A synchronous machine model for unbalanced analyses

A new simultaneous solution method using module bi-directional iteration is proposed for power system transient stability simulation. In this method, power network is partitioned into a tree hierarchy; computation modules are established for decomposed power networks and various power system components respectively. Through representing every computation module by a computation node, a computation tree is constructed by connecting the nodes together according to their electrical relations in power systems. A tree-traversing procedure called forward reduction and backward evaluation is performed to calculate correction factors of the variables in Newton iterations. This high-efficiency simulation method is feasible to be applied in parallel computation for large interconnected systems. Simulation tests are conducted on the New England 10-generator test power system and the North China-Northeast interconnected system, and the results are compared with those of the commercial software BPA to validate the effectiveness and correctness of this method.

Preface. Chapter 1: INTRODUCTION. 1.1 A Brief History of Electric Power Systems. 1.2 The Structure of the Power System. 1.3 Outline of the Text. Chapter 2: BASICS OF ELECTRIC ENERGY SYSTEM THEORY. 2.1 Introduction. 2.2 Concepts of Power in Alternating Current Systems. 2.3 Three-Phase Systems. 2.4 The Per Unit System. 2.5 Electromagnetism and Electromechanical Energy Conversion. 2.6 Permeability and Magnetic Field Intensity. 2.7 Flux Linkages, Induced Voltages, Inductance, and Energy. 2.8 Hysteresis Loop. 2.9 Eddy Current and Core Losses. 2.10 Energy Flow Approach. 2.11 Multiply Excited Systems. 2.12 Doubly Excited Systems. 2.13 Salient-Pole Machines. 2.14 Round or Smooth Air-Gap Machines. 2.15 Machine-Type Classification. 2.16 P-Pole Machines. 2.17 Power System Representation. Problems. Chapter 3: POWER GENERATION AND THE SYNCHRONOUS MACHINE. 3.1 Introduction. 3.2 The Synchronous Machine: Preliminaries. 3.3 Synchronous Machine Fields. 3.4 A Simple Equivalent Circuit. 3.5 Principal Steady-State Characteristics. 3.6 Power-Angle Characteristics and the Infinite Bus Concept. 3.7 Accounting for Saliency. 3.8 Salient-Pole Machine Power Angle Characteristics. Problems. Chapter 4: THE TRANSFORMER. 4.1 Introduction. 4.2 General Theory of Transformer Operation. 4.3 Transformer Connections. Problems. Chapter 5: ELECTRIC POWER TRANSMISSION. 5.1 Introduction. 5.2 Electric Transmission Line Parameters. 5.3 Line Inductance. 5.4 Line Capacitance. 5.5 Two-Port Networks. 5.6 Transmission Line Models. Problems. Chapter 6: INDUCTION AND FRACTIONAL HORSEPOWER MOTORS. 6.1 Introduction. 6.2 Three-Phase Induction Motors. 6.3 Torque Relations. 6.4 Classification of Induction Motors. 6.5 Rotating Magnetic Fields in Single-Phase Induction Motors. 6.6 Equivalent Circuits for Single-Phase Induction Motors. 6.7 Power and Torque Relations. 6.8 Starting Single-Phase Induction Motors. 6.9 Single-Phase Induction Motor Types. Problems. Chapter 7: FAULTS AND PROTECTION OF ELECTRIC ENERGY SYSTEMS. 7.1 Introduction. 7.2 Transients during a Balanced Fault. 7.3 The Method of Symmetrical Components. 7.4 Sequence Networks. 7.5 Line-to-Ground Fault. 7.6 Double Line-to-Ground Fault. 7.7 Line-to-Line Fault. 7.8 The Balanced Three-Phase Fault. 7.9 System Protection, An Introduction. 7.10 Protective Relays. 7.11 Transformer Protection. 7.12 Transmission Line Protection. 7.13 Impedance-Based Protection Principles. 7.14 Computer Relaying. Problems. Chapter 8: THE ENERGY CONTROL CENTER. 8.1 Introduction 8.2 Overview of EMS Functions. 8.3 Power Flow Control 8.4 Power Flow 8.5 Stability Considerations 8.6 Power System State Estimation 8.7 Power System Security 8.8 Contingency Analysis 8.9 Optimal Preventive and Corrective Actions 8.10 Dynamic Security Analysis Chapter 9: THE PRESENT AND FUTURE OF ELECTRIC ENERGY SYSTEMS. 9.1 Introduction. 9.2 Challenges Facing the System. 9.3 Blackouts and their Impact. 9.4 Mitigating and Coping. REFERENCES. INDEX.

