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To ensure successful islanding of microgrids after a fault has occurred, the transient stability should be analyzed under a set of expected operating conditions during the design and operation of microgrids. Transient stability analysis is conventionally performed with time-domain analysis which is computationally expensive and does not quantify the stability margin. Energy-based methodologies can determine the stability margin, however existing methodologies require significant simplifications to be applied to the microgrid model. The energy-based stability analysis methodology proposed in this paper enables the analysis of high-dimension nonlinear microgrid systems and quantification of the stability margin within reasonable time. The performance of the methodology is validated by analyzing a case study microgrid and comparing the results to time-domain analysis and to a state-of-the-art methodology proposed in the literature. The results indicate that the proposed methodology has a significantly lower computational burden and similar accuracy compared to existing energy-based methodologies. The methodology is able to improve the probability of stable islanding of the case study microgrid from 74% up to 94% when only optimizing the design, and up to 100% when optimizing design and control actions.

This paper presents the modular-multilevel-converter (MMC) control interoperability (IOP) and interaction within the High Voltage Direct Current (HVDC)-based power system. IOP is a crucial issue in the large-scale HVDC grid with different suppliers. To accommodate future multi-vendor HVDC grids developments, this article comprehensively investigates the MMC control IOP issue. Firstly, the most commonly adopted proportional-integral (PI) control and other non-linear controllers, e.g., model predictive control (MPC), back-stepping control (BSC), and sliding mode control (SMC), are constructed for MMC. Then, the IOP simulations are carried out in a multi-terminal direct current (MTDC) system in real-time digital simulator (RTDS) environment. The most frequent transients of the practical projects, e.g., power flow changing, wind speed changing, and DC/AC grid faults, are simulated with eight different scenarios. Each scenario presents different control capabilities in maintaining system stability, more precisely, the scenarios with non-linear controllers show faster settling time and fewer DC voltage and power variations. Controller switchings are also achieved without bringing large system oscillations. This paper provides the optimal allocation strategy of controllers to cope with system transients.

This paper introduces the concept of the operating region of a virtual synchronous generator (VSG). The main objective of the operating region is to help take a decision on choosing proper VSG parameters. A VSG based on a diesel generator (Genset) model was used as the study case. The theoretical analysis examined the impact of relevant genset-based VSG parameters, such as droop factor, ${m_{\mathrm {dr}}}$ , inertia, $J$ , and damping, $D$ , on the output electrical frequency. The main result of this analysis showed that it is possible to define inertia-damping surfaces which are parameterized upon different values of the droop factor. The operating region of the VSG is then defined as the locus of the triples ( ${m_{\mathrm {dr}}},\,J,\,D$ ) where the frequency transient response satisfies certain specifications in terms of peak frequency, peak time and rate of change. Experimental results showed that the VSG achieved a satisfactory performance for different values of speed droop during a transient and also in steady-state, validating the model of the genset. In comparison with simulation results, the measured peak frequencies deviated with a mean absolute error of 0.2% and the steady-state frequencies with a mean absolute error of 0.12%, validating the concept of the operating region.

Fast-front transients play an important role in the insulation design of any power system. When a stroke hits the shield wire or the tower of high-voltage overhead power lines, flashover may occur either along the span or across tower insulators, depending on the relevant voltages and insulation strength. As a result, backflashover may take place from the tower structure to the phase conductor whenever a huge impulse current flows along the tower towards considerably high footing impedances. For these reasons, tower modeling for transients studies is an important step in the insulation design, and also for lower voltage applications, where indirect lightning effects may play a predominant role. However, after decades of research on tower modeling, starting from the 1930s with the first model proposed by Jordan, no consensus has been reached neither on a widely accepted tower model nor on the quantitative effect of the tower models on insulation design. Moreover, the fundamental mechanisms at the base of the transient response of towers and the definition of some fundamental parameters have not been totally clarified yet. The aim of this review is to present the available tower models developed through the years in the power community, focussing mainly on lumped/distributed circuit models, and to help the reader to obtain a deeper understanding of them.

