The Ferranti Effect

The Ferranti EffectAs the outer space of the slewal ontogenesiss specially in extra heights potentiality (EHV) rakes, beyond 200km, we observe a phenomenon called Ferranti Effect in no load or first base load pin downs. This is ascribable to the fact that as the business organization duration outgrowths the mental ability of the string increases, and the beltway capacitor generates the unstable magnate in the bank bill. Since on that point is no load or low load to occupy that excessive military group, this results in excessive reactive government agency in the bloodline and hence the receiving block voltaic potential gets higher than the s butting extirpate emf. This rise in potential drop whitethorn well go beyond the operative ratings of the terminal and hence might give rise to m both cascading rasets damaging the equipments.The unbroken increase of the potency of infection, line space and count of sub-conductors per bundle has emphasized the importance of the excessive line MVAR in EHV systems as well as associated potential and reactive deems. During the line charging volt-amperes of the line which have exceeded the inductive VARs consumed and operating theatre at light loads, there is an undesirable voltage rises a abundant the line. This voltage rise in turn back demands a much higher disengagement level, which poses a great problem. Moreover, if the insulation against these over-voltages were to be provided in the system, wherefore the cost of the line becomes enormous.To overcome this phenomenon, shunt reactors argon required to be installed at optimized location to conduct over the excessive reactive power. Though this solution has a financial cost, but this is inevitable, since the load is a random variable and the generation of the power can non be exactly planned for sudden tripping off of the loads.Aims and objectivesThe remove of this thesis project is to investigate the Ferranti lay out for lon g length transmitting lines development PowerWorld simulations on a radial system. The following argon the key objectives covered in this project.Impact by varying telegraph line lengthsInvestigate the system behavior regarding Ferranti effect with different transmission line lengths. This was finished with(p) by investigate the pen of the effect for long length lines and hence distributed models were considered for this analytic thinking.2-Impact by varying encumbrance levelsSince Ferranti effect is the phenomenon where receiving residuum voltage (Loads) is lower than s exterminate nullify, it was all important(predicate) to look into the make full factor by varying the onus levels for different line lengths.3- Investigation for optimum load levels to sign effectA series of experiments were done to find the minimum determine of load required for varied line lengths in order to avoid Ferranti Effect and to contain the terminal voltage near 1p.u.4- Minimum ratings for reactors for compensationWith a varied number of simulations and experiments, the minimum ratings of required reactors have been realized in order to maintain optimized terminal ratings at receiving curiosity. orbital cavity of thesisThis thesis will commence with an overview of the problems encountered with EHV long transmission line. This would be followed up by a literature review that covers the research of useful background theories. The result from the performed simulations will be discussed in detail. Finally, most recomm abateation for future works in this bea of research.Chapter 2. INTRODUCTION TO TXN LINESThe electric lines which ar use to go electric wavings are called transmission lines. The transmission line parameters like induction and capacitance are non separable unlike the lumped electric circuits. The transmission parameters are distributed all along the length of the transmission line. Hence the method of analyzing the transmission lines is differ ent from analyzing the lumped circuits. In the analysis of the transmission line, only steady state accrediteds and voltages are concerned. The analysis takes the measurementment of received and voltages at any length of the line, when a known voltage is applied at one end of the transmission line. The end at which the voltages are applied is called sending end and the end at which the signals are received is called receiving end of the transmission line.2.1-transmission line parametersFor the analysis and design of transmission lines, it is important to have knowledge of electric circuit parameters, associated with the transmission lines. Various electric parameters associated with the transmission lines are as down the stairs,1-Resistance Depending upon the cross sectional area of the conductors, the transmission lines has safeguard associated with them. The guard is uniformly distributed all along the transmission line. Its total place depends upon the total length of the transmission line. Hence its value is given per whole length of the transmission line. It is denoted as R and is given in ohms per unit length.2- Inductance When the conductors carry the received, the magnetic hang is produced around the conductors. It depends upon the magnitude of the live flux throw the conductors. The flux linkages per ampere of the current, gives rise to the effect called inductance of the transmission line. It is also distributed all along the length of the transmission line. It is denoted as L and measured in Henry per unit length of the transmission line.3- Capacitance The transmission lines consist of two parallel conductors or single line w.r.t earth separated by dielectric like air. Such conductors separated by an insulating dielectric produce a capacitive effect. Due to this, there exists a capacitance associated with the transmission line which is also distributed all along the length of the conductor. It is denoted as C and measured in Farads per u nit length of the transmission