Accounting for the influence of grounding disconnected phases on asymmetry in an electrical system
Abstract Generated abstract
This paper examines how grounding a disconnected phase in long high-voltage transmission lines affects asymmetry during incomplete-phase operation, including cases arising from sustained ground faults or phase-by-phase repair. It argues that although grounding changes the sequence parameters of the affected line section, the problem can be reduced to calculation of a symmetrical three-phase circuit by representing the grounding influence through equivalent shunts or active three-terminal networks in the positive-sequence circuit. Parameters are provided for several break and short-circuit configurations, enabling practical calculation of these regimes. Calculations for a Kuibyshev to Moscow type transmission system indicate that grounding may reduce current asymmetry in a block circuit, but can increase asymmetry in an interconnected system and strengthen effects on nearby communication lines, making its consideration necessary.
Full Text
Accounting for the Effect of Grounding Disconnected Phases on Asymmetry in an Electrical System
R. I. Borisov
(Presented by Professor, Doctor V. K. Shcherbakov)
When a long high-voltage transmission line is equipped with phase-by-phase control, the disconnected phase may turn out to be grounded if the ground fault that caused the disconnection is sustained. In addition, when phase-by-phase repairs are carried out, the disconnected conductor must be grounded in accordance with the requirements of the “Safety Regulations” [1]. The presence of grounding leads to a change in the parameters of the healthy phases of the line, which complicates the calculation of the unbalanced operating condition under such circumstances.
In this case, the general calculation method proposed by N. A. Melnikov [2] for calculating unbalanced regimes in an unbalanced three-phase electrical circuit proves acceptable, since the line phases in the damaged section will have different values of resistances and conductances for each sequence. However, even in this case the calculation can be reduced to the calculation of a symmetrical three-phase circuit, since the source of unbalance is nevertheless local in character. Thus, if repairs are being performed on a disconnected phase while the other phases remain energized, then the disconnected conductor, in accordance with the requirements of the “Safety Regulations,” will be grounded at several points; but the imposition of groundings in excess of one has little effect on subsequent changes in the field pattern and, consequently, in the line parameters, and therefore, from the computational point of view, may be regarded as a single grounding. The presence of such a grounding will cause the potential of the disconnected conductor to become equal to zero. From the computational point of view this can be taken into account by short-circuiting the grounded phases in the equivalent circuits of the different sequences compiled for an open circuit. At the break points of the disconnected phases, for the circuit of each sequence, e.m.f.’s should be inserted equal to the corresponding voltage components determined without taking the grounding into account [3]. In this case, the e.m.f.’s of each sequence at the break points will cause currents of all three sequences to flow through the grounding point and in other elements of the electrical system. However, taking into account the boundary conditions at the break and grounding points, it can be proved that the principle of independence of action of the symmetrical components will be preserved and
in this case. The entire electrical circuit, including the section with the break, can then be regarded as a symmetrical three-phase system.
To take into account the influence of grounding of the disconnected phase of the line, it is necessary, at the grounding point, to insert into the positive-sequence circuit a shunt between the calculation phase and ground, consisting of active and passive elements. When disconnected conductors are grounded, if they are located on different sections of the line, an active three-terminal network composed of negative- and zero-sequence circuits should be introduced into the positive-sequence circuit.
The parameters of the equivalent three-terminal networks that take into account the influence of groundings for various cases of breaks are given in the table.
Table
| Parameters / Type of fault | Break and short circuit of a phase on one section | Break and short circuit of two phases on one section | Break and short circuit on different sections |
|---|---|---|---|
| \(\overline{A}\) | \(1\) | \(1\) | \(\dfrac{\overline{A}_2\overline{C}_0+\overline{A}_0\overline{C}_2}{\overline{C}_0+\overline{C}_2}\) |
| \(\overline{B}\) | \(0\) | \(0\) | \(-\,\dfrac{\lvert z\rvert\,\overline{C}_2\overline{C}_0}{\overline{C}_2+\overline{C}_0}\) |
| \(\overline{C}\) | \(\dfrac{\overline{C}_2\overline{C}_0}{\overline{A}_2\overline{C}_0+\overline{A}_0\overline{C}_2}\) | \(\dfrac{\overline{A}_2\overline{C}_0+\overline{A}_0\overline{C}_2}{\overline{A}_2\overline{A}_0}\) | \(\dfrac{\overline{C}_0\overline{C}_2}{\overline{C}_0+\overline{C}_2}\) |
| \(\overline{D}\) | \(1\) | \(1\) | \(\dfrac{\overline{D}_2\overline{C}_0+\overline{D}_0\overline{C}_2}{\overline{C}_2+\overline{C}_0}\) |
| \(\overline{E}\) | \(0\) | \(0\) | \(\overline{E}_0+\overline{E}_2+\dfrac{(\overline{A}_0-\overline{A}_2)(\overline{F}_2-\overline{F}_0)}{\overline{C}_2+\overline{C}_0}\) |
| \(\overline{F}\) | \(\dfrac{\overline{A}_2\overline{F}_2\overline{C}_0-\overline{C}_2\overline{F}_0(\overline{E}_2+\overline{E}_0)+\overline{A}_0\overline{F}_0\overline{C}_2}{\overline{A}_2\overline{C}_0+\overline{A}_0\overline{C}_2}\) | \(\dfrac{(\overline{E}_2-\overline{F}_2\dfrac{\overline{A}_2}{\overline{C}_2})\overline{A}_0\overline{C}_2+(\overline{E}_0-\overline{F}_0\dfrac{\overline{A}_0}{\overline{C}_0})\overline{A}_2\overline{C}_0}{\overline{A}_0\overline{A}_2}\) | \(\dfrac{\overline{F}_2\overline{C}_0+\overline{F}_0\overline{C}_2}{\overline{C}_2+\overline{C}_0}\) |
As calculations [3] have shown, for a transmission system of the Kuibyshev—Moscow type, grounding the conductor of the disconnected phase is a favorable factor in the block circuit, since this leads to an approximately twofold reduction in current asymmetry; however, even then the asymmetry coefficients in the calculation network exceeded the limits that can be taken as permissible.
This effect of grounding is explained by an increase in the conductivity in the zero-sequence circuit, which in turn leads to an intensification of the influence of the incomplete-phase mode on the conductors of nearby communication lines; the latter is undesirable.
The influence of grounding of the disconnected phase leads, in the interconnected system, to a certain increase in the asymmetry coefficients—appreciable from the standpoint of generator heating—and in this case accounting for the influence of grounding on asymmetry in the electrical system is mandatory.
Calculations of incomplete-phase operating conditions were carried out using the values of the e.m.f. of the equivalent generator of the transmitting station and the receiving system, as well as the phase-shift angle between the vectors of these e.m.f.’s, equal to the corresponding quantities of the normal symmetrical operating condition.
REFERENCES
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Materials on single-phase automatic reclosing (OAPV) and repair of high-voltage transmission lines. Gosenergoizdat, 1946.
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Melnikov N. A. A method for calculating complex asymmetrical multiphase electrical systems. Proceedings of VEEI. Issue 3. Gosenergoizdat, 1954.
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Borisov R. I. Candidate dissertation. Steady-state asymmetrical operating conditions during incomplete-phase operation of long transmission lines. Tomsk, 1955.