This study proposes a dual-loop supplementary frequency control (SFC) scheme for back-to-back voltage source converter high-voltage DC (BTB-VSC-HVDC) interconnecting asynchronous AC grids, to provide frequency support for each other after a large disturbance. The proposed dual-loop SFC consists of the frequency-active power (f–P) loop and the frequency-reactive power (f–Q) loop. The former deployed on the P-loop of VSC-HVDC can provide frequency support for the disturbed grid during the primary frequency regulation and improve the steady-state characteristics of the frequency response, while the latter attached to the Q-loop of VSC-HVDC supports virtual inertia to ameliorate the transient characteristics of the frequency response. Simulation studies are conducted based on the equivalently simplified model of Southwest Power Grid and Hubei Power Grid interconnected by Chongqing-Hubei BTB-VSC-HVDC. Simulation results show that the proposed SFC scheme can effectively improve the transient and steady-state characteristics of the system frequency response under a wide range of operating condition.

In this paper, an accurate parameter identification algorithm is proposed for transient voltage profile calculation of the unknown transmission lines. This method is based on the virtual black-box method and uses single-ended data sampling, where the input data include voltage and current samples obtained by measuring at one end of the line in transient mode. A mathematical formulation is proposed to separate the sampled data and form a virtual black-box system with virtual inputs and outputs. The virtual black-box is designed, such that the system coefficients relating the virtual outputs and inputs are the known functions of transmission line parameters in the real world. The coefficient values are then calculated by employing the recursive least squares estimation method, which minimizes the sum of squared errors of observations. Using this method, transmission line parameters and transient voltage profile are calculated from only one terminal data with no need of measuring devices, data synchronization, and communication devices at both sides. The efficiency of the proposed method is tested and proved through the EMTP simulations.

Battery energy storage system (BESS) services will be of great help when operating power systems at high renewable energy penetrations. This paper demonstrates the requirements for effective frequency and inertia services. Some system operators currently apply scalars to financially reward improved performance. This paper demonstrates a method of validating and improving these scalars by considering the delay time and ramp time of the BESS. The importance of the method used to measure the rate of change of frequency is discussed in the paper. While rate of change of frequency services improve with reduced delivery times, limits are identified where further reductions produce negligible impact. This demonstrates the tangible benefits of a rapid response and that current technology could meet the criteria. A variety of BESS capacities are trialled which demonstrate consistency in performance and the occurrence of diminishing returns.

In this paper we present the dilemma dealing with the choice of speech segment duration and the calculation of speech signal quality in the packet telephone network of Electricity supply industry (ESI). The analyzed signal is packetized by one packet. The characteristic of this network is that disturbances of long duration in power system produce burst packet loss. The longer speech segments increase the packet delay, but decrease the number of lost packets in one burst, and vice versa. Here we present why it is better to choose speech segments of short duration. Also, we suggest the corrected method for the calculation of speech signal quality in packet network under the influence of long duration disturbances. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR32007 and Grant no. TR32051]

According to the actual requirements of the project, when the pole-to-pole fault occurs in the DC system, the fault must be cleared during the capacitor discharge phase, so the requirements of the calculation of the current transient expression at the fault point are made. To solve this problem, this study proposes a dual-port network model with fault flags. First, analyse the equivalent circuit diagram of the tree and ring DC system after fault, and compare it with the dual-port network model. The relationship between the parameters of the original system and the parameters of the proposed model is given. Second, put the relationship expression into the short-circuit current expression of the dual-port network model and obtain the final transient expression for multi-ended systems. Finally, the 3-end tree and ring DC system model are set up on the MATLAB/Simulink software platform. The simulation of the model is verified. The error is below 5%, which proves the reliability of the model.

