Transient Analysis of Power Systems: Solution Techniques, Tools and Applications

Introduction to Electromagnetic Transient Analysis of Power Systems
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The first developments of transients tools were mostly aimed at calculating overvoltages. Presently, these tools are applied into a myriad of studies e. FACTS and Custom Power applications, protective relay performance, power quality studies for which detailed models and fast solution methods can be of paramount importance. Despite the powerful numerical techniques, simulation tools, and graphical user interfaces currently available, those involved in electromagnetic transients studies face, sooner or later, limitations of models available in transients packages, the lack of reliable data and conversion procedures for parameter estimation or insufficient studies for validating models.

Although parallel computation is covered in the chapters related to real-time simulation, readers interested in the computation of electromagnetic transients using a multicore environment are advised to consult reference [22]. Modelling and Parameter Determination: Despite the powerful numerical techniques, simulation tools and graphical user interfaces currently available, a lack of reliable data, standard tests and conversion procedures generally makes the determination of parameters one of the most challenging aspects of creating a model [4].

Although there is no specific chapter of this book dedicated to these topics, many issues connected to modelling guidelines are presented in several chapters, and two annexes covering. Although similar fitting techniques can be used for all power components whose behaviour can be derived from a frequency response test, the optimal procedure to be applied in each case is different. Annex A presents the application of fitting techniques for extracting rational models of lines, cables and transformers from frequency response tests [23].

Dynamic System Equivalents: A common practice when dealing with large power systems in transient studies is to divide the system into a study zone, where transient phenomena occur, and an external system encompassing the rest of the system. The study zone is represented in detail, while the rest of the system is modelled by an equivalent. Given the frequency range with which transients are generated, there is a need for suitable techniques that could accurately determine the parameters of the external equivalent system from low- to high-frequency behaviours.

Annex B reviews current techniques for obtaining dynamic system equivalents [24]. Readers interested in modelling guidelines and parameter determination for electromagnetic transients studies can consult references [17]. Overvoltage Calculations: An overvoltage is a voltage having a crest value exceeding the corresponding crest of the maximum system voltage. Overvoltages can occur with very wide range of waveshapes and durations. The magnitude of external lightning overvoltages remains essentially independent of the system design, whereas that of internal switching overvoltages increases with the operating voltage of the system.

The estimation of overvoltages is fundamental to the insulation design of power components, and to the selection of protection devices [25, 26]. Chapter 5 summarizes the different types of overvoltages and their causes, provides modelling guidelines for digital simulation using a time-domain tool e. Power Electronics Applications: Power electronics applications have quickly spread to all voltage levels, from extra high voltage EHV transmission to low voltage circuits in end-user facilities.

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Power electronics modelling and simulation are especially important for a concept validation and design iteration during new product development. Four chapters of this book have been dedicated to the simulation of power electronics components. They provide general modelling guidelines and procedures for simulation of the main power electronics applications using a time-domain tool e.

Dynamic Average Modelling: Detailed switching models of power electronics converters are computationally intensive and can be the bottleneck for system-level studies with a large number of components and controllers. These drawbacks have led to the development of the so-called dynamic average-value models AVM in which the effect of fast switching is neglected or averaged within a prototypical switching interval [31].

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The resulting models are computationally efficient and can run orders of magnitudes faster than the original models. Chapter 10 describes methods of constructing AVMs and demonstrates their advantages with some practical examples. Protection Systems: Protection systems are critical power system components and their behaviour is an important part of power system response to a transient event. A system aimed at protecting against overcurrents consists of three major parts: instrument transformers current, wound electromagnetic voltage, and coupling capacitor voltage transformers , protective relays, and circuit breakers [].

Smart Grids: The smart grid may be seen as an upgrade of the current power system, in which present and new functionalities will monitor, protect and automatically optimize the operation of its interconnected elements to maintain a reliable and secure environment. The smart grid will offer better management of energy consumption by the use of advanced two-way metering infrastructure and realtime communication; improved power reliability and quality; enhanced security by reducing outages and cascading problems; and better integration of DERs.

