# The Price of Synchrony:Evaluating Transient Power Losses inRenewable Energy IntegratedPower Networks

University essay from KTH/Reglerteknik

Keywords: ;

Abstract:

This thesis investigates the resistive losses incurred in returning a power network to a synchronous state following a transient stability event, or in maintaining this state in the presence of persistent stochastic disturbances. We quantify these transient power losses, the so-called “Price of Synchrony”, using the squared H2 norm of a linear system of generator and load dynamics subject to distributed disturbances. We first consider a large network of synchronous generators and use the classical machine model to form a system with coupled second order swing equations. We then extend this model to explicitly include dynamics of loads and asynchronous generators, which represent solar and wind power plants. These elements are modeled as frequency-dependent power injections (extractions), and the resulting system is one of coupled firstand second order dynamics. In both cases, the disturbance inputs represent power fluctuations due to transient stability events or the inherent variability of loads and intermittent energy sources. The network structure is captured through a weighted graph Laplacian of the network admittance. In order to simplify the analysis for both models, we use the concept of grounded graph Laplacians to obtain an asymptotically stable reduced system. We then evaluate the transient losses in the reduced system and show that this system’s H2 norm is in fact equivalent to the H2 norm of the original system. Furthermore we show that although the transient behaviours of the first order, second order or mixed dynamical systems are in general fundamentally different, for same-sized networks they may all have the same H2 norm if the damping coefficients are uniform.

The H2 norms for both system models are shown to be a function of transmission line and generator properties and to scale with the network size. These transient losses do not, however, depend on the network connectivity. This is in contrast to related power system stability notions that predict better synchronous stability properties for highly connected networks. The equivalence of the norms for different order systems indicate that renewable energy sources will not increase transient power losses if their controllers can be adjusted to match the dampings of existing synchronous generators. However, since the losses scale linearly with the number of generators, our results also demonstrate that increased amounts of distributed generation in low-voltage grids will lead to larger transient losses, and that this effect cannot be alleviated by increasing the network connectivity.