Traditionally, extra high voltage (EHV) transmission systems consist exclusively of overhead lines (OHL) but in the recent years the utilization of high voltage AC (HVAC) power cables is increasing due to environmental, political and operational aspects. To study the impact of HVAC power cables on temporary overvoltages and slow front transients, a simulation model of the large-scale network is required. Guidelines concerning the modeling detail for the surrounding network need to be established to ensure sufficient accurate results. Existing guidelines for purely OHL transmission networks may not be adequate since the integration of HVAC power cables shift the harmonic impedance of the network to lower frequencies and that can affect the extent of the needed simulation model. Much effort can be saved from obtaining detailed data for an extensive but proper model, but a less detailed model might not describe the network behavior with sufficient accuracy. In this study, simplification options are considered, for which the time to construct and analyze a simulation model can be reduced. The simplification options are compared with the reference model (full detail), and judged based on three indicators for the level of accuracy: frequency and amplitude of the main resonance, and maximum over-voltage. As a result, guidelines on the extent of the simulated network and in which detail the model has to be built are proposed. The inverse approach, i.e. increasing level of detail until simulation results hardly change leads to similar results, but requires equivalent short-circuit networks for the rest of the grid. The method is tested for the Dutch 380 kV grid where an underground cable connection of 10.8 km length is introduced in 2013 and a second connection is planned for 2017.

U ovoj doktorskoj disertaciji je predstavljena je nova metoda za detekciju propada napona, zasnovana na Rekurentnoj neuronskoj mreži i analizi u harmonijskom domenu. Metoda je namenjena za primenu u savremenim distributivnim mrežama koje sadrže obnovljive izvore, i u skladu sa tim je optimizovana i testirana. Pametna metoda postiže izuzetne rezultate u brzini detekcije, sa prosečnim vremenom detekcije manjim od 1 ms, uz izuzetnu pouzdanost (preko 97%). U doktorskoj disertaciji dokazana je i druga hipoteza, a to je da je moguće predvideti dubinu propada algoritmom zasnovanim na harmonijskoj analizi. In this PhD thesis, a novel method for the detection of voltage dips (sags), based on the Recurrent Neural Network and analysis in the frequency domain, is presented. The method is intended for use in the modern distribution grids that contains renewable sources, and accordingly it is optimized and tested. The smart method achieves exceptional results in detection speed, with an average detection time of less than 1 ms and with high reliability (over 97%). In the PhD thesis, another hypothesis is proved, which claims that is possible to predict the depth of dip with algorithm based on the harmonic analysis.

Power systems require a reliable supply and good power quality. The impact of power supply interruptions is well acknowledged and well quantified. However, a system may perform reliably without any interruptions but may have poor power quality. Although poor power quality has cost implications for all actors in the electrical power systems, only some users are aware of its impact. Power system operators are much attuned to the impact of low power quality on their equipment and have the appropriate monitoring systems in place. However, over recent years certain industries have come increasingly vulnerable to negative cost implications of poor power quality arising from changes in their load characteristics and load sensitivities, and therefore increasingly implement power quality monitoring and mitigation solutions. This paper reviews several historical studies which investigate the cost implications of poor power quality on industry. These surveys are largely focused on outages, whilst the impact of poor power quality such as harmonics, short interruptions, voltage dips and swells, and transients is less well studied and understood. This paper examines the difficulties in quantifying the costs of poor power quality, and uses the chi-squared method to determine the consequences for industry of power quality phenomenon using a case study of over 40 manufacturing and data centres in Ireland.

HVDC short-circuit calculation standards will be required to simplify the dimensioning and selection of circuit breakers (CBs) in future HVDC networks. This paper proposes new analytical formulas for the calculation of the ac-side contribution through the blocked half-bridge-based converters during pole-to-ground faults in multiterminal HVDC cable networks. Analytic approximations are derived for the steady-state short-circuit currents and the peak of the transient response for point-to-point HVDC links and extended to multiterminal HVDC cable networks with arbitrary grid topology. The results of the proposed expressions are compared with simulations in PSCAD and provide accurate calculations for the transient peak and steady-state values of the ac-side fault current contribution to the prospective CB current.