Although the smart grid will build upon the basic design of the current power grid, it will have features essential to its operation that will involve monitors, sensors, switching devices and sophisticated two-way communication systems that will allow it to be a highly automated power delivery system [35, 36]. The complete model of an actual smart grid should include the representation of: 1 conventional power components that will generate and transmit the electric energy, 2 various types of powerelectronic interfaces, loads and DERs, plus their corresponding controllers, and 3 the two-way communication system.

To date, there is no software tool capable of coping with such a complex model, although some work is in progress [37]. Chapter 12 presents the application of time-domain solution techniques to the study of large actual distribution systems. The chapter covers the study of DER integration and its possible effects on system reliability and voltage violations, the application of system reconfigurations by large numbers of switching operations to exploit the advantage of automation and self-healing capabilities and the analysis of distribution system overvoltages.

The chapter also describes some experiences with the development of industrial-grade translators for interfacing Power-Flow programs with EMTP-like tools, which can facilitate the simulation of electromagnetic transients to utilities. Interfacing Techniques: Interfacing an electromagnetic transient tool with external programs or algorithms expands their applicability to areas where techniques are available through the external agent program or algorithm []. Chapter 13 describes methods for interfacing a transient simulation tool with other mathematical algorithms to extend their application for both analysis and design of complex power systems.

Course Coord. Vasca and L. Iannelli , Springer, London, UK. Popovici and P. International Journal of Energy Sector Management, 2 3 , Read Free For 30 Days. Description: for transient analysis. Flag for inappropriate content. Ch1] Martine For Later. Ch1] Martinez-Velasco, Juan a. Related titles. Carousel Previous Carousel Next. Load-following performance analysis of a microturbine for islanded and grid connected operation. The model is single-phase since the transient process is assumed symmetrical. Under steady-state conditions, the excitation of the generator and the regulation of the step-up trans- former are controlled in such a way that the operating voltages do not exceed the highest permissible voltage of the system.

Due to the loading, the internal voltage of the generator will be higher or much higher than 1 p. After a sudden load shedding, an overexcited generator will remain supplying the transformer and the open-circuited transmission line. The phenomena that occur after load rejection in the three main components are as follows: Figure 5.

Calculation of Power System Overvoltages r Generator: If the current change is assumed to be sudden, the subtransient voltage that appears at the terminal voltage depends on both the initial steady state voltage and the subtransient reactance. Without a voltage regulator, the terminal voltage of the generator rises, the process being governed by the no-load time constants.

Since such a voltage stress may not be acceptable, a fast voltage regulation is needed. In the moment of load rejection the exciting voltage may even reverse, and after a few hundred milliseconds it is set to the no-load exciting voltage. This voltage drop can be compensated by the voltage regu- lator of the transformer. In any case, the secondary voltage will not exceed the maximum permissible voltage. However, after load rejection the secondary voltage goes up and may exceed the maximum voltage; that is, the magnitude of the secondary voltage rises to the no-load voltage condition, which, due to the transformation ratio of the transformer prior to the switching event, can exceed the rated voltage.

These equations were derived by assuming that the load is disconnected at the terminals of the respective component. This is not the case of the system shown in Figure 5. After load rejection, the line remains under voltage and generating capacitive power, so the currents at the secondary side of the transformer and the generator terminals are not zero; in fact, the currents for these two components can be large and capacitive, which will produce the Ferranti effect and voltage rises that are larger than those obtained from the expressions given in the table.

In this condition, the voltage rise at the generator and transformer terminals can be more accurately obtained by increasing the reactive power of the load with the capacitive power generated by the transmission line under no-load condition. The transformer is delta-wye connected with grounded neutral at the line side.

The load at the end of the transmission line is MVA, Calculation of Power System Overvoltages with a power factor of 0. The entire load is suddenly disconnected by opening a switch at the receiving end of the line. Since the line is not too long and the voltage not too high, the Ferranti effect will not take place, so it should be assumed that there will not be a voltage rise at the receiving end of the line with respect to its sending end.

