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Center for Nonlinear Studies |
We propose a dedicated control method, denoted by AVS, for networks whose links are governed by the wave equation. The unique aspect of this method is that it is accurate, physically oriented and fully utilizes the exact partial differential equation (PDE) model by exploiting the system traveling wave characteristics. The AVS was originally designed for mechanical flexible structures with boundaries, such as vibrating strings and membranes or rotating rods, in a possibly damped or elastic media, thus being governed by a generalized form of the wave equation. The underlying principle of the AVS is active rigidization of the flexible system in closed loop, i.e. without changing its geometrical or physical parameters. It is achieved by a complete elimination of the wave motion, and stabilization of the resulting rigid system. For structures with boundaries the working principle of the algorithm is absolutely absorbing waves incoming into these boundaries, hence preventing their further reflections. A network, however, may consist of complex interconnections of links, including topology with no boundaries, which can be thus regarded as a collection of strings and rings - closed and open ended lines, respectively. Since the original boundary control can handle the string components only, a conceptually different technique for wave elimination in a ring topology was required. In this talk we propose such technique, specifically how to generate in-domain uni-directional waves using a minimal number of sensors and localized actuators. We demonstrate the AVS control approach via regulation of swing dynamics in a large electrical power network comprising widely dispersed generators interconnected through tie lines. The essential characteristic that provides flawless power transmission through the network is synchronized rotation of all generators. However, in the presence of any disturbances such as generation trips, asynchronous motion can result. Such a motion leads to oscillations in the rotation frequency and angle, which poses a serious concern, as it can lead to increasing frequency swings and therefore brown-outs and black-outs. Most of the existing approaches are based on spatially discrete modeling, implemented by ordinary differential equations (ODEs), and focus on analysis and synthesis using the ODE-models. However, when the number of generators on a line is large, the fundamental mechanism that produces the oscillations can be better represented by a continuous one and is described by the wave equation. The swing dynamics in a power string is then the electrical analogue of vibrations in a mechanical string, with the generators as the inertia and the tie line admittance as the string tension. Disturbances are thus propagate over the grid as electro-mechanical waves, where the perceived oscillations are only a local effect. Designing the AVS algorithm to operate on practical power grid actuators such as voltage excitation devices and Thyristor Controlled Series Compensators (TCSC), makes it readily implementable.
Host: Anatoly Zlotnik