The Price of Synchrony: Evaluating the Resistive Losses in Synchronizing Power Networks

Abstract

This paper investigates the resistive power losses that are incurred in keeping a network of synchronous generators in a synchronous state. These losses arise due to the transient power flow fluctuations that occur when the system is perturbed from a synchronous state by a small transient event or in the face of persistent stochastic disturbances. We term these losses the "price of synchrony", as they reflect the real power flow costs incurred in resynchronizing the system. In the case of small fluctuations at each generator node, we show how the total network's resistive losses can be quantified using an H2 norm of a linear system of coupled swing equations subject to distributed disturbances. This norm is shown to be a function of transmission line and generator properties, to scale unboundedly with network size, and to be weakly dependent on the network topology. This conclusion differentiates the price of synchrony from typical power systems stability notions, which show highly connected networks to be more coherent and thus easier to synchronize. In particular, the price of synchrony is more dependent on a network's size than its topology. We discuss possible implications of these results in terms of the design of future power grids, which are expected to have highly distributed generation resources leading to larger networks with the potential for greater transient losses.

Global Analysis of Synchronization Performance for Power Systems: Bridging the Theory-Practice Gap

“…the system frequency is a weighted mean of bus frequencies, in proportion to their rating. Noting that m i = mf i , it follows that w(t) is exactly the COI frequency from (11). Also, returning to (14) we have…”

“…A popular research topic in recent years [11]- [17] has been the application of global metrics from robust control to this kind of synchronization dynamics, as a tool to shed light on the role of various parameters, e.g. system inertia.…”

“…The analysis of grid synchronization from a global perspective has been pursued in academia, going back to eigenvalue methods for reduced order modelling of inter-area oscillations (slow coherency [9], participation factors [10]). More recently, researchers from the control field have proposed to use H 2 or H ∞ norms of global transfer functions [11]- [20] as figures of merit for synchronization performance. Ideally, these measures should isolate the effect of different aspects of the network structure (topology, damping, inertia, etc.).…”

Optimal Placement of Inertia and Primary Control: A Matrix Perturbation Theory Approach

“…To that end, we use performance measures which evaluate the overall disturbance magnitude over time and the whole power grid. Performance measures have been proposed, which can be formulated as L 2 and squared H 2 norms of linear systems [6], [7], [12], [17], [18], [19], [20], [21], [22], [23] and are time-integrated quadratic forms in the angle, δθ, or frequency, ω, deviations. Here we focus on frequency deviations and use the following performance measure…”

Quadratic Performance Analysis of Secondary Frequency Controllers

“…In what follows we will derive results on the H 2 performance for different algorithms under disturbances by explicitly solving (5) for particular cases. Recent applications of the H 2 norm to power system performance may be found in [25]- [28].…”