Plots of Figure 5. These results may be justified as follows. Since the generator exciter is included, the generator voltage comes back to its nominal value, and since the Ferranti effect is negligible, voltages at the transformer secondary and the receiving end of the line are basically the same once the load has been disconnected.

In this case, the voltage rise at the remote end of the line is the result of several effects: the internal voltage drop in the transformer, which is almost negligible after load rejection; the voltage increase caused by the transformer ratio, which is working with a tap that produces a secondary voltage above the rated voltage i. Without the exciter model, there would be voltage rises at the generator terminals, at the secondary side of the transformer and at the remote end line terminals; consequently, the rise would be even higher and rather unrealistic. Shunt reactors are placed at the ends of the line sections and their effect is to increase the effective shunt reactance of the line, and consequently to reduce the TOV.

They reduce transient overvoltages in the same way as TOVs. They can also provide the draining of trapped charges on isolated line sections, which avoids excessive transient voltages when reclosing the line. Shunt compensation may also be seen as a reduction of the surge impedance, which can be a desirable condition in the initial phase of the system; that is, when it operates with a light load. When the system is later operated at higher loads, the increased reactive demand of a line will cause an elevated excitation in the generators; this can have, on the one hand, the favourable effect that the system becomes stiffer and exhibits a better performance with respect to stability, but, on the other hand, an unfavourable effect on both temporary and transient overvoltages, which will be higher.

The application of shunt compensation may take advantage of shunt reactors with a variable magnetiz- ing characteristic i. Reactors of this type produce harmonics which may act in an unfavourable way and even cause TOVs. These reactors can be successfully applied to line lengths beyond km. Below km the third harmonic voltage is superimposed in an unfavourable way, producing TOVs with a frequency of oscillation higher than the power frequency.

Load rejection overvoltages can be reduced from a level of 1. When employing permanently connected reactors, reactive current has to be supplied during normal operation causing increased losses and an elevated excitation in the generators. This can be avoided by switching the reactors, connecting them when energizing the line and when shedding load. This can only be made to a limited extent because the switching operation during load shedding cannot be carried out fast enough. This may justify the use of reactors with an extreme magnetizing characteristic — a negligible magnetizing current in the normal operating region and a rather flat characteristic above the Calculation of Power System Overvoltages rated flux [13].

These reactors require special design to compensate the harmonics, which makes the equipment relatively expensive. A more flexible compensation can be achieved by means of a static VAr compensator SVC , in which thyristors are used to control the reactive current through the inductance. To take full advantage of the potential of reactive-power control, the compensator is usually complemented by capacitor banks to allow the supply of reactive power at a leading power factor to the system.

For reduction of TOVs, the decisive parameter is the inductance of the compensator. This compensation scheme can reduce reactive power during normal operation and quickly restore compensation in the case of load rejection. As a first approach, power system models may be seen as composed of different combinations of series and parallel circuits consisting of RLC elements. After a change of the system configuration that may result from some switching operations or short-circuits, a match between a natural oscillation of the power system and the frequency of an external sinusoidal source can occur.

Different types of the resonance phenomenon can be distinguished: 1 natural resonance, when a natural oscillation frequency is equal to the source frequency; 2 ultra-harmonic resonance, when a natural oscillation frequency is equal to a harmonic frequency of the source; 3 subharmonic resonance, when a natural oscillation frequency is equal to a subharmonic frequency of the source. Typical harmonic voltage sources are synchronous generators and asynchronous machines slope- ripple harmonics , and transformers current harmonics that cannot spread in the magnetization current in transformers with isolated neutral and without a delta winding.

Typical harmonic current sources are corona, static converters or rectifiers, and transformers e. The resonance phenomenon in nonlinear circuits, known as ferroresonance, basically caused by the nonlinear saturation characteristics of inductances with an iron core, is analysed in Section 5. The rest of this section is dedicated to introducing resonance in linear circuits and resonance overvoltages caused by harmonic currents in the presence of capacitor banks.