line.4- Conductance The dielectric between the conductors is not perfect. Hence a very small numerate of current flows through the dielectric called displacement current. This is nothing but leakage current and this gives rise to the leakage conductance associated with the transmission line. It exists between the conductors and is distributed all along the transmission line. It is denoted as G and measured as mho per unit length of the line.Thus the four important parameters of the transmission line are R, L, C and G. as the current flows from one conductor and complete the path through other conductor, the resistance of both the electrifys is included when specifying the resistance per unit length of the line. These line parameters are unbroken and are called the primary constants of the transmission line.Revisit snaps(4-16(1))2.2-performance equality of long transmission line kundar bookWe can analyze the performance of the line on per shape bas is. The relationship between current and voltage along the one phase of the line in damage of distributed parameters can be seen in the FIG below= series ohmic resistance per unit length/phase.= shunt entranceway per unit length/phase.= length of the line.The voltages and current in the tropeure are the phasors representing sinusoidal m varying quantities.For a differential coefficient section of the line of length at a standoffishness from receiving end, the differential voltage can be given as.hence (2.1)The differential current flowing through shunt admittance can be given asSimilarly (2.2)Differentiating eq 1 and 2 yeilds(2.3)and (2.4)Now for the general equation for voltage and current at distance x from receiving end, if the receiving end voltage and current are known, can be given as(2.5)(2.6)Whereas this is called feature article resistivity.and = = this is called propagation constant.The constant and are complex quantities. The real lead off of propagation constan t () is called the attenuation constant , while the imaginary part is called the phase constant .Now the first term in eq.5 increase in magnitude and advances in phase as the distance increases. This term is called possibility voltage. While the second term in eq.5 decreases in magnitude and distorts in phase from receiving end towards sending end, this term is called reflected voltage. At any orchestrate along the line the voltage is the sum of incident and reflected voltage. The same is true for eq.6 .If a line is terminated at its characteristic impedance , and so there is no reflected voltage and the line is called a flat line or unfathomable line.For a typical power line, G is practically zero and RZc = = (2.7)= = (2.8)If losses are completely neglected the is a real number and is an imaginary number.Similarly for a loss little line eq.5 and 6 can be simplified as(2.9)(2.10)The voltage and current vary h outgrowthonically along the line length. A full cycle of voltage and current along the line length corresponds to 2 radians. If is the phase shift in radians per meter, the wavelength in meters is(2.11)2.3- similar circuit representation of long transmission lineA line with length more than clxkm is considered a long transmission line and the parameters are expect to be distributed uniformly along the line as a result of which the currents and voltages would vary from point to point. let us consider the figure belowseries impedance per unit lengthshunt admittance per unit lengthlength of the linetotal series impedancetotal shunt admittanceThe elemental like weight of the supra figure can be re force as follows.For analysis purpose we take receiving end as reference for measuring the distance. Assume we have an elemental length at the distance of x from the receiving end. If the voltage and current at distance x are and, so at the distance of so the voltage and current becomes + and + respectively.2.12By manipulating supra equationsSimilarly 2.13Wit h above can be constrain verbally as2.14And 2.15By differentiating eq 2.142.16The solution of eq 2.16 is2.17From eq 2.14 and 2.162.18Where is the characteristic impedance and is the propagation constant.Eq 2.17 and 2.18 can be written as2.192.20If receiving end voltage and current are known thenSubstituting above values in eq 8 and 9Again substituting values of A and B in eq 2.19 and 2.202.212.22Since and are the voltage and current at any point distance x from receiving end as evident from expression and (magnitude and phase) are lives of distance , receiving end voltage and receiving end current , which mode that they vary as we move from receiving end towards sending end.Now the quantities and are complexFor a lossless lineWhen dealing with high frequencies or boots normally the losses are neglected and the characteristic impedance becomes surge impedance. Due to large capacitance and lower inductance in the cables the surge impedance values can be very low.For = = the real part of propagation constant () is called the attenuation constant , while the imaginary part is called the phase constant .Eq 2.11 can be written as2.23The first term in the above expression is called incident voltage wave and its value increases as x is increased. Since receiving end is our reference end and as x increases the value of voltage increases meaning the magnitude of voltage decreases as it travel towards the receiving end. Thats why the first part of expression is called incident voltage and the second is called reflected voltage for the similar reason. Same can be said about the current expression as well.Voltage and current expressions can be rearranged as below2.24And for current2.25For , and2.262.27The above derived quantities are related by the general equations2.282.29Where are such thatCom opposeing the coefficients of above expression with eq 2.28 and 2.29From this it is lite that2.3.1-Equivalent representationConsidering the same two terminal condition with s ending and receiving end voltage