Transient Stability of Power Generating Stations synchronously connected to Low Inertia Electrical Power systems

Abstract

The ever-present requirement to decarbonize energy generation, consequently the impetus to increase energy levels from sustainable sources means that wind turbines and solar photovoltaic installations have become major contributors to the energy pool. All studies of isolated grids (e.g. Ireland) indicate that increase of these sources weakens the ability of the frequency in the transmission and distribution system to remain stable after transient disturbances because of the consequent decreased inertia in the electrical power system. The behaviour of the grid and in particular the grid frequency is manifested as an increase of the Rate of Change of Frequency (ROCOF) which may give rise to oscillations in the entire transmission system. Therefore, the goal of maximizing the renewable energy level on a transmission system when the grid inertia is low without compromising the safety and integrity of the existing generator assets should be attained. Hence a rigorous approach permitting quantitavie understanding of low inertia grids based on dynamical models is developed. These are torsional nonlinear oscillators which may oscillate about a temporary equilibrium orientation and so may describe the response of the grid and the grid connected assets to transient frequency changes. They are inspired by previous applications in statistical mechanics, and comprise two bodies rotating about a fixed axis connected by a nonlinear spring subject to external torques. This stimulus causes a change in the angular velocity of both masses resulting in a oscillatory motion of the entire coupled system. The models are verified by comparison with actual measurements in existing power generating stations so highlighting limitations to the operational range of synchronous generators. Thus one may identify the minimum system inertia and so the limit to the quantity of grid connected non-synchronous generation. The governing nonlinear equations of motion are solved by adapting techniques similar to those developed for stochastic differential equations (v. The Langevin Equation, 4th edition, W.T. Coffey and Yu.P. Kalmykov, World Scientific, 2017). The results allow simple analytic description of systems with high wind electricity generation or other asynchronous renewable energy sources and so support the overall goal of decarbonizing electricity generation.