The Ferranti Effect
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Published: Mon, 08 May 2017
As the length of the line increases specially in extra high voltage (EHV) lines, beyond 200km, we observe a phenomenon called Ferranti Effect in no load or low load conditions. This is due to the fact that as the line length increases the capacitance of the line increases, and the shunt capacitance generates the reactive power in the line. Since there is no load or low load to consume that excessive power, this results in excessive reactive power in the line and hence the receiving end voltage gets higher than the sending end voltage. This rise in voltage may well go beyond the operative ratings of the terminal and hence might give rise to many cascading events damaging the equipments.
The continuous increase of the voltage of transmission, line length and number of sub-conductors per bundle has emphasized the importance of the excessive line MVAR in EHV systems as well as associated voltage and reactive controls. During the line charging volt-amperes of the line which have exceeded the inductive VARs consumed and operation at light loads, there is an undesirable voltage rises along the line. This voltage rise in turn demands a much higher insulation level, which poses a great problem. Moreover, if the insulation against these over-voltages were to be provided in the system, then the cost of the line becomes enormous.
To overcome this phenomenon, shunt reactors are required to be installed at optimized location to absorb 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 cannot be exactly planned for sudden tripping off of the loads.
Aims and objectives:
The aim of this thesis project is to investigate the Ferranti effect for long length transmission lines using PowerWorld simulations on a radial system. The following are the key objectives covered in this project.
Impact by varying Line lengths:
Investigate the system behavior regarding Ferranti effect with different transmission line lengths. This was done by investigating the profile of the effect for long length lines and hence distributed models were considered for this analysis.
2-Impact by varying loading levels:
Since Ferranti effect is the phenomenon where receiving end voltage (Loads) is lower than sending end, it was important to look into the loading factor by varying the loading levels for different line lengths.
3- Investigation for optimum load levels to avoid effect:
A series of experiments were done to find the minimum values 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 compensation:
With 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 end.
Scope of thesis:
This 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, some recommendation for future works in this area of research.
Chapter 2. INTRODUCTION TO TXN LINES:
The electric lines which are used to carry electric waves are called transmission lines. The transmission line parameters like inductance and capacitance are not separable unlike the lumped circuits. The transmission parameters are distributed all along the length of the transmission line. Hence the method of analyzing the transmission lines is different from analyzing the lumped circuits. In the analysis of the transmission line, only steady state currents and voltages are concerned. The analysis includes the measurement of current 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 parameters:
For 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 below,
1-Resistance: Depending upon the cross sectional area of the conductors, the transmission lines has resistance associated with them. The resistance is uniformly distributed all along the transmission line. Its total value depends upon the total length of the transmission line. Hence its value is given per unit 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 current, the magnetic flux is produced around the conductors. It depends upon the magnitude of the current flowing 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 unit length of the transmission line.
4- Conductance: The dielectric between the conductors is not perfect. Hence a very small amount 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 wires is included when specifying the resistance per unit length of the line. These line parameters are constant and are called the primary constants of the transmission line.
2.2-performance equation of long transmission line: kundar book
We can analyze the performance of the line on per phase basis. The relationship between current and voltage along the one phase of the line in terms of distributed parameters can be seen in the FIG below
= series impedance per unit length/phase.
= shunt admittance per unit length/phase.
= length of the line.
The voltages and current in the figure are the phasors representing sinusoidal time varying quantities.
For a differential section of the line of length at a distance from receiving end, the differential voltage can be given as
The differential current flowing through shunt admittance can be given as
Differentiating eq 1 and 2 yeilds
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
Whereas this is called characteristic impedance.
and = = this is called propagation constant.
The constant and are complex quantities. The real part of propagation constant () 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 incident 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 point 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 , then there is no reflected voltage and the line is called a flat line or infinite line.
For a typical power line, G is practically zero and R<< , therefore
Zc = = (2.7)
= = (2.8)
If losses are completely neglected the is a real number and is an imaginary number.
Similarly for a lossless line eq.5 and 6 can be simplified as
The voltage and current vary harmonically 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
2.3-Equivalent circuit representation of long transmission line:
A line with length more than 160km is considered a long transmission line and the parameters are assumed 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 below
series impedance per unit length
shunt admittance per unit length
length of the line
total series impedance
total shunt admittance
The elemental equivalent of the above figure can be redrawn 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.
By manipulating above equations
With above can be written as
By differentiating eq 2.14
The solution of eq 2.16 is
From eq 2.14 and 2.16
Where is the characteristic impedance and is the propagation constant.
Eq 2.17 and 2.18 can be written as
If receiving end voltage and current are known then
Substituting above values in eq 8 and 9
Again substituting values of A and B in eq 2.19 and 2.20
Since and are the voltage and current at any point distance x from receiving end as evident from expression and (magnitude and phase) are functions of distance , receiving end voltage and receiving end current , which means that they vary as we move from receiving end towards sending end.
