Julian Fritzsch

We propose a general methodology for identifying critical lines in the long-distance transmission of power across large electrical networks. When the system is pushed to its limits of operation due to large power imbalances or contingencies, the network may lose synchrony. We analyze the Continental Europe grid as a case study and find that instabilities emerge due to topological constraints by which the system loses its stable fixed point (synchronized state), causing the grid to split into two asynchronous zones. We discuss also how the modes of the system provide information on which areas are more susceptible to lose synchrony.

The increasing penetration of new renewable sources of energy in today’s power grids is accompanied by a decrease in available electromechanical inertia. This leads to a reduced dynamical stability. To counterbalance this effect, virtual synchronous generators have been proposed to emulate conventional generators and provide inertia to power systems. The high flexibility of these devices makes it possible to control the synthetic inertia they provide and to have them operate even more efficiently than the electromechanical inertia they replace. Here, we propose a novel control scheme for virtual synchronous generators, where the amount of inertia provided is large at short times - thereby absorbing local faults and disturbances as efficiently as conventional generators - but decreases over a tunable time interval to prevent long-time coherent oscillations from setting in. This new model is used to investigate the effect of adaptive inertia on large-scale power grids. Our model outperforms conventional constant inertia in all scenarios and for all performance measures considered. We show how an optimized geographical distribution of adaptive inertia devices not only effectively absorbs local faults, but also significantly improves the damping of inter-area oscillations.

With the current energy crisis affecting Europe and Switzerland in particular, efficient new generations of electricpower are urgently needed. In this context, a number of proposals has been put forward to increase our country’s renewable electricity production. One such project is the Grengiols–Saflischtal solar power plant. The projectis still in an early developmental stage and quantitatively reliable numbers for power production capacity and annualenergy generation do not truly exist. Given a potential area of 5 km², an upper bound for the plant’s peak power is in the 1 GW_p range, which, given the plant’s location and panel orientation may generate as much as 1.5 TWh to 2 TWh annually for bifacial photovoltaic panels. These numbers sound rather optimistic, but regardless of their accuracy, electric power generation in the range of hundreds of megawatts can only be injected into the grid at extra-high voltages of 220 kV or 380 kV, therefore, a question that naturally arises is whether Switzerland’s transmission gridcan safely absorb this additional power injection. In this report, we evaluate the maximal peak electric power that a large solar photovoltaic farm in the Grengiols–Saflischtal area could safely inject into Switzerland’s extra-high voltage grid, without jeopardizing its stability. We consider two different grids: (i) the current extra-high voltage grid operated by Swissgrid as of October 2022, and (ii) Swissgrid’s strategic grid 2025, which will be finalized no earlier than 2028.

This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. Following Seymlyen (1974) and Thorpe, Seyler, and Phadke (1999), we suggest to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. We illustrate our method on the synchronous transmission grid of continental Europe. We show that, when properly coarse-grained, i.e., with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based modeling will initialize a physics-informed machine learning approach for real-time modeling, n−1 feasibility assessment and transient stability analysis of power systems.

We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their existence in networks of weakly connected areas is well captured by singular perturbation theory. However, they are also observed in strongly connected networks without time-scale separation, where applying singular perturbation theory is not justified. We show that the occurrence of these oscillations is actually generic. Applying matrix perturbation theory, we show that, because these modes have the lowest oscillation frequencies of the system, they are only moderately sensitive to increased network connectivity between well chosen, initially weakly connected areas, and that their general structure remains the same, regardless of the strength of the inter-area coupling. This is qualitatively understood by bringing together the standard singular perturbation theory and Courant’s nodal domain theorem.

Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may jeopardize the overall system stability with the emergence of so-called inter-area oscillations, which are coherent oscillations involving groups of rotating machines separated by large distances up to thousands of kilometers. These often weakly damped modes may have harmful consequences for grid operation, yet despite decades of investigations, the mechanisms that generate them are still poorly understood, and the existing theories are based on assumptions that are not satisfied in real power grids where such modes are observed. Here we construct a matrix perturbation theory of large interconnected power systems that clarifies the origin and the conditions for the emergence of inter-area oscillations. We show that coherent inter-area oscillations emerge from the zero-modes of a multi-area network Laplacian matrix, which hybridize only weakly with other modes, even under significant capacity of the inter-area tie-lines, i.e. even when the standard assumption of area partitioning is not satisfied. The general theory is illustrated on a two-area system, and numerically applied to the well-connected PanTaGruEl model of the synchronous grid of continental Europe.