A fully parallel nested bordered block diagonal form (BBDF) method for power system transient stability simulations is proposed in this paper. The fully parallel nested BBDF (FNBBDF) method is developed by combining the fully parallel BBDF method with the nested BBDF method based on subnet-core mapping and mixed programming of MPI and OpenMP. The FNBBDF method is compared with existing methods from the perspectives of computational burden, parallel overhead, and subnet-core mapping. Detailed tests of the FNBBDF method are carried out in the 2383wp system and two practical power systems (13490-node and 24886-node). The test results prove the efficiency of the proposed method. The FNBBDF method can increase the speedup ratio to more than 21x with 64 CPU cores in the 24886-node test power system.

The faults in a power system may be of various nature and they may affect the stability of the power system by causing outage of the line, there by overloading other connected lines and also causing cascading effect in the system. In order to access the nature of fault and analyze the impact of the same in a power system, fault analysis is required to be carried out as the same will be useful for the system operation and to take quick decisions in securing the system. In this paper we discuss the various types of faults in EHV system that may occur in line or substation. These faults are identified by Numerical relays which use IEDs [Intelligent Electronic Device]. The faults identified includes symmetrical and unsymmetrical faults in power system. Further in this project, we have taken into consideration the theoretical and practical study of the fault analysis through Numerical relays. In case of occurrence of Transient faults, Auto re-closure works with dead time of 1 sec. Current, voltage, Breaker status (open, close) are graphically represented by Disturbance Recorder. Events are recorded by Event logger. The above mentioned project for faults and analysis of faults in line or substation were carried out at Power grid Corporation Limited, 400 / 230kv Sub-Station Shoolagiri.

There have been quite a few attempts to compute synchronous generator parameters based on voltage and current synchrophasors taken under power system transients. However, we have not seen any publications with thorough analysis as to how soon the phasor measurement unit reacts to disturbance conditions, which components of the transient are filtered out and which are passed through, as well as what the total vector error is. The goal of this research is to determine all of these characteristics of a phasor measurement unit when playing back transient oscillograms for a stator short circuit obtained through mathematical modeling. The transient oscillograms have been derived via both a full Park-Gorev system of flux linkage equations as well as the MATLAB/Simulink Synchronous Machine block. Physical modeling was then conducted via a real-time digital simulator (RTDS) along with a dedicated phasor measurement unit ENIP-2 (PMU), and the stator current phasors were recorded. Our analysis has shown that both RTDS and ENIP-2 (PMU) almost entirely filter out the exponentially decaying DC component of the fault current while closely following the periodical signal envelope. The total vector error has been estimated to become below 1–2 % after around 0,02–0,03 s into the fault when selecting the “P” class filters according to IEEE C37.118. We have come to a conclusion that synchrophasor measurements under power system disturbances could be utilized for estimating the synchronous, transient, and subtransient generator parameters. The selected synchronous machine model in the form of flux linkage equations is correct, as the obtained transient oscillograms are exactly the same as those produced by Simulink. “P” class phasor measurements can be recommended for representing transients in the stator circuit of a synchronous generator. The results of this investigation are meant to be employed for synchronous machine parameter estimation based on phasors sourced from RTDS and, hopefully, from phasor measurement units installed at power plants.

With the method of instantaneous symmetrical components, positive, negative and zero sequence components can be gained. The traditional instantaneous symmetrical components are usually implemented under dq0 synchronization reference frame on condition that low-pass filter is adopted in, which causes aggravated dynamic performance. To solve this problem, this paper presents a novel algorithm of instantaneous symmetrical components, and gives its corresponding equations and results. The principal of proposed algorithm is based on ab0 static axis. By trigonometric function transform method, the positive, negative and zero sequence components are deduced as a sum of sine and cosine, both of them with a multiplier factor. According to this analysis, three-phase sequence components can be solved out by using of variable step-size LMS adaptive filter. The dynamic and accuracy performance is testified by the results of simulation in unsymmetrical faults and short circuit faults, which prove this algorithm is suitable for unsymmetrical faults in power system.

