Transients overhead lines

The first few turns of the line end coil of a motor or transformer and short lengths of interconnecting cables and overhead lines and their associated terminal equipment, will thus be subject to severe stresses and will be rendered vulnerable to damage by such sleep-fronted transient voltages. 

If generators are physically remote from the switchboard, e.g. interconnected by long cables or overhead lines, then the impedance between the generators and the switchboard may be large enough to swamp the sub-transient and transient current contributions, as well as reducing the DC component effects. 

Generators and motors are often connected to their associated switchboards or networks by an impedance. This impedance can be a cable, an overhead line, a unit transformer or a combination of these components. The intermediate circuit introduced in the stator circuit will contain resistance and inductive reactance, the effect of which is to modify the time constants in the generator and motor equations, and the performance of these machines under most transiently disturbed conditions. This aspect has been mentioned in the literature e.g. References 24, 25 and 26 but is easily overlooked when developing computer programs. 

First, this book will illustrate a transient on a single-phase line from a physical viewpoint, and how it can be solved analytically by an electric circuit theory. The impedance and admittance formulas of an overhead line will also be described. Approximate formulas that can be computed using a pocket calculator will be explained to show that a transient can be analytically evaluated via hand calculation. Since a real power line contains three phases, a theory to deal with a multiphase line will be developed. Finally, the book describes how to tackle a real transient in a power system. A computer simulation tool is necessary for this— specifically the well-known simulation tool Electro Magnetic Transients Program (EMTP), originally developed by the U.S. Department of Energy, Bonneville Power Administration— which is briefly explained in Chapter 1. 

In Chapter 2, wave propagation characteristics and transients in an overhead transmission line are described. The distributed parameter circuit theory is applied to solve the transients anal5 cally. The EMTP is then applied to calculate the transients in a power system composed of the overhead line and a substation. Various simulation examples are demonstrated, together with the comparison of field test results. 

Chapter 3 examines the transients in a cable system. A cable system is, in general, more complicated than an overhead line system, because one phase of the cable is composed of two conductors called a metallic core and a metallic sheath. The former carries a current and the latter behaves as an electromagnetic shield against the core current. Another reason why a cable system is complicated is that most long cables are cross-bounded, that is, the metallic sheaths on phases a, b, and c in one cable section are connected to that of phases b, c, and a in the next section. Each section is called a minor section and the length of each normally ranges from some 100 m to 1 km. Three minor sections comprise one major section. The sheath impedances of three phases thus become nearly equal to each other. As a result, a transient on a cable system is quite different from that on an overhead line system. 

Almost always, the following well-known admittance is used in steady-state and transient analyses of overhead lines ... 

Frequency dependence is very significant when an accurate transient simulation on a distributed-parameter line, such as an overhead line and an underground cable, is to be carried out from the viewpoint of insulation design and coordination in a power system. However, a simulation can be carried out neglecting frequency dependence if a safer-side result is required because simulation with frequency dependence, in general, results in a lower overvoltage than that neglecting frequency dependence. 

There are a number of papers on nonuniform lines [30,31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48-49]. EMC-related transients or surges in a gas-insulated substation and on a tower involve nonuniform lines, such as short-line, nonparallel, and vertical conductors. Pollaczek s [7], Caron s [8], and Sunde s [50] impedance formulas for an overhead line are well known and have been widely used in the analysis of the transients mentioned earlier. However, it is not well known that these formulas were derived assuming an infinitely long and thin conductor, that is, a uniform and homogeneous line. Thus, impedance formulas are restricted to the uniform line where the concept of per-unit-length impedance is applicable. 

This section explains impedance and admittance formulas of nonuniform lines, such as finite-length horizontal and vertical conductors based on a plane wave assumption. The formulas are applied to analyze a transient on a nonuniform line by an existing circuit theory-based simulation tool such as the EMTP [9,11]. The impedance formula is derived based on Neumann s inductance formula by applying the idea of complex penetration depth explained earlier. The admittance is obtained from the impedance assuming the wave propagation velocity is the same as the light velocity in free space in the same manner as an existing admittance formula, which is almost always used in steady-state and transient analyses on an overhead line. 

Similar to overhead line projects, switching transients such as cable energization, ground fault, and fault clearing are also studied for EHV AC cable projects as standard work. However, severe overvoltages related to these switching transients on cable systems have not been reported in the literature. 

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