Now the quantities and are complex
For a lossless line;
When dealing with high frequencies or surges 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 as
The 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. That’s 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 below
And for current
For , and
The above derived quantities are related by the general equations
Where are such that
Compairing the coefficients of above expression with eq 2.28 and 2.29
From this it is clear that
Considering the same two terminal condition with sending and receiving end voltage and current, the network can be represented as figure below.
From the above network we can derive the following expressions
By comparing eq 2.30 and 2.31 with eq 2.26 and 2.27
From eq 2.33 we can derive
We can conclude from this that to get the series impedance should be multiplied with . Now to get the shunt arm of equivalent circuit we substitute in eq 2.32
Here 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 line:
A similar derivation of equivalent circuit can be, the equivalent circuit can be represented as Figure below.
By analyzing the circuit following expression can be extracted
Comparing eq 2.36, 2.37 with 2.26, 2.27.
Now using eq 2.40 for shunt branch of equivalent circuit we get,
Therefore its evident that to get the shunt 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 gives
So 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 transmission:
Bulk transmission of electrical power by ac in possible only if the following two fundamental requirements are satisfied.
Major synchronous machines must remain stable in synchronism:
The major synchronous machines in a transmission system are the generators which are incapable of operating usefully other than in synchronism with all the others. And this also is the fundamental of stability.
Voltages must be kept near to their rated values:
The second main requirement in ac transmission is the maintenance of correct voltage levels. Power systems are not inherently tolerant of abnormal voltages even for short 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 limit. 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 parts of the daily load cycle causes a gradual voltage rise. Uncontrolled, this overvoltage would shorten the useful life 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 switching 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 lines
3.1-Charging current in lines:
Despite 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 energy results in an opposition to change 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 voltage’s rate of change over time. Thus, when the switch is closed, the capacitance between conductors will react against the sudden voltage increase by charging up and drawing current from the source. According 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 magnitude:
Equivalent circuit showing stray capacitance and inductance.
The effect of capacitance of an overhead transmission line above 160km 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 determined 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 sufficiently 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 line even the line is open circuited.
3.2-Surge Impedance Loading (sil pdf)
As power flows along a transmission line, there is an electrical phase shift, which
increases with distance and with power flow. As this phase shift increases, the system in which the line is embedded can become increasingly unstable 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 delivered 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 flow 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.
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 .
Using (3.1) and (3.2), the complex power flowing at any point along the transmission line can be calculated as.
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 crucial 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 sufficient 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 below:
3.3-The uncompensated line on open circuit: tjmiller
The lossless line that is energized by the generators at the sending end and is open circuited at the receiving end is described by following equation with .
Voltage and current at the sending end can be given as
and 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 .
Phasor diagram of uncompensated line on open-circuit
Voltage 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 ðœ½=6*3=180. Then and based 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 absorption capability of a synchronous machine is limited for two main reasons
The heating of the ends of the stator core increases during the under excited operation.
The reduced field currents results in reduced internal emf of the machine and this weakens the stability.
Note that a line for which ðœ½=ð›½ð›¼=ðœ‹/2 has a length of Î»/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 means of compensation.
In case of the sudden open-circuit of the line at the receiving end, the sending end voltage tends to rise immediately 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 lines:
Reactive power compensation means the application of reactive devices
To produce a substantially flat voltage profile at all levels of power transmission.
To improve stability by increasing the maximum transmissible power, and/or
To supply 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 virtual 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 ðœ½’shorter than the uncompensated value, resulting in an increase in the steady state stability limit
This 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 compensators:
Passive 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 incapable 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 compensation may be necessary in conjunction with series capacitors, and this may be provided by shunt reactors or by a dynamic compensator.
Active compensators are usually 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. Compensation by sectioning is fundamentally different in that it is possible only with active compensators, which must be capable of virtually immediate response to the smallest variation in power transmission or voltage. The table below summarizes the classification of the main type of compensators according to their usual functions.
Shunt 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 below
voltage 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 pure voltage source at the sending end. The receiving end voltage can be given as
Equation 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 by
The sending end current can be given as
using equation 3.9 and 3.11
Since , this means that the generator at the sending end behaves exactly like the shunt reactor at the receiving end in that both absorb the same amount of reactive which is evident from equation below.
Chapter 4 Ferrenti effect
4.1 Ferranti effect:
A 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 capacitance generates the reactive power. If the line loading corresponds to the surge impedance loading, the voltage is same everywhere 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 as
OM = receiving end voltage Vr
OC = Current drawn by capacitance = Ic
MN = Resistance drop
NP = Inductive reactance drop
OP = 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.
For open circuit, no load,
By neglecting resistance
The quantity is constant in all line and is equal to velocity of propagation of electromagnetic waves (= 3 Ã- 102 km/sec)
By substituting the values in the above derived equation
From the above equation
Receiving end voltage is greater than sending end voltage and this effect is called Ferranti Effect .
5.1, fig 4.10,4.6,4.4,4.2,4.1,3.5,3.4,2.1
Chapter 5 results and discussion
Results and discussions:
To 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 acquisition 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
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