Power quality (PQ) phenomena characterizing the voltage and current signals of railway electricity networks differ from those present in transmission and distribution electricity grids. Presently, there are no standardized procedures focused on PQ measurement techniques explicitly for railway applications. This paper evaluates whether the standard power quality measurement algorithms used in monitoring 50 Hz electrical grids are sufficient for an accurate evaluation and classification of PQ parameters of voltage dips, swells and interruptions present in 25 kV AC railways. An algorithm is presented to better characterize different types of interruption, distinguishing between causes due to network configuration or by other factors. For voltage dips and swells it is also shown that a smaller window size (less than 1 cycle) produces a more accurate estimate of the disturbance magnitude and duration. The two methods are verified against recorded signals of pantograph voltage and current. Recommendations are therefore provided for PQ measurement algorithms for AC railways.

Transients from lightning strikes can enter underground cables at overhead line to power cable transitions. Possible overvoltages on these surges at cross-bonding connections of the cable screens are of major concern. A model is developed for modelling overvoltages from transient signal propagation through a combined cross-bonding cable and box. This model is applied to the first Dutch 400 kV cable connection. Such model incorporates model parameters whose values depend on design details of the cross-bonding box. The values for these model parameters are extracted from the measured transmission and reflection signal on steep pulses injected into the actual cross-bonding box configuration. The model combines transmission line description for the cross-bonding cables with mainly inductive behaviour of the cross-bonding box. The obtained results are verified by measurements. The model is applied to investigate overvoltages induced at the cross-bonding cable and box on 1.2/50 µs impulse voltage injection representing a lightning impulse voltage applied to the core conductor of the cross-bonding cable. Furthermore, the effectiveness of surge arresters to reduce overvoltages at the cross-bonding cable screen is demonstrated by simulations with this model in PSCAD.

In this paper, the Wedepohl-Wilcox series, proposed for calculating ground-return impedances of buried cables and electromagnetic transients, are analyzed in detail. The origin of this series goes back to the original integral derived by Pollaczek. To enhance the analysis developed here, a numerical comparison between the series, the direct numerical integration of Pollaczek integral, and a proposed hybrid numerical algorithm is presented in this paper. The later consists on: a) the use of a vector-type efficient algorithm for the converging series for low frequencies, and b) trapezoidal numerical integration for the high frequency range. In addition, and based on the analysis, a criterion for switching between series and direct numerical integration is proposed here.

Microgrids (MGs) represent surely the most challenging topic in electrical engineering, promising the decreasing of carbonization, the totally integration of different renewable sources and a cheap solution for those rural areas where electric distribution is economically unsustainable. The most important feature of a MG is represented by the possibility to work in islanded configuration in order to satisfy its own load without the support of the main grid. Literature is poor of experimental results on islanded MG and the research has focused on theoretical approaches on several topics, such as frequency, voltage stability, modeling, software simulations and energy management systems. The purpose of this article is to provide some experimental results such as power supply, voltage and frequency measurement during islanded operation. This test campaign was performed in the Smart Polygeneration Microgrid, a test tool of University of Genova created for experimental validation for grid-connected and islanded MG operation.

For the study of switching transients in Extra High Voltage (EHV) networks it is common practice to model a relatively small part of the EHV network. The downstream network is either disregarded or modeled as a parallel RC or RL circuit, based on the powerflow, directly at the secondary side of the transmission transformer. In this paper an investigation for the extent and model type of the downstream network (below 380 kV) is performed. A detailed model for an example downstream network is developed. Different simplifications and equivalent models are compared in frequency domain and in time domain, during cable energization. The impact of the lower voltage network on both the maximum overvoltage and the harmonic content during energization is assessed. Moreover, components that are of major importance are identified and proper equivalent models for the downstream network are proposed. Simulation results show that in particular the type of the 150 kV network (underground cable or overhead line) affects greatly both the maximum overvoltage and the harmonic content during energization. On the other hand, the parameters of end customer loads have only minor effect.

HVDC transmission is an integral part of various power system networks. This article presents an Unscented Kalman Filter dynamic state estimator algorithm that considers the presence of HVDC links. The AC - DC power flow analysis, which is implemented as power flow solver for Dynamic State Estimation (DSE), creates an updated admittance matrix. First, a hybrid AC/DC network model is developed to combine the AC network and DC links. Then a non-linear state estimator can solve for hybrid AC/DC states by applying the unscented Kalman filter (UKF) algorithm. It is demonstrated that UKF is easy to implement and accurate in estimation. The dynamic state variables of multi-machine power systems, which are generator rotor speed and rotor angle, are estimated to study transient behavior of the power system network. Finally, a dynamic state estimation model is built for a 14 bus power system network to evaluate the proposed algorithm for hybrid AC/DC networks.