and current, the network can be represented as figure below.From the above network we can derive the following expressions2.302.31By comparing eq 2.30 and 2.31 with eq 2.26 and 2.272.322.332.342.35From eq 2.33 we can deriveWe can conclude from this that to get the series impedance should be multiplied with . Now to get the shunt arm of equivalent circuit we alternate(a) in eq 2.32Here is the total shunt admittance. So to get the total shunt arm of the equivalent th eshunt arm of the nominal should be multiplied with , so the equivalent circuit can be drawn as below.2.3.2 Equivalent representation of long lineA similar stock of equivalent circuit can be, the equivalent circuit can be represented as auspicate below.By analyzing the circuit following expression can be extracted2.362.37Comparing eq 2.36, 2.37 with 2.26, 2.27.2.382.392.402.41Now using eq 2.40 for shunt tree branch of equivalent circuit we get, therefrom its evident that to get the shu nt branch of equivalent circuit, we have to multiply with the shunt branch of nominal circuit.For series impedance eq 2.40 is substituted in eq 2.38, which givesSo here we get the factor for multiplication with nominal circuit to get equivalent circuit impedance. And the resultant circuit can be drawn as figure below.2.4-Fundamental requirements in ac power transmissionBulk transmission of electrical power by ac in practical only if the following two fundamental requirements are satisfied.Major synchronous machines must(prenominal) remain shelter in synchronismThe major synchronous machines in a transmission system are the generators which are in open(a) of operating usefully other than in synchronism with all the others. And this also is the fundamental of constancy.Voltages must be kept near to their rated valuesThe second main requirement in ac transmission is the maintenance of correct voltage levels. Power systems are not inherently tolerant of abnormal voltages even for sh ort periods.Undervoltage this is generally associated with heavy loading and/or shortage of generation, causes degradation in the performance of loads. In heavy loaded systems, undervoltage may be an indication that the load is approaching the steady state stability arrange. Sudden undervoltages can result from the connection of very large loads.Over voltages this is a dangerous condition because of the risk of flashover or the breakdown of insulation. Over voltages arise from several causes. The reduction of load during certain split of the daily load cycle causes a gradual voltage rise. Uncontrolled, this overvoltage would shorten the useful career of insulation even if the breakdown level were not reached. Sudden overvoltage can result from the disconnection of loads or other equipment, while overvoltages of extreme rapidly and severity can be caused by the line electric flick operation, faults and lightning. In the long transmission line this would limit the power transfer and the transmission distance if no compensating measures were taken.Chapter 3 compensated/uncompensated lines3.1-Charging current in linesDespite being able to avoid wire resistance through the use of superconductors in this thought experiment, we cannot eliminate capacitance along the wires lengths. Any pair of conductors separated by an insulating medium creates capacitance between those conductors (Figure )Voltage applied between two conductors creates an electric field between those conductors. Energy is stored in this electric field, and this storage of efficacy results in an opposition to transfer in voltage. The reaction of a capacitance against changes in voltage is described by the equation i = C(de/dt), which tells us that current will be drawn proportional to the voltages rate of change over time. Thus, when the confound is closed, the capacitance between conductors will react against the sudden voltage increase by charging up and plan current from the source. Accor ding to the equation, an instant rise in applied voltage (as produced by perfect switch closure) gives rise to an infinite charging current.However, the current drawn by a pair of parallel wires will not be infinite, because there exists series impedance along the wires due to inductance. (Figure below) Remember that current through any conductor develops a magnetic field of proportional magnitude. Energy is stored in this magnetic field, (Figure below) and this storage of energy results in an opposition to change in current. Each wire develops a magnetic field as it carries charging current for the capacitance between the wires, and in so doing drops voltage according to the inductance equation e = L(di/dt). This voltage drop limits the voltage rate-of-change across the distributed capacitance, preventing the current from ever reaching an infinite magnitudeEquivalent circuit showing stray capacitance and inductance.The effect of capacitance of an overhead transmission line above 1 60km long is taken into consideration for all calculations. The effect of the line capacitance is to produce a current called charging current. This current will be in quadrate of the applied voltage. It flows through the line even if the receiving end is open-circuited. The charging current of the open circuit line is referred to as the amount of current flowing into the line from sending end to receiving end where there is no load. In many cases, the total charging current of the line is contumacious by multiplying the total admittance of the line by the receiving end of the voltage. This would be correct if the entire length of line has the same voltage as that of receiving end voltage. However this method of finding the charging current is competently accurate for most lines.The actual value of the charging current will decrease uniformly from its maximum value at sending end to the minimum value at receiving end. Due to the charging current, there will be power loss in the li ne even the line is