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1463145378-STEADYSTATEERRORESTIMATIONINDISTANCERELAYFORSINGLEPHASETOGROUNDFAULTINADOUBLECIRCUITLINE.docx (Size: 875.01 KB / Downloads: 5)
INTRODUCTION
Conventional distance relay protecting a double circuit transmission line may mal-operate because of a well known problem- zero sequence mutual coupling between the two circuits in case of a short circuit fault, if additional logics are not incorporated to handle this issue. Even though the solution for this problem is present in the form of zero sequence mutual compensation still having a clear idea about the error in measured impedance will help in fixing the relay setting. Basically without the presence of residual compensation and zero sequence mutual compensation the impedance measured will be erroneous. This is further complicated by providing series compensation to the parallel transmission line because of the problems such as sub-synchronous resonance, voltage inversion and current inversion. This phase of the project deals with a uncompensated parallel transmission line thus we are mainly worried about zero sequence mutual coupling between the two circuits.
Here the error in impedance measurement is reduced by providing ZMC, but however, this ensures accurate positive sequence error estimation only in the case of a faulty line and it may mal-operate for a healthy line. However this issue of healthy line mal-operation can be prevented by using earth current balance assisted distance protection.
But on the other hand the different operating conditions demand for a adaptive setting or individual group setting for each operating condition, that is, parallel line in service, parallel line out of service, parallel line not grounded and parallel line grounded at both ends.
Different methods are adopted to analyze the actual error in the impedance measurement of the relay. Initially the different double circuit line transposition methods are considered and they are solved using,
ELECTROMAGNETIC TRANSIENTS PROGRAM software and the zero sequence mutual coupling for different transposition methods is compared. Then four different methods are adopted to determine the positive sequence impedance and a comparative study is done.
The four methods are as follows,
• EMTP solution using phase quantities.
• EMTP solution using lane quantities.
• Using impedance estimation formula as mentioned in [2].
• Hand calculation using network reduction of lane quantities.
LITERATURE SURVEY
The work basically involves the steady state error estimation in a double circuit transmission line due to various system conditions. It basically follows the work done in [1] which is for series compensated parallel transmission line. But the first phase of this work is performed for a uncompensated parallel transmission line thus neglecting the effects such as sub-synchronous resonance, voltage and current inversion which are considered in [1]. These conditions will be considered in the second phase of the work.
Some basic concepts of distance protection are understood from [5] which are essential for the work; it gives some very important equations for the impedance estimation such as the one involving residual compensation.
Basic analysis methodologies used for Double circuit transmission lines are obtained from [2]. The different transposition methods are used and the zero sequence mutual coupling between the two circuits is determined for the different methods. The solution is obtained using EMTP analysis.
The important concepts which will help in understanding the EMTP software as well as for line parameter analysis (MICROTRAN) software are also obtained from [2].
Example problems for line parameters using MICROTRAN from [2] are simulated and the steady state solution for the obtained values is performed using EMTP software.
As mentioned before the first phase of the work is concerned the steady state error estimation for an uncompensated double circuit line is considered, with the effect of zero sequence mutual coupling. An equation is derived in [3] for the impedance estimation for uncompensated double circuit lines.
This particular equation includes the residual compensation factor in it included and there is no need of adding the residual compensation factor separately.
The physical parameters for different tower configurations are given in [3]. The EMTP solution is performed for these parameters as done with case of [2] example problem.
The impedance matrix for the given physical parameters from [3] is obtained by adopting the different transposition schemes (three-section and nine-section) from [2]. The impedance value is a averaged value of the impedances in various sections of the transposed line.
Symmetrical coordinate transformations from [4] are used to obtain simplified impedance matrix expressions for the transposed line. This symmetrical coordinate transform is also called as three phase symmetrical coordinate transform. It gives a inter-circuit coupling in the zero sequence component. This is the factor which gives a erroneous value in the estimated impedance.
For analysing the circuit to determine to the error in impedance value a two phase symmetrical coordinate or also called as super symmetrical coordinate transform is used. The relevant equations used for super symmetrical coordinate transform is obtained from
ANALYSIS METHODOLOGY OF DOUBLE CIRCUIT LINES
3.1 INTRODUCTION
Three phase double circuit lines are very common being necessitated by difficulties associated with obtaining the right of way. A three phase double circuit line consists of two circuits or lines with each of them having 3 phases. These two lines run in parallel all through the transmission distance.
Power lines are transposed to equalize the series impedance and shunt capacitance among the phases to avoid unbalance in voltage and/or current. Generally long distance transmission line will be series compensated with help of a series capacitor, but here a uncompensated line is considered.
This is done with the help of symmetrical component transformation which is used to decouple the circuits into sequence components. Sequence component transformation is performed since it will help in analysing the system as a very simple network rather than a complex one with distributed parameters.