This paper proposes an optimized transmission line modeling (TLM) method for the real-time transient simulation of systems with multiple nonlinearities. The proposed method allows the simulation to be carried out with larger time-steps while maintaining the accuracy. A detailed case study of a nonlinear bridge circuit is presented to illustrate the advantages of the optimized TLM method in comparison with other methods. The new formulation is then implemented in real-time for the transient simulation of the nonlinear bridge. Real-time simulation results are validated by comparing them with experimental measurements. A second case study includes a power system with several surge arresters which is also simulated in real-time by the aid of the optimized TLM method and verified using offline simulation.

This paper presents a system for detection and classification of power quality (PQ) voltage disturbances. The proposed system applies the following methods to detect and classify PQ disturbances: digital filtering and mathematical morphology are used to detect and classify transients and waveform distortions, whereas for short- and long-duration disturbances (such as sags, swells, and interruptions), the analysis of the root-mean-square (RMS) value of the voltage is employed. The proposed combined approach identifies the type of disturbance and its parameters such as time localization, duration, and magnitude. The proposed system is suitable for real-time monitoring of the power system and implementation on a digital signal processor (DSP).

The paper investigates the applicability of some closed form expressions for the ground impedance and ground admittance of buried horizontal wires (bare and insulated) for lightning or switching transient analyses based on transmission line (TL) theory. In view of the frequency contents that typically characterize such transients, the behavior of the ground impedance and admittance is studied for a wide frequency range up to 10 MHz. Low frequency approximation of the ground impedance is not always appropriate for transient analysis. Sensitivity analyses show that, unlike overhead wires, the ground impedance for buried wires is little sensitive to the ground conductivity. On the other hand, the ground admittance varies strongly with the ground conductivity. The paper also discusses the results of transient analysis of buried cables performed by means of electromagnetic transient programs (EMTP) that neglect the ground admittance. The limits of such an approximation are discussed in order to evaluate the applicability of EMTP-like programs to the transient analysis of buried conductors. Transient pulse propagation in time domain based on finite difference time domain (FDTD) method of solution of TL equations is also discussed for a future inclusion of non-linear phenomena, like soil ionization and arcing/breakdown mechanisms, in the soil. The analysis presented could be useful in estimating surge propagation characteristics of buried wires for appropriate insulation coordination and transient protection. © 2007 IEEE.

The overvoltage level of a system is strongly dependent on the connected loads and with more precise models, better and more reliable simulation results are obtained. This paper presents the input impedance characteristics, measured over a wide range of frequencies, of various actual low-voltage residential installations. The measured frequency responses were fitted by effective RLC models and a general model was also developed. The range of frequencies considered in the study, nearly d.c. up to 5 MHz, allows the use of these models for lightning or switching studies. It is also presented overvoltage simulations, using different residential installations models presented in the paper, of a distribution network subjected to lightning surges on the medium voltage circuit.

In this paper, we first extend the Sunde logarithmic approximation for the single-wire line ground impedance to the case of a multiconductor line. The new approximate forms are compared to the general expressions which involve integrals over an infinitely long interval and an excellent agreement is found. The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the transmission line equations. The order of the singularity is reduced by 1, and a careful numerical treatment is then employed to derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term. Finally, finite-difference time-domain (FDTD) solutions of the coupling equations are presented and the theory is applied to calculate lightning-induced voltages on a multiconductor line. The lightning-induced voltages are calculated for the case of lossless/lossy, single-conductor/multiconductor lines and the effect of ground losses and the presence of other conductors on the magnitude and shape of induced voltages are illustrated.

