Abstract
Interarea oscillations are predominantly governed by the slower electromechanical modes which, in turn, are determined by the coherent machine rotor angles and speeds. The issue is that, although these rotor angles and speeds provide the best visibility of such modes, currently they are not available from phasor measurement units (PMU). As such, the aim of this chapter is to demonstrate that interarea oscillations are observable in the network variables, such as voltages and line currents, which are measured by PMU. By analyzing the electromechanical modes in the network variables, we can trace how electromechanical oscillations are spread through the power network following a disturbance. Applying eigenvalue and sensitivity analysis, we provide an analytical framework to understand the nature of these network oscillations through a relationship termed network modeshapes. Using this relationship, a novel concept, “dominant interarea oscillation paths,” is developed to identify the passageways where the interarea modes of concern travel the most. We demonstrate the concept of the dominant path with an equivalent two-area system. We propose an algorithm for identification of the dominant paths and illustrate with a reduced model of a large-scale network. Finally, we end this chapter with an important application of the concept: feedback input signal selection for damping controller design.
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Notes
- 1.
The subscript (0) denotes the evaluation of the sensitivity at a stable equilibrium point.
- 2.
A formal proof for each property can be found in [12].
- 3.
These are similar to the characteristics of voltage change and angle change of the first swing mode in Fig. 13 [21] where the mode is described by a single wave equation with one spatial dimension.
- 4.
For algorithms dealing with other set of information such as known system model or transient measurements, refer to [22].
- 5.
The model with controls is studied in [24].
- 6.
Observe from Table 10.1 that the path 42-43-44-49-50 has considerably high content of Mode 1; however, it has lesser content than that of the specified dominant path. This second path is thus termed “secondary dominant interarea oscillation path.” For details regarding multiple interaction paths, refer to [26].
- 7.
Note that the generator speed is not currently available from PMUs.
- 8.
\(\omega _2\) is in anti-phase to any signals starting from \(\omega _1\) to the interarea pivot (middle point in Fig. 10.15b). Thus, two compensators are required for a rotation of 180\(^\circ \) and an additional stage for the needed phase compensation.
- 9.
Although not shown here, the angle of departure of \(\omega _2\) is negative while the others are positive. This is the reason why not only an additional stage compensator is required but also a very high gain.
- 10.
The effective gain for the generator speed signals is naturally higher comparing to the angles due to the scaling introduced by the system frequency, \(2\pi f_{b} = 314.16\).
- 11.
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Vanfretti, L., Chompoobutrgool, Y., Chow, J.H. (2013). Interarea Mode Analysis for Large Power Systems Using Synchrophasor Data. In: Chow, J. (eds) Power System Coherency and Model Reduction. Power Electronics and Power Systems, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1803-0_10
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