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For a thorough analysis of both phenomena, resonance and ferroresonance, including several actual case studies, see the CIGRE Brochure [22]. For the sake of simplicity the circuits are lossless. Note that the supplying source is a voltage source Figure 5. This may be seen as a magnification of the voltage. This may be seen as a magnification of the current. A possible network configuration where resonance overvoltages may occur is a system feeding a transformer and an unloaded transmission line.

The magnetizing inductance of the transformer changes periodically with double frequency due to the modulation of the saturation characteristic by the voltage source. If the natural frequency of the resulting circuit is equal to the frequency of magnetizing inductance, even ultra-harmonic resonance is possible. This phenomenon is called parametric resonance. Similar overvoltages can be originated when an unloaded transformer is switched on — see the following subsection. TOVs due to resonance can be reduced or avoided by detuning the resonance frequency of the system, by changing the system configuration or by introducing or increasing the damping of the system.

In general, system configurations prone to resonance overvoltages have to be detected from field measurements or by means of detailed studies. If L and C remain invariant with frequency, resonance will occur when the inductive and capacitive inductance of the denominator in 5. At the resonant frequency fr, the condition given by equation 5. Without the presence of the capacitor bank, the natural resonant frequency of the power system is usually high.

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The capacitor bank and the rest of the system act like the parallel branches of a tuned circuit. Such a circuit, when excited at the resonant frequency, will result in the magnification of the harmonic current, which may even exceed the fundamental frequency current. This will overload the capacitor and all the system components with damaging results. The condition 5. This type of resonance is a major concern in power systems, and must be avoided in any application of power capacitors.

This simple analysis can be used to size capacitor banks for a given distribution system to avoid resonance. A capacitor bank size has to be selected so that the resonant frequency does not coincide with any load-generated harmonic. However, the short-circuit level in a power system is not a constant parameter, and it will vary with the switching conditions: for example, a generator or a tie-line circuit may be out of service or part of the motor loads may have been shut down, which will lower the Therefore, the resonant frequency will vary, depending on the switching conditions, and a reorganization of the system may bring about a resonant condition where none existed before.

A method of predicting the resonant frequency of the system in the presence of capacitors is to run a frequency scan. A current source of variable frequency is applied at the point of common coupling PCC for the range of harmonics to be studied. For a unit current injection, the calculated voltages give the driving point and transfer impedances, both in modulus and phase angle.

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That is, plots of modulus and phase angle impedance are obtained at varying frequency, which provides the loci of resonant frequencies. The procedure is valid regardless of the number of harmonic-producing loads, as long as the principle of superimposition is valid; that is, when the system contains only linear elements for the range of frequencies.

System component e. Resonance phenomena caused by the installation of capacitor banks can be propagated and can impact remotely. A study aimed at detecting the possibility of resonance is therefore important to prevent this situation and to apply a solution technique. A harmonic source can be considered as a harmonic generator. Apart from the overloading of capacitors, the harmonic currents can seriously de-rate transformers, produce additional losses in conductors, result in negative sequence overloading of generators, give rise to transient torques and torsional oscillations in rotating machinery or negatively affect protective relays.

Figure 5. To improve the load power factor, a 9 Mvar capacitor bank will be installed at the PCC. After installing the capacitor bank, a resonance problem may occur due to the presence of harmonic currents injected by the diode rectifier. This problem can be predicted by performing a frequency scan of the system once the capacitor bank has been placed.

A frequency scan of the system from the PCC after installing the capacitor bank is performed to detect resonance problems. The plot in Figure 5. The harmonic currents going to the rectifier can be seen as harmonic currents injected into the PCC; they will flow to the HV system through the transformer and divide into other components connected to the PCC, depending upon their harmonic impedances. It is evident, as predicted from the frequency scan, that a resonance phenomenon occurs, and the capacitor bank can be damaged as a consequence of the large current.