Full-wave numerical electromagnetic analysis (NEA) methods are defined as methodologies allowing the direct numerical solution of Maxwell's equations in both frequency and time domain. These methods are becoming the most promising approach to study complex transient phenomena that cannot be straightforwardly solved by means of circuit-theory or transmission line approaches (e.g. by using Electromagnetic Transient Program - EMTP). Indeed, as known, circuit-theory/transmission line based approaches cannot solve transients that involve non-TEM propagation modes. Furthermore, they cannot be applied in case of unknown circuit parameters. Within the context of NEA, this paper describes the basic theory of the finite-difference time-domain (FDTD) method as a representative NEA method. Also, some typical examples are presented to demonstrate its usefulness and advantages. © 2011 IEEE.

Power factor correction is the main application for shunt capacitor units in the power system. The advantage of improved power factor is reduced line and transformer losses, improved voltage profile, reduced maximum demand, and improved power quality. The capacitors are installed in a distribution system on pole-mounted racks, substation banks, and high voltage (HV) or extra-high voltage (EHV) units for bulk power applications. Capacitors have many applications in power systems: they can be used in series to compensate the inductance of transmission lines to transmit more power. They can also be used as surge capacitors, starting motors, and static VAR compensators. Capacitor banks installed in power substations are vital in the sense that they provide the reactive power needed for the power system, which in turn improves the voltage profile in the system. There is always the option of grounding the banks or leaving them ungrounded. Each of the above configurations has its own advantages and disadvantages; to name a few, ungrounded banks are slightly more expensive compared to grounded banks as the neutral point needs to be insulated up to system basic insulation level; whilst grounded banks are prone to inject high-frequency transients (e.g., switching, ground faults) into the ground mat. This study is intended to address the recent incident in a high-voltage substation which led to the explosion of a capacitor bank. The study goes on to suggest grounding as a method to prevent such incidents. Furthermore, the effects of grounding and induction on control/signal cables as well as protecting relays are investigated.

Voltage transients are the main causes of complaints from medium-voltage customers. For this reason, utilities and independent authorities are focusing their attention on investigation techniques capable of providing information useful for classifying voltage transients depending on their origin. Distributed measurement systems for power quality monitoring able to detect, measure, and classify impulsive transients can be used in coordination with lightning location systems to assess whether there is a relation between a given transient and a lightning event. In this paper, a criterion for evaluating the above correlation is proposed and a numerical example, which is based on real accuracy specifications, is presented. The results show that attempting a correlation between lightning events and induced transients is quite reasonable. © 2004 IEEE.

This paper presents three basic approaches for determining the transient stability of a power network by using an analog VLSI chip for simulating or emulating the system behavior. The main advantages of using this method are the much shorter computation time and lower complexity compared to the currently used methods that are based on numerical calculations or discrete analog simulators.

This paper presents a low-power analog simulator for the transient stability of a two-machine power system. The simulator is implemented in a standard digital CMOS process. Its building blocks are: sine shaper, transconductor with extended linear range, and parametric current amplifier. All these circuits operate in weak inversion and use the bulk as an active terminal. Simulation time is typically 104 times shorter than the real time simulated phenomena

The present work studies the disturbances created in the electric system of a pumped storage power plant, which is an hydraulic generation facility where the machines can work as turbines or pumps, by the operation of a static frequency converter (SFC). The SFC is used for starting the synchronous machines at the station when in the pump mode. During the starting process several equipment is connected to the SFC being possible to get affected by the disturbances generated. These disturbances mainly include the creation of transient overvoltages during the commutation of the semiconductor devices of the SFC and the introduction of harmonics in the network currents and voltages. This work analyzes the possible effects of the SFC operation over the station equipment based on computer simulations. For this purpose, the complete system was modeled and the starting process simulated in a computer transient simulator program. The work begins with a general review of the effects of electric disturbances over high voltage equipment and in particular of the disturbances generated by power electronics conversion equipment. Then the models for the different kind of equipment present in the system are discussed and formulated. The control system that governs the operation of the SFC during the starting process is analyzed later as well as the operation conditions. Once the model of the system is set up, the harmonic analysis of the electric network is done by frequency domain and time domain methods. Time domain methods are also employed for the analysis of the commutation transient produced by the SFC operation. Finally, the simulation results are used to evaluate the impact of the SFC operation on the station equipment, especially on the generator step up transformer. Master of Science

