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Distributed schemes for stability and optimality in power networks

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The generation, transmission and distribution of electricity underpins modern technology and constitutes a necessary element for our development, economic functionality and prosperity. In the recent years, as a result of environmental concerns and technological advances, private and public investment have been steadily turning towards renewable sources of energy, resulting in a growing penetration of those in the power network. This poses additional challenges in the control of power networks, since renewable generation is in general intermittent, and a large penetration may cause frequent deviations between generation and demand, which can harm power quality, damage equipment and even cause blackouts.

Load side participation in the power grid is considered by many a means to counterbalance intermittent generation, due to its ability to provide fast response at urgencies. Industrial loads as well as household appliances, such as refrigerators and air-conditioners, may respond to frequency deviations adjusting their demand accordingly in order to support the network. This is backed by the development of relevant sensing and computation technologies.

The increasing numbers of local renewable sources of generation along with the introduction of controllable loads dramatically increases the number of active elements in the power network, making traditionally implemented, centralised control difficult and costly. This shows the need for the employment of highly distributed schemes in the control of generation and demand. Such schemes need to ensure the smooth and stable operation of the network. Furthermore, an issue of fairness among controllable loads needs to be considered, such that it is ensured that all load participants share the burden to support the network evenly and with minimum disruption.

We consider the dynamic behaviour of power networks within the primary and secondary frequency control timeframes. Using tools from linear and non-linear control and optimisation, we present methods to design distributed control schemes for generation and demand that guarantee stability and fairness in power allocation. Our analysis provides relaxed stability conditions in comparison with current literature and allows the inclusion of practically relevant classes of generation and demand dynamics that have not been considered within this setting, such as of higher order dynamics. Furthermore, fairness in the power allocation between loads is guaranteed by ensuring that the equilibria of the system are solutions to appropriately constructed optimisation problems. It is evident that a synchronising variable is required for optimality to be achieved and frequency is used as such in primary control schemes whereas for secondary frequency control a synchronising variable that follows from a ‘primal-dual’ control scheme is adopted. For the latter case, the requirements of the synchronising feedback scheme have been relaxed with the use of an appropriate observer, showing that stability and optimality guarantees are retained.

The problem of secondary frequency regulation where ancillary services are provided from switching loads is also considered. Such loads switch on and off when some prescribed frequency threshold is reached in order to support the power network at urgencies. To study their behaviour, tools from discontinuous and hybrid systems analysis have been employed. We show that the presence of switching loads does not compromise the stability of the power network and reduces the frequency overshoot, potentially saving the network from collapsing. Furthermore, we explain that when the on and off switching frequencies are equivalent, then arbitrarily fast switching phenomena might occur, something undesirable in practical implementations. As a solution to this problem, hysteresis schemes where the switch on and off frequencies differ are proposed and stability guarantees are provided within this setting.

All our analytic results are distributed and network independent and have been verified with realistic simulations on well accepted benchmarks.

This talk is part of the CUED Control Group Seminars series.

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