This paper proposes a new approach for power system transient stability simulation, which is based on a semianalytical solution (SAS) of power system differential-algebraic equations. In this paper, an SAS is derived using the Adomian decomposition method as a closed-form explicit function of symbolic variables such as time, the initial state and other variables on system conditions, and hence it can directly give a power system's dynamic trajectory being accurate for a certain time window. Unlike a traditional numerical integration based simulation approach, the proposed new approach offline derives an SAS and online evaluates the SAS by plugging in values of symbolic variables for a series of time windows making up the desired simulation period. This paper further studies the maximum length of the time window for an SAS being accurate and proposes a divergence indicator for simulation using adaptive time windows. Implementation of this new approach on parallel computers is also studied. The new approach is validated through contingency simulation of the IEEE 10-generator 39-bus system with detailed generator models.

There are some factors that render a power system network unbalanced: UHV transmission lines in which three-phase transmission lines are not transposed, an unbalanced transformer, unbalanced load as well as sustained unbalanced faults. On the other hand, the number of variable-speed generators used in pumping-up power stations has recently been increasing in Japan. This paper presents a new means of calculating unbalanced power flow of a power system which contains variable-speed pumping-up generators. This new technique is based on the phase coordinate method, because a power system which has elements of unsymmetrical impedance can easily be analyzed by using it. In this paper, phase coordinate models of the variable-speed generator and its secondary exciting circuit, composed of a GTO converter/inverter, are analyzed first. Procedures of power flow calculation of unbalanced power systems follow. © 2000 Scripta Technica, Electr Eng Jpn, 134(3): 34–43, 2001

Electrical faults in the power system refer to a variety of abnormalities in the power equipment, and these faults may lead to equipment damage or even cause dangerous events such as fires and explosions, which pose a serious threat to people's lives and property. Therefore, it is very important to find and deal with these faults in time. In this paper, based on the electrical fault dataset of power system, SVM, decision tree, KNN and random forest model are used to detect electrical faults. After the confusion matrix results are analyzed, most of the predictions of the four models are correct, and only a few instances that should not be predicted as electrical faults are predicted as electrical faults. All the four machine learning models achieved more than 99% accuracy in detecting electrical faults in the power system and were able to detect electrical faults very accurately. Among them, the SVM model has the highest prediction accuracy of 99.6%, followed by the KNN model prediction accuracy of 99.5%. In summary, this paper adopts machine learning method to detect electrical faults in power systems, and achieves better results in the experimental results. This method can help power system supervisors find and deal with faults in time, and improve the safety and stability of the power system. In the future, we can further study how to optimize the model to improve the detection accuracy and apply it in practical production.

This efficient application of any numerical integration method depends on accurate estimation of the local truncation error to govern step size control. In this paper, the local truncation error of the multirate method using the forward Euler integration is derived leading to the calculation of the optimal step ratio. The techniques of applying multirate method in power systems are discussed. By implementing the multirate method in a practical power system example, the multirate strategies are proved to be efficient compared with traditional simulation methods.

Mixed three-phase and six-phase power system analysis using symmetrical components method

When solving network algebraic equations during power system transient stability simulations, the nonzero elements in the independent vector and the elements needed in the solution vector are determined by the location of source nodes. Different kinds of source nodes will have a different influence on the solution process of the network equations. According to these features of source nodes, sparsity techniques, more specifically, the node ordering algorithm and sparse vector method, are improved in this paper. A new heuristic ordering algorithm is proposed to enhance the efficiency of the sparse vector method by reducing the number of nodes in the factorization path set of source nodes while maintaining the sparsity of the factorized matrix. A multipath sparse vector method is proposed to avoid the unnecessary computation in the iterative solution process of the network equations, whereby the idea of the method is to form different paths for different types of source nodes. Different paths are used to solve different elements in the solution vector. The correctness and effectiveness of these improvements is proven by the simulation results of three practical power systems (up to 13 490 nodes) and six IEEE examples (up to 162 nodes).

The analysis and calculation of short-circuit fault of power system is an important task for the programming, designing and running of power system. With the rapid growth of power system, the traditional ways and means can not satisfy the needs of power system, so it is necessary to use computer to simulate and calculate. Firstly this paper analyzes all kinds of short-circuit fault of a single source power system and then this paper simulates this system, sets the system parameters and fault types, finally calculates the fault current and voltage by MATLAB and the results of the simulation verifies the correctness of analysis above. It avoids the commonly programmable language to set a complex model ,making the fault simulation experiment and data analysis fast and accurate.