The paper discusses the problem of reliability evaluation of power system devices subjected to transient overvoltages. The problem is solved in the framework of “Stress-Strength” models, resorting to a few simplifying hypotheses, among which that a certain degree of knowledge is available about the degradation of component insulation strength with time and about the pdf of stress (overvoltage). By doing so, a novel class of reliability models is developed that can be regarded as an improvement and a generalization of a first model already put forward by the authors in previous papers. The properties of such new models are illustrated by means of some numerical applications, relevant to primary and secondary distribution cables, subjected to either switching or lightning voltage surges.

This paper treats the problem of primary and secondary control design in low-inertia power grids with mixed lines and a large amount of inverter-interfaced generation. A dynamic phasor model is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines and constant power loads. The model offers a straightforward way to combine white-, grey- and black-box models, and its structure lends itself well to control design. In a next step, a novel method to design fixed-structure robust controllers based on the frequency response of multivariable systems and convex optimization is presented. The method offers an intuitive way to define the control performance specifications, and is able to directly design discrete-time controllers. Finally, the potential of the control design method and the dynamic phasor model is demonstrated in a comprehensive example. In three scenarios it is illustrated how the approach can be used to significantly improve frequency and voltage transient performance in low-inertia power grids. Decentralized as well as distributed architectures for primary and secondary control are studied, and results are validated in simulation.

Two corona models, applicable to the calculation of lightning-induced overvoltages in multiconductor overhead lines, are considered in this paper. The first model represents corona by an increase in each conductor self capacitance after the voltage has reached a threshold value, and in the second model, the influence of corona on the mutual coupling between conductors is also taken into account. Results show that corona (using any of the models) produces an increase in the overvoltage amplitudes, confirming that found in a previous work concerning single-conductor lines. It can also be seen that the results obtained by each model are quite different from each other. The effect of corona in mutual coupling should not be disregarded

In this chapter, we discussed the TL theory and its application to the problem of lightning electromagnetic field coupling to transmission lines. After a short discussion on the underlying assumptions of the TL theory, we described seemingly different but completely equivalent approaches that have been proposed to describe the coupling of electromagnetic fields to transmission lines. The field-to-transmission line coupling equations were then extended to deal with the presence of losses and multiple conductors and expressions for the line parameters, including the ground impedance and admittance were presented. The time-domain representation of the field-to-transmission line coupling equations, which allows for a straightforward treatment of nonlinear phenomena as well as the variation in the line topology, was also described. Solution methods in the frequency domain and in the time domain were given and application examples with reference to lightning-induced voltages were presented and discussed. Specifically, the effect of ground losses was illustrated and discussed. When the travelling voltage and current waves are originated from lumped excitation sources located at a specific location along a transmission line (direct lightning strike), both the corona phenomenon and ground losses result in an attenuation and dispersion of propagating surges along transmission lines. However, when distributed sources representing the action of the electromagnetic field from a nearby lightning illuminating the line are present, ground losses and the corona phenomenon could result in important enhancement of the induced voltage magnitude. Finally, we reviewed the theory of electromagnetic field coupling to a buried cable. Solution methods in the frequency and the time domain were also presented. Examples of lightning-induced currents and comparison with experimental data were presented.

This paper suggests several approaches for determining the transient stability of a power network by using an analog VLSI chip for simulating the system behavior. The main advantages of using this method are the much shorter computation time and lower complexity compared to the existing methods that are based on numerical calculations or discrete analog emulators

In the determination of lightning-induced voltages on overhead power lines, ground losses play a role in both the evaluation of the lightning radiated electromagnetic fields and of the line parameters. The aim of this paper is to assess the effect of these losses through each of these two mechanisms. The authors show, in particular, that for lines whose length does not exceed a certain `critical' value, the surge propagation along the line is not appreciably affected by the ground finite conductivity, and, therefore, it can be neglected in the computation process. Further, it has been shown that, for typical power lines, the wire impedance and the ground admittance, both frequency-dependent, can be neglected in the computations for typical overhead power lines