open circuited.3.2- mickle Impedance Loading (sil pdf)As power flows along a transmission line, there is an electrical phase shift, whichincreases with distance and with power flow. As this phase shift increases, the system in which the line is embedded can become increasingly bad during electrical disturbances. Typically, for very long lines, the power flow must be limited to what is commonly called the Surge Impedance Loading (SIL) of the line. (dr) or SIL is defined as the amount of power haveed by a lossless transmission line when terminated by a load resistance equal to surge or characteristics impedance.Surge Impedance Loading is equal to the product of the end bus voltages divided by the characteristic impedance of the line. Since the characteristic impedance of various HV and EHV lines is not dissimilar, the SIL depends approximately on the square of system voltage.A transmission line loaded to its surge impedance loading(i) Has no net reactive power fl ow into or out of the line, and(ii) Will have approximately a flat voltage profile along its length.(dr) with load at the receiving end equal to SIL.Volts (3.1)It is clear from the equation that voltage magnitude at any point along the transmission line is constant with the magnitude equal to the receiving end voltage.Also, at SIL the general expression for current can be rewritten as .Amperes (3.2)Using (3.1) and (3.2), the complex power flowing at any point along the transmission line can be calculated as.(3.3)Hence, the amount of real power flowing along a lossless transmission line loaded at SIL is constant as expected. Also, noticed that the reactive power flowing in the line is zero. This point is pivotal in understanding the phenomenon called Ferranti effect. When the line is terminated at SIL the net reactive power needed to deliver the real power by keeping the voltage constant is zero. In other words, the reactive power internally produced by shunt capacitance is just suf ficient to fulfill reactive power required. However, when the loading conditions change from SIL or moderate loading to light load to heavy load, there will be imbalance in reactive power required to transmit the real power. In the absence of devices to control and compensate for reactive power, situation could result in lack or surplus of reactive power. Hence, create a low or high voltage profile, respectively in the receiving end of the transmission line.Typically, stability limits may determine the maximum allowable power flow on lines that are more than 160 km in length. For very long lines, the power flow limitation may be less than the SIL as shown in Table 0-1. Stability limits on power flow can be as low as 20% of the line thermal limit.Typical stability limits as a function of system voltage are given in table below3.3-The uncompensated line on open circuit tjmillerThe lossless line that is energized by the generators at the sending end and is open circuited at the receivi ng end is described by following equation with .3.4And3.5Voltage and current at the sending end can be given as3.63.7and are in phase, which is in consistent , with the fact that there is no power transfer. The phasor diagram shown in the figure.The voltage and current profiles in equation 1 and 2 are more conveniently expressed in terms of .3.8Phasor diagram of uncompensated line on open-circuitVoltage and current profile at no load condition.The general form of these profiles shown in fig 3.5 above. For a line 300km in the length at 50Hz, 3600 60 per 100km, so =6*3=180. past and establish on the SIL. The voltage rise on open circuit is called Ferranti Effect.Although the voltage rise of 5% seems small, the charging current is appreciable and in such a line it must all be supplied by the generator, which is forced to run at leading power factor, for which it must be underexcited. The reactive power assimilation capability of a synchronous machine is limited for two main reasonsTh e heating of the ends of the stator center increases during the under excited operation.The reduced field currents results in reduced internal emf of the machine and this weakens the stability. find that a line for which ==/2 has a length of /4 (one quarter length wavelength, i.e, 1500km at 50Hz) producing an infinite voltage rise. Operation of any line approaching this length is completely impractical without some government agency of compensation.In case of the sudden open-circuit of the line at the receiving end, the sending end voltage tends to rise at once to open-circuit voltage of the sending end generators, which exceeds the terminal voltage by approximately the voltage drop due to the prior current flowing in their short circuit reactances.3.4-Compensated transmission linesReactive power compensation means the application of reactive devicesTo produce a substantially flat voltage profile at all levels of power transmission.To improve stability by increasing the maximum t ransmissible power, and/orTo hang on the reactive power requirements in the most economical way.Ideally the compensation would modify the surge impedance by modifying the capacitive and/or inductive reactances of the line, so as to produce a realistic surge impedance loading that was always equal to the actual power being transmitted. Yet this is not sufficient to ensure the stability of the transmission, which depends also on the electrical line length. The electrical length can itself be modified by the compensation to have a virtual shorter than the uncompensated value, resulting in an increase in the steady state stability limitThis consideration suggests two broad classification scheme, Surge impedance compensation and line length compensation. Line length compensation in particular is associated with series capacitors used in long distance transmission. Another compensation is called compensation by sectioning, which is achieved by connecting constant voltage compensators