3.2 TRANSFORMATIONS OF DOUBLE CIRCUIT LINES
3.2.1 Transposition schemes for double circuit lines
Three phase lines are best modelled as three phase pi-circuits. The line is assumed to be continuously transposed to be perfectly balanced. A perfectly balanced line will give rise to a balanced impedance and admittance matrix. The balanced impedance matrix is transformed to a diagonal matrix by symmetrical component transformation. The diagonal element of the resulting matrix are zero and positive/negative sequence parameters. The parameters of pi-circuits are computed from the sequence parameters using inverse symmetrical component transform. In practice, the sequence parameters are normally available and for creating an EMTP simulation data for pi-circuits, the data can be obtained by working backwards using the inverse transformation.
With the symmetrical component transformation the coupled equations of the transposed line in the phase domain, become three uncoupled equations in the symmetrical components domain (SCD).
Two basic types of transposition schemes for double circuit lines, they are
• Nine section transposition and
• Three section transposition
3.2.1.1 Nine section transposition
In the case of nine section transposition eight transposition towers will be used for a particular distance of the transmission line. In this scheme after transposition in the symmetrical coordinate domain there will be zero sequence inter-circuit coupling between the two lines.
The impedance value obtained is an averaged value of the impedances values of the nine different sections considered in this scheme.
The ordering of rows and columns are: zero, positive, negative sequence of circuit I followed by zero, positive, negative sequence of circuit II.
The impedance matrix for a double circuit line will contain 4 sub matrices 2 self impedance and 2 mutual impedance matrices.
The things observed in a nine section transposition scheme,
• The coupling between the two circuits is only in zero sequence-component.
• This scheme achieves best possible decoupling but with eight transposition towers. Hence, it is costlier than three section transposition scheme, with only two transposition towers.
• Self zero and positive sequence impedances for each circuit can be calculated as though the other circuit does not exist.
3.2.1.2 Three section transposition
This transposition scheme is a more widely and practically used type of double circuit line transposition. A three section transposition scheme has only two transposition towers for the particular distance where there is eight towers used for the nine section transposition scheme.
The ordering of rows and columns are same as in nine section transposition: zero, positive, negative sequence of circuit I followed by zero, positive, negative sequence of circuit II.
Symmetrical component transformation for double lines: zero sequence inter-circuit coupling
Direct three-phase analytical circuits of power systems cannot be obtained even for a small, local part of a network, although their connection diagrams can be obtained. First, mutual inductances/mutual capacitances existing between different phases (typically of generators) cannot be adequately drawn as analytical circuits of phases a, b, c. Furthermore, the analytical solution of such circuits, including some mutual inductances or capacitances, is quite hard and even impossible for smaller circuits.
In other words, straightforward analysis of three-phase circuit quantities is actually impossible regardless of steady-state phenomena or transient phenomena of small circuits.
The symmetrical coordinate method can give us a good way to draw the analytical circuit of a three-phase system and to solve the transient phenomena (including surge phenomenon) as well as steady-state phenomena.
The symmetrical coordinate method (symmetrical components) is a kind of variable transformation technique from a mathematical viewpoint. That is, three electrical quantities on a, b, c phases are always handled as one set in the a–b–c domain, and these three variables are then transformed into another set of three variables named positive 1, negative 2 and zero 0 sequence quantities in the newly defined 0–1–2 domain. An arbitrary set of three variables in the a–b–c domain and the transformed set of three variables in the 0–1–2 domain are mathematically in one-to-one correspondence with for each other.
Therefore, the phenomena of a–b–c phase quantities in any frequency zone can be transformed into the 0–1–2 domain and can be observed, examined and solved from the standpoint in the defined 0–1–2 domain. Then the obtained behaviour or the solution in the 0–1–2 domain can be retransformed into the original a–b–c domain. It can be safely said that the symmetrical coordinate method is an essential analytical tool for any kind of three-phase circuit phenomenon, and inevitably utilized in every kind of engineering work of power systems. Only symmetrical components can provide ways to obtain the large and precise analytical circuits of integrated power systems including generators, transmission lines, station equipment as well as loads.
One set of a, b, c phase currents Ia, Ib, Ic (or phase voltages Va, Vb, Vc) at an arbitrary point in the three-phase network based on the a–b–c domain is transformed to another set of three variables named I0, I1, I2 (or V0, V1, V2) in the 0–1–2 domain, by the particularly defined transformation rule. The equations of the original a–b–c domain will be changed into new equations of the 0–1–2 domain, by which three-phase power systems can be described as precise and quite simple circuits.
Transformation for complete decoupling of the double circuit lines
When we go for transposition of double circuit lines, either 3-section or 9-section the zero sequence mutual coupling between the two circuits is prominent and it will lead to erroneous impedance measurement by the relay. But for the purpose of analysis of this effect we need to eliminate this inter-circuit zero sequence coupling. For this purpose we adopt a two phase symmetrical component transformation which will eliminate the mutual coupling effects.
This transformation also called as super symmetrical coordinate transformation is formulated in reference