An electrical substation consists of a complex set of interconnected equipment items, such as transformers, circuit breakers, surge arresters, capacitor banks, and disconnect switches, many of which support fragile elements, such as ceramic bushings or insulators. These equipment items are usually connected to each other through conductor buses or cables. During an earthquake, the connections effect dynamic interaction between the equipment items. Field investigations following recent earthquakes have revealed that this interaction may be largely responsible for the observed damage to connected electrical substation equipment. Unfortunately, design guidelines and analysis methods that account for this effect are currently lacking.
The title study aimed at quantifying the effect of interaction on connected equipment items and at identifying parameters and circumstances that may produce critical conditions for such equipment. A further objective was to develop practical design rules and guidelines to avoid the adverse effect of interaction on connected equipment items. The study was conducted through PEER, UC Berkeley, by Professors Armen Der Kiureghian and Jerome L. Sackman, and by graduate research assistant Kee-Jeung Hong. The research was sponsored by the Pacific Gas & Electric Company and the California Energy Commission.
Owing to the variety of equipment types and configurations in typical electrical substations, it was necessary to develop simple, generic models that incorporate the most salient features of the connected system. With this requirement in mind, each equipment item was modeled as a linear system with distributed mass, damping, and stiffness properties and, through the use of a prescribed displacement shape function, was characterized by a single degree of freedom. For the connecting conductor, several models were investigated. These include a linear bus conductor modeled as a simple spring-dashpot-mass element, a nonlinear bus conductor consisting of an essentially rigid bus and a spring that provides flexibility and energy dissipation, and a flexible conductor cable made of braided strands of aluminum wire.
The effect of interaction on the connected equipment item is quantified in terms of the response ratio
where ui(t) and ui0 (t) are the displacements of the equipment item, relative to the ground, in the connected system and in a stand-alone configuration, respectively. Clearly, if Ri > 1, the equipment response is amplified as a result of the interaction effect, and if Ri < 1, the equipment response is de-amplified.
Parametric studies with two equipment items connected by a
conductor bus modeled as a linear spring-dashpot-mass element
have revealed that parameters having significant influences on
the interaction effect include the relative frequencies of the
two equipment items, 
, the ratio
of equipment masses, m / m2,
the ratio of the stiffness of the connecting spring to the sum
of the stiffnesses of the two equipment items,
, and
the attachment coordinates. Figure 1 shows the influence of the
stiffness ratio as a function of
for m1 / m2 = 2.
It can be seen that the interaction effect reduces the response of the lower frequency equipment item (relative to its stand-alone response) while significantly amplifying the response of the higher frequency equipment item. This adverse interaction effect on the higher frequency equipment item may explain the cause for some of the damage observed for electrical substation equipment during past earthquakes.
To provide flexibility in the rigid bus conductor, often a flexible copper spring in the form of an inverted U is inserted between the rigid bus and one of the equipment items. Experimental investigations at the University of California San Diego (UCSD) were performed to determine the cyclic behavior of the spring under large deformations. In the present study, an elastoplastic, large deformation finite element (FE) model in conjunction with the computer program FEAP (by R. L. Taylor) was used to predict the hysteretic behavior.
As a first approximation, this model did not account for contact between bars making up the spring. Figure 2 shows a comparison of the experimental and predicted hysteresis loops for the spring, and the deformed configurations under extreme tension and compression forces.
The overlapping under compression is due to our neglect of the contact between the bars of the spring. In spite of this approximation, the result based on the FE model is in close agreement with the experimental result. A more refined finite element model including the contact effect is now being developed to more accurately predict the behavior of the spring.
To investigate the effectiveness of the spring, three sets of dynamic analyses were conducted using ground motions from the 1994 Northridge, California, and 1978 Tabas, Iran, earthquakes. The first set considered the rigid bus conductor without the spring. The second set included the spring with the rigid bus, but assumed that the spring behaved linearly with its initial stiffness. This analysis accounted for the flexibility of the spring, but not its energy dissipation and softening. The third set of analysis used the hysteresis model in figure 2, hence fully accounting for the inelastic nonlinear behavior of the spring. The results for the response ratios, summarized in the table, show that the flexibility and inelastic behavior of the spring significantly reduced the adverse interaction effect on the higher frequency equipment item.
Extensive investigations with the flexible cable conductor were carried out. The cable used in the power industry for conduction is typically made of braided aluminum wire strands. Under dynamic loading, the strands may slide against one another under friction forces. As a result, the section properties of the cable, such as its axial and flexural rigidities, as well as its energy dissipation characteristics, are unknown. Previous experimental results for cables under imposed harmonic excitation at end points have revealed very large amplification of the cable force due to vertical inertia effects. In this study, a finite element model of the cable was used to predict the experimental results. While quantitative agreement is not possible due to uncertainties in the actual cable properties and experimental conditions, good qualitative agreement between the FE model and the test result was achieved. Figure 3 shows the result for one cable, where the maximum cable force spectrum is plotted as a function of the excitation frequency.
Note that the cable experiences significant compression forces. Furthermore, the maximum tension and compression forces for high frequency excitations can be considerably larger than the forces at quasi-static conditions.
To investigate the effect of interaction between cable-connected
equipment items, the "interaction" parameter 
was
introduced, where s is the length of the cable, L
is the span, and 
is the maximum relative displacement
between the two equipment items under stand-alone (unconnected)
conditions. Figure 4 shows plots of the response ratio R2
against the interaction parameter 
for selected recorded
ground motions for a 5 Hz equipment item that is connected to
another equipment item of 1 Hz natural frequency.
This analysis shows that to avoid the adverse interaction effect,
the cable length should be selected in such a way that parameter
has a value of less than about 1.0. Based on this finding, a preliminary
estimate for the minimum cable length to avoid the adverse interaction
effect is determined as 
.
More details about this work can be found in PEER Report 1999/01 and another upcoming PEER report.
Fig.
1 Influences of the frequency ratio and the stiffness of the connecting
element on the interaction between two equipment items.
Fig.
2. Comparison of finite element predicted force-eleongation relation
of the spring with UCSD test results, and finite element predicted
deformed shapes.
Fig.
3. Horizontal support force spectrum predicted by the finite element
model of the cable for imposed out-of-phase harmonic support motions
Response
ratios for five earthquakes as fucntions of the interaction parameter,
including the flexural rigidity and inertia of the cable