at intervals along the line. The maximum transmissible power is that of the weakest section but since this is necessarily shorter than the whole line, an increase in maximum power and , therefore , in stability can expected.3.4.1-Passive and active compensatorsPassive compensators include shunt reactors and capacitors and series capacitors. They modify the inductance and capacitance of the line. Apart from the switching, they are uncontrolled and in unfastened of continuous variation. For example, shunt reactors are used to compensate the line capacitance to limit voltage rise at the light load or no load condition. They increase the virtual surge impedance and reduce the virtual natural load Shunt capacitor may be used to augment the capacitance of the line under heavy loading. They generate reactive power which tend to boost the voltage. They reduce the virtual surge impedance and increase . Series capacitors are used for line length compensation. A measure of surge impedance compen sation may be necessary in conjunction with series capacitors, and this may be provided by shunt reactors or by a dynamic compensator.Active compensators are unremarkably shunt connected devices which have the property of tending to maintain a substantially constant voltage at their terminals. They do this by generating or absorbing precisely the required amount of corrective reactive power in response to any small variation of voltage at their point of connection. They are usually capable of continuous variation and rapid response.Active compensators may be applied either for surge impedance compensation or for compensation by sectioning. In compensation they are capable of all the functions performed by fixed shunt reactors and capacitors and have additional advantages of continuous variability with rapid response. salary by sectioning is fundamentally different in that it is possible only with active compensators, which must be capable of virtually immediate response to the sma llest variation in power transmission or voltage. The table below summarizes the classification of the main type of compensators according to their usual functions.3.4.2-Shunt compensationShunt reactors are used to limit the voltage rise at the light load or no load conditions. On long transmission they may be distributed at intermediate substations in shown in figure belowvoltage and current profile of shunt compensated system at no load.Consider the simple circuit above in figure, it has a single shunt reactor of reactance at the receiving end and a native voltage source at the sending end. The receiving end voltage can be given as3.93.10Equation 7 shows that and are in phase, in keeping with the fact that the real power is zero. For receiving end voltage to be equal to sending end voltage , must be given by3.11The sending end current can be given as3.12using equation 3.9 and 3.113.13Since , this means that the generator at the sending end behaves exactly like the shunt reactor a t the receiving end in that both absorb the same amount of reactive which is evident from equation below.3.14Chapter 4 Ferrenti effect4.1 Ferranti effectA long transmission line draws a substantial quantity of charging current. If such a line is open circuited or very lightly loaded at the receiving end, the voltage at receiving end may become greater than voltage at sending end. This is known as Ferranti Effect and is due to the voltage drop across the line inductance (due to charging current) being in phase with the sending end voltages. therefore both capacitance and inductance is responsible to produce this phenomenon.Another way of explaining Ferranti effect is based on net reactive power flow in the line. It is known that if the net reactive power generated in lie is more than the reactive power absorbed, the voltage at that point in the line becomes higher than the normal value and vice versa. The inductive reactance behaves like a sink in the line whereas the shunt capacita nce generates the reactive power. If the line loading corresponds to the surge impedance loading, the voltage is same everyplace as reactive power absorbed in the line is equal to the reactive power generated. If the loading is less than SIL, generated power is more than generated power absorbed, therefore, the receiving end voltage is higher than sending end voltage.The capacitance (and charging current) is negligible in short line but significant in medium line and appreciable in long line. Therefore this phenomenon occurs in medium and long lines.Represent line by equivalent model.And the vector diagram can be given asOM = receiving end voltage VrOC = Current drawn by capacitance = IcMN = Resistance dropNP = Inductive reactance dropThereforeOP = Sending end voltage at no load and is less than receiving end voltage (Vr)Since, resistance is small compared to reactance resistance can be neglected in calculating Ferranti effect.From model,For open circuit, no load,There foreOrOrBy ne glecting resistanceThe quantity is constant in all line and is equal to velocity of propagation of electromagnetic waves (= 3 - 102 km/sec)By substituting the values in the above derived equationAndAnd finallyFrom the above equationSo orReceiving end voltage is greater than sending end voltage and this effect is called Ferranti Effect .5.1, fig 4.10,4.6,4.4,4.2,4.1,3.5,3.4,2.1Chapter 5 results and discussionResults and discussionsTo simulate for my analysis, a radial system in the following figure was modeled as test system. Practical industrial data was acquired from Queensland Electric Commission which follows the Australian standard for conductors and enforces the transmission and distribution company to follow the standards. This achievement was important to incorporate for more realistic analysis and observe the phenomenon as it is appeared in the real life transmission systems.Conductor types for the simulation were chosen from the provided list