Spreading of Disturbances in Realistic Models of Transmission Grids: Dependence on Topology, Inertia and Heterogeneity

Abstract

The energy transition towards more renewable energy resources (RER) together with the reduction of conventional energy sources profoundly affects the frequency dynamics and electromechanical stability of electrical power networks. Here, we investigate the effect of different levels of grid inertia and its heterogeneous distribution on propagation patterns of disturbances in realistic models of power grids, including the Nigerian transmission network, the Ghana transmission network and the IEEE 118 bus test-grid as well as a Cayley-tree network, as a model grid without cycles, and the Square-grid power network as a strongly meshed model grid. These studies are conducted with the DigSILENT PowerFactory software and compared with results obtained from swing equations.Results show that the times of arrival of frequency deviations as function of geodesic distance from the contingency are more clustered and decay faster in more meshed grids than in tree- like or weakly meshed grids. In order to take into account the inhomogeneous distribution of inertia, we define an effective distance and find it to be more strongly correlated with the arrival time than the geodesic distance. A ballistic equation for the arrival time, with a velocity derived from the swing equation, provides then a strict lower bound for all effective distances. The fitted velocity decays with a power law with grid inertia. Decreasing the magnitude of grid inertia by increasing the magnitude of RER is thereby found to increase the travel velocity of disturbances and reduce the time a disturbance needs to spread throughout the grid.

Transient Dynamics and Propagation of Voltage and Frequency Fluctuations in Transmission Grids

“…Thereby, the electromechanical velocity of disturbances increases according to Eq. ( 1), in agreement with simulations [23], [26]. Moreover, the same power imbalance results typically in a larger change of frequency as more renewable energy is fed into the power grid, as has been observed in the US power grid [27], which has been related to both a decrease of the inertia and the reduction of governor response.…”

“…In realistic grid models with inhomogeneous parameters it was found in Ref. [23] that the times of arrival of a disturbance are widely distributed, but that there is still on average a linear relation with the distance, which allows to define an effective electromechanical velocity of propagation in realistic networks…”

“…where K and ā are the average power capacity and average length of transmission line, respectively, and J is the aggregated inertia in the power grid [23], [24]. The spreading of frequency disturbances in real grid topologies has been studied in Refs.…”

Dynamics of Momentary Reserves under Contingency: Observations from Numerical Experiments

“…We also want to understand how momentary reserve tentatively contributes to damping of disturbances as they propagate along the network. A reference to the network buses numbers is in [18]. Keeping all system parameters, generations, losses and loads constant under undisturbed operations, a synchronous machine outage event (disturbance/contingency) is induced at bus 24 at exactly t = 5s of the 90s transient electromechanical stability simulation time frame with a 200ms switching, enabling the observations on the buses in PowerFactory power simulation software.…”

“…From the nodal points described in 2, we observe at each study case node, the frequency's time of arrival (ToA), as defined when the frequency deviation first reaches a small threshhold of δν = 0.0001 Hz, as defined in more detail in Ref. [18]. Furthermore we record the time of the first maximum (maxima t ) of the transient and its magnitude (maxima mag ), the time of the first minimum (minima t ) and its magnitude (minima mag ).…”