significant improvements in frequency regulation by coordinating the modulation of the DC current and generator excitation of the rectifier side AC system.

This paper proposes a novel method to estimate Control Performance Standard 1 (CPS1) using the probability distribution of area load change. The proposed method predicts an estimation of the CPS1 value for the future, which could be used in deciding operating strategies to achieve a target CPS1 value. NERC standards on frequency control performance define two indices known as Control Performance Standards 1 and 2 (CPS1 and CPS2). This paper focuses on CPS1, which is used to evaluate control area performance in normal interconnected power system operation. The most straightforward method of estimating CPS1 is to perform a time domain simulation provided that the area load forecast is available. However, if only the probability distribution of load change is available, then a random load curve must be generated to use in time domain simulation. This paper proposes a simple technique to estimate CPS1 directly from the probability distribution of load change without performing a time domain simulation which significantly reduces computing time. Hence predictive evaluation of CPS1 value is a novel concept which could be very useful in practice. A two-area test system is used to demonstrate the accuracy of the proposed method against the time domain simulation method.

A novel method for the design of power system damping controllers is proposed in this paper. The problem of selecting the controller parameters is formulated as a nonlinear optimization problem and the simulated annealing algorithm is used to solve it. By using this method, design criteria for all the controllers can be considered simultaneously. The proposed method can also be used to design controllers which are robust for a given set of operating conditions.

This paper studies the application of controlled series compensator (CSC) to damp power swings in multi-machine power systems. For the design of CSC damping controllers, a necessary step is the derivation of the linear state equation for the system. In order to consider the dynamics of the CSC, it is important to present the change in the CSC reactance as one of the state variables. In this case, unlike the traditional network representation, the network admittance matrix is no longer a constant matrix. Under this situation, the conventional linearization method for obtaining the linear state equation for the system must be modified. In this paper, a linear dynamic model for a multi-machine power system equipped with controlled series compensators (CSCs) is derived. Based on this linear dynamic model, a state feedback controller is designed for CSC control. The feedback control gains are obtained by using the pole placement technique. Given that CSCs are to be installed in a meshed system, the optimum location for installing CSCs is determined by analyzing the mode controllability. The effectiveness of this controller for damping the oscillations caused by power system disturbances is verified by simulation studies.

This paper demonstrates that wind farms connected to a grid through a series compensated transmission line may exhibit sub-synchronous oscillations. It is shown that the flux in the stator winding and the currents in the transmission line are the major participants of this mode. Dynamic Phasors are used to model the small signal model of the transmission network so that the network is accurately represented at sub-synchronous frequencies. An SVC is used to introduce damping to this oscillation mode, with line current as the feedback signal. The application is demonstrated for a large practical power system.

The paper first shows that the transient stability status of a power system following a large disturbance such as a fault can be early predicted based on the measured post-fault values of the generator voltages, speeds, or rotor angles. Synchronously sampled values provided by phasor measurement units (PMUs) of the generator voltages, frequencies, or rotor angles collected immediately after clearing a fault are used as inputs to a support vector machines (SVM) classifier which predicts the transient stability status. Studies with the New England 39-bus test system and the Venezuelan power network indicated that faster and more accurate predictions can be made by using the post-fault recovery voltage magnitude measurements as inputs. The accuracy and robustness of the transient stability prediction algorithm with the voltage magnitude measurements was extensively tested under both balanced and unbalanced fault conditions, as well as under different operating conditions, presence of measurement errors, voltage sensitive loads, and changes in the network topology. During the various tests carried out using the New England 39-bus test system, the proposed algorithm could always predict when the power system is approaching a transient instability with over 95% success rate.

This paper presents a novel technique for predicting transient stability status of a power system following a large disturbance. The prediction is based on the synchronously measured samples of the fundamental frequency voltage magnitudes at each generation station. The voltage samples taken immediately after clearing the faults are input to a support vector machine classifier to identify the transient stability condition. The classifier is trained using examples of the post-fault recovery voltage measurements (inputs) and the corresponding stability status (output) determined using a power angle-based stability index. Studies with the New England 39-bus system indicate that the proposed algorithm can correctly recognize when the power system is approaching to the transient instability.

This paper introduces the use of regression analysis in the study of small signal stability in large interconnected power systems. Results demonstrate the usefulness of this approach in better understanding the nature of dominant electromechanical modes of oscillation and in accurately predicting the damping on these modes. The usefulness of this approach in identifying strong correlations between system damping and distinct measurable and adjustable power system quantities such as generator output, line flows, bus voltages and bus angles, is presented. Results suggest that this approach may be useful in optimizing the location of traditional power system on-line recording devices, such as Dynamic Swing Recorders (DSRs) as well as real time monitoring devices such as Phasor Measurement Units (PMUs). Sensitivity studies show that power system information obtained may be useful in providing an additional tool to help system operators optimize the dispatch of generating resources. It would also be useful in providing more realistic feedback from the power system and aid in the decision making regarding dynamic stability and its effect on appropriate system topology, loading levels and allowable transfer levels, in real time.

Competitive electricity markets use marginal prices to settle the transactions with generator owners and consumers. This results in charging the consumers more than the average cost of production of electricity due to the nonlinear relationship between the losses and power transmission. This difference in revenue collection, referred to as the network rental in this paper, is further increased if the dispatch is constrained due to any operating limits such as power flow limits. There are two main components that constitute the network rental, loss rental and the constraint rental. This paper presents a theoretical analysis based on Karush-Kuhn-Tucker (KKT) optimality conditions to calculate these different rental components. In this way each rental component can be quantitatively analyzed, which in turn can be used to get a better insight of the operation of the electricity market. Some case studies on the IEEE 30 bus system is presented to demonstrate the application of the proposed method.

A power system is secure against a given contingency if it operates within acceptable operating limits before and after the occurrence of the contingency. In practice, it is not possible to secure a power system against all possible contingencies. Therefore, only the most critical contingencies (imminent disturbances) are considered. The paper gives an overview of power system security and different ways of loosing stability. Then, a statistical learning based technique for determining the boundary of the secure operating region in terms of pre-contingent state of the power system is reviewed. The paper discusses possible applications of the boundary and some issues related to practical application of this method.

This paper proposes the inclusion of transient stability constraints in generation dispatch algorithms used in electricity markets to ensure dynamic security. The proposed security constraint is derived by applying a non-linear surface fitting technique to a database generated off-line. The technique used has two key features that enables the derivation of an accurate transient stability constraint with a relatively short computing time compared to other comparable methods. One feature is that it uses a linear estimation technique to estimate a non-linear function by means of a non-linear transformation. The second important feature is that it employs an implicit technique to gain significant reduction in computing burden. The potential of the proposed method is demonstrated using the New England 39 bus system and a larger power system with 470 buses. The security constraint derived for the New England 39 bus system is used in an optimal power flow (OPF) program for market clearance. The locational marginal prices (LMP) obtained from the OPF are further analyzed to determine the component of LMP due to dynamic security

This Paper presents a model which facilitates the allocation of spinning reserve in a power network which includes a large HVDC infeed. The basic area control model of the power system is developed and subsequently fine-tuned using a non-linear optimization procedure. The model is then used to evaluate the frequency control performance in the face of a known load forecast considering NERC performance standards.

This paper proposes the inclusion of transient stability constraints in generation dispatch algorithms used in electricity markets to ensure dynamic security. The proposed security constraint is derived by applying a non-linear surface fitting technique to a database generated off-line. The technique used has two key features that enables very fast computation of an accurate transient stability constraint. One feature is that it uses a linear estimation technique to estimate a non-linear function by means of a non-linear transformation. The second important feature is that it employs an implicit technique to gain significant reduction in computing burden. The security constraints derived for each credible contingency can be used in an optimal power flow program for market clearance. The effectiveness and efficiency of the proposed method is demonstrated using the New England 39 bus system and a larger power system with 470 buses.

In a restructured power system, locational marginal prices (LMP) are important pricing signals to the participants. LMP at a given node of a power system is the incremental cost of supplying power at that node. In a lossless system with no active constraints, the LMPs at all the nodes are equal. However, due to the losses in the power system, the LMPs at different nodes is different. Any operating constraint such as line flow limits also contribute to the LMP at a node. This paper investigates the effect of a dynamic security constraint on the LMPs. The transient stability margin expressed as a function of nodal voltages and phase angles, is used as a constraint in an optimal power flow (OPF) program to determine the LMPs at all the nodes of a power system. The Lagrange multiplier associated with the transient stability constraint gives the marginal cost of the transient stability constraint. A case study on the New England 39 bus system is presented to demonstrate the effect of the dynamic security constraint on the LMPs. In a nodal pricing scheme, any active constraint results in an additional revenue to the system operator. This revenue, known as the network rental, is also investigated in the paper.

Manitoba Hydro has dynamic swing recorders (DRSs) located on tie-lines between the Manitoba power system and neighbouring Canadian provinces, as well as the USA. These DSRs are triggered by major system contingencies and record post contingency data. This paper shows that off-line analysis of this data can provide useful information on the behaviour of dominant electromechanical modes of oscillation in the system which can be correlated to system loading and topology. Results obtained are compared to off-line eigenvalue analysis using available small signal analysis tools. Results suggest that with the development of suitable on-line measurement and analysis techniques, this information may be used to correlate system behaviour with particular events, provide useful information to help system operators regarding appropriate system topology, allowable transfer levels and in general provide more insight regarding the state of the system.

The work reported in this paper highlights differences and similarities between conventional linear analysis and the method of normal forms. The paper is focused on the effect that second order modal interactions have in the dynamic performance of a power system and identifies dynamic characteristics not captured by conventional linear analysis.

This work describes the simulation of the effects of GIC (Geomagnetically Induced Currents) in a power system using a new transformer model. The simulation studies demonstrate that it is important to accurately model the remanence effects in the core of the power transformer.

In normal form (NF) analysis, the nonlinear dynamical system being analyzed is modeled with nonlinearities. If the second order NF is used in the analysis, the nonlinearities only up to second order are modeled. Due to the presence of nonlinearities in the model, the results of second order NF analysis is dependent in the initial conditions [C.-M. Lin et al., May 1996] [S. Zhu et al., November 2001]. If the state of the power system with respect to the stable equilibrium point (SEP), /spl Delta/X/spl Delta//sub 0/, at the instant of removal of the fault is used as an initial condition, then NF analysis may fail to give correct results. It is shown in this paper that the initial condition must be chosen such that the two main assumptions made in NF analysis are met. If the system being studied is stable, the post fault system will eventually reach the SEP. We propose to select an initial condition at an instant subsequent to clearing a fault, to achieve more reliable results from the NF analysis. The time domain simulations are presented to support the analysis.

This paper demonstrates how the simulated annealing algorithm and genetic algorithms can be used as means to solve the power system unit commitment problem. In addition, this paper presents parallel approaches to speed up the computational requirement of the simulated annealing algorithm. The algorithms were tested with two different problems. The results have demonstrated the success of the algorithms in consistently reaching good solutions.