High temperature superconducting (HTS) power cables are expected to be used in the future in electric ships that will have integrated power and energy systems (IPES). There have been a few studies on understanding electrical faults in power systems consisting of HTS cables; however, there are no comprehensive studies on the response of HTS cables for various types of electrical faults. We have recently initiated a research project on understanding various electrical faults in shipboard medium voltage direct current (MVDC) power systems and the duration of the fault, maximum voltage, and maximum current that the HTS cables will encounter during the fault. This paper presents investigations on the potential cable architectures being developed for MVDC power systems, and the type of faults that HTS cables will encounter in such systems. The paper will assess the relative merits of these architectures in terms of their suitability for accommodating the limitations of cryogenically cooled HTS cables and offer design suggestions for resilient power systems. Electrical and cryogenic thermal models of HTS cables that are suitable for assessing the response of HTS cables for electrical faults, as well as HTS cable designs that can endure electrical faults without catastrophic damage will also be discussed.

Wind energy is becoming a major source of generation in many countries because of its zero fuel cost and no air pollution. Due to the integration of large-scale wind power in conventional grids, synchronous generators are being economically replaced. Modern wind turbine generators (WTGs) are based on power electronic interfaces. Hence, unlike synchronous generators, they do not usually provide inertia and governor response. Therefore, from a power system security point of view, wind penetration can be limited by frequency response criteria. Up to now, several methodologies have been proposed to estimate the maximum wind penetration level. However, none of them suggest how a system operator could be immediately informed about a secured wind penetration limit as soon as a generation profile is known. Therefore, a tool to estimate the maximum wind penetration level by maintaining an adequate frequency response is proposed in this thesis. The proposed tool is able to instantly provide the highest margin of wind power that could be dispatched at a particular load condition without violating frequency response constraints. In some power systems, the combined generation capacity of wind and distributed photovoltaic (PV) sources is close to reaching the level of average demands (e.g. South Australia). Under high availability of wind and PV, a few synchronous machines may be required to be committed for frequency regulation and hence the system can be viewed as a low inertia grid. Such a grid could be potentially at risk of experiencing an excessive rate of change of frequency (ROCOF) after a contingency. A high ROCOF may initiate tripping of other synchronous generators. As a result, network frequency response may become more vulnerable and the system may be subject to significant under frequency load shedding (UFLS) or even at risk of a blackout. Furthermore, some existing distributed PV units may have a default under frequency protection setting, which is higher than the UFLS threshold. Hence, a contingency may cause a subsequent trip of those PV units. It may result in an unacceptable low frequency, triggering further load shedding. To explore the above issues, the effects of cascading contingencies triggered by high ROCOF and PV tripping on the frequency response of a low inertia grid are investigated in this thesis. Remedial measures using synchronous condenser and WTG frequency support to prevent the cascading contingencies are also suggested. Any mismatch between load and generation is intended to be balanced by contingency reserve, which is also known as contingency Frequency Control Ancillary Services (FCAS) requirement. Load frequency relief (LFR), which represents the effect of frequency dependent loads on power system frequency excursion, is crucial for correctly evaluating contingency FCAS requirement during a generation dispatch to ensure an adequate frequency response. Conventionally, the LFR is considered as a fixed quantity during the estimation of frequency response and FCAS requirement. However, recent experience in the Australian power system suggests that such an assumption may lead to an inaccurate outcome. To explore the above issue, the LFR is investigated based on field measurement data. Data were captured from different locations in the Southern states of Australia. An approach is developed to identify the predominating factors affecting the LFR. A technique is then proposed to appropriately determine the LFR and contingency FCAS requirement at any operating conditions. Along with frequency response, short-circuit performance is another vital index regarding power system security. Modern WTGs have limited fault current contributions, which may cause unacceptable short-circuit ratios at the grid connection point of those wind power plants. Traditionally, frequency response and short-circuit performance are individually improved. However, both of them are simultaneously affected by high wind penetration. Hence, a common approach to concurrently enhance both indices is essential. Therefore, an idea of operating some of the retired synchronous generators in the synchronous condenser mode, which is termed as ‘post-retirement scheme’, is introduced in this thesis. Such a second use of the retired synchronous generators can jointly improve frequency response and short-circuit strength during high wind penetration. A methodology is proposed to determine when and how much post-retirement scheme should be deployed for ensuring adequate security performances in a wind dominated power system.