This is a characteristic of a parallel-tuned circuit: while the exciting current i. This problem can be solved by installing a filter tuned to the fifth harmonic; that is, the capacitor bank is replaced by a shunt filter, whose tuned frequency is five times the fundamental. The new frequency Figure 5. The application of a band-pass filter has not eliminated resonances, but now they occur at frequencies below the tuned frequency and correspond to points that are away from the load-generated harmonics. For a practical filter design, it is important to account for some variations in the tuned and resonant frequency with various system switching conditions.

However, re-energizing the transformer can cause high inrush currents due to the nonlinear behaviour of its core.

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Transformer inrush currents can have a high magnitude with a Figure 5. Calculation of Power System Overvoltages significant harmonic content note that the inrush current contains both odd and even harmonics , so when a line and a transformer are energized together, resonance overvoltages can occur. The inrush currents interact with the power system, whose resonant frequencies are a function of the series inductance associated with the short-circuit strength of the system and the shunt capacitances of lines and cables.

This may result in long-duration resonant TOVs. A transmission system will generally be weak during the first steps of a system restoration following a blackout. The equivalent system inductances are then relatively high because relatively few generators are on line and the grid tends to be sparse. Therefore, the first system resonant frequency can be much lower than during normal system operation.

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Large capacitances also contribute to the low resonant frequencies. One of the major concerns during the early stages of a power system restoration is the occurrence of res- onance overvoltages as a result of switching procedures [24]. During a restoration phase, the capacitive voltage rise due to charging currents can be sufficient to overexcite transformers and generate significant harmonics. If the combination of the system impedance and the line capacitance is adverse, then a har- monic resonance will result. Harmonic distortions produced by transformer saturation will excite these resonances, which can cause damaging overvoltages that result from several factors that are characteristic of networks during restoration [24]: 1 the natural frequency of the series circuit formed by the source inductance and line charging capacitance may, under normal operating conditions, be a low multiple of the power frequency; 2 the magnetizing inrush caused by energizing a transformer produces many harmon- ics; 3 during early stages of restoration, the lines are lightly loaded while transients are lightly damped, which means that the resulting resonance voltages may be very high.

If transformers become overex- cited due to power frequency overvoltage, harmonic resonance voltage will be sustained or even grow. Energizing equipment during black-start conditions can result in overvoltages higher than during normal operation, and they can cause arrester failures and system faults, and prolong system restoration [24].

However, as the trans- former comes into saturation its impedance drops rather quickly, resulting in an increase in current and in a rapid discharge of the cable. As the core comes out of saturation the process reverses and the interchange of stored energies will continue to repeat it. The voltage will oscillate with a square wave and, with each oscillation, a certain amount of the original energy will be dissipated until the oscillation dies out.

Temporary resonant harmonic overvoltages may also develop when transformers are switched in high voltage cable systems and HVDC stations [25]. The AC filter circuits connected at the HVDC stations produce several parallel resonance points in the impedance—frequency characteristic of the system, so high saturation overvoltages may occur if the system also has a low degree of damping.

These internal overvoltages develop whenever the resonant frequencies of the feeder and of the transformer match themselves. Another option is connecting capacitors at the secondary terminals of the transformer.

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Transient Analysis of Power Systems: Solution Techniques, Tools and Applications. Book Abstract: The simulation of electromagnetic transients is a mature field. Illustrates the application of EMT tools to the analysis and simulation of smart grids. Transient Analysis of Power Systems: Solution Techniques, Tools and.

For more details on transformer energization studies, including some actual case studies, see the CIGRE Brochure [26]. However, the magnetizing current of an unloaded transformer during energization may become extremely high when the transformer core Since saturation is a highly nonlinear phenomenon, the inrush current contains a DC component and harmonics besides its fundamental. When a power transformer has been switched off from the system, the transformer core is left with residual flux.

When the power transformer is connected to the network again at an instant when the polarity of the system voltage is the same as the polarity of the residual flux, then at maximum voltage the total flux density in the core would have increased. The core is forced into saturation and the transformer draws a large current from the supplying network. When the voltage reverses its polarity in the next half cycle, then the maximum flux in the core is less than the maximum flux density in the no-load situation. The transformer inrush current is therefore asymmetrical and also contains a DC component, and may need seconds to disappear.

V h and I h are the vectors of harmonic voltages and currents, respectively. The harmonic current components of the same frequency that the system resonance frequencies are amplified in the case of parallel resonance, thereby creating high voltages at the transformer terminals, as seen in the previous section. This leads to a higher level of saturation resulting in higher harmonic components of the inrush current, which again results in increased voltages. This can happen particularly in lightly damped systems, common at the beginning of a restoration procedure when a path from a black-start source to a large power plant is being established and only a few loads have been restored [24, 28].

It is a very simplified representation of a power system at the early stages of a restoration procedure in which the analysis is concentrated on the energization of a transformer that is assumed to be unloaded. One conclusion from a frequency scan from the point of connection of the transformer is that the impedance seen from this bus shows a parallel resonance peak at the second harmonic.

When the transformer is energized, this resonance condition results in the overvoltage depicted in Figure 5. The equipment can withstand higher overvoltages if the duration of the overvoltage is shorter, but the magnitude of resonance overvoltages may exceed 1.

However, the withstand capability of equipment may deteriorate due to aging or other internal defects; therefore, sustained resonance overvoltages may damage the system equipment, even if they are below the specified overvoltage withstand capability. This situation is not desirable, and the risk of resonance overvoltage should be minimized. The key factors for analysis of harmonic overvoltages include: the resonance frequency of the network; the system damping including the network losses and the load connected to the network ; the voltage level at the transformer terminals; the saturation characteristic and the remanent flux in the core of the transformer; and the closing time of the circuit breaker pole.

Factors that contribute to a higher level of resonance overvoltage are [29]: 1 higher rating of the transformer to be energized; 2 lower value of source fault level; 3 longer circuit length; 4 smaller amount of load in the system; 5 higher system voltage profile; 6 higher working flux density of the transformer; and 7 transformer energized at the point near the maximum voltage. Harmonic TOVs during transformer energization are sensitive to several parameters: circuit breaker closing times, switching angles, transformer saturation curve, residual flux in transformers, source impedances and system capacitances.

The methods that have been proposed to prevent harmonic reso- nance overvoltages are: r adding as much load as possible before energizing a transformer: This leads to a decrease in the magnitude of the impedance and, consequently, to a reduced amplification of the injected harmonic currents. To ensure that resonance is damped, sufficient load should be connected to the underlying system. Analysis for a kV line has shown that a load of about 3 MW per mile is adequate [24].

This means that if generators are added, the resonance peak is shifted to higher frequencies and if generators are omitted, it is shifted to lower frequencies. Calculation of Power System Overvoltages r reducing the system voltage before energizing a transformer: The reactive power of a lightly loaded system can be reduced by minimizing the number of unloaded lines to be energized and setting the sending-end transformers at the lowest tap position. Sustained harmonic overvoltages caused by over-excitation of transformers can be controlled by selecting a transformer tap which equals or exceeds the power-frequency voltage applied or lowering system voltage to at or below the tap before energizing.

This effect results in a change of the transformer inrush current. This method is based on the measurement of the residual flux, which can significantly affect inrush currents. This technique is the most effective method for the limitation of the switching transients, since the magnitudes of the created transients are strongly dependent on the closing instants of the switch.

The determination of the optimal switching time aimed at reducing harmonic overvoltages caused by transformer energization during power system restoration has been analysed in [30]. Up to three different strategies rapid, delayed and simultaneous closing were proposed in [31,32] for controlled energization of multiphase transformers. The general requirements for ferroresonance are an applied or induced source voltage, a saturable magnetizing inductance of a transformer, a capacitance and low damping [22, 33, 34].

The capacitance can be in the form of the capacitance of underground cables or transmission lines, capacitor banks, coupling capacitances between double circuit lines or in a temporarily ungrounded system, and voltage grading capacitors in HV circuit breakers. Other possibilities are generator surge capacitors and SVCs in long transmission lines. In fact, ferroresonance may also arise solely due to transformer winding capacitance.

System events that may initiate ferroresonance include single-phase switching or